899: Number Line
Title text: The Wikipedia page List of Numbers opens with "This list is incomplete; you can help by expanding it."
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).
- 0.99.... is equal to 1 because there is no number between 0.99.... and 1. 1 - 0.0000000372 is 1 bit less than the IEEE 754 32-bit floating-point representation of 1.
- The golden ratio or "phi" is the number (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 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 a President's Day reference. It is the average of e and pi 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 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.). Canon and orthodox are references to organised religions. Gird could be a reference to any or all of:
- Site of the Battle of 4.108 is another map joke, implying that 4.108 is an actual location, where an eponymous battle was previously fought. It may be a reference (or homage) to the Battle of Wolf 359, a famous military conflict in the fictional universe of Star Trek.
- An Unexplored region obscures the line approximately ranging all values from 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, and the humor seems to derive solely from how nonsensical and unbelievable it is.
- 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, 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 pure mathematics, which focuses 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.
The title text is a literalism joke, implying that Wikipedia would like its "List of numbers" page to include every number from negative infinity to infinity. It could also be a reference to Gödel's incompleteness theorems, which Randall has used as comic fodder before in 468: Fetishes. Gödel's theorems roughly assert that a number theory could never be fully complete. The equivalent for a list of numbers is Cantor's diagonal argument, which is a proof that any list of real numbers can never be complete even if the list is infinitely long. Either way, any "true" Wikipedia article named "List of numbers" would perforce forever be incomplete, no matter how much it was expanded. Both Gödel's incompleteness theorems and Cantor's diagonal argument feature prominently in Gödel, Escher, Bach by Douglas Hofstadter, to whom Randall devoted later comic 917: Hofstadter. 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.
- [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 a ribbon 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
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