899: Number Line

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Number Line

Title text: The Wikipedia page List of Numbers opens with "This list is incomplete; you can help by expanding it."

Explanation

Once again, Randall seems to be just messing around, this time with a number line.

• Negative numbers have the same magnitude as positive numbers but can only be used to represent the removal of that same magnitude (hence the term "difference" being used for subtraction). Negative numbers may be called imitator numbers in the comic because of their similarities to positive numbers.

• 0.99.... is equal to 1 because if you subtract any number from one, however small, you will get a number that is less than 0.99. 1 − 0.0000000372 is 1 bit less than the IEEE 754 32-bit floating-point representation of 1.

• The golden ratio or ϕ (phi) is the number $\tfrac{1+\sqrt{5}}{2}$, about 1.61803. It has many interesting mathematical properties, mostly relating to geometry, and has occasional appearances in nature, such as spirals formed by the seeds in sunflowers. It is also subject to many less credible claims, such as the belief that phi appears in Parthenon (a well-disputed claim) or that rectangles proportioned after phi are more aesthetically pleasing. The speaker seems to drive off his listeners as soon as he brings it up; the golden ratio is infamous for being brought up by know-it-alls, which Randall has mocked in other comics.

• The approximate range from 2.1 to 2.3 is marked as The Forbidden Region. Why Randall marked this range as forbidden is really anyone's guess; it seems to be an entirely arbitrary designation.

• e (Euler's number) is 2.71828... and π (pi) is 3.14159265...

• 2.9299372 is probably a President's Day reference. It is the average of e and π just as the American Presidents' Day is always observed on the 3rd Monday of February (between George Washington and Abraham Lincoln's birthdays). Washington and Lincoln were the 1st and 16th Presidents of the USA, respectively. Each has a celebrated place in American history.

• Gird, ᛟ is a purely fictional number. (The glyph that Randall uses seems to resemble an older shape of the digit 4, such as seen on archaic maps.). The glyph bears some resamblance to the odal rune but given its associations (especially in the version with serifs) this was probably unintentional. Canon and orthodox could mean "accepted as the offical story" and "most science-based followers", but they could also reference to organised religions. Gird could be a reference to any or all of:
  • Bleem - a fictional integer between 3 and 4
  • iCarly's Derf - a fictional integer between 5 and 6
  • George Carlin's Bleen - a fictional integer between 6 and 7
  • SCP-033 - a fictional "missed number" consisting of complex formulae that causes mathematical systems to break down when it is introduced to them (manifesting as the physical destruction of the objects the mathematical formulae are contained in, such as paper and computers)
  • Saturday Morning Breakfast Cereal's Sorf - a fictional integer between 2 and 3

• Site of Battle of 4.108 is another map joke, implying that 4.108 is an actual location, where an eponymous battle was previously fought. 4.108 was also referenced in 2861: X Value, though with an added 3 in the ten-thousandths place.

• An Unexplored region obscures the line approximately ranging all values from 4.5 to 6.7. In the days when the Earth was still being mapped out, territories that had yet to be properly explored and charted were labelled in a similar manner. The placement of the Unexplored region on the number line indicates that all numbers in that range, including the integers 5 and 6, are completely unknown. This is, of course, patently ridiculous,^{[citation needed]} and the humor seems to derive solely from how nonsensical and unbelievable it is. Correspondingly, the digits 5 and 6 cannot be found in the comic.

• It is often the case in the media that "It has been 7 years..." or "In the last 7 years..." etc. It is made to seem like a believable statistic but cannot always be true. Alternatively, it is intended as an absurd joke that the number 7 is just "not to be believed".

• 8 is not the largest even prime number, nor is it a prime at all. The largest (and only) even prime is 2 (which is a subprime number). A joke intended for those who clearly know that the claim is false.

• The last entry seems to be a reference to certain fields of pure mathematics, which focus less on performing calculations with numbers and more on understanding structures that may be described using logic. It finishes off the tone of the comic that seems to be shaping the number line terms of what is commonly useful to certain areas of applied mathematics, rather than a complete, accurate version of the number line.
  • A possible alternate reason for suggesting that any digit beyond 8 (i.e. 9) would not be 'real' mathematics is Benford's law. Taken at the level of individual digits, true data tends to have far fewer 9s in it than (in decimal representation) any other non-zero digit. While it would not be true to say that the presence of a 9 itself indicates invalid values, concocted or stochastically randomised values may have far more 9s than would naturally emerge from true data. Any use of those numbers would then be based upon lies, and highly suspect. The two-digit 10, also illustrated, might be excluded from any analysis of digit-frequency, or (prominantly featuring a trailing zero) might further underline the point by being being more likely rounded to the nearest ten (or even a convenient order of magnitude), where its accuracy and precision are both more open to doubt than in the case of either 9 or (also neighbouring it, though not shown here or necessarily subject to any comment) 11.

The title text is a literalism joke; at the time the comic was published, all Wikipedia articles with incomplete lists began with the message template "This list is incomplete; you can help by expanding it." In the case of the List of numbers page, one could infer the absurd notion that Wikipedia wanted to have the list include every number from negative infinity to infinity. But because all Wikipedia articles are necessarily finite, such a list would always be incomplete, no matter how much it was expanded. It may also be referencing his previous statements about Wikipedia being the home of compulsive list-makers, who make the most astonishingly complete lists imaginable.

As of 2022, Wikipedia's List of numbers page, as well as all pages including lists that cannot ever reach a state of completion, are headed by the message template "This is a dynamic list and may never be able to satisfy particular standards for completeness. You can help by adding missing items with reliable sources."

2956: Number Line Branch also features a number line with additional (fictional) numbers.

Transcript

[Number line ranging from −1 to 10.]

[Arrow pointing left, towards negative numbers] Negative "imitator" numbers (do not use)

[Line right before the number one] 0.99... (actually 0.0000000372 less than 1)

[Line at the golden ratio.] Φ Parthenon; sunflowers; golden ratio; wait, come back, I have facts!

[Line at a region between two and 2.2] forbidden region

[Line at Euler's number.] e

[Line a bit before 3] 2.9299372 (e and pi, observed)

[Line at π.] π

[Line at 3.5 with ᛟ as the numeral] Gird – accepted as canon by orthodox mathematicians

[Line a bit after 4.] site of battle of 4.108

[Blob between 4.5 and 6.5 labeled unexplored.]

[Line at seven.] Number indicating a factoid is made up ("every 7 years...", "science says there are 7...", etc)

[Line at eight.] Largest even prime

[Line at 8.75.] If you encounter a number higher than this, you're not doing real math

Trivia

• As for the "Gird" between 3 and 4, one might argue that the arithmetic square root of 11 may have some "integer" properties, because there exists an integer-to-integer^{[citation needed]} function f(x) such that f(f(x))=11x. (details needed)
• The "unexplored" area is actually famous for some numbers, such as twice π (also known as tau (τ), approximately 6.283185).

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Discussion

Where does sqrt(-1) go? 67.78.183.206 19:07, 2 January 2013 (UTC)

It goes up (literally above 0). A number line can be extended to a complex plane with sqrt(-1) as the unit of measurement in the vertical direction. Or at least, that's where it actually goes. I don't know where Randall would put it. 75.69.96.225 01:04, 5 March 2013 (UTC)

I'm sorry...are you indicating the ACTUAL location for an IMAGINARY number? -- ‎74.213.186.41 (talk) (please sign your comments with ~~~~)

Yes, that's exactly where it is (up to switching clockwise for counterclockwise). There is nothing strange about providing a location for imaginary or complex numbers, the location described is logical, and the adjective 'imaginary' is an artifact of nomenclature and nothing more.173.48.140.216 20:40, 30 March 2013 (UTC)

In fact, complex numbers are nearly more real than real ones! Complex analysis really opened my eyes to how much "stepping out" can help in solving problems. The complex notion of analyticity yields fruit in real analysis. Extensions to hypercomplex numbers are weirder, however. --Quicksilver (talk) 20:27, 17 August 2013 (UTC)

Analyticity must be an imaginary word, and therefore would be found one unit directly above any dictionary. 50.203.89.169 14:19, 9 October 2013 (UTC)

Oh my god, I can't believe how hard I laughed at that. Would an imaginary friend actually be above you then? I'm going to use that sometime. 108.162.219.61 21:25, 24 April 2014 (UTC)

"I'm sorry, you have reached an imaginary number. Please rotate the phone by 90 degrees and try again."141.101.98.250 17:01, 21 October 2017 (UTC)

Is unexplored a map reference? Halfhat (talk) 17:53, 13 January 2014 (UTC)

Note that the digits 5 and 6 do not show up on any of the numbers in the comic, reinforcing the fact that the integers 5 and 6 are unexplored. Blitzer (talk) 02:34, 15 May 2014 (UTC)

So the 5th digit of pi can not be known either? Tharkon (talk) 03:56, 12 July 2014 (UTC)

The whath digit of pi? 108.162.215.119 01:59, 1 January 2015 (UTC)

Thank God (or someone else, I'm not choosy) that the SCP link here still works. The rest of the site's gone private. 108.162.250.223 (talk) (please sign your comments with ~~~~)

It appears that Wikipedia had noticed the implications of the title text here. The message now says that it might never be complete, but can be expanded with reliably sourced articles. I'm not 100% sure it's due to Randall's involvement, but I like to think so. --141.101.104.17 22:01, 9 December 2014 (UTC)

I am not American, but the linked Wikipedia Article does not support the claims about president's day being observed between the 2 birthdays of Washington and Lincoln in general, but just that in some states Lincoln is also referenced on that day. Even if it was put as a day between these birthdays by definition and on purpose, I do not see the reference here... Especially as this number is given as specific, unlike presidents day, which can occur in a range of days... Someone who knows more of American culture, and also what "observed" (which would link it to holidays....) can mean in English language please revert this. --Lupo (talk) 12:41, 18 September 2019 (UTC)

The link to "bleem" does not work for me, but the word can be found in Urban Dictionary. ——172.69.63.161 02:12, 21 August 2020 (UTC)

While 8 is not the "largest even prime", 9 is in fact the lowest odd composite number. So 8 is the largest in the unbroken line of natural numbers that are even or prime (or whatever 1 is). 141.101.76.205 10:48, 18 January 2023 (UTC)

1 is a unit. With natural numbers, that's literally just 1, but when you extend the concept of primes to arbitrary rings there's more like that so it's worth giving a name to. DanielLC (talk) 06:17, 15 May 2024 (UTC)

Surely Gird is a reference to Bleem and to the philosophical concepts of Grue and Bleen? Just as they derive from Blue and Green, so we would have Bird and Gleem. 172.71.98.86 20:33, 29 November 2023 (UTC)

1 pixel ~ 0.012 start of unexplored zone ~ 4.381 end of unexplored zone ~ 6.714 length of unexplored zone ~ 2.333 coincedence? plushie fan (talk) 00:07, 30 November 2023 (UTC)

For f(f(x))=11x, one example is: write x=a*11^b where a%11>0. If a%11 is odd, let f(x)=(a+1)11^b; otherwise a%11 is even, let f(x)=(a-1)11^(b+1).172.71.222.235 03:01, 1 December 2023 (UTC)

Even simpler, let f(x)=-x for x<0 and f(x)=-11x for x>=0.172.70.175.54 17:46, 3 December 2023 (UTC)

How is Tau also called "Twice Euler's constant"? IMO, the name Tau, or the value 6.28~, equals to and is used to replace 2pi, so it is not related to "Twice Euler's constant". --162.158.166.146 08:33, 31 December 2023 (UTC)