explain xkcd - User contributions [en]

Talk:2343: Mathematical Symbol Fight

2020-08-07T22:04:45Z

172.69.68.197:

Can I get aleph-null aleph-shaped throwing stars? [[User:LunarNapolean|LunarNapolean]] ([[User talk:LunarNapolean|talk]]) 20:18, 7 August 2020 (UTC)

Apologies to whoever added the "citation needed" that I stepped on. -- brad

That zeta looks conspicuously bad. I wonder if this comic will get a cleaned-up version uploaded. [[Special:Contributions/108.162.237.16|108.162.237.16]] 20:51, 7 August 2020 (UTC)

[[Megan]] usually has shoulder-length hair, so the person being attacked by Ponytail is probably not Megan... except in so far as all brunettes in this comic are called 'Megan'. [[User:LtPowers|LtPowers]] ([[User talk:LtPowers|talk]]) 20:53, 7 August 2020 (UTC)

I think Randall is underestimating the weapon utility of psi. There's a real-world martial arts [https://en.wikipedia.org/wiki/Sai_(weapon) weapon] that looks somewhat like it.[[Special:Contributions/172.69.68.197|172.69.68.197]] 22:04, 7 August 2020 (UTC)

1456: On the Moon

2020-08-06T16:31:53Z

172.69.68.197: added Wiki link to Artemis Program

{{comic
| number = 1456
| date = December 5, 2014
| title = On the Moon
| image = on_the_moon.png
| titletext = "I believe that this nation should commit itself to achieving the goal, before this decade is out, of landing a man on Venus and returning him safely to--" [an aide frantically whispers in the president's ear for a moment] "... of landing a man on Venus."
}}

==Explanation==
The phrase "If we can land a man on the Moon, why can't we <blank>" is commonly used to question a perceived shortcoming of some company, government or humanity in general. The {{w|Apollo program}} landed {{w|List of Apollo astronauts#Apollo astronauts who walked on the Moon|twelve astronauts}} on the {{w|Moon}} in six landing missions from July 1969 to December 1972 and returned all of those twelve astronauts safely to the Earth. However, from 1964 to 1967, there were eight deaths of astronauts or men training to be astronauts: three in the Apollo One fire, four in T-38 crashes, and one in an F-104 crash. The premise is usually that if "we" (whether referring generally to humanity, or specifically to the United States) have been able to achieve this extraordinary feat, our inability to achieve some lesser goal is questionable and/or ironic. Right after the Philae landing, the similar hashtag [https://twitter.com/hashtag/wecanlandonacometbutwecant #WeCanLandOnACometButWeCant] began on Twitter.

Here, Megan cuts Cueball's argument's short by implicitly reminding him that humanity has not put another human on the Moon since the end of the Apollo program in December 1972 (nearly 42 years at the time this comic was published). New manned programs to return to the Moon, such as the {{w|Constellation Program}}, have been repeatedly cancelled. The {{w|Orion (spacecraft)|Orion spacecraft}}, which will be capable of carrying humans beyond {{w|low Earth orbit}} for the first time in over 40 years, executed its first test flight on the day after this comic was published, Although this is outdated because Nasa is planning to go to the moon again with the {{w|Artemis Program}}.

The title text is a retelling of {{w|John F. Kennedy|President Kennedy's}} famous inspirational [http://www.jfklibrary.org/Asset-Viewer/xzw1gaeeTES6khED14P1Iw.aspx address to the U.S. Congress in May 1961] ("I believe that this nation should commit itself to achieving the goal, before this decade is out, of landing a man on the Moon and returning him safely to the Earth"), which set into motion the Apollo program, except that this time, the speaker is talking about putting a man on planet {{w|Venus}}. The aide presumably explains to the president that, unlike Moon, Venus has gravity close to that of the Earth, but what's more, its surface {{w|Atmosphere_of_Venus|atmosphere}} density and pressure, and other factors including high temperature, strong winds and sulfuric acid clouds would make manned launch back to orbit practically impossible at our current technological level. As a result, the president backtracks from the goal of returning the astronauts safely to the Earth and comically limits the aspiration to landing an astronaut on Venus, full stop, without regard to the astronaut's safe return. This differs slightly from Kennedy's goal, which included the safe return of at least one astronaut from the moon. Although the overall 8:12 ratio of deaths to moonwalkers (during the period for Kennedy's speech to the end of the Apollo program) was too high to be considered "safe" by most standards, Kennedy had specified the safety only of the men who landed on the moon, and set a goal of "a" man returning safely. Technically, even if most of the men who landed died, as long as one returned safely by the end of 1969, Kennedy's goal would have been met.

Kennedy's 1961 speech was also mentioned in the title text of [[753: Southern Half]].

==Transcript==
:[Cueball and Megan are walking together.]
:Cueball: If we could land a man on the Moon, why can't we-
:Megan: -land a man on the Moon?
:Cueball: ...ok, fair. But we're working on it, OK?

{{comic discussion}}

[[Category:Comics featuring Cueball]]
[[Category:Comics featuring Megan]]
[[Category:Space]]

2333: COVID Risk Chart

2020-07-15T16:51:02Z

172.69.68.197:

{{comic
| number = 2333
| date = July 15, 2020
| title = COVID Risk Chart
| image = covid_risk_chart.png
| titletext = First prize is a free ticket to the kissing booth.
}}

==Explanation==
{{incomplete|Created by THE WINNER OF A TEST-TUBE EATING CONTEST. Please mention here why this explanation isn't complete. Do NOT delete this tag too soon.}}
This comic is a graph showing the risk COVID-19 infection of numerous activities on the horizontal axis, while showing the other (ie. safety) risks of the activity on the vertical axis. The activities are also color coded green, yellow, orange, or red, presumably indicating whether engaging in them is a good idea.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}

{{comic discussion}}

2295: Garbage Math

2020-04-18T17:02:37Z

172.69.68.197: Undo revision 190896; the line should be drawn here; see discussion

{{comic
| number = 2295
| date = April 17, 2020
| title = Garbage Math
| image = garbage_math.png
| titletext = 'Garbage In, Garbage Out' should not be taken to imply any sort of conservation law limiting the amount of garbage produced.
}}

==Explanation==
{{incomplete|Created by a ZILOG Z80. Please mention here why this explanation isn't complete. Do NOT delete this tag too soon.}}
This comic explains the "{{w|garbage in, garbage out}}" concept using arithmetical expressions. Just like the comic says, if you get garbage in any part of your workflow, you get garbage as a result. Except when you multiply by zero. That one always fixes everything.

Some of these rules correspond to the rules of {{w|floating point arithmetic}}, while others may be inspired by the rules of {{w|Propagation_of_uncertainty#Example_formulae| propagation of uncertainty}} where a "garbage" number would correspond to an estimate with a high degree of uncertainty, and the uncertainty of the result of arithmetic operations will tend to be dominated by the term with the highest uncertainty. The rule about N pieces of independent garbage reflects the {{w|central limit theorem}} and how it predicts that the uncertainty (or {{w|standard error}}) of an estimate will be reduced when independent estimates are averaged. The comic oddly omits raising garbage to the 0th power, which transforms even NaN, the platonic ideal of garbage, to exactly 1.

This comic is about the propagation of errors in numerical analysis and statistics, but described in much more colloquial terms. Numbers with low precision are termed "garbage" and numbers with high precision are labeled "precise".

This comic is not related to the {{w|2019–20 coronavirus outbreak|2020 pandemic}} of the {{w|coronavirus}} {{w|SARS-CoV-2}}, which causes {{w|COVID-19}}, breaking the streak of comics preceding this on [[:Category:COVID-19|topics relating to COVID-19]], after (rather appropriately) 19 comics (not counting the [[2288: Collector's Edition|April Fools' comic]]).

{| class="wikitable"
!Formula
!Statistical Expression
!Explanation
|-
|Precise number + Precise number = Slightly less precise number
|<math>\mathop\sigma(X+Y)=\sqrt{(\mathop\sigma(X))^2+(\mathop\sigma(Y))^2}</math>
|If we know absolute error bars, then adding two precise numbers will at worst add the sizes of the two error bars. For example, if our precise numbers are 1 (±10-6) and 1 (±10-6), then our sum is 2 (±2·10-6). It is possible to lose a lot of relative precision, if the resultant sum is close to zero as a result of adding a number and then close to its inverse. This phenomenon is known as catastrophic cancellation. Therefore, it is likely that all numbers referred here are positive numbers, which does not exhibit this phenomenon.
|-
|Precise number × Precise number = Slightly less precise number
|<math>\mathop\sigma(X\times Y)=\sqrt{(\mathop\sigma(X)\times Y)^2+(\mathop\sigma(Y)\times X)^2}</math>
|Here, instead of absolute error, relative error will be added. For example, if our precise numbers are 1 (±10-6) and 1 (±10-6), then our product is 1 (±2·10-6).
|-
|Precise number + Garbage = Garbage
|<math>\mathop\sigma(X+Y)=\sqrt{(\mathop\sigma(X))^2+(\mathop\sigma(Y))^2}</math>
|If one of the numbers has a high absolute error, and the numbers being added are of comparable size, then this error will be propagated to the sum.
|-
|Precise number × Garbage = Garbage
|<math>\mathop\sigma(X\times Y)=\sqrt{(\mathop\sigma(X)\times Y)^2+(\mathop\sigma(Y)\times X)^2}</math>
|Likewise, if one of the numbers has a high relative error, then this error will be propagated to the product. Here, this is independent of the sizes of the numbers.
|-
|<math>\sqrt{\text{Garbage}} = \text{Less bad garbage}</math>
|<math>\mathop\sigma(\sqrt X)=\frac{\mathop\sigma(X)}{2\times\sqrt X} </math>
| When the square root of a number is computed, its relative error will be halved. Depending on the application, this might not be all that much ''better'', but it's at least ''less bad''.
|-
|Garbage2 = Worse garbage
|<math>\mathop\sigma(X^2)=2\times X\times\mathop\sigma(X)</math>
|Likewise, when a number is squared, its relative error will be doubled. This is a corollary to multiplication adding relative errors.
|-
|<math>\frac{1}{N}\sum(\text{N pieces of statistically independent garbage}) = \text{Better garbage}</math>
|
|By aggregating many pieces of statistically independent observations (for instance, surveying many individuals), it is possible to reduce relative error. This is the basis of statistical sampling.
|-
|Precise numberGarbage = Much worse garbage
|<math>\mathop\sigma(b^X)=b^{2\times X}\times\mathop{\mathrm{ln}}b\times\sigma(X)</math>
|The exponent is very sensitive to changes, which may also magnify the effect based on the magnitude of the precise number.
|-
|Garbage – Garbage = Much worse garbage
|<math>\mathop\sigma(X-Y)=\sqrt{(\mathop\sigma(X))^2+(\mathop\sigma(Y))^2}</math>
|This line involves catastrophic cancellation. If both pieces of garbage are about the same (e.g. if their error bars overlap), then it is possible that the answer is positive, zero, or negative.
|-
|<math>\frac{\text{Precise number}}{\text{Garbage}-\text{Garbage}}</math> = Much worse garbage, possible division by zero
|<math>\mathop\sigma(\frac{a}{X-Y})=|\frac a{X-Y}|\times\sqrt{(\mathop\sigma(X))^2+(\mathop\sigma(Y))^2}</math>
|Indeed, as with above, if error bars overlap then we might end up dividing by zero.
|-
|Garbage × 0 = Precise number
|<math>\mathop\sigma(0)=0</math>
|Multiplying anything by 0 results in 0, an extremely precise number in the sense that it has no error whatsoever since we supply the 0 ourselves. This is equivalent to discarding garbage data from a statistical analysis.
|}

The title text refers to the computer science maxim of "garbage in, garbage out," which states that when it comes to computer code, supplying incorrect initial data will produce incorrect results, even if the code itself accurately does what it is supposed to do. As we can see above, however, when plugging data into mathematical formulas, this can possibly magnify the error of our input data, though there are ways to reduce this error (such as aggregating data). Therefore, the quantity of garbage is not necessarily conserved.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}

[A series of mathematical equations are written from top to bottom]

Precise number + Precise number = Slightly less precise number

Precise number × Precise number = Slightly less precise number

Precise number + Garbage = Garbage

Precise number × Garbage = Garbage

√Garbage = Less bad garbage

1/N Σ (N pieces of statistically independent garbage) = Better garbage

(Precise number)Garbage = Much worse garbage

Garbage – Garbage = Much worse garbage

Precise number / ( Garbage – Garbage ) = Much worse garbage, possible division by zero

Garbage × 0 = Precise number

{{comic discussion}}
[[Category:Math]]

Talk:2295: Garbage Math

2020-04-18T17:02:12Z

172.69.68.197: /* Inclusion in Series */ no, the line should be drawn here

== Inclusion in Series ==

This is not a Covid19 comic. One could think that this is a comment on the difficulties of modeling the corona virus outbreak, but since discussions of exponential functions are only a small part in the comic I believe it is just a general comment on floating point arithmetic mixed in with statistical considerations. --[[Special:Contributions/108.162.229.242|108.162.229.242]] 17:28, 17 April 2020 (UTC)
:I disagree that this is not a COVID-19 comic. I also believe the one about visualizing large numbers was COVID-19 related. On the other hand, I like the idea that Randall might produce exactly 19 comics related to SARS CoViD 2019, so I'm prepared to concede the point for the sake of arbitrary numerological appeal.
:[[User:ProphetZarquon|ProphetZarquon]] ([[User talk:ProphetZarquon|talk]]) 18:42, 17 April 2020 (UTC)
::I think Exa-Exabyte was a real stretch (the virus doesn't even have DNA), but there is a tenuous link so whatever. The idea that ''this'' comic is related, on the other hand, stretches past the breaking point. There's hardly anything that can't be linked to global events if we try hard enough, but that doesn't mean there's an actual link. Sometimes a comic about garbage math is just a comic about garbage math. [[Special:Contributions/172.69.71.58|172.69.71.58]] 19:33, 17 April 2020 (UTC)
:::I think this one's much more likely to be a coronavirus comic than Exa-Exabyte was. There's an awful lot of COVID data, much of it either very imprecise or outright garbage; and the comic directly before this one ([[2294]]) involved bad modeling of said COVID data, so clearly COVID data (and its limitations) is something Randall's currently thinking of and drawing comics about. [[User:Pelosujamo|Pelosujamo]] ([[User talk:Pelosujamo|talk]]) 20:25, 17 April 2020 (UTC)
::::Exa-Exabyte was centered around biology, which gives reason to believe it was covid19 related. This one seems much more uncertain. Any conclusion that it is related is based on garbage. Jokes aside, It seems like much more of a stretch to me. Randall thinking in those terms is a reasonable argument, but personally I am going to assume this is the chain breaker unless a direct reference is made in the next couple comics since ending at 19 is would be appropriate. [[Special:Contributions/172.69.70.209|172.69.70.209]]
:: While this comic has no ''direct'' reference to Covid-19 it does appear that the math might be related. At this point we can't know if the series has ended. As such I've edited the paragraph in the explanation to identify the known ambiguities. And now I realize I've made an explanatory paragraph about "knowledge error bars" in the explanation of a comic about numerical error bars.[[User:Iggynelix|Iggynelix]] ([[User talk:Iggynelix|talk]]) 14:42, 18 April 2020 (UTC)
:::No. The reason it appears the math might be related is ''because the math relates to everything, everywhere''. That's not enough of a connection. During this pandemic, there will be a lot of comics related to the coronavirus, many of them in a row, but that doesn't mean that every comic that could be tangentially related if you squint just right should qualify as a COVID-19 comic (I ''still'' think Exa-Exabyte doesn't). There needs to be a real link, because just about ''anything'' could be twisted into a relation if you try hard enough. As a test, I hit [[Special:Random]] and got [[346: Diet Coke+Mentos]]. Wouldn't you know, that's a coronavirus comic! The father, you see, actually had COVID-19 and died, but Diet Coke and Mentos has brought him back! No. The line should be drawn here. The streak has ended. [[Special:Contributions/172.69.68.197|172.69.68.197]] 17:02, 18 April 2020 (UTC)

== Math and Error bars ==

Well this is surprising came here thinking I understood it just to see what the discussion looked like. Ended up learning something new. I was able to understand intuitively the comic. But this is my first exposure to actually doing math on the error bars. I think I was supposed to do that in college but I don't remember anyone ever explaining how it should work. --[[Special:Contributions/162.158.63.208|162.158.63.208]] 18:14, 17 April 2020 (UTC)

In recent days, there have been a number of math "quizzes" in this same type of format, albeit generally with only addition and maybe multiplication, appearing on Facebook. Should the explanation include a reference to this as a possible contributing reason for Randall's comic? One could also argue that those quizzes have been appearing on Facebook as a way to spend/waste time during the coronavirus pandemic lock-down, making he comic at least tangentially related to Covid19 LIES.
:: Unsigned vandalism? /\ [https://www.explainxkcd.com/wiki/index.php?title=Talk:2295:_Garbage_Math&diff=190866&oldid=190856 change history] @user Please feel free to move your discussion to an appropriate forum and remove both the edit and this comment at such time. [[User:Iggynelix|Iggynelix]] ([[User talk:Iggynelix|talk]])

What's the difference between relative error and absolute error? I don't understand these terms. Maybe add?
: Absolute error is the amount of uncertainty in a value measured as a given number. e.g. 5.7 ± 1.2 means that actual value lies somewhere between 5.7 - 1.2 and 5.7 + 1.2 = 4.5 to 6.9. If you change the 5.7 to another value, you still get the same absolute difference of maximum and minimum values. Relative error depends on the value you are comparing to. e.g. 5.7 ± 10% would be between 5.7 - 0.57 and 5.7 + 0.57 = 5.13 to 6.27. The absolute difference of maximum and minimum would change if the main number changes. e.g. 11.3 ± 10% would be between 10.17 and 12.43, which has a greater absolute difference of maximum and minimum than the previous example. [[User:Nutster|Nutster]] ([[User talk:Nutster|talk]]) 01:54, 18 April 2020 (UTC)

Are all of these equations consistent with garbage = infinity?
: Unfortunately, as written, these equations would not make sense by defining Garbage as an infinity. Infinity is not a number you can count to or measure in between integers. Infinity is the idea of unending-ness. Trying to use infinity as if it a finite number yields all sorts of invalid results. In this case Garbage is defined as an arbitrary finite number with a large amount of uncertainty in its value. [[User:Nutster|Nutster]] ([[User talk:Nutster|talk]]) 01:40, 18 April 2020 (UTC)
::: That's a pretty good definition of 'garbage' in ''any'' case, plus or minus 10%. ( See also [https://www.weforum.org/agenda/2017/06/landfill-mining-recycling-eurelco/ valuable garbage]) [[User:Iggynelix|Iggynelix]] ([[User talk:Iggynelix|talk]]) 14:19, 18 April 2020 (UTC)

Would the summation divided by ''n'' just give you the arithmatic mean of the data set? [[User:Nutster|Nutster]] ([[User talk:Nutster|talk]]) 01:55, 18 April 2020 (UTC)
:Pretty much, but the point is probably more that (without consistent bias across the set, just 'random' errors for each item) it suppresses the degree of garbagicity as outliers are increasingly nullified by the greater number of more competently accurate values and (if it's a symmetric error) opposing outliers. [[Special:Contributions/162.158.34.222|162.158.34.222]] 09:29, 18 April 2020 (UTC)