explain xkcd - User contributions [en]

1047: Approximations

2015-11-04T03:41:08Z

108.162.218.11:

{{comic
| number = 1047
| date = April 25, 2012
| title = Approximations
| image = approximations.png
| titletext = Two tips: 1) 8675309 is not just prime, it's a twin prime, and 2) if you ever find yourself raising log(anything)^e or taking the pi-th root of anything, set down the marker and back away from the whiteboard; something has gone horribly wrong.
}}

==Explanation==
This comic lists some approximations for numbers, most of them mathematical and physical constants, but some of them jokes and cultural references.

Approximations like these are sometimes used as {{w|mnemonic}}s by mathematicians and physicists, though most of Randall's approximations are too convoluted to be useful as mnemonics. Perhaps the best known mnemonic approximation (though not used here by Randall) is that "pi is approximately equal to 22/7". Randall does mention (and mock) the common mnemonic among physicists that the {{w|fine structure constant}} is approximately 1/137. Although Randall gives approximations for the number of seconds in a year, he does not mention the common physicist's mnemonic that it is "pi times 10^7," though he later added a statement to the top of the comic page addressing this point.

At the bottom of the comic are expressions involving {{w|transcendental numbers}} (namely pi and e) that are tantalizingly close to being exactly true but are not (indeed, they cannot be, due to the nature of transcendental numbers). Such near-equations were previously discussed in [[217: e to the pi Minus pi]]. One of the entries, though, is a "red herring" that is exactly true.

Randall says he compiled this table through "a mix of trial-and-error, ''{{w|Mathematica}}'', and Robert Munafo's [http://mrob.com/pub/ries/ Ries] tool. "Ries" is a "{{w|Closed-form expression#Conversion from numerical forms|reverse calculator}}" that forms equations matching a given number.

The first part of the title text notes that "Jenny's constant," which is actually a telephone number referenced in Tommy Tutone's 1982 song {{w|867-5309/Jenny}}, is not only prime but a {{w|twin prime}} because 8675311 is also a prime. Twin primes have always been a subject of interest, because they are comparatively rare, and because it is not yet known whether there are infinitely many of them. Twin primes were also referenced in [[1310: Goldbach Conjectures]].

The second part of the title text makes fun of the unusual mathematical operations contained in the comic. {{w|Pi}} is a useful number in many contexts, but it doesn't usually occur anywhere in an exponent. Even when it does, such as with complex numbers, taking the pi-th root is rarely helpful. Similarly, {{w|e (mathematical constant)|e}} typically appears in the basis of a power (forming the {{w|exponential function}}), not in the exponent. (This is later referenced in [http://what-if.xkcd.com/73/ Lethal Neutrinos]).

:{| class="wikitable"
|-
|align="center"|Thing to be approximated:
|align="center"|Formula proposed:
|align="center"|Resulting approximate value:
|align="center"|Correct value:
|align="center"|Discussion:
|-
|align="center"|One light year(m)
|align="center"|998
|align="center"|9,227,446,944,279,201
|align="center"|9,460,730,472,580,800 (exact)
|align="left"|998 and 698 are sexual references.
|-
|align="center"|Earth Surface(m2)
|align="center"|698
|align="center"|513,798,374,428,641
|align="center"|5.10072*1014
|align="left"|998 and 698 are sexual references.
|-
|align="center"|Ocean's volume(m3)
|align="center"|919
|align="center"|1,350,851,717,672,992,089
|align="center"|1,332*1018
|align="left"|
|-
|align="center"|Seconds in a year
|align="center"|754
|align="center"|31,640,625
|align="center"|31,557,600 (Julian calendar) 31,556,952 (Gregorian calendar)
|align="left"|After this comic was released [[Randall]] got many responses by viewers. So he did add this statement to the top of the comic page:
"Lots of emails mention the physicist favorite, 1 year = pi x 107 seconds. 754 is a hair more accurate, but it's hard to top 3,141,592's elegance." Pi x 107 is nearly equal to 31,415,926.536, and 754 is exactly 31,640,625. Randall's elegance belongs to the number pi, but it should be multiplied by the factor of ten.

Using the traditional definitions that a second is 1/60th of a minute, a minute is 1/60th of an hour, and an hour is 1/24th of a day, a 365-day year is exactly 31,536,000 seconds (the "for rent method" approximation). Until the calendar was reformed by Pope Gregory, there was one leap year in every four years, making the average year 365.25 days, or 31,557,600. On the current calendar system, there are only 97 leap years in every 400 years, making the average year 365.2425 days, or 31,556,952 seconds. In technical usage, a "second" is now defined based on physical constants, even though the length of a day varies inversely with the changing angular velocity of the earth. To keep the official time synchronized with the rotation of the earth, a "leap second" is occasionally added, resulting in a slightly longer year.
|-
|align="center"|Seconds in a year (rent method)
|align="center"|525,600 x 60
|align="center"|31,536,000
|align="center"|31,557,600 (Julian calendar) 31,556,952 (Gregorian calendar)
|align="left"|"Rent Method" refers to the song "Seasons of Love" from the musical "{{w|Rent (musical)|Rent}}." The song asks, "How do you measure a year?" One line says "525,600 minutes" while most of the rest of the song suggests the best way to measure a year is moments shared with a loved one.
|-
|align="center"|Age of the universe (seconds)
|align="center"|1515
|align="center"|437,893,890,380,859,375
|align="center"|4.354±0.012*1017 (best estimate; exact value unknown)
|align="left"|
|-
|align="center"|Planck's constant
|align="center"|1/(30πe)
|align="center"|6.68499014108082*10−34 (rounded)
|align="center"|6.62606957*10−34
|align="left"|Informally, the {{w|Planck constant}} is the smallest action possible in quantum mechanics.
|-
|align="center"|Fine structure constant
|align="center"|1/140
|align="center"|0.00714285717142857171428571, etc. (repeating 71428571)
|align="center"|0.00729735257 (accepted value as of 2011), close to 1/137
|align="left"|The {{w|fine structure constant}} indicates the strength of electromagnetism. It is unitless and around 0.007297, close to 1/137. At one point it was believed to be exactly the reciprocal of 137, and many people have tried to find a simple formula explaining this (with a pinch of {{w|numerology}} thrown in at times), including the infamous {{w|Arthur Eddington|Sir Arthur Adding-One}}.
|-
|align="center"|Fundamental charge
|align="center"|3/(14 * πππ)
|align="center"|1.59895121062716*10−19 (rounded)
|align="center"|1.602176565*10−19 (rounded)
|align="left"|This is the charge of the proton, symbolized "e" for electron (whose charge is actually -e. You can blame Benjamin Franklin [[567|for that]])
|-
|align="center"|Telephone number for the White House Switchboard
|align="center"|1/ 
π√(e(1 + (e-1)√8))
|align="center"|.2024561414 (truncated)
|align="center"|2024561414
|align="left"|
|-
|align="center"|Jenny's Constant
|align="center"|(7(e/1 - 1/e) - 9) * π2
|align="center"|867.530901981685 (approximately)
|align="center"|8675309
|align="left"|"Jenny's constant" is actually a telephone number referenced in Tommy Tutone's 1982 song {{w|867-5309/Jenny}}. As mentioned in the title text, the number not only prime but a {{w|twin prime}} because 8675311 is also a prime.
|-
|align="center"|World Population Estimate (billions)
|align="center"|Equivalent to 6+((3/4 Year + 1/4 (Year mod 4) - 1499)/10) billion
|align="center"|2005 6.5
2006 6.6
2007 6.7
2008 6.7
2009 6.8
2010 6.9
2011 7
2012 7
2013 7.1
2014 7.2
2015 7.3
2016 7.3
2017 7.4
2018 7.5
2019 7.6
2020 7.6
2021 7.7
2022 7.8
2023 7.9
2024 7.9
2025 8
2026 8.1
2027 8.2
2028 8.2
2029 8.3
2030 8.4
2031 8.5
2032 8.5
|align="center"|
|align="left"|
|-
|align="center"|U.S. Population Estimate (millions)
|align="center"|Equivalent to 310+3*(Year - 2010) million
|align="center"|2000 280
2001 283
2002 286
2003 289
2004 292
2005 295
2006 298
2007 301
2008 304
2009 307
2010 310
2011 313
2012 316
2013 319
2014 322
2015 325
2016 328
2017 331
2018 334
2019 337
2020 340
2021 343
2022 346
2023 349
2024 352
2025 355
2026 358
2027 361
2028 364
2029 367
2030 370
2031 373
2032 376
|align="center"|
|align="left"|
|-
|align="center"|Electron rest energy
|align="center"|e/716 Joules
|align="center"|8.17948276564429*10−14
|align="center"|8.18710438*10−14 (rounded)
|align="left"|
|-
|align="center"|Light-year(miles)
|align="center"|2(42.42)
|align="center"|5884267614436.97 (rounded)
|align="center"|9460730472580800 (meters in a light-year, by definition) / 1609.344 (meters in a mile) = 8212439646337500/1397 (exact) = 5878625373183.61 (rounded)
|align="left"|{{w|42 (number)|42}} is, according to Douglas Adams' ''The Hitchhiker's Guide to the Galaxy'', the Answer to the Ultimate Question of Life, the Universe, and Everything.
|-
|align="center"|sin(60°) = √3/2
|align="center"|e/π
|align="center"|0.8652559794 (rounded)
|align="center"|0.8660254038 (rounded)
|align="left"|
|-
|align="center"|√3
|align="center"|2e/π
|align="center"|1.7305119589 (rounded)
|align="center"|1.7320508076 (rounded)
|align="left"|
|-
|align="center"|gamma(Euler's gamma constant)
|align="center"|1/√3
|align="center"|0.5773502692 (rounded)
|align="center"|0.5772156649015328606065120900824024310421...
|align="left"|In {{w|mathematics}}, the {{w|Euler-Mascheroni constant}} (Euler gamma constant) is a mysterious number describing the relationship between the {{w|Harmonic series (mathematics)|harmonic series}} and the {{w|natural logarithm}}.
|-
|align="center"|Feet in a meter
|align="center"|5/(e√π)
|align="center"|3.2815481951
|align="center"|1/.3048 (exact) = 3.280839895 (rounded)
|align="left"|
|-
|align="center"|√5
|align="center"|2/e + 3/2
|align="center"|2.2357588823 (rounded)
|align="center"|2.2360679775 (rounded)
|align="left"|
|-
|align="center"|Avogadro's number
|align="center"|69π√5
|align="center"|6.02191201246329*1023 (rounded)
|align="center"|6.02214129*1023 (rounded)
|align="left"|Also called a Mole for shorthand, this is (roughly) the number of individual atoms in twelve grams of pure Carbon. Used in basically every application of chemistry.
|-
|align="center"|Gravitational constant G
|align="center"|1 / e(pi - 1)(pi + 1)
|align="center"|6.67361106850561*10−11 (rounded)
|align="center"|6.67385*10−11 (rounded)
|align="left"|The universal {{w|gravitational constant}} G is equal to F*r2/Mm, where F is the gravitational force between two objects, r is the distance between them, and M and m are their masses.
|-
|align="center"|R(gas constant)
|align="center"|(e+1) √5
|align="center"|8.3143309279 (rounded)
|align="center"|8.3144622 (rounded)
|align="left"|The {{w|gas constant}} relates energy to temperature in physics, as well as a gas's volume, pressure, temperature and {{w|mole (unit)|molar amount}} (hence the name).
|-
|align="center"|Proton-electron mass ratio
|align="center"|6*π5
|align="center"|1836.1181087117 (rounded)
|align="center"|1836.15267246 (rounded)
|align="left"|
|-
|align="center"|Liters in a gallon (U.S. liquid gallon, defined by law as 231 cubic inches)
|align="center"|3 + π/4
|align="center"|3.7853981634 (rounded)
|align="center"|3.785411784 (exact)
|align="left"|
|-
|align="center"|''g''0 or ''g''n
|align="center"|6 + ln(45)
|align="center"|9.8066624898 (rounded)
|align="center"|9.80665 (standard)
|align="left"|Standard gravity, or standard acceleration due to free fall is the nominal gravitational acceleration of an object in a vacuum near the surface of the Earth. It is defined by standard as 9.80665 m/s2, which is exactly 35.30394 (km/h)/s (about 32.174 ft/s2, or 21.937 mph/s). This value was established by the 3rd CGPM (1901, CR 70) and used to define the standard weight of an object as the product of its mass and this nominal acceleration. The acceleration of a body near the surface of the Earth is due to the combined effects of gravity and centrifugal acceleration from rotation of the Earth (but which is small enough to be neglected for most purposes); the total (the apparent gravity) is about 0.5 percent greater at the poles than at the equator. Randall used a letter g without a suffix, which can also mean the local acceleration due to local gravity and centrifugal acceleration, which varies depending on one's position on Earth.
|-
|align="center"|Proton-electron mass ratio
|align="center"|(e8 - 10) / ϕ
|align="center"|1836.1530151398 (rounded)
|align="center"|1836.15267246 (rounded)
|align="left"|ϕ is the {{w|golden ratio}}, or (1 + √5)/2. It has many interesting geometrical properties.
|-
|align="center"|Ruby laser wavelength
|align="center"|1 / (12002)
|align="center"|.00000069444444444444... (repeating decimal)
|align="center"|694.3 nm
|align="left"|The ruby laser wavelength varies because "ruby" is not clearly defined.
|-
|align="center"|Mean Earth Radius
|align="center"|(58)*6e
|align="center"|2343750e (exact), 6,370,973.035450887 (6370 km, 973 m, 3 cm, 5 mm, 450,887 nm) (rounded)
|align="center"|6,371,008.7 (International Union of Geodesy and Geophysics definition)
|align="left"|The {{w|Earth radius#mean radii|mean earth radius}} varies because there is not one single way to make a sphere out of the earth. Randall's value lies within the actual variation of Earth's radius. The International Union of Geodesy and Geophysics (IUGG) defines the mean radius as 2/3 of the equatorial radius (6,378,137.0 m) plus 1/3 of the polar radius (6,356,752.3 m).
|-
|align="center"|√2
|align="center"|3/5 + π/(7-π)
|align="center"|1.4142200581 (rounded)
|align="center"|1.4142135624 (rounded)
|align="left"|There are reoccurring math jokes along the lines of, "3/5 + π/(7 – π) – √2 = 0, but your calculator is probably not good enough to compute this correctly".
|-
|align="center"|cos(π/7) + cos(3π/7) + cos(5π/7)
|align="center"|1/2
|align="center"|0.5
|align="center"|0.5 (exact)
|align="left"|This is the exactly correct equation referred to in the note, "Pro tip - Not all of these are wrong", as shown below and also [http://math.stackexchange.com/questions/140388/how-can-one-prove-cos-pi-7-cos3-pi-7-cos5-pi-7-1-2 here]. If you're still confused, the functions use {{w|radians}}, not {{w|degrees (angle)|degrees}}.
|-
|align="center"|γ(Euler's gamma constant)
|align="center"|e/34 + e/5
|align="center"|0.5772154006 (rounded)
|align="center"|0.5772156649015328606065120900824024310421...
|align="left"|In {{w|mathematics}}, the {{w|Euler-Mascheroni constant}} (Euler gamma constant) is a mysterious number describing the relationship between the {{w|Harmonic series (mathematics)|harmonic series}} and the {{w|natural logarithm}}.
|-
|align="center"|√5
|align="center"|(13 + 4π) / (24 - 4π)
|align="center"|2.2360678094 (rounded)
|align="center"|2.2360679775 (rounded)
|align="left"|
|-
|align="center"|Σ 1/nn
|align="center"|ln(3)e
|align="center"|1.2912987577 (rounded)
|align="center"|1.2912859971 (rounded)
|align="left"|
|}

===Proof===

One of the "approximations" actually is precisely correct: cos(π/7) + cos(3π/7) + cos(5π/7) = 1/2. Here is a proof:

cos(π/7) + cos(3π/7) + cos(5π/7)

* Multiplying by 1 (or by a number divided by itself) leaves the equation unchanged.

= (cos(π/7) + cos(3π/7) + cos(5π/7)) (2sin(π/7)/2sin(π/7))

* The 2sin(π/7) on the top of the fraction is multiplied through the original equation.

= (2cos(π/7)sin(π/7) + 2cos(3π/7)sin(π/7) + 2cos(5π/7)sin(π/7)) (1/2sin(π/7))

* Use the trigonometric identity 2cos(A)sin(B)=sin(A+B)-sin(A-B) on the 2nd two terms ([2cos(3π/7)sin(π/7)] + {2cos(5π/7)sin(π/7)}) (1/2sin(π/7))

= (2cos(π/7)sin(π/7) + [sin(3π/7+π/7) - sin(3π/7-π/7)] + {sin(5π/7+π/7) - sin(5π/7-π/7)}) (1/2sin(π/7)) 
= (2cos(π/7)sin(π/7) + [sin(4π/7) - sin(2π/7)] + {sin(6π/7) - sin(4π/7)}) (1/2sin(π/7))

* Use the trigonometric identity 2cos(A)sin(A) = sin(2A) on the first term (2cos(π/7)sin(π/7))

= (sin(2π/7) + [sin(4π/7) - sin(2π/7)] + {sin(6π/7) - sin(4π/7)}) (1/2sin(π/7)) 
= (sin(6π/7) + [sin(2π/7) - sin(2π/7)] + {sin(4π/7) - sin(4π/7)}) (1/2sin(π/7)) 
= (sin(6π/7)) (1/2sin(π/7))

* Note that 6π/7 = (7π - π)/7 = 7π/7 - π/7 = π - π/7.

= (sin(π - π/7)) (1/2sin(π/7))

*Since sines of supplementary angles are equal.

= (sin(π/7)) (1/2sin(π/7)) 
= (sin(π/7)/2sin(π/7)) 
= (1/2) (sin(π/7)/sin(π/7)) 
= 1/2

==Transcript==
:'''A table of slightly wrong equations and identities useful for approximations and/or trolling teachers.'''
:(Found using a mix of trial-and-error, ''Mathematica'', and Robert Munafo's ''Ries'' tool.)
: All units are SI MKS unless otherwise noted.

:{| class="wikitable"
|-
|colspan="2" align="center" | Relation:
|align="center" | Accurate to within:
|-
|align="center" | One light year(m)
|align="center" | 998
|align="center" | one part in 40
|-
|align="center" | Earth Surface(m2)
|align="center" | 698
|align="center" | one part in 130
|-
|align="center" | Ocean's volume(m3)
|align="center" | 919
|align="center" | one part in 70
|-
|align="center" | Seconds in a year
|align="center" | 754
|align="center" | one part in 400
|-
|align="center" | Seconds in a year (rent method)
|align="center" | 525,600 x 60
|align="center" | one part in 1400
|-
|align="center" | Age of the universe (seconds)
|align="center" | 1515
|align="center" | one part in 70
|-
|align="center" | Planck's constant
|align="center" | 1/(30πe)
|align="center" | one part in 110
|-
|align="center" | Fine structure constant
|align="center" | 1/140
|align="center" | [I've had enough of this 137 crap]
|-
|align="center" | Fundamental charge
|align="center" | 3/(14 * πππ)
|align="center" | one part in 500
|-
|align="center"|White House Switchboard
|colspan="2" align="center"|1/ 
π√(e(1 + (e-1)√8))
|-
|align="center"|Jenny's Constant
|colspan="2" align="center"|(7(e/1 - 1/e) - 9) * π2
|-
|colspan="3" align="center"|Intermission: World Population Estimate which should stay current for a decade or two: 
Take the last two digits of the current year

Example: 20[14]

Subtract the number of leap years since hurricane Katrina

Example:14 (minus 2008 and 2012) is 12

Add a decimal point

Example: 1.2

Add 6

Example: 6 + 1.2

7.2 = World population in billions.

Version for US population:

Example: 20[14]

Subtract 10

Example: 4

Multiply by 3

Example: 12

Add 10

Example: 3[22] million
|-
|align="center"|Electron rest energy
|align="center"|e/716 Joules
|align="center"|one part in 1000
|-
|align="center"|Light-year(miles)
|align="center"|2(42.42)
|align="center"|one part in 1000
|-
|colspan="2" align="center"|sin(60°) = √3/2 = e/π
|align="center"|one part in 1000
|-
|colspan="2" align="center"|√3 = 2e/π
|align="center"|one part in 1000
|-
|align="center"|gamma(Euler's gamma constant)
|align="center"|1/√3
|align="center"|one part in 4000
|-
|align="center"|Feet in a meter
|align="center"|5/(e√π)
|align="center"|one part in 4000
|-
|colspan="2" align="center"|√5 = 2/e + 3/2
|align="center"|one part in 7000
|-
|align="center"|Avogadro's number
|align="center"|69π√5
|align="center"|one part in 25,000
|-
|align="center"|Gravitational constant G
|align="center"|1 / e(pi - 1)(pi + 1)
|align="center"|one part in 25,000
|-
|align="center"|R(gas constant)
|align="center"|(e+1) √5
|align="center"|one part in 50,000
|-
|align="center"|Proton-electron mass ratio
|align="center"|6*π5
|align="center"|one part in 50,000
|-
|align="center"|Liters in a gallon
|align="center"|3 + π/4
|align="center"|one part in 500,000
|-
|align="center"|g
|align="center"|6 + ln(45)
|align="center"|one part in 750,000
|-
|align="center"|Proton-electron mass ratio
|align="center"|(e8 - 10) / ϕ
|align="center"|one part in 5,000,000
|-
|align="center"|Ruby laser wavelength
|align="center"|1 / (12002)
|align="center"|[within actual variation]
|-
|align="center"|Mean Earth Radius
|align="center"|(58)*6e
|align="center"|[within actual variation]
|-
|colspan="3" align="center"|Protip - not all of these are wrong:
|-
|colspan="2" align="center"|√2 = 3/5 + π/(7-π)
|align="center"|cos(π/7) + cos(3π/7) + cos(5π/7) = 1/2
|-
|align="center"|γ(Euler's gamma constant) = e/34 + e/5
|align="center"|√5 = (13 + 4π) / (24 - 4π)
|align="center"|Σ 1/nn = ln(3)e
|}

{{comic discussion}}
[[Category:Charts]]
[[Category:Math]]
[[Category:Physics]]
[[Category:Protip]]

1351: Metamaterials

2014-04-04T09:57:06Z

108.162.218.11:

{{comic
| number = 1351
| date = April 4, 2014
| title = Metamaterials
| image = metamaterials.png
| titletext = If I developed a hue-shifting metamaterial, I would photobomb people's Instagram pics with a sheet of material that precisely undid the filter they were using.
}}

==Explanation==
{{incomplete|Feels incomplete, and the title text needs to be explained.}}
{{w|Metamaterials}}, artificially created materials typically composed of very finely structured “conventional” materials, may cause light passing through them to shift. The exact color it shifts to varies based on the design of the material.
In today’s comic, Megan uses her metamaterial to shift the colors of the cliché Valentine’s Day poem, “Roses are red, violets are blue, sugar is sweet and so are you.”

The title text references this with Randall pondering making a metamaterial that reverses the effect of instagram filters, likely by placing the material between the camera and the subject just before the picture is taken.

==Transcript==

:[Picture of a red violet.]
:Megan (off-screen): Violets are red.

:[Picture of a blue rose.]
:Megan (off-screen): And roses are blue.

:[Megan holding sheet of transparent material in front of the two flowers: red violet, blue rose. Cueball stands nearby.]
:Megan: When metamaterials

:[Megan moves the object away from the flowers. Now violet is blue, and rose is red]
:Megan: Alter their hue.

{{comic discussion}}
[[Category:Comics featuring Cueball]]
[[Category:Comics featuring Megan]]
[[Category:Comics with color]]

Talk:810: Constructive

2014-03-01T01:32:22Z

108.162.218.11:

I know just the guy to create this system. I'm going to PM him now :D {{unsigned ip|184.11.73.88}}

No guys, if spammers invent a bot which can give constructive comments, that will be an ***AI***, i.e. a major breakthrough in itself. {{unsigned ip|173.245.53.200}}

Mission. A-Fucking. Complished. {{unsigned ip|108.162.238.7}}

One problem: trolls who rate everything as non-constructive. [[Special:Contributions/108.162.218.11|108.162.218.11]] 01:32, 1 March 2014 (UTC)

1313: Regex Golf

2014-01-06T21:52:45Z

108.162.218.11: /* Explanation */

{{comic
| number = 1313
| date = January 6, 2014
| title = Regex Golf
| image = regex_golf.png
| titletext = <nowiki>/bu|[rn]t|[coy]e|[mtg]a|j|iso|n[hl]|[ae]d|lev|sh|[lnd]i|[po]o|ls/ matches the last names of elected US presidents but not their opponents.</nowiki>
}}

== Explanation ==

It is a direct reference to [[http://regex.alf.nu/ Regex Golf]] which was released shortly before this comic.

This comic revolves around a set of increasingly complicated {{w|regular expressions}}, which are patterns used to search through text for blocks of text matching the pattern. There is a saying in professional programming that goes like this (see [[1171]]):

: Some people, when confronted with a problem, think “I know, I'll use regular expressions.” Now they have two problems.

The comic exemplifies this as Megan's problems grow increasingly more convoluted - originally she was writing regex as a game, then moved on to automatically building regex on arbitrary lists of text, to searching through her files for code that appears to be a regex golf generator. At the end, Cueball quips that she now has "Infinite Problems" as a result of her efforts, tying back to the saying above.

Code golf is a game where by programmers attempt to solve a problem using as few characters as possible, analogous to the number of golf shots it takes to reach the goal.

=== Regular Expressions ===

Regular expressions are a way to specify textual patterns. One can later search for the pattern inside a text string: if the pattern is found it's said that the pattern "matches" the string; if it's not found, it's said they do not match. The "Regex Golf" challenge is to make a regular expression that matches all of the strings in one group and none of the strings in another. As in "Code golf" the challenge is to find the shortest possible Regex that does this.

The first regex Megan uses is /m | [tn]|b/, said to match Star Wars subtitles but not Star Trek. Subtitles are the secondary titles of the movies, after the "Star Trek: " or "Star Wars Episode N: ". For example, in "Star Wars Episode I: The Phantom Menace" the subtitle is "The Phantom Menace".

The forward slashes just mark the start and end of the regex. The | character means "or", so the regex matches any string that contains the patterns "m ", " [tn]" or "b" (including the spaces). The square brackets match one of the enclosed characters, meaning that " [tn]" matches either " t" or " n". The regex is apparently case-insensitive, because it wouldn't work otherwise.

The Star Wars subtitles match the parts of the regex in the following way:
* "The Phantom Menace" is matched by "m ".
* "Attack of the Clones" is matched by " [tn]".
* "Revenge of the Sith" is matched by " [tn]".
* "A New Hope" is matched by " [tn]".
* "The Empire Strikes Back" is matched by "b".
* "Return of the Jedi" is matched by " [tn]".
Note that the animated film "Star Wars: The Clone Wars" is not included.

On the other hand, none of the Star Trek subtitles contains an M followed by a space, a T or an N preceded by a space, or any B, so the regex does not match any of them. Note that in the original series all subtitles start with a "T" but it's the first character so it's not preceded by a space.

Here is the list that Megan probably used:
* Original series:
** The Motion Picture
** The Wrath of Khan
** The Search For Spock
** The Voyage Home
** The Final Frontier
** The Undiscovered Country
* The Next Generation:
** Generations
** First Contact
** Insurrection
** Nemesis
* Reboot series:
** ''the one without a subtitle''
** Into Darkness

"Grepping" refers to using the Unix/Linux command line tool "grep", which is short for "Globally search a Regular Expression and Print", thus continuing to use regular expressions in search for the lost files.

In the last panel "and beyond" Megan uses the regular expression "/(meta-)*regex golf/" to describe her problem. * means "zero or more" of the preceding character/group (parentheses group characters). So this regex matches "regex golf", "meta-regex golf", "meta-meta-regex golf", etc. In a way this is regex golf in itself, matching all levels of meta-regex golf while not matching anything else.

In the title text there is a long regex that is the solution of another regex golf challenge: matching the last names of all elected US presidents but not their opponents. Note that the list of opponents include some people who were previously or later became presidents, so taken literally this is impossible. To make this work the list of opponents must exclude anyone who was also president. The regular expression itself works in a very similar way to the Star Wars/Trek one, including several different patterns separated by |. Each elected president matches one pattern while each opponent matches none.
Here is a list of elected president and the patterns they match:
{| class="wikitable"
!President
!Matched expression
|-
|George Wa'''sh'''ington
|sh
|-
|John '''Ad'''ams
|[ae]d
|-
|Thomas '''J'''efferson
|j
|-
|James '''Ma'''dison
|[mtg]a
|-
|James Monr'''oe'''
|[coy]e
|-
|John Quincy '''Ad'''ams
|[ae]d
|-
|Andrew '''J'''ackson
|j
|-
|Martin Van '''Bu'''ren
|bu
|-
|William Henry Harr'''iso'''n
|iso
|-
|James K. '''Po'''lk
|[po]o
|-
|Zachary '''Ta'''ylor
|[mtg]a
|-
|Franklin Pier'''ce'''
|[coy]e
|-
|James '''Bu'''chanan
|bu
|-
|Abraham '''Li'''ncoln
|[lnd]i
|-
|Andrew '''J'''ohnson
|j
|-
|Ulysses S. Gra'''nt'''
|[rn]t
|-
|Rutherford B. Ha'''ye'''s
|[coy]e
|-
|James A. '''Ga'''rfield
|[mtg]a
|-
|Grover C'''lev'''eland
|lev
|-
|Benjamin Harr'''iso'''n
|iso
|-
|Grover C'''lev'''eland
|lev
|-
|William McKi'''nl'''ey
|n[hl]
|-
|Theodore R'''oo'''sevelt
|[po]o
|-
|William Howard '''Ta'''ft
|[mtg]a
|-
|Woodrow Wi'''ls'''on
|ls
|-
|Warren G. Har'''di'''ng
|[lnd]i
|-
|Calvin Coo'''li'''dge
|[lnd]i
|-
|Herbert H'''oo'''ver
|[po]o
|-
|Franklin D. R'''oo'''sevelt
|[po]o
|-
|Harry S. Tru'''ma'''n
|[mtg]a
|-
|Dwight D. Eise'''nh'''ower
|n[hl]
|-
|John F. Kenn'''ed'''y
|[ae]d
|-
|Lyndon B. '''J'''ohnson
|j
|-
|Richard '''Ni'''xon
|[lnd]i
|-
|Jimmy Ca'''rt'''er
|[rn]t
|-
|Ronald Rea'''ga'''n
|[mtg]a
|-
|George H. W. '''Bu'''sh
|bu
|-
|Bill Cli'''nt'''on
|[rn]t
|-
|George W. '''Bu'''sh
|bu
|-
|Barack Oba'''ma'''
|[mtg]a
|}

Note that some presidents are missing because they weren't elected but became presidents after the resignation/death of their formers. This regular expression must be modified slightly, it also matches John C. Fremo''nt'', the loser to James Buchanan in 1856.

== Trivia ==
There are now at least four comics that references regular expressions. The other three are:

[[208: Regular Expressions]], [[224: Lisp]] and [[1171: Perl Problems]].

== Transcript ==
:Regex golf:
:[Megan is sitting at a laptop. Cueball is standing behind her.]
:Megan: You try to match one group but not the other.
:Megan: /m | [tn]|b/ matches ''Star Wars'' subtitles but not ''Star Trek''.
:Cueball: Cool.

:Meta-regex golf:
:Megan: So I wrote a program that plays regex golf with arbitrary lists...
:Cueball: Uh oh...

:Meta-meta-regex golf:
:Megan: ...But I lost my code, so I'm grepping for files that look like regex golf solvers.

:...And beyond:
:Megan: Really, this is all /(meta-)*regex golf/.
:Cueball: Now you have ''infinite'' problems.
:Megan: No, I had those already.

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

986: Drinking Fountains

2014-01-02T18:24:52Z

108.162.218.11: /* Explanation */

{{comic
| number = 986
| date = December 5, 2011
| title = Drinking Fountains
| image = drinking_fountains.png
| imagesize =
| titletext = I've always wondered whether you could drink slowly enough, and eliminate fast enough, that you just sort of peed continuously. But I'm afraid to try because I worry someone might call while I'm doing it and ask what I'm up to, and I won't be able to think of a lie.
}}

==Explanation==
Here, we see [[Cueball]], using the restroom, as the title text indicates, he is eliminating the liquid waste from his body, or peeing. He says that he avoids the use of the drinking fountain right after peeing, because he is afraid that he will be forced into immediately peeing again. And as in the image above, he would be stuck in a loop. A loop is a computer science term, but also used elsewhere, to indicates going through the same steps over and over again. In this case, the bathroom and drinking fountain form an infinite loop, which, when used about computers, refers to a loop which never ends, eventually crashing the computer, which is therefore a situation to be avoided at all costs.

==Transcript==
:[Cueball leaving the bathroom, headed towards a nearby water fountain. Cueball having a drink at said water fountain. Cueball grumblingly reentering the bathroom. Cueball leaving the bathroom. Cycle repeats endlessly in a horrific sisyphean loop.]

:I avoid drinking fountains outside bathrooms because I'm afraid of getting trapped in a loop.

{{comic discussion}}
[[Category:Comics featuring Cueball]]