https://www.explainxkcd.com/wiki/api.php?action=feedcontributions&user=CRGreathouse&feedformat=atomexplain xkcd - User contributions [en]2024-03-29T12:22:51ZUser contributionsMediaWiki 1.30.0https://www.explainxkcd.com/wiki/index.php?title=2118:_Normal_Distribution&diff=1703972118: Normal Distribution2019-03-03T04:11:56Z<p>CRGreathouse: /* Explanation */ phrasing</p>
<hr />
<div>{{comic<br />
| number = 2118<br />
| date = March 1, 2019<br />
| title = Normal Distribution<br />
| image = normal_distribution.png<br />
| titletext = It's the NORMAL distribution, not the TANGENT distribution.<br />
}}<br />
<br />
==Explanation==<br />
{{incomplete|Created by PEOPLE NEW ENOUGH TO STATISTICS TO NOT LEAVE IN ANNOYANCE. Please mention here why this explanation isn't complete. Do NOT delete this tag too soon.}}<br />
[[File:Empirical_Rule.PNG|thumb|{{w|Normal distribution}}s and the intervals of the standard deviation are a topic commonly seen in introductory statistics. Randall's chart is similar, but his lines are perpendicular.]]<br />
In statistics, a {{w|Probability distribution|distribution}} is a representation that can be understood in terms of how much of a sample is expected to fall into either discrete bins or between particular ranges of values. For example, if you wanted to represent an age distribution using bins of ten years (0-9, 10-19, etc.), you could produce a bar chart, one bar for each bin, where the height of each bar represents a count of the portion of the sample matching that bin. To turn that bar chart into a distribution, you'd get an infinite number of people, put them into age bins that are infinitely narrow, and then divide each bin count by the total count so that the whole thing added up to 1. It is common to ask how much of the distribution lies between two vertical lines; that would correspond to asking what percent of people are expected to fall between two ages.<br />
<br />
Many statistical samplings resemble a pattern called a "{{w|normal distribution}}". A theoretically perfect normal distribution would have an infinite sample size and infinitely small bins. That would produce a bar chart matching the shape of the curve in the comic.<br />
<br />
The area between two vertical lines of the distribution represents the probability that the value is between the x-values of the lines, and the total area is 1. Randall finds the area between two ''horizontal'' lines instead, which is mathematically meaningless, because the y-axis of a probability distribution represents {{w|absolute magnitude|magnitude}} as a fraction of unity (although we do have half of the normal curve between the two lines). The items represented by the magnitude at any given horizontal position are indistinguishable, unordered, and interchangeable; the idea that one could be above another is meaningless, and the fact that two items happen to fall at the same position on the y-axis doesn't mean they have anything in common. So, the comic explores the humor of annoying people by deliberately misunderstanding their work.<br />
<br />
The title text refers to the {{w|Normal (geometry)|normal line}}, which is perpendicular to the {{w|tangent}} line at a given point. Given a shape of interest, a normal line points perpendicularly away from it at a point, making a 90-degree angle with it in all directions, while a tangent line crosses a point on it and is exactly parallel to it at that point. The normal line is not at all related to the normal distribution, as the former is a geometry concept and the latter is probability/statistics one. Saying this to a statistician would only annoy the statistician further. This refers to the fact that the diagram attempts to divide the graph with horizontal lines when such a division would usually be done with perpendicular vertical lines.<br />
<br />
==Transcript==<br />
{{incomplete transcript|Do NOT delete this tag too soon.}}<br />
<br />
:[A bell curve of a normal distribution, with the area between two horizontal lines shaded.]<br />
<br />
<br />
:[The center of the chart is marked between the two lines:]<br />
:Midpoint<br />
<br />
:[The distance between the lines is marked to the right of the midpoint, with the label:]<br />
:52.7%<br />
<br />
:[A label on the outside of the graph, describing the distance between the two lines:]<br />
:"Remember, 50% of the distribution falls between these two lines!"<br />
<br />
<br />
:[Caption below the panel:]<br />
:How to annoy a statistician<br />
<br />
<br />
{{comic discussion}}<br />
[[Category:Charts]]<br />
[[Category:Statistics]]</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=Talk:2118:_Normal_Distribution&diff=170396Talk:2118: Normal Distribution2019-03-03T03:59:32Z<p>CRGreathouse: symbolic integration is out</p>
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<div><!--Please sign your posts with ~~~~ and don't delete this text. New comments should be added at the bottom.--><br />
Is there a statistician in the house? [[User:Hawthorn|Hawthorn]] ([[User talk:Hawthorn|talk]]) 15:32, 1 March 2019 (UTC)<br />
I think they all got annoyed at the graph and left. [[User:Margath|Margath]] ([[User talk:Margath|talk]]) 15:46, 1 March 2019 (UTC)<br />
Of course there is! [[Special:Contributions/162.158.214.22|162.158.214.22]] 15:44, 1 March 2019 (UTC)<br />
<br />
As an example: When measuring the height of people in the same age bracket, then you'll expect the number of people at each height to look like this graph. There will be a lot of people around the average height, fewer a foot shorter/taller, some (but very few) exceptionally tall people, and some (but very few) exceptionally short people. The x-value represents the height, the y-value essentially represents the amount of population that share that height. When we measure the middle 50% of the population using vertical bars, then people at a certain height are either inside '''OR''' outside the middle. Randall uses horizontal bars here, which means some people at a certain height will be counted in the middle 50%, but other people with the same height won't be. In fact, some people with the exact average height of the whole population would fall outside the middle. [[Special:Contributions/108.162.241.214|108.162.241.214]] 16:01, 1 March 2019 (UTC)<br />
<br />
Feel free to rip me apart for referring to it as the "number of people at each height", since y-axis is more complicated than a simple count. [[Special:Contributions/108.162.241.214|108.162.241.214]] 16:03, 1 March 2019 (UTC)<br />
<br />
Just to say, Randall's horizontal slice isn't entirely meaningless. It's a calculation I've had to do, where I have a series of binned samples of a population (say I knew how many fell in -10..10, how many fell in -5..5, how many fell in -2..2) and wanted to combine them with an appropriate weighting to approximate a Gaussian. I was using it for filtering, but it's logically similar. [[User:Fluppeteer|Fluppeteer]] ([[User talk:Fluppeteer|talk]]) 16:19, 1 March 2019 (UTC)<br />
::Also, the slice sampler for MCMC is a trick for sampling from a distribution by "turning it on its side". But I don't think the 50% figure would be meaningful in that context. (Though the 52.7% number on this graph would be.) [[Special:Contributions/172.68.54.136|172.68.54.136]] 21:16, 1 March 2019 (UTC)<br />
<br />
Pedant: etymologically, there *is* actually a connection between a normal (to a surface or line) and the normal distribution; the former comes from the Latin for a set square (giving you perpendicular), and it later came to mean "standard". The "tangential distribution" certainly fits the etymology of "odd/unusual" though. [[User:Fluppeteer|Fluppeteer]] ([[User talk:Fluppeteer|talk]]) 16:26, 1 March 2019 (UTC)<br />
<br />
This reminds me of the difference between Riemann(-Stieltjes) and Lebesgue integration. [[Special:Contributions/172.68.54.160|172.68.54.160]] 20:16, 1 March 2019 (UTC)<br />
<br />
As the axis are not labeled (see comic 833) we could consider this a multivariate distribution where one parameter is uniform and the other is normal. That was my first thought when I saw this. [[Special:Contributions/172.68.34.88|172.68.34.88]] 18:43, 1 March 2019 (UTC)<br />
<br />
Is there any meaning to midpoint: 52.7%? Maybe that is the arbitrary center he formed the horizontal bounds around? Maybe it relates to data? Is this a reference to something? It's certainly reminiscent of how normal distributions produce statistically meaningful numbers that have weird decimals in them (like the % represented by being within so many standard deviations). [[Special:Contributions/162.158.78.178|162.158.78.178]] 19:45, 1 March 2019 (UTC)<br />
::Maybe it's because the meaning of "50% of the chart lies between these lines" specifically becomes roughly useless for discerning error if the lines are not centered around the origin. [[Special:Contributions/162.158.78.178|162.158.78.178]] 19:52, 1 March 2019 (UTC)<br />
::I might get it!!! The area between the lines is 52.7% of the total area: which means that 50% is technically included in what lies between them. [[Special:Contributions/162.158.78.220|162.158.78.220]] 23:07, 1 March 2019 (UTC)<br />
<br />
The correct way to do this is to have the topmost vertical line equal to or above the top of the normal plot. Then the bottom-most line would represent the same values as vertical lines would. [[Special:Contributions/162.158.78.220|162.158.78.220]] 23:32, 1 March 2019 (UTC)<br />
<br />
Say I want to build a diverse team or a representative council. And it is more important that the selection is representative of several subpopulations (who should not be voted down by the majority) than that it gives an equal fair chance to anybody. I would cut away the absolute outliers and reduce the weight of the most abundant group - this gives just the area between the two lines. Sebastian --[[Special:Contributions/172.68.110.70|172.68.110.70]] 23:40, 1 March 2019 (UTC)<br />
:That's actually... not a horrible idea. Problem is, it's not robust to transformations of the X axis, because of the Jacobian multiplier that comes with such transformations. Which in practice would look like people loudly insisting they have nothing in common with each other ("we wear baseball hats with the brim to the RIGHT while those other completely unrelated people wear them with the brim to the LEFT")[[Special:Contributions/162.158.63.244|162.158.63.244]] 16:26, 2 March 2019 (UTC)<br />
<br />
Has somebody measured or calculated (by assuming normal distribution) the areas? It seems that the upper area is way smaller than the lower one, but both having the same 'height' in the middle. Is the 52.7% graphically correct? I tried half of the height at 0: .398942 and integrated, then I get 52,6% for the white area and 47,4% for the gray area. On the y-axis it seems that the three visible ticks are .1, .2, .3, then the gray area would be a bit broader than .2 and centered at .1. Sebastian --[[Special:Contributions/172.68.110.70|172.68.110.70]] 23:40, 1 March 2019 (UTC)<br />
<br />
Got [[356:_Nerd_Sniping|Nerd Sniped]] by the number "52.7%", but failed on an analytic solution and settled for a quick and dirty numerical integration instead, which suggested that the exact number might be somewhere between .5268 and .5269, so I think I'm not far from the truth. As I see it, the shaded area is vertically centered around the vertical midpoint, with a relative vertical width chosen such that the shaded area is exactly 50% of the total area under the curve. Just as usual, only with vertical instead of horizontal binning, which of course is the twist that makes this graph puzzling, funny, and completely useless for meaningful interpretation. <br />
The label "52.7%" is not an addition to the Midpoint label but instead gives the width of the vertical bin, as a percentage of the vertical height of the curve. I read the tics on the vertical axis to indicate just quarters of the curve maximum, which is consistent with my understanding of "Midpoint". <br />
Oh, and you are certainly right in that the marginal distributions at the top and the bottom are asymmetric, as is the gaussian when viewed sideways. <br />
[[Special:Contributions/172.68.110.64|172.68.110.64]] 23:56, 1 March 2019 (UTC)<br />
: Feh. You merely have to integrate something like Sqrt[Log[x]] which I'm too lazy for and use Mathematica instead which gives...<covers eyes>...what was #2117 about again? [[Special:Contributions/162.158.94.2|162.158.94.2]] 11:57, 2 March 2019 (UTC)<br />
:: There's a way to (attempt to) symbolically integrate functions involving things like e^(-x^2) like you have with the normal distribution (Cherry's extension of the Risch algorithm, see his thesis or his 1985 paper), but I have no idea how to apply it here. It's definitely a very complex procedure. As I understand even Mathematica has not implemented it in full. - [[User:CRGreathouse|CRGreathouse]] ([[User talk:CRGreathouse|talk]]) 03:59, 3 March 2019 (UTC)<br />
<br />
How to annoy a Democratic Liberal Statician- Point out that every identity group that they're trying to make "normal" falls to the far left or the far right of the normal distribution curve.[[User:Seebert|Seebert]] ([[User talk:Seebert|talk]]) 14:50, 2 March 2019 (UTC)<br />
:As somebody who happens to be all 3 of those things, I can confirm that your comment annoyed me. But only for bringing politics into a discussion that isn't political, and for misusing "normal" in a way like Randall's alt-text. The actual "edgy" political content of your post I find wrong but not particularly annoying. YMMV. [[Special:Contributions/162.158.63.244|162.158.63.244]] 16:26, 2 March 2019 (UTC)<br />
<br />
'''"Completely meaningless?"'''<br><br />
The explanation currently says, "Randall finds the area between two horizontal lines instead, which is mathematically completely meaningless." This doesn't seem right. Each of the two horizontal lines intersect the curve at points and those points have meaningful values on the x axis. I'm not sure if they represent anything interesting (or rather, what their significance might be), but the result is the horizontal lines are not meaningless. I'm a little reluctant to edit it because I'm not sure how meaning to ascribe (and I also haven't measured the or calculated what those points are), but the explanation as-written seems improper. Do I have it wrong? [[User:JohnHawkinson|JohnHawkinson]] ([[User talk:JohnHawkinson|talk]]) 15:02, 2 March 2019 (UTC)<br />
:Nothing is ever completely meaningless. I think the change to "completely meaningless" may have been added by an annoyed statistician. I wrote the previous phrasing of it rarely being used for anything meaningful, so it seems impolite for me to edit it back. It's notable that implying there is meaning to the horizontal lines could be misleading to those new to statistics. It's also notable that the area between them represents a calculable portion of the samplesets, and that the points of intersection are just as meaningful as with vertical lines, two uses mentioned in comments above. [[Special:Contributions/162.158.79.245|162.158.79.245]] 15:13, 2 March 2019 (UTC)</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=Talk:2117:_Differentiation_and_Integration&diff=170306Talk:2117: Differentiation and Integration2019-03-01T01:34:47Z<p>CRGreathouse: /* Risch algorithm */</p>
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<div><!--Please sign your posts with ~~~~ and don't delete this text. New comments should be added at the bottom.--><br />
Darn, I have no idea what this comic is about. Randal has eluded my yet again. [[User:Linker|Linker]] ([[User talk:Linker|talk]]) 17:43, 27 February 2019 (UTC)<br />
:Calculus. [[Special:Contributions/162.158.79.143|162.158.79.143]] 18:16, 27 February 2019 (UTC)<br />
Basically, integration is easy to do by hand, but integration, even of things that look simple on paper, can be very difficult, as well as easy to mess up or get lost in. <br />
And Calc 2 is why I stopped being a Computer Science major and moved (eventually) to majoring in English. Consistent 4.0s in math through Trig and Calc I ... 1.6 in Calc II, retook and got a 1.8. Without the Calc, couldn't do the physics; without the physics, couldn't get my 2-yr degree and move on from community college to a full university. I don't know what all the integration stuff in the flowchart is (since I didn't do well in Calc and it was a long time ago), but there's so very many things that become [https://en.wikipedia.org/wiki/Nonelementary_integral nonelementary integrals] that all sorts of special tricks have to be employed for things that look like they should be easy. It's like having a problem that's very easy to do division on, but requires special advanced mathematical tricks to use multiplication upon.[[Special:Contributions/108.162.216.208|108.162.216.208]] 19:07, 27 February 2019 (UTC)<br />
<br />
Basic ideas:<br />
Integration by parts is the reverse of the Product Rule.<br />
Substitution is the reverse of the Chain Rule.<br />
Cauchy's Formula gives the result of a contour integration in the complex plane, using "singularities" of the integrand.<br />
Partial fractions is just splitting up one complex fraction into a sum of simple fractions, which is relevant because they are easier to integrate.<br />
Stokes theorem is the relationship between an integral over an area, and an integral over the boundary of said area.<br />
Riemann integration was the first rigorous definition of integration. This has been superseded by Lesbesgue integration.<br />
Bessel functions are like 2d versions of sin and cos, and turn up sometimes when doing integration.[[Special:Contributions/162.158.89.61|162.158.89.61]] 20:14, 27 February 2019 (UTC)<br />
:"Lesbesgue integration." Best. Freudian. Slip. Ever. SCNR :P [[Special:Contributions/162.158.91.59|162.158.91.59]] 08:28, 28 February 2019 (UTC)<br />
I know what you mean ;). After all, Gen 8 Pokemon was announced the other day, so you read it as "Pokemon League Integration". Completely understandable. [[Special:Contributions/172.68.78.28|172.68.78.28]] 14:40, 28 February 2019 (UTC)<br />
Shouldn't Wolfram Alpha be somewhere in that flowchart? [[Special:Contributions/162.158.255.142|162.158.255.142]] 20:54, 27 February 2019 (UTC)<br />
<br />
Glad to see I'm not the only one who is too dumb to integrate [[Special:Contributions/162.158.90.36|162.158.90.36]] 21:02, 27 February 2019 (UTC)<br />
:Symbolic differentiation is just going through algorithm ; there are few functions which don't have it but they tend to be constructed in complicated way, and if function have differentiation it's usually easy to find it. Symbolic integration requires lot of thinking and trial and error ; even very easy function may lack primitive function and even if they don't, you may be unable to find it except randomly. If it's exercise in book, the ones for differentiation are done by thinking about some interesting function and putting it there. The ones for integration are done by thinking about some interesting function and putting it's differentiation there. -- [[User:Hkmaly|Hkmaly]] ([[User talk:Hkmaly|talk]]) 23:38, 27 February 2019 (UTC)<br />
<br />
Oddly enough it mentions Riemann integration, but that is the integral most people know how to use. Turns out there are a lot more (e.g. lebesgue and generalized riemann integrals). I'm halfway through a second semester of real analysis and was floored by how involved integration can be. [[Special:Contributions/172.68.34.106|172.68.34.106]] 21:36, 27 February 2019 (UTC)<br />
<br />
One of my professors once said: "Never try to integrate a function. Almost all (in a strict mathematical sense) functions are impossible to integrate, so there is no reason why you should even try." --[[Special:Contributions/162.158.88.128|162.158.88.128]] 07:52, 28 February 2019 (UTC)<br />
<br />
How is there no "+ C" joke in there [[User:Blagae|Blagae]] ([[User talk:Blagae|talk]]) 13:16, 28 February 2019 (UTC)<br />
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== Risch algorithm ==<br />
<br />
I thought I could contribute to the article with a better explanation of the Risch algorithm, since I have a bit of expertise here -- I've read all the original papers, plus the Cherry papers that add the extra features like Li and erf. I pulled out some of the old papers to review my knowledge of symbolic differential algebra (it's been a while!) then typed up a careful explanation which corrected some errors in the original description and fleshed out many more details... possibly excessively, but hey, that's kind of our calling here.<br />
<br />
Then I saw that Glassvein completely removed my version for what appears to be the original without so much as a mention in the edit description. What gives? I<br />
<br />
[[User:CRGreathouse|CRGreathouse]] ([[User talk:CRGreathouse|talk]]) 04:59, 28 February 2019 (UTC)<br />
: Probably due to simultaneous editing. I've restored your definition. [[Special:Contributions/162.158.88.128|162.158.88.128]] 16:52, 28 February 2019 (UTC)<br />
<br />
:: OK, wasn't sure if it was intentional (if somehow it was worse). Thanks! [[User:CRGreathouse|CRGreathouse]] ([[User talk:CRGreathouse|talk]]) 01:34, 1 March 2019 (UTC)<br />
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== Numerical Integration ==<br />
Better still...plot the graph - cut along the line - weigh the part under the line. :-) [[User:SteveBaker|SteveBaker]] ([[User talk:SteveBaker|talk]]) 20:46, 28 February 2019 (UTC)</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=User_talk:Glassvein&diff=170273User talk:Glassvein2019-02-28T05:23:04Z<p>CRGreathouse: Differentiation and Integration / Risch</p>
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<div>== Differentiation and Integration ==<br />
Hi! Did you intentionally revert my changes to the description of the Risch algorithm at [[2117: Differentiation and Integration]], or was that just an edit conflict? - [[User:CRGreathouse|CRGreathouse]] ([[User talk:CRGreathouse|talk]]) 05:23, 28 February 2019 (UTC)</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=Talk:2117:_Differentiation_and_Integration&diff=170271Talk:2117: Differentiation and Integration2019-02-28T04:59:26Z<p>CRGreathouse: /* Risch algorithm */ new section</p>
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<div><!--Please sign your posts with ~~~~ and don't delete this text. New comments should be added at the bottom.--><br />
Darn, I have no idea what this comic is about. Randal has eluded my yet again. [[User:Linker|Linker]] ([[User talk:Linker|talk]]) 17:43, 27 February 2019 (UTC)<br />
:Calculus. [[Special:Contributions/162.158.79.143|162.158.79.143]] 18:16, 27 February 2019 (UTC)<br />
Basically, integration is easy to do by hand, but integration, even of things that look simple on paper, can be very difficult, as well as easy to mess up or get lost in. <br />
And Calc 2 is why I stopped being a Computer Science major and moved (eventually) to majoring in English. Consistent 4.0s in math through Trig and Calc I ... 1.6 in Calc II, retook and got a 1.8. Without the Calc, couldn't do the physics; without the physics, couldn't get my 2-yr degree and move on from community college to a full university. I don't know what all the integration stuff in the flowchart is (since I didn't do well in Calc and it was a long time ago), but there's so very many things that become [https://en.wikipedia.org/wiki/Nonelementary_integral nonelementary integrals] that all sorts of special tricks have to be employed for things that look like they should be easy. It's like having a problem that's very easy to do division on, but requires special advanced mathematical tricks to use multiplication upon.[[Special:Contributions/108.162.216.208|108.162.216.208]] 19:07, 27 February 2019 (UTC)<br />
<br />
Basic ideas:<br />
Integration by parts is the reverse of the Product Rule.<br />
Substitution is the reverse of the Chain Rule.<br />
Cauchy's Formula gives the result of a contour integration in the complex plane, using "singularities" of the integrand.<br />
Partial fractions is just splitting up one complex fraction into a sum of simple fractions, which is relevant because they are easier to integrate.<br />
Stokes theorem is the relationship between an integral over an area, and an integral over the boundary of said area.<br />
Riemann integration was the first rigorous definition of integration. This has been superseded by Lesbesgue integration.<br />
Bessel functions are like 2d versions of sin and cos, and turn up sometimes when doing integration.[[Special:Contributions/162.158.89.61|162.158.89.61]] 20:14, 27 February 2019 (UTC)<br />
<br />
Shouldn't Wolfram Alpha be somewhere in that flowchart? [[Special:Contributions/162.158.255.142|162.158.255.142]] 20:54, 27 February 2019 (UTC)<br />
<br />
Glad to see I'm not the only one who is too dumb to integrate [[Special:Contributions/162.158.90.36|162.158.90.36]] 21:02, 27 February 2019 (UTC)<br />
:Symbolic differentiation is just going through algorithm ; there are few functions which don't have it but they tend to be constructed in complicated way, and if function have differentiation it's usually easy to find it. Symbolic integration requires lot of thinking and trial and error ; even very easy function may lack primitive function and even if they don't, you may be unable to find it except randomly. If it's exercise in book, the ones for differentiation are done by thinking about some interesting function and putting it there. The ones for integration are done by thinking about some interesting function and putting it's differentiation there. -- [[User:Hkmaly|Hkmaly]] ([[User talk:Hkmaly|talk]]) 23:38, 27 February 2019 (UTC)<br />
<br />
Oddly enough it mentions Riemann integration, but that is the integral most people know how to use. Turns out there are a lot more (e.g. lebesgue and generalized riemann integrals). I'm halfway through a second semester of real analysis and was floored by how involved integration can be. [[Special:Contributions/172.68.34.106|172.68.34.106]] 21:36, 27 February 2019 (UTC)<br />
<br />
== Risch algorithm ==<br />
<br />
I thought I could contribute to the article with a better explanation of the Risch algorithm, since I have a bit of expertise here -- I've read all the original papers, plus the Cherry papers that add the extra features like Li and erf. I pulled out some of the old papers to review my knowledge of symbolic differential algebra (it's been a while!) then typed up a careful explanation which corrected some errors in the original description and fleshed out many more details... possibly excessively, but hey, that's kind of our calling here.<br />
<br />
Then I saw that Glassvein completely removed my version for what appears to be the original without so much as a mention in the edit description. What gives? I<br />
<br />
[[User:CRGreathouse|CRGreathouse]] ([[User talk:CRGreathouse|talk]]) 04:59, 28 February 2019 (UTC)</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=2117:_Differentiation_and_Integration&diff=1702672117: Differentiation and Integration2019-02-28T03:09:04Z<p>CRGreathouse: /* Integration */ better description of Risch algorithm</p>
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<div>{{comic<br />
| number = 2117<br />
| date = February 27, 2019<br />
| title = Differentiation and Integration<br />
| image = differentiation_and_integration.png<br />
| titletext = "Symbolic integration" is when you theatrically go through the motions of finding integrals, but the actual result you get doesn't matter because it's purely symbolic.<br />
}}<br />
<br />
==Explanation==<br />
{{incomplete|Created by a BESSEL FUNCTION? Please mention here why this explanation isn't complete. Do NOT delete this tag too soon.}}<br />
This comic provides a {{w|flowchart}} purporting to show the process of differentiation, and another for integration.<br />
<br />
{{w|Derivative|Differentiation}} and {{w|Antiderivative|Integration}} are two major components of {{w|calculus}}. As many Calculus 2 students are painfully aware, integration is much more complicated than the differentiation it undoes.<br />
<br />
However, Randall dramatically overstates this point here. After the first step of integration, Randall assumes that any integration can not be solved so simply, and then dives into a step named "????", suggesting that it is unknowable how to proceed. The rest of the flowchart is (we can assume deliberately) even harder to follow, and does not reach a conclusion. This is in contrast to the simple, straightforward flowchart for differentiation. The fact that the arrows in the bottom of the integration part leads to nowhere indicates that "Phone calls to mathematicians", "Oh no" and "Burn the evidence" are not final steps in the difficult journey. The flowchart could be extended by Randall to God-know-where extents.<br />
<br />
It should be noted that Randall slightly undermines his point by providing four different methods, and an "etc", for attempting differentiation with no guidelines for selecting between them.<br />
<br />
===Differentiation===<br />
'''{{w|Chain rule}}'''<br />
<br />
For any <math> \frac{d}{dx}f(x)=f'(x)</math> and <math> \frac{d}{dx}g(x)=g'(x) </math>, it follows that <math> \frac{d}{dx}(f(g(x)))=f'(g(x))*g'(x)</math>.<br />
<br />
'''{{w|Power Rule}}'''<br />
<br />
For any <math> f(x)=x^a </math>, it follows that <math> \frac{d}{dx}f(x)=a*x^{a-1} </math>.<br />
<br />
'''{{w|Quotient rule}}'''<br />
<br />
For any <math> \frac{d}{dx}f(x)=f'(x)</math> and <math> \frac{d}{dx}g(x)=g'(x) </math>, it follows that <math> \frac{d}{dx} \frac{f(x)}{g(x)}=\frac{f'(x)g(x)-f(x)g'(x)}{(g(x))^2}</math> if <math>g(x)\ne 0</math>.<br />
<br />
'''{{w|Product rule}}'''<br />
<br />
For any <math> \frac{d}{dx}f(x)=f'(x)</math> and <math> \frac{d}{dx}g(x)=g'(x) </math>, it follows that <math> \frac{d}{dx}(f(x)*g(x))=f'(x)*g(x)+f(x)*g'(x)</math>.<br />
<br />
===Integration===<br />
'''{{w|Integration by parts}}'''<br />
<br />
The "product rule" run backwards. Since <math>(uv)' = uv' + u'v</math>, it follows that by integrating both sides you get <math> uv = \int u dv + \int v du</math>, which is more commonly written as <math>\int u dv = uv - \int v du</math>. By finding appropriate values for functions <math>u, v</math> such that your problem is in the form <math>\int u dv</math>, your problem ''may'' be simplified.<br />
<br />
'''{{w|Integration by substitution|Substitution}}'''<br />
<br />
The "chain rule" run backwards. Since <math> d(f(u)) = (df(u))du</math>, it follows that <math>f(u) = \int df(u) du</math>. By finding appropriate values for functions <math>f, u</math> such that your problem is in the form <math>\int df(u) du</math> your problem ''may'' be simplified.<br />
<br />
'''{{w|Cauchy's integral formula|Cauchy's Formula}}'''<br />
<br />
Cauchy's Integral formula is a result in complex analysis that relates the value of a contour integral in the complex plane to properties of the singularities in the interior of the contour. It is often used to compute integrals on the real line by extending the path of the integral from the real line into the complex plane to apply the formula, then proving that the integral from the parts of the contour not on the real line has value zero. <br />
<br />
'''{{w|Partial_fraction_decomposition#Application_to_symbolic_integration|Partial Fractions}}'''<br />
<br />
Partial fractions is a technique for breaking up a function that comprises one polynomial divided by another into a sum of functions comprising constants over the factors of the original denominator, which can easily be integrated into logarithms.<br />
<br />
'''{{w|Install Mathematica}}'''<br />
<br />
{{w|Mathematica}} is a modern technical computing system spanning most areas. One of its features is to compute mathematical functions. This step in the flowchart is install and use Mathematica to compute to do the integration for you.<br />
<br />
'''{{w|Riemann integral|Riemann Integration}}'''<br />
The Riemann integral is a definition of definite integration. Elementary textbooks on calculus sometimes present finding a definite integral as a process of approximating an area by strips of equal width and then taking the limit as the strips become narrower. Riemann integration removes the requirement that the strips have equal width, and so is a more flexible definition. However there are still many functions for which the Riemann integral doesn't converge, and consideration of these functions leads to the Lesbegue Integral. Riemann integration is not a method of calculus appropriate for finding the anti-derivative of an elementary function.<br />
<br />
'''{{w|Stokes' Theorem}}'''<br />
???<br />
<br />
'''{{w|Risch algorithm}}'''<br />
The Risch algorithm is a notoriously complex procedure that, given a certain class of symbolic integrand, either finds a symbolic integral or proves that no elementary integral exists. (Technically it is only a semi-algorithm, and cannot produce an answer unless it can determine if a certain symbolic expression is {{w|Constant problem|equal to 0}} or not.) Many computer algebra systems have chosen to implement only the simpler Risch-Norman algorithm, which does not come with the same guarantee. A series of extensions to the Risch algorithm extend the class of allowable functions to include (at least) the error function and the logarithmic integral.<br />
<br />
'''{{w|Bessel function}}'''<br />
The Bessel function is a second-order differential equation used in solving problems in cylindrical and spherical coordinate systems.<br />
<br />
'''{{w|Symbolic integration}}'''<br />
Mentioned in the title text. ???<br />
<br />
''' Burn the evidence '''<br />
In a parody of detective novels, this may refer to the burning of your work to avoid the shame of being unable to solve the integration problem. <br />
Alternatively, this could be an ironic hint to the fact that in order to find the integral, it may even be necessary to break the law or upset higher powers, so that the negative consequences of a persecution can only be avoided by destroying the evidence.<br />
<br />
==Transcript==<br />
{{incomplete transcript|Do NOT delete this tag too soon.}}<br />
:[Two flow charts are shown.]<br />
<br />
:[The first flow chart has four steps in simple order, one with multiple recommendations.]<br />
:DIFFERENTIATION<br />
:Start<br />
:Try applying<br />
::Chain Rule<br />
::Power Rule<br />
::Quotient Rule<br />
::Product Rule<br />
::Etc.<br />
:Done?<br />
::Yes<br />
::No<br />
:Done!<br />
<br />
[The second flow chart begins like the first, then descends into chaos.]<br />
:INTEGRATION<br />
:Start<br />
:Try applying<br />
::Integration by Parts<br />
::Substitution<br />
:Done?<br />
:Haha, Nope!<br />
<br />
:[Chaos, Roughly from left to right, top to bottom, direction arrows not included.]<br />
::Cauchy's Formula<br />
::????<br />
::???!?<br />
::???<br />
::???<br />
::?<br />
::Partial Fractions<br />
::??<br />
::?<br />
::Install Mathematica<br />
::?<br />
::Riemann Integration<br />
::Stokes' Theorem<br />
::???<br />
::?<br />
::Risch Algorithm<br />
::???<br />
::[Sad face.]<br />
::?????<br />
::???<br />
::What the heck is a Bessel Function??<br />
::Phone calls to mathematicians<br />
::Oh No<br />
::Burn the Evidence<br />
<!--::More arrows pointing out of the image to suggest more steps--><br />
<br />
{{comic discussion}}<br />
[[Category:Analysis]]</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=2117:_Differentiation_and_Integration&diff=1702632117: Differentiation and Integration2019-02-28T02:14:16Z<p>CRGreathouse: category</p>
<hr />
<div>{{comic<br />
| number = 2117<br />
| date = February 27, 2019<br />
| title = Differentiation and Integration<br />
| image = differentiation_and_integration.png<br />
| titletext = "Symbolic integration" is when you theatrically go through the motions of finding integrals, but the actual result you get doesn't matter because it's purely symbolic.<br />
}}<br />
<br />
==Explanation==<br />
{{incomplete|Created by a BESSEL FUNCTION? Please mention here why this explanation isn't complete. Do NOT delete this tag too soon.}}<br />
This comic provides a {{w|flowchart}} purporting to show the process of differentiation, and another for integration.<br />
<br />
{{w|Derivative|Differentiation}} and {{w|Antiderivative|Integration}} are two major components of {{w|calculus}}. As many Calculus 2 students are painfully aware, integration is much more complicated than the differentiation it undoes.<br />
<br />
However, Randall dramatically overstates this point here. After the first step of integration, Randall assumes that any integration can not be solved so simply, and then dives into a step named "????", suggesting that it is unknowable how to proceed. The rest of the flowchart is (we can assume deliberately) even harder to follow, and does not reach a conclusion. This is in contrast to the simple, straightforward flowchart for differentiation. The fact that the arrows in the bottom of the integration part leads to nowhere indicates that "Phone calls to mathematicians", "Oh no" and "Burn the evidence" are not final steps in the difficult journey. The flowchart could be extended by Randall to God-know-where extents.<br />
<br />
It should be noted that Randall slightly undermines his point by providing four different methods, and an "etc", for attempting differentiation with no guidelines for selecting between them.<br />
<br />
===Differentiation===<br />
'''{{w|Chain rule}}'''<br />
<br />
For any <math> \frac{d}{dx}f(x)=f'(x)</math> and <math> \frac{d}{dx}g(x)=g'(x) </math>, it follows that <math> \frac{d}{dx}(f(g(x)))=f'(g(x))*g'(x)</math>.<br />
<br />
'''{{w|Power Rule}}'''<br />
<br />
For any <math> f(x)=x^a </math>, it follows that <math> \frac{d}{dx}f(x)=a*x^{a-1} </math>.<br />
<br />
'''{{w|Quotient rule}}'''<br />
<br />
For any <math> \frac{d}{dx}f(x)=f'(x)</math> and <math> \frac{d}{dx}g(x)=g'(x) </math>, it follows that <math> \frac{d}{dx} \frac{f(x)}{g(x)}=\frac{f'(x)g(x)-f(x)g'(x)}{(g(x))^2}</math> if <math>g(x)\ne 0</math>.<br />
<br />
'''{{w|Product rule}}'''<br />
<br />
For any <math> \frac{d}{dx}f(x)=f'(x)</math> and <math> \frac{d}{dx}g(x)=g'(x) </math>, it follows that <math> \frac{d}{dx}(f(x)*g(x))=f'(x)*g(x)+f(x)*g'(x)</math>.<br />
<br />
===Integration===<br />
'''{{w|Integration by parts}}'''<br />
<br />
The "product rule" run backwards. Since <math>(uv)' = uv' + u'v</math>, it follows that by integrating both sides you get <math> uv = \int u dv + \int v du</math>, which is more commonly written as <math>\int u dv = uv - \int v du</math>. By finding appropriate values for functions <math>u, v</math> such that your problem is in the form <math>\int u dv</math>, your problem ''may'' be simplified.<br />
<br />
'''{{w|Integration by substitution|Substitution}}'''<br />
<br />
The "chain rule" run backwards. Since <math> d(f(u)) = (df(u))du</math>, it follows that <math>f(u) = \int df(u) du</math>. By finding appropriate values for functions <math>f, u</math> such that your problem is in the form <math>\int df(u) du</math> your problem ''may'' be simplified.<br />
<br />
'''{{w|Cauchy's integral formula|Cauchy's Formula}}'''<br />
<br />
Cauchy's Integral formula is a result in complex analysis that relates the value of a contour integral in the complex plane to properties of the singularities in the interior of the contour. It is often used to compute integrals on the real line by extending the path of the integral from the real line into the complex plane to apply the formula, then proving that the integral from the parts of the contour not on the real line has value zero. <br />
<br />
'''{{w|Partial_fraction_decomposition#Application_to_symbolic_integration|Partial Fractions}}'''<br />
<br />
Partial fractions is a technique for breaking up a function that comprises one polynomial divided by another into a sum of functions comprising constants over the factors of the original denominator, which can easily be integrated into logarithms.<br />
<br />
'''{{w|Install Mathematica}}'''<br />
<br />
{{w|Mathematica}} is a modern technical computing system spanning most areas. One of its features is to compute mathematical functions. This step in the flowchart is install and use Mathematica to compute to do the integration for you.<br />
<br />
'''{{w|Riemann integral|Riemann Integration}}'''<br />
The Riemann integral is a definition of definite integration. Elementary textbooks on calculus sometimes present finding a definite integral as a process of approximating an area by strips of equal width and then taking the limit as the strips become narrower. Riemann integration removes the requirement that the strips have equal width, and so is a more flexible definition. However there are still many functions for which the Riemann integral doesn't converge, and consideration of these functions leads to the Lesbegue Integral. Riemann integration is not a method of calculus appropriate for finding the anti-derivative of an elementary function.<br />
<br />
'''{{w|Stokes' Theorem}}'''<br />
???<br />
<br />
'''{{w|Risch Algorithm}}'''<br />
The Risch Algorithm is a complex procedure that reduces the process of symbolic integration to purely algebraic steps. It is implemented in Computer Algebra software, such as Mathematica.<br />
<br />
'''{{w|Bessel function}}'''<br />
???<br />
<br />
'''{{w|Symbolic integration}}'''<br />
Mentioned in the title text. ???<br />
<br />
''' Burn the evidence '''<br />
In a parody of detective novels, this may refer to the burning of your work to avoid the shame of being unable to solve the integration problem. <br />
Alternatively, this could be an ironic hint to the fact that in order to find the integral, it may even be necessary to break the law or upset higher powers, so that the negative consequences of a persecution can only be avoided by destroying the evidence.<br />
<br />
==Transcript==<br />
{{incomplete transcript|Do NOT delete this tag too soon.}}<br />
:[Two flow charts are shown.]<br />
<br />
:[The first flow chart has four steps in simple order, one with multiple recommendations.]<br />
:DIFFERENTIATION<br />
:Start<br />
:Try applying<br />
::Chain Rule<br />
::Power Rule<br />
::Quotient Rule<br />
::Product Rule<br />
::Etc.<br />
:Done?<br />
::Yes<br />
::No<br />
:Done!<br />
<br />
[The second flow chart begins like the first, then descends into chaos.]<br />
:INTEGRATION<br />
:Start<br />
:Try applying<br />
::Integration by Parts<br />
::Substitution<br />
:Done?<br />
:Haha, Nope!<br />
<br />
:[Chaos, Roughly from left to right, top to bottom, direction arrows not included.]<br />
::Cauchy's Formula<br />
::????<br />
::???!?<br />
::???<br />
::???<br />
::?<br />
::Partial Fractions<br />
::??<br />
::?<br />
::Install Mathematica<br />
::?<br />
::Riemann Integration<br />
::Stokes' Theorem<br />
::???<br />
::?<br />
::Risch Algorithm<br />
::???<br />
::[Sad face.]<br />
::?????<br />
::???<br />
::What the heck is a Bessel Function??<br />
::Phone calls to mathematicians<br />
::Oh No<br />
::Burn the Evidence<br />
<!--::More arrows pointing out of the image to suggest more steps--><br />
<br />
{{comic discussion}}<br />
[[Category:Analysis]]</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=2063:_Carnot_Cycle&diff=1697382063: Carnot Cycle2019-02-17T21:06:26Z<p>CRGreathouse: /* Explanation */</p>
<hr />
<div>{{comic<br />
| number = 2063<br />
| date = October 24, 2018<br />
| title = Carnot Cycle<br />
| image = carnot_cycle.png<br />
| titletext = The Carnot cycle is more properly known by its full title, the "Carnot-Tolkien-Wagner Ring Cycle."<br />
}}<br />
<br />
==Explanation==<br />
{{incomplete|At the discussion page there are still unsolved issues mentioned about "Decline and fall". Please help to fix this or at least add your comments at the discussion page.}}<br />
<br />
This comic shows a {{w|Pressure–volume diagram}} which is used in this case for a {{w|Carnot cycle}}, a theoretical thermodynamic cycle and covers most thermodynamics classes which looks very much like the figure drawn. The most common example of a (suboptimal) Carnot cycle is the {{w|Heat_pump_and_refrigeration_cycle|vapor compression cycle}} used in {{w|Refrigerator|refrigerators}}. However in this case, [[Randall]] has replaced the labels of the 4 stages of the real Carnot cycle with new ones.<br />
<br />
Pressure–volume diagrams were first developed to understand the efficiency of steam engines and plot the change of pressure ''P'' with respect to volume ''V'' for a specific process. The process forms a cycle and the amount of energy involved can be estimated by the area under the curve on the chart. The Carnot cycle describes the ideal efficiency that such an engine can achieve during the conversion of heat into work, or vice versa like in a refrigeration system. The real steps are called (explained in short):<br />
#'''Isothermal expansion''' (An external force by heat causes an increase of volume but also a small decrease of pressure on the first place.)<br />
#'''Isentropic expansion''' (The volume of the gas remains nearly constant while the pressure decreases dramatically, the external heat is now absent.)<br />
#'''Isothermal compression''' (No external forces still involved, the volume of the gas decreases and leads to the last step:)<br />
#'''Isentropic compression''' (Now the volume of the gas collapses, increasing the pressure significantly usable for engineering.)<br />
<br />
An isothermal process is a change of a system, in which the temperature remains constant but in this diagrams the volume increases (expansion) or decreases (compression). The term isentropic describes a lossless process where no matter or energy is transferred, here the increased volume only causes a further decrease in pressure; it is also called adiabatic process.<br />
<br />
The prefix ''iso-'' is derived from the Ancient Greek word ''ísos'' which translates to ''equal'' and used widely in modern days in science like here to indicate a process at the same temperature (-thermal) which is not shown in the graph. The prefix ''is-'' to the term {{w|Entropy|entropy}} is only used in thermodynamics.<br />
<br />
In the comic, the cycle also has two phases of expansion followed by two phases of contraction (or "decline"), but the names of steps one to three are replaced with other words beginning with the prefix "iso-" meaning same or equal, and the factors that are held constant are absurd.<br />
<br />
Each step in this comic is explained below:<br />
<br />
'''1. Isometric expansion.''' When heated, the gas becomes larger due to increasing volume<br />
<br />
Isometric (literally "equal dimensions") can refer to a property or process that is symmetrical in all dimensions (i.e. the gas is expanding radially) or to a [[wikipedia:Isometric process | type of thermodynamic process]] where volume is held constant but temperature is free to vary, the exact opposite of the first step in the real Carnot cycle. Additionally, the comic text uses a circular argument (become larger due to increasing volume).<br />
<br />
In mathematics, an {{w|isometric mapping}} (between metric spaces) is a map that keeps all the distances intact. If we measure the distance the same way throughout the cycle, then isometric expansion (or for that matter, isometric compression) is not really an expansion (or a compression). <br />
<br />
'''2. Isotonic expansion.''' The gas expands further due to dark energy while percent milkfat remains constant.<br />
<br />
{{w|Isotonic}} is a descriptor commonly associated with sports drinks (and not thermodynamics), which contain similar concentrations of salt and sugar as in the human body. {{w|Dark energy}} is hypothesized to be a cause for the expansion of the universe, which obviously isn't relevant to thermodynamics. The [https://hypertextbook.com/facts/2002/AliciaNoelleJones.shtml density of milk] depends on milkfat and solids-non-fat, which includes lactose. Fortified milk has increased solids-non-fat but the same percentage of milkfat, resulting in increased calories and an increased density. So the fortification of milk results in increased calories, possibly referred to as dark energy, and a contraction, as less space is needed for 1 kg of milk. However, this explanation does not match the expansion suggested in the comic.<br />
<br />
'''3. Isopropyl compression.''' While inflation is held constant, the gas contracts due to tightening interest rates.<br />
<br />
{{w|Isopropyl alcohol}} is commonly used for cleaning. Inflation and contraction could refer to changes in gas volume, but the reference to {{w|interest rate}}s puts them in the context of {{w|macroeconomics}}. Raising ("tightening") interest rates tends to reduce {{w|inflation}} and/or "contract" the economy. High interest rates are a feature of the third stage (recession) of the {{w|Juglar cycle}}. In economics (and other sciences) to better understand model parameter relations, some parameter may be held constant in theory. This could refer to the {{w|Fisher equation}}. Holding one parameter constant is also done in the Carnot cycle (for a physical parameter): not only in theory but also in practice! (In free market economies the inflation cannot be directly held constant).<br />
<br />
But inflation my also refer to ''dark energy'' mentioned at the ''isotonic expansion'' section above. {{w|Inflation (cosmology)|Inflation}} in cosmology is a theory of the exponential expansion of space in the early universe, an effect associated with the "accelerating universe" and for which findings the 2011 Nobel Prize in Physics was given. The NationalGeographic blog entry [https://blog.nationalgeographic.org/2011/10/12/nobel-prize-in-physics-2011-the-accelerating-universe/ Nobel Prize in Physics 2011 – The Accelerating Universe] explains that "...Today, most physicists, influenced by inflation, would ... call it dark energy."<br />
<br />
'''4. Decline and fall.''' The gas diminishes and goes into the West while remaining Galadriel, completing the cycle.<br />
<br />
{{w|Galadriel}} is a character in ''{{w|The Lord of the Rings}}''. She is one of the leading {{w|Elf (Middle-earth)|elves}}, a race that in the time of the book is said to be dwindling (in number and importance) in {{w|Middle Earth}} and migrating westward to {{w|Valinor}}. Galadriel is one of the last elves to leave, after successfully resisting temptation to take the One Ring and become an all-powerful queen who dominates Middle-earth, instead saying "I will diminish, and go into the West, and remain Galadriel." The title may be a reference to {{w|Edward Gibbon}}'s 18th century masterpiece ''{{w|The History of the Decline and Fall of the Roman Empire}}'', or to the novel ''{{w|Decline and Fall}}'' by {{w|Evelyn Waugh}} (which is itself a reference to Gibbon's book).<br />
<br />
The title text refers to {{w|Richard Wagner}} and {{w|J.R.R Tolkien}}. Wagner's ''{{w|Der Ring des Nibelungen|Ring Cycle}}'' consists of four operas. Tolkien wrote ''{{w|The Lord of the Rings}}'', which some have [[wikipedia:J. R. R. Tolkien's influences#Wagnerian_influences|suggested]] was inspired by Wagner's Ring. Their works are known as {{w|literary cycle}}s.<br />
<br />
==Transcript==<br />
:[A cartesian plot in the first quadrant with axes labeled "P" on the vertical axis and "V" on the horizontal axis, with a rhombus-shaped set of four points with arrows between them.]<br />
:[Caption above the graph:]<br />
:The four stages of the<br />
:'''Carnot Cycle'''<br />
<br />
:[The first line starts at the top-left point and goes right and slightly downwards to the next point. The label is:]<br />
:'''1. Isometric Expansion'''<br />
:When heated, the gas becomes larger due to increasing volume<br />
<br />
:[The next line starts at the last point and goes downwards and a little to the right.]<br />
:'''2. Isotonic Expansion'''<br />
:The gas expands further due to dark energy while percent milkfat remains constant<br />
<br />
:[The next line starts at this last point and goes to the left and slightly upwards.]<br />
:'''3. Isopropyl Compression'''<br />
:While inflation is held constant, the gas contracts due to tightening interest rates<br />
<br />
:[The last line goes upwards and slightly to the left, returning to the first point.]<br />
:'''4. Decline and Fall'''<br />
:The gas diminishes and goes into the west while remaining Galadriel, completing the cycle<br />
<br />
{{comic discussion}}<br />
<br />
[[Category:Line graphs]]<br />
[[Category:Physics]]<br />
[[Category:LOTR]]</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=2110:_Error_Bars&diff=1694882110: Error Bars2019-02-12T04:06:38Z<p>CRGreathouse: category</p>
<hr />
<div>{{comic<br />
| number = 2110<br />
| date = February 11, 2019<br />
| title = Error Bars<br />
| image = error_bars.png<br />
| titletext = ...an effect size of 1.68 (95% CI: 1.56 (95% CI: 1.52 (95% CI: 1.504 (95% CI: 1.494 (95% CI: 1.488 (95% CI: 1.485 (95% CI: 1.482 (95% CI: 1.481 (95% CI: 1.4799 (95% CI: 1.4791 (95% CI: 1.4784...<br />
}}<br />
<br />
==Explanation==<br />
{{incomplete|Created by an INFINITE SERIES OF ERROR BARS. Please mention here why this explanation isn't complete. Do NOT delete this tag too soon.}}<br />
<br />
On statistical charts and graphs, it is common to include {{w|error bars}} showing the probable variation of the actual value from the value shown (or the possible error of the value shown). Since there is always uncertainty in any given measurement, the error bars help an observer evaluate how accurate the data shown is, or the implications if the true value is within the likely error, rather than the exact value shown. There are statistical methods for calculating error bars (they can show a {{w|standard deviation}}, a {{w|standard error}}, or a {{w|confidence interval}}) but the fact that there are multiple ways of calculating them - plus general unfamiliarity with statistical methods - means that people often misinterpret or misunderstand them.<br />
<br />
As charts may be of data that has been mathematically processed, the known error from the recording process must also be mathematically processed in order to determine the likely error in the final result. Different transformations of the data result in different transformations of the error, and the correctness of the transformations used can sometimes depend on the subtle differences in the distribution of the source data. At a loss as to how to correctly propagate his error, Randall instead puts error bars on the ends of his error bars, to reflect the fact that the error has been combined with other error, or the fact that the error bars also have uncertainty or errors themselves. However, since his second error bar calculations are also suspect, he puts a third set of error bars on them. This repeats {{w|ad infinitum}} creating a fractal similar to a [https://en.wikipedia.org/wiki/Cantor_set Cantor set]<br />
<br />
In the title text, he states that the {{w|effect size}} is 1.68 and follows it with the 95% confidence interval (a range of possible values which has a 95% estimated probability of containing the true value), which would normally be represented by something like "1.68 (95% CI 1.56 - 1.80)." Since he is stating that those bounds are uncertain, he starts with "1.68 (95% CI 1.56" but then puts the 95% CI for that lower bound of the interval, "95% CI 1.52," followed by the lower bound for that value, "95% CI 1.504," and so on. He goes 11 layers deep before resorting to an ellipsis.<br />
<br />
==Transcript==<br />
{{incomplete transcript|Do NOT delete this tag too soon.}}<br />
<br />
:[A line graph with eight marks on the Y-axis and five marks on the X-axis. The graph has four points represented by dots and connected by three lines between them. Each dot has error bars coming out of the top and bottom of it. The horizontal line delineating the end of each error bar has another set of smaller error bars attached to it. These second error bars in turn have a still smaller third set of error bars attached to the end of them. There is a final fourth set of very small error bars attached to the third set.]<br />
<br />
:[Caption below the panels:]<br />
:I don't know how to propagate error correctly, so I just put error bars on all my error bars.<br />
<br />
<br />
{{comic discussion}}<br />
[[Category:Statistics]]</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=2097:_Thor_Tools&diff=1680342097: Thor Tools2019-01-12T05:24:08Z<p>CRGreathouse: /* Explanation */ plausible alternate explanation</p>
<hr />
<div>{{comic<br />
| number = 2097<br />
| date = January 11, 2019<br />
| title = Thor Tools<br />
| image = thor_tools.png<br />
| titletext = CORRECTION: After careful evaluation, we have determined that the axis label on this chart was printed backward.<br />
}}<br />
<br />
==Explanation==<br />
{{incomplete|Add a list of the tools in the comic. Do NOT delete this tag too soon.}}<br />
<br />
{{w|Thor}} is a god of lightning and thunder in Norse mythology. His signature weapon is a magic hammer called {{w|Mjölnir}}. He's likely best known for his role in {{w|Thor (Marvel Comics)|Marvel comics and films}}, which his appearance here seems to be referencing.<br />
<br />
Although the hammer was historically a weapon, this comic interprets it as it would more commonly be interpeted today -- as a tool. The comic is listing various hand tools in order of utility and viability as Thor's weapon, besides his actual, enchanted hammer. Hammers are heavy, blunt, and can do large amounts of damage to an opponent, whereas a hand plane is sharp, but only in one place, and will only inflict surface wounds. <br />
<br />
Some of these tools require power, which would generally require Thor to stay near an outlet or keep a battery charging, such as the circular saw, or Dremel. However, being the god of lightning may allow him to circumvent this. Thor would also need compressed air for the nail gun or jackhammer, only allowing Thor so many shots before reloading the air tank at an outlet, or via a concentrated wind storm.<br />
<br />
The nail gun and staple gun would also require nails or staples respectively to function as a weapon. Although Mjölnir is believed to return to Thor if thrown, it's not clear how similar system could work with nails and staples.<br />
<br />
In the title text, Munroe says the the order should be reversed. Considering that the title of the comic is "Thor Tools" ("tools", instead of "weapons"), the argument seems to be that a hammer is less useful than the rest, by seeing them as tools and not as weapons.<br />
<br />
A few other interpretations of this could be:<br />
* Randall proposes that Thor armed with a plane or digital calipers would be much more fearsome than with a hammer.<br />
* The "value" of the more strange-seeming items would be much higher than his tradition hammer, perhaps more gory or more humorous.<br />
* Thor tends to cause collateral damage, and would cause less with a plane or calipers.<br />
* "Best" and "worst" are to be interpreted for Thor's enemies rather than Thor himself.<br />
<br />
==Transcript==<br />
{{incomplete transcript|Do NOT delete this tag too soon.}}<br />
[A timeline labeled "Hand tools Thor could have ended up with" with "Best" on the left and "Worst" on the right.] <br />
<br />
[Points on the line are labeled "Hammer", "Axe", "Claw hammer", "Circular saw", "Jackhammer", "Shovel", "Socket wrench", "Bolt cutters", "Hacksaw", "Nail gun", "Staple gun", "Coping saw", "Screwdriver (flat)", "Ball-peen hammer", "Screwdriver (phillips)", "Awl", "Digital Caliper", "Dremel", "Plane"]<br />
<br />
[A figure wearing a winged helmet is seen preparing to use: a Circular saw, a Socket wrench, a Nail or Staple gun, and a Dremel.]<br />
<br />
{{comic discussion}}</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=2063:_Carnot_Cycle&diff=1646982063: Carnot Cycle2018-10-24T18:55:46Z<p>CRGreathouse: /* Explanation */ point out reference to The Decline and Fall of the Roman Empire</p>
<hr />
<div>{{comic<br />
| number = 2063<br />
| date = October 24, 2018<br />
| title = Carnot Cycle<br />
| image = carnot_cycle.png<br />
| titletext = The Carnot cycle is more properly known by its full title, the "Carnot-Tolkien-Wagner Ring Cycle."<br />
}}<br />
<br />
==Explanation==<br />
{{incomplete|Please edit the explanation below and only mention here why it isn't complete. Do NOT delete this tag too soon.}}<br />
<br />
This comic shows a {{w|Pressure–volume diagram}} which is used in this case for a {{w|Carnot cycle}}, a theoretical thermodynamic cycle and covers most thermodynamics classes which looks very much like the figure drawn. However in this case, [[Randall]] has replaced the labels of the 4 stages of the real Carnot cycle with new ones.<br />
<br />
Each step is explained below:<br />
<br />
'''1. Isometric expansion.''' When heated, the gas becomes larger due to increasing volume<br />
<br />
The comic text uses a circular argument. Additionally, "isometric" (equal dimensions) could mean that the gas does ''not'' change in volume, in contrast to the change in volume here.<br />
<br />
'''2. Isotonic expansion.''' The gas expands further due to dark energy while percent milkfat remains constant.<br />
<br />
Isotonic is commonly associated with sports drink (and not thermodynamics). Dark energy is hypothesized to be a cause for the expansion of the universe.<br />
<br />
'''3. Isopropyl compression.''' While inflation is held constant, the gas contracts due to tightening interest rates.<br />
<br />
Isopropyl alcohol is commonly used for cleaning. Inflation and contraction could refer to changes in gas volume, but the reference to interest rates puts them in the context of {{w|macroeconomics}}. Raising ("tightening") interest rates tends to reduce {{w|inflation}} and/or "contract" the economy. In economics (and other sciences) to better understand model parameter relations, some parameter may be held constant in theory. This could refer to the {{w|Fisher equation}} Holding one parameter constant is also done in the Carnot cycle (for a physical parameter): not only in theory but also in practice! (In free market economies the inflation cannot be directly held constant).<br />
<br />
'''4. Decline and fall.''' The gas diminishes and goes into the West while remaining Galadriel, completing the cycle.<br />
<br />
{{w|Galadriel}} is a character in {{w|The Lord of the Rings}}. She is one of the leading {{w|Elf (Middle-earth)|elves}}, a race that in the time of the book is said to be dwindling (in number and importance) in {{w|Middle Earth}} and migrating westward to {{w|Valinor}}. Galadriel is one of the last elves to leave, after successfully resisting temptation to take the One Ring and become an all-powerful queen who dominates Middle-earth, instead saying "I will diminish, and go into the West, and remain Galadriel." The title is a reference to {{w|Edward Gibbon}}'s 18th century masterpiece ''{{w|The History of the Decline and Fall of the Roman Empire}}''.<br />
<br />
<br />
Title text: Richard Wagner's Ring cycle consists of four operas. J.R.R. Tolkien wrote The Lord of the Rings, which some have [[wikipedia:J. R. R. Tolkien's influences#Wagnerian_influences|suggested]] was inspired by Wagner's Ring. Their works are known as {{w|Literary cycle}}s.<br />
<br />
==Transcript==<br />
{{incomplete transcript|Do NOT delete this tag too soon.}}<br />
:[A cartesian plot in the first quadrant with axes labeled "P" on the y-axis and "V" on the x-axis, with a rhombus-shaped set of four points with arrows between them.]<br />
:[Caption above the graph:]<br />
:The four stages of the '''Carnot Cycle'''<br />
<br />
:[The first line starts at the point at top left and goes right and slightly downwards to the next point. The label is:]<br />
:'''1. Isometric expansion'''<br />
:When heated, the gas becomes lager due to increasing volume<br />
<br />
:[The next line starts at the last point and goes downwards, also still a little bit to the right.]<br />
:'''2. Isotonic expansion'''<br />
:The gas expands further due to dark energy while percent milkfat remains constant<br />
<br />
:[The next line starts at this last point and to the left and slightly upwards.]<br />
:'''3. Isoprophyl compression'''<br />
:While inflation is held constant, the gas contracts due to tightening interest rates<br />
<br />
:[The last line goes upwards and slightly to the left, reaching the first point.]<br />
:'''4. Decline and fall'''<br />
:The gas diminishes and goes into the west while remaining Galadriel, completing the cycle<br />
<br />
{{comic discussion}}<br />
<br />
[[Category:Line graphs]]<br />
[[Category:Physics]]<br />
[[Category:LOTR]]</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=1023:_Late-Night_PBS&diff=1642961023: Late-Night PBS2018-10-17T14:26:07Z<p>CRGreathouse: wording</p>
<hr />
<div>{{comic<br />
| number = 1023<br />
| date = February 29, 2012<br />
| title = Late-Night PBS<br />
| image = late night pbs.png<br />
| titletext = Then it switched to these old black-and-white tapes of Bob Ross slumped against the wall of an empty room, painting the least happy trees you've ever seen. Either PBS needs to beef up studio security or I need to stop using Ambien to sleep.<br />
}}<br />
<br />
==Explanation==<br />
This comic examines the way the world seems different for adults today compared with how we remember it as a child, due to complex subtext or naïvety, to a humorous extreme, and with a specific reference to television programs for children.<br />
<br />
{{w|PBS}} is a US television station known for high brow and educational programming, and shows a high proportion of {{w|BBC}} programming. The show "''{{w|Where in the World Is Carmen Sandiego? (game show)|Where in the World Is Carmen Sandiego}}''" was a light-hearted educational game show that ran from 1991 to 1995. In the show players followed geography-based clues to find out where a master criminal, Carmen Sandiego, was going, and catch her. After catching (or failing to catch) Carmen Sandiego, a character called The Chief would congratulate or encourage the players. Rockapella was an {{w|a cappella}} band featured on the show that gave clues, punctuated the show with humor, and closed the show. <br />
<br />
[[Megan]] recounts her surprise as to the nature of programming on late night PBS to [[Cueball]]. She claims to have fallen asleep after watching ''{{w|Downton Abbey}}'' and woken up to see that ''Where in the World Is Carmen Sandiego'' is still making new episodes, but is significantly darker than she remembers it. The host has aged poorly (the show would have been off the air for 20 years) and developed a drinking problem; the locations the child contestants visit are traumatizing; and the children are clearly freaked out. In the end they find Carmen Sandiego hiding behind a Dutch bookcase, an allusion to "{{w|The Diary of a Young Girl|The Diary of Anne Frank}}", thus implying that instead of aiding legitimate law enforcement in finding thieves they have been aiding the Nazis in their search for Jews (and others) to murder. The Chief admonishes the children for their actions and Rockapella glares at the children disapprovingly until the children break down in tears. <br />
<br />
After Megan concludes her story, Cueball remarks that he did not remember the show being that dark. In response Megan replies that as kids, they may not have been able to understand the darker subtext of the show. It is true that some programs intended for children often have subtle themes for adults who may be watching the show with their children that the children do not usually remember or pick up on. The joke is that although young viewers may not be able to pick up on everything, they would certainly have noticed if the show was as dark as Megan described.<br />
<br />
The title text describes the next program, an episode of {{w|The Joy of Painting}}, in which a depressingly weary painter paints unhappy trees. This contrasts with the usual mood of the show where {{w|Bob Ross}} was upbeat and the components of his paintings were described as "happy little" objects. Megan then postulates that either people are breaking into the television station to produce horrible programming, or she is experiencing hallucinations due to her sleep aid {{w|Ambien}}. This gives hallucination as an alternate explanation for the main comic.<br />
<br />
===Locations visited===<br />
{{w|Mogadishu}} is a battle-torn city in {{w|Somalia}}, where the "{{w|Battle of Mogadishu (1993)|Battle of Mogadishu}}" took place in 1993, which would coincide with the air dates of "Where in the World Is Carmen Sandiego".<br />
<br />
The {{w|Killing Fields}} are a number of sites in {{w|Cambodia}} where large numbers of people were killed and buried by the {{w|Khmer Rouge}} regime, during its rule of the country from 1975 to 1979, following the end of the {{w|Cambodian Civil War}} (1970-1975).<br />
<br />
The reference to "A Bookshelf in a Dutch Apartment" is a reference to {{w|Anne Frank}}, a Jewish girl who hid from the {{w|Nazi}}s with her family in a secret annex hidden behind a bookshelf in an apartment in {{w|Amsterdam}}. Her diary recounting her experiences was later published as the {{w|The Diary of a Young Girl|Diary of Anne Frank}}.<br />
<br />
===Carmen Sandiego===<br />
"{{w|Where in the World Is Carmen Sandiego}}" was originally an educational {{w|Video game}} released in 1985. {{w|Carmen Sandiego}} was a mysterious character that the player tracked around the globe, attempting to find clues as to where she was heading to next. The game helped players learn geography and facts about the world while having fun. The video game inspired the TV show {{w|Where in the World Is Carmen Sandiego? (game show)|Where in the World Is Carmen Sandiego?}}.<br />
<br />
The show was split into three rounds. In the first round, there were three child contestants, called “gumshoes” on the show, who scored points for every question they answered correctly. The top two scoring gumshoes moved onto the next round, where they had to play a game based on the card game {{w|Concentration (game)|Concentration}}, in which they had to find the thief, warrant, and loot in the correct order. Whichever gumshoe did so captured the thief, saved the loot, and moved onto the next round, where they had a chance to catch Carmen Sandiego herself. Success was not always guaranteed in this round, as contestants had to plant flags correct on seven different countries in a continent within a very short time. If successful, they captured Carmen and won the grand prize (a trip to a place of their choosing in the continental US). If not, Carmen would escape and the contestant would win a lesser prize (such as a computer).<br />
<br />
The role of The Chief was played by {{w|Lynne Thigpen}}. She explained the mission to the contestants, and gave some clues to the thief's last whereabouts. When the mission was over The Chief would appear and congratulate them if successful or console them if Carmen got away.<br />
<br />
The host of the TV show was an actor named {{w|Greg Lee (actor)|Greg Lee}}. His role was to ask the contestants questions, provide clues, and tell them which flags to plant on the map in the final round, as well as engage with The Chief and Rockapella to keep the show moving.<br />
<br />
{{w|Rockapella}} was an {{w|A cappella|a cappella}} group (a group that sings without any instruments), which sang the theme song to "Where in The World Is Carmen Sandiego." Rockapella also acted as a "house band", singing songs while the contestants transitioned between events, providing clues, and playing pranks on the host along with other gags. At the end of each show, the host and the episode's winning contestant would shout "Do it, Rockapella!" at which point the band would sing the show's theme song.<br />
<br />
===Continuity Issues===<br />
The locations the contestants visit in the episode depicted in this comic seem to require traveling backwards in time (1993 for the Battle of Mogadishu, 1975-1979 for the Cambodian killing fields, and 1944 for the arrest of Anne Frank). Episodes of Where in the World Is Carmen Sandiego did not deal with this, but its successor, {{w|Where in Time Is Carmen Sandiego? (game show)|Where in Time Is Carmen Sandiego?}}, did.<br />
<br />
==Transcript==<br />
:[Megan with disheveled hair is rubbing sleep out of her eyes and talking to Cueball.]<br />
:Megan: Have you ever watched PBS late at night?<br />
:Megan: I fell asleep after ''Downton'' and woke up at like 3 AM.<br />
<br />
:[The next panel is split in two. The upper portion, which is not in a frame, continues Megan's dialogue, while the lower part, in a frame, shows a drunk game-show host (indicated with two small bobbles and a third exploding next to his head). He has stubble and only little hair on his head. He is holding a bottle in one hand and the other hand is up over a TV monitor showing a black field filled with crosses, presumably graves, going out to the far off horizon. In front of him are three kids, who are contestants in the game. They stand behind three lecterns to the left. The first kid is a boy with thin black hair, who has turned away from the monitor. The middle kid is a girl with blonde hair in a ponytail who looks at the host, and the last kid looks like Cueball and he looks down at his lectern.]<br />
:Megan (off-panel): ''Where in the World Is Carmen Sandiego'' was back on, except the host hadn't aged well and he'd clearly been drinking.<br />
:Megan (off-panel): Every question took them to some horrible place like Mogadishu or the Cambodian killing fields.<br />
<br />
:[In a room with tiles on the floor, a bookshelf full of books has been moved away from the wall revealing that is was a door to be opened with a hidden room behind it. Megan continues to speak, her text is above the shelf but inside the frame this time.]<br />
:Megan (off-panel): The kids were freaked out, but they kept playing. Eventually they were told they'd found Carmen Sandiego hiding behind a bookshelf in a Dutch apartment.<br />
<br />
:[Megan has stopped rubbing her eyes but still talks to Cueball.]<br />
:Megan: The Chief appeared and asked "Are you proud of what you've become?"<br />
:Megan: Then Rockapella walked out and just glared at the kids until they started crying.<br />
:Cueball: I, uh, don't remember the old show being that dark.<br />
:Megan: Maybe we were too young to pick up on it.<br />
<br />
==Trivia==<br />
*This is the second comic posted on a Leap Day ({{w|February 29}}), it was a Wednesday in 2012.<br />
**The previous leap day was the first after xkcd began, and that day fell on a Friday in 2008, and the first leap day comic [[390: Nightmares]] was released then.<br />
**The leap day after this comic also fell on a Friday in 2016 and [[1649: Pipelines]] was released then.<br />
**If the current M-W-F schedule continues, the next such comic will not happen before 2036 when the leap day again falls on a Friday.<br />
**Interesting to note that the first three leap years after xkcd began (in just over 10 years) all fell on a release day, then followed by a break of 20 years. And three of these first four leap days all fell on a Friday.<br />
<br />
{{comic discussion}}<br />
<br />
[[Category:Comics featuring Cueball]]<br />
[[Category:Comics featuring Megan]]<br />
[[Category:Comics featuring real people]] <!-- Bob Ross for certain and maybe the TV host --><br />
[[Category:Dreams]] <!-- Apart from the title text note, it is clearly not real what Megan has experiences at 3 AM.--></div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=216:_Romantic_Drama_Equation&diff=163898216: Romantic Drama Equation2018-10-09T16:46:40Z<p>CRGreathouse: /* Assumptions */ reword/clarify</p>
<hr />
<div>{{comic<br />
| number = 216<br />
| date = January 29, 2007<br />
| title = Romantic Drama Equation<br />
| image = romantic drama equation.png<br />
| titletext = Real-life prospective-pairing curves over things like age can get depressing.<br />
}}<br />
<br />
==Explanation==<br />
The equations in the comic and the graph show how many different love pairs can be made if you know the number of females and males in a group. The text explains that it was inspired by TV Romantic Drama (in this case, the gay drama {{w|Queer as Folk (U.S. TV series)|Queer as Folk}}), but of course the formula is valid for any group of people. There are two graphs and equations - gay option is the case when we are looking for pairs with same gender, straight option is for heterosexual pairs. The interesting/funny part about the results is that in most cases there are more possibilities when we consider the homosexual option. Also it is interesting to observe what is kind of obvious - in the heterosexual case, the "best" case is if both genders are present equally, and the possibilities drop very fast if there is substantial difference between genders.<br />
<br />
The graph makes a note that it only holds true for large casts. Case in point, with a cast of only four people: a two-to-two female-to-male ratio will have four straight pairings to two gay pairings, while a three-to-one female-to-male ratio will have three straight pairings and three gay pairings.<br />
<br />
The title-text mentions that Randall made a chart of his own prospective dating pool as he gets older and was depressed by the results. A dating pool show how many possible partners you can choose from. As you get older, fewer of these will be single. But as he later shows in [[314: Dating Pools]], the age is not the problem... He is!<br />
<br />
===Formulas===<br />
The formulas may be derived as follows:<br />
<br />
Each straight couple needs to include one of the x males and one of the (n-x) females so there are x(n-x) possible ways of combining one of each. E.g., if there are n=5 people, of whom x=2 are male, then there will be 3 possible pairings involving the first male, and three possible pairings involving the second, yielding 2(5-2)=6 possible pairings.<br />
<br />
Each gay couple needs to include either two males or two females. To choose two males, we can start with any of the x males and choose any of the (x-1) remaining males. However, that counts each possible pairing twice. E.g., Adam&Steve got counted when we chose Adam first and Steve second, and again when we chose Steve first and Adam second. To avoid double counting the possible couples, we therefore need to divide that total by 2. So there are x(x-1)/2 possible male-male pairings. Similar reasoning involving the (n-x) females tells us that there are (n-x)(n-x-1)/2 possible female-female pairings. Multiplying these out and combining the male and lesbian couples together, we get the total number of possible gay couples as [x^2 - x + n^2 - nx - n - xn + x^2 + x]/2. That simplifies to [n^2 - n + 2 x^2 - 2 xn]/2. The left two terms can be combined together as n(n-1) and the right two terms can be combined together as -2x(n-x) or 2x(x-n) [which is negative, because x-n<0]. Since the sum of these terms was divided by 2, we get that the total number of possible same-sex pairs is n(n-1)/2 - x(n-x), or n(n-1)/2 + x(x-n), which is what the cartoon says.<br />
<br />
===Equations and links to wolfram-alpha===<br />
<br />
* Formula for Gay pairing: [https://www.wolframalpha.com/input/?i=n*%28n-1%29%2F2%2Bx*%28x-n%29 n*(n-1)/2+x*(x-n)]<br />
<br />
* Formula for Straight pairing: [https://www.wolframalpha.com/input/?i=x*%28n-x%29 x*(n-x)]<br />
<br />
As a worked example, for Firefly, of the 9 principal cast, 5 are men and 4 are women. If all were gay, there would be 16 possible hook-ups; if all were straight, there would be 20.<br />
<br />
===Assumptions===<br />
<br />
The chart and the calculations assume that:<br />
<br />
#No one is bisexual, asexual, polyamorous, celibate, or of some other sexuality. <br />
#The ENTIRE cast, male AND female, will ALL be of the same sexuality (all homosexual OR all heterosexual).<br />
#All genders are constant. (If sex-change operations are allowed, then the number of possible pairings is n(n-1)/2, because any two individuals can undergo surgery to become a possible pair.)<br />
#Everyone is available, and gender is the only criterion for determining if a hook-up is possible.<br />
<br />
==Transcript==<br />
:TV Romantic Drama Equation (Derived during a series of 'Queer as Folk' episodes)<br />
:[A table shows equations for possible romantic pairings in a TV show. The equation under "gay" is n(n-1) 2+x(x-n); the equation under "straight" is x(n-x).]<br />
:x: Number of male (or female) cast members.<br />
:n: total number of cast members.<br />
<br />
:[A graph plots pairings (for large casts) against cast makeup. Each of the above equations forms a curve. "Gay cast" starts high for an all male cast, dips down at 50/50 cast makeup, and then rises again for all female. "Straight cast" starts at zero for an all male cast, peaks at 50/50 cast makeup, and then drops to zero again for an all female cast. The two curves intersect at two points close to the middle.]<br />
<br />
{{comic discussion}}<br />
[[Category:Line graphs]]<br />
[[Category:Homosexuality]]<br />
[[Category:Math]]<br />
[[Category:Romance]]</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=Talk:2050:_6/6_Time&diff=163344Talk:2050: 6/6 Time2018-09-26T16:57:21Z<p>CRGreathouse: common descent</p>
<hr />
<div><!--Please sign your posts with ~~~~ and don't delete this text. New comments should be added at the bottom.--><br />
This is actually how time worked in ancient Greece, minus the 6 o'clock part. Sunrise was at 12, sunset at 12 and the length of each hour varied depending on the part of the year [[Special:Contributions/172.68.189.163|172.68.189.163]] 16:15, 24 September 2018 (UTC)<br />
<br />
Not just Greece but most of medeaval Europe. The concept of a fixed length hour only arises with clockwork. that Noon, the ninth hour, now occurs at the sixth hour - that we call 12 - is mainly due to post black death labour shortages. {{unsigned|Arachrah}}<br />
<br />
: Also ancient Rome. I ''think'' Romans borrowed this system from Greeks and it later spread along with the Roman Empire's influence. [[Special:Contributions/172.68.10.22|172.68.10.22]] 16:52, 24 September 2018 (UTC)<br />
<br />
:: To be fair, the Romans "borrowed" (stole) a lot of other things from the Greeks, not the least of which was their pantheon. [[Special:Contributions/108.162.216.172|108.162.216.172]] 18:21, 24 September 2018 (UTC)<br />
<br />
::: Or rather, both descended from a common pantheon. (A few gods were re-borrowed wholesale, like Apollo, and I think a few were misidentified, but for the most part this is how it worked.) - [[User:CRGreathouse|CRGreathouse]] ([[User talk:CRGreathouse|talk]]) 16:57, 26 September 2018 (UTC)<br />
<br />
: Before clockwork (as mentioned above) was created, variable hours/minutes/seconds were necessary (at least during daylight hours) as the sundial obviously <sup>({{w|citation needed}})</sup> is just based off of the sun's angle in the sky.[[User:Rajakiit|Raj-a-Kiit]] ([[User talk:Rajakiit|talk]]) 17:42, 24 September 2018 (UTC)<br />
<br />
:Wait ... labor shortage? How would moving noon help with labor shortage? -- [[User:Hkmaly|Hkmaly]] ([[User talk:Hkmaly|talk]]) 03:41, 25 September 2018 (UTC)<br />
<br />
Some facts: {{w|September equinox}} was at 01:54 UTC on September 23 when in the entire US it still was September 22 as can be seen here: [http://aa.usno.navy.mil/seasons?year=2018&tz=-5&dst=1 U.S. Naval Observatory Astronomical Applications Department (Apsides and Seasons 2018)]. This comic was released two days later. --[[User:Dgbrt|Dgbrt]] ([[User talk:Dgbrt|talk]]) 16:32, 24 September 2018 (UTC)<br />
<br />
Could the timing of this comic be related to the [https://www.bbc.com/news/world-europe-45366390 EU voting to end DST within its borders?] [[Special:Contributions/108.162.241.100|108.162.241.100]] 16:51, 24 September 2018 (UTC)<br />
:This isn't about daylight saving time, which just moves clocks forwards and backwards by one hour in most cases. Cueball refers to an equinox when day and night are both 12 hours. --[[User:Dgbrt|Dgbrt]] ([[User talk:Dgbrt|talk]]) 17:05, 24 September 2018 (UTC)<br />
:: This comic is about "unfixably messy and complicated" time standards (of which DST is one) at least as much as equinoxes (which aren't quite what you say they are; I won't get a 12-hour interval between sunrise and sunset at my latitude for another few days yet). [[Special:Contributions/108.162.241.220|108.162.241.220]] 19:51, 24 September 2018 (UTC)<br />
<br />
<br />
The hours/minutes/seconds get really short/long in the polar regions. {{unsigned ip|162.158.74.243}}<br />
<br />
The caption can also be referring to the alteration of time zones for political reasons, such as China having only one now rather than the five it used to use, or the Republic of Kiribati pushing the International Date Line east of its entire territory.[[Special:Contributions/172.69.22.140|172.69.22.140]] 17:50, 24 September 2018 (UTC)<br />
<br />
Here is a YouTube video explaining the Japanese system (and how they created mechanical clocks to support it) - [https://youtu.be/3iclecbIgN0?t=135 Begin Japanology - Clocks and Watches]. -- [[User:Dhericean|Dhericean]] ([[User talk:Dhericean|talk]]) 18:15, 24 September 2018 (UTC) <br />
<br />
Swatch time: Still more sensible than any other division of the day I've ever heard. <br />
<br />
Seriously though, isn't it about time we all switched to metric? 10 segments in a day, not 24. 100 units in a segment. Straightforward, easy to figure pay rates, & pretty simple to convert to & from. <br />
<br />
Increments of 24 & 60 have no relevance to anything these days. The only reason to continue using a 24hr day is because "that's how it's been done for ages" & that's no excuse for anything. <br />
<br />
[[User:ProphetZarquon|ProphetZarquon]] ([[User talk:ProphetZarquon|talk]]) 18:23, 24 September 2018 (UTC)<br />
:I wouldn't mind redefining the division of a day. My problem would be with redefining the second, which would necessarily be a consequence of switching to metric time, and thus also the three base and nineteen derived SI units that depend on the current definition of s.<br />
:If you can switch us to metric time without redefining the length of a second, nor having an excessive number of leap seconds, I'm all for that. [[Special:Contributions/108.162.241.118|108.162.241.118]] 21:19, 24 September 2018 (UTC)<br />
:The length of a day isn't even constant. If you had even divisions, the length of those divisions would be changing constantly. "'It's been done that way for ages' is no excuse" is irrelevant reasoning. A consistent system of time is needed (because good luck updating every computer constantly), and any one consistent method is as good as another because they can all be converted to each other (much like feet and meters can be). The one that's been in use the longest tends to have the most support. It's similar to how people don't have much of a reason to change keyboard layouts even though QWERTY or AZERTY or whatever regional preference may not actually be the most efficient. [[Special:Contributions/172.69.210.34|172.69.210.34]] 23:52, 24 September 2018 (UTC)<br />
<br />
:{{w|Decimal time|You are not first with this idea}}. -- [[User:Hkmaly|Hkmaly]] ([[User talk:Hkmaly|talk]]) 03:51, 25 September 2018 (UTC)<br />
<br />
Here's a [https://www.youtube.com/watch?v=-5wpm-gesOY Youtube video] that talks about just how bad time systems can get. [[Special:Contributions/172.69.210.34|172.69.210.34]] 23:52, 24 September 2018 (UTC)<br />
<br />
Jewish practice today still uses the system of relative hours (see Wikipedia quotes, below). The earliest and latest times where various prayers must be said, and a variety of other time-based obligations are based on specific numbers of relative hours since dawn. Most of the time, this isn't a problem, but Jews living in extreme latitudes can find this very difficult. [[User:Shamino|Shamino]] ([[User talk:Shamino|talk]]) 15:59, 25 September 2018 (UTC)<br />
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Weird numbers and the metric system? Before you try to get rid of 24 and 60 from time, why not get rid of the weird number that runs all through the metric system: 10. It really doesn't have any relevance except to a fluke of biology. And don't forget, they started with one ten millionth of the distance from the north pole to the equator, through Paris. --[[User:Divad27182|Divad27182]] ([[User talk:Divad27182|talk]]) 20:17, 25 September 2018 (UTC)<br />
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Some ICs use 65536 "seconds" per day internally, for example, 6AM is 0x4000 and 6PM is 0xC000.<br />
<br />
'''From Wikipedia'''<br />
<br />
In Judaism, an hour is defined as 1/12 of the time from sunrise to sunset, so, during the winter, an hour can be much less than 60 minutes, and during the summer, it can be much more than 60 minutes. This proportional hour is known as a sha'ah z'manit (lit. "temporal hour" [[https://en.wiktionary.org/wiki/temporal_hour]]). A Jewish hour is divided into 1080 halakim (singular: helek) or parts. A part is 3⅓ seconds or 1/18 minute. The ultimate ancestor of the helek was a small Babylonian time period called a barleycorn, itself equal to 1/72 of a Babylonian time degree (1° of celestial rotation).[6] These measures are not generally used for everyday purposes. {{unsigned|Kg}}<br />
<br />
[https://en.wikipedia.org/wiki/Hebrew_calendar#Day_and_hours Wikipedia: Hebrew Calendar: Days and hours]<br />
<br />
: Also:<br />
: In old times, the hour was detected by observation of the position of the sun, or when the first three stars appeared in the night sky. During the first six hours of the day, the sun is seen in the eastern sky. At the sixth hour, the sun is always at its zenith in the sky, meaning, it is either directly overhead, or parallel (depending on the hemisphere). Those persons living in the Northern Hemisphere, the sun at noon time will appear overhead slightly towards the south, whereas for those living in the Southern Hemisphere, the sun at noon time will appear overhead slightly towards the north. From the 6th and a half hour to the 12th hour, the sun inclines towards the west, until it sets. The conclusion of a day at the end of twilight may slightly vary in minutes from place to place, depending on the elevation and the terrain. Typically, nightfall ushers in more quickly in the low-lying valleys, than it does on a high mountaintop.<br />
: The conventional Jewish way of calibrating the time of day is to reckon the "first hour" of the day with the rise of dawn (Hebrew: עמוד השחר), that is to say, approximately 72 minutes before sunrise, and the end of the day commencing shortly after sunset when the first three medium-size stars have appeared in the night sky. From the moment of sunset when the sun is no longer visible until the appearance of the first three medium-size stars is a unit of time called evening twilight (Hebrew: בין השמשות). In the Talmud, twilight is estimated at being the time that it takes a person to walk three quarters of a biblical mile (i.e. 1,500 cubits, insofar that a biblical mile is equal to 2,000 cubits). According to Maran's Shulhan Arukh, a man traverses a biblical mile in 18 minutes, meaning, one is able to walk three quarters of a mile in 13½ minutes. According to Maimonides, a man walks a biblical mile in 24 minutes, meaning, three quarters of a mile is done in 18 minutes. In Jewish law, the short period of dusk or twilight (from the moment the sun has disappeared over the horizon until the appearance of the first three stars) is a space of time whose designation is doubtful, partly considered day and partly considered night. When the first medium-size star appears in the night sky, it is still considered day; when the second star appears, it is an ambiguous case. When the third star appears, it is the beginning of the first hour of the night. Between the break of dawn and the first three medium-size stars that appear in the night sky there are always 12 hours.<br />
: In the Modern Age of astral science and of precise astronomical calculations, it is now possible to determine the length of the ever-changing hour by simple mathematics. To determine the length of each relative hour, one needs but simply know two variables: (a) the precise time of sunrise, and (b) the precise time of sunset. Since the actual day begins approximately 72 minutes before sunrise, and ends 13½ minutes after the sun has already set and can no longer be seen over the horizon (according to Maran), or 18 minutes (according to Maimonides), by collecting the total number of minutes in any given day and dividing the total number of minutes by 12, the dividend that one is left with is the number of minutes to each hour. In summer months, when the days are long, the length of each hour during daytime can be as much as 77 minutes or more, whereas the length of each hour during nighttime can be less than 42 minutes.<br />
: [https://en.wikipedia.org/wiki/Relative_hour_(Jewish_law) Wikipedia: Relative hour (Jewish law)]<br />
:{{unsigned|Shamino}}<br />
<br />
'''Compound time'''<br />
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It struck me that 6/6 would be a musical time signature with six beats each of wich were a sixth note - so someing like dotted quaver. {{unsigned|Arachrah}}<br />
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'''Similarity in Temperature'''<br />
<br />
The arbitrary selection of sunrise and sunset seems to take stab at how celsius is defined - at freezing and boiling points of water (at least before 1954), which can also shift with elevation. But of course fahrenheit is even worse. [[User:Colonelheero|Colonelheero]] ([[User talk:Colonelheero|talk]]) 19:12, 25 September 2018 (UTC)<br />
<br />
'''Corrections required'''<br />
<br />
The second paragraph is just wrong in stating that sunrise and sunset are determined by longitude. The time of sunrise and sunset vary both by longitude and latitude. Picture the nearly sinewave shape of the terminator line on a Mercator map. Only when the sun crosses the ecliptic does the terminator become a "square wave" and the sunrise and sunset are the same regardless of latitude.<br />
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Also the statement that at 12am the sun isn't always at the zenith is a strong understatement; 12am is midnight and the sun would be closer to the nadir point than to the zenith point. The correction would be to refer to 12pm. [[Special:Contributions/172.69.70.179|172.69.70.179]] 01:48, 26 September 2018 (UTC)</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=Talk:2048:_Curve-Fitting&diff=163016Talk:2048: Curve-Fitting2018-09-21T14:20:23Z<p>CRGreathouse: WAIT NO, NO, DON'T EXTEND IT!</p>
<hr />
<div><!--Please sign your posts with ~~~~ and don't delete this text. New comments should be added at the bottom.--><br />
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Anyways, what is the actual regression of the plot?<br />
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House of Cards: Not a real method, but a common consequence of mis-application of statistical methods: a curve can be generated that fits the data extremely well, but immediately becomes absurd as soon as one glances outside the training data sample range, and your analysis comes crashing down "like a house of cards". This is a type of _overfitting_<br />
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I'm pretty sure it refers to the TV show house of cards, the dots representing the quality of the series increasing until Netflix renewed it a bit too much {{unsigned ip|172.68.26.65}}<br />
:This was my initial interpretation as well, since you can hypothetically extend a literal house of cards indefinitely.[[Special:Contributions/172.68.58.83|172.68.58.83]] 14:23, 20 September 2018 (UTC)<br />
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Could someone familiar with the show expand on this? ''Also a potential reference to the TV show, House of Cards ("WAIT NO, NO, DON'T EXTEND IT!").'' Some context on what that line meant in House of Cards would be helpful. - [[User:CRGreathouse|CRGreathouse]] ([[User talk:CRGreathouse|talk]]) 14:20, 21 September 2018 (UTC)<br />
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I'm a little mystified by the alt-text. Cauchy and Lorentz both seem like mathematically capable people. What am I missing? [[Special:Contributions/172.69.62.226|172.69.62.226]] 17:46, 19 September 2018 (UTC)<br />
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: Google-Fu reveals that it's a continuous probability distribution. This isn't bad per se, but it is quite visually distinctive and also can be quite...concerning if the data set isn't one where probability should be an issue. [[User:Werhdnt|Werhdnt]] ([[User talk:Werhdnt|talk]]) 18:00, 19 September 2018 (UTC)<br />
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:: This is not the issue, but the fact that the moments (such as mean and variance) of the distribution don't exist = converge. See edited explanation. So if you wanted to estimate the parameters of the distribution, taking the sample mean for example will not converge with the number of data points, and is therefore bad to attempt. It is more mathematically alarming than alarmingly mathematical. [[User:GamesAndMath|GamesAndMath]] <br />
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:: My own Google-Fu brought me to a page with this information: “The distribution is important in physics as it is the solution to the differential equation describing forced resonance, while in spectroscopy it is the description of the line shape of spectral lines.” (from here: https://www.boost.org/doc/libs/1_53_0/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/cauchy_dist.html) [[User:Justinjustin7|Justinjustin7]] ([[User talk:Justinjustin7|talk]]) 18:09, 19 September 2018 (UTC)<br />
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:: True, but the "check what field I originally worked in" indicates that there might be something else going on with the meaning. [[Special:Contributions/108.162.237.238|108.162.237.238]] 12:47, 20 September 2018 (UTC)<br />
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:: I believe the point of "check what field I originally worked in" is that if somebody wasn't trained in statistics using an exotic distribution is highly suspect and suggest that either they are torturing the data to get desired results or have no idea what they are doing. [[Special:Contributions/108.162.246.11|108.162.246.11]] 05:19, 21 September 2018 (UTC)<br />
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To be honest, I'm a bit disappointed. I kinda expected a special comic with such a nice round number.. Been counting down since comic #2000... [[Special:Contributions/162.158.92.184|162.158.92.184]] 18:14, 19 September 2018 (UTC)<br />
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Different anon here, I think this is very special and if Randall makes a poster available I will be buying several to give away. Of course, part of my business is experimental data analysis and modeling...and this is a fantastic summary of common errors. {{unsigned ip|162.158.75.22}}<br />
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: Agreed. This is a very special comic, and a highly subtle title text. Direct any of your friends who do data analysis here. Sort of the next stage from the classic "correlation is not causation" comic https://xkcd.com/552/ . {{unsigned|GamesAndMath}}<br />
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'''Curve-Fitting'''<br />
<br />
How fitting works needs to be explained. f(x)=mx+b works fine for single values, but how do we get that red line from the data set? --[[User:Dgbrt|Dgbrt]] ([[User talk:Dgbrt|talk]]) 20:12, 19 September 2018 (UTC)<br />
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:Generally, you decide for some error function and then search for parameters where the sum of errors for all data points is minimal. -- [[User:Hkmaly|Hkmaly]] ([[User talk:Hkmaly|talk]]) 22:07, 19 September 2018 (UTC)<br />
<br />
:A typical error function is the square of the difference between the fit and the actual data point, hence "sum of squares" method. There are well-known standard formulas for finding m and b in the case of linear regression. In a linear algebra class, I saw a general method that would work for several of these (any where the fit is y = af(x)+bg(x)+...+ch(x), which includes log, exponential, quadratic, cubic, etc). I wish I could remember it. [[User:Blaisepascal|Blaisepascal]] ([[User talk:Blaisepascal|talk]]) 22:39, 19 September 2018 (UTC)<br />
::I'm still looking for an easy example. Let's say five points (x/y) and then calculating the straight line (without and maybe with the zero-point because this is often the assumed start). Just be simple, everything else derives from that. --[[User:Dgbrt|Dgbrt]] ([[User talk:Dgbrt|talk]]) 21:00, 20 September 2018 (UTC)<br />
<br />
:I wish we could include the graphics at the top of [https://en.wikipedia.org/wiki/Linear_regression#Introduction] and [https://en.wikipedia.org/wiki/Linear_regression#Interpretation] in the explanation. A lot of people are going to look at this one. [[Special:Contributions/172.68.133.168|172.68.133.168]] 17:51, 20 September 2018 (UTC)<br />
::I've included one picture with a small explanation to the linear regression section. I think that explains it well. --[[User:Dgbrt|Dgbrt]] ([[User talk:Dgbrt|talk]]) 21:00, 20 September 2018 (UTC)<br />
<br />
The data points do not have error bars, which makes the choice of fit even more ludicrous, in my opinion. If the data are that good, then I don't believe there is a correlation, it's random with some distribution. I might hang this up at work...[[User:Arppix|Arppix]] ([[User talk:Arppix|talk]]) 02:46, 20 September 2018 (UTC)<br />
:And of course in serious science data points have error bars. This makes the fitting even more complicated and should be mentioned at the explanation. Because Randall doesn't use error bars I'm sure he refers to presentations not based on real science. Also this should be mentioned here. --[[User:Dgbrt|Dgbrt]] ([[User talk:Dgbrt|talk]]) 21:06, 20 September 2018 (UTC)<br />
<br />
I hate to be negative here, as obviously some users have put a lot of effort into explaining the details behind each of the curve-fitting methods, but there's absolutely no explanation for Randall's comments on each method. While someone might learn something about the various methods by reading the explanation, they would not gain any insight on what Randall is saying about each method. In addition, the Connecting Lines explanation totally missed the fact that this isn't really even a curve-fitting method - it's just a feature of graphing software (in this case, Excel) where a smooth line is drawn through each data point from left to right rather than an example of overfitting to the data set. I think we could do better. [[User:Ianrbibtitlht|Ianrbibtitlht]] ([[User talk:Ianrbibtitlht|talk]]) 02:53, 21 September 2018 (UTC)<br />
<br />
Everyone is missing the deeper trolling here of the fisheries community at large, which shall become blindingly clear here. First, this is cartoon number 2048 (2^11), a highly interesting number. Notably, this is the year all fisheries were projected to be collapsed by Worm et al. (2006) Science 314:787-790, a prediction which gained huge attention in the media and took on a life of its own. The prediction was based on fitting a power curve to some data on collapses in catch trends. Numerous rebuttals followed, one of which pointed out that a linear fit to the data is a better fit, and predicts all fisheries collapsed in 2114 (Jaenike et al. 2007, Science 316:1285a). A list of rebuttals is found here: https://sites.google.com/a/uw.edu/most-cited-fisheries/controversies/2048-projection. Later work by the same author and critics found a different prediction and showed rebuilding of fisheries is likely (Worm et al. 2009 Science 325:578-585). Second, lest you think this is a conspiracy theory, I note that in xkcd cartoon 887, Munroe specifically notes this prediction "The future according to google search results... 2048: "Salt-water fish extinct from overfishing" https://xkcd.com/887/. Third, this kind of model-fitting exercise has long plagued fisheries researchers attempting to predict recruitment from spawning biomass.<br />
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"Ad hoc filter: Drawing a bunch of different lines by hand, keeping in only the data points perceived as "good". Also not useful. " – I guess it rather refers to data filtering, where for each point you take several points around and try to calculate some kind of mean, e.g. by rejecting most extreme points, or calculating median (see https://en.wikipedia.org/wiki/Median_filter). So it is an algorithm, not actually drawing lines by hand. Still it is tricky to draw conclusions and you can easily fool yourself with this method.</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=2042:_Rolle%27s_Theorem&diff=1626372042: Rolle's Theorem2018-09-12T17:10:05Z<p>CRGreathouse: more specific category</p>
<hr />
<div>{{comic<br />
| number = 2042<br />
| date = September 5, 2018<br />
| title = Rolle's Theorem<br />
| image = rolles_theorem.png<br />
| titletext = I mean, if it's that easy to get a theorem named for you ... "a straight line that passes through the center of a coplanar circle always divides the circle into two equal halves." Can I have that one? Wait, can I auction off the naming rights? It can be the Red Bull Theorem or the Quicken Loans Theorem, depending who wants it more.<br />
}}<br />
<br />
==Explanation==<br />
{{incomplete|Go a little bit more into the explanation.Explain the museum reference. Do NOT delete this tag too soon.}}<br />
<br />
In mathematics, a {{w|differentiable function}} is a function that is "smooth" everywhere, without any sudden breaks or pointy "kinks" or similar. The derivative of such a function is a new function that represents the "slope" or "rate of change" of the original. The function in this comic curves up from point (a) until a point above (c), smoothly turns around, and then curves down from (c) to (b). As a result, the derivative of this function is positive from (a) to (c), and then is negative from (c) to (b). At (c) itself, the function is "flat": the more one zooms in, the more horizontal it looks. The function is moving neither up nor down, so the derivative is neither positive nor negative, but zero. This is what ''f'(c) = 0'' means, as ''f''' is a common notation for the derivative of the function ''f'' in {{w|differential calculus}}.<br />
<br />
A {{w|theorem}} in mathematics is a statement that has been ''proven'' from former accepted statements, like other theorems or {{w|axiom}}s. This comic references {{w|Rolle's theorem}}. The theorem essentially states that, if a smoothly changing function has the same output at two different inputs, then it must have one or more turning points in between, as the derivative is zero at each one. As a special case, should the function remain flat between the two inputs, then its derivative is actually zero for every point between the inputs. To [[Randall]], this is obvious. However, the proof of this theorem is not as obvious as the result.<br />
<br />
The seeming triviality of the theorem, coupled with the honour bestowed on the theorem namer, leads Randall to make a comparison to attendees of art museums who look at abstract art pieces and perceive only an apparent technical simplicity in the work. Such a visitor might exclaim "My child could paint that!". However, such works of art typically are seen as having value from attributes other than the painterly difficulty in achieving the piece. For example, an artist's work in this style may be lauded for its visionary qualities, or the emotions expressed through the choice of colours or textures. One such artist is [http://www.bbc.co.uk/guides/zqhgr82 Jackson Pollock]. The 'clueless' visitor does not see these aspects and believes their child could imitate the piece. Randall suggests he experiences a similar feeling looking at Rolle's Theorem and noting only the obvious correctness without acknowledging the complicated nature of the proof, or other hidden aspects of the theorem. <br />
<br />
In the title text, Randall mentions a line together with a ''coplanar'' circle. This simply means that both those two-dimensional objects must lay in the same plane in a higher, three-or-more-dimensional space. And by this means, every line drawn through the center of a circle is just a diameter which divides it into two equal parts. Even if this fact is trivial, {{w|Proclus}} says that the first man who proved it was {{w|Thales of Miletus|Thales}}. Auctioning of {{w|naming rights}}, also noted in the title text, refers to the practice of naming entertainment venues for companies which pay for the privilege, such as any of the three {{w|Red Bull Arena}}s or {{w|Quicken Loans Arena}}. Furthermore, "Rolle's" sounds like "Rolls", a common abbreviation for the {{w|Rolls-Royce Motor Cars|Rolls Royce}} brand implying possible sponsorship by the British car manufacturer. The naming of mathematical theorems (along with lemmas, equations, laws, methods, etc.) is [http://www.maa.org/external_archive/devlin/devlin_09_05.html not always straightforward] and {{w|List of misnamed theorems|often results in misleading names}}.<br />
<br />
Randall implies that there are many seemingly easy theorems like this. For instance the Dirichlet's box principle, also known as the {{w|Pigeonhole principle}}, that states that if you have more objects than containers, you're going to have to put at least two objects in one container<br />
<br />
==Transcript==<br />
:[A single framed picture shows a colored x-y-graph with a text above:]<br />
:'''Rolle's Theorem'''<br />
:<small>From Wikipedia, the free encyclopedia</small><br />
<br />
:Rolle's theorem states that any real, differentiable function that has the same value at two different points must have at least one "stationary point" between them where the slope is zero.<br />
<br />
:[The graph shows a sine like curve in blue intersecting the x-axis at points "a" and "b" marked in red while in the middle a point "c" has a vertical dashed green line to the apex and on top also in green f'(c)=0 is drawn with a horizontal line.]<br />
<br />
:[Caption below the frame:]<br />
:Every now and then, I feel like the math equivalent of the clueless art museum visitor squinting at a painting and saying "c'mon, my kid could make that." <br />
<br />
{{comic discussion}}<br />
<br />
[[Category:Comics with color]]<br />
[[Category:Line graphs]]<br />
[[Category:Analysis]]<br />
[[Category:Wikipedia]]</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=2036:_Edgelord&diff=1617162036: Edgelord2018-08-22T14:03:12Z<p>CRGreathouse: /* Explanation */ more cleanup</p>
<hr />
<div>{{comic<br />
| number = 2036<br />
| date = August 22, 2018<br />
| title = Edgelord<br />
| image = edgelord.png<br />
| titletext = If you study graphs in which edges can link more than two nodes, you're more properly called a hyperedgelord.<br />
}}<br />
<br />
==Explanation==<br />
{{incomplete|Please change this comment when editing this page. Do NOT delete this tag too soon.}}<br />
<br />
"Edgelord" is modern slang describing a provocateur, often one with an adolescent mindset and lacking subtlety or restraint. The term derives from the word "edgy", which is used to describe things which are designed to be provocative.<br />
<br />
In mathematics, {{w|graph theory}} is the study of graphs, mathematical structures made up of nodes (points) which are connected by edges (or lines).<br />
<br />
This comic plays on the fact that graphs have edges. Calling someone with a Graph Theory Ph.D. an 'edgelord' (a master of edges) is somewhat analogous to calling an engineering student a 'forcelord', an astronomy PhD a 'starlord', or a pharmacologist a 'druglord'.<br />
<br />
Also, [[White Hat]] seems to shout "No", which is ironic, because he seems to be on edge. Because "edgelord" is perceived as an insult by socially aware adults, [[Cueball]] is actually provoking White Hat, making Cueball an edgelord in this interaction. Humor here also lies in that Cueball, in accusing White Hat of being an Edgelord, is being provocative himself and therefore somewhat edgy. Similar situational humor is also found in [[2008: Irony Definition]].<br />
<br />
The title text makes the same joke, except that the title would be hyperedgelord instead of edgelord. A {{w|hypergraph}} is a generalization of a graph in which each edge may have more than two endpoints.<br />
<br />
==Transcript==<br />
:[Cueball and White Hat are standing next to each other and are discussing.]<br />
:Cueball: So, I hear you're a real edgelord.<br />
:White Hat: '''''No!'''''<br />
<br />
:[Caption below the frame:]<br />
:How to annoy a graph theory Ph.D.<br />
<br />
{{comic discussion}}<br />
[[Category:Comics featuring Cueball]]<br />
[[Category:Comics featuring White Hat]]<br />
[[Category:Math]]<br />
[[Category:Social interactions]]</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=2036:_Edgelord&diff=1617142036: Edgelord2018-08-22T14:00:10Z<p>CRGreathouse: /* Explanation */ cleanup</p>
<hr />
<div>{{comic<br />
| number = 2036<br />
| date = August 22, 2018<br />
| title = Edgelord<br />
| image = edgelord.png<br />
| titletext = If you study graphs in which edges can link more than two nodes, you're more properly called a hyperedgelord.<br />
}}<br />
<br />
==Explanation==<br />
{{incomplete|Please change this comment when editing this page. Do NOT delete this tag too soon.}}<br />
<br />
"Edgelord" is modern slang describing a provocateur, often one with an adolescent mindset and lacking subtlety or restraint. The term derives from the word "edgy", which is used to describe things which are designed to be provocative.<br />
<br />
In mathematics, {{w|graph theory}} is the study of graphs, mathematical structures made up of nodes (points) which are connected by edges (or lines).<br />
<br />
This comic plays on the fact that Graphs (or, at least, the objects in graphs) have edges. Saying someone with a Graph Theory Ph.D. is an 'edgelord' (a master of edges) is somewhat analogous to calling an engineering student a 'forcelord', an astronomy PhD a 'Starlord', or a pharmacologist a 'Druglord'.<br />
<br />
Also, [[White Hat]] seems to shout "No", which is ironic, because he seems to be on edge. Because "edgelord" is perceived as an insult by socially aware adults, [[Cueball]] is actually provoking White Hat, making Cueball the edgelord in this interaction. Humor here also lies in that Cueball, in accusing White Hat of being an Edgelord, is being provocative himself and therefore somewhat edgy. Similar situational humor is also found in [[2008: Irony Definition]]<br />
<br />
The title text makes the same joke, except that the title would be Hyperedgelord (master of Hyperedges) instead of Edgelord (a master of edges that aren't hyperedges). A {{w|Hypergraph|hypergraph}} is a generalization of a graph in which each edge may have more than two endpoints.<br />
<br />
==Transcript==<br />
:[Cueball and White Hat are standing next to each other and are discussing.]<br />
:Cueball: So, I hear you're a real edgelord.<br />
:White Hat: '''''No!'''''<br />
<br />
:[Caption below the frame:]<br />
:How to annoy a graph theory Ph.D.<br />
<br />
{{comic discussion}}<br />
[[Category:Comics featuring Cueball]]<br />
[[Category:Comics featuring White Hat]]<br />
[[Category:Math]]<br />
[[Category:Social interactions]]</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=1663:_Garden&diff=1613191663: Garden2018-08-17T07:06:49Z<p>CRGreathouse: /* Explanation */ link</p>
<hr />
<div>{{comic<br />
| number = 1663<br />
| date = April 4, 2016<br />
| title = Garden<br />
| image = garden.png <!--This is the starting point and should be used here. Other images need to go in the explanation --><br />
| titletext = Relax.<br />
}}<br />
<div class="toclimit-3" style="float:right; margin-left: 10px;">__TOC__</div><br />
*'''Note''' this is an interactive comic. Go to {{xkcd|1663|xkcd}} to try it out.<br />
**Also '''note''' that a few weeks after the comic was released a change was made so growth only seems to appear when the gardens is actively running in a browser window! <br />
**(This is opposed to what happened during the first few weeks after release!)<br />
<br />
==Explanation==<br />
{{incomplete|Fill out the [[#Items in the garden|tables]] with images of all the possible items. General explanations/comment are missing as well as link to screenshots of gardens where each item "grows".}}<br />
<br />
This was the seventh [[:Category:April fools' comics|April fools' comic]] released by [[Randall]]. The previous fools comic was <br />
[[1506: xkcloud]] from Wednesday April 1st 2015. The next [[1818:_Rayleigh_Scattering#No_April_Fools.27_Day_comic_in_2017|did not come out in 2017]], but first in 2018 when [[1975: Right Click]] was released on Sunday April 1st 2018.<br />
<br />
This comics represents the April fools' comic of 2016, and it is [[Randall|Randall's]] celebration of {{w|April Fools' Day}} Friday, April 1, 2016. It represents the third time in a row that user input changes the April Fool's comic. Although in the last two [[1350: Lorenz]] and [[1506: xkcloud]] it was written (or drawn) input that became part of the comics. This time the user input is like a game, as the user actively adds, moves and deletes items, and new items appear based on these actions. In this way it actually more resembles the game comic [[1608: Hoverboard]], than the previous April Fool's comics.<br />
<br />
Due to technical problems (or to make fools of his fans, see more about the [[#April Fool's header text|header text]] below) the comic did not go live until Sunday evening (after midnight, so technically first on Monday April 4th) so there was no Friday release the week before, see [[#Monday 4th of April release|more details below]].<br />
<br />
The comic begins with a [http://www.explainxkcd.com/wiki/images/f/f1/Garden_Loading_collage.png loading screen] with a revolving tree and the text "loading..." This is because the first time a computer loads this dynamic comic it can take a while.<br />
<br />
Once it is loaded it displays "your '''Garden'''", being a barren landscape, with a small pond to the left, some rocks at the far left and right, and a single lamp shining light yellow light on most of the ground. This is what is shown at the top of the explanation here. But if you leave the lights on and wait (or "relax", as the reader is told to do by the title text), then plants and other items will start to appear. <br />
<br />
The reason it is correct to call it "your garden" is that every time this comic is loaded from scratch, a new garden will be created with a unique url-address. By [[#Saving garden with url|saving this link]] (making a bookmark for it), the user will be able to return to their garden again and again. As the garden only develops very slowly this is important. (If users wish to share their garden they can do it in the table on the page for '''[[1663: Garden/Users gardens|Users gardens]]''').<br />
<br />
[http://www.explainxkcd.com/wiki/images/7/78/1663_garden_Three_colors_over_everything_not_very_interesting.png Plants appear] one at a time, and sometimes it takes a long time. Only a few of the plants actually grow. For instance there are some large trees that begins as [http://www.explainxkcd.com/wiki/images/2/27/1663_garden_Fast_growing_tree_-_leafless.png a large trunk] and from there [http://www.explainxkcd.com/wiki/images/6/67/1663_garden_Fast_growing_tree_-_lots_of_leaves.png grows branches and leaves]. This can sometimes happen quite fast. Most other plants just appear, the only other exception being one type of flowers. All plants, except the cactus, clearly sway in the breeze.<br />
<br />
Also [http://www.explainxkcd.com/wiki/images/5/5a/1663_garden_Pruned_garden_with_birds_deer_gate_cactus_turtles_snake_gate.png animals] and [http://www.explainxkcd.com/wiki/images/d/de/1663_garden_Three_lamps_two_along_ground_with_pillars_not_in_blue_world_and_symmetric_gates.png building-like structures] such as [http://www.explainxkcd.com/wiki/images/1/15/1663_garden_Megan_Monolith_Animals_and_more.png a monolith and birdbaths] appear, together with lots of other items like [http://www.explainxkcd.com/wiki/images/a/ad/1663_garden_Office_space_with_star_plant_balloon_with_bird_and_grass_on_Cueball.png office furniture] with [http://xkcd.com/1663/#98dc3452-fcf2-11e5-8010-42010a8e0008 balloons swaying in the wind] or even one of the [http://www.explainxkcd.com/wiki/images/3/3f/1663_garden_One_color_Between_orange_red_and_red_First_thing_Mars_rover.png Mars rovers] which so [[:Category:Mars rovers|often have been featured]] in xkcd.<br />
<br />
On top of all this, several known characters may appear in different poses including [[Cueball]] and [[Megan]] (for instance with a sword, see [http://www.explainxkcd.com/wiki/images/6/6b/1663_garden_Megan_with_sword%2C_trees_octopuses_with_Cueball_bunny_ducklings.png here]), [[Ponytail]] (see [http://www.explainxkcd.com/wiki/images/e/eb/1663_garden_Ponytail_and_two_Cueballs_cat_pillar_and_trunk_sE.png here]) and [[Beret Guy]] from the torso and up (see [http://www.explainxkcd.com/wiki/images/9/9b/1663_garden_Three_colors_more_separate_Beret_Guy_in_shrubbery_and_Octopus_on_office_desk.png here]). Megan and also Cueball can both be seen [http://www.explainxkcd.com/wiki/images/0/06/1663_garden_Giant_planter_on_pillars_and_both_Cueball_and_Megan_with_black_hat.png with a black hat], but it is one that "grows" on top of their heads after they first appear. However, Cueball with a black hat automatically turns into [[Black Hat]], so he can also be said to be in this comic. There is also an unknown character, a [http://www.explainxkcd.com/wiki/images/0/0c/1663_garden_One_color_Between_Light_yellow_and_yellow_First_thing_stilts.png girl on stilts] with black hair in a ponytail who like plants and balloons [http://xkcd.com/1663/#e774b4b8-fcd4-11e5-8001-42010a8e0017 sways in the wind]. A possible origin of this girl could be the What If article [https://whatif.xkcd.com/97/ Burning Pollen]. The article involves a character with seasonal allergies that is trying unsuccessfully to avoid their allergen (pollen) with giant stilts.<br />
<br />
All the [[#Items in the garden|items that can appear]] in the garden are listed below in several tables. During the first week new items kept appearing, but after the eighth day (April 12th), no new items have appeared. Also the growth rate (and thus the fun of this comic) has decreased with time (maybe due to the enormous amount of gardens that the server has to keep track of?) .<br />
<br />
Every so often the image will refresh. You can change the number of lamps, their position, direction, beam width and the color temperature which always begins somewhere between white and yellow, but can change all the way from red to blue (See this [http://www.explainxkcd.com/wiki/images/b/b8/Garden_Three_Lamp_screen_shot.png example] with one lamp selected and three colors of light). Other colors than those four may appear where two lamps' cones of different colored light overlap.<br />
<br />
The color of light [[#Effect of light|affects the growth]] with a strong correlation for what appears in the garden depending on the [[#Colors of light|color of light]], and this is not only split between red, yellow and blue, but rather [http://www.explainxkcd.com/wiki/images/4/4a/1663_garden_Numbered_color_scale_1-17.png 10 different colors]. <br />
<br />
Early on it became clear that pure red light results in a desert theme with [http://www.explainxkcd.com/wiki/images/9/98/1663_garden_Desert_with_red_light_only.png cacti and turtles] and pure blue light gives an aquatic theme with [http://www.explainxkcd.com/wiki/images/2/23/1663_garden_Octopus_garden_with_Cueball_hand_up_and_a_black_hat_octopus.png lots of octopuses] that may also wear a black hat. For the most interesting gardens the [http://www.explainxkcd.com/wiki/images/1/15/1663_garden_Megan_Monolith_Animals_and_more.png light colors should be mixed]; see more below under [[#Effect of light|Effect of light]].<br />
<br />
If this comic is scientifically accurate, that correlation will be based on {{w|photosynthetically active radiation}}.<br />
<br />
Some users manage to create fantastic gardens (by using lots of time on them, pruning them at the right time and changing the light and lamp position to get what they strive for). Especially one user have created a series of amazing gardens that is posted on another [http://forums.xkcd.com/viewtopic.php?f=7&t=114415&start=600 xkcd forum]. Here is a collection of screenshots with some of [[1663:_Garden/Screen-shots#Blitz_Girls_amazing_gardens|Blitz Girls amazing gardens]]!<br />
<br />
The title text "Relax" can be debated. Is it to let the users know they should just sit back and relax as the garden grows.? Or should they relax and don't worry so much about how it works (not working here on explain xkcd though!)? Or is he teasing the users by giving them a garden that they need to tend to, and then telling them to relax? And also giving them many more colors than lamps... Given that this comic was supposed to come out on April 1st, there is a good chance that it is, also, to tease the users. There are actually [[#Trivia|two other title texts]] as well.<br />
<br />
===Extra Garden pages===<br />
*Since this comic is so complicated extra pages have been created to include much more information than is wished for on this main page (which is already of considerable size).<br />
*These pages are listed here for convenience, but they are also linked in the relevant sections below:<br />
**[[1663: Garden/Images]]. The images of items that can appear in the comic.<br />
***This page is linked in the section below with table for ''[[#Items in the garden|Items in the garden]]''.<br />
**[[1663: Garden/Screen-shots]]. Since there are no permalink it in order to save a particular moment of a garden a screen shot is needed. These can be posted here. <br />
***This page is linked in the section below about for ''[[#Saving images|Saving images]]''.<br />
**[[1663: Garden/Users gardens]]. A place for users of explain xkcd to post links to their own garden, and also for experimental gardens.!<br />
***This page is linked in the section below about for ''[[#Saving garden with url|Saving garden with url]]''.<br />
<br />
==Transcript==<br />
:[After a '''loading image''' with a rotating tree in the middle and the text "Loading..." with the three dots appearing one at a time, and then disappear when all three have been there the image shown above in the explanation will appear:]<br />
<br />
:['''Description of the image above''': A piece of bare landscape is shown. At the edges there are some rocks or stones raising the level from the general level through the center of the panel. Above the middle, a little more than halfway to the to of the panel, is a light bulb sitting inside a lamp that reminds of the desk lamp from the movie Luxo Jr. The lamp shines a yellow light down on the landscape in a broad cone that jus reaches the first rock to the left, but not those to the right. The lamp just hovers in the air. In the top right corner are two gray icons. The top one has a black frame and shows an image of a lamp, tilted left as opposed to the straight position of the lamp in the image. There is a + sign below in the left corner. The second icon without a frame has a large white cross in the middle.]<br />
<br />
:[This turns out to be a '''web applet''' and using the "+ lamp" icon two more lamps can be added getting up to three. They are all adjustable both regarding position, direction, color of light and beam width. When selecting a lamp a red circle appear around it with a small circle on top that can be used to control the light color from blue to the left to red to the right. In front is a red arrow that can turn the lamp and it can also be used to change the beam width by pulling it away from the lamp or pushing it back. The lamps can be moved by just clicking on it and moving it. The other icon with a X can be used to remove the lamps (and later any object that appear in the garden). When any object is selected there is a red circle around it. When this is done the gray cross icon becomes red and can the be used to delete the selected item. When no item is selected (either because it is deleted, or by clicking in a part of the screen with no items), then the cross icon turns gray again. When all three lamps are on, then the "+ lamp" icon is faded out.]<br />
<br />
:['''If you wait''' (or relax, as in the title text), then a plant will grow or animals, humans and other items may appear. This could be birds, snakes, octopuses or turtles, Megan or Cueball or a birdbath, a monolith or a tall gate just as a few examples. Most of the items appear in one go, but at least the largest trees grow up with a big stem first and then adds parts later with leaves or empty branches. Also one item may appear on top of another item and for instance birds may fly in the air.]<br />
<br />
:[There is but one word in the entire comic, which appears when you grow a sign:]<br />
:Sign: Sale<br />
<br />
==Functionality==<br />
===Saving garden with url===<br />
*There is no [[1350#Permalink|permalink button]] as in the last two years' April Fool's comics.<br />
*The URL is different for every garden that is loaded, but stays the same. It links to a server-side copy of the scene, which then changes depending on what the users does with their gardens.<br />
**Sharing a URL will connect a new browser to the same garden session, but only the original browser will be allowed to edit.<br />
**The user can always return to change the garden with the link, but only from the same browser on the same computer.<br />
**This means that a specific moment in a gardens life has to be [[#Saving images|saved as an image]] for future references.<br />
*The garden itself will thus continue to develop further from the time when the url was copied, and events will happen from now on even though the garden is not opened in any browser.<br />
**If the user doesn't keep it, it will become infested with weeds.<br />
**So most likely the garden is serverside, as all browsers are allowed to see the development of this garden, but users following the url are not allowed to edit anything.<br />
*Here is an example garden [http://www.xkcd.com/1663/#0d11a2c8-fa8f-11e5-8001-42010a8e000e linked by ID] versus the same garden:<br />
**In the original [http://www.explainxkcd.com/wiki/images/7/7f/1663_garden_tree_turtle_birdbath.png screenshot from April 4th] from when the url was created<br />
**In a [http://www.explainxkcd.com/wiki/images/7/7c/1663_garden_Flying_birds_deer_gate_with_cactus_turtles_snake_etc.png screenshot from April 5th] the day after.<br />
**Here [http://www.explainxkcd.com/wiki/images/5/5a/1663_garden_Pruned_garden_with_birds_deer_gate_cactus_turtles_snake_gate.png example] after the user pruned the garden in the examples.<br />
**Other [[1663: Garden/Users gardens|user gardens]] can be found on the link.<br />
*Starting two browser windows or tabs pointing to the same URL will allow you to edit from either window.<br />
**linden.xkcd.com holds all the data; the UUID just corresponds to your access key, held in your browser's local storage.<br />
<br />
====Saving images====<br />
*Since the [[#Saving garden with url|urls are changing]] the only way to save a particular garden is to save an image of the current garden.<br />
**Alternatively by deleting all lamps (or changing them to laser beams or turning them upwards) the no new growth will occur. But then the garden will no longer develop.<br />
*In Edge, Firefox and Chrome, the image plus light cones but minus lamps and icons elements, can be saved by right clicking in the image. (Not possible in explorer).<br />
**They do not always save in the same way as some browsers saves the part of the background without any light cones as white, and other save it as no background, in which case it may render black, basically hiding any black items outside the light.<br />
***For those images it depends on which viewer is used to see the image, if everything can be seen or only that in the light cones.<br />
****See examples of how it looks with black background in these two color maps collections using [http://www.explainxkcd.com/wiki/images/5/50/1663_garden_Single_colors.png a single lamp] and [http://www.explainxkcd.com/wiki/images/9/90/1663_garden_Three_colors.png three lamps].<br />
****See more details about how these [[1663:_Garden/Screen-shots#Color_maps|color maps]] have been made.<br />
****See also (at least) two examples of saved images as the are here on explain xkcd [[1663:_Garden/Screen-shots#Saved_image_from_xkcd|here]].<br />
*An image of the whole screen can be captured, by pressing the PrtScn (Print Screen) key on the keyboard & then pasting the content into a blank image in an image-editing program.<br />
**An even better solution is to use a tool like {{w|Snipping Tool}} which can take the part of the screen that are relevant. This is how most of the [[1663: Garden/Screen-shots|screen shots]] for this explanation has been aquired.<br />
**In both way the lamps and icons can also be displayed, which is not an option with saved images.<br />
<br />
===Lamps===<br />
*Additional lamps, up to a total of three lamps, can be added by clicking the black plus lamp icon along the right of the window.<br />
*Lamps can be removed by clicking to select a lamp, then clicking the red X icon along the right of the window, or pressing the Delete or Backspace key on the keyboard. All lights can be deleted.<br />
*The position of the lamp can be moved by clicking and dragging the lamp within the scene.<br />
*The angle and area of the light cone emitted by the lamp can be changed by [http://www.explainxkcd.com/wiki/images/0/09/Garden_Red_Lamp_screen_shot.png clicking to select the lamp and to reveal the red control triangle]. Rotating the control triangle around the lamp will change the aim of the lamp to point in the direction of the triangle, dragging the control triangle towards the lamp will [http://www.explainxkcd.com/wiki/images/c/cc/1663_garden_One_color_Light_blue.png widen the beam], and dragging the control triangle towards away from the lamp will [http://www.explainxkcd.com/wiki/images/5/5a/1663_garden_Pruned_garden_with_birds_deer_gate_cactus_turtles_snake_gate.png narrow the beam].<br />
*The color emitted by the lamp can be changed by clicking the lamp to reveal the colored control dot, and by rotating the dot around the lamp. The small color control circle changes color to match the color of the lamps beam of light. new lights default to a center position, emitting a pale green. '''rotating the control right''' changes the color to yellow, orange, and finally red, and '''rotating the control left''' changes the color to white, then blue.<br />
<br />
===Colors of light===<br />
*The color control moves in a smooth gradient between colors, along the spectrum without any set positions.<br />
*Small changes in the color can have an effect on the garden, even though there is no clear change in the color. <br />
*[http://www.explainxkcd.com/wiki/images/5/50/1663_garden_Single_colors.png As many as nine colors] can be identified from the emitted light of a single lamp, and many more colors are evident when [http://www.explainxkcd.com/wiki/images/9/90/1663_garden_Three_colors.png two or three lamps overlap].<br />
*There is reason to believe that even half the change will create different gardens, i.e. there can be at least one more position between those nine settings that will change the effect, giving eight more settings for a total of 17 "different" colors. An experiment with such '''17 settings''' for just [[1663:_Garden/Screen-shots#One_lamp_one_color|One lamp with one color]].<br />
*Several unique elements only seem to appear using the eight half-colors. Both the [http://www.explainxkcd.com/wiki/images/3/3f/1663_garden_One_color_Between_orange_red_and_red_First_thing_Mars_rover.png Mars rover] and the [http://www.explainxkcd.com/wiki/images/1/1b/1663_garden_One_color_Between_Light_yellow_and_yellow_First_thing_stilts_right.png Stilts girl] might be missed.<br />
*Colors can thus be indicated from these 17 divisions:<br><br />
**Below is a table with these 17 division shown and what to expect. <br />
**This may change over time, but was as it about a week after release. <br />
***If updating, please make a note that this may have only applied during the first week(s) and add new feature without deleting.<br />
**There has been an [[1663:_Garden/Screen-shots#One_lamp_one_color|experiment made]] with these 17 colors, see that for more details. <br />
***The color names links to these experimental gardens, that will never be changed after the initiation.<br />
***But there are reasons to believe that two gardens made identical may develop quite differently, as it seems some gardens have very limited growth in spite of the same light. Some of these gardens may be of that persuasion.<br />
****This was proven when 34 more gardens using the 17 colors where started in a [[1663:_Garden/Screen-shots#Second_experiment|similar experiment]].<br />
*The debugger reveals that each light has a "temp" property which ranges from 0 (red) to 1 (blue). The default setting is 0.5.<br />
**The RGB color corresponding to "temp" is determined by this function in linden.js:<br />
::<tt>function u(t){return.32>t?[1,.5+.5*t/.32,.5]:.64>t?[1,1,.5+.5*(t-.32)/.32]:[.75+.25*(1-t)/.36,.75+.25*(1-t)/.36,1]}</tt><br />
[[File:1663 garden Numbered color scale 1-17.png]]<br><br />
{| class="wikitable"<br />
! #<br />
! Color<br />
! Description of items etc<br />
|-<br />
| 1 <br />
| [http://xkcd.com/1663/#f65c4906-fcf1-11e5-8001-42010a8e0016 Blue]<br />
| '''Pure blue'''! Aquatic theme with octopus (some with black hat), Cueball checking for rain with hand up. Less growth after the first week and octopus only over the pond (see [[1663:_Garden/Screen-shots#Growth_speed_vs_blue_light|growth speed vs blue light]]).<br />
|-<br />
| 2<br />
| [http://xkcd.com/1663/#d5b7fed6-fd94-11e5-8001-42010a8e000a Blue -> light blue]<br />
| Octopus over pond and boats in pond, Cueball hands up and down (the latter possibly with black hat), {{w|Cairn}}s of '''stones''' and {{w|obelisk}}.<br />
|-<br />
| 3<br />
| [http://xkcd.com/1663/#3afb7988-fcf2-11e5-8001-42010a8e0019 Light blue]<br />
| Cueball hands down (but can be with [http://www.explainxkcd.com/wiki/images/6/64/1663_garden_Color_03_8d.png hand up] as well), Cairns of '''stones''', obelisk, wading bird and boats.<br />
|-<br />
| 4<br />
| [http://xkcd.com/1663/#303c341c-fd95-11e5-8001-42010a8e0016 Light blue -> blue white]<br />
| Obelisk, flower base and stems and balloon string with normal and huge balloons, Cueball hands up (and [http://www.explainxkcd.com/wiki/images/a/a5/1663_garden_Color_04_2_8d.png also down] with {{w|column}} and wadding bird), fish, shark fins and boats.<br />
|-<br />
| 5<br />
| [http://xkcd.com/1663/#98dc3452-fcf2-11e5-8010-42010a8e0008 Blue white]<br />
| Office landscape with desks and chairs, table, column, obelisk, pots with star plant or other flowers base and stems, Beret Guy in pond, Cueball hands up and down, balloon string with normal and huge balloons drifting far left and right on their strings in the wind. [http://www.explainxkcd.com/wiki/images/a/ac/1663_garden_Color_05_8d.png Also wadding bird], boats and shark fin<br />
|-<br />
| 6<br />
| [http://xkcd.com/1663/#5a45a1f8-fd95-11e5-8001-42010a8e000e Blue white -> white]<br />
| Both kinds of Cueball, Ponytail, Beret Guy, both types of cats, office desk, table, standing bird, wading bird, heron, owl, shark fin, bunny boat, flowers base and stems, balloon string with normal and huge balloons. Also [http://www.explainxkcd.com/wiki/images/3/36/1663_garden_Color_06_2_8d.png fish] and [http://www.explainxkcd.com/wiki/images/7/75/1663_garden_Color_06_8d.png flying fish].<br />
|-<br />
| 7<br />
| [http://xkcd.com/1663/#ba6b4ac2-fcf2-11e5-8001-42010a8e0019 White]<br />
| Balloon string with normal and huge balloons (here '''three in one garden'''), Megan hand up, cats, bunnies, shark fin, fish, Beret Guy, flowers base and stems and trees. [http://www.explainxkcd.com/wiki/images/c/c7/1663_garden_Color_07_8d.png Also] platform in tree, beehive base, Ponytail, water bird and flying fish and [http://www.explainxkcd.com/wiki/images/8/82/1663_garden_Color_07_2_8d.png Heron].<br />
|-<br />
| 8<br />
| [http://xkcd.com/1663/#8874be6a-fd95-11e5-8001-42010a8e0016 White -> light yellow]<br />
| Megan hands up, {{w|shrub}}s, flowers base stems, '''hilt''' and '''some blooms''', trees, bunnies, fish, shark fin, water bird, owl, bunnies. [http://www.explainxkcd.com/wiki/images/2/2a/1663_garden_Color_08_2_8d.png Also] birdbath and stilt girl.<br />
|-<br />
| 9<br />
| [http://xkcd.com/1663/#db338968-fcf2-11e5-8001-42010a8e0016 Light yellow]<br />
| '''Starting color'''. Megan hands down and with sword on platform, trees, shrub, flowers base and stems, grass, platform in tree, birdbath, ducks, wading bird, pots, with star plants, tall platform. [http://www.explainxkcd.com/wiki/images/c/c3/1663_garden_Color_09_8d.png Also] deer, stilt girl, fish and [http://www.explainxkcd.com/wiki/images/1/1f/1663_garden_Color_09_2_8d.png shark fin].<br />
|-<br />
| 10<br />
| [http://xkcd.com/1663/#b28f8522-fd95-11e5-8001-42010a8e0013 Light yellow -> Yellow]<br />
| Girl on stilts, Megan with swords on platform, trees, flowers base and stems, grass, reeds in pond, platform in trees, tall platforms, deer, snake, pots<br />
|-<br />
| 11<br />
| [http://xkcd.com/1663/#efccf292-fcf2-11e5-8010-42010a8e0003 Yellow]<br />
| Sale signs, tall platform, snakes, armadillo, flowers base and stems, reeds in pond. Also [http://www.explainxkcd.com/wiki/images/c/ce/1663_garden_Color_11_2_8d.png deer].<br />
|-<br />
| 12<br />
| [http://xkcd.com/1663/#de4fd3b0-fd95-11e5-8001-42010a8e0011 Yellow -> Orange]<br />
| Sale signs, snakes, turtles, tulips and wavy plants. Also [http://www.explainxkcd.com/wiki/images/b/bb/1663_garden_Color_12_2_8d.png tall platform] and armadillo.<br />
|-<br />
| 13<br />
| [http://xkcd.com/1663/#0d6bca62-fcf3-11e5-8019-42010a8e0005 Orange]<br />
| Wavy plants, turtles, [[#Linsang_-_cat_like_animal|linsang]], flying birds and flying Megan (and thus also bird risers and their roots). Also [http://www.explainxkcd.com/wiki/images/9/98/1663_garden_Color_13_8d.png armadillos].<br />
|-<br />
| 14<br />
| [http://xkcd.com/1663/#578b80bc-fd96-11e5-8001-42010a8e000a Orange -> orange red]<br />
| Snakes, turtles, linsang, armadillo, tulips wavy plants, flying birds and flying Megan (and thus also bird risers and their roots).<br />
|-<br />
| 15<br />
| [http://xkcd.com/1663/#28b238b0-fcf3-11e5-8001-42010a8e0018 Orange red]<br />
| Desert landscape with turtles, cactus sale, signs, lamp post poles without lamps, platform on cactus resulting in inverted pyramids. Also [http://www.explainxkcd.com/wiki/images/d/d4/1663_garden_Color_15_2_8d.png linsang].<br />
|-<br />
| 16<br />
| [http://xkcd.com/1663/#ad7ca596-fd96-11e5-8020-42010a8e0006 Orange red -> red]<br />
| Desert landscape with Mars rover, turtles, cactus sale, signs, lamp post poles without lamps but no platforms. Also [http://www.explainxkcd.com/wiki/images/e/e3/1663_garden_Color_16_2_8d.png linsang].<br />
|-<br />
| 17<br />
| [http://xkcd.com/1663/#46cc4e08-fcf3-11e5-8001-42010a8e0013 Red]<br />
| '''Pure red'''! Desert landscape with turtles and cactus only.<br />
|}<br />
<br />
===Effect of light===<br />
*How much the color affects the growth took some time to find out but already from the stat it was clear that there definitely was a correlation<br />
*For instance areas under lights set to the the outer position or the starting position was very different.<br />
**[http://www.explainxkcd.com/wiki/images/2/23/1663_garden_Octopus_garden_with_Cueball_hand_up_and_a_black_hat_octopus.png Pure blue light] (left most) develop into a boring aquatic theme with only lots of octopuses (maybe with a black hat) and the Cueball holding a hand out to check for rain. <br />
***The appearance of pure blue gardens have changed with time so octopuses now only appear over the pond [http://www.explainxkcd.com/wiki/images/1/1d/1663_garden_One_color_Blue_9d.png like this].<br />
**[http://www.explainxkcd.com/wiki/images/7/70/1663_garden_One_color_red_9d.png Pure red light] (far right) develop into a boring desert theme with only cactus and turtles.<br />
**[http://www.explainxkcd.com/wiki/images/9/9c/1663_garden_One_color_Light_yellow_9d.png Light yellow] or [http://www.explainxkcd.com/wiki/images/2/2e/1663_garden_Color_09_3d.png starting light] grows lots of plants like trees, grass and scrubs and several animals like ducks, deer, fish and wadding bird and also birdbath, stilt girl and both standing Megan and sword Megan.<br />
*Soon after the release of the comic some research into a single lamp with unchaining light, that covering the whole light range split into 17 divisions was undertaken.<br />
*[[File:1663 garden Numbered color scale 1-17.png]]<br />
**See these gardens [[1663:_Garden/Users_gardens#Locked_gardens_only_for_explanation_use|locked for explanation use only]] and also see more about the 17 split in the color range [[#Colors of light|above]].<br />
*Mixed light seems to be able to do the same, but it is unclear if what grows only depends on the final mixed color, or if it is a mix of what would grow under those two colors.<br />
**There are some indications that it is not a clear mix as pure blue together with pure red, does not seem to produce neither Octopuses or desert theme.<br />
**If there are any items that can only grow under a mix of light this has not been proven. Most objects that can grow directly from the ground, has been observed in the experimental single color gardens mentioned above.<br />
**But there may be items that needs to grow on top of other objects, and these may require a change of color from what the base needs. And thus they will not appear under one color light. Possible examples of these items could be:<br />
***[http://www.explainxkcd.com/wiki/images/f/f3/Garden_Desk_lamp.png Desk lamp] (needing some kind of platform forming in another color range like the [http://www.explainxkcd.com/wiki/images/e/ee/Garden_Tall_platform.png tall platform], yellow or the small [http://www.explainxkcd.com/wiki/images/1/11/Garden_Platform_1.png platform], orange).<br />
***[http://www.explainxkcd.com/wiki/images/8/88/Garden_Giant_Planter.png Giant Planter] (needing for instance a [http://www.explainxkcd.com/wiki/images/c/c4/Garden_PlatformColumn_3.png platform column], light blue light]<br />
***[http://www.explainxkcd.com/wiki/images/e/e0/Garden_lamp-topper.png Lamp pole tops] (needing [http://www.explainxkcd.com/wiki/images/8/81/Garden_Lamppost_1.png lamp poles] forming under orange light)<br />
***[http://www.explainxkcd.com/wiki/images/a/a4/Garden_Flower_bloom_1.png Flower blooms] (any type) (needing [http://www.explainxkcd.com/wiki/images/d/d1/Garden_Flower_segment_1.png flower segments], several colors)<br />
***[http://www.explainxkcd.com/wiki/images/7/7e/Garden_Actual_flying_fish_1.png Actual flying fish] (needing bird raiser, orange light)<br />
***[http://www.explainxkcd.com/wiki/images/5/5d/Garden_Saucer.png Flying saucer] (needing bird raiser, orange light)<br />
*What happens when using only one color (other than the two outer points red and blue and the starting light yellow color) has been explored in great depth in no less than two different [[1663:_Garden/Screen-shots#One_lamp_one_color|One lamp one color]] experiments with [[1663:_Garden/Users_gardens#Locked_gardens_only_for_explanation_use|51 gardens]] created using 17 different color settings.<br />
**[http://www.explainxkcd.com/wiki/images/2/27/1663_garden_One_color_Between_blue_and_light_blue_6d.png Blue light] (just right of pure blue) creates a landscape with stones forming cairns, together with monoliths, both kinds of Cueballs (with black hat on the standing one) and still octopuses. <br />
**[http://www.explainxkcd.com/wiki/images/7/75/1663_garden_One_color_Light_blue_9d.png Light blue light] (just a little farther from pure blue than above), the octopuses disappear, but the rest remains the same, although boats and wadding bird now appear in the water, and still both [http://www.explainxkcd.com/wiki/images/a/a6/1663_garden_Color_03_5d.png Cueballs] can occur. Going just slightly further away [http://www.explainxkcd.com/wiki/images/e/e4/1663_garden_Color_04_2_5d.png fish and columns] start to appear.<br />
**[http://www.explainxkcd.com/wiki/images/d/d1/1663_garden_One_color_White_Blue_12h.png Blue white light] grow a sort of office theme, with desks, balloons and Cueballs. Moving towards white light [http://www.explainxkcd.com/wiki/images/d/d0/1663_garden_One_color_Between_Blue_White_and_White_5d.png Ponytail appears] with less office items together with cats (and now no Beret Guys in the pond but [http://www.explainxkcd.com/wiki/images/d/df/1663_garden_One_color_Between_Blue_White_and_White_8d.png lots of animals]).<br />
**[http://www.explainxkcd.com/wiki/images/f/f7/1663_garden_One_color_White_9d.png White light] gives a forest of balloons with Megan holding her hands up.<br />
**[http://www.explainxkcd.com/wiki/images/3/3e/1663_garden_One_color_Yellow_2d.png Yellow light] (somewhat right of the starting color) produce sale signs and snakes.<br />
**[http://www.explainxkcd.com/wiki/images/4/4f/1663_garden_One_color_Between_orange_and_orange_red_8d.png Orange light] produce flying bird and flying Megans and on the ground snakes, turtles, linsangs and armadillos, plus tulips and wavy plants.<br />
**[http://www.explainxkcd.com/wiki/images/0/02/1663_garden_One_color_Between_orange_red_and_red_8d.png Orange red light] (just left of red) produce lamp posts (without the top), in addition to the same desert theme as red with cactus and turtles. If it is very close to red the Mars rover appears (as in the example above). If it is a little longer from red, the platforms can form, which can then act as a catalyst for growth and create [http://www.explainxkcd.com/wiki/images/5/58/1663_garden_One_color_Orange_red_9d.png large towers] on top of cactus's.<br />
*Nothing seems to be able to grow under several conditions:<br />
**If no lamps are pointing towards the ground for instance because:<br />
***All [http://xkcd.com/1663/#21374f9e-fbbd-11e5-8001-42010a8e0015 lamps are deleted].<br />
***The [http://xkcd.com/1663/#4896b678-fbbe-11e5-8001-42010a8e0011 beam is laser thin.]<br />
***The lamps points towards the sky without [http://www.xkcd.com/1663/#6a6a7be0-fbbe-11e5-800d-42010a8e0008 touching the ground.]<br />
***The lamps are [http://xkcd.com/1663/#c75991f6-fbbe-11e5-8001-42010a8e0011 below the ground pointing down]. (In this case the one over the pond was not far enough down and a single water plant has formed anyway.)<br />
****On the other hand if the lamps are below the ground but pointing up it can result in growth well enough as shown in this [http://www.explainxkcd.com/wiki/images/7/7c/1663_garden_Different_light_from_below_the_ground.png example] and this [http://www.explainxkcd.com/wiki/images/3/3a/1663_garden_Yellow_light_from_below_the_ground.png example].<br />
**It was believed that if the lamps where very close to the ground pointing straight down there would be no growth.<br />
***However this can be because only a very small area is illuminated<br />
****In this [http://www.xkcd.com/1663/#9733dff4-fbbe-11e5-8001-42010a8e0012 example] there are turtles under the red light in the pond, plants under the yellow and octopus, column and Cueball under the blue (from the time that columns could appear under pure blue light).<br />
****Similar in this [http://xkcd.com/1663/#357a48d8-fbbf-11e5-8019-42010a8e0006 example] there are octopus (in the pond), deer/plants and a cactus from even lower lamps.<br />
****Of course the lamp has to be so high as not to be underground as mentioned above.<br />
**Also if lamps point towards the ground there can still only grow something from the ground [http://www.explainxkcd.com/wiki/images/3/3e/1663_garden_Two_light_on_small_area_nothing_outside_the_light.png where the light touches]. The growth can move outside the light cones up in the air, but the base has to be within an area with light.<br />
**Similar with items that can grow new things on top of them like tree trunks or platforms, this will only happen if light shines on the relevant places. <br />
***For instance the tall tree trunks can easily grow outside a light cone. Then leaves and branches will [http://www.explainxkcd.com/wiki/images/e/e9/1663_garden_One_color_Between_Light_yellow_and_yellow_3d.png only grow below] the point where the light hits<br />
****Similar with platform, that [http://www.explainxkcd.com/wiki/images/3/3e/1663_garden_One_color_Yellow_2d.png grows partially outside] the light cone. More items will only appear where this lamp still hits the platform.<br />
***One exemption to the rule mentioned here seems to be the bird raisers. The bird raisers are used to hold anything that flies up in the air. And the bird raiser it self needs to grow from either another bird riser or from a bird riser root (which in the end holds all bird raisers). This root has to have light on the ground to grow and thus have light on it self. But from the top of the bird raisers growing from such a root, items are able to grow even if the tip pf the bird raiser is not in the light. <br />
****Thus flying items can appear to grow where there has [http://www.explainxkcd.com/wiki/images/4/4f/1663_garden_One_color_Between_orange_and_orange_red_8d.png never been light]! <br />
****See much more about this under the description of bird raisers in the [[#Helper_structures|table below]].<br />
**Of course lights can be moved and changed without destroying what has already grown there (or so it seems). So a tended garden cannot be used to determine this.<br />
***This is why some [[1663:_Garden/Users_gardens#Locked_gardens_only_for_explanation_use|locked gardens]] have been set up where there will be no changes ever. <br />
***Examples from above has mainly been taken from screen shots of these locked gardens.<br />
<br />
===Grown items===<br />
*Grown items may be highlighted by clicking on them. Selected grown items will be highlighted with a red circle, and appear slightly lighter then other items.<br />
*Grown items may be "pruned" by the red X icon along the right of the window, or pressing the Delete key on the keyboard.<br />
*Some items (such as the large tree) can be deleted in minor parts by selecting a branch or smaller set of leaves without deleting the entire tree.<br />
*See the images (with links to xkcd) of all 250 items that can appear, here below in the [[#Items_in_the_garden|tables]].<br />
<br />
===Growth development===<br />
*'''After a few weeks''' growth no only seems to appear when the garden is actively running in a browser window (maybe only in the original users browser?)<br />
*There continued to appear new items that was not available on the release day.<br />
**This lasted about a week (maybe 8 days).<br />
**For instance many new items and animals like the columns and the owls started to appear after a few days.<br />
**Also tulips and lightning poles did not appear at first.<br />
***A last burst of new animals occurred about a week after release (either 11th or 12th of April). This burst included the following animals:<br />
***Herons, Wadding birds, Sharks fins, jumping fish and flying fish plus actual flying fish (flying without water), armadillos and no less than 12 different linsangs (see [[1663:_Garden#Linsang_-_cat_like_animal|Linsang - cat like animal]]).<br />
*But it also seems to change what might appear, so that the result of a particular color will change dramatically, not only by adding new, but also by not growing what used to be.<br />
**A clear example of this is that for the first half week pure blue light resulted in lots of octopuses all along the ground and also Cueballs cheeking for rain.<br />
**Later also columns appeared.<br />
***But after a week the growth rate under blue light almost stopped, and it seems that octopuses now only grow over the pond to the left, and much less Cueball and no columns under that color.<br />
**See details here: [[1663:_Garden/Screen-shots#Growth_speed_vs_blue_light|Growth speed vs blue light]].<br />
<br />
===Debug mode===<br />
{{notice|Anyone who can explain what the debug mode is, how it works, why it is there and why there is difference between the linden and the normal xkcd?}}<br />
*By changing the url address it is possible to get into a debug mode.<br />
**This may not work from for instance explorer, but seems to work from Firefox and chrome.<br />
*Normal mode: http://xkcd.com/1663/#ID <br />
**[http://xkcd.com/1663/#98dc3452-fcf2-11e5-8010-42010a8e0008 Normal mode example].<br />
*Debug mode works from this address http://xkcd.com/1663/?debug#ID<br />
*http://linden.xkcd.com/?debug#ID does not work anymore.<br />
**[http://linden.xkcd.com/?debug#98dc3452-fcf2-11e5-8010-42010a8e0008 Linden debug mode].<br />
**In this mode each item can clearly be seen as the image is framed, and thus invisible lifter images for flying things can be seen.<br />
***See this [http://linden.xkcd.com/?debug#d12a0932-faaa-11e5-8012-42010a8e0006 example].<br />
**This last mode can be used to find the names of the [[1663:_Garden/Images#Images|images of each item]] in a garden.<br />
***See this section on [[1663:_Garden/Images#How_to_find_new_links|How to find new links]].<br />
***By preventing the browser from loading specific images (''e.g.'' with an ad blocker), all instances can be pruned temporarily.<br />
*On the forum, [http://forums.xkcd.com/viewtopic.php?f=7&t=114415&start=600#p3959056 yan provides some jQuery] which can be entered in the javascript console to add an interactive sidebar listing the objects in the garden.<br />
<br />
===Limitations===<br />
*The beam produced by each lamp is normally restricted to spread between 0&deg; (which results in no growth) and 95&deg;. The "create new light" button chooses a random angle between 45&deg; and 90&deg;.<br />
*Attempting to view several gardens simultaneously may cause some to hang on the "loading" image, likely due to the server refusing additional connections. The maximum number which can load successfully is usually six, but may be as low as three.<br />
<br />
===Bugs===<br />
*There have been several bugs mentioned already after the first day. Please include any spotted here:<br />
**Also some problems that may now be fixed.<br />
*May not run on some tablets or smart phones (i.e. touch-screen only devices).<br />
*There are some browser versions of Chrome and Firefox where it doesn't run.<br />
*The lamps may be invisible for a few seconds after loading.<br />
*The whole page used to refresh at random intervals and lose the whole progress.<br />
**It still does on April 5th.<br />
**Sometimes (in some browsers?) the garden is reloaded when refreshing.<br />
***This may though be because of the url which is a [[#Saving garden with url|link to a given garden]].<br />
***See examples of this [[1663: Garden/Users gardens|here]].<br />
***Seems to be dependent on the browser type.<br />
*Some lamps jumped back to their starting position after a few minutes, without the whole page reloading.<br />
*For a few hours after its apparition, the loading didn't seem to stop for some people, making them think that the rotating tree was the whole joke, with people expected to "relax" while looking at it.<br />
*Occasionally invisible objects are added. They can be deleted, and they have bounding boxes in the [[#Debug mode|debugger]]: [http://linden.xkcd.com/?debug#d12a0932-faaa-11e5-8012-42010a8e0006 Example].<br />
*Doesn't work over https, you have to use http instead.<br />
*It is possible to save the image in Chrome and in Firefox, but not in Explorer.<br />
**It is possible to save the visible portion of the image (in any browser) by pressing the Print-Screen key to perform a screen capture.<br />
**But in Chrome the image is black where there is no light.<br />
**In Firefox everything is visible, wth the light cones (in color) shown.<br />
*Appears to have a memory leak at least in some Windows/Firefox versions, as keeping the page open for a long time will cause Windows to kill Firefox for insufficient memory.<br />
**On the forum, Weeks tries to summon davean! [http://forums.xkcd.com/viewtopic.php?f=7&t=114415&start=320#p3951923]<br />
*Does not work in many Linux versions.<br />
*Tree trunks will sometimes grow endlessly without leaves depending on the lights hitting them.<br />
*If you are dragging a light, the arrow, or the color slider when a refresh happens, the refresh will enter an infinite loop.<br />
**This seems to cause corruption of the garden because refreshing the whole page will result in a loop that never loads the page.<br />
**Clearing your local data for xkcd.com solves the issue but also makes you unable to edit your garden.<br />
*On April 6, gardens viewed from [http://xkcd.com/1663/#7877bdfc-fc03-11e5-8001-42010a8e000c http://xkcd.com/1663/] links began to include double-size objects, while they appeared <s>normally</s> with different objects enlarged when viewed from [http://linden.xkcd.com/#7877bdfc-fc03-11e5-8001-42010a8e000c http://linden.xkcd.com/].<br />
**Apparently some of the server's art files were <s>misdirected to the larger versions</s> replaced with new large images. [https://web.archive.org/web/20160407054439/http://linden.xkcd.com/art/rover.png] [http://linden.xkcd.com/art/2x-rover.png]<br />
**New giant objects are still placed according to their original sizes. [http://forums.xkcd.com/viewtopic.php?f=7&t=114415&start=320#p3951908]<br />
**This was suddenly fixed on April 7, possibly inducing browser memory issues at that time. [http://forums.xkcd.com/viewtopic.php?f=7&t=114415&start=360#p3952207]<br />
***However, some giant images remained cached (where?) for a long time. [http://forums.xkcd.com/viewtopic.php?f=7&t=114415&start=400#p3952527]<br />
*Although there are six bee images, they have not been reported in any gardens[[File:Garden_Bee_1.png]]<br />
<br />
==Trivia==<br />
*There are three different title text in this comic, as there are also one over each of the two icons. <br />
**This is special as with some of the newest "game like comics" there are [[:Category:No title text|no title text]]!<br />
**The normal one "Relax" is mentioned above in the main explanation.<br />
**The other two are explanations for what the two icons in the top right corner does and appear when the cursor hovers over them.<br />
***They are ''Create new light'' explaining that this icon introduces new lamps and<br />
***''Remove selected (delete key)'', which explain that this icon can be used to remove (delete) selected items like lamps, plants or items. It also explains that the delete key can be used instead of the icon.<br />
<br />
===Linsang - cat like animal===<br />
*In the second week of release no less than 12 [http://www.explainxkcd.com/wiki/images/3/38/Garden_Linsang_1.png images] of the animal called {{w|linsang}} appeared [http://www.explainxkcd.com/wiki/images/1/1d/1663_garden_My_first_linsang_cat_like_creature_in_SC.png in the garden].<br />
**See all of them [[1663:_Garden/Images#Images|here]].<br />
*This animal was referenced in ''[[Thing Explainer]]'' in ''Tree of life'' where the animal is drawn in the ''cat-shaped'' section with the following caption:<br />
::'''Almost cat'''<br />
::This animal looks like a cat with a long neck. It's the closest thing to a cat that's not actually in the cat family.<br />
::*Next to the section another one is drawn in front of Cueball (obvsiously it's Randall).<br />
::*The linsang says "Mrowl?" and Cueball says "I wan't one!"<br />
*Randall has in an interview discussed these [http://www.wsj.com/articles/randall-munroe-creator-of-xkcd-on-google-search-tricks-and-cat-like-creature-videos-1447945313 Cat-Like-Creatures] and in is quoted for saying<br />
::Q: '''An animal I’m obsessed with is:'''<br />
::A: The linsang, which looks almost like a cat but has this weird long neck. I find them both unnerving and adorable. I found some footage of one running; it’s like watching a cat video from a parallel universe.<br />
::*The linsang is related to the animal {{w|Genet (animal)|genet}}, and here are two videos/photos of a genet running:<br />
::**[https://www.youtube.com/watch?v=mRdJSVlPrGo Genet on a rhino]<br />
::**[https://www.youtube.com/watch?v=Ehq3ssg7zwk Genet on other things]<br />
<br />
===Monday 4th of April release===<br />
*Due to technical problems (or to make [[#April Fool's header text|fools of his fans?]]) the comic did not go live until Sunday evening (after midnight, so technically first on '''Monday April 4th''').<br />
**There was thus no Friday release in the week before<br />
**So the Wednesday comic [[1662: Jack and Jill]] got a lot more attention than it would usually have had. <br />
*This comic thus turned in to the Monday release instead, as no other comic was released later that Monday, as this would have taken attention away from this very special comic.<br />
**But it was called the ''April 1st comic'' and later the ''Friday comic'' in the [[#April Fool's header text|header text]] displayed at the top of xkcd to explain why there was no Friday comic. <br />
***A header text continued to stay a the top but changed two more times until the release past midnight Sunday in the US. It was even past midnight {{w|Pacific Time}}, but not yet on Hawaii.<br />
**There were thus only two comics released in the week before this Monday, which may be the first time since xkcd went live on {{xkcd||xkcd.com}} in 2006.<br />
<br />
===April Fool's header text===<br />
*There is some debate as to whether this comic is an April Fool's comic or not.<br />
**Was instead the April fool's joke the text written above the comic in the header of xkcd?<br />
**There is reason to believe this was [[#April Fool's comic|not the case]] based on among other thing these header text.<br />
*Below it a list of the different header text displayed from Friday until the comic was just released.<br />
**The header text continued to change regularly [[#Header text after release|after release]] in regard to this comic at least until next Friday (April 8th).<br />
**Here below is the different header text with info on when it appeared.<br />
***Links are given when possible to a [[1663:_Garden/Screen-shots#Screen-shots_of_header_text|screen shots]] on the word ''message'' and to a webarchive in another link when both are available.<br />
*On Friday, April 1st, 2016, the xkcd website changed to a new [http://www.explainxkcd.com/wiki/images/8/81/1663_garden_April_1st_comic_is_currently_experiencing_technical_difficulties.png message] where the standard message "XKCD updates every Monday, Wednesday, and Friday." usually is. (This [http://www.explainxkcd.com/wiki/images/6/69/1663_garden_Commercial_header_text_before_April_1st_problems.png message] had, however, up to this point and for a long time been a [http://web.archive.org/web/20160401175527/https://www.xkcd.com/ commercial] for ''[[Thing Explainer]]''). But now it [http://web.archive.org/web/20160401204749/https://xkcd.com/ began displaying] this instead:<br />
::The xkcd April 1st comic is currently experiencing technical difficulties. <br />
::Please stand by!<br />
*Early Saturday April 2nd the [http://www.explainxkcd.com/wiki/images/e/e0/1663_garden_Calendar_systems_in_which_Saturday_is_April_1st.png message] was [http://web.archive.org/web/20160402050932/http://xkcd.com updated]:<br />
::The xkcd April 1st comic is currently experiencing technical difficulties.<br />
::Status update: Please stand by.<br />
::Status update: This is fine. Everything is fine.<br />
::Status update: Everything is on fire.<br />
::Status update: Searching for calendar systems in which Saturday is April 1st.<br />
*Later on Saturday the [http://www.explainxkcd.com/wiki/images/0/06/1663_garden_Delayed_until_Sunday_night.png message] was again [http://web.archive.org/web/20160402175822/http://www.xkcd.com changed] to:<br />
::The Friday xkcd comic is currently experiencing technical difficulties<br />
::[Editor's note: Everything is on fire] and has been delayed until Sunday night.<br />
*The comic did not come out until past midnight in the entire North America (coming out just before midnight in Hawaii).<br />
*It was finally released very early on Monday April 4th, and the [http://www.explainxkcd.com/wiki/images/5/53/Garden_Loading_screen_shot.png message] then [http://web.archive.org/web/20160404123555/http://xkcd.com/ returned] to the old standard text for xkcd for a short while:<br />
::XKCD updates every Monday, Wednesday, and Friday.<br />
<br />
===Header text after release===<br />
*During April 4th, after the release the message changed from the old standard to display a [[:Category:Protip|Protip]]:<br />
::'''Protip:''' If you don't like how your garden is growing, you can click to prune it.<br />
*And then later on April 4th, the [http://www.explainxkcd.com/wiki/images/a/a2/1663_garden_Protip_and_url_hint.png message] was again [http://web.archive.org/web/20160404185353/http://www.xkcd.com/#5dbfbb82-fc20-11e5-8001-42010a8e000d changed] to:<br />
::'''Protip:''' If you don't like how your garden is growing, you can click to prune it.<br />
::You can copy the URL to share your garden. From other browsers, it will be view-only.<br />
*When the next comic came out, the [http://www.explainxkcd.com/wiki/images/6/61/1663_garden_Note_if_seeing_todays_comic.png message] then [http://web.archive.org/web/20160408105110/http://xkcd.com/1663/#4b04323a-fddc-11e5-8001-42010a8e0016 changed], (also for the [http://web.archive.org/web/20160406194653/http://xkcd.com/1664/ new comic]) to<br />
::'''Protip:''' If you don't like how your garden is growing, you can click to prune it.<br />
::You can copy the URL to share your garden. From other browsers, it will be view-only.<br />
<br><br />
::Note: If you're seeing today's comic in place of your garden, change the URL from xkcd.com/#<your code> to xkcd.com/1663/#<your code>.<br />
*[http://web.archive.org/web/20160408145017/http://xkcd.com/ After] the Friday comic came out on April 8th, the [http://www.explainxkcd.com/wiki/images/c/c5/1663_garden_Back_to_pro_tips_only_after_Friday_comic.png message] then [http://web.archive.org/web/20160408195958/http://xkcd.com/ changed] back to<br />
::'''Protip:''' If you don't like how your garden is growing, you can click to prune it.<br />
::You can copy the URL to share your garden. From other browsers, it will be view-only.<br />
*The [http://www.explainxkcd.com/wiki/images/c/c6/1663_garden_Still_pro_tip_on_Friday_22nd_comic.png message stayed] like the one above at least until Friday April 22th before that Friday's comic [http://web.archive.org/web/20160422102754/http://xkcd.com/ was released]. But either at the time of release or at least on Saturday the day after the release the [http://www.explainxkcd.com/wiki/images/a/ae/1663_garden_Back_to_normal_text_after_Friday_22nd_comic.png message returned] to [http://web.archive.org/web/20160423103108/http://xkcd.com/ the original].<br />
::XKCD updates every Monday, Wednesday, and Friday.<br />
:*The pro tip, however, remained as [http://web.archive.org/web/20160425022201/https://www.xkcd.com/1663/ the header text] when displaying the {{xkcd|1663|Garden comic}}.<br />
<br />
===April Fool's comic===<br />
*This comic '''was indeed supposed to be''' the Friday 1st of April, April Fool's comic!<br />
**This statement is based on several things, which can can be deduced from the above header text and the subsequent issues with the many [[#Bugs|bugs in this comic]].<br />
*It is clear that this comic did actually come out as promised, at least as promised in the third message about release on Sunday night.<br />
**It is also clear that it is regarded as the Friday comic, even in the last update before the release, which was two days after April 1st.<br />
*It is also clear that this was a very complex comic, and it is realistic that Randall did have problems with making it work. <br />
**On day two there still seemed to be several minor bugs, which seemed to improve over time so Randall was still working on it after release.<br />
***But then new bugs appeared when the next comic was released.<br />
*Both of the last two April Fool's comics, [[1350: Lorenz]] and [[1506: xkcloud]], have had no real meaning or joke in the comic. The jokes appeared from user input, and here it comes from waiting.<br />
**This makes people who spend too much time on these comics ''April Fool's'' (or if they rather wish to be called a ''nerds'' than fools, then they can claim to have been a victim of [[356: Nerd Sniping|nerd sniping]]).<br />
**So, even if Randall ''did'' play a joke on people who [[Talk:1662: Jack and Jill#What happened to Friday's comic|eagerly awaited the comic]], then he did deliver as promised a spectacular comic Sunday night.<br />
*There are several reasons to believe that Randall would have preferred the comic to get out on Friday April 1st.<br />
**Apart from it being a time consuming comic that in it self is April Fool's comic material, then by getting it out Friday this special comic, which he obviously have used a lot of time to prepare, would have had one more day as the first comic.<br />
**Getting it out before a weekend would have let many more users spend time looking at their garden. Now many would not spend enough time to appreciate the comic, as it came out right when the new work week began.<br />
***And it is a very complicated comic that just to get to understand how to really use it could take a days time even for someone with time.<br />
***And this is not talking about how the comic works, but just how to use the program, i.e. the whole [[#Functionality|functionality]] of the comic is way more complex than even a game like [[1608: Hoverboard]].<br />
**And before next weekend two more comics were released taking some of the focus away from this one too soon, and also before the next weekend. <br />
***Of course die hard fans will not forget this one, but many xkcd fans may only come by in the weekend etc. and such a hard to come by comic like this, that demands patience and that you return does not profit from being bumped down to number three as it would be next Friday.<br />
*Randall lives of his fans goodwill and to deliberately make a pun on them like this would probably not seem like a good business proposal, apart from the fact that the comic now gets less attention than by coming out before the weekend.<br />
<br />
==Items in the garden==<br />
*Below in the section are several tables displaying all the known images of items that may grow (appear) in the garden. <br />
**They have been sorted based on type like characters, animals (by type), plants (by type), platforms, others and helper structures.<br />
**In time each item will have a link to a screen shot where they appear.<br />
**Also explanations for each item can be written in these tables<br />
*For colors reference refer (also) to the numbers in this image:<br><br />
*[[File:1663 garden Numbered color scale 1-17.png]]<br />
**The color under which a given item may grow should be noted. <br />
***Particularly if they can grow under just one color if light (maybe a range, but with only one lamp lit as one specific color). <br />
***But almost more important if some items needs more than one color<br />
****Especially if the items base, the base on which they have to grow, needs another color than they do, as seems to be the case with flower blooms and the lamp to go at the top of the lamp poles.<br />
*All the images can be seen without the table here: [[1663: Garden/Images|Images of items]].<br />
===Characters===<br />
{| class="wikitable collapsible collapsed" |<br />
! To see/hide images click here:<br />
! Description of images<br />
! Relevant colors<br />
! Link to screen-shots<br />
|-<br />
! [[Cueball]]<br>[[File:Garden Man 1a.png]]&nbsp;[http://xkcd.com/1663/art/2x-man-1a.png Man 1a]<br><br />
[[File:Garden Man 2a.png]]&nbsp;[http://xkcd.com/1663/art/2x-man-2a.png Man 2a]<br />
| <br />
*Here are the two different images of Cueball.<br />
*The first Cueball just stands with his hands down. <br />
**In this position he always looks left.<br />
**Some items can grow on his head, most obviously [http://www.explainxkcd.com/wiki/images/2/27/1663_garden_One_color_Between_blue_and_light_blue_6d.png the hat], turning him into [[Black Hat]]. But also animals like the [http://www.explainxkcd.com/wiki/images/9/92/1663_garden_Blitz_Girls_UFO_and_birds_garden.png water bird], [http://www.explainxkcd.com/wiki/images/3/32/1663_garden_One_color_Between_Blue_White_and_White_6d.png standing bird or cats] and [http://www.explainxkcd.com/wiki/images/d/d4/1663_garden_Crazy_cat_peoples_garden.png owls] can perch on his head. <br />
**He never seems to appears in pure blue light, and also only appears when the light is turned left of white.<br />
*The second Cueball has one hand out.<br />
**In this position he always looks right.<br />
**He is the only character that appears under pure blue light (color 1).<br />
**It seems like he cannot wear the hat or anything else on his head.<br />
**In stead he can hold object on his hand, like a [http://www.explainxkcd.com/wiki/images/1/1e/1663_garden_S_shaped_empty_balloon_string_left.png balloon string] (later [http://www.explainxkcd.com/wiki/images/0/0e/1663_garden_Office_space_with_two_herons_in_lake_and_huge_balloon_on_long_string.png with balloon] or the [http://www.explainxkcd.com/wiki/images/c/c2/1663_garden_Blitz_Girls_strong_Megan_garden.png huge balloon]), the [http://www.explainxkcd.com/wiki/images/e/e5/1663_garden_Blitz_Girls_Armadillo_tower.png small platform] or some of the smaller animals like [http://www.explainxkcd.com/wiki/images/3/32/1663_garden_One_color_Between_Blue_White_and_White_6d.png the bird], the [http://www.explainxkcd.com/wiki/images/0/09/1663_garden_Cueball_holds_a_Turtle_in_front_of_Megan_looking_like_a_cap_on_her.png turtle], or [http://www.explainxkcd.com/wiki/images/d/d4/1663_garden_Crazy_cat_peoples_garden.png cat and owls].<br />
| <br />
*Standing Cueball with color [http://www.explainxkcd.com/wiki/images/9/92/1663_garden_One_color_Between_blue_and_light_blue_2d.png 2 blue], [http://www.explainxkcd.com/wiki/images/c/c9/1663_garden_One_color_Light_blue_12h.png 3 light blue], [http://www.explainxkcd.com/wiki/images/e/e4/1663_garden_Color_04_2_5d.png 4 light blue] and [http://www.explainxkcd.com/wiki/images/b/b2/1663_garden_One_color_Blue_white_2d.png 5 Blue white]<br />
*Hand out Cueball with color [http://www.explainxkcd.com/wiki/images/b/bf/1663_garden_One_color_Blue_6d.png 1 blue], [http://www.explainxkcd.com/wiki/images/9/92/1663_garden_One_color_Between_blue_and_light_blue_2d.png 2 blue], [http://www.explainxkcd.com/wiki/images/a/a6/1663_garden_Color_03_5d.png 3 light blue], [http://www.explainxkcd.com/wiki/images/5/5e/1663_garden_One_color_Between_light_blue_and_Blue_White_6d.png 4 light blue] and [http://www.explainxkcd.com/wiki/images/d/d1/1663_garden_One_color_White_Blue_12h.png 5 Blue white]<br />
| [http://www.explainxkcd.com/wiki/images/c/c9/1663_garden_One_color_Light_blue_12h.png Standing]<br />
[http://www.explainxkcd.com/wiki/images/e/e5/1663_garden_One_color_Blue_18h.png Hand out]<br><br />
|-<br />
! [[Megan]]<br>[[File:Garden Woman 1a.png]]&nbsp;[http://xkcd.com/1663/art/2x-woman-1a.png Woman 1a]<br>[[File:Garden Handfig 1.png]]&nbsp;[http://xkcd.com/1663/art/2x-handfig-1.png Handfig 1]<br><br />
[[File:Garden Handfig 2.png]]&nbsp;[http://xkcd.com/1663/art/2x-handfig-2.png Handfig 2]<br>[[File:Garden Sword fig.png]]&nbsp;[http://xkcd.com/1663/art/2x-sword-fig.png Sword fig]<br>[[File:Garden Flying fig.png]]&nbsp;[http://xkcd.com/1663/art/2x-flying-fig.png Flying fig]<br />
|<br />
*Here are the images of Megan. <br />
**Megan with sword seems to only occur on top of a platform or a piece of furniture. <br />
***She seem to not be willing to pull out the sword when just standing on the ground.<br />
***This means that she can only occur under a one color setting if that setting can also produce a platform. This is the case though see the color column.<br />
| <br />
*Standing (Yellow 9 standard)<br />
*Hands up (L and R) (White 7)<br />
*Sword ([http://www.explainxkcd.com/wiki/images/9/9c/1663_garden_One_color_Light_yellow_9d.png Yellow 9 standard] and [http://www.explainxkcd.com/wiki/images/6/6d/1663_garden_One_color_Between_Light_yellow_and_yellow_2d.png Yellow 10])<br />
*Flying (Orange 15)<br />
| [http://www.explainxkcd.com/wiki/images/c/cb/1663_garden_One_color_Light_yellow_12h.png Standing ]<br><br />
[http://www.explainxkcd.com/wiki/images/9/99/1663_garden_One_color_White_12h.png Hands up]<br><br />
[http://www.explainxkcd.com/wiki/images/6/6b/1663_garden_Megan_with_sword%2C_trees_octopuses_with_Cueball_bunny_ducklings.png Sword-tree platform]<br> [http://www.explainxkcd.com/wiki/images/c/cb/1663_garden_Megan_with_sword_and_owl_on_gate.png Sword-gate]<br> [http://www.explainxkcd.com/wiki/images/1/1d/1663_garden_My_first_linsang_cat_like_creature_in_SC.png Sword-desk] <br> <br />
[http://www.explainxkcd.com/wiki/images/8/87/1663_garden_One_color_Orange_d7.png Flying]<br />
|-<br />
! [[Beret Guy]]<br>[[File:Garden Beret shrub.png]]&nbsp;[http://xkcd.com/1663/art/2x-beret-shrub.png Beret shrub]<br />
|<br />
*Here is the image of Beret Guy.<br />
| White 7 or mix of yellow and blue<br />
| [http://www.explainxkcd.com/wiki/images/9/99/1663_garden_One_color_White_12h.png In lake]<br><br />
[http://www.explainxkcd.com/wiki/images/2/24/1663_garden_Shark_finn_and_Beret_Guy_in_same_bird_bath_fish_boat_heron_and_more.png In birdbath]<br><br />
[http://www.explainxkcd.com/wiki/images/9/9b/1663_garden_Three_colors_more_separate_Beret_Guy_in_shrubbery_and_Octopus_on_office_desk.png In shrub]<br />
|-<br />
! [[Ponytail]]<br>[[File:Garden Fig 1.png]]&nbsp;[http://xkcd.com/1663/art/2x-fig-1.png Fig 1]<br />
|<br />
*Here are the images of Ponytail.<br />
| Color?<br />
| [http://www.explainxkcd.com/wiki/images/e/eb/1663_garden_Ponytail_and_two_Cueballs_cat_pillar_and_trunk_sE.png Example]<br />
|-<br />
! Stilt girl<br>[[File:Garden Stilt walker.png]]&nbsp;[http://xkcd.com/1663/art/2x-stiltwalker.png Stilt walker]<br />
|<br />
*Here is the image of the girl on stilts.<br />
| Light yellow 10<br />
| [http://www.explainxkcd.com/wiki/images/1/1b/1663_garden_One_color_Between_Light_yellow_and_yellow_First_thing_stilts_right.png Example]<br />
|}<br />
<br />
===Animals===<br />
====Mammals====<br />
{| class="wikitable collapsible collapsed" |<br />
! To see/hide images click here:<br />
! Description of images<br />
! Relevant colors<br />
! Link to screen-shots<br />
|-<br />
! Armadillo<br>[[File:Garden Armadillo L.png]]&nbsp;[http://linden.xkcd.com/art/2x-armadillo-l.png Armadillo L]<br><br />
[[File:Garden Armadillo R.png]]&nbsp;[http://linden.xkcd.com/art/2x-armadillo-r.png Armadillo R]<br />
|<br />
*Here are the images of Armadillo.<br />
| Color: Combination of 17 and 9<br />
| [ Example]<br />
|-<br />
! Cats<br>[[File:Garden Cat Balanced.png]]&nbsp;[http://xkcd.com/1663/art/2x-cat-balanced.png Cat Balanced]<br><br />
[[File:Garden Cat Ground.png]]&nbsp;[http://xkcd.com/1663/art/2x-cat-ground.png Cat Ground]<br />
|<br />
*Here are the images of cats.<br />
| Color?<br />
| [ Example]<br />
|-<br />
! Deer<br>[[File:Garden Deer 1.png]]&nbsp;[http://xkcd.com/1663/art/2x-deer-1.png Deer 1]<br><br />
[[File:Garden Deer 2.png]]&nbsp;[http://xkcd.com/1663/art/2x-deer-2.png Deer 2]<br />
|<br />
*Here are the images of Deer.<br />
| Color?<br />
| [ Example]<br />
|-<br />
! Bunny<br>[[File:Garden Important bun.png]]&nbsp;[http://xkcd.com/1663/art/2x-important-bun.png Important bun]<br />
|<br />
*Here is the image of the Bunny.<br />
| Color?<br />
| [ Example]<br />
|-<br />
! Linsang<br>[[File:Garden Linsang 1.png]]&nbsp;[http://linden.xkcd.com/art/2x-linsang-1.png Linsang 1]<br><br />
[[File:Garden Linsang 2.png]]&nbsp;[http://linden.xkcd.com/art/2x-linsang-2.png Linsang 2]<br><br />
[[File:Garden Linsang 3.png]]&nbsp;[http://linden.xkcd.com/art/2x-linsang-3.png Linsang 3]<br><br />
[[File:Garden Linsang 4.png]]&nbsp;[http://linden.xkcd.com/art/2x-linsang-4.png Linsang 4]<br><br />
[[File:Garden Linsang 5.png]]&nbsp;[http://linden.xkcd.com/art/2x-linsang-5.png Linsang 5]<br><br />
[[File:Garden Linsang 6.png]]&nbsp;[http://linden.xkcd.com/art/2x-linsang-6.png Linsang 6]<br><br />
[[File:Garden Linsang 7.png]]&nbsp;[http://linden.xkcd.com/art/2x-linsang-7.png Linsang 7]<br><br />
[[File:Garden Linsang 8.png]]&nbsp;[http://linden.xkcd.com/art/2x-linsang-8.png Linsang 8]<br><br />
[[File:Garden Linsang 9.png]]&nbsp;[http://linden.xkcd.com/art/2x-linsang-9.png Linsang 9]<br><br />
[[File:Garden Linsang 10.png]]&nbsp;[http://linden.xkcd.com/art/2x-linsang-10.png Linsang 10]<br><br />
[[File:Garden Linsang 11.png]]&nbsp;[http://linden.xkcd.com/art/2x-linsang-11.png Linsang 11]<br><br />
[[File:Garden Linsang 12.png]]&nbsp;[http://linden.xkcd.com/art/2x-linsang-12.png Linsang 12]<br />
|<br />
*Here are the images of linsangs.<br />
**See more about [[#Linsang - cat like animal|Linsang - cat like animal]] in the trivia section.<br />
| Color?<br />
| [http://www.explainxkcd.com/wiki/images/6/68/1663_Garden_Ophiocordyceps_linsang.png Linsang infected by fungus]<br />
|}<br />
<br />
====Birds====<br />
{| class="wikitable collapsible collapsed" |<br />
! To see/hide images click here:<br />
! Description of images<br />
! Relevant colors<br />
! Link to screen-shots<br />
|-<br />
! Flying birds<br>[[File:Garden Bird 1.png]]&nbsp;[http://xkcd.com/1663/art/2x-bird-1.png Bird 1]<br><br />
[[File:Garden Bird 2.png]]&nbsp;[http://xkcd.com/1663/art/2x-bird-2.png Bird 2]<br><br />
[[File:Garden Bird 3.png]]&nbsp;[http://xkcd.com/1663/art/2x-bird-3.png Bird 3]<br><br />
[[File:Garden Bird 4.png]]&nbsp;[http://xkcd.com/1663/art/2x-bird-4.png Bird 4]<br><br />
[[File:Garden Bird 5.png]]&nbsp;[http://xkcd.com/1663/art/2x-bird-5.png Bird 5]<br />
|<br />
*Here are the images of flying birds.<br />
| Color?<br />
| [ Example]<br />
|-<br />
! Standing bird<br>[[File:Garden Bird standing.png]]&nbsp;[http://xkcd.com/1663/art/2x-bird-standing.png Bird standing]<br />
|<br />
*Here are the images of Standing bird.<br />
| Color?<br />
| [ Example]<br />
|-<br />
! Duck <br>[[File:Garden Duck 1.png]]&nbsp;[http://xkcd.com/1663/art/2x-duck-1.png Duck 1]<br />
|<br />
*Here is the image of the duck.<br />
| Color?<br />
| [ Example]<br />
|-<br />
! Heron<br>[[File:Garden Heron L.png]]&nbsp;[http://linden.xkcd.com/art/2x-heron-l.png Heron L]<br><br />
[[File:Garden Heron R.png]]&nbsp;[http://linden.xkcd.com/art/2x-heron-r.png Heron R]<br />
|<br />
*Here are the images of Herons.<br />
| Color?<br />
| [ Example]<br />
|-<br />
! Owl<br>[[File:Garden Owl.png]]&nbsp;[http://xkcd.com/1663/art/2x-owl.png Owl]<br />
|<br />
*Here is the image of the Owl.<br />
| Color?<br />
| [ Example]<br />
|-<br />
! Wading bird<br>[[File:Garden Wading bird L.png]]&nbsp;[http://linden.xkcd.com/art/2x-wading-bird-l.png Wading bird L]<br><br />
[[File:Garden Wading bird R.png]]&nbsp;[http://linden.xkcd.com/art/2x-wading-bird-r.png Wading bird R]<br />
|<br />
*Here are the images of wading birds.<br />
| Color?<br />
| [ Example]<br />
|-<br />
! Water bird<br>[[File:Garden Water bird 1.png]]&nbsp;[http://xkcd.com/1663/art/2x-waterbird-1.png Water bird 1]<br><br />
[[File:Garden Water bird 2.png]]&nbsp;[http://xkcd.com/1663/art/2x-waterbird-2.png Water bird 2]<br />
|<br />
*Here are the images of water bird.<br />
| Color?<br />
| [ Example]<br />
|}<br />
<br />
====From the sea====<br />
{| class="wikitable collapsible collapsed" |<br />
! To see/hide images click here:<br />
! Description of images<br />
! Relevant colors<br />
! Link to screen-shots<br />
|-<br />
! Fish <br>[[File:Garden Fish 1.png]]&nbsp;[http://linden.xkcd.com/art/2x-fish-1.png Fish 1]<br><br />
[[File:Garden Fish 2.png]]&nbsp;[http://linden.xkcd.com/art/2x-fish-2.png Fish 2]<br />
|<br />
*Here are the images of Fish.<br />
| Color?<br />
| [ Example]<br />
|-<br />
! Flying fish<br>[[File:Flying fish 1.png]]&nbsp;[http://xkcd.com/1663/art/2x-flying-fish-1.png Flying fish 1]<br><br />
[[File:Flying fish 2.png]]&nbsp;[http://xkcd.com/1663/art/2x-flying-fish-2.png Flying fish 2]<br><br />
[[File:Garden Actual flying fish 1.png]]&nbsp;[http://linden.xkcd.com/art/2x-actual-flying-fish-1.png Actual flying fish 1]<br><br />
[[File:Garden Actual flying fish 2.png]]&nbsp;[http://linden.xkcd.com/art/2x-actual-flying-fish-2.png Actual flying fish 2]<br />
|<br />
*Here are the images of Flying fish.<br />
| Color?<br />
| [http://forums.xkcd.com/download/file.php?id=51476&mode=view Flying fish in Megan's hair] [http://forums.xkcd.com/download/file.php?id=51543&mode=view Flying fish and UGO]<br />
|-<br />
! Octopus<br>[[File:Garden Octopus.png]]&nbsp;[http://xkcd.com/1663/art/2x-octopus.png Octopus]<br><br />
[[File:Garden Octopus hat capable.png]]&nbsp;[http://xkcd.com/1663/art/2x-octopus-hat-capable.png Octopus hat capable]<br />
|<br />
*Here are the images of Octopuses.<br />
| Color: Blue (Only On the Pond)<br />
| [ Example]<br />
|-<br />
! Sharks<br>[[File:Garden Shark fin L.png]]&nbsp;[http://linden.xkcd.com/art/2x-shark-fin-l.png Shark fin L]<br><br />
[[File:Garden Shark fin R.png]]&nbsp;[http://linden.xkcd.com/art/2x-shark-fin-r.png Shark fin R]<br />
|<br />
*Here is the image of the shark fins.<br />
| Color?<br />
| [http://www.explainxkcd.com/wiki/images/6/6e/1663_Garden_Megan_there%27s_a_shark_in_the_water.png Shark in birdbath]<br />
|-<br />
! Tentacle<br>[[File:Garden Tentacle 1.png]]&nbsp;[http://xkcd.com/1663/art/2x-tentacle-1.png Tentacle 1]<br><br />
[[File:Garden Tentacle 2.png]]&nbsp;[http://xkcd.com/1663/art/2x-tentacle-2.png Tentacle 2]<br><br />
[[File:Garden Tentacle 3.png]]&nbsp;[http://xkcd.com/1663/art/2x-tentacle-3.png Tentacle 3]<br><br />
[[File:Garden Tentacle 4.png]]&nbsp;[http://xkcd.com/1663/art/2x-tentacle-4.png Tentacle 4]<br><br />
[[File:Garden Tentacle 5.png]]&nbsp;[http://xkcd.com/1663/art/2x-tentacle-5.png Tentacle 5]<br><br />
[[File:Garden Tentacle 6.png]]&nbsp;[http://xkcd.com/1663/art/2x-tentacle-6.png Tentacle 6]<br />
|<br />
*Here are the images of tentacles.<br />
| Color?<br />
| [ Example]<br />
|}<br />
<br />
====Reptiles====<br />
{| class="wikitable collapsible collapsed" |<br />
! To see/hide images click here:<br />
! Description of images<br />
! Relevant colors<br />
! Link to screen-shots<br />
|-<br />
! Snake<br>[[File:Garden Snake 1.png]]&nbsp;[http://xkcd.com/1663/art/2x-snake-1.png Snake 1]<br><br />
[[File:Garden Snake 2.png]]&nbsp;[http://xkcd.com/1663/art/2x-snake-2.png Snake 2]<br />
|<br />
*Here are the images of snakes.<br />
| Color?<br />
| [ Example]<br />
|-<br />
! Turtle<br>[[File:Garden Turtle 1.png]]&nbsp;[http://xkcd.com/1663/art/2x-turtle-1.png Turtle 1]<br><br />
[[File:Garden Turtle 2.png]]&nbsp;[http://xkcd.com/1663/art/2x-turtle-2.png Turtle 2]<br />
|<br />
*Here are the images of turtles.<br />
| Color reddish?<br />
| [http://www.explainxkcd.com/wiki/images/6/6c/1663_Garden_octopus_turtle_capable.png Octopus turtle capable]<br />
|}<br />
<br />
====Insects====<br />
{| class="wikitable collapsible collapsed" |<br />
! To see/hide images click here:<br />
! Description of images<br />
! Relevant colors<br />
! Link to screen-shots<br />
|-<br />
! Bees<br>[[File:Garden Bee 1.png]]&nbsp;[http://xkcd.com/1663/art/2x-bee-1.png Bee 1]<br><br />
[[File:Garden Bee 2.png]]&nbsp;[http://xkcd.com/1663/art/2x-bee-2.png Bee 2]<br><br />
[[File:Garden Bee 3.png]]&nbsp;[http://xkcd.com/1663/art/2x-bee-3.png Bee 3]<br><br />
[[File:Garden Bee 4.png]]&nbsp;[http://xkcd.com/1663/art/2x-bee-4.png Bee 4]<br><br />
[[File:Garden Bee 5.png]]&nbsp;[http://xkcd.com/1663/art/2x-bee-5.png Bee 5]<br><br />
[[File:Garden Bee 6.png]]&nbsp;[http://xkcd.com/1663/art/2x-bee-6.png Bee 6]<br />
|<br />
*Here are the images of bees.<br />
| Color?<br />
| [ Example]<br />
|-<br />
! Beehive<br><br />
[[File:Garden Beehive-base.png]]&nbsp;[http://xkcd.com/1663/art/2x-beehive-base.png Beehive-base]<br><br />
[[File:Garden Beehive entrance a.png]]&nbsp;[http://xkcd.com/1663/art/2x-beehive-entrance-a.png Beehive entrance a]<br><br />
[[File:Beehive section.png]]&nbsp;[http://xkcd.com/1663/art/2x-beehive-section.png Beehive section]<br />
|<br />
*Here are the images that construct the beehive.<br />
| Color?<br />
| [http://forums.xkcd.com/download/file.php?id=51487&mode=view BlitzGirl's beehive]<br />
|}<br />
<br />
===Plants===<br />
====Trees====<br />
{| class="wikitable collapsible collapsed" |<br />
! To see/hide images click here:<br />
! Description of images<br />
! Relevant colors<br />
! Link to screen-shots<br />
|-<br />
! Tall trunks<br>[[File:Garden Tall trunk 1.png]]&nbsp;[http://xkcd.com/1663/art/2x-talltrunk-1.png Tall trunk 1]<br><br />
[[File:Garden Tall trunk 2.png]]&nbsp;[http://xkcd.com/1663/art/2x-talltrunk-2.png Tall trunk 2]<br><br />
[[File:Garden Tall trunk 3.png]]&nbsp;[http://xkcd.com/1663/art/2x-talltrunk-3.png Tall trunk 3]<br><br />
[[File:Garden Tall trunk 4.png]]&nbsp;[http://xkcd.com/1663/art/2x-talltrunk-4.png Tall trunk 4]<br />
|<br />
*Here are the images of tall trunks.<br />
| Color?<br />
| [ Example]<br />
|-<br />
! Trunks<br>[[File:Garden Trunk 1.png]]&nbsp;[http://xkcd.com/1663/art/2x-trunk-1.png Trunk 1]<br><br />
[[File:Garden Trunk 2.png]]&nbsp;[http://xkcd.com/1663/art/2x-trunk-2.png Trunk 2]<br><br />
[[File:Garden Trunk 3.png]]&nbsp;[http://xkcd.com/1663/art/2x-trunk-3.png Trunk 3]<br><br />
[[File:Garden Trunk 4.png]]&nbsp;[http://xkcd.com/1663/art/2x-trunk-4.png Trunk 4]<br><br />
[[File:Garden Trunk 5.png]]&nbsp;[http://xkcd.com/1663/art/2x-trunk-5.png Trunk 5]<br><br />
[[File:Garden Trunk 6.png]]&nbsp;[http://xkcd.com/1663/art/2x-trunk-6.png Trunk 6]<br><br />
[[File:Garden Trunk 7.png]]&nbsp;[http://xkcd.com/1663/art/2x-trunk-7.png Trunk 7]<br><br />
[[File:Garden Trunk 8.png]]&nbsp;[http://xkcd.com/1663/art/2x-trunk-8.png Trunk 8]<br />
|<br />
*Here are the images of smaller trunks.<br />
| Color?<br />
| [ Example]<br />
|-<br />
! Branches<br>[[File:Garden Branch 1.png]]&nbsp;[http://xkcd.com/1663/art/2x-branch-1.png Branch 1]<br><br />
[[File:Garden Branch 2.png]]&nbsp;[http://xkcd.com/1663/art/2x-branch-2.png Branch 2]<br><br />
[[File:Garden Branch 3.png]]&nbsp;[http://xkcd.com/1663/art/2x-branch-3.png Branch 3]<br><br />
[[File:Garden Branch 4.png]]&nbsp;[http://xkcd.com/1663/art/2x-branch-4.png Branch 4]<br><br />
[[File:Garden Branch 5.png]]&nbsp;[http://xkcd.com/1663/art/2x-branch-5.png Branch 5]<br><br />
[[File:Garden Branch 6.png]]&nbsp;[http://xkcd.com/1663/art/2x-branch-6.png Branch 6]<br><br />
[[File:Garden Branch 7.png]]&nbsp;[http://xkcd.com/1663/art/2x-branch-7.png Branch 7]<br><br />
[[File:Garden Branch 8.png]]&nbsp;[http://xkcd.com/1663/art/2x-branch-8.png Branch 8]<br><br />
[[File:Garden Branch 9.png]]&nbsp;[http://xkcd.com/1663/art/2x-branch-9.png Branch 9]<br><br />
[[File:Garden Branch 10.png]]&nbsp;[http://xkcd.com/1663/art/2x-branch-10.png Branch 10]<br><br />
[[File:Garden Branch 11.png]]&nbsp;[http://xkcd.com/1663/art/2x-branch-11.png Branch 11]<br><br />
[[File:Garden Branch 12.png]]&nbsp;[http://xkcd.com/1663/art/2x-branch-12.png Branch 12]<br><br />
[[File:Garden Branch 13.png]]&nbsp;[http://xkcd.com/1663/art/2x-branch-13.png Branch 13]<br><br />
[[File:Garden Branch 14.png]]&nbsp;[http://xkcd.com/1663/art/2x-branch-14.png Branch 14]<br><br />
[[File:Garden Branch 15.png]]&nbsp;[http://xkcd.com/1663/art/2x-branch-15.png Branch 15]<br><br />
[[File:Garden Branch 16.png]]&nbsp;[http://xkcd.com/1663/art/2x-branch-16.png Branch 16]<br><br />
[[File:Garden Branch 17.png]]&nbsp;[http://xkcd.com/1663/art/2x-branch-17.png Branch 17]<br><br />
[[File:Garden Branch 18.png]]&nbsp;[http://xkcd.com/1663/art/2x-branch-18.png Branch 18]<br><br />
[[File:Garden Branch 19.png]]&nbsp;[http://xkcd.com/1663/art/2x-branch-19.png Branch 19]<br><br />
[[File:Garden Branch 20.png]]&nbsp;[http://xkcd.com/1663/art/2x-branch-20.png Branch 20]<br><br />
[[File:Garden Branch 21.png]]&nbsp;[http://xkcd.com/1663/art/2x-branch-21.png Branch 21]<br><br />
[[File:Garden Branch 22.png]]&nbsp;[http://xkcd.com/1663/art/2x-branch-22.png Branch 22]<br><br />
[[File:Garden Branch 23.png]]&nbsp;[http://xkcd.com/1663/art/2x-branch-23.png Branch 23]<br><br />
[[File:Garden Branch 24.png]]&nbsp;[http://xkcd.com/1663/art/2x-branch-24.png Branch 24]<br />
|<br />
*Here are the images of branches.<br />
| Color?<br />
| [ Example]<br />
|-<br />
! Leaves<br>[[File:Garden Leaves 1.png]]&nbsp;[http://xkcd.com/1663/art/2x-leaves-1.png Leaves 1]<br><br />
[[File:Garden Leaves 2.png]]&nbsp;[http://xkcd.com/1663/art/2x-leaves-2.png Leaves 2]<br><br />
[[File:Garden Leaves 3.png]]&nbsp;[http://xkcd.com/1663/art/2x-leaves-3.png Leaves 3]<br><br />
[[File:Garden Leaves 4.png]]&nbsp;[http://xkcd.com/1663/art/2x-leaves-4.png Leaves 4]<br><br />
[[File:Garden Leaves 5.png]]&nbsp;[http://xkcd.com/1663/art/2x-leaves-5.png Leaves 5]<br><br />
[[File:Garden Leaves 6.png]]&nbsp;[http://xkcd.com/1663/art/2x-leaves-6.png Leaves 6]<br><br />
[[File:Garden Leaves 7.png]]&nbsp;[http://xkcd.com/1663/art/2x-leaves-7.png Leaves 7]<br><br />
[[File:Garden Leaves 8.png]]&nbsp;[http://xkcd.com/1663/art/2x-leaves-8.png Leaves 8]<br><br />
[[File:Garden Leaves 9.png]]&nbsp;[http://xkcd.com/1663/art/2x-leaves-9.png Leaves 9]<br><br />
[[File:Garden Leaves 10.png]]&nbsp;[http://xkcd.com/1663/art/2x-leaves-10.png Leaves 10]<br><br />
[[File:Garden Leaves 11.png]]&nbsp;[http://xkcd.com/1663/art/2x-leaves-11.png Leaves 11]<br><br />
[[File:Garden Leaves 12.png]]&nbsp;[http://xkcd.com/1663/art/2x-leaves-12.png Leaves 12]<br><br />
[[File:Garden Leaves 13.png]]&nbsp;[http://xkcd.com/1663/art/2x-leaves-13.png Leaves 13]<br><br />
[[File:Garden Leaves 14.png]]&nbsp;[http://xkcd.com/1663/art/2x-leaves-14.png Leaves 14]<br><br />
[[File:Garden Leaves 15.png]]&nbsp;[http://xkcd.com/1663/art/2x-leaves-15.png Leaves 15]<br><br />
[[File:Garden Leaves 16.png]]&nbsp;[http://xkcd.com/1663/art/2x-leaves-16.png Leaves 16]<br><br />
[[File:Garden Leaves 17.png]]&nbsp;[http://xkcd.com/1663/art/2x-leaves-17.png Leaves 17]<br><br />
[[File:Garden Leaves 18.png]]&nbsp;[http://xkcd.com/1663/art/2x-leaves-18.png Leaves 18]<br><br />
[[File:Garden Leaves 19.png]]&nbsp;[http://xkcd.com/1663/art/2x-leaves-19.png Leaves 19]<br><br />
[[File:Garden Leaves 20.png]]&nbsp;[http://xkcd.com/1663/art/2x-leaves-20.png Leaves 20]<br><br />
[[File:Garden Leaves 21.png]]&nbsp;[http://xkcd.com/1663/art/2x-leaves-21.png Leaves 21]<br><br />
[[File:Garden Leaves 22.png]]&nbsp;[http://xkcd.com/1663/art/2x-leaves-22.png Leaves 22]<br><br />
[[File:Garden Leaves 23.png]]&nbsp;[http://xkcd.com/1663/art/2x-leaves-23.png Leaves 23]<br><br />
[[File:Garden Leaves 24.png]]&nbsp;[http://xkcd.com/1663/art/2x-leaves-24.png Leaves 24]<br><br />
[[File:Garden Leaves 25.png]]&nbsp;[http://xkcd.com/1663/art/2x-leaves-25.png Leaves 25]<br><br />
[[File:Garden Leaves 26.png]]&nbsp;[http://xkcd.com/1663/art/2x-leaves-26.png Leaves 26]<br><br />
[[File:Garden Leaves 27.png]]&nbsp;[http://xkcd.com/1663/art/2x-leaves-27.png Leaves 27]<br><br />
[[File:Garden Leaves 28.png]]&nbsp;[http://xkcd.com/1663/art/2x-leaves-28.png Leaves 28]<br><br />
[[File:Garden Leaves 29.png]]&nbsp;[http://xkcd.com/1663/art/2x-leaves-29.png Leaves 29]<br><br />
[[File:Garden Leaves 30.png]]&nbsp;[http://xkcd.com/1663/art/2x-leaves-30.png Leaves 30]<br />
|<br />
*Here are the images of leaves.<br />
| Color?<br />
| [ Example]<br />
|}<br />
<br />
====Flowers====<br />
{| class="wikitable collapsible collapsed" |<br />
! To see/hide images click here:<br />
! Description of images<br />
! Relevant colors<br />
! Link to screen-shots<br />
|-<br />
! Blooms<br>[[File:Garden Flower bloom 1.png]]&nbsp;[http://xkcd.com/1663/art/2x-flower-bloom1.png Flower bloom 1]<br><br />
[[File:Garden Flower bloom 2.png]]&nbsp;[http://xkcd.com/1663/art/2x-flower-bloom2.png Flower bloom 2]<br><br />
[[File:Garden Flower bloom 3.png]]&nbsp;[http://xkcd.com/1663/art/2x-flower-bloom3.png Flower bloom 3]<br><br />
[[File:Garden Flower bloom 4.png]]&nbsp;[http://xkcd.com/1663/art/2x-flower-bloom4.png Flower bloom 4]<br><br />
[[File:Garden Flower bloom 5.png]]&nbsp;[http://xkcd.com/1663/art/2x-flower-bloom5.png Flower bloom 5]<br><br />
[[File:Garden Flower bloom 6.png]]&nbsp;[http://xkcd.com/1663/art/2x-flower-bloom6.png Flower bloom 6]<br><br />
[[File:Garden Flower bloom 7.png]]&nbsp;[http://xkcd.com/1663/art/2x-flower-bloom7.png Flower bloom 7]<br />
|<br />
*Here are the images of blooms.<br />
| Color?<br />
| [ Example]<br />
|-<br />
! Hilt<br>[[File:Garden Flower hilt 1.png]]&nbsp;[http://xkcd.com/1663/art/2x-flower-hilt1.png Flower hilt 1]<br><br />
[[File:Garden Flower hilt 2.png]]&nbsp;[http://xkcd.com/1663/art/2x-flower-hilt2.png Flower hilt 2]<br />
|<br />
*Here are the images of hilt.<br />
| Color?<br />
| [ Example]<br />
|-<br />
! Stem segments<br>[[File:Garden Flower base.png]]&nbsp;[http://xkcd.com/1663/art/2x-flower-base.png Flower base]<br><br />
[[File:Garden Flower segment 1.png]]&nbsp;[http://xkcd.com/1663/art/2x-flower-segment1.png Flower segment 1]<br><br />
[[File:Garden Flower segment 2.png]]&nbsp;[http://xkcd.com/1663/art/2x-flower-segment2.png Flower segment 2]<br><br />
[[File:Garden Flower segment 3.png]]&nbsp;[http://xkcd.com/1663/art/2x-flower-segment3.png Flower segment 3]<br><br />
[[File:Garden Flower segment 4.png]]&nbsp;[http://xkcd.com/1663/art/2x-flower-segment4.png Flower segment 4]<br><br />
[[File:Flower segment 5.png]]&nbsp;[http://xkcd.com/1663/art/2x-flower-segment5.png Flower segment 5]<br><br />
[[File:Flower segment 6.png]]&nbsp;[http://xkcd.com/1663/art/2x-flower-segment6.png Flower segment 6]<br><br />
[[File:Flower segment 7.png]]&nbsp;[http://xkcd.com/1663/art/2x-flower-segment7.png Flower segment 7]<br><br />
[[File:Flower segment 8.png]]&nbsp;[http://xkcd.com/1663/art/2x-flower-segment8.png Flower segment 8]<br><br />
[[File:Flower segment 9.png]]&nbsp;[http://xkcd.com/1663/art/2x-flower-segment9.png Flower segment 9]<br><br />
[[File:Flower segment 10.png]]&nbsp;[http://xkcd.com/1663/art/2x-flower-segment10.png Flower segment 10]<br><br />
[[File:Flower segment 11.png]]&nbsp;[http://xkcd.com/1663/art/2x-flower-segment11.png Flower segment 11]<br><br />
[[File:Flower segment 12.png]]&nbsp;[http://xkcd.com/1663/art/2x-flower-segment12.png Flower segment 12]<br />
|<br />
*Here is the image of the base and segments of the flower stems.<br />
| Color?<br />
| [ Example]<br />
|-<br />
! Star plant<br>[[File:Garden Star Plant.png]]&nbsp;[http://xkcd.com/1663/art/2x-starplant.png Star Plant]<br />
|<br />
*Here are the images the star plant.<br />
| Color?<br />
| [ Example]<br />
|-<br />
! Tulips<br>[[File:Garden Tulip 1.png]]&nbsp;[http://xkcd.com/1663/art/2x-tulip-1.png Tulip 1]<br><br />
[[File:Garden Tulip 2.png]]&nbsp;[http://xkcd.com/1663/art/2x-tulip-2.png Tulip 2]<br />
|<br />
*Here are the images of Tulips.<br />
| Color?<br />
| [http://www.explainxkcd.com/wiki/images/0/03/1663_Garden_tulip_Megan.png Tulip Megan]<br />
|}<br />
<br />
====Other plants====<br />
{| class="wikitable collapsible collapsed" |<br />
! To see/hide images click here:<br />
! Description of images<br />
! Relevant colors<br />
! Link to screen-shots<br />
|-<br />
! Cactus <br>[[File:Garden Cactus 1.png]]&nbsp;[http://xkcd.com/1663/art/2x-cactus-1.png Cactus 1]<br><br />
[[File:Garden Cactus 2.png]]&nbsp;[http://xkcd.com/1663/art/2x-cactus-2.png Cactus 2]<br />
|<br />
*Here are the images of cactus.<br />
| Color?<br />
| [ Example]<br />
|-<br />
! Grass<br>[[File:Garden Grass 1.png]]&nbsp;[http://xkcd.com/1663/art/2x-grass-1.png Grass 1]<br><br />
[[File:Garden Grass 2.png]]&nbsp;[http://xkcd.com/1663/art/2x-grass-2.png Grass 2]<br><br />
[[File:Garden Grass 3.png]]&nbsp;[http://xkcd.com/1663/art/2x-grass-3.png Grass 3]<br><br />
[[File:Garden Grass 4.png]]&nbsp;[http://xkcd.com/1663/art/2x-grass-4.png Grass 4]<br><br />
[[File:Garden Grass 5.png]]&nbsp;[http://xkcd.com/1663/art/2x-grass-5.png Grass 5]<br><br />
[[File:Garden Grass 6.png]]&nbsp;[http://xkcd.com/1663/art/2x-grass-6.png Grass 6]<br><br />
[[File:Garden Grass 7.png]]&nbsp;[http://xkcd.com/1663/art/2x-grass-7.png Grass 7]<br><br />
[[File:Garden Grass 8.png]]&nbsp;[http://xkcd.com/1663/art/2x-grass-8.png Grass 8]<br><br />
[[File:Garden Grass 9.png]]&nbsp;[http://xkcd.com/1663/art/2x-grass-9.png Grass 9]<br />
|<br />
*Here are the images of grass.<br />
| Color?<br />
| [ Example]<br />
|-<br />
! Reeds<br>[[File:Garden Reeds 1.png]]&nbsp;[http://xkcd.com/1663/art/2x-reeds-1.png Reeds 1]<br><br />
[[File:Garden Reeds 2.png]]&nbsp;[http://xkcd.com/1663/art/2x-reeds-2.png Reeds 2]<br><br />
[[File:Garden Reeds 3.png]]&nbsp;[http://xkcd.com/1663/art/2x-reeds-3.png Reeds 3]<br><br />
[[File:Garden Reeds 4.png]]&nbsp;[http://xkcd.com/1663/art/2x-reeds-4.png Reeds 4]<br><br />
[[File:Garden Reeds 5.png]]&nbsp;[http://xkcd.com/1663/art/2x-reeds-5.png Reeds 5]<br><br />
[[File:Garden Reeds 6.png]]&nbsp;[http://xkcd.com/1663/art/2x-reeds-6.png Reeds 6]<br><br />
[[File:Garden Reeds 8.png]]&nbsp;[http://xkcd.com/1663/art/2x-reeds-8.png Reeds 8]<br><br />
[[File:Garden Reeds 9.png]]&nbsp;[http://xkcd.com/1663/art/2x-reeds-9.png Reeds 9]<br><br />
[[File:Garden Reeds 10.png]]&nbsp;[http://xkcd.com/1663/art/2x-reeds-10.png Reeds 10]<br><br />
[[File:Garden Reeds 11.png]]&nbsp;[http://xkcd.com/1663/art/2x-reeds-11.png Reeds 11]<br><br />
[[File:Garden Reeds 12.png]]&nbsp;[http://xkcd.com/1663/art/2x-reeds-12.png Reeds 12]<br><br />
[[File:Garden Reeds 13.png]]&nbsp;[http://xkcd.com/1663/art/2x-reeds-13.png Reeds 13]<br />
|<br />
*Here are the images of reeds.<br />
| Color?<br />
| [ Example]<br />
|-<br />
! Shrub<br>[[File:Garden Shrub 1.png]]&nbsp;[http://xkcd.com/1663/art/2x-shrub-1.png Shrub 1]<br><br />
[[File:Garden Shrub 2.png]]&nbsp;[http://xkcd.com/1663/art/2x-shrub-2.png Shrub 2]<br><br />
[[File:Garden Shrub 3.png]]&nbsp;[http://xkcd.com/1663/art/2x-shrub-3.png Shrub 3]<br><br />
[[File:Garden Shrub 4.png]]&nbsp;[http://xkcd.com/1663/art/2x-shrub-4.png Shrub 4]<br><br />
[[File:Garden Shrub 5.png]]&nbsp;[http://xkcd.com/1663/art/2x-shrub-5.png Shrub 5]<br><br />
[[File:Garden Shrub 6.png]]&nbsp;[http://xkcd.com/1663/art/2x-shrub-6.png Shrub 6]<br><br />
[[File:Garden Shrub 7.png]]&nbsp;[http://xkcd.com/1663/art/2x-shrub-7.png Shrub 7]<br><br />
[[File:Garden Shrub 8.png]]&nbsp;[http://xkcd.com/1663/art/2x-shrub-8.png Shrub 8]<br><br />
[[File:Garden Shrub 9.png]]&nbsp;[http://xkcd.com/1663/art/2x-shrub-9.png Shrub 9]<br><br />
[[File:Garden Shrub 10.png]]&nbsp;[http://xkcd.com/1663/art/2x-shrub-10.png Shrub 10]<br><br />
[[File:Garden Shrub 11.png]]&nbsp;[http://xkcd.com/1663/art/2x-shrub-11.png Shrub 11]<br />
|<br />
*Here are the images of shrubs.<br />
| Color?<br />
| [ Example]<br />
|-<br />
! Wavy plant<br>[[File:Garden Wavy plant 1.png]]&nbsp;[http://xkcd.com/1663/art/2x-wavyplant-1.png Wavy plant 1]<br><br />
[[File:Garden Wavy plant 2.png]]&nbsp;[http://xkcd.com/1663/art/2x-wavyplant-2.png Wavy plant 2]<br><br />
[[File:Garden Wavy plant 3.png]]&nbsp;[http://xkcd.com/1663/art/2x-wavyplant-3.png Wavy plant 3]<br><br />
[[File:Garden Wavy plant 4.png]]&nbsp;[http://xkcd.com/1663/art/2x-wavyplant-4.png Wavy plant 4]<br />
|<br />
*Here are the images of wavy plants.<br />
| Color?<br />
| [ Example]<br />
|}<br />
<br />
===Platforms===<br />
{| class="wikitable collapsible collapsed" |<br />
! To see/hide images click here:<br />
! Description of images<br />
! Relevant colors<br />
! Link to screen-shots<br />
|-<br />
! Tree platform<br>[[File:Garden Left platform.png]]&nbsp;[http://xkcd.com/1663/art/2x-left-platform.png Left platform]<br>[[File:Garden Right platform.png]]&nbsp;[http://xkcd.com/1663/art/2x-right-platform.png Right platform]<br />
|<br />
*Here are the images of platforms in trees.<br />
| Color?<br />
| [ Example]<br />
|-<br />
! Platform<br>[[File:Garden Platform 1.png]]&nbsp;[http://xkcd.com/1663/art/2x-platform-1.png Platform 1]<br />
|<br />
*Here is the image of the basic platform.<br />
| Color?<br />
| [ Example]<br />
|-<br />
! Platform Column<br>[[File:Garden PlatformColumn 1.png]]&nbsp;[http://xkcd.com/1663/art/2x-platform-column-1.png PlatformColumn 1]<br><br />
[[File:Garden PlatformColumn 2.png]]&nbsp;[http://xkcd.com/1663/art/2x-platform-column-2.png PlatformColumn 2]<br><br />
[[File:Garden PlatformColumn 3.png]]&nbsp;[http://xkcd.com/1663/art/2x-platform-column-3.png PlatformColumn 3]<br />
|<br />
*Here are the images of platform columns.<br />
| Color?<br />
| [ Example]<br />
|-<br />
! Stone Platform<br>[[File:Garden Stone Platform 1 Wide.png]]&nbsp;[http://xkcd.com/1663/art/2x-stone-platform-1wide.png Stone Platform 1 Wide]<br><br />
[[File:Garden Stone Platform 3 Wide.png]]&nbsp; [http://xkcd.com/1663/art/2x-stone-platform-3wide.png Stone Platform 3 Wide]<br><br />
[[File:Garden Stone Platform 5 Wide.png]]&nbsp;[http://xkcd.com/1663/art/2x-stone-platform-5wide.png Stone Platform 5 Wide]<br />
|<br />
*Here are the images of stone platforms.<br />
| Color?<br />
| [ Example]<br />
|-<br />
! Tall platform<br>[[File:Garden Tall platform.png]]&nbsp;[http://xkcd.com/1663/art/2x-tall-platform.png Tall platform]<br />
|<br />
*Here is the image of the tall platform.<br />
| Color?<br />
| [ Example]<br />
|}<br />
<br />
===Other items===<br />
{| class="wikitable collapsible collapsed" |<br />
! To see/hide images click here:<br />
! Description of images<br />
! Relevant colors<br />
! Link to screen-shots<br />
|-<br />
! Balloon<br>[[File:Garden Balloon.png]]&nbsp;[http://xkcd.com/1663/art/2x-balloon.png Balloon]<br><br />
[[File:Garden Balloon Huge.png]]&nbsp;[http://xkcd.com/1663/art/2x-balloon-huge.png Balloon Huge]<br><br />
[[File:Garden Balloon Segment.png]]&nbsp;[http://xkcd.com/1663/art/2x-balloon-segment.png Balloon Segment]<br><br />
[[File:Balloon segment short.png]]&nbsp;[http://xkcd.com/1663/art/2x-balloon-segment-short.png Balloon segment short]<br />
|<br />
*Here are the images of balloons and their strings.<br />
| Color?<br />
| [http://www.explainxkcd.com/wiki/images/3/34/1663_garden_S_shaped_empty_balloon_string_right.png S-shaped balloon string]<br />
|-<br />
! Birdbath<br>[[File:Garden Birdbath.png]]&nbsp;[http://xkcd.com/1663/art/2x-birdbath.png Birdbath]<br />
|<br />
*Here is the image of the birdbath.<br />
| Color?<br />
| [http://www.explainxkcd.com/wiki/images/a/a1/1663_garden_Purple_garden_with_Heron.png Birdbath legged deer]<br />
|-<br />
! Boat<br>[[File:Garden Boat 1 L.png]]&nbsp;[http://linden.xkcd.com/art/2x-boat-1-l.png Boat 1 L]<br><br />
[[File:Garden Boat 1 R.png]]&nbsp;[http://linden.xkcd.com/art/2x-boat-1-r.png Boat 1 R]<br />
|<br />
*Here are the images of boats.<br />
| Color?<br />
| [ Example]<br />
|-<br />
! Cairn stones<br>[[File:Garden Cairn Base 1.png]]&nbsp;[http://xkcd.com/1663/art/2x-cairn-base-1.png Cairn Base 1]<br><br />
[[File:Garden Cairn Base 2.png]]&nbsp;[http://xkcd.com/1663/art/2x-cairn-base-2.png Cairn Base 2]<br><br />
[[File:Garden Cairn Base 3.png]]&nbsp;[http://xkcd.com/1663/art/2x-cairn-base-3.png Cairn Base 3]<br><br />
[[File:Garden Cairn Base 4.png]]&nbsp;[http://xkcd.com/1663/art/2x-cairn-base-4.png Cairn Base 4]<br><br />
[[File:Garden Cairn Base 5.png]]&nbsp;[http://xkcd.com/1663/art/2x-cairn-base-5.png Cairn Base 5]<br><br />
[[File:Garden Cairn Mid 1.png]]&nbsp; [http://xkcd.com/1663/art/2x-cairn-mid-1.png Cairn Mid 1]<br><br />
[[File:Garden Cairn Mid 2.png]]&nbsp;[http://xkcd.com/1663/art/2x-cairn-mid-2.png Cairn Mid 2]<br><br />
[[File:Garden Cairn Mid 3.png]]&nbsp;[http://xkcd.com/1663/art/2x-cairn-mid-3.png Cairn Mid 3]<br><br />
[[File:Garden Cairn Mid 4.png]]&nbsp;[http://xkcd.com/1663/art/2x-cairn-mid-4.png Cairn Mid 4]<br><br />
[[File:Garden Cairn Mid 5.png]]&nbsp;[http://xkcd.com/1663/art/2x-cairn-mid-5.png Cairn Mid 5]<br><br />
[[File:Garden Cairn Top 1.png]]&nbsp;[http://xkcd.com/1663/art/2x-cairn-top-1.png Cairn Top 1]<br><br />
[[File:Garden Cairn Top 2.png]]&nbsp;[http://xkcd.com/1663/art/2x-cairn-top-2.png Cairn Top 2]<br><br />
[[File:Garden Cairn Top 3.png]]&nbsp;[http://xkcd.com/1663/art/2x-cairn-top-3.png Cairn Top 3]<br><br />
[[File:Garden Cairn Top 4.png]]&nbsp;[http://xkcd.com/1663/art/2x-cairn-top-4.png Cairn Top 4]<br><br />
[[File:Garden Cairn Top 5.png]]&nbsp;[http://xkcd.com/1663/art/2x-cairn-top-5.png Cairn Top 5]<br />
|<br />
*Here is the image of the stones used to form cairns.<br />
| Color?<br />
| [http://www.explainxkcd.com/wiki/images/2/23/1663_Garden_An_Engineer_cairns.png Gigantic rock pile]<br />
|-<br />
! Furniture<br>[[File:Garden Desk 1.png]]&nbsp;[http://xkcd.com/1663/art/2x-desk-1.png Desk 1]<br><br />
[[File:Garden Desk lamp.png]]&nbsp;[http://xkcd.com/1663/art/2x-desk-lamp.png Desk lamp]<br><br />
[[File:Garden Table 1.png]]&nbsp;[http://xkcd.com/1663/art/2x-table-1.png Table 1]<br />
|<br />
*Here are the images of furniture for the office and other places.<br />
| Color?<br />
| [ Example]<br />
|-<br />
! Giant Planter<br>[[File:Garden Giant Planter.png]]&nbsp;[http://xkcd.com/1663/art/2x-giant-planter.png Giant Planter]<br />
|<br />
*Here is the image of the giant Planter.<br />
| Color?<br />
| [http://www.explainxkcd.com/wiki/images/1/1a/1663_garden_Underground_light_gives_large_tub_on_top_of_pillar_then_filled_with_trees.png Giant planter with trees]<br />
|-<br />
! Hat<br>[[File:Garden Hat 1a.png]]&nbsp;[http://xkcd.com/1663/art/2x-hat-1a.png Hat 1a]<br />
|<br />
*Here is the image of the black hat.<br />
| Color?<br />
| [ Example]<br />
|-<br />
! Lamppost<br>[[File:Garden Lamp crossbar left.png]]&nbsp;[http://xkcd.com/1663/art/2x-lamp-crossbar-left.png Lamp crossbar left]<br><br />
[[File:Garden Lamp crossbar right.png]]&nbsp;[http://xkcd.com/1663/art/2x-lamp-crossbar-right.png Lamp crossbar right]<br><br />
[[File:Garden Lamppost 1.png]]&nbsp;[http://xkcd.com/1663/art/2x-lamppost-1.png Lamppost 1]<br><br />
[[File:Garden lamp-topper.png]]&nbsp;[http://xkcd.com/1663/art/2x-lamp-topper.png lamp-topper]<br />
|<br />
*Here are the images that may form the complete lamppost. <br />
*The lamp post looks exactly like the one in [[665: Prudence]], and that is the one from {{w|Narnia}} which actually grew up in the forest when Narnia was created in the chronologically first book {{w|The Magician's Nephew}} when Aslan created Narnia.<br />
<br />
| Color?<br />
| [http://www.explainxkcd.com/wiki/images/7/7a/1663_garden_Blitz_Girls_lamp_posts_and_flowers_garden.png Example with lamp]<br> [http://www.explainxkcd.com/wiki/images/8/81/1663_garden_Lamp_post_poles_and_mars_rover.png Example with crossbar]<br />
|-<br />
! Obelisk<br>[[File:Garden Obelisk.png]]&nbsp;[http://xkcd.com/1663/art/2x-obelisk.png Obelisk]<br />
|<br />
*Here is the image of the obelisk.<br />
| Color?<br />
| [ Example]<br />
|-<br />
! Pot<br>[[File:Garden Pot 1.png]]&nbsp;[http://xkcd.com/1663/art/2x-pot-1.png Pot 1]<br><br />
[[File:Garden Pot 2.png]]&nbsp;[http://xkcd.com/1663/art/2x-pot-2.png Pot 2]<br><br />
[[File:Garden Pot 3.png]]&nbsp;[http://xkcd.com/1663/art/2x-pot-3.png Pot 3]<br />
|<br />
*Here are the images of pots.<br />
| Color?<br />
| [ Example]<br />
|-<br />
! Rover<br>[[File:Garden Rover.png]]&nbsp;[http://xkcd.com/1663/art/2x-rover.png Rover]<br />
|<br />
*Here is the image of the Mars rover.<br />
| Color 16<br />
| [http://www.explainxkcd.com/wiki/images/3/3f/1663_garden_One_color_Between_orange_red_and_red_First_thing_Mars_rover.png Mars rover]<br />
|-<br />
! Sale sign<br>[[File:Garden Sale sign.png]]&nbsp;[http://xkcd.com/1663/art/2x-sale-sign.png Sale sign]<br />
|<br />
*Here is the image of the sale sign.<br />
| Color?<br />
| [ Example]<br />
|-<br />
! Saucer<br>[[File:Garden Saucer.png]]&nbsp;[http://xkcd.com/1663/art/2x-saucer.png Saucer]<br />
|<br />
*Here is the image of the flying saucer.<br />
| Color?<br />
| [http://forums.xkcd.com/download/file.php?id=51432&mode=view BlitzGirl's UFO garden]<br />
|}<br />
<br />
===Helper structures===<br />
{| class="wikitable collapsible collapsed" |<br />
! To see/hide images click here:<br />
! Description of images<br />
! Relevant colors<br />
! Link to screen-shots<br />
|-<br />
! Bird riser<br>[[File:Garden Bird riser.png]],&nbsp;[[File:Garden Bird riser with background.png]]&nbsp;[http://xkcd.com/1663/art/2x-bird-riser.png Bird riser], and with background<br><br />
[[File:Garden Bird riser root.png]]&nbsp;[[File:Garden Bird riser root with frame.png]][http://linden.xkcd.com/art/2x-bird-riser-root.png Bird riser root], and with frame<br><br />
|<br />
*Here are the images of the bird riser and it's root. <br />
**They only seem to appear in the orange color range.<br />
**The riser is invisible (white) and would have to have a background to be seen (both versions are shown to the left). This will never be the case in the garden as the raiser does not show up in front of other black items.<br />
***However, the risers can be seen using the [[#Debug_mode|debug mode]], and this is used as the example to the right.<br />
***Also using the debug mode on this [http://www.xkcd.com/1663/#1e853af8-055f-11e6-8001-42010a8e000f garden] the [http://www.explainxkcd.com/wiki/images/e/e0/1663_garden_Color_13_2_5d_debug_with_count.png number of items can be counted] as shown in the link. <br />
****From this link it is clear that there are three bird risers attached to two of the seven bird riser roots. <br />
****Here only single bird risers are displayed, but they can be connected see below.<br />
**The root can often be seen on the ground, but it can be hidden behind other objects. <br />
***Also the root has the first short part of a bird riser above the root, which is invisible (by any means). The bird riser takes hold at the top of this invisible part. That it is there can best be seen by putting a frame around the image of the root, to see that it is twice as high as the root itself. Such an image is also shown to the left. (But the end can also be seen in the debug mode images).<br />
*The riser are used to make items fly in the air. <br />
**I.e. the five types of flying birds, the saucer, flying Megan and the two "actual flying fish", can attach them selves to the end of a bird riser.<br />
**Whereas the risers need to have a root to begin, then more risers can attach to the end already existing risers, thus getting much higher up in the air than one riser (all the way up!).<br />
**Risers can have any angles to each others, even going further down, which can explain birds and other flying objects touching the ground (even making an object be situated partially beneath the ground, like [http://www.explainxkcd.com/wiki/images/c/cf/1663_garden_One_color_Orange_6d.png this flying Megan] from this [http://xkcd.com/1663/#0d6bca62-fcf3-11e5-8019-42010a8e0005 garden] or maybe even outside the frame, see last example below).<br />
**As opposed to anything else the light that creates a bird (or other flying item) does not need to touch the actually bird, but rather the place from where the bird riser is rooted. <br />
***This indicates that the birds etc. can grow from light touching the base of the risers rather than the tip. <br />
****Since many bird risers can grow in layers above the first riser it is clear that the bird riser does not appear with a bird on them in one go! <br />
***There are many examples with [http://www.explainxkcd.com/wiki/images/4/48/1663_garden_One_color_Orange_9d.png birds] or [http://www.explainxkcd.com/wiki/images/4/4f/1663_garden_One_color_Between_orange_and_orange_red_8d.png flying Megan] "growing" outside the light, where no light ever was, as seen from some of the [[1663:_Garden/Users_gardens#Locked_gardens_only_for_explanation_use|locked experimental gardens]].<br />
*When selecting a bird riser root all bird risers and all flying things connected to these will also be selected (and deleted if the root is deleted).<br />
**Here are two examples from the same [http://xkcd.com/1663/#578b80bc-fd96-11e5-8001-42010a8e000a garden] where two different roots have been selected:<br />
***In this [http://www.explainxkcd.com/wiki/images/b/b9/1663_garden_14_Between_orange_and_orange_red_15d_selected_bird_riser_root.png example] the selected root is hidden by the tulip in the red circle. Seven birds are selected both right and left of this root. (Two of them on top of each other).<br />
***In this [http://www.explainxkcd.com/wiki/images/2/27/1663_garden_14_Between_orange_and_orange_red_15d_selected_bird_riser_root_Megan.png example] the root in the red circle is completely hidden by turtles etc. It connects to three birds and one flying Megan, showing that it is the bird riser roots that also connect to her.<br />
**In this next example [http://xkcd.com/1663/#59246c86-fcce-11e5-8001-42010a8e0010 garden] the links between a root and four birds are displayed in detail.<br />
***The [http://www.explainxkcd.com/wiki/images/7/73/1663_garden_SF_final.png first image] is just the normal garden view screen-shot (lamps deleted). 10 birds can be seen; there are six birds over the lamp post; two near the ground under the high platform; one near the right crown of the tree; and one to the left that looks like it is a part of the linsang. Several bird riser roots (at least five) can be seen on the ground from the middle of the platform and right past the cat (two under it) and then at the sign.<br />
***In the [http://www.explainxkcd.com/wiki/images/8/8d/1663_garden_SF_final_selected.png second image] the root at the foot of the Sale sign has been selected. Four birds have been selected, spread out over the entire section with birds, including the lowest, the highest, the left most and one over the lamp post.<br />
***In the [http://www.explainxkcd.com/wiki/images/7/73/1663_garden_SF_final_debug.png third image] debug mode has been used. All the long purple lines (of equal length) indicate bird risers.<br />
***In the last [http://www.explainxkcd.com/wiki/images/3/35/1663_garden_SF_final_debug_drawing.png fourth image] the links between the root and the four birds have been indicated. A zero (0) has been written under the root. Then 1 indicates the single bird riser that goes to the right bird over the lamp post. Bird riser 2, 3 and 4 connect to each other from the root up to the highest bird right of the crown. Then bird riser 5 goes from that to the bird near the linsang left of the tree, and finally bird riser 6 and 7 goes straight back and down to the lowest bird near the ground. <br />
****Several bird risers seems to go beneath the ground!<br />
**That bird risers can go beneath the ground has already been show with flying Megan partly under ground.<br />
***In this last example it is made clear that birds can then appear either under ground (or under the top of other structures blocking their view) or even totally outside the frame (as indicated above the bird risers seem to be able to sprout items outside the cones of light, as long as they grow in the light them selves).<br />
***The proof for this comes in this [http://www.explainxkcd.com/wiki/images/1/16/1663_garden_Color_13_5d_debug_with_count.png example] with the debug version of this [http://www.xkcd.com/1663/#fa1b5c92-055e-11e6-8001-42010a8e000f garden] showing the count:<br />
****At the time of [http://www.explainxkcd.com/wiki/images/7/73/1663_garden_Color_13_5d.png these images] there where only 8 visible birds<br />
****But the count lists 20 birds, indicating that no less than 12 birds are hidden from view!<br />
| Color [http://www.explainxkcd.com/wiki/images/4/48/1663_garden_One_color_Orange_9d.png 13 Orange] and [http://www.explainxkcd.com/wiki/images/4/4f/1663_garden_One_color_Between_orange_and_orange_red_8d.png 14 Orange].<br />
| [http://www.explainxkcd.com/wiki/images/e/e7/1663_garden_Color_13_2_5d_debug_bird_risers.png Bird riser debug]<br><br />
[http://www.explainxkcd.com/wiki/images/5/5e/1663_garden_Color_14_3d.png Root]<br />
|-<br />
! Null<br>[[File:Garden Null.png]]&nbsp;[http://xkcd.com/1663/art/2x-null.png Null]<br>[[File:Garden Null continue.png]]&nbsp;[http://xkcd.com/1663/art/2x-null-continue-air.png Null continue]<br><br />
[[File:Garden Null continue air.png]],&nbsp;[[File:Garden Null continue air with background.png]]&nbsp;[http://xkcd.com/1663/art/2x-null-continue-air.png Null continue air], and with background<br><br />
|<br />
*Here are the images of ''null''. They cannot normally be seen, the air version even have to have a background to be seen (both versions are shown). They are used for ??.<br />
| Color<br />
| [ Example]<br />
|}<br />
<br />
<br />
{{comic discussion}}<br />
<br />
[[Category:April fools' comics]] <!-- This was delayed but if not directly an April fool's comic then the comments leading up to it was, and this is the only comic to list as April fools' this year --><br />
[[Category:Comics with color]]<br />
[[Category:Dynamic comics]]<br />
[[Category:Interactive comics]]<br />
[[Category:Comics with animation]] <!-- The trees and plants wave in the breeze --><br />
[[Category:Comics featuring Megan]] <br />
[[Category:Comics featuring Cueball]]<br />
[[Category:Comics featuring Beret Guy]] <br />
[[Category:Comics featuring Ponytail]] <br />
[[Category:Comics featuring Black Hat]] <!-- Can appear when a Cueball gets on the Black Hat, but that would thus turn him into Black Hat --><br />
[[Category:Animals]]<br />
[[Category:Sharks]] <!-- Shark fins appeared after more than a week --><br />
[[Category:Mars rovers]]<br />
[[Category:Protip]]<br />
[[Category:Buns]]<br />
<!-- The tip given in the header of xkcd as a reaction to the comic. Maybe that will not be permanent, but it will be mentioned in the explanation here and should stay--></div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=2030:_Voting_Software&diff=1612982030: Voting Software2018-08-17T05:07:53Z<p>CRGreathouse: alternate take</p>
<hr />
<div>{{comic<br />
| number = 2030<br />
| date = August 8, 2018<br />
| title = Voting Software<br />
| image = voting_software.png<br />
| titletext = There are lots of very smart people doing fascinating work on cryptographic voting protocols. We should be funding and encouraging them, and doing all our elections with paper ballots until everyone currently working in that field has retired.<br />
}}<br />
<br />
==Explanation==<br />
{{incomplete|Created by a BLOCKCHAIN - Do NOT delete this tag too soon.}}<br />
The first two panels of this comic involve a reporter talking to professionals of a given field regarding the given safety of the products/solutions that each of their fields help to produce, or are at least partially involved in said production (Airplanes from aircraft designers in Panel 1, Elevators from building engineers in Panel 2). While the two inventions selected are relatively new when compared to how long humans have existed, the two fields mentioned have existed for multiple human generations, giving enough time to find flaws in their products/solutions and solve said flaws to the point that they can be considered safe for the general public to use.<br />
<br />
The comic from Panel 3 onwards contrasts this with [[Megan]] and [[Cueball]] both agreeing that their given field (computer science / software development / software engineering) does not have the overall consistent competency that other fields have or, at the very least, appear to have. This is true (at least anecdotally) since there are very few ethical and security restrictions for what developers can/cannot do, and relatively minor consequences when catastrophes arise from poor decisions. <br />
<br />
Computer systems, operating primarily in a digital domain, fail differently from most traditional areas of engineering, which operate in analog (or continuous) domains. A small error in an analog part often gives a result which is close to the desired properties (it almost fits, it works most of the time). By contrast, a small error in a digital system (just one bit being changed) can easily make the system function in radically different ways. So not only is software engineering younger than other areas of engineering, but the domain is much less forgiving. Even small errors/variations are likely to produce radically different behavior.<br />
<br />
The title text confirms the comic's stance by implicitly saying that any digital voting systems that are produced are to not be used under any circumstances. It may also highlight that anyone working in the field is vulnerable to corruption, or at least that the field is far from maturity.<br />
<br />
The main joke of the comic is that when other engineers say something is safe, people don't believe them: People are scared of flying and elevators even though they are, statistically, very safe. However, the opposite is true for software engineers: When software engineers say something is dangerous, people don't believe them.<br />
<br />
This is a result of a fundamental difference between computer security and other types of safety measures -- in cryptography, there is ''always'' somebody trying to undo what you've built. Not only that, but new advances in cryptography tend to point out vulnerabilities with previous versions, making them not only obsolete, but dangerously so.<br />
<br />
For these reasons, it is especially important to make sure that whoever is selling you the security method is both competent and non-malicious, but because crypto software is highly technical and often confidential/proprietary, it can be hard to verify this if you're not an expert in the field (which you won't be, if you're buying it).<br />
<br />
These issues are especially pertinent to {{w|voting machine}}s, which store incredibly sensitive information but are often catastrophically outdated due to lack of funding. There are also major issues with electronic voting in general; for example, [https://www.youtube.com/watch?v=w3_0x6oaDmI this video from Computerphile] raises issues of malware infections, transferring the votes to the election authorities without having them intercepted, and needing to trust both the machine's software and central counting system to present an accurate account of the votes. Furthermore, the people purchasing them, the politicians, are generally not known for their technical understanding -- or their impartiality.<br />
<br />
{{w|Blockchain}} is a relatively new technology that is intended to solve some computer security issues by making it difficult to doctor old data. However, in the process of solving the old computer security issues, it has introduced new computer security issues that have not yet been ironed out. It also doesn't solve input fraud issues, only data-doctoring fraud, so if a program caused the voting machine to record a vote for candidate B whenever a vote for candidate A was cast (such a program could be uploaded to the voting machines through USB, or through the internet which the voting machine must be connected to for blockchain), blockchain would not prevent it. Blockchain has also had a large number of high-profile scams, thefts, and implementations with critical security holes. Thus, [[Megan]] and [[Cueball]] may not trust this blockchain solution because of this history.<br />
<br />
Most computer security specialists are more worried about programs that randomly deliberately misrecord a vote, than people changing the votes after they're already recorded, so blockchain would solve an issue that most computer security specialists are less worried about, while causing new issues (the perpetual internet connection among them).<br />
<br />
Also, the security issues that Blockchain solves could also be solved via write-once memory, which would be more secure and more difficult to doctor.<br />
<br />
The topic of voting machines has been covered before in [[463: Voting Machines]], where the use of anti-virus software on the machines has been discussed.<br />
<br />
==Transcript==<br />
<br />
:Asking aircraft designers about airplane safety:<br />
:Hairbun: Nothing is ever foolproof, but modern airliners are incredibly resilient. Flying is the safest way to travel.<br />
<br />
:Asking building engineers about elevator safety:<br />
:Cueball: Elevators are protected by multiple tried-and-tested failsafe mechanisms. They're nearly incapable of falling.<br />
<br />
:Asking software engineers about computerized voting:<br />
:Megan: That's ''terrifying''.<br />
<br />
:Ponytail: Wait, really?<br />
:Megan: Don't trust voting software and don't listen to anyone who tells you it's safe.<br />
:Ponytail: Why?<br />
:Megan: I don't quite know how to put this, but our entire field is bad at what we do, and if you rely on us, everyone will die.<br />
<br />
:Ponytail: They say they've fixed it with something called "blockchain."<br />
:Megan: AAAAA!!!<br />
:Cueball: Whatever they sold you, don't touch it.<br />
:Megan: Bury it in the desert.<br />
:Cueball: Wear gloves.<br />
<br />
{{comic discussion}}<br />
<br />
[[Category:Comics featuring Megan]]<br />
[[Category:Comics featuring Hairbun]]<br />
[[Category:Comics featuring Cueball]]<br />
[[Category:Comics featuring Hairy]]<br />
[[Category:Comics featuring Ponytail]]</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=2034:_Equations&diff=1612962034: Equations2018-08-17T04:59:57Z<p>CRGreathouse: category</p>
<hr />
<div>{{comic<br />
| number = 2034<br />
| date = August 17, 2018<br />
| title = Equations<br />
| image = equations.png<br />
| titletext = All electromagnetic equations: The same as all fluid dynamics equations, but with the 8 and 23 replaced with the permittivity and permeability of free space, respectively.<br />
}}<br />
<br />
==Explanation==<br />
{{incomplete|Created by a BOT - Please change this comment when editing this page. Do NOT delete this tag too soon.}}<br />
<br />
==Transcript==<br />
{{incomplete transcript|Do NOT delete this tag too soon.}}<br />
[Nine equations are listed and labeled as followed:]<br />
<br><br />
<math>E = K_0t + \frac{1}{2}pvt^2</math><br><br />
ALL KINEMATICS EQUATIONS<br><br />
<br><br />
<math>K_n = \sum_{i=0}^{\infty}\sum_{\pi=0}^{\infty}(n-\pi)(i-e^{\pi-\infty})</math><br><br />
ALL NUMBER THEORY EQUATIONS<br><br />
<br><br />
<math>\frac{\partial}{\partial t}\triangledown\cdot p = \frac{8}{23}<br />
\int\!\!\!\!\int\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\bigcirc\,\,<br />
\rho\,ds\,dt\cdot \rho\frac{\partial}{\partial\triangledown}<br />
</math><br><br />
ALL FLUID DYNAMIC EQUATIONS<br><br />
<br><br />
<math>?placeholder?</math><br><br />
ALL QUANTUM MECHANIC EQUATIONS<br><br />
<br><br />
<math>?placeholder?</math><br><br />
ALL CHEMISTRY EQUATIONS<br><br />
<br><br />
<math>?placeholder?</math><br><br />
ALL QUANTUM GRAVITY EQUATIONS<br><br />
<br><br />
<math>?placeholder?</math><br><br />
ALL GAUGE THEORY EQUATIONS<br><br />
<br><br />
<math>H(t) + \Omega + G \cdot \land \, ... \begin{cases} ... > 0 & \text{(HUBBLE MODEL)} \\ ... = 0 & \text{(FLAT SPHERE MODEL)} \\ ... < 0 & \text{(BRIGHT DARK MATTER MODEL)} \end{cases}<br />
</math><br><br />
ALL COSMOLOGY EQUATIONS<br><br />
<br><br />
<math>\hat H - \mu_{0} = 0</math><br><br />
ALL TRULY DEEP PHYSICS EQUATIONS<br />
<br><br />
{{comic discussion}}<br />
[[Category:Math]]</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=1026:_Compare_and_Contrast&diff=1612321026: Compare and Contrast2018-08-15T15:36:11Z<p>CRGreathouse: template</p>
<hr />
<div>{{comic<br />
| number = 1026<br />
| date = March 7, 2012<br />
| title = Compare and Contrast<br />
| image = compare_and_contrast.png<br />
| titletext = Frankly, I see no difference between thee and a summer's day. Only Ron Paul offers a TRUE alternative!<br />
}}<br />
<br />
==Explanation==<br />
<br />
<br />
A reference to the most well-known {{w|sonnet}} in the English-speaking world: {{w|William Shakespeare|William Shakespeare's}} "{{w|Sonnet 18}}", the first line of which is: "Shall I compare thee to a summer's day?". In this comic [[Randall]] sets about this in a typically goal-oriented chart, as opposed to the rather more romantic poetry of the Bard.<br />
<br />
"Thee" is a form of the archaic second-person singular pronoun "thou". In Shakespeare's day, English had more second-person pronouns in common use, thou/thee (informal/singular), and you (formal/plural). This is similar to second-person pronouns in many modern European languages, such as French. {{w|English personal pronouns#Full list of personal pronouns|Wikipedia}} has a nice chart for all of English's personal pronouns, current and archaic.<br />
<br />
For both the chart and the original sonnet, whether or not the work is autobiographical is unknown. Also unknown is the identity of the person whom each work refers to. It is believed that Sonnet 18 is addressed to a {{w|Shakespeare's Sonnets#Fair Youth|young man}}.<br />
<br />
The lines are:<br />
<br />
1. The first line is a reference to the sonnet itself, which reads: "Thou art more lovely and more temperate". He considers both thee and a summer's day to be "fair" (this is a pun; depending on context, "fair" can refer to complexion or weather) and "temperate" (meaning "warm", which again can describe a person or the weather).<br />
<br />
2. "Hot, sticky" also refers to both, in different ways. "Hot" can mean sexually attractive or simply that the temperature is high. A "sticky" day refers to humidity.<br />
<br />
3. "Short" is another pun. "Thee" (the subject of the comparison with the summer's day) is not tall. A summer day is chronologically long (time from dawn to dusk.)<br />
<br />
4. "Harbinger of hurricane season" is technically accurate; hurricane season does follow the summer.<br />
<br />
5. "Required for a good beach party" is not a pun, although it is another example of a word with slightly different meanings. The party is required to be held on a summer's day and with "thee" present at the party. The party would not be held on "thee", although some of the other lines suggest that the writer might personally be on top of "thee" during the party.<br />
<br />
6. Heat stroke is a condition mainly affecting children and the elderly. Heat waves and excessively hot days are highly linked with heat stroke incidence; see [https://en.wikipedia.org/wiki/Heat_stroke#cite_ref-23 Epidemiology]<br />
<br />
7. "Linked to higher rates of juvenile delinquency" refers to juveniles committing crimes. Apparently, "thee" is either a juvenile delinquent or inspires juvenile delinquency (or both). Summer is also linked to juvenile delinquency. This results, to some degree, from school not being in session, rather than simply as a direct result of the summer weather.<br />
<br />
8. "Sometimes too stifling" is another pun. It is also unusual in that it expresses a negative feeling about "thee", unlike the other entries which express what the author likes or admires about thee.<br />
<br />
9. "Arrested for releasing snakes in the library" is a fairly self-explanatory criterion. Apparently "thee" has been caught doing this. A summer's day, n the other hand, cannot be arrested at all, much less for this. This is possibly inspired by the movie ''{{w|Snakes on a Plane}}''.<br />
<br />
10. The last line "difficult to focus on work while I'm in" is a sexual reference, on the "thee" side, not on the "summer's day" side. To be "in" someone refers to the penetrative part of sex, which would occupy a typical person's attention.{{Citation needed}} Summer can be distracting from work due to heat, excitement, or just the general feeling of the season.<br />
<br />
The title text is a reference to {{w|Ron Paul}}, a 2012 {{w|Republican Party (United States)|Republican}} candidate for {{w|President of the United States|President}} who was on top in the {{w|Republican Party presidential primaries, 2012|Republican Primary}} against a few other challengers for the nomination. Ron Paul was frequently represented on the internet using similar language to the title text (with Paul offering an alternative to typical Republican and Democratic candidates. Paul was seen by many as an alternative because of his {{w|Libertarian Party (United States)|Libertarian}} views.<br />
<br />
==Transcript==<br />
:[A checklist comparing thee to a summer's day:<br />
:Fair, Temperate: Thee & A Summer's Day<br />
:Hot, Sticky: Thee & A Summer's Day<br />
:Short: Thee<br />
:Harbinger of Hurricane Season: A Summer's Day<br />
:Required for a Good Beach Party: Thee & A Summer's Day<br />
:Major Cause of Heat Stroke in the Elderly: A Summer's Day<br />
:Linked to Higher Rates of Juvenile Delinquency: Thee & A Summer's Day<br />
:Sometimes Too Stifling: Thee & A Summer's Day<br />
:Arrested for Releasing Snakes in Library: Thee<br />
:Difficult to Focus on Work While I'm In: Thee & A Summer's Day]<br />
<br />
{{comic discussion}}<br />
[[Category:Comics featuring Ron Paul]]<br />
[[Category:Charts]]<br />
[[Category:Sex]]<br />
[[Category:Politics]]<br />
[[Category:Romance]]</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=1838:_Machine_Learning&diff=1612311838: Machine Learning2018-08-15T15:30:32Z<p>CRGreathouse: category</p>
<hr />
<div>{{comic<br />
| number = 1838<br />
| date = May 17, 2017<br />
| title = Machine Learning<br />
| image = machine_learning.png<br />
| titletext = The pile gets soaked with data and starts to get mushy over time, so it's technically recurrent.<br />
}}<br />
<br />
==Explanation==<br />
{{w|Machine learning}} is a method employed in automation of complex tasks. It usually involves creation of algorithms that deal with statistical analysis of data and pattern recognition to generate output. The validity/accuracy of the output can be used to give feedback to make changes to the system, usually making future results statistically better.<br />
<br />
Cueball stands next to what looks like a pile of garbage (or compost), with a Cueball-like friend standing atop it. The pile has a funnel (labelled "data") at one end and a box labelled "answers" at the other. Here and there mathematical matrices stick out of the pile. As the friend explains to the incredulous Cueball, data enters through the funnel, undergoes an incomprehensible process of linear algebra, and comes out as answers. The friend appears to be a functional part of this system himself, as he stands atop the pile stirring it with a paddle. His machine learning system is probably very inefficient, as he is integral to both the mechanical part (repeated stirring) and the learning part (making the answers look "right").<br />
<br />
The main joke is that, despite this description being too vague and giving no intuition or details into the system, it is close to the level of understanding most machine learning experts have of the most popular class of techniques in machine learning, namely support vector machines. <!--''(Replaced reference to neural networks, but still needs explanation of vector machines.)''--><br />
<br />
====Composting====<br />
This comic compares a machine learning system to a compost pile. {{w|Composting}} is the process of taking organic matter, such as food and yard waste, and allowing it to decompose into a form that serves as fertilizer. A common method of composting is to mound the organic matter in a pile with a certain amount of moisture, then "stirring" the pile occasionally to move the less-decomposed material from the top to the interior of the pile, where it will decompose faster. <br />
<br />
In large-scale composting operations, the raw organic matter added to the pile is referred to as "input". This cartoon implies a play on the term "input", comparing a compost input to a data input.<br />
<br />
==Transcript==<br />
<br />
[Cueball Prime, holds a canoe paddle at his side and stands on top of a "big pile of linear algebra" containing a funnel labeled "data" and box labeled "answers". Cueball II stands to the left side of the panel.)]<br />
<br />
Cueball II: <i>This</i> is your machine learning system?<br />
<br />
Cueball Prime: Yup! You pour the data into this big pile of linear algebra, then collect the answers on the other side.<br />
<br />
Cueball II: What if the answers are wrong?<br />
<br />
Cueball Prime: Just stir the pile until they start looking right. <br />
<br />
{{comic discussion}}<br />
<br />
[[Category:Multiple Cueballs]]<br />
[[Category:Artificial Intelligence]]<br />
[[Category:Math]]</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=2017:_Stargazing_2&diff=1611802017: Stargazing 22018-08-14T13:26:41Z<p>CRGreathouse: /* Explanation */ visible triangles</p>
<hr />
<div><noinclude>:''"2017", this comic's number, redirects here. For the comic named "2017", see [[1779: 2017]].''</noinclude><br />
{{comic<br />
| number = 2017<br />
| date = July 9, 2018<br />
| title = Stargazing 2<br />
| image = stargazing_2.png<br />
| titletext = I mean, it wasn't exactly MY thesis. When the FAA came to shut down our observatory for using the telescope mirror to shine light at airplanes, I took a thesis and a bunch of doctorates from the supply cabinet on my way out.<br />
}}<br />
<br />
==Explanation==<br />
This is the second comic in the [[:Category:Stargazing|Stargazing]] series: The first was [[1644: Stargazing]], two and a half years earlier.<br />
<br />
This comic continues with the TV host mixing accurate astronomical information with trivialities, as well as utterly bizarre statements. In the first panel, the host voices surprise that the stars are visible again after disappearing during daylight. (See the explanation of the first comic in the series, for why this is certainly a male host, as the comics are probably spoofing {{w|Brian Cox (physicist)|Brian Cox}} who is one of the hosts on {{w|Stargazing Live}}. As can be seen he would end up looking like [[Megan]] in xkcd style).<br />
<br />
The host mentions three stars in a constellation which he says is called The Triangle. This could mean the constellation {{w|Triangulum}}, which is in fact just three main stars in a narrow triangle. However, this may also simply be intended to show the host's lack of knowledge of constellations, since he then goes on to point out three other stars forming a triangle and concludes that one can form lots of triangles by connecting groups of three stars. In Euclidean and non-Euclidean geometry, any set of three non-collinear points will form a triangle, so to say that there are a "lotta triangles" is both trivial and an understatement.{{Citation needed}} (There are about 125 billion triangles visible in the night sky with around 9096 visible stars.)<br />
<br />
Then he points to planets, calling them dots known as "fool's stars" (like fool's gold). This is understandable as planets such as Venus and Jupiter are often mistaken as stars, and one Latin term for a planet was "stella errans", meaning "wandering star". He also notes that lacking interstellar transportation, humanity will likely only reach the planets within our solar system. However, he then makes the seemingly ludicrous assertion that humans will turn these planets into interplanetary landfills, which might be a comment on how humans have used the Earth. <br />
<br />
The host also notices a dot of "space trash": An artificial satellite. Since the nascent Space Age, the Earth's orbit has gradually accumulated artificial materials that include satellites, spent rockets, and space stations. There are concerns such debris accumulation will increasingly imperil current and future space projects. However, the host claims there is an app that can tell you "whose fault it is," presumably a satellite-tracking smartphone app such as [http://itunes.apple.com/us/app/skyview-satellite-guide-find/id694309958?mt=8 SkyView] which can inform you who launched a given satellite and thus whose "fault" that particular bit of space-junk might be.<br />
<br />
The host eventually goes off on a tangent when someone from the audience points out something blinking in the sky. The host says it is a plane, and tells them what is inside it. The host continues, "don't bother trying to catch that one." This could be understood as he means it's too hard to point the telescope at it properly because it is moving too fast. In the title text, however, he means this literally, revealing that at one point during his studies he apparently used the reflective mirror of a telescope to shine light directly at airplanes, which caused the {{w|Federal Aviation Administration}} (FAA) to close down the observatory. He claims it was worth getting shut down by the FAA because he completed his thesis for his graduate degree. "Got a thesis out of it" is a phrase typically used by a scholar after discussing a research project, as a way of indicating that it was actually the main research they had conducted as a student in graduate school. Conducting research and writing it up in a thesis is one of the major hurdles toward earning a graduate degree (masters or doctorate).<br />
<br />
In the title text, he clarifies that as he was exiting the observatory, he literally "got", as in "stole", someone else's thesis paper and multiple doctorates (presumably framed degrees), either to fraudulently claim them as his own accomplishments, or perhaps just because he wanted to steal stuff. Usually "got a thesis" is shorthand for the process of "writing a lengthy thesis paper and having it be accepted as a requirement for graduation", however in this case he simply swiped someone else's document. The revelations that he's extremely unqualified (and unethical) would explain his many bizarre statements.<br />
<br />
==Transcript==<br />
:[In a dark panel, a TV host is standing in front of a group of 5 people: two Cueballs, Ponytail, Hairbun and Megan.]<br />
:Host: Welcome back to stargazing.<br />
:Host: When the stars disappeared this morning, I figured I had to find a new job, but they're ''back!'' This ''rules!''<br />
<br />
:[A frame-less white panel in which the host points to the upper right with Megan, ponytail and Cueball looking in that direction.]<br />
:Host: Those three stars form a constellation called the triangle.<br />
:Host: Those three are another triangle.<br />
:Host: Lotta triangles. Very important shape.<br />
<br />
:[Back to a dark panel with the host now pointing to the upper left in a close-up.]<br />
:Host: Those dots are planets, or "fool's stars." Without interstellar travel, they're the only ones we can realistically hope to dump trash on.<br />
:Host: Speaking of space trash, that dot is a satellite. There are apps that will tell you whose fault it is.<br />
<br />
:[The host is now turned right not pointing, still in a close-up.]<br />
:Off-panel voice: What's that blinking one?<br />
:Host: Airplane. They're full of snacks and money and stuff, but don't bother trying to catch them- they're ''way'' too high up.<br />
:Host: Learned that the hard way in grad school.<br />
:Host: Got a thesis out of it, at least.<br />
<br />
<br />
{{comic discussion}}<br />
<br />
[[Category:Stargazing|Stargazing]]<br />
[[Category:Comics sharing name|Stargazing]]<br />
[[Category:Comics with inverted brightness]]<br />
[[Category:Comics featuring Cueball]]<br />
[[Category:Comics featuring Hairbun]]<br />
[[Category:Comics featuring Ponytail]]<br />
[[Category:Comics featuring Megan]] <!-- Although the host is not Megan, she is still in the comic, as one of the audience in the 2nd frame! --><br />
[[Category:Multiple Cueballs]]<br />
[[Category:Astronomy]]</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=2002:_LeBron_James_and_Stephen_Curry&diff=1611202002: LeBron James and Stephen Curry2018-08-13T16:47:37Z<p>CRGreathouse: category</p>
<hr />
<div>{{comic<br />
| number = 2002<br />
| date = June 4, 2018<br />
| title = LeBron James and Stephen Curry<br />
| image = lebron_james_and_stephen_curry.png<br />
| titletext = The 538TR attempts to capture a player's combined skill at basketball (either real-life or NBA 2K18) and election forecasting.<br />
}}<br />
<br />
==Explanation==<br />
At the time of this comic, the {{w|2018 NBA Finals}} were going on, between the {{w|Cleveland Cavaliers}} and the {{w|Golden State Warriors}} with the Warriors leading 2 games to 0 in a best of seven series. At first glance, the comic looks like an in-depth analysis of two of the star players on those teams, {{w|LeBron James}} and {{w|Stephen Curry}}. The joke is that while comprehensive, all the statistics are completely meaningless - many don't show any correlation, and if there is one, it's extremely unlikely there is any causal link in there. <br />
<br />
The first graph includes a nine-digit {{w|Social Security number}} issued for US citizens which is typically not considered a metric related to athletic ability. As Social Security numbers are essentially random numbers ([https://www.ssa.gov/employer/randomization.html until 2011], there was a geographic correspondence for the first three digits), the graph shows only the {{w|free throw}} percentage of a large number of players, artificially spread vertically. Also note that Social Security numbers are not usually made public, barring security leaks.<br />
<br />
The second graph is a graph of 2018 points per game vs teammate's APGAR score. {{w|APGAR score}} is used to quickly summarize the health of newborn children, with scores of 7 and above indicating an infant has generally normal health; its use to rank adult NBA players is odd, if not improper. This graph indicates LeBron's teammates have an average APGAR score of approximately 2.1. Scores of 3 and below are generally regarded as critically low and possibly requiring medical attention. Low APGAR scores can also be associated with increased risk of neurological disorders such as cerebral palsy. The joke appears to be in giving LeBron's less-than-impressive teammates a low APGAR score.<br />
<br />
The shot map shows from what position Curry's shots were scored compared to other NBA players. It shows that he scored several times from outside the playing field, including twice from the {{w|bleacher}}s (which isn't a legal play), and once from the {{w|locker room}} (which is physically impossible due to multiple walls in between). This references Stephen Curry's propensity to take (and make) shots from well beyond the normal distance required for 3 points.[https://thebiglead.com/2016/02/26/stephen-currys-shooting-percentage-from-28-feet-out-is-mind-boggling/]<br />
<br />
Next is a graph of (team) win percentage vs sandwiches eaten during play. Average win percentage seems to go down as number of sandwiches eaten goes up to 3. It does indicate that the Golden State Warriors still have quite high win rate even though they have eaten either 4 sandwiches per game, or 4 sandwiches total during games, over the course of the 2018 season (the graph is unclear on this point). Golden State Warriors seem to be an outlier as their win percentage is much higher than the one of the teams that have eaten 2-3 sandwiches.<br />
<br />
In the "2018 total points" table, the highlighted {{w|Golden State Warriors}} and {{w|Cleveland Cavaliers}} represent the teams of Stephen Curry and LeBron James respectively. {{w|Magnetic north}} is the south pole of the {{w|Earth's magnetic field}}. Certain animals use the magnetic field to navigate and align themselves (including migratory birds, bees, and foxes), but there is no evidence that humans are affected by the earth's magnetic field. This means that there should not be any correlation between orientation of a basketball court and points scored. But Cleveland Cavaliers have a much a higher percentage of goals scored when orientation is towards magnetic North than other teams, probably it is implied that LeBron James and/or his team somehow actually senses magnetic field and uses that to direct shots, but more likely explanation would be that it is just the orientation of the court during their home games.<br />
<br />
The title text is a continuation of the joke in the bottom table. {{w|FiveThirtyEight}}, sometimes referred to as 538, is a website that focuses on opinion poll analysis, politics, economics, and sports blogging. <br />
<br />
The table at the bottom includes more unrelated comparisons:<br />
<br />
;Have You Heard of Him<br />
: Although both players are well known in their native United States, elsewhere basketball is considered a minority sport. Of the 7 billion people in the world it is likely that less than 2% of the total population will have heard of either player.{{Citation needed}} According to Randall, LeBron James is a more well known player than Stephen Curry. <br />
;President During Most Recent Game 7 Loss<br />
: In the NBA, the top 16 teams qualify for a single elimination play-off to determine the season champion, with each series played as a {{w|Playoff_format#Best-of-seven_playoff|best-of-seven}} series (first to win 4 games). After the fourth game, fixtures are only played as required. Most fixtures are therefore resolved before the last game. Lebron James has participated in seven playoff game 7s in his career (winning 5 of 7), and the last time his team lost a game seven was on May 18, 2008 ({{w|George W. Bush}} was still President). This also highlights that James is an older athlete, yet has been fairly dominant through his career. Stephen Curry's last game 7 loss came at the hands of Lebron James in the {{w|2016 NBA Finals}} ({{w|Barack Obama}} was President). It is notable that both the Golden State Warriors and Cleveland Cavaliers won their respective games 7 in their Conference Finals to make it to this year's NBA Finals.<br />
;Pog Collection<br />
: {{w|Milk caps (game)|Pogs}} were a {{w|fad}} in the 1990s. It is unclear why James would have a "staggeringly large" collection of pogs, besides being 4 years older than Curry.<br />
<br />
;Career Average Fed Interest Rate<br />
:The Federal Interest Rate, or {{w|federal funds rate}}, is an interest rate set by the {{w|United States Federal Reserve}}. This rate is increased or decreased periodically based on the health of the U.S. economy. As of the time of publishing, the federal interest rate was targeted at 1.75%. The rate has fluctuated from a high of around 5% to a low of near 0% (during the time of the {{w|Great Recession in the United States|2008 recession}}). James' career average federal interest rate is higher than Curry's, because James began his career before Curry, when interest rates were higher.<br />
;Name Scrabble Score<br />
:Both "lebronjames" and "stephencurry" are worth 22 points in {{w|Scrabble}}, however both being names are not recognized as scorable words and would be worth nothing. <br />
;Best Sport<br />
: It is claimed that their best sport is basketball. However, although they have chosen basketball as a career, this does not mean they were not better at a sport that does not offer a professional career. On the other hand with amount of training they did in basketball, it is extremely likely that basketball is the best sport for both of them at the moment.<br />
;Height<br />
: Both are listed as over 6 feet tall, which is not at all unusual for professional basketball players. Stephen Curry is 6'3" and LeBron James is 6'8", although this chart does not distinguish the exact heights. In most contexts, bucketing humans into broad height-groups would be unsurprising, but in basketball more detail is relevant. Thus, the information is accurate but uninformative --- like the rest of the data in this comic.<br />
;Retirement Year<br />
: In 2027, Stephen Curry will be 39 years old, which is a typical retirement age for NBA players. LeBron James's retirement age is listed as ''Unknown''. <br />
: This may refer to James's high level of play through his mid-30s, when typical players have a decline in their performance.{{Citation needed}}<br />
;FiveThirtyEight Total Rating<br />
: {{w|Nate Silver}} is a political commentator and founder of the website {{w|FiveThirtyEight}}, which uses and promotes statistical approaches in explaining the world. The site's two major areas of focus are in politics (especially on elections - it became famous for correctly predicting for whom 49 of 50 states would vote in the 2008 US presidential election and every US state in the 2012 election, and though it wasn't as accurate in 2016 it had given Donald Trump a larger chance of Electoral College victory than other mainstream media sources) and sports (Silver first got into statistical analysis via baseball). The presence of both sports-related and politics-related topics in the comic, however related they are (or not) with each other, seems to be a nod towards FiveThirtyEight's content.<br />
: Nate Silver has a much higher 538TR than either Curry or James. As explained in the title text, the 538TR combines basketball skill (either real-life or video game basketball) with election forecasting. This could suggest that Silver is proficient at basketball, presumably the video game kind, or else that election forecasting is heavily weighted.<br />
<br />
==Transcript==<br />
{{incomplete transcript|Do NOT delete this tag too soon.}}<br />
:'''NBA Playoffs ''DataDive'' '''<br />
:'''LeBron James and Stephen Curry'''<br />
:'''What makes these superstars so extraordinary?'''<br />
<br />
:[The comic consists of several plots and tables, listed here from top to bottom, left to right.]<br />
<br />
:'''Scatter plot of Social Security number vs Free throw percentage'''<br />
:The Social Security numbers range from 000-00-0000 to 999-99-9999. No pattern discernable, aside from points being a bit denser in the middle of the plot. Steven Curry is marked as a point on the right edge of the plot with a high free throw percentage.<br />
<br />
:'''Scatter plot of 2018 points per game vs Average teammate APGAR score'''<br />
:The APGAR scores range from 0 to 10. Pattern suggests a somewhat positive link between the two factors. LeBron James is marked as having a lot of points, but a low teammate APGAR score of approximately 2.1.<br />
<br />
:'''Shot map'''<br />
:Legend: grey dot for all players, black dot for Stephen Curry<br />
:A diagram of a basketball court is shown with dots placed where players have taken shots at the goal. For the all players category the dots generally cluster next to the goal basket and in front of the three point line. Steven has 3 dots next to the basket (one is behind it), but does cluster next to the three point line. He also has several dots on the other side of the playing field, and outside it, including three in the bleachers and one in the locker room.<br />
<br />
:'''Sandwiches eaten during play vs Win %'''<br />
:A plot that suggests no relation between the factors because practically all dots are in the zero sandwiches column. 2018 Warriors have one dot at around 60 win percentage and 4 sandwiches.<br />
<br />
:'''2018 total points'''<br />
:A table listing teams and their points overall and "When net is within 15° of magnetic north". The rows for the Golden State Warriors and the Cleveland Cavaliers are highlighted, the latter shows an abnormally high score in the magnetic north column.<br />
<br />
:{| class = "wikitable"<br />
! 2018 total points<br />
! Overall <br />
! When net is within 15° of magnetic north<br />
|-<br />
|'''Golden State Warriors'''<br />
|'''9304'''<br />
|'''330'''<br />
|-<br />
|Houston Rockets<br />
|9213<br />
|268<br />
|-<br />
|New Orleans Pelicans<br />
|9161<br />
|219<br />
|-<br />
|Toronto Raptors<br />
|9156<br />
|341<br />
|-<br />
|'''Cleveland Cavaliers'''<br />
|'''9091'''<br />
|'''1644'''<br />
|-<br />
|Denver Nuggets<br />
|9020<br />
|280<br />
|}<br />
<br />
:[A table at the bottom:]<br />
<br />
:{| class = "wikitable"<br />
!<br />
! Stephen Curry<br />
! LeBron James<br />
|-<br />
|Have you heard of him<br />
|Probably<br />
|Yes<br />
|-<br />
|President during most recent game 7 loss<br />
|Obama<br />
|Bush<br />
|-<br />
|Pog collection<br />
|Large<br />
|Staggeringly large<br />
|-<br />
|Career average Fed interest rate<br />
|3.42%<br />
|4.41%<br />
|-<br />
|Name Scrabble score<br />
|22<br />
|22<br />
|-<br />
|Best sport<br />
|Basketball<br />
|Basketball<br />
|-<br />
|Height<br />
|Over 6'<br />
|Over 6'<br />
|-<br />
|Retirement year<br />
|2027<br />
|Unknown<br />
!Nate Silver<br />
|-<br />
|FiveThirtyEight total rating<br>(devised by Nate Silver to combine all metrics into a single stat)<br />
|'''37.4'''<br />
|'''31.8'''<br />
|'''86.6'''<br />
|}<br />
<br />
==Trivia==<br />
This comic was posted the day after the second game in the 2018 NBA Finals between the Golden State Warriors (Stephen Curry's team) and the Cleveland Cavaliers (LeBron James' team). It is the fourth consecutive time the two teams faced each other at the finals, which is unprecedented in major sports leagues in North America. The Warriors won in 2015 and 2017, the Cavaliers won in 2016, and the Warriors are leading the current series 2-0.<br />
<br />
{{comic discussion}}<br />
<br />
[[Category:Sport]]<br />
[[Category:Basketball]]<br />
[[Category:Comics featuring Nate Silver]]<br />
[[Category:Politics]]<br />
[[Category:Statistics]]</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=2002:_LeBron_James_and_Stephen_Curry&diff=1611192002: LeBron James and Stephen Curry2018-08-13T16:47:05Z<p>CRGreathouse: /* Explanation */ better explanation of 538TR</p>
<hr />
<div>{{comic<br />
| number = 2002<br />
| date = June 4, 2018<br />
| title = LeBron James and Stephen Curry<br />
| image = lebron_james_and_stephen_curry.png<br />
| titletext = The 538TR attempts to capture a player's combined skill at basketball (either real-life or NBA 2K18) and election forecasting.<br />
}}<br />
<br />
==Explanation==<br />
At the time of this comic, the {{w|2018 NBA Finals}} were going on, between the {{w|Cleveland Cavaliers}} and the {{w|Golden State Warriors}} with the Warriors leading 2 games to 0 in a best of seven series. At first glance, the comic looks like an in-depth analysis of two of the star players on those teams, {{w|LeBron James}} and {{w|Stephen Curry}}. The joke is that while comprehensive, all the statistics are completely meaningless - many don't show any correlation, and if there is one, it's extremely unlikely there is any causal link in there. <br />
<br />
The first graph includes a nine-digit {{w|Social Security number}} issued for US citizens which is typically not considered a metric related to athletic ability. As Social Security numbers are essentially random numbers ([https://www.ssa.gov/employer/randomization.html until 2011], there was a geographic correspondence for the first three digits), the graph shows only the {{w|free throw}} percentage of a large number of players, artificially spread vertically. Also note that Social Security numbers are not usually made public, barring security leaks.<br />
<br />
The second graph is a graph of 2018 points per game vs teammate's APGAR score. {{w|APGAR score}} is used to quickly summarize the health of newborn children, with scores of 7 and above indicating an infant has generally normal health; its use to rank adult NBA players is odd, if not improper. This graph indicates LeBron's teammates have an average APGAR score of approximately 2.1. Scores of 3 and below are generally regarded as critically low and possibly requiring medical attention. Low APGAR scores can also be associated with increased risk of neurological disorders such as cerebral palsy. The joke appears to be in giving LeBron's less-than-impressive teammates a low APGAR score.<br />
<br />
The shot map shows from what position Curry's shots were scored compared to other NBA players. It shows that he scored several times from outside the playing field, including twice from the {{w|bleacher}}s (which isn't a legal play), and once from the {{w|locker room}} (which is physically impossible due to multiple walls in between). This references Stephen Curry's propensity to take (and make) shots from well beyond the normal distance required for 3 points.[https://thebiglead.com/2016/02/26/stephen-currys-shooting-percentage-from-28-feet-out-is-mind-boggling/]<br />
<br />
Next is a graph of (team) win percentage vs sandwiches eaten during play. Average win percentage seems to go down as number of sandwiches eaten goes up to 3. It does indicate that the Golden State Warriors still have quite high win rate even though they have eaten either 4 sandwiches per game, or 4 sandwiches total during games, over the course of the 2018 season (the graph is unclear on this point). Golden State Warriors seem to be an outlier as their win percentage is much higher than the one of the teams that have eaten 2-3 sandwiches.<br />
<br />
In the "2018 total points" table, the highlighted {{w|Golden State Warriors}} and {{w|Cleveland Cavaliers}} represent the teams of Stephen Curry and LeBron James respectively. {{w|Magnetic north}} is the south pole of the {{w|Earth's magnetic field}}. Certain animals use the magnetic field to navigate and align themselves (including migratory birds, bees, and foxes), but there is no evidence that humans are affected by the earth's magnetic field. This means that there should not be any correlation between orientation of a basketball court and points scored. But Cleveland Cavaliers have a much a higher percentage of goals scored when orientation is towards magnetic North than other teams, probably it is implied that LeBron James and/or his team somehow actually senses magnetic field and uses that to direct shots, but more likely explanation would be that it is just the orientation of the court during their home games.<br />
<br />
The title text is a continuation of the joke in the bottom table. {{w|FiveThirtyEight}}, sometimes referred to as 538, is a website that focuses on opinion poll analysis, politics, economics, and sports blogging. <br />
<br />
The table at the bottom includes more unrelated comparisons:<br />
<br />
;Have You Heard of Him<br />
: Although both players are well known in their native United States, elsewhere basketball is considered a minority sport. Of the 7 billion people in the world it is likely that less than 2% of the total population will have heard of either player.{{Citation needed}} According to Randall, LeBron James is a more well known player than Stephen Curry. <br />
;President During Most Recent Game 7 Loss<br />
: In the NBA, the top 16 teams qualify for a single elimination play-off to determine the season champion, with each series played as a {{w|Playoff_format#Best-of-seven_playoff|best-of-seven}} series (first to win 4 games). After the fourth game, fixtures are only played as required. Most fixtures are therefore resolved before the last game. Lebron James has participated in seven playoff game 7s in his career (winning 5 of 7), and the last time his team lost a game seven was on May 18, 2008 ({{w|George W. Bush}} was still President). This also highlights that James is an older athlete, yet has been fairly dominant through his career. Stephen Curry's last game 7 loss came at the hands of Lebron James in the {{w|2016 NBA Finals}} ({{w|Barack Obama}} was President). It is notable that both the Golden State Warriors and Cleveland Cavaliers won their respective games 7 in their Conference Finals to make it to this year's NBA Finals.<br />
;Pog Collection<br />
: {{w|Milk caps (game)|Pogs}} were a {{w|fad}} in the 1990s. It is unclear why James would have a "staggeringly large" collection of pogs, besides being 4 years older than Curry.<br />
<br />
;Career Average Fed Interest Rate<br />
:The Federal Interest Rate, or {{w|federal funds rate}}, is an interest rate set by the {{w|United States Federal Reserve}}. This rate is increased or decreased periodically based on the health of the U.S. economy. As of the time of publishing, the federal interest rate was targeted at 1.75%. The rate has fluctuated from a high of around 5% to a low of near 0% (during the time of the {{w|Great Recession in the United States|2008 recession}}). James' career average federal interest rate is higher than Curry's, because James began his career before Curry, when interest rates were higher.<br />
;Name Scrabble Score<br />
:Both "lebronjames" and "stephencurry" are worth 22 points in {{w|Scrabble}}, however both being names are not recognized as scorable words and would be worth nothing. <br />
;Best Sport<br />
: It is claimed that their best sport is basketball. However, although they have chosen basketball as a career, this does not mean they were not better at a sport that does not offer a professional career. On the other hand with amount of training they did in basketball, it is extremely likely that basketball is the best sport for both of them at the moment.<br />
;Height<br />
: Both are listed as over 6 feet tall, which is not at all unusual for professional basketball players. Stephen Curry is 6'3" and LeBron James is 6'8", although this chart does not distinguish the exact heights. In most contexts, bucketing humans into broad height-groups would be unsurprising, but in basketball more detail is relevant. Thus, the information is accurate but uninformative --- like the rest of the data in this comic.<br />
;Retirement Year<br />
: In 2027, Stephen Curry will be 39 years old, which is a typical retirement age for NBA players. LeBron James's retirement age is listed as ''Unknown''. <br />
: This may refer to James's high level of play through his mid-30s, when typical players have a decline in their performance.{{Citation needed}}<br />
;FiveThirtyEight Total Rating<br />
: {{w|Nate Silver}} is a political commentator and founder of the website {{w|FiveThirtyEight}}, which uses and promotes statistical approaches in explaining the world. The site's two major areas of focus are in politics (especially on elections - it became famous for correctly predicting for whom 49 of 50 states would vote in the 2008 US presidential election and every US state in the 2012 election, and though it wasn't as accurate in 2016 it had given Donald Trump a larger chance of Electoral College victory than other mainstream media sources) and sports (Silver first got into statistical analysis via baseball). The presence of both sports-related and politics-related topics in the comic, however related they are (or not) with each other, seems to be a nod towards FiveThirtyEight's content.<br />
: Nate Silver has a much higher 538TR than either Curry or James. As explained in the title text, the 538TR combines basketball skill (either real-life or video game basketball) with election forecasting. This could suggest that Silver is proficient at basketball, presumably the video game kind, or else that election forecasting is heavily weighted.<br />
<br />
==Transcript==<br />
{{incomplete transcript|Do NOT delete this tag too soon.}}<br />
:'''NBA Playoffs ''DataDive'' '''<br />
:'''LeBron James and Stephen Curry'''<br />
:'''What makes these superstars so extraordinary?'''<br />
<br />
:[The comic consists of several plots and tables, listed here from top to bottom, left to right.]<br />
<br />
:'''Scatter plot of Social Security number vs Free throw percentage'''<br />
:The Social Security numbers range from 000-00-0000 to 999-99-9999. No pattern discernable, aside from points being a bit denser in the middle of the plot. Steven Curry is marked as a point on the right edge of the plot with a high free throw percentage.<br />
<br />
:'''Scatter plot of 2018 points per game vs Average teammate APGAR score'''<br />
:The APGAR scores range from 0 to 10. Pattern suggests a somewhat positive link between the two factors. LeBron James is marked as having a lot of points, but a low teammate APGAR score of approximately 2.1.<br />
<br />
:'''Shot map'''<br />
:Legend: grey dot for all players, black dot for Stephen Curry<br />
:A diagram of a basketball court is shown with dots placed where players have taken shots at the goal. For the all players category the dots generally cluster next to the goal basket and in front of the three point line. Steven has 3 dots next to the basket (one is behind it), but does cluster next to the three point line. He also has several dots on the other side of the playing field, and outside it, including three in the bleachers and one in the locker room.<br />
<br />
:'''Sandwiches eaten during play vs Win %'''<br />
:A plot that suggests no relation between the factors because practically all dots are in the zero sandwiches column. 2018 Warriors have one dot at around 60 win percentage and 4 sandwiches.<br />
<br />
:'''2018 total points'''<br />
:A table listing teams and their points overall and "When net is within 15° of magnetic north". The rows for the Golden State Warriors and the Cleveland Cavaliers are highlighted, the latter shows an abnormally high score in the magnetic north column.<br />
<br />
:{| class = "wikitable"<br />
! 2018 total points<br />
! Overall <br />
! When net is within 15° of magnetic north<br />
|-<br />
|'''Golden State Warriors'''<br />
|'''9304'''<br />
|'''330'''<br />
|-<br />
|Houston Rockets<br />
|9213<br />
|268<br />
|-<br />
|New Orleans Pelicans<br />
|9161<br />
|219<br />
|-<br />
|Toronto Raptors<br />
|9156<br />
|341<br />
|-<br />
|'''Cleveland Cavaliers'''<br />
|'''9091'''<br />
|'''1644'''<br />
|-<br />
|Denver Nuggets<br />
|9020<br />
|280<br />
|}<br />
<br />
:[A table at the bottom:]<br />
<br />
:{| class = "wikitable"<br />
!<br />
! Stephen Curry<br />
! LeBron James<br />
|-<br />
|Have you heard of him<br />
|Probably<br />
|Yes<br />
|-<br />
|President during most recent game 7 loss<br />
|Obama<br />
|Bush<br />
|-<br />
|Pog collection<br />
|Large<br />
|Staggeringly large<br />
|-<br />
|Career average Fed interest rate<br />
|3.42%<br />
|4.41%<br />
|-<br />
|Name Scrabble score<br />
|22<br />
|22<br />
|-<br />
|Best sport<br />
|Basketball<br />
|Basketball<br />
|-<br />
|Height<br />
|Over 6'<br />
|Over 6'<br />
|-<br />
|Retirement year<br />
|2027<br />
|Unknown<br />
!Nate Silver<br />
|-<br />
|FiveThirtyEight total rating<br>(devised by Nate Silver to combine all metrics into a single stat)<br />
|'''37.4'''<br />
|'''31.8'''<br />
|'''86.6'''<br />
|}<br />
<br />
==Trivia==<br />
This comic was posted the day after the second game in the 2018 NBA Finals between the Golden State Warriors (Stephen Curry's team) and the Cleveland Cavaliers (LeBron James' team). It is the fourth consecutive time the two teams faced each other at the finals, which is unprecedented in major sports leagues in North America. The Warriors won in 2015 and 2017, the Cavaliers won in 2016, and the Warriors are leading the current series 2-0.<br />
<br />
{{comic discussion}}<br />
<br />
[[Category:Sport]]<br />
[[Category:Basketball]]<br />
[[Category:Comics featuring Nate Silver]]<br />
[[Category:Politics]]</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=1587:_Food_Rule&diff=1611181587: Food Rule2018-08-13T16:28:35Z<p>CRGreathouse: /* Explanation */ grammar</p>
<hr />
<div>{{comic<br />
| number = 1587<br />
| date = October 7, 2015<br />
| title = Food Rule<br />
| image = food_rule.png<br />
| titletext = I won't eat invertebrates, because I can fight a skeleton, but I have no idea what kind of spooky warrior a squid leaves behind.<br />
}}<br />
<br />
==Explanation==<br />
There are various {{w|Vegetarianism|vegetarian}} diets which restrict certain foods for ethical or personal concerns. Real vegetarians do not eat any kind of meat, but some only refrain from eating red meat, although this means they are not true vegetarians. Vegetarianism can go as far as to not eating (or even using) any kind of products coming from an animal (i.e. {{w|veganism}}). The comic is a joke on one of the vegetarian rules, namely ''[http://intelligencesquaredus.org/debates/past-debates/item/910-dont-eat-anything-with-a-face don't eat anything with a face]''. This rule is difficult to follow, because it is subjective whether people think a given animal has a {{w|face}}, causing disagreement about what is allowed and what is forbidden to eat.<br />
<br />
[[Randall]] presents a list (see [[#Items on the list|details]] below) of allowed and forbidden food in his diet. For example, he eats meat from typical-looking animals like beef, pork, chicken, and fish. He will also eat plants like fruit, vegetables and grain. But he refuses to eat some of the more odd-looking creatures from the sea like squids, shrimps and oysters. Below the list he explains his rule for what can be eaten: ''I won't eat something if I have to Google to figure out whether or not it has a face'', which is a joke on the disagreements about the ''don't eat anything with a face'' rule. The joke is particularly teasing as it allows most (if not all) kinds of meat, which are the most strictly forbidden foods for even the mildest of vegetarians. Randall does not care about food having faces, he is worried apparently only about having to defend the position that some particular food has a face or not. While it's clear, at least to Randall, that a cow has a face and an apple does not, some beings are harder to classify into one of these categories. For Randall this goes for shrimps, oysters and squids; and apparently actual vegetarians also struggle with these creatures, as can be seen in several on-line questions ([https://answers.yahoo.com/question/index?qid=20080613194541AAwlN90 1], [http://www.chacha.com/question/do-shrimp-have-a-face 2], [http://www.chacha.com/question/do-clams-and-oysters-and-mussels-have-faces 3], [http://www.chacha.com/question/do-octopus-have-faces 4]).<br />
<br />
The title text gives another rule that also would make these same three omissions. This rule is about not eating {{w|Invertebrate|invertebrates}} (animals without a {{w|vertebral column}}, i.e. spineless creatures). As the first four items on the list are meat from four different animals of the type {{w|Vertebrate|vertebrates}} (with vertebral column) and the last three items are from {{w|Plant|plants}}, that explains why these are all OK to eat. But the middle three items are three different animals of the type invertebrates, which Randall does not eat.<br />
<br />
Randall's reason for avoiding invertebrates is somewhat outlandish: he fears that the spirits from creatures he has eaten will come back to haunt him. In horror movies, as well as in video games and roleplaying games with fantastic elements, {{w|undead}} creatures often appear as spooky skeletons (i.e. the [http://zelda.gamepedia.com/Stalfos Stalfos] of the ''{{w|Legend of Zelda}}''); however invertebrates have no skeleton so Randall can't figure out what kind of spooky undead creature will come after him if he eats them (invertebrates may have a {{w|Mollusc shell|shell}} or another type of {{w|exoskeleton}}, but these do not look at all like the typical mental image of a skeleton). Randall imagines that he'll be able to fight a typical skeleton, but is afraid of the unknown ghostly creature an invertebrate may become after dying.<br />
<br />
The comic may also be a joke on the modern {{w|Paleolithic diet|paleo diet}} trend, which emphasizes eating fruit, vegetables, and meat ("anything with a face"). <br />
<br />
Randall has previously depicted cuttlefish as spooky in [[520: Cuttlefish]], and he's also mentioned his dislike of certain foods (namely {{w|lobster}} - another invertebrate) in [[1268: Alternate Universe]].<br />
<br />
===Items on the list===<br />
Here is a list with explanation for each item on Randalls food list:<br />
*{{w|Red meat}}, includes meat from most adult {{w|mammals}}, but many people will probably think of {{w|beefsteak}} from {{w|cattle}}.<br />
*{{w|Pork}}, is meat from {{w|Domestic pig|pigs}}. While technically a "red meat" (according to the US Department of Agriculture) it is popularly considered "the other {{w|white meat}}", hence its own bullet point. <br />
*{{w|Poultry}} are domesticated birds; most people will think of {{w|Chicken (food)|chicken}}.<br />
*{{w|Fish}} covers a very large group of animals, most of them are not eaten on a regular basis, but a large group of fish are {{w|Fish as food|used as food}}.<br />
*{{w|Shrimp}} is used to refer to {{w|Decapoda|ten-footed}} {{w|crustacean}} and some of these are {{w|Shrimp (food)|used for food}}. In the UK they often go under the name {{w|prawns}}.<br />
*{{w|Oysters}} refers to a family of {{w|mollusca}} within the class {{w|bivalvia}} (i.e. body enclosed in shells consisting of two hinged parts). Most people will probably think of the {{w|Ostreidae|true oysters}} specifically the {{w|Ostrea edulis|edible oyster}}, which are not the only edible oyster!. Note that {{w|pearl oyster}} is not a true oyster.<br />
*{{w|Squid}} are {{w|cephalopods}} (also of the mollusca family ) with eight arms arranged in pairs and two longer tentacles. They are closely related to {{w|cuttlefish}} and {{w|octopuses}}.<br />
*{{w|Fruit}} is a part of a flowering plant. Common fruits are {{w|apples}}, {{w|oranges}}, {{w|bananas}} and {{w|pear|pears}}. But in principle anything that comes from a flower is a fruit, including grains. Although in a culinary sense there is a distinction between vegetables and fruit, any part of a flower is actually a vegetable. See below and also see [[388: Fuck Grapefruit]].<br />
*{{w|Vegetables}} are any kind of plant. But in everyday it refers to any part of a plant that is consumed by humans as food as part of a {{w|Umami|savoury}} meal, thus excluding fruit, {{w|Nut (fruit)|nuts}} and cereal grains. For instance a {{w|tomato}} would be seen as a vegetable due to its taste and as a fruit botanically – see the Venn diagram {{w|Fruit#Botanic fruit and culinary fruit|here}}.<br />
*{{w|Grain|Grains}} are small, hard, dry {{w|seeds}}. Usually when mentioning these people will think of breakfast {{w|cereal}} grains. Typical grains are {{w|corn}}, {{w|rice}} and {{w|wheat}}. As mentioned above grains are botanically both a fruit and a vegetable.<br />
<br />
==Transcript==<br />
:[There is a caption above a list of food with indication whether it is OK or not to eat. Below is another caption.]<br />
<br />
:My food rule:<br />
:{| class="wikitable" style="border: 0px;"<br />
|-<br />
| style="border: 0px; text-align: right" | Red meat<br />
| style="border: 0px; color:green;" | ✓<br />
|-<br />
| style="border: 0px; text-align: right" | Pork<br />
| style="border: 0px; color:green;" | ✓<br />
|-<br />
| style="border: 0px; text-align: right" | Poultry<br />
| style="border: 0px; color:green;" | ✓<br />
|-<br />
| style="border: 0px; text-align: right" | Fish<br />
| style="border: 0px; color:green;" | ✓<br />
|-<br />
| style="border: 0px; text-align: right" | Shrimp<br />
| style="border: 0px; color:red;" | X<br />
|-<br />
| style="border: 0px; text-align: right" | Oysters<br />
| style="border: 0px; color:red;" | X<br />
|-<br />
| style="border: 0px; text-align: right" | Squid<br />
| style="border: 0px; color:red;" | X<br />
|-<br />
| style="border: 0px; text-align: right" | Fruit<br />
| style="border: 0px; color:green;" | ✓<br />
|-<br />
| style="border: 0px; text-align: right" | Vegetables<br />
| style="border: 0px; color:green;" | ✓<br />
|-<br />
| style="border: 0px; text-align: right" | Grains<br />
| style="border: 0px; color:green;" | ✓<br />
|}<br />
:I won't eat something if I have to Google to figure out whether or not it has a face.<br />
<br />
{{comic discussion}}<br />
[[Category:Charts]]<br />
[[Category:Food]]</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=1798:_Box_Plot&diff=1611041798: Box Plot2018-08-13T14:53:37Z<p>CRGreathouse: category</p>
<hr />
<div>{{comic<br />
| number = 1798<br />
| date = February 13, 2017<br />
| title = Box Plot<br />
| image = box_plot.png<br />
| titletext = You have to be careful doing this. Sometimes, when you push the whisker down, dynamite explodes.<br />
}}<br />
<br />
==Explanation==<br />
This comic shows three vertical {{w|Box plot|box plots}} in the first panel, hence the title.<br />
<br />
In {{w|descriptive statistics}}, a box plot is a convenient way of graphically depicting groups of numerical data through their {{w|quartiles}}. The second quartile is the median and it is not indicated in this comic, as it should be a line through the box (see the {{w|Quartile#Definitions|definitions of quartiles}}). But the top and bottom of the box is the first and third quartile, which splits the lowest/highest 25% off data of from the highest/lowest 75%, respectively. <br />
<br />
Box plots may also have lines extending vertically from the boxes (whiskers) indicating variability outside the upper and lower quartiles, (that is, the ''highest'' and ''lowest'' values in the data,) hence the terms box-and-whisker plot. These can be used to indicate the {{w|interquartile range}}, a measure of {{w|statistical dispersion}}. These have been included on the three boxes in the plot. <br />
<br />
The joke in the comic arises, because it turns out that the box plot is actually three real world objects and [[Cueball]] walks into the plot in the second panel, climbs up on the lower first box and on to the highest middle box. When the boxes are depicted in the orientation shown, the boxes can look like they are pumps, where the middle part, the box, can be pumped up. And Cueball does just that in the fourth panel, by pushing the top whisker down and when he leaves in the fifth and last panel, this box stays inflated, with the whisker visibly lower than in the first three panels, although higher than when he pushed it down in the fourth panel. (Inflating things that cannot be inflated was also the joke in [[1395: Power Cord]]. But as opposed to inflating the meaning of data, which many researchers sadly do in the real world, what [[Beret Guy]] does in that comic, is strictly [[:Category:Strange powers of Beret Guy|supernatural]].)<br />
<br />
It could be said that the "data" in this comic was "inflated" and thus Cueball has been trying to show a smaller interquartile range than there actually is, thus inflating the possible conclusions that could be drawn from the data. <br />
<br />
The title text refers to how {{w|dynamite}}, an explosive, often used to have detonator boxes (aka. {{w|blasting machine}}s) which also looked similar to the top part of the box (without the lower whisker). These detonators were most commonly used for mining, with long wires leading to the explosives. Modern blasting machines are operated by push buttons and key switches, but the old push-handle design still resonates in the public consciousness today, due to its exposure in classic slapstick cartoon shorts like {{w|Looney Tunes}}, especially often used by {{w|Wile E. Coyote and the Road Runner|Wile E. Coyote}} against the Road Runner. See [https://youtu.be/0R66Fvhx0vQ?t=1m2s this compilation] for examples.<br />
<br />
The title text also refers to so-called [http://biostat.mc.vanderbilt.edu/wiki/pub/Main/TatsukiRcode/Poster3.pdf dynamite plots]. This type of plot used to be very common in scientific publications, but since it hides most details about one's actual data, it is now frowned upon. The recommended alternative is the box plot.<br />
<br />
The title text thus warns against this kind of data inflation, since sometimes it can go awry and lead to explosions. [[Randall]] has often made comics about presenting data as more important that they are, in one way or another, and this comics clearly falls into that category. See for example [[882: Significant]], [[1132: Frequentists vs. Bayesians]], [[1478: P-Values]] and [[1574: Trouble for Science]], and this one for manipulating the way data is presented: [[558: 1000 Times]].<br />
<br />
A box plot was also used in [[539: Boyfriend]], maybe the only other time in xkcd. There are many other types of [[:Category:Charts|data carts]] that have their own subcategories, but not this type.<br />
<br />
==Transcript==<br />
:[A box plot with three vertical data points is shown. Each point consists of a shaded rectangular box, and a T-shaped whisker on each end.]<br />
<br />
:[Cueball walks in; revealing that the box plot is a physical object which he looks up on.]<br />
<br />
:[Cueball climbs on top of the diagram, holding onto the top whisker of the leftmost data point.]<br />
<br />
:[Cueball, now standing upright on top of the box plot, bends over, grips the whisker of the center data point and starts pumping. The shaded box of the data point bulges. Cueball's movements are accompanied by sounds:]<br />
:''Pump''<br />
:''Pump''<br />
:''Pump''<br />
<br />
:[The box has been inflated so much that it almost touches the left and right data points. Cueball walks away.]<br />
<br />
*'''Click''' to expand for a more detailed description:<br />
<div class="mw-collapsible mw-collapsed leftAlign" style="width:100%"><br />
<br><br />
:[A box plot with three data points are shown. Each point consist of a standing rectangular box shaded gray and from each end of the box there extend a whisker which ends in a short line orthogonal to the whiskers line. The middle box is the longest and extends both above and below the other two, as does its whiskers. The first box is larger than the last, but those two are at the same level at their bottoms. But the bottom whisker of the first is longer than the last. If the middle box is about 1.9 cm high it will have a 1 cm whiskers below and an 0.8 cm whisker at the top for a total length of 3.7 cm. Then the first box would be 1.7 cm high with the bottom whisker 0.8 cm, and the top whisker 0.5 cm for a total length of 3 cm. The last box is then 1.4 cm high with the top whisker being 0.6 cm and the bottom 0.5 cm, for a total length of 2.5 cm. The boxes are 0.7 cm wide and the end lines for the whiskers are 0.5 cm wide. The data points stay in the same place and have the same dimensions through all five panels, except the middle point which changes as explained below in the last two panels.]<br />
<br />
:[Cueball walks into the panel from the left looking up at the top of the first box.]<br />
<br />
:[Cueball climbs on to the first box, by holding on to the top and stem of the first whisker, while putting a bend leg on the top of the box, while the other legs hangs down the side of the box.]<br />
<br />
:[Cueball now stands on top of the plot, with one foot on the first box and a second foot on the middle box. He is bend over the whisker on the middle box, holding on to it with both hands, one on either side of the middle stem. He is pushing it up and down, as indicated with two light gray version of Cueball's arms and the stem, with the stem in the top gray version being about 0.1 cm above the original height and with Cueball thus with more bend arms than in the normal black version. He has thus pulled the "lever" a bit further up. The second gray version is in between these two, about 0.2 cm below the upper gray, and thus 0.1 cm below the original position and thus with a bit less bend arms that the top gray. In the final black version where the arms are almost stretched, the top is now only 0.5 cm over the box, 0.3 cm below the original position, further 0.2 cm below the second gray. On top of all this the middle box also increases its width bulging out in the top part with a maximum bulge around 0.6 cm below the top, to a width of 1.1 cm. That the movement of Cueball goes both ways are indicated both with 6 small double lines around Cueball's shoulders, arms and hands, but also by the sound his actions make.]<br />
<br />
:[Finally Cueball has climbed down and walks away to the right, the panel panning a bit after him so the inflated box plot moves to the left in the panel. The middle box is now inflated evenly so the maximum bulge is at the middle and it is almost touching the other two boxes with a width of 1.4 cm, double the original thickness. There have all the time been 1.5 cm between the edges of the two other boxes, so the inflated box does not interfere with the other two, but is very close to their edges. The whisker at the bottom of the middle box is unchanged but the top whisker ended up being only 0.6 cm high, 0.2 cm lower than original position, but a 0.1 cm higher than when Cueball pushed down on it in the previous panel.]<br />
</div><br />
<br><br />
<br />
{{comic discussion}}<br />
<br />
[[Category:Comics featuring Cueball]]<br />
[[Category:Charts]]<br />
[[Category:Science]]<br />
[[Category:Statistics]]</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=1835:_Random_Obsessions&diff=1610171835: Random Obsessions2018-08-09T15:21:28Z<p>CRGreathouse: category</p>
<hr />
<div>{{comic<br />
| number = 1835<br />
| date = May 10, 2017<br />
| title = Random Obsessions<br />
| image = random obsessions.png<br />
| titletext = I take the view that "open-faced sandwiches" are not sandwiches, but all other physical objects are.<br />
}}<br />
<br />
==Explanation==<br />
<br />
This comic is formatted as a graph showing various Internet trends over the years according to [https://trends.google.com/trends/explore?date=all&q=robot%20monkeys,pirates%20vs%20ninjas,zombies,bacon,definition%20of%20sandwich Google Trends]. The caption states that these "random obsessions," as stated in the title, have 9-10 year cycles, and so predicts that the sandwich debate will be over by around 2024.<br />
<br />
Discussions about the definition of "sandwich" are surprisingly common on the web, such as "Is hot dog a sandwich?" (See this [https://www.reddit.com/r/Sandwiches/comments/6587ub/what_is_a_sandwich_debate/ discussion] on Reddit)<br />
<br />
<br />
The title text is a joke based on the debate over the definition of a sandwich. The speaker, presumably [[Randall]], starts out with the fairly reasonable stance that open-faced sandwiches are not true sandwiches, but then veers off into the absurd by claiming that literally every other physical object in the universe ''is'' a sandwich. We can only hope that Randall does not extend this view to {{w|Cannibalism|human beings}}. (On the other hand, Randall may simply be defining a sandwich in an unusual way without implying that all other items are edible. Such strange definitions have been seen before, in the title text of [[1405: Meteor]].)<br />
<br />
The other obsessions mentioned are, in order: robot monkeys, pirates vs ninjas, zombies, and bacon.<br />
<br />
"Robot Monkeys" likely refers to people being obsessed with a movie or robots of some kind. It may specifically refer to the American/Japanese animated TV series, {{w|Super Robot Monkey Team Hyperforce Go!}}, which aired from September 18, 2004 to December 16, 2006. It is possible that, based on this, that the trend curve does not actually begin in 2001, but does actually begin in 2004 as shown.<br />
<br />
"Pirates vs Ninjas" refers to a longstanding internet meme, popular in roughly the years shown on the chart, that held that ninjas and Caribbean pirates were arch-enemies.<br />
<br />
"Zombies" refers to the recent occurrence of zombie themed television shows (The Walking Dead) and movies (World War Z etc).<br />
<br />
Though the trend is dying out, as seen by the fact the graph is past the peak, there has been an explosion in bacon flavored/scented products as well as items of clothing and decor that look like bacon. The YouTube channel Epic Meal Time was also part of the bacon fad, as adding large quantities of bacon to the meal being prepared was one of the running gags of the channel.<br />
<br />
==Transcript==<br />
:[The comic shows curves plotted in an (x,y)-plane. The x-axis shows years from 2004 to 2017, with every even year labeled. The y-axis is labeled "popularity relative to peak (based on google trends)". There are five vaguely bell-shaped curves, each stretching over 9-10 years. It is implied that they rise from a value close to zero, to which they also return.]<br />
<br />
:The curve labeled "robot monkeys" peaks in early 2005 and ends near the x-axis in late 2011.<br />
:The curve labeled "pirates vs ninjas" peaks in late 2008 and ends in late 2014. <br />
:[The remaining three curves all end in mid 2017, the comic release date. ]<br />
:The curve labeled "zombies" starts in late 2007 and peaks in early 2013. By 2017 it has fallen to about 30% of its peak value.<br />
:The curve labeled "bacon" starts in late 2009 and peaks in mid-2015. By 2017 it shows a value of about 90% of its peak value.<br />
:The curve labeled "definition of a sandwich" starts in late 2013 and in 2017 it has reached approximately half its peak value.<br />
<br />
:[Text below the panel:]<br />
:Judging from Google Trends, these random semi-ironic obsessions seem to last about nine or ten years, so we should be done with the sandwich thing by 2024.<br />
<br />
{{comic discussion}}<br />
[[Category:Line graphs]]<br />
[[Category:Zombies]]</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=54:_Science&diff=16101654: Science2018-08-09T15:06:54Z<p>CRGreathouse: category</p>
<hr />
<div>{{comic<br />
| number = 54<br />
| date = January 18, 2006<br />
| title = Science<br />
| image = science.jpg<br />
| titletext = Bonus points if you can identify the science in question<br />
}}<br />
<br />
==Explanation==<br />
The solid line represents the theoretical {{w|blackbody radiation|radiation for a blackbody}} at 2.73 K according to {{w|Planck's Law}} (derived as early as 1900 by {{w|Max Planck}}). The formula, almost as written in the graph, can be found {{w|Black-body radiation#Planck's law of black-body radiation|here}}. The only changes are that on Wikipedia, the frequency f is represented by the Greek letter ν (nu) and the temperature T is included as an independent variable, so I(f) becomes I(v,T). However, I(v,T) still represents the {{w|Radiance#Spectral radiance|spectral radiance}} (similar to energy density). In this formula, h is the Planck constant, c is the speed of light in a vacuum, and k is the Boltzmann constant. The frequency (f or v) along the x-axis is measured in {{w|GHz}} (Giga (or billion) Hertz). The curve peaks at 160.4&nbsp;GHz. There is no scale or unit on the {{w|energy density}} on the y-axis.<br />
<br />
The theory is that the blackbody in question was the universe at the point when it had cooled down enough {{w|Decoupling (cosmology)|to allow photons to escape}}, {{w|Chronology of the universe|0.38 million years}} into its {{w|Big Bang|13.8 billion years}} history. The photons that reach us today are the ones that have been travelling to us at lightspeed since then. As the light from astronomical objects suffers from {{w|redshift}} due to the expansion of the universe, and this shift becomes more pronounced with distance from the observer, this light displays in the infrared range.<br />
<br />
The title text praises viewers who can identify where this equation and corresponding graph come from (without consulting this wiki, of course).<br />
<br />
===Official T-shirt explanation===<br />
This comic was made into a T-shirt, but is no longer available.<br />
<br />
On the xkcd store, there was both an '''explanation for the title:'''<br />
<!-- Begin Quote DO NOT CORRECT This is a copy paste from xkcd with errors.--><br />
Science: We finally figured out that you could separate fact from superstition by a completely radical method: observation. You can try things, measure them, and see how they work! {{w|Bitch (insult)|Bitches}}. <br />
<!-- End Quote DO NOT CORRECT --><br />
<br />
And specifically an '''explanation for the graph:''' <br />
<!-- Begin Quote DO NOT CORRECT This is a copy paste from xkcd with errors.--><br />
The graph on the back of the shirt is data from the {{w|COBE|COBE mission}} which looked at the background microwave glow of the universe and found that it fit perfectly with the idea that the universe used to be really hot everywhere. This strongly reinforced the Big Bang theory and was one of the most dramatic examples of an experiment agreeing with a theory in history -- the data points fit perfectly, with error bars too small to draw on the graph. It's one of the most triumphant scientific results in history.<br />
<!-- End Quote DO NOT CORRECT --><br />
<br />
The above is a direct copy paste, with errors. The current wiki page of the COBE mission can be found at {{w|Cosmic Background Explorer|http://en.wikipedia.org/wiki/Cosmic_Background_Explorer}}<br />
<br />
==Transcript==<br />
:[A graph with a curve that begins at zero, then peaks at a given frequency, indicated via a thin vertical line, and then fades down towards zero. It is possible to see the data points, which fit the curve perfectly. The y-axis is labelled. Along the x-axis the zero point and the frequency where the peak has its maximum are labelled and close to the arrow the unit of this axis is written.]<br />
:y-axis: Energy Density<br />
:Along the x-axis:<br />
::0 <br />
::160.4 <br />
::GHz<br />
:[Above the graph to the right is the following formula, with the last inner parentheses only included to make the formula clear, since in the drawing the fractions are written above and below horizontal lines:]<br />
:I(f) = (2hf<sup>3</sup>/c<sup>2</sup>)(1/(e<sup>hf/kT</sup>-1))<br />
:[Below the graph is written the following:]<br />
:'''Science.'''<br />
:It works, bitches.<br />
<br />
==Trivia==<br />
*This was the 48th comic originally posted to [[LiveJournal]].<br />
**The previous was [[50: Penny Arcade]].<br />
**The next was [[51: Malaria]].<br />
*This comic kept its original title: "Science"<br />
**It is part of the last six comics on LiveJournal that all had a title without the word "Drawing" in it. <br />
**Five of these had exactly the same title on both sites.<br />
**Only 11 comics have the same title on both sites.<br />
**Apart from the [[:Category:First day on LiveJournal|thirteen first comics]] posted to LiveJournal, there were only three other comics without the word "Drawing" in the title before these last six.<br />
*Original [[Randall]] quote: "Bonus points if you can identify the science in question."<br />
**Only difference between this and the title text on xkcd is the last period: "."<br />
**It is rare that these two texts are so similar.<br />
*This comic was one of the last 11 comics posted on LiveJournal.<br />
**These 11 comics were [[:Category:Posted on LiveJournal after xkcd|posted both on LiveJournal and xkcd]] after the [[xkcd]] site opened on the 1st of January 2006. <br />
**The first six comics were posted on both sites on the same day. But not this one.<br />
*For some reason, this comic was first posted a week later on xkcd (25 January 2006), on the day that [[53: Hobby]] was released on LiveJournal.<br />
**On the day 54: Science was released on LiveJournal (18 January 2006), another comic ([[51: Malaria]]) was released on xkcd.<br />
**[[51: Malaria]] also became the next comic released on LiveJournal, but this meant that three comics in a row were posted a release day earlier on xkcd than on LiveJournal.<br />
**Only with the last comic released on LiveJournal, [[55: Useless]], did the two sites release the same comic on the same day again.<br />
* "It works, bitches" has been quoted by Richard Dawklins in 2013, when questioned on the superiority of science. It is not sure whether he was quoting xbcd, though. See https://www.theverge.com/2013/4/2/4173576/richard-dawkins-on-science-it-works-bitches<br />
<br />
{{comic discussion}}<br />
<br />
[[Category:Comics posted on livejournal| 48]]<br />
[[Category:Posted on LiveJournal after xkcd]]<br />
[[Category:Line graphs]]<br />
[[Category:Analysis]]<br />
[[Category:Math]]<br />
[[Category:Physics]]<br />
[[Category:Science]]</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=1275:_int(pi)&diff=1610151275: int(pi)2018-08-09T15:05:18Z<p>CRGreathouse: more specific category</p>
<hr />
<div>{{comic<br />
| number = 1275<br />
| date = October 9, 2013<br />
| title = int(pi)<br />
| image = int pi.png<br />
| titletext = If replacing all the '3's doesn't fix your code, remove the 4s, too, with 'ceiling(pi) / floor(pi) * pi * r^floor(pi)'. Mmm, floor pie.<br />
}}<br />
<br />
==Explanation==<br />
This comic purports to provide a tip to programmers, that the number "{{w|3 (number)|3}}" is cursed and shouldn't be used. There is no explanation given as to why the number 3 is cursed, and it could well have been chosen arbitrarily. The title text hints that the consequence for using the cursed number is non-functioning code, a pain for any programmer. The absurdity of the number 3 somehow being cursed is part of the humor.<br />
<br />
To assist the programmer, the comic gives an example of how to avoid the use of the number 3, by using a slightly convoluted method of using <code>int(pi)</code>, which means the {{w|integer}} part of {{w|pi}}, without the {{w|fractional part}}. Pi, an {{w|irrational number}}, has a value starting <code>3.14159...</code>, making <code>int(pi)</code> equal to 3. This is demonstrated in a formula to calculate the {{w|Sphere#Enclosed volume|volume of a sphere}}, normally (4/3)*pi*(r^3), but converted for avoidance of the number 3 to (4/int(pi))*pi*(r^int(pi)).<br />
<br />
For a number of reasons it is a good programming practice to use {{w|Variable (computer science)|variables}} and {{w|Constant (programming)|constants}} where a value is used in multiple places, however this is not typically used in the case of natural numbers. There are unusual situations where this type of programming is a valid method, however typically for more specific circumstances, and not a certain number being seen as cursed.<br />
<br />
In the title text, Randall takes the joke a step further, suggesting the usage of {{w|floor and ceiling functions}}: <code>ceiling(pi)</code> would be pi rounded ''up'' to the next integer, which is {{w|4 (number)|4}}; and <code>floor(pi)</code> is pi rounded ''down'' to the next integer, which is 3. (Note that <code>int(n)</code> and <code>floor(n)</code> have the same value when <code>n</code> is greater than or equal to zero. For values less than zero, <code>int(n)</code> is equal to <code>ceiling(n)</code>.)<br />
<br />
The joke here plays on the fact that basic rules of programming are confusing and novice programmers are often told to simply not do certain things without any explanation (see [[292: goto]]). This includes, in particular, a general proscription against "{{w|Magic number (programming)#Unnamed numerical constants|magic numbers}}" in the code. Replacing all significant magic numbers with named constants makes programs easier to read, understand and maintain. Randall takes this to an extreme by suggesting that certain numbers could be inherently problematic, but the general idea is perfectly believable.<br />
<br />
[https://www.youtube.com/watch?v=1WsDtn-feuI ''Mmm... Floor pie.''] is a reference to Homer Simpson.<br />
<br />
See also {{w|Cargo cult programming}}.<br />
<br />
==Transcript==<br />
:volume(r) = (4/int(pi))*pi*r^int(pi)<br />
:Programming Tip: The number "3" is cursed. Avoid it.<br />
<br />
{{comic discussion}}<br />
[[Category:Programming]]<br />
[[Category:Geometry]]</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=1184:_Circumference_Formula&diff=1610141184: Circumference Formula2018-08-09T15:05:03Z<p>CRGreathouse: more specific category</p>
<hr />
<div>{{comic<br />
| number = 1184<br />
| date = March 11, 2013<br />
| title = Circumference Formula<br />
| image = circumference_formula.png<br />
| titletext = Assume r' refers to the radius of Earth Prime, and r'<nowiki/>' means radius in inches.<br />
}}<br />
<br />
==Explanation==<br />
The {{w|circumference}} C of a {{w|circle}} is 2{{w|pi|π}}''r'', where ''r'' is the {{w|radius}} of the circle. [[Randall]] then makes a {{w|Note (typography)|footnote}} about ''r'', using <sup>2</sup>. This creates a typographical ambiguity, since a superscript 2 can also be an exponent (as in ''x''<sup>2</sup>). The comical purpose of this ambiguity is that the formula initially makes an appearance of a mistake and confusion with the formula for the ''{{w|area}}'' of the circle: A = π''r'' <sup>2</sup>. If and only if the reader realizes that the superscript text is a reference to a footnote will they understand that the author has in fact supplied the correct formula.<br />
<br />
The title text makes a related joke. Randall has used r' (r-{{w|Prime (symbol)|prime}}) and r" (r-prime-prime, typically pronounced as ''r double prime''). The title text can be explained thusly:<br />
<br />
Like many symbols, prime has widely differing meanings depending on context. In mathematics prime is often employed to distinguish corresponding components in analogous systems. For example, in a description of a basic physical system, if the velocity of an object is denoted with the variable ''v'', the velocity of that object at time=0 may be denoted with ''v′''. Playing off this use of prime, Randall has selected the radius of {{w|Earth Prime}}, a concept used in speculative fiction with parallel universes and multiple Earths. Earth Prime is our Earth (or at least the Earth from which the protagonists originate).<br />
<br />
However, other disciplines use prime to mean other things. In timekeeping and navigations ' denotes minutes (fractions of hours or degrees, respectively) and " denotes seconds (fractions of minutes). In the United States and some other places not using meters to measure distance, ' denotes feet and " denotes {{w|inches}}.<br />
<br />
The suggestion of using r' or r" does not cause any mathematical confusion, but using the former to denote the radius of a specific object and the latter to denote a radius using a specific unit of measurement would be highly esoteric. Furthermore, r' and r" can be used in calculus as a method of denoting, respectively, a first derivative and a second derivative. For someone attempting to use the formula and some derivative representing a circle's radius, trouble could result quite easily.<br />
<br />
<small><sup>2</sup> These are not intended to indicate the presence of a footn... oh, never mind.</small><br />
<br />
==Transcript==<br />
:Circumference of a circle:<br />
:2πr<sup>2</sup><br />
:<sup>2</sup>The circle's radius<br />
<br />
{{comic discussion}}<br />
[[Category:Geometry]]</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=866:_Compass_and_Straightedge&diff=161013866: Compass and Straightedge2018-08-09T15:04:38Z<p>CRGreathouse: more specific category</p>
<hr />
<div>{{comic<br />
| number = 866<br />
| date = February 28, 2011<br />
| title = Compass and Straightedge<br />
| image = compass and straightedge.png<br />
| titletext = The Greeks long suspected this, but it wasn't until April 12th of 1882 that Ferdinand von Lindemann conclusively proved it when he constructed himself the most awesome birthday party possible and nobody showed up.<br />
}}<br />
<br />
==Explanation==<br />
{{w|Compass-and-straightedge construction|Compass and straightedge constructions}} are a class of problems in classical geometry. They take the form "Using only a compass and a straightedge, construct X", where X is a geometric figure such as a regular pentagon. The subject is typically covered in high school mathematics. Three such constructions ({{w|squaring the circle}}, {{w|Angle trisection|trisecting the angle}} and {{w|doubling the cube}}) remained unsolved for thousands of years before being shown impossible with the use of modern algebraic techniques.<br />
<br />
The comic begins as if it were stating a problem in classical geometry but veers into an observation that no amount of technical knowledge can substitute for human companionship. An additional layer of humor is that [[Cueball]] is a stick figure so technically it is possible to create friends with a straightedge and a compass, a figure constructed like Cueball is.<br />
<br />
{{w|Ferdinand von Lindemann}} was a German mathematician who showed in 1882 that pi is not a zero of any polynomial with rational coefficients, i.e. it is a transcendental number. Transcendental numbers cannot be constructed with straightedge and compass. This proves that {{w|squaring the circle}} (a problem where it is required to construct a square with the same area as a given circle) is impossible, being as the sides of the square would need to be √π times the radius of the circle, and pi is not constructible.<br />
<br />
==Transcript==<br />
:I learned in high school what geometers discovered long ago:<br />
:[Cueball, holding a compass and straightedge, looks sad.]<br />
:Using only a compass and straightedge, it's impossible to construct friends.<br />
<br />
{{comic discussion}}<br />
[[Category:Comics featuring Cueball]]<br />
[[Category:Geometry]]</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=721:_Flatland&diff=161012721: Flatland2018-08-09T15:04:12Z<p>CRGreathouse: more specific category</p>
<hr />
<div>{{comic<br />
| number = 721<br />
| date = March 31, 2010<br />
| title = Flatland<br />
| image = flatland.png<br />
| titletext = Also, I apologize for the time I climbed down into your world and everyone freaked out about the lesbian orgy overseen by a priest.<br />
}}<br />
<br />
==Explanation==<br />
This comic is a reference to the satirical novel {{w|Flatland|''Flatland: A Romance of Many Dimensions''}}, in which a society of flat shapes live in a {{w|Two-dimensional space|2D}} world. Half the book is a direct satire of {{w|Victorian era|Victorian}} society, and the other half explores the experience of discovering a new dimension, where a sphere introduces a square (named A. Square) to {{w|Three-dimensional space|3D}}. [[Cueball]] appears to have taken the place of this sphere, and the comic takes place after the square knows the third dimension exists.<br />
<br />
Humans will never fully be able to grasp the concept of a four spatial dimensions (at least not in the foreseeable future), but there are ways of squashing or slicing four dimensions to create partial visualizations of 4D space. {{w|Miegakure}} is a 4D game that uses cross-sections of 4D space. Cueball attempted to play it, but after having his mind blown, he gained more sympathy for A. Square, who'd had similar trouble understanding 3D. A. Square accepts his apology.<br />
<br />
The joke here is that Cueball was being silly and drew lines on A. Square to make him look like {{w|SpongeBob SquarePants (character)|SpongeBob}}, which did not make the square happy. Cueball apologizes again.<br />
<br />
The title text is a third apology for when Cueball crawled down into the second dimension. Being a stick figure, he is comprised of a circle and straight lines. In Flatland, circles are priests (Flatland's highest social level), and all women are lines; thus, to a watcher in Flatland, Cueball would look very much like a priest above many connected women, which may look like a lesbian orgy.<br />
<br />
==Transcript==<br />
:[Cueball encounters a square on the ground.]<br />
:Cueball: Hey, A. Square. How's Flatland?<br />
:Square: Still flat. What's up?<br />
:Cueball: I just spent an hour playing a demo of this 4D game called Miegakure.<br />
<br />
:[A character in Miegakure jumps around the 4D landscape.]<br />
:Trying to jump from block to block in four dimensions hurt my brain.<br />
<br />
:Cueball: So I apologize for giving you a hard time when you were slow to understand 3D space. I sympathize now.<br />
:Square: It's okay.<br />
<br />
:Cueball: Also, I apologize for drawing arms, legs, and eyes on you to make you look like SpongeBob. That was out of line.<br />
:Square: Yes, it was.<br />
<br />
==Trivia==<br />
*There is actually a SpongeBob episode featuring a flat creature that resembles a crude drawing of SpongeBob.<br />
<br />
===UniXKCD===<br />
*This comic was released on March 31, 2010 and was still up on April 1st, 2010. <br />
**On {{w|April_Fools%27_Day|April Fools' Day}} in 2010 [[Randall]] altered the website to mimic a {{w|Unix}} command line interface. <br />
**This interface is still available on [https://uni.xkcd.com uni.xkcd.com] and the source code is available on [https://github.com/chromakode/xkcdfools GitHub]. <br />
**See more on the [[UniXKCD]] April Fools' Day joke.<br />
<br />
{{comic discussion}}<br />
<br />
[[Category:Comics with color]]<br />
[[Category:Comics featuring Cueball]]<br />
[[Category:Geometry]]<br />
[[Category:Video games]]<br />
[[Category:Homosexuality]]<br />
[[Category:Sex]]</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=88:_Escher_Bracelet&diff=16101188: Escher Bracelet2018-08-09T15:03:52Z<p>CRGreathouse: more specific category</p>
<hr />
<div>{{comic<br />
| number = 88<br />
| date = April 12, 2006<br />
| title = Escher Bracelet<br />
| image = escher_wristband.jpg<br />
| titletext = The only downside is that it would be a little uncomfortable.<br />
}}<br />
<br />
==Explanation==<br />
This image parodies "WWJD" bracelets, which is an acronym for "What Would Jesus Do?". Christians (primarily) wear such bracelets (or other "WWJD" paraphernalia) as a reminder to act in a way that Jesus would act, which presumably is the "Christian" way to act. It is not entirely clear, but this particular bracelet appears to be the rubber type most famously popularized by the yellow ones of cyclist Lance Armstrong's {{w|Livestrong}} charity, which later became a popular fad for all sorts of charitable and non-charitable causes.<br />
<br />
In this comic, the "J" has been replaced by an "E" for {{w|M. C. Escher}}, a Dutch graphic artist (1898–1972) best known for art containing imagery that would be impossible in the real world (often referred to as impossible constructions or optical illusions). Among his most famous works are "{{w|Drawing Hands}}" – two hands drawing each other on paper; "{{w|Relativity (M. C. Escher)|Relativity}}", in which a series of staircases and arches come from the floor, ceiling, and the walls in all directions, each with people standing on them as if each direction is "down"; and "{{w|Ascending and Descending}}" – a building with a staircase on its roof that is a closed square that appears to ascend or descend infinitely, depending on the direction that is walked.<br />
<br />
In keeping with Escher's art, the WWED bracelet has a single half-twist in it, creating what is known as a {{w|Mobius strip}}. Although this is not an impossible construction, it is still an apparently confusing structure that Escher used in his art. Most notably, his work "Mobius Strip II" depicts ants crawling around a Mobius strip. One can create this shape simply by taking a strip of paper (or any bendable material), making a half twist, and attaching the ends together. If you draw a single continuous line starting down the centre of the bracelet from the middle of the "W" going left, you will end up drawing from the "WWED", going around again on the "inside" of the bracelet, before coming back around to the front again and ending up at the "D". In other words, the surface of the bracelet has only one side (the front and the back are the same side). The phrase "the only downside" in the image-text may be a pun referencing this one-sidedness. As the title text suggests, the twist in the bracelet might make it uncomfortable to wear.<br />
<br />
==Transcript==<br />
:[A Livestrong-type bracelet is featured, but with an Escher twist in it. The band is a Mobius strip. The band has the letters "WWED" printed on it.]<br />
:What Would Escher Do?<br />
<br />
{{comic discussion}}<br />
<br />
[[Category:Geometry]]</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=85:_Paths&diff=16101085: Paths2018-08-09T15:03:38Z<p>CRGreathouse: more specific category</p>
<hr />
<div>{{comic<br />
| number = 85<br />
| date = April 5, 2006<br />
| title = Paths<br />
| image = paths.jpg<br />
| titletext = It's true, I think about this all the time.<br />
}}<br />
<br />
== Explanation ==<br />
This comic centers around the consideration of what is the shortest path available to a person traveling by foot. [[Cueball]] has to travel across a rectangular distance, which has an established path around the periphery. When Cueball follows these paths, he has to walk for 60 seconds. He realises that by ignoring the paths and taking the {{w|Desire path|desire lines}} from corner to corner, his route will be shorter, and he calculates that he could cut up to 26% of his time. As a result, every time he has to travel this rectangle, he worries about the extra time taken as a result of following the path.<br />
<br />
==Transcript==<br />
:[Blueprint of a campus. Two buildings in the upper and lower left corners, respectively, and a rectangular lawn. A road encloses the lawn, another road traverses horizontally through the center of the lawn. The character is in the lower left and the upper right corner, where it says "my apartment".]<br />
:[Dashed line 1, from the lower-left along the road to the top-left corner, then to the top-right corner.] 60 seconds<br />
:[Dashed line 2, from the lower-left along the road up to the center crossroads, then diagonally over the lawn to the top-right corner.] 48 seconds (80%)<br />
:[Dashed line 3, diagonally from the lower-left to the top-right corner.] 44.7 seconds (74%)<br />
:My apartment<br />
:#1=t<br />
:#2=(t*(1+√2))/3<br />
:#3=(t*√5)/3<br />
:When I'm walking, I worry a lot about the efficiency of my path.<br />
<br />
{{comic discussion}}<br />
[[Category:Geometry]]<br />
[[Category:Comics featuring Cueball]]<br />
[[Category:Maps]]</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=1029:_Drawing_Stars&diff=1610091029: Drawing Stars2018-08-09T15:03:17Z<p>CRGreathouse: category</p>
<hr />
<div>{{comic<br />
| number = 1029<br />
| date = March 14, 2012<br />
| title = Drawing Stars<br />
| image = drawing_stars.png<br />
| titletext = Screw these 36-degree angles. I'm converting to Judaism.<br />
}}<br />
<br />
==Explanation==<br />
[[Randall]] attempts to draw a {{w|five-pointed star}}; the easiest way to do this free-hand is by drawing a {{w|pentagram}}, the simplest regular star figure in geometry. Once you've seen it done, you can usually draw a pentagram in one continuous motion.<br />
<br />
Simply put, Randall gets self-conscious and messes up.<br />
<br />
The title text explains the fact that a five-pointed star has all angles at 36 degrees which sums to 180, like a common {{w|Triangle|triangle}}. So Randall converts to {{w|Judaism}} with its {{w|Star of David|six pointed star}} symbol, which he hopes is easier to draw because it is composed of two {{w|equilateral triangle}}s. This also suggests that he is converting from {{w|Modern paganism|neopaganism}} just to have a religious star he can draw well.<br />
<br />
==Transcript==<br />
:HOW TO DRAW A STAR:<br />
:[A slightly curved line is drawn, starting with a point near the top center of the panel, and going downward and to the left at approximately a 23-degree angle, with an arrow at the end.]<br />
<br />
:[Another slightly curved line goes up and to the right, creating a 34-degree angle with the first line.]<br />
:So far so good...<br />
<br />
:[A third line goes up and to the left, creating a 58-degree angle with the last line. The drawing now sort of resembles a tent being blown over in the wind.]<br />
:Steady as she goes...<br />
<br />
:[The fourth line goes down and to the right, creating an approximately 47-degree angle with the last line, and our star is beginning to look a bit askew.]<br />
:...uh oh.<br />
<br />
:''Shitshitshit''<br />
<br />
:[The fifth line comes up at a 48-degree angle, completely missing the first point by a mile, and our star has failed spectacularly.]<br />
:''ABORT!''<br />
:''ABORT!''<br />
<br />
{{comic discussion}}<br />
[[Category:Religion]]<br />
[[Category:Geometry]]</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=Category:Geometry&diff=161008Category:Geometry2018-08-09T15:02:54Z<p>CRGreathouse: basic category</p>
<hr />
<div>{{w|Geometry}} is a branch of mathematics concerned with shape and form. It includes basic Euclidean geometry but also more advanced topics such as topology, differential geometry, algebraic geometry, and non-<br />
Euclidean geometries.<br />
<br />
[[Category:Comics by topic]]<br />
[[Category:Math]]</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=Talk:866:_Compass_and_Straightedge&diff=160931Talk:866: Compass and Straightedge2018-08-08T06:17:09Z<p>CRGreathouse: agree</p>
<hr />
<div>No, the comic is funny because many geometrical theorems prove something along the lines of "With a compass and straightedge you cannot construct..." (e.g. a square and a circle with the same area) If you have knowledge of this type of proof, the humor is that you think he's about to talk about something that is impossible in geometry, but really he's talking about the inapplicability of geometry to real life. This is often a difficulty with nerds and brainy people, they try to apply their theoretical knowledge to human relationships and fail. [[Special:Contributions/75.103.23.206|75.103.23.206]] 19:53, 13 December 2012 (UTC)<br />
:And then there's the converse: people who are able to apply theoretical knowledge and succeed. [[Special:Contributions/76.106.251.87|76.106.251.87]] 04:33, 5 June 2013 (UTC)<br />
<br />
The explanation mentions that there are "three such constructions", but doesn't go any further. What they are should at least be addressed (or linked to), even if we're not going to elaborate on the "why" of their impossibility. For the uninitiated, they are squaring the circle, trisecting any angle, and doubling the cube. [[Special:Contributions/76.106.251.87|76.106.251.87]] 04:33, 5 June 2013 (UTC)<br />
<br />
If such constructions are "impossible with the use of modern algebraic techniques," then why don't we just use older algebraic techniques? ;){{unsigned ip|213.203.138.251}}<br />
:Those "modern algebraic techniques" just did prove that you can't solve this constructions by using only "classical geometry".--[[User:Dgbrt|Dgbrt]] ([[User talk:Dgbrt|talk]]) 18:14, 29 June 2013 (UTC)<br />
<br />
I tried forming a club for compasses and straight edges but no one signed up :( ~JFreund<br />
<br />
Could the “most awsome birthday party“ bear another deeper meaning, for example be analogue to the rational polynom with rational coefficients?<br />
[[Special:Contributions/162.158.202.100|162.158.202.100]] 04:30, 9 April 2017 (UTC)<br />
<br />
Could this "most awesome birthday party" be a reference to Stephen Hawking's party for time travelers?<br />
[[User:Spagovir|Spagovir]] ([[User talk:Spagovir|talk]]) 18:33, 10 August 2017 (UTC)<br />
: I'm pretty sure you're right, it sounds like a Hawking party reference to me too. - [[User:CRGreathouse|CRGreathouse]] ([[User talk:CRGreathouse|talk]]) 06:17, 8 August 2018 (UTC)</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=2028:_Complex_Numbers&diff=1609302028: Complex Numbers2018-08-08T06:11:09Z<p>CRGreathouse: category</p>
<hr />
<div>{{comic<br />
| number = 2028<br />
| date = August 3, 2018<br />
| title = Complex Numbers<br />
| image = complex_numbers.png<br />
| titletext = I'm trying to prove that mathematics forms a meta-abelian group, which would finally confirm my suspicions that algebreic geometry and geometric algebra are the same thing.<br />
}}<br />
<br />
==Explanation==<br />
{{incomplete|Created by a MATHEMATICIAN - Do NOT delete this tag too soon.}}<br />
<br />
The {{w|complex number}}s can be thought of as pairs <math>(a,\ b)\in\mathbb{R}\times\mathbb{R}</math> of real numbers with rules for addition and multiplication.<br />
<br />
: <math>(a,\ b) + (c,\ d) = (a+c,\ b+d)</math><br />
<br />
: <math>(a,\ b) \cdot (c,\ d) = (ac - bd,\ ad + bc)</math><br />
<br />
As such, they are two-dimensional {{w|Euclidean vector|vectors}}, with an interesting rule for multiplication. The justification for this rule is to consider a complex number as an expression of the form <math>a+bi</math>, where <math>i^2 = -1</math>, i.e. ''i'' is the square root of negative 1. Applying the common rules of algebra and the definition of ''i'' yields rules for addition and multiplication above.<br />
<br />
Regular two-dimensional vectors are pairs of values, with the same rule for addition, and no rule for multiplication.<br />
<br />
The usual way to introduce complex numbers is by starting with ''i'' and deducing the rules for addition and multiplication, but Cueball is correct to say that complex numbers are really just vectors and can be defined without consideration of the square root of a negative number.<br />
<br />
The teacher, [[Miss Lenhart]], counters that to ignore the natural construction of the complex numbers would hide the relevance of the {{w|fundamental theorem of algebra}} (Every polynomial of degree ''n'' has exactly ''n'' roots, when counted according to multiplicity) and much of {{w|complex analysis}} (calculus with complex numbers; the study of analytic and meromorphic functions), but she also agrees that mathematicians are too cool for "regular vectors."<br />
<br />
In mathematics, a {{w|group (mathematics)|group}} is the pairing of a binary operation (say, multiplication) with the set of numbers that operation can be used on (say, the real numbers), such that you can describe the properties of the operation by its corresponding group. An {{w|Abelian group}} is one where the operation is commutative, that is, where the terms of the operation can be exchanged: <math> a \cdot b = b \cdot a</math> The title text argues that the "link" between algebra and geometry in "algebreic [sic] geometry" and "geometric algebra" is the operation in an Abelian group, such that both of those fields are equivalent. Algebraic geometry and geometric algebra are mostly unrelated areas of study in mathematics. {{w|Algebraic geometry}} studies the properties of sets of zeros of polynomials. It runs relatively deep. Its tools were used for example in Andrew Wiles' celebrated proof of Fermat's Last Theorem. For its part, a {{w|geometric algebra| geometric algebra}} (a {{w|Clifford algebra| Clifford algebra}} with some specific properties) is a construct allowing one to do algebraic manipulation of geometric objects (e.g., vectors, planes, spheres, etc.) in an arbitrary space that has a resultant geometric interpretation (e.g., rotation, displacement, etc.). The algebra of quaternions, often used to handle rotations in 3D computer graphics, is an example of a geometric algebra, as is the algebra of complex numbers. {{w|Metabelian group|Meta-Abelian groups}} (often contracted to metabelian groups) is a class of groups that are not quite abelian, but close to being so. <br />
<br />
Randall's joke in the mouseover text is a wordplay combining the concepts of (meta-)abelian groups and change in the order of word orders with the general idea of "meta".<br />
<br />
==Transcript==<br />
{{incomplete transcript|Do NOT delete this tag too soon.}}<br />
:[Cueball (the student) is raising his hand and writing with his other hand. He is sitting down at a desk, which has a piece of paper on it.]<br />
:Cueball: Does any of this really have to do with the square root of -1? Or do mathematicians just think they're too cool for regular vectors?<br />
<br />
:[Miss Lenhart (the teacher) is standing in front of a whiteboard.]<br />
:Miss Lenhart: Complex numbers aren't just vectors. They're a profound extension of real numbers, laying the foundation for the fundamental theorem of algebra and the entire field of complex analysis.<br />
<br />
:[Miss Lenhart is standing slightly to the right in a blank frame.]<br />
:Miss Lenhart: '''''And''''' we're too cool for regular vectors.<br />
:Cueball (off-screen): I '''''knew''''' it!<br />
<br />
==Trivia==<br />
This comic is similar to [[1724: Proofs]].<br />
{{comic discussion}}<br />
<br />
[[Category:Comics featuring Cueball]]<br />
[[Category:Comics featuring Miss Lenhart]]<br />
[[Category:Math]]<br />
[[Category:Analysis]]</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=2028:_Complex_Numbers&diff=1609292028: Complex Numbers2018-08-08T06:08:51Z<p>CRGreathouse: /* Explanation */ more informative definition of complex analysis</p>
<hr />
<div>{{comic<br />
| number = 2028<br />
| date = August 3, 2018<br />
| title = Complex Numbers<br />
| image = complex_numbers.png<br />
| titletext = I'm trying to prove that mathematics forms a meta-abelian group, which would finally confirm my suspicions that algebreic geometry and geometric algebra are the same thing.<br />
}}<br />
<br />
==Explanation==<br />
{{incomplete|Created by a MATHEMATICIAN - Do NOT delete this tag too soon.}}<br />
<br />
The {{w|complex number}}s can be thought of as pairs <math>(a,\ b)\in\mathbb{R}\times\mathbb{R}</math> of real numbers with rules for addition and multiplication.<br />
<br />
: <math>(a,\ b) + (c,\ d) = (a+c,\ b+d)</math><br />
<br />
: <math>(a,\ b) \cdot (c,\ d) = (ac - bd,\ ad + bc)</math><br />
<br />
As such, they are two-dimensional {{w|Euclidean vector|vectors}}, with an interesting rule for multiplication. The justification for this rule is to consider a complex number as an expression of the form <math>a+bi</math>, where <math>i^2 = -1</math>, i.e. ''i'' is the square root of negative 1. Applying the common rules of algebra and the definition of ''i'' yields rules for addition and multiplication above.<br />
<br />
Regular two-dimensional vectors are pairs of values, with the same rule for addition, and no rule for multiplication.<br />
<br />
The usual way to introduce complex numbers is by starting with ''i'' and deducing the rules for addition and multiplication, but Cueball is correct to say that complex numbers are really just vectors and can be defined without consideration of the square root of a negative number.<br />
<br />
The teacher, [[Miss Lenhart]], counters that to ignore the natural construction of the complex numbers would hide the relevance of the {{w|fundamental theorem of algebra}} (Every polynomial of degree ''n'' has exactly ''n'' roots, when counted according to multiplicity) and much of {{w|complex analysis}} (calculus with complex numbers; the study of analytic and meromorphic functions), but she also agrees that mathematicians are too cool for "regular vectors."<br />
<br />
In mathematics, a {{w|group (mathematics)|group}} is the pairing of a binary operation (say, multiplication) with the set of numbers that operation can be used on (say, the real numbers), such that you can describe the properties of the operation by its corresponding group. An {{w|Abelian group}} is one where the operation is commutative, that is, where the terms of the operation can be exchanged: <math> a \cdot b = b \cdot a</math> The title text argues that the "link" between algebra and geometry in "algebreic [sic] geometry" and "geometric algebra" is the operation in an Abelian group, such that both of those fields are equivalent. Algebraic geometry and geometric algebra are mostly unrelated areas of study in mathematics. {{w|Algebraic geometry}} studies the properties of sets of zeros of polynomials. It runs relatively deep. Its tools were used for example in Andrew Wiles' celebrated proof of Fermat's Last Theorem. For its part, a {{w|geometric algebra| geometric algebra}} (a {{w|Clifford algebra| Clifford algebra}} with some specific properties) is a construct allowing one to do algebraic manipulation of geometric objects (e.g., vectors, planes, spheres, etc.) in an arbitrary space that has a resultant geometric interpretation (e.g., rotation, displacement, etc.). The algebra of quaternions, often used to handle rotations in 3D computer graphics, is an example of a geometric algebra, as is the algebra of complex numbers. {{w|Metabelian group|Meta-Abelian groups}} (often contracted to metabelian groups) is a class of groups that are not quite abelian, but close to being so. <br />
<br />
Randall's joke in the mouseover text is a wordplay combining the concepts of (meta-)abelian groups and change in the order of word orders with the general idea of "meta".<br />
<br />
==Transcript==<br />
{{incomplete transcript|Do NOT delete this tag too soon.}}<br />
:[Cueball (the student) is raising his hand and writing with his other hand. He is sitting down at a desk, which has a piece of paper on it.]<br />
:Cueball: Does any of this really have to do with the square root of -1? Or do mathematicians just think they're too cool for regular vectors?<br />
<br />
:[Miss Lenhart (the teacher) is standing in front of a whiteboard.]<br />
:Miss Lenhart: Complex numbers aren't just vectors. They're a profound extension of real numbers, laying the foundation for the fundamental theorem of algebra and the entire field of complex analysis.<br />
<br />
:[Miss Lenhart is standing slightly to the right in a blank frame.]<br />
:Miss Lenhart: '''''And''''' we're too cool for regular vectors.<br />
:Cueball (off-screen): I '''''knew''''' it!<br />
<br />
==Trivia==<br />
This comic is similar to [[1724: Proofs]].<br />
{{comic discussion}}<br />
<br />
[[Category:Comics featuring Cueball]]<br />
[[Category:Comics featuring Miss Lenhart]]<br />
[[Category:Math]]</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=505:_A_Bunch_of_Rocks&diff=160928505: A Bunch of Rocks2018-08-08T05:59:39Z<p>CRGreathouse: category</p>
<hr />
<div>{{comic<br />
| number = 505<br />
| date = November 17, 2008<br />
| title = A Bunch of Rocks<br />
| image = a_bunch_of_rocks.png<br />
| titletext = I call Rule 34 on Wolfram's Rule 34.<br />
}}<br />
<br />
==Explanation==<br />
[[Cueball]] awakens to find himself trapped for eternity in an endless expanse of sand and rocks. At first, he uses this time to derive all of mathematics and physics, including {{w|quantum mechanics}} and {{w|general relativity}}. Next Cueball creates a computer that can process any possible function, out of rocks and rules for the interaction between rocks. He then simulates a particle followed by the interactions between particles, followed by the entire universe. The amount of time it takes to simulate the change in the universe from one instant to the next takes an extremely long time as the time it takes to update just one row of rocks can be measured in googols of years, assuming a realistic time to place each rock.<br />
<br />
Cueball then apologizes for any flaws we see in the simulation. This implies that the audience is living in Cueball's simulation, making Cueball essentially God.<br />
<br />
The final frame cuts to a classroom where a bored student stares at his hands waiting for class to end. Cueball admonishes the student for thinking that class is lasting forever. The joke being that the boredom felt in a classroom is nothing compared to the boredom that inspires Cueball to spend his time toiling to keep the universe moving. Indeed, the minutes of lecture actually took many "billions and billions of millennia" for Cueball to simulate.<br />
<br />
The title text suggests that {{w|Rule 34 (Internet meme)|Rule 34}} should be called on {{w|Elementary cellular automaton#Random initial state|Wolfram's Rule 34}}. Rule 34 (see [[305: Rule 34]]) is a humorous rule of the Internet which states "If you can imagine it, there is porn of it. No exceptions." Wolfram's Rule 34 is a cellular automaton. Therefore, the title text says that someone has made pornography featuring the cellular automaton in question.<br />
<br />
===Graphs===<br />
The three diagrams in the "Physics, too. I worked out the kinks..." panel are, from left to right:<br />
# The {{w|Normal distribution}} of the {{w|Gaussian curve}} marking the points that represent a standard deviation of σ and 2σ. This is one of the fundamental building blocks of statistics. In quantum mechanics particles are viewed as inherently random, therefore the time at which a particle will decay, the position of a particle and its velocity are all calculated using similar curves. A deviation of at least σ occurs 32% of the time where a deviation of 2σ or more occurs about 5% of the time.<br />
# The {{w|Inclined plane#History|Epitaph of Stevinus}}, an explanation of the mechanical advantage of using an {{w|inclined plane}}. The inclined plane is one of the six classical {{w|simple machine}}s, one of the fundamental building blocks of mechanical and civil engineering.<br />
# The last graph is unknown. It may represent coupled pendulums, {{w|length contraction}}, or a hypothetical solution to something we haven't derived yet.<br />
<br />
The graph that represents particle interaction is a {{w|Feynman Diagram}}. This shows the interaction of subatomic particles that collide and exchange some momentum via a photon. The slope of the middle line represents the distance moved and the time lost/gained during the interaction.<br />
<br />
===Notes===<br />
The Swiss patent office line refers to {{w|Albert Einstein}}, who was employed as a Swiss patent clerk while coming up with his theory of special relativity. This joke is also referenced in [[1067|1067: Pressures]]. Also, there is a standing joke that very few important inventions have come from Switzerland, since the country hadn't been involved in the world wars, and thus has not been part of the weapons race, nor was it a driving force in the preceding Industrial Revolution.<br />
<br />
In the center of the comic, the binary numbers pointing to the particle are both 42. This is a reference to the comedic answer to the ''Ultimate Question of Life, the Universe, and Everything'' from the ''The Hitchhiker's Guide to the Galaxy'' series.<br />
<br />
Cueball mentions that if we see an artifact flutter in and out of reality he must have made a mistake in the last "billions and billions of millennia." This implies that the small period of time the artifact is present in his time is much longer than our universe has existed. That is a ''very'' long time. However, because it was a really long time, the difference would be [https://en.wikipedia.org/wiki/Butterfly_effect more than just a small mote of dust disappearing].<br />
<br />
===Cellular Automaton===<br />
Cueball uses the rocks to build a {{w|cellular automaton}}, a computational model based on simple rules to advance from one state to the next. Certain cellular automata are {{w|Turing-complete}}, which means that they can be used to represent any conceivable algorithm if expanded infinitely. He specifically seems to be running Wolfram's {{w|Rule 110}}, which is capable of universal computation.<br />
When using Rule 110 for universal computation, one builds a background pattern, which can be seen in the comic as the pattern of smaller triangles, and then performs computation by sending out "rockets" to collide and interact with each other.<br />
<br />
==Transcript==<br />
:[Cueball is standing in a desert with lots of rocks lying around. He is narrating his own situation. The first panel spans the entire width of the comic. The first line of text is written to the left of him, the second line to the right.]<br />
:So I'm stuck in this desert for eternity.<br />
:I don't know why. I just woke up here one day.<br />
<br />
:[The next four panels take up the second line of the comic.]<br />
:[Cueball stand in the desert.]<br />
:I never feel hungry or thirsty.<br />
<br />
:[Cueball walks in the desert.]<br />
:I just walk.<br />
<br />
:[Zooming out while Cueball continues to walk in the desert.]<br />
:Sand and rocks<br />
<br />
:[Zooming far out as Cueball again just stands in the desert. First line of text, above him, is a continuation of the text in the previous panel. The second line is below him.]<br />
:stretch to infinity.<br />
:As best as I can tell.<br />
<br />
:[The next three panels take up the third line of the comic. The last takes up half the width.]<br />
:[Cueball is sitting in the desert, in a contemplative position. First line of text above him the second below.]<br />
:There's plenty of time for thinking out here.<br />
:An eternity really.<br />
<br />
:[Cueball is sketching stuff in the sand. First line of text above him the second below.]<br />
:I've rederived modern math in the sand<br />
:and then some.<br />
<br />
:[Three different graph types are depicted. First line of text above them the second below.]<br />
:Physics too. I worked out the kinks in quantum mechanics and relativity.<br />
:Took a lot of thinking, but this place has fewer distractions than a Swiss patent office.<br />
<br />
:[The next eight panels take up the fourth and fifth line of the comic. All pictures are the same size.]<br />
:[Cueball is walking along the desert, laying out rocks on a line. Four has been deployed, he is laying down the fifth and has a sixth in his other hand.]<br />
:One day I started laying down rows of rocks.<br />
<br />
:[Cueball with a rock in his hand, continues to deploy rocks 16, in a more intricate pattern. There are grid-lines in the sand (5 rows, 6 columns), with each intersection either empty of filled with a rock. No rocks lay anywhere but at an intersection on the grid.]<br />
:Each new row followed from the last in a simple pattern.<br />
<br />
:[Zooming out showing even more laid out rocks. Cueball is seen directly from above, and we see his shadow falling on the grid of rocks (7 rows, 14 columns).]<br />
:With the right set of rules and enough space,<br />
<br />
:[Continues to zoom further out showing clear triangular patterns (with no rocks) in the laid out grid of rocks. Cueball is not seen. (8 rows, 42 columns). First line of text above the grid, the second line below.]<br />
:I was able to build a computer.<br />
:Each new row of stones is the next iteration of the computation.<br />
<br />
:[Zooming far out (no Cueball) with rows intersected by five clear V lines on top of them. The V's are drawn inside each other, with the smallest V at the top right, and the other V's starting just to the right of the previous one, and then continuing the same distance past the previous V, as the total length of the first V. The "*" in the first line of text above this grid, references to the footnote below written in a smaller font.]<br />
:Sure it's rocks instead of electricity, but it's the same* thing. Just slower.<br />
:<nowiki>*Turing-complete</nowiki><br />
<br />
:[Cueball stands in contemplative pose (on a clean white background - i.e. no dessert).]<br />
:After a while, I programmed it to be a physics simulator.<br />
<br />
:[A black panel with white drawings and text. A small white dot (a particle) is labeled by two arrows coming of two binary strings.]<br />
:Every piece of information about a particle was encoded as a string of bits written in the stones.<br />
:00101010<br />
:00101010<br />
<br />
:[A Feynman diagram showing two particles interacting. Two arrows going in and out with a snaking line between them.]<br />
:With enough time and space, I could fully simulate two particles interacting.<br />
<br />
:[The next two panels take up the sixth line of the comic. The second panel takes up three quarter of the width.]<br />
:[Cueball standing before the vastness of the desert, with his programmed lines of rock stretching to infinity.]<br />
:But I have <u>infinite</u> time and space.<br />
<br />
:[A black panel with white drawings and text. Depiction of two large galaxies, one with four jets coming out of it's center, the other a flat disc. Several smaller galaxies and/or stars are shown around them.]<br />
:So I decided to simulate a universe.<br />
<br />
:[The next four panels take up the seventh line of the comic. They are of similar widths.]<br />
:[Cueball is walking by his grid of rocks, lines indicate he has just thrown another rock down in it's place. It falls so hard it thinks into the sand that splashes out around it. The 14 rocks above him lies on the grid, four other below this grid, have not been used yet.]<br />
:The eons blur past as I walk down a single row.<br />
<br />
:[Zoom far far out to show multiple rows of rocks. It is not very clear that there are several triangular patterns (with no rocks) in different sizes in the laid out grid of rocks. There are about 50 rows and 90 columns. There are six large triangles on top of each other at the left edge. To the right there are three even larger triangles from top to bottom, the one in the middle further to the left than the one above, but further right than the bottom one.]<br />
:The rows blur past to compute a single step.<br />
<br />
:[Shows the placement of two particles in the simulation.]<br />
:And in the simulation...<br />
<br />
:[The two particles have moved just long enough as to not overlap with their the previous position which are shown as an after-image with faint gray lines. The text continues directly the one from the previous panel.]<br />
:another instant ticks by.<br />
<br />
:[The next two panels take up the eight line of the comic. They each take up half the width.]<br />
:[A Cueball like person (you) observes a mote of dust vanish.]<br />
:So if you see a mote of dust vanish from your vision in a little flash or something<br />
<br />
:[Cueball is standing between two rocks on the ground, while holding two rocks, one lifted up to his head. The first line of text is above him. It is a direct continuation of the text in the previous panel. The second line stands below to the right of him.]<br />
:I'm sorry. I must have misplaced a rock<br />
:sometime in the last few billions and billions of millennia.<br />
<br />
:[Cueball stands in the "clean" part of his infinite desert, in front of the vastness of his infinity of infinite lines or rocks.]<br />
:Oh and...<br />
<br />
:[A Cueball like student sitting in a classroom with his head in his hands, Megan sits behind him and a teacher points to the blackboard; A clock shows the time at five minutes to ten.]<br />
:If you think the minutes in your morning lecture are taking a long time to pass for <u>''you''</u>...<br />
<br />
{{comic discussion}}<br />
[[Category:Comics featuring Cueball]]<br />
[[Category:Comics featuring Megan]]<br />
[[Category:Multiple Cueballs]]<br />
[[Category:Math]]<br />
[[Category:Physics]]<br />
[[Category:Programming]]</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=1856:_Existence_Proof&diff=1609241856: Existence Proof2018-08-07T20:16:06Z<p>CRGreathouse: more specific category</p>
<hr />
<div>{{comic<br />
| number = 1856<br />
| date = June 28, 2017<br />
| title = Existence Proof<br />
| image = existence_proof.png<br />
| titletext = Real analysis is way realer than I expected.<br />
}}<br />
<br />
==Explanation==<br />
In mathematics, an existence proof is a proof that only shows that an object with a specific property exists, but does not tell what this object is. For instance, if f is a continuous function such that f(0) = 0 and f(100) = 2, it is easy to prove that there exists an x between 0 and 100 such that f(x) = 1 (as in the comic). However, this proof gives no way to find such an x.<br />
<br />
In many situations, a proof of existence is enough to satisfy a mathematician, but in others, it is desirable to actually identify the object whose existence has been proven.<br />
<br />
The full statement itself seems like a solution to some kind of {{w|function composition}} problem. Seems like what the class has proven is that if you apply certain function G(x) to a starting point of function f(0), then what it will do is just give you a value of f(x) at some other value of x, existence of which is stated to be proven. The sentence "There exists some number x such that f(x)=G(f(0))=1." boils down to "There is an x such that f(x)=1". The part with G(f(0)) is only a way to arrive at 1. For some reason there is an x that satisfies f(x)=G(f(0)), and since G(f(0))=1, it is equivalent to f(x)=1.<br />
<br />
In the comic, [[Miss Lenhart]] (and students) take this one step further, by taking up arms to destroy the function value, which they have proven to exist. In the last panel, some students off screen begin to wonder if they are in the right class, as normal math classes do not take up swords to fight abstract concepts.{{Citation needed}} Another student remarks that they are finally in the right math class, implying that this is the kind of thing they wanted from their math curriculum all along.<br />
<br />
The phrase "''We ride''" is commonly used in rallying battle cries, particularly in fantasy or medieval dramas where characters are preparing to enter combat on horseback. Variations of the phrase are used several times in ''{{w|The Lord of the Rings}}'', for example.<br />
<br />
The title text refers to {{w|Real Analysis}}, a branch of mathematics dealing with {{w|real number}}s and real-valued functions (as opposed to studies dealing with {{w|integer}}s, {{w|rational number}}s, {{w|imaginary number}}s in the complex plane, etc.). As the speaker implies, Real Analysis is supposed to remain confined to the theoretical realm of mathematics; certainly nobody signing up for such a class would ever expect to be embroiled in a crusade against intangible constructs! Taken out of its mathematical context, "analysis" literally means "breaking down", referring to the teacher's intention to cut things up with a sword. The use of the uncommon word "realer" conveys that the situation has suddenly developed unusually high stakes. This nuance would be lost if the word "realer" were replaced with the technically correct phrasing of "more real".<br />
<br />
This may be a continuation of [[982: Set Theory]], where numbers were "executed" to prove a point.<br />
<br />
==Transcript==<br />
<br />
:[Miss Lenhart stands in front of a whiteboard and points at calculations written on it.]<br />
:Miss Lenhart: There exists some number x such that f(x)=G(f(0))=1.<br />
<br />
:[Miss Lenhart moves her arm in a frameless panel.]<br />
:Miss Lenhart: Oh yes.<br />
:Miss Lenhart: Somewhere out there, it exists.<br />
<br />
:[Zoom-in on Miss Lenhart raising a fist.]<br />
:Miss Lenhart: And we must find it... and ''destroy'' it.<br />
<br />
:[Miss Lenhart raises a sword.]<br />
:Miss Lenhart: Grab your swords, students! We ride!<br />
:Student #1 (off-screen): I think I'm in the wrong math class?<br />
:Student #2 (off-screen): I'm finally in the right one.<br />
{{comic discussion}}<br />
<br />
[[Category:Comics featuring Miss Lenhart]]<br />
[[Category:Analysis]]</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=1201:_Integration_by_Parts&diff=1609231201: Integration by Parts2018-08-07T20:15:48Z<p>CRGreathouse: more specific category</p>
<hr />
<div>{{comic<br />
| number = 1201<br />
| date = April 19, 2013<br />
| title = Integration by Parts<br />
| image = integration by parts.png<br />
| titletext = If you can manage to choose u and v such that u = v = x, then the answer is just (1/2)x², which is easy to remember. Oh, and add a '+C' or you'll get yelled at.<br />
}}<br />
<br />
==Explanation==<br />
{{w|Integration by parts}} is an integration strategy that is used to evaluate difficult integrals by trying to find simpler integrals derived from the original. It is commonly a source of confusion or irritation for students when they first learn it, due to the fact that there is really no way to accurately predict the proper u/dv separation just by looking at an integral. Integration by parts requires patience, trial and error, and experience.<br />
<br />
[[Randall]] shows a somewhat complicated math problem and, in an attempt to "help", simplifies it into a more compact integral. This is the first part of performing integration by parts, which involves the guessing. Having gotten it into integration by parts format, he then leaves without describing the actual solution. The general integral '''''∫'''(u dv)'' is equal to ''uv - '''∫'''(v du)'', and this is the more tedious part of the math and where problems will arise if you picked the wrong u and dv at the beginning. The narrator makes a point of leaving here, so we can't ask for help or complain if the choice of u and dv was wrong.<br />
<br />
The title text points out that if the integral of x can be divided so that u = x and dv = dx and implying v = x, then it leads to the result (1/2)x². This implies the original integral was just ∫x dx, and not needing integration by parts in the first place. Mathematics teachers and extreme math geeks will also cringe at this answer, however, since an {{w|indefinite integral}} requires an integration constant. The correct answer is actually (1/2)x² + C, as Randall hints. The +C symbolizes that an indefinite integral can be shifted by any constant and still gets the same answer on the reverse {{w|derivative}}. {{w|Integral|Definite integrals}} specify a range that they're valid on and thus there is no need to add this constant.<br />
<br />
==Transcript==<br />
:A Guide to<br />
:Integration by Parts:<br />
<br />
:Given a problem of the form:<br />
::∫f(x)g(x)dx=?<br />
:Choose variables u and v such that<br />
::u=f(x)<br />
::dv=g(x)dx<br />
:Now the expression becomes:<br />
::∫udv=?<br />
:Which ''definitely'' looks easier.<br />
:Anyway, I gotta run.<br />
:But good luck!<br />
<br />
{{comic discussion}}<br />
[[Category:Analysis]]<br />
[[Category:Sarcasm]]</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=626:_Newton_and_Leibniz&diff=160922626: Newton and Leibniz2018-08-07T20:15:27Z<p>CRGreathouse: more specific category</p>
<hr />
<div>{{comic<br />
| number = 626<br />
| date = August 21, 2009<br />
| title = Newton and Leibniz<br />
| image = newton_and_leibniz.png<br />
| titletext = YEEEEEEAAAAAAHHHHHH!<br />
}}<br />
<br />
==Explanation==<br />
{{w|Isaac Newton}} and {{w|Gottfried Leibniz}} both developed {{w|calculus}} independently of each other about eight years apart, as it says in the comic. However, although Newton had begun working on calculus before Leibniz, he didn't publish it, and Leibniz was the first to publish it (see the {{w|Leibniz–Newton calculus controversy}}).<br />
<br />
In calculus a {{w|derivative}} is the result of mathematical differentiation: the instantaneous rate of change of a function relative to its argument, and denoted df(x)/dx. As taught in schools, if a function is drawn as a graph, the derivative of that function at a given point is equal to the slope of that graph at that point. However, the literary word [http://www.thefreedictionary.com/derivative derivative means] developed from something older or copied/adapted from others, as Newton claims is the case here.<br />
<br />
The pun is that Newton is claiming that Leibniz's mathematical derivative is a derivative, or descendant, from his earlier development of this calculus.<br />
<br />
The comic as a whole is mocking the pattern of corny one-liners that {{w|David Caruso}} often spurts out during the opening scenes of {{w|CSI: Miami}}. The one liner is followed by him dramatically pulling off or [[:Category:Puts on sunglasses |putting on his sunglasses]] and then the show breaks into the title sequence which starts with Roger Daltrey singing an extended "YEEEEAAAAAAAH", the opening to the song [https://en.wikipedia.org/wiki/Won%27t_Get_Fooled_Again Won't Get Fooled Again] by [https://en.wikipedia.org/wiki/The_Who The Who] as noted in the title text. This has become a [http://knowyourmeme.com/memes/csi-4-pane-comics popular Internet meme] and was used frequently with {{w|Death of Michael Jackson|Michael Jackson's death}}. The sunglasses joke was also used in the title text of [[977: Map Projections]].<br />
<br />
==Transcript==<br />
<br />
:[Newton with long white hair, facing right, holds up a sheet of paper, with several lines indicating the writing on it, in one hand and the other hand is also held up. He stands in front of an empty desk. A smaller frame breaking the border at the top of the frame has a caption:]<br />
:Caption: Newton, 1666<br />
:Newton: I've invented calculus!<br />
<br />
:[Leibniz with long black hair, facing left, holds up a sheet of paper, with several lines indicating the writing on it, in one hand. He stands in front of a desk with a book and two pieces of paper, one lying below the other paper but up above the book. A smaller frame breaking the border at the top of the frame has a caption:]<br />
:Caption: :Leibniz, 1674<br />
:Leibniz: I've invented calculus!<br />
<br />
:[Back to a similar image of Newton, but he has now taken his arms down, still holding his paper.]<br />
:Newton: Really? Sounds a little bit...<br />
<br />
:[Zoom in on Newton as he puts on a pair of sunglasses in a panel without a frame. The table is not included.]<br />
<br />
:[Newton now with sunglasses on, again in front of the table.]<br />
:Newton: ... '''''Derivative.'''''<br />
<br />
{{comic discussion}}<br />
<br />
[[Category:Comics featuring real people]]<br />
[[Category:Analysis]]<br />
[[Category:Puts on sunglasses]]<br />
[[Category:Puns]]</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=622:_Haiku_Proof&diff=160921622: Haiku Proof2018-08-07T20:15:07Z<p>CRGreathouse: more specific category</p>
<hr />
<div>{{comic<br />
| number = 622<br />
| date = August 12, 2009<br />
| title = Haiku Proof<br />
| image = haiku_proof.png<br />
| titletext = After somewhere around 40 hours, there's no academic reason to go to the class. Only go for the hallucinations.<br />
}}<br />
<br />
==Explanation==<br />
In this comic [[Cueball]] attends a math class after having been awake for two full days (48 hours). After that he begins to {{w|hallucinate}} and dreams that the teacher [[Miss Lenhart]] (a [http://xkcd.com/622/info.0.json professor] in this comic) answers [[Megan|Megan's]] question, about a proof that there are an infinite number of {{w|prime numbers}}, in {{w|haiku}}. After the first line she floats up and during the third and final line she flies over the students heads. Basically it is a dream, as also indicated with Cueball's thought that are "outside" this {{w|lucid dream}} where it could be seen as it was the entire comic, except Cueball's thoughts, that are inside the dream bubble. (Dreams being a [[:Category:Dreams|recurring theme]] in xkcd). Note also that where Cueball looks up after the flying teacher when she takes off, Megan never moves her head to watch her teacher fly, because it's not happening in her world, and Cueball only dream the teachers moves.<br />
<br />
{{w|Euclid's theorem}} states that there are an infinite number of primes, prime numbers being numbers that are only divisible by themselves and 1. The most notable proof of this theorem, and the one presented in this comic, was first given by Euclid himself in his ''{{w|Euclid's Elements|Elements}}''. A more traditional form of this proof follows:<br />
<br />
:If we suppose that there are a finite number of primes, then they must have a product, i.e. ''p''<sub>1</sub>''p''<sub>2</sub>...''p''<sub>n</sub> = ''q''. Now consider ''q'' + 1. If this number is prime itself, then we have discovered a new prime number, contrary to the assumption that we had listed them all. If it is not prime, it must have a prime divisor. Since all of the ''p''<sub>k</sub> are a factor of ''q'', they cannot be a divisor of ''q'' + 1. So ''q'' + 1 is divisible by a prime not on the list, which again is a contradiction. Therefore, there must be infinitely many primes.<br />
<br />
The comic essentially takes this proof and states it in the form of a {{w|haiku}}, which is a traditional form of Japanese poetry which is in Japanese broken up into patterns of {{w|morae}} (or {{w|syllables}}), a unit that measures the length of sound. A haiku consists of three lines with 5, 7 and 5 syllables respectively per line. An English Haiku has 5, 7 and 5 syllables per line. And the proof poem goes like this:<br />
:Top prime's divisors'<br />
:Product (plus one)'s factors are...?<br />
:Q.E.D., bitches!<br />
<br />
Which can be [http://www.syllablecount.com/ divided in syllables] like this:<br />
:Top - prime's - di - vi - sors'<br />
:Pro - duct - (plus - one)'s - fac - tors - are...?<br />
:Q. - E.- D., - bit - ches!<br />
<br />
The haiku proof given is slightly off, as the first line talks about the "top prime's divisors," which makes no sense because the top prime doesn't have any divisors besides itself and one. You need to take the product of ''all'' primes, not just one. But, hey, it's a hallucination.<br />
<br />
Haiku was also referred to before in [[554: Not Enough Work]].<br />
<br />
The comic and title text conclude that going to class while sleep-deprived is an interesting, but entirely noneducational, experience. So do go for the sake of the hallucinations.<br />
<br />
==Transcript==<br />
:[Miss Lenhart teaching a class gestures with both hands up as Megan, sitting at the first desk on a stool, raises a hand and asks a question. Cueball sits at the desks behind her supporting his head in both hands with the elbows on the desk.]<br />
:Megan: How do you know there are an infinite number of primes?<br />
:Miss Lenhart: I'll answer in haiku!<br />
<br />
:[In a frame-less panel, Miss Lenhart lifts a hand up while answering. Both students sit upright on their stools.]<br />
:Miss Lenhart: Top prime's divisors'<br />
<br />
:[Miss Lenhart floats into the air with three lines beneath her legs. Cueball looks up. Megan does not change position.]<br />
:Miss Lenhart: Product (plus one)'s factors are...?<br />
<br />
:[Miss Lenhart flies over the students heads with a curved line behind her. Neither student look up. The bottom frame of the panel is a curving thought/dream bobble that goes through the middle of the panel at a height just below the desk tops. Two thought circles goes from Cueball's head down to this frame, and Cueball's thoughts are shown below outside of the panel - without any frame around.]<br />
:Miss Lenhart: Q.E.D., bitches!<br />
:Cueball (thinking): Wow, after the 48-hour sleep-dep mark, lectures get ''really'' interesting.<br />
<br />
{{comic discussion}}<br />
<br />
[[Category:Comics featuring Miss Lenhart]]<br />
[[Category:Comics featuring Megan]]<br />
[[Category:Comics featuring Cueball]]<br />
[[Category:Analysis]]<br />
[[Category:Dreams]]</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=602:_Overstimulated&diff=160920602: Overstimulated2018-08-07T20:14:47Z<p>CRGreathouse: category</p>
<hr />
<div>{{comic<br />
| number = 602<br />
| date = June 26, 2009<br />
| title = Overstimulated<br />
| image = overstimulated.png<br />
| titletext = My favorite thing to do at parties is to talk judgmentally about people who aren't there.<br />
}}<br />
<br />
==Explanation==<br />
<br />
After being cooped up working on papers, [[Cueball]] goes to a party, only to find himself tuning out the gossip of his friends in order to work on math problems in his head. He writes down the prime numbers on cards, and then stretches them out such that the area of the card is the same (say, 1), but one of the sides has been elongated to a length equal to the number on the card. This reduces the length on the other dimension to the reciprocal of the number on the card (i.e. 1/''n'', with ''n'' being the number on the card), according to the area formula for rectangles.<br />
<br />
Stacking these reciprocals all up will eventually diverge, meaning the sum will be infinite without ever leveling off. This is referred to as the {{w|divergence of the sum of the reciprocals of the primes}}, and was proven by {{w|Euler}} in 1737.<br />
<br />
[http://aq.server8.org/ The Cambridge Aspergers Test] includes questions on preferences for, and ability to cope with, social situations. It also asks the person taking the test if they have an affinity for numbers and see patterns in every day objects. Cueball would score high on the Asperger's scale — or he could just be introverted, or find math more interesting than criticizing others which is generally considered in science circles a dull thing to do considering the vast variety of other topics and activities available. {{w|Introversion}} is an idea from psychology. Thinking about things on one's own is often relaxing for an introvert, while hanging out with other people is not. Hence the irony of the comment in the last panel. Cueball's friends fail to realize that hanging out with them is actually more stressful for him than doing math - especially when people are doing nothing but talking negatively about those not present.<br />
<br />
This comic is related to [[324: Tapping]], where Cueball has fun tapping the Jurassic Park theme on a table.<br />
<br />
The title text mentions people that talk negatively about people that aren't there, which isn't uncommon. A much later comic; [[1176: Those Not Present]], is about just that.<br />
<br />
==Transcript==<br />
:[There is a group of people. Three women and four men. They are standing around a table with a drink on it.]<br />
:Man #3: Have you seen John lately?<br />
<br />
:Woman #3: He and Claire blew off this party to see Jeff.<br />
:Man #4: They do that a lot.<br />
<br />
:Man #1: Yeah; I don't know what his problem is with hanging out lately.<br />
:Man #3: He's like Katie—ever noticed how she only goes somewhere if Jeff's there?<br />
<br />
:[Cueball is cringing away from all the text; none of the text is attributed to specific people.]<br />
:Somebody: It's so lame how she hangs around him even when he's not single:<br />
:Somebody: HE LIKES IT.<br />
:Somebody: SOMEONE SERIOUSLY NEEDS TO DATE HER.<br />
:Somebody: TOTALLY.<br />
:Somebody: And honestly I feel like a jerk but I wouldn't mind if she hung around with us a little less. She needs other friends, you know!<br />
<br />
:[Cueball peels a hole in the panel. The numbers '1', '2', and '3' are visible through the gap.]<br />
:Somebody: HAVE YOU NOTICED HOW EVERY DUDE SHE DATES IS A TOTAL DRUGGIE?<br />
:Somebody: NOPE<br />
:Somebody: I'm glad I'm not the only one who thought that was weird.<br />
:Somebody: Michelle dates potheads like Elaine but at least they both have real jobs.<br />
:Somebody: Michelle does? She designs those book covers, right?<br />
:Somebody: And it's not like she smokes a lot.<br />
:Somebody: Elaine is one of those girls who<br />
<br />
:[The previous panel's text appears again, but peeled back even further. Cueball looks up.] <br />
:1 2 3 4 5 6 7 8 9 10 11 12<br />
<br />
:Somebody: NOTICED HOW<br />
:Somebody: NOPE<br />
:Somebody: -es is a tota-<br />
:Somebody: -t th- -ought<br />
<br />
:[The man starts taking down the prime numbers.]<br />
:1 4 6 8 9 10 12 14 15 2 3 5 7 11 13<br />
:[The man grabs and squeezes the 2, so it is half as wide and twice as tall.]<br />
<br />
:[A formula: \Sum_{i=1}^{\infty}{1 P_i} = h]<br />
::[ie. The sum from 1 to infinity of the inverse of each prime.]<br />
:[The panel shows a 2 that is 2 units tall and 1 2 wide, a 3 that is 3 units tall and 1 3 wide, and so on. Cueball is moving the 7.]<br />
<br />
:[Cueball writes h = infinity. The numbers are piled on their side next to a scale.]<br />
:Voice: Don't you agree?<br />
:Voice: Hey, wake up.<br />
<br />
:Man #1: You zoned out or something.<br />
:Cueball: Sorry; I must be... tired.<br />
:Man #1: I don't blame you. All day cooped up working on papers.<br />
:Man #3: Must be nice to get out and relax, huh?<br />
:Cueball: Yeah.<br />
:[Girl #3 reaches for the glass on the table.]<br />
<br />
{{comic discussion}}<br />
[[Category:Comics featuring Cueball]]<br />
[[Category:Comics featuring Megan]]<br />
[[Category:Comics featuring Ponytail]]<br />
[[Category:Analysis]]<br />
[[Category:Number theory]]</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=569:_Borders&diff=160919569: Borders2018-08-07T20:14:27Z<p>CRGreathouse: more specific category</p>
<hr />
<div>{{comic<br />
| number = 569<br />
| date = April 15, 2009<br />
| title = Borders<br />
| image = borders.png<br />
| titletext = Eventually a UN is set up. And then a lone rebel runs down the line of flags in front of it, runs back to his base, and gets a kajillion points.<br />
}}<br />
<br />
==Explanation==<br />
{{w|Capture the flag}} (CTF) is a common way of playing games where the objective is to capture the opponent's flag while protecting your own team's flag. This comic describes a CTF server for an online war game where peace has been established and no one is trying to capture each other's flags, therefore making the game unexciting and pointless.<br />
<br />
The title text refers to the line of flags in front of UN buildings. If such a collection of flags of all the teams were established on a server, one could get a very high score by quickly capturing all of them. <br />
<br />
A {{Wiktionary|kajillion}} is slang for "an unspecified large number."<br />
<br />
LIATE is an acronym sometimes used when {{w|Integration by parts|integrating by parts}}. The preferred part to integrate is "Logarithmic, Inverse-trig, Algebraic, Trig, Exponential." "Yarbis" could be a reference to an acronym in Turkish for "Yıldız ARastirmaci BIlgi Sistemi" which means "Yildiz Researcher Information System" in English. "Yildiz" refers to Yildiz Technical University in Turkey.<br />
<br />
==Transcript==<br />
:[Two Cueball-like guys stand on a hill overlooking a great city. One of them points at the city. Between them and the city stands an embassy flying a red flag. The text is not spoken by either of the guys.]<br />
:Three years ago, the kingdom of Liate overthrew their old order and established a constitutional monarchy. Our leaders signed a treaty with their queen, and our borders were set by the Yarbis Accords.<br />
:Many said war would be unending, that peace would always be a dream deferred. But today, our flag flies proudly over our embassy in their kingdom, and they walk our lands without fear.<br />
:So come, traveller. Lay down your grudges and join us in brotherhood. It is time not to fight, but to live.<br />
:[Cueball sitting at computer.]<br />
:Cueball: This is the worst capture-the-flag server ever.<br />
<br />
{{comic discussion}}<br />
<br />
[[Category:Analysis]]<br />
[[Category:Comics with color]]<br />
[[Category:Comics featuring Cueball]]<br />
[[Category:Multiple Cueballs]]<br />
[[Category:Video games]]</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=128:_dPain_over_dt&diff=160918128: dPain over dt2018-08-07T20:14:00Z<p>CRGreathouse: more specific category</p>
<hr />
<div>{{comic<br />
| number = 128<br />
| date = July 14, 2006<br />
| title = dPain over dt<br />
| image = dPain_over_dt.png<br />
| titletext = You laugh to keep from crying, you do math to keep from crying...<br />
}}<br />
<br />
==Explanation==<br />
<br />
Another one of the math-love relationship comics, a mathematical depiction of pain as a {{w|differential equation}} is shown. It is hoped that ''dPain/dt'', or the rate of pain (in this case, shrinking), decreases quickly so that the pain will vanish quickly. He's hoping the value for ''d'' will not be larger than a few days or some weeks. Assuming that ''How much she's still in my life'' is a constant ''G'' then [http://www.wolframalpha.com/input/?i=dP%2Fdt+%3D+%28-k1*P%2BG%29*%281%2F%281%2Bexp%28-%28t-k2%29%2Fd%29%29%29 solving the differential equation] leads to the following solution (with unknown ''c<sub>1</sub>''):<br />
P(t) = c<sub>1</sub>*(e<sup>k<sub>2</sub>/d</sup>+e<sup>t/d</sup>)<sup>-d*k<sub>1</sub></sup>+G/k<sub>1</sub><br />
<br />
If ''k<sub>1</sub>'' was positive or if ''k<sub>2</sub>'' was a large value, the value of ''dPain/dt'' would approach zero. Ideally, ''k<sub>1</sub>'' would be "How much she's in my life"/''Pain'' (we assume both these values are positive), while ''k<sub>2</sub>'' would ideally be extremely large. Either of these scenarios approach what would be a situation where the value of ''dPain/dt'' is close to zero. But we don't know the meaning of ''k<sub>1</sub>'' or ''k<sub>2</sub>'', these variables are just unpredictable.<br />
<br />
In the title text, [[Randall]] changes the famous "laugh to keep from crying" statement to Math.<br />
<br />
==Transcript==<br />
:dPain/dt = (-k<sub>1</sub> Pain + [Image of Megan]) (1/(1 + e ^ -(t-k<sub>2</sub>)/d))<br />
:k<sub>1</sub>=?<br />
:k<sub>2</sub>=?<br />
:[Image of Megan]=How much she's still in my life<br />
:Please let ''d'' only be a few days... or weeks<br />
:I guess there's some kind of a cutoff after years, where it stops mattering and we can be friends. Do I <u>want</u> that?<br />
:Is k<sub>1</sub> positive? Is k<sub>2</sub> large?<br />
:Will I ever stop feeling like this?<br />
<br />
{{comic discussion}}<br />
[[Category:Analysis]]<br />
[[Category:Romance]]<br />
[[Category:Comics featuring Megan]]</div>CRGreathousehttps://www.explainxkcd.com/wiki/index.php?title=113:_Riemann-Zeta&diff=160917113: Riemann-Zeta2018-08-07T20:13:38Z<p>CRGreathouse: more specific category</p>
<hr />
<div>{{comic<br />
| number = 113<br />
| date = June 9, 2006<br />
| title = Riemann-Zeta<br />
| image = riemann-zeta.jpg<br />
| titletext = The graph is of the magnitude of the function with the real value between 0 and 2 and the imaginary between about 35 and 40. I've misplaced the exact parameters I used.<br />
}}<br />
<br />
==Explanation==<br />
A {{w|prime number}} is any natural number with exactly two natural factors (1 and itself). The set of prime numbers is infinite, but they are somewhat elusive; there is no known way to find or identify very large prime numbers except by trial and error. Some regularities in the primes have been found, but none that can fully predict their distribution.<br />
<br />
The {{w|Riemann zeta function}}, errantly referred to as the Riemann-Zeta function in the comic, is a function that takes in {{w|complex numbers}} and returns complex numbers. It is defined for Re(s)>1 as <math>\zeta(s)=\sum_{n=1}^{\infty} \frac{1}{n^s}</math>. For the rest of its domain (all complex numbers except 1) it is defined with {{w|analytic continuation}}. Its magnitude can be graphed in 3D, producing the "rippled curtain" referenced and depicted in the comic. There is a particular relationship between the Riemann zeta function and prime numbers, which makes the function a viable target for those attempting to understand primes.<br />
<br />
Here, [[Randall]] appears to be talking to his significant other, comparing her to prime numbers and himself to the Riemann zeta function. It is mathematically correct and quite poetic, until he mentions that his relationship differs from the comparison because "The Riemann-Zeta function couldn't have given you {{w|herpes}}." This implies that he has infected his lover with an incurable venereal disease. The comic effect of an abrupt change in tone like this is known as {{w|bathos}}.<br />
<br />
As the title text indicates, the graph in the picture is of the magnitude of ζ(s) for some section of the complex plane. Randall has forgotten the exact imaginary bounds of the graph, but he knows that the real axis goes from 0 to 2 and the imaginary axis goes from about 35i to about 40i.<br />
<br />
==Transcript==<br />
:[A z = fn(x, y) plot, with pointy spikes on the back sloping to a relatively flat front.]<br />
<br />
:You are like the prime numbers<br />
:Unpredictable turns, unconstrainable<br />
:Tantalizingly regular but never quite the same<br />
<br />
:I am like the Riemann-Zeta function<br />
:A rippled curtain of the imagined and real<br />
:Deeply tied with you in ways incomprehensible<br />
<br />
:Although, strictly speaking, The Riemann-Zeta function couldn't have given you herpes<br />
<br />
{{comic discussion}}<br />
[[Category:Analysis]]<br />
[[Category:Number theory]]<br />
[[Category:Charts]]</div>CRGreathouse