explain xkcd - User contributions [en]

475: Further Boomerang Difficulties

2016-07-23T18:50:00Z

108.162.229.33: /* Explanation */ english

{{comic
| number = 475
| date = September 12, 2008
| title = Further Boomerang Difficulties
| image = further_boomerang_difficulties.png
| titletext = An eternity later, the universe having turned out to have positive curvature and lots of mass, the boomerang hits him in the back of the head.
}}

==Explanation==
This comic is a sequel of sorts to [[445: I Am Not Good with Boomerangs]], as it deals with the same subject manner with the same panel layout.

The first strip shows [[Cueball]] throwing a boomerang, which doesn't come back. In [[939: Arrow]], a boomerang returns to Cueball, which can either be the same Cueball from this comic or another person.

In the second strip he throws another boomerang, which somehow manage to hurt the {{w|ozone layer}} (as indicated by an off-screen voice). This is of course not possible with a boomerang, as it is a layer of ozone molecules very high up in the atmosphere.

The third strip shows Cueball throwing something that ''appears'' to be a boomerang, but then [[Megan]] enters and reveals that it was their last banana - which she probably had expected to eat since she calls him an asshole.

The final strip shows Cueball throwing one last boomerang, which breaks the frame of the comic, already after two out of the four frames used in each of the first three strips. Then panning down we find the last panel, much larger and suddenly mainly black instead of white. It shows that this time he was actually inside a spacecraft (which resembles an {{w|Apollo Lunar Module}} in a very bad manner), and the boomerang has just broken out through the hull. We see the boomerang and Cueball tumbling out into space with the escaping air. To certain death...

The title text notes that, assuming a theory, that is {{w|Accelerating universe|no longer generally accepted}}, where the universe has a positive (closed) {{w|curvature}} and lots of mass, the boomerang would, after a (very) long time hit Cueball in the back of his head. This would happen because under those conditions the entire universe would eventually fall back on itself in the {{w|Big Crunch}}. Before this happens, everything would again get pressed close together, and it is during this process that the boomerang would finally returns to his frozen (but quite possibly preserved) head. (So at least one "success" in four attempts.)

Boomerangs also became a main theme in the interactive comic [[1350: Lorenz]]. The same format of multiple bad endings to the same starting set-up is used in [[1515: Basketball Earth]].

==Transcript==
:[Cueball is throwing boomerang.]
:[Holding his hands up.]
:[Cueball waits for return; continual waiting.]
:[Cueball is dejected, head hangs low.]

:[Cueball throws boomerang.]
:[Cueball waits for boomerang.]
:Outside: Oh God
:Outside: The ozone layer!
:[Cueball is surprised.]

:[Cueball throws boomerang banana.]
:[Cueball waits.]
:[Megan walks in.]
:Megan: That was our last banana.
:Megan: You're such an asshole.
:[Cueball throws boomerang.]
:[Boomerang breaks out of the panel box.]

:[Boomerang breaks out of a spacecraft, followed by Cueball.]

==Trivia==
*Part of this comic and [[939: Arrow]] is the picture for the [http://tvtropes.org/pmwiki/pmwiki.php/Main/BrickJoke Brick Joke] page on TV Tropes.

{{comic discussion}}
[[Category:Comics featuring Cueball]]
[[Category:Comics featuring Megan]]
[[Category:Boomerangs]]
[[Category:Physics]]

1292: Pi vs. Tau

2014-04-30T15:26:14Z

108.162.229.33: It's also important to mention when the bug was first found, not only when it was last seen. My wording is cumbersome, but I'm not sure how to give both dates in less words.

{{comic
| number = 1292
| date = November 18, 2013
| title = Pi vs. Tau
| image = pi vs tau.png
| titletext = Conveniently approximated as e+2, Pau is commonly known as the Devil's Ratio (because in the octal expansion, '666' appears four times in the first 200 digits while no other run of 3+ digits appears more than once.)
}}

==Explanation==
{{incomplete|Too complex, non Math people should also be able to understand this. Randalls mistake has to be emphasised, everything else here is still too much, it even doesn't belong to a trivia section. See the discussion page.}}

This is yet another of [[Randall]]'s [[:Category:Compromise|compromise comics]]. A few mathematicians argue as to whether to use pi, which is the ratio between a circle's circumference and its diameter, or tau, which is the ratio between a circle's circumference and its radius.

Most will know π (Pi) by the approximation 3.14, but not knowing τ (tau) which is just twice as large as pi. Randall is suggesting using "pau", which is a portmanteau of "pi" and "tau", as a number situated, appropriately enough, halfway between pi and tau. But of course his number would be inconvenient, as there are currently no commonly used formulas that involve 1.5 pi (or 0.75 tau). Additionally, it is highly unlikely that substituting e+2 for pau would ever result in 'convenience'.

Some consider pi as being the wrong convention and are in favor of using tau as ''the'' circle constant (see the [http://tauday.com/tau-manifesto Tau Manifesto], which was inspired by the article "[http://www.math.utah.edu/~palais/pi.html Pi is wrong!]" by mathematician Robert Palais). Others consider proponents of tau to be foolish and remain loyal to pi (see the [http://www.thepimanifesto.com Pi Manifesto]). Of course, regardless of which convention is used, the fundamental mathematics will remain unaltered. But the choice of pi vs tau can affect the clarity of equations, analogies between different equations, and how easy various subjects are to teach.

===Title text===

The title text is a bunch of slightly-incorrect mathematical [[356: Nerd Sniping|nerd sniping]] that Randall included for seemingly no better reason than trolling us. It consists of some of advanced trigonometry and other assorted college-level concepts that will in all likelihood just bore you if you don't care about them already. You can walk away right now thinking "Randall is just nerd sniping us" and still get the joke. If you REALLY want to know what all the math means, we'll try and work through it below...

"Octal expansion" refers to writing out the number in base-8. In base-8, only the numerals 0-7 are used to express numbers. This does not mean that values such as 18, 19, 28, 29, and so on do not exist; rather, said values are represented with a more limited range of numerals.

For the sake of simplicity in this next demonstration, we will only acknowledge whole numbers with positive values.

In base-8, the numbers 1 through 7 have the same values as in base-10. The next number, eight, is written out as 10. This is because the "ones" digit has run out of unique numerals to express this value, so it rolls over to the "eights" digit. Nine is 11. Ten is 12. Numbering continues in this manner, up to fifteen (17). The "ones" digit must roll over to the "eights" digit again, so sixteen is 20. Seventeen is 21. After twenty-three (27), it rolls over again, giving us twenty-four (30).

Counting by eights, the next numbers are thirty-two (40), forty (50), forty-eight (60), and fifty-six (70). At sixty-three (77), both the "ones" and "eights" digit has run out of unique numerals, so the excess value must roll over to the "sixty-fours" digit, giving us sixty-four (100). If we keep counting, we will eventually reach five-hundred-eleven (777). A new "five-hundred-twelves" digit is created. The next number is five-hundred-twelve (1000).

As you can see, numbers written in base-8 tend to be longer and less economical to write than in base-10, but it does serve its purpose. Trust us on this.

In this next demonstration, we will look at how to write non-integers in base-8. Again, we will acknowledge only positive values.

In base-8, all the numerals that follow the period are not known as the "decimal", but as the "octal". This is because "decimal" specifically refers to tenths, while "octal" refers to eighths.

In decimal, the first place after the periods depicts "tenths", the next place "hundredths", the next "thousandths", and so on. In octal, the first place represents "eighths", the next "sixty-fourths", the next "five-hundred-twelfths", etc.

One eighth is 0.1. Two eighths, or one fourth, is 0.2. Four eighths, or one half, is 0.4.
One sixty-fourth is 0.01. Five sixty-fourths is 0.05. Nine sixty-fourths, or one eighth plus one sixty-fourth, is 0.11.
One five-hundred-twelfth is 0.001. Five-hundred-eleven five-hundred-twelfths is 0.777.

Unfortunately, this entire lesson has a very disappointing end. As it turns out, the title text for the comic is incorrect. The first 200 digits of 'pau' in octal are:
<pre>
4.5545743763144164432362345144750501224254715730156503147633545270030431677126116550546747570313312523403514716576464333172731124310201076447270723624573721640220437652155065544220143116155742515634462
</pre>
The sequence '666' does not occur at all in it.

Possibly, [[Randall]] used [http://www.wolframalpha.com/ Wolfram|Alpha] to calculate the result (he uses it a lot, for example [http://what-if.xkcd.com/70/ What-if 70: The Constant Groundskeeper] or [http://what-if.xkcd.com/62/ What-if 62: Falling With Helium]).
However, at the date of the comic publication and up to (at least) April 29, 2014, there's a bug in Wolfram|Alpha so that, when getting 200 octal digits from "pau", it just calculates the decimal value rounded to 15 significant digits (this is 4.71238898038469) and expands that as octal digits as far as needed.

This gives a periodically repeating number. In the first 200 digits of the octal expansion, the sequences 666 and 6666 do occur, but each only once. There are 4 occurrences, however, in the first 300 digits:
<pre>
4.554574376314416445676661714336617116240444076666510533533077631151350452060436452476274022621206136310000177621674175071262255702044274154476005744176002676623042402346036604733130522524127534777714554305412763636566643022106616734723661726160312772574551366370203115523402704104015532221722772357666</pre>
Expansion that long indeed does contain 666 (the {{w|Number of the beast|number of the beast}}) four times (with one instance as 6666). It also contains 0000, 222, 444, and 7777, but they only appear once in a run.

{{w|Mathematical coincidence|Coincidentally}}, e+2 is also very similar to 1.5pi, although only to a few digits.
<pre>
1.5π = 4.71238898038...
e+2 = 4.71828182845...
</pre>

The "Devil's Ratio" may be an allusion to the "{{w|Tritone|Devil's Interval}}", aka the "Devil's Chord" or 'Diabolus in Musica' ('The Devil in music'), which is the name sometimes given to the harmony between a root note and its tritone/augmented fourth/diminished fifth. This note is situated halfway between octaves, and is named for its dissonant quality. It is possibly a cross-reference between this and the "{{w|golden ratio}}".

==Transcript==
:[On the left is a "forbidden"-style slashed circle with the π symbol, captioned "Pi". On the right is a "forbidden"-style slashed circle with 2π, captioned "Tau". In the middle it reads 1.5π, captioned "Pau".]
:A compromise solution to the Pi Tau dispute

==Trivia==
*For Pi the sequence '666' occurs for the first time at position 2440. Many more occurrences can be found here: [http://www.angio.net/pi/ The Pi-Search Page].
* Note that pau is Catalan for peace, which is a good solution for the pi/tau dispute.
* In the discussion it has been theorized that Randall used [[356: Nerd Sniping|Nerd Sniping]]. In which case he was aware of the mistake in Wolfram!
*For an entertaining introduction to the concept, see this [https://www.khanacademy.org/math/recreational-math/vi-hart/pi-tau/v/pi-is--still--wrong Vi Hart video].

{{comic discussion}}
[[Category:Comics with color]]
[[Category:Math]]
[[Category:Compromise]]

Talk:1362: Morse Code

2014-04-30T15:13:27Z

108.162.229.33:

Does the way the panels of the comic go 0101 mean anything, being more code and all? [[User:Cheeselord99|Cheeselord99]] ([[User talk:Cheeselord99|talk]]) 06:58, 30 April 2014 (UTC)

: The Morse sequence · – · – (dot dash dot dash) corresponds to letter Ä (A umlaut), also æ and ą, outside US-ASCII. – · – · is C. --[[User:JakubNarebski|JakubNarebski]] ([[User talk:JakubNarebski|talk]]) 07:52, 30 April 2014 (UTC)

It seems to translate in the question mark. --07:11, 30 April 2014 (UTC)[[Special:Contributions/141.101.96.205|141.101.96.205]]

Randall mentioned in one of the "what ifs" that when he sees 1010 he involuntarily thinks "ten." So I guess it's "five?" Or an extended-Morse "a-umlaut" or "a-ogonek" or "ae digraph." Or a wild goose chase, maybe...[[User:Taibhse|Taibhse]] ([[User talk:Taibhse|talk]]) 07:25, 30 April 2014 (UTC)

Can someone explain the livejournal? -- [[User:Hkmaly|Hkmaly]] ([[User talk:Hkmaly|talk]]) 09:59, 30 April 2014 (UTC)
:And it is still a nice and a quiet place for people devoted to their interests,[http://raskalov-vit.livejournal.com/130686.html like urban exploration,etc.]Contrasted with Tumblr or Facebook,which are often drama-filled.[[User:Guru-45|Guru-45]] ([[User talk:Guru-45|talk]]) 11:03, 30 April 2014 (UTC)
livejournal is a website that was popular with the "goth" subculture way back in the day where people would post similar things to the last morse message.
:It's commonly used by Russians nowadays.[[User:Guru-45|Guru-45]] ([[User talk:Guru-45|talk]]) 11:05, 30 April 2014 (UTC)

"Cueball and Megan are 'lying' in a grassy, lonely plain." "Laying" has quite a different connotation. Ahem. [unsigned]

I was looking at one of my livejournal entries just yesterday. I left it for Posterous. Then Twitter bought that and shut it down. I thik Wordpress will be around for a while. http://purl.net/net/tbc/blog/about

To the subject at hand. 'I Googled and found a 1999 article about Morse code in ''The Economist'' that is fascinating. I Instapapered http://www.economist.com/node/183572 ''– [[User:Tbc|tbc]] ([[User talk:Tbc|talk]]) 13:03, 30 April 2014 (UTC)''

Perhaps Cueball was simply inspired by the quote and wanted to close his LiveJournal account in a similar manner. He did not necessarily intend to use those exact words.--[[Special:Contributions/108.162.242.8|108.162.242.8]] 14:31, 30 April 2014 (UTC)

The landscape keeps changing from panel to panel: the lines in the horizon, the lines in the front big rock, the bunches of grass, etc. Also, grassy plains are usually thought of as peaceful and quiet, while the internet is not. I think the point (at least, one of the points) in the last panel is that Cueball turns this upside down by wanting to visit livejournal for peace and quietness,

1292: Pi vs. Tau

2014-04-29T10:24:35Z

108.162.229.33: Added the idea that the Wolfram bug hasn't been corrected, the plan being to have an idea of the exact date when it's corrected, if ever.

{{comic
| number = 1292
| date = November 18, 2013
| title = Pi vs. Tau
| image = pi vs tau.png
| titletext = Conveniently approximated as e+2, Pau is commonly known as the Devil's Ratio (because in the octal expansion, '666' appears four times in the first 200 digits while no other run of 3+ digits appears more than once.)
}}

==Explanation==
{{incomplete|Too complex, non Math people should also be able to understand this. Randalls mistake has to be emphasised, everything else here is still too much, it even doesn't belong to a trivia section. See the discussion page.}}

This is yet another of [[Randall]]'s [[:Category:Compromise|compromise comics]]. A few mathematicians argue as to whether to use pi, which is the ratio between a circle's circumference and its diameter, or tau, which is the ratio between a circle's circumference and its radius.

Most will know π (Pi) by the approximation 3.14, but not knowing τ (tau) which is just twice as large as pi. Randall is suggesting using "pau", which is a portmanteau of "pi" and "tau", as a number situated, appropriately enough, halfway between pi and tau. But of course his number would be inconvenient, as there are currently no commonly used formulas that involve 1.5 pi (or 0.75 tau).

Some consider pi as being the wrong convention and are in favor of using tau as ''the'' circle constant (see the [http://tauday.com/tau-manifesto Tau Manifesto], which was inspired by the article "[http://www.math.utah.edu/~palais/pi.html Pi is wrong!]" by mathematician Robert Palais). Others consider proponents of tau to be foolish and remain loyal to pi (see the [http://www.thepimanifesto.com Pi Manifesto]). Of course, regardless of which convention is used, the fundamental mathematics will remain unaltered. But the choice of pi vs tau can affect the clarity of equations, analogies between different equations, and how easy various subjects are to teach.

===Title text===

The title text is a bunch of slightly-incorrect mathematical [[356: Nerd Sniping|nerd sniping]] that Randall included for seemingly no better reason than trolling us. It consists of some of advanced trigonometry and other assorted college-level concepts that will in all likelihood just bore you if you don't care about them already. You can walk away right now thinking "Randall is just nerd sniping us" and still get the joke. If you REALLY want to know what all the math means, we'll try and work through it below...

"Octal expansion" refers to writing out the number in base-8. In base-8, only the numerals 0-7 are used to express numbers. This does not mean that values such as 18, 19, 28, 29, and so on do not exist; rather, said values are represented with a more limited range of numerals.

For the sake of simplicity in this next demonstration, we will only acknowledge whole numbers with positive values.

In base-8, the numbers 1 through 7 have the same values as in base-10. The next number, eight, is written out as 10. This is because the "ones" digit has run out of unique numerals to express this value, so it rolls over to the "eights" digit. Nine is 11. Ten is 12. Numbering continues in this manner, up to fifteen (17). The "ones" digit must roll over to the "eights" digit again, so sixteen is 20. Seventeen is 21. After twenty-three (27), it rolls over again, giving us twenty-four (30).

Counting by eights, the next numbers are thirty-two (40), forty (50), forty-eight (60), and fifty-six (70). At sixty-three (77), both the "ones" and "eights" digit has run out of unique numerals, so the excess value must roll over to the "sixty-fours" digit, giving us sixty-four (100). If we keep counting, we will eventually reach five-hundred-eleven (777). A new "five-hundred-twelves" digit is created. The next number is five-hundred-twelve (1000).

As you can see, numbers written in base-8 tend to be longer and less economical to write than in base-10, but it does serve its purpose. Trust us on this.

In this next demonstration, we will look at how to write non-integers in base-8. Again, we will acknowledge only positive values.

In base-8, all the numerals that follow the period are not known as the "decimal", but as the "octal". This is because "decimal" specifically refers to tenths, while "octal" refers to eighths.

In decimal, the first place after the periods depicts "tenths", the next place "hundredths", the next "thousandths", and so on. In octal, the first place represents "eighths", the next "sixty-fourths", the next "five-hundred-twelfths", etc.

One eighth is 0.1. Two eighths, or one fourth, is 0.2. Four eighths, or one half, is 0.4.
One sixty-fourth is 0.01. Five sixty-fourths is 0.05. Nine sixty-fourths, or one eighth plus one sixty-fourth, is 0.11.
One five-hundred-twelfth is 0.001. Five-hundred-eleven five-hundred-twelfths is 0.777.

Unfortunately, this entire lesson has a very disappointing end. As it turns out, the title text for the comic is incorrect. The first 200 digits of 'pau' in octal are:
<pre>
4.5545743763144164432362345144750501224254715730156503147633545270030431677126116550546747570313312523403514716576464333172731124310201076447270723624573721640220437652155065544220143116155742515634462
</pre>
The sequence '666' does not occur at all in it.

Possibly, [[Randall]] used [http://www.wolframalpha.com/ Wolfram|Alpha] to calculate the result (he uses it a lot, for example [http://what-if.xkcd.com/70/ What-if 70: The Constant Groundskeeper] or [http://what-if.xkcd.com/62/ What-if 62: Falling With Helium]).
However, as of November 18, 2013, there's a bug in Wolfram|Alpha so that, when getting 200 octal digits from "pau", it just calculates the decimal value rounded to 15 significant digits (this is 4.71238898038469) and expands that as octal digits as far as needed [Update: as of April 29, 2014, Wolfram's bug is still there].

This gives a periodically repeating number. In the first 200 digits of the octal expansion, the sequences 666 and 6666 do occur, but each only once. There are 4 occurrences, however, in the first 300 digits:
<pre>
4.554574376314416445676661714336617116240444076666510533533077631151350452060436452476274022621206136310000177621674175071262255702044274154476005744176002676623042402346036604733130522524127534777714554305412763636566643022106616734723661726160312772574551366370203115523402704104015532221722772357666</pre>
Expansion that long indeed does contain 666 (the {{w|Number of the beast|number of the beast}}) four times (with one instance as 6666). It also contains 0000, 222, 444, and 7777, but they only appear once in a run.

{{w|Mathematical coincidence|Coincidentally}}, e+2 is also very similar to 1.5pi, although only to a few digits.
<pre>
1.5π = 4.71238898038...
e+2 = 4.71828182845...
</pre>

The "Devil's Ratio" may be an allusion to the "{{w|Tritone|Devil's Interval}}", aka the "Devil's Chord" or 'Diabolus in Musica' ('The Devil in music'), which is the name sometimes given to the harmony between a root note and its tritone/augmented fourth/diminished fifth. This note is situated halfway between octaves, and is named for its dissonant quality. It is possibly a cross-reference between this and the "{{w|golden ratio}}".

==Transcript==
:[On the left is a "forbidden"-style slashed circle with the π symbol, captioned "Pi". On the right is a "forbidden"-style slashed circle with 2π, captioned "Tau". In the middle it reads 1.5π, captioned "Pau".]
:A compromise solution to the Pi Tau dispute

==Trivia==
*For Pi the sequence '666' occurs for the first time at position 2440. Many more occurrences can be found here: [http://www.angio.net/pi/ The Pi-Search Page].
* Note that pau is Catalan for peace, which is a good solution for the pi/tau dispute.
* In the discussion it has been theorized that Randall used [[356: Nerd Sniping|Nerd Sniping]]. In which case he was aware of the mistake in Wolfram!
*For an entertaining introduction to the concept, see this [https://www.khanacademy.org/math/recreational-math/vi-hart/pi-tau/v/pi-is--still--wrong Vi Hart video].

{{comic discussion}}
[[Category:Comics with color]]
[[Category:Math]]
[[Category:Compromise]]

1322: Winter

2014-01-27T12:42:17Z

108.162.229.33: /* Explanation */

{{comic
| number = 1322
| date = January 27, 2014
| title = Winter
| image = winter.png
| titletext = Stay warm, little flappers, and find lots of plant eggs!
}}

==Explanation==
Beret Guy and Cueball are walking. Beret Guy is making several remarks about the situation. It is cold, the pond is frozen, and the birds are chirping in the trees. When making these observations, however, he does not use the correct terms. Instead he uses compounds of monosyllabic words, similar to "[[1133: Up Goer Five|Up Goer Five]]". When Cueball brings up Beret Guy's poor vocabulary, he retorts by declaring that the name does not matter, as long as the things themselves are what they should be. This is the same concept that is communicated in the line from the Shakespearean play, "Romeo and Juliet": "What's in a name? That which we call {{w|A rose by any other name would smell as sweet|a rose/by any other name would smell as sweet}}."

The title text further builds upon this idea.

;Dictionary

*The sky is cold: The air is cold
*floor water: pond ''or'' snow
*hard to drink: frozen ''or'' snow
*handcoats: mittens ''or'' gloves
*spacelight: sun
*flappy planes: birds
*beeping: chirping
*stick towers: trees
*little flappers: birds
*plant eggs: seeds

==Transcript==
{{incomplete transcript}}
:[Beret Guy talking with Cueball, walking through a cold forest with snow on the ground]
:Beret Guy: The sky is cold and the floor water is too hard to drink.
:Beret Guy: But I have my handcoats and the spacelight is warm.
:Beret Guy: Listen–the flappy planes are beeping in the stick towers.
:Cueball: Those are all the wrong words for those things.
:Beret Guy: Maybe.
:Beret Guy: But the things themselves are all right. So who cares?

{{comic discussion}}
[[Category:Comics featuring Beret Guy]]
[[Category:Language]]