explain xkcd - User contributions [en]

1344: Digits

2014-03-20T20:26:07Z

RainbowDash: /* Explanation */

{{comic
| number = 1344
| date = March 19, 2014
| title = Digits
| image = digits.png
| titletext = It's taken me 20 years to get over skyline tetris.
}}

==Explanation==
[http://gabrielecirulli.github.io/2048/ 2048] is a popular browser-based game in which players must move tiles in a 4 by 4 grid with numbers on them. When two tiles of the same number touch they can be merged into one tile with a value of the two tiles combined. So when two 4-tiles touch and are merged they form one 8-tile. The player can move the tiles by pressing an arrow key (or swiping in a direction on the mobile version), which will move all the tiles in that direction. Every time the player makes such a move another tile will appear on a random cell. The goal of the game is to get a tile with the number 2048.

In the comic the room number can be seen as 4 tiles with the values 8, 2, 2 and 4. If these occur in the game the player can merge the two 2-tiles into one 4-tile. This will then cause two 4-tiles to lie next to each other, so these can be merged into one 8-tile. Finally, the two 8-tiles can be merged into one 16-tile.

[[File:8224.gif]]

The title text refers to {{w|Tetris effect}}, which takes its name from the game {{w|Tetris}}. People who play Tetris for extended periods tend to imagine real-life objects (like skylines) as tetris landscapes and pieces. Randall, as many others,[http://s3-external-1.amazonaws.com/wootdesigncontestentries/fackoph/chicago_skyline_%28Tetris_Redux%29-q71p5a-s.jpg] apparently got hooked on Tetris so much when it came out that, for 20 years, he would look at city skylines and see Tetris-like patterns in it. Similarly, he has now been hooked onto 2048 and notices number patterns that would be desirable to obtain during the game.

Comics [[724: Hell]] and [[888: Heaven]] also refer to Tetris.

==Transcript==
:[A guy is walking and Cueball is following him.]
:Guy: The talk is in room 8224.
:Cueball: Ooh, nice.
:Guy: What?
:Cueball: ...Sorry. Nothing.

:Great, now I'll spend the rest of my life noticing numbers that would make good 2048 combos.

{{comic discussion}}

[[Category:Comics featuring Cueball]]
[[Category:Video games]]
[[Category:Math]]

File:8224.gif

2014-03-20T20:22:17Z

RainbowDash: A simple gif that demonstrates how 8224 will combine into 16.

A simple gif that demonstrates how 8224 will combine into 16.

1292: Pi vs. Tau

2013-11-18T17:21:06Z

RainbowDash: /* Explanation */ The reference to 3+ digits is only single digits. The e+2 approximation is also unnecessary, because Randall states that 1.5pi can be conveniently written as e+2 but doesn't mention anything about its digits.

{{comic
| number = 1292
| date = November 17, 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}}

This is yet another of Randall's 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. Randall is suggesting using pau, which is a portmanteau between pi and tau, and is a number situated halfway between pi and tau. This number would be effectively useless, as there are currently no commonly used formulas that involve 1.5 pi or 0.75 tau.

Some consider pi has being the wrong convention in favor of tau (see the [http://tauday.com/tau-manifesto Tau Manifesto]). Some consider proponents of tau to be foolish and remain loyal to pi (see the [http://www.thepimanifesto.com Pi Manifesto]). Occasionally, the argument is that the food, pi(e), is the whole thing, not half and have made a [http://www.piday.org/ day about it]. Others say on tau day you get twice as much pi(e).

The inspiration for pi is wrong is found [http://www.math.utah.edu/~palais/pi.html here].

The trivial nature of the argument is made plain in this comic. Regardless of which convention is used, the fundamental mathematics will remain unaltered

The title text for the comic is also incorrect. The first 200 digits of 'pau' in octal are:
<pre>
4.5545743763144164432362345144750501224254715730156503147633545270030431677126116550546747570313312523403514716576464333172731124310201076447270723624573721640220437652155065544220143116155742515634462
</pre>
The sequence '666' does not occur at all.

Apparently, [[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/ here] and [http://what-if.xkcd.com/62/ here]).
However, as of 2013-11-18, 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. The number of digits is also represented in octal, so instead of 200 digits it is actually 310 digits, finally giving:
<pre>
4.5545743763144164456766617143366171162404440766665105335330776311513504520604364524762740226212061363100001776216741750712622557020442741544760057441760026766230424023460366047331305225241275347777145543054127636365666430221066167347236617261603127725745513663702031155234027041040155322217227723576660045156156</pre>
This number indeed does contain 666 four times (with one instance as 6666). It also contains 0000, 222, 444, and 7777, but they only appear once in a run.

[http://en.wikipedia.org/wiki/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 = 4.71828182846
</pre>

The "Devil's Ratio" may be an allusion to the "[http://en.wikipedia.org/wiki/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 "[http://en.wikipedia.org/wiki/Golden_ratio Golden Ratio]".

==Transcript==
{{incomplete transcript}}
:(π, 'Pi', crossed out) (1.5 π, 'Pau') (2 π, 'Tau', also crossed out)
:A compromise solution to the Pi/Tau dispute
{{comic discussion}}
[[Category:Comics with color]]
[[Category:Math]]

Talk:1292: Pi vs. Tau

2013-11-18T16:59:09Z

RainbowDash:

I started an explanation. Hopefully others will help improve it, as I don't think it's quite adequate. [[Special:Contributions/199.27.130.174|199.27.130.174]] 05:32, 18 November 2013 (UTC)

The comic currently shows the symbol π (pi) in all three cases, but it should have the symbol τ (tau) in the rightmost case. I'm sure there is a compromise symbol "pau" too. Maybe with a deformed left leg? [[Special:Contributions/141.101.97.4|141.101.97.4]] 07:07, 18 November 2013 (UTC)

WolframAlpha gives
<pre>
4.5545743763144164456766617143366171162404440766665105335330776311513504520604364524762740226212061363100001776216741750712622557020442741544760057441760026766230424023460366047331305225241275347777145543054127636365666430221066167347236617261603127725745513663702031155234027041040155322217227723576660045156156303357534162372112340027743775672417274565277274565735325624457113522164166560115654407251403563246444122664066521461311773474046032763760765740133706761276420415672577471077133607673035331070364705651055376634161405567176532346433567731715723623721267302576735154761375545411215522177775706407470673020025353246535120744232706060324711633457720155013202527060250466252665661576165164140301645132275526153126363575631176312270212441433434206352313125326760006365710744276056412434626534152021052065172556442150110056601034116570607064550553636566432544260105637423220411372664024454234201642615033200331506013362432026775605543212342336511350621361642654426372425415023071413764173735461042064323757413414533013..._8</pre> which does indeed have four 666 sequences. [[Special:Contributions/141.101.99.254|141.101.99.254]] 08:06, 18 November 2013 (UTC)
This number contains 7777, 000 and 444 twice, though. [[Special:Contributions/141.101.93.11|141.101.93.11]] 09:08, 18 November 2013 (UTC)

Wrote the transcript, not sure if I explained the visual well enough, so I left the incomplete tag if someone else has a better idea. Should suffice for understanding however, considering the content [[Special:Contributions/108.162.248.18|108.162.248.18]] 08:55, 18 November 2013 (UTC)

----

(The discussion about different results was trimmed)

Wolfram gives the result with 666

http://www.wolframalpha.com/input/?i=1.5+pi+octal
<pre>
4.554574376314416445676661714336617116240444076666510533533077631151350452060436452476274022621206136310000177621674175071262255702044274154476005744176002676623042402346036604733130522524127534777714554305412763636566643022
</pre>
The Unix arbitrary precision calculator gives the result without

$ echo "scale=200; obase=8; 6*a(1)" | bc -l
<pre>
4.554574376314416443236234514475050122425471573015650314763354527003043167712611655054674757031331252340351471657646433317273112431020107644727072362457372164022043765215506554422014311615574251563446213636251744101107770257
</pre>
Any suggestions how we can check them?

"Randall says so" is probably correct, but insufficient :-) {{unsigned|Mike}}

:Please use the <nowiki><pre></nowiki> tag for this long numbers.--[[User:Dgbrt|Dgbrt]] ([[User talk:Dgbrt|talk]]) 09:20, 18 November 2013 (UTC)

Testing Wolfram Alpha with <pre>4.55457437631441644567666171433661711624044407666651053353307763115135045206043645247627402262120613631000177621674175071262255_8 in decimal</pre> and <pre>4.55457437631441644567666171433661711624044407666651053353307763115135045206043645247627402262120613631000_8 in decimal</pre> both indicate the approximation is only accurate to a limited degree.
http://www.wolframalpha.com/input/?i=4.55457437631441644567666171433661711624044407666651053353307763115135045206043645247627402262120613631000177621674175071262255_8+in+decimal
http://www.wolframalpha.com/input/?i=4.55457437631441644567666171433661711624044407666651053353307763115135045206043645247627402262120613631000177621674175071262255_8+in+decimal

The method I used to get the value I put in the text was; I used the following command to generate my approximation:
<pre>echo 'scale=200; obase=8; a(1) * 6' | bc -l | tr -d ' \\\n' ; echo</pre> which outputs<pre>
4.554574376314416443236234514475050122425471573015650314763354527003043167712611655054674757031331252340351471657646433317273112431020107644727072362457372164022043765215506554422014311615574251563446213636251744101107770257
</pre>
In 'bc'', a(1) is arctangent of 1 (i.e. 45 degrees, or pi/4); (pi/4 * 6) should be equal to 'pau'. I additionally checked the result using base 2 encoding, and converted each three bit binary value into an octal value. The decimal value of pi (using a(1) * 4) matches with the value of pi to at lease 1000 digits.
[[Special:Contributions/173.245.54.86|173.245.54.86]] 09:21, 18 November 2013 (UTC)

Both Maxima and the GNU Emacs calculator output as the first 1000 octal digits:
<pre>
4.5545743763144164432362345144750501224254715730156503147633545270030431677126116550546747570313312523403514716576464333172731124310201076447270723624573721640220437652155065544220143116155742515634462136362517441011077702611156024117447125224176203716336742057353303216470257662666744627534325504334506002730517102547504145216661211250027531716641276765735563341721214013553453654106045245066401141437740626707757305450703606440651111775270032710035521352101513622062164457304326450524432531652666626042202562202550566425643040556365710250031642467447605663240661743600041052212627767073277600402572027316222345356036301002572541750000114422036312122341474267232761775450071652613627306745074150251171507720277250030270442257106542456441722455345340370205646442156334125564557520336340223313312556634450170626417234376702443117031135045420165467426237454754566012204316130023063506430063362203021262434464410604275224606523356702572610031171344411766505734615256121034660773306140032365326415773227551
</pre>
This also agrees with the first 220 digits of the previous result (last two digits above are 57 vs 61 here, maybe due to rounding when converting to octal). Again, no 666 within the first 200 digits. The Wolfram result deviates from this at the 18th digit already. --[[User:Ulm|ulm]] ([[User talk:Ulm|talk]]) 10:21, 18 November 2013 (UTC)

Also e+2 does not contain the substring '666':
<pre>echo "scale=200; obase=8; e(1) + 2" | bc -l</pre>
<pre>4.55760521305053551246527734254200471723636166134705407470551551265170233101050620637674622347347044466373713722774330661414353543664033100253542141365517370755272577262541110317650765740633550205306625</pre>--[[User:Dgbrt|Dgbrt]] ([[User talk:Dgbrt|talk]]) 10:43, 18 November 2013 (UTC)

: A sudden flash of realization: are we getting nerd-sniped here?--[[Special:Contributions/108.162.254.168|108.162.254.168]] 11:55, 18 November 2013 (UTC)

: The claim is clearly about e+2, making Dgbrt's comment closest to the right direction. [[Special:Contributions/173.245.54.40|173.245.54.40]] 12:03, 18 November 2013 (UTC)

When I take Wolfram alpha's octal(pi*1.5) I get the first 303 (base 10) characters as this:
<pre>
4.554574376314416445676661714336617116240444076666510533533077631151350452060436452476274022621206136310000177621674175071262255702044274154476005744176002676623042402346036604733130522524127534777714554305412763636566643022106616734723661726160312772574551366370203115523402704104015532221722772357666
</pre>
200(base 10) is 310(base 8) so in the fist '200' characters, 666 shows up 4 times (5 if you count 6666 as twice?) [[User:Xami|Xami]] ([[User talk:Xami|talk]]) 14:01, 18 November 2013 (UTC)

: The Wolfram result is what you get when you calculate pi*3/2 in decimal, round to 14 digits after the decimal point and then convert to octal. That is, 4.71238898038469<sub>10</sub> converted to octal. Definitely, this won't give you 200 digits precision. --[[User:Ulm|ulm]] ([[User talk:Ulm|talk]]) 15:15, 18 November 2013 (UTC)
:: It lines up too perfectly to be a coincidence. It fits all the requirements: has 666 four times within 200<sub>8</sub> digits, and although 0000, 222, 444, and 7777 appear, they only appear once as a run. You can't double count 7777 as two 777's because it is a single run. If WolframAlpha doesn't give the correct precision, it is likely that Randall made the same error. --[[User:RainbowDash|RainbowDash]] ([[User talk:RainbowDash|talk]]) 16:59, 18 November 2013 (UTC)

Being τ, tau, is already being expressed in terms of π, pi, it shows bias. (Though I think Pau would lead to some interesting spherical geometry equations. ~~Drifter

Talk:1241: Annoying Ringtone Champion

2013-07-22T18:15:26Z

RainbowDash:

can somebody add the link to the audio files for the other annoying ringtones mentioned her?
[[Special:Contributions/188.65.166.110|188.65.166.110]] 10:21, 22 July 2013 (UTC)
:"That sound" https://www.youtube.com/watch?v=0cVlTeIATBs --[[User:RainbowDash|RainbowDash]] ([[User talk:RainbowDash|talk]]) 18:15, 22 July 2013 (UTC)
According to Wikipedia (http://en.wikipedia.org/wiki/Sound_pressure#Sound_pressure_level) 194db is the loudest sound possible without distortion in Earth's atmosphere, so unlikely that you could update an audio file of it.
:And you would most likely die from that sound pressure level. --[[Special:Contributions/129.110.242.8|129.110.242.8]] 16:58, 22 July 2013 (UTC)
:Wouldn't it be rather a question of your sound equipment if you can achieve 194dB? --[[User:Chtz|Chtz]] ([[User talk:Chtz|talk]]) 17:10, 22 July 2013 (UTC)

Talk:1213: Combination Vision Test

2013-05-17T05:28:57Z

RainbowDash:

Number is "42".
The 4 is composed of 2's and 3's and 7's.
The 2 is composed of 3's and 7's and 9's.
--[[User:RainbowDash|RainbowDash]] ([[User talk:RainbowDash|talk]]) 05:16, 17 May 2013 (UTC)

Also both have 5's. I'm not very good at this counting thing. That link below is way better, anyhow. --[[User:RainbowDash|RainbowDash]] ([[User talk:RainbowDash|talk]]) 05:28, 17 May 2013 (UTC)

http://i.imgur.com/BLIQR6w.png

Credit: http://www.reddit.com/user/silly-moose

User:RainbowDash

2013-05-17T05:23:18Z

RainbowDash: Created page with "Test post please ignore"

Test post please ignore

User talk:RainbowDash

2013-05-17T05:23:11Z

RainbowDash: Created page with "Test comment please ignore"

Test comment please ignore

Talk:1213: Combination Vision Test

2013-05-17T05:20:06Z

RainbowDash:

Number is "42".
The 4 is composed of 2's and 3's and 7's.
The 2 is composed of 3's and 7's and 9's.
--[[User:RainbowDash|RainbowDash]] ([[User talk:RainbowDash|talk]]) 05:16, 17 May 2013 (UTC)

Talk:1213: Combination Vision Test

2013-05-17T05:18:21Z

RainbowDash:

Number is "42".
The 4 is composed of 2's and 3's.
The 2 is composed of 3's and 9's.
--[[User:RainbowDash|RainbowDash]] ([[User talk:RainbowDash|talk]]) 05:16, 17 May 2013 (UTC)

Talk:1213: Combination Vision Test

2013-05-17T05:16:28Z

RainbowDash:

Number is "42".
The 4 is composed of 2's and 3's.
The 2 is composed of just 3's.
--[[User:RainbowDash|RainbowDash]] ([[User talk:RainbowDash|talk]]) 05:16, 17 May 2013 (UTC)

Talk:1213: Combination Vision Test

2013-05-17T05:16:10Z

RainbowDash: Created page with "Number is "42". The 4 is composed of 2's and 3's. The 2 is composed of just 3's."

Number is "42".
The 4 is composed of 2's and 3's.
The 2 is composed of just 3's.