Editing 899: Number Line

{{comic
| number    = 899
| date      = May 16, 2011
| title     = Number Line
| image     = number line.png
| titletext = 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.<span style="text-decoration: overline;">99</span>'''.... is {{w|0.999...|equal to 1}} because if you subtract any number from one, however small, you will get a number that is less than 0.<span style="text-decoration: overline;">99</span>. 1 &minus; '''0.0000000372''' is 1 bit less than the {{w|IEEE_floating_point|IEEE 754 32-bit floating-point representation}} of 1.

*The '''{{w|golden ratio}}''' or '''ϕ''' (phi) is the number <math>\tfrac{1+\sqrt{5}}{2}</math>, 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 {{w|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.

*'''{{w|e (mathematical constant)|e}}''' (Euler's number) is 2.71828... and '''π''' (pi) is 3.14159265...

*'''2.9299372''' is probably a {{w|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 {{w|George Washington}} and {{w|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.

*'''{{w|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 [https://web.archive.org/web/20230908075930/http://www.bl.uk/learning/images/mappinghist/large2296.html archaic maps].). 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:
**[http://strangehorizons.com/fiction/the-secret-number/ Bleem] - a fictional integer between 3 and 4
**iCarly's [http://icarly.wikia.com/wiki/Derf Derf] - a fictional integer between 5 and 6
**George Carlin's [http://www.urbandictionary.com/define.php?term=bleen Bleen] - a fictional integer between 6 and 7
**[https://scp-wiki.wikidot.com/scp-033 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 [http://www.smbc-comics.com/index.php?id=3913 Sorf] - a fictional integer between 2 and 3 <!--This is incorrect as the SMBC comic is predated by this xkcd-->

*'''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,{{cn}} 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 {{w|prime number}}, nor is it a prime at all. The largest (and only) even prime is 2. 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 {{w|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 {{w|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 [[2205: Types of Approximation|order of magnitude]]), where its [[2696: Precision vs Accuracy|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 {{w|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 {{w|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 &minus;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).

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