Base 13

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Base-13, tridecimal, tredecimal, or triskaidecimal is a positional numeral system with thirteen as its base. It uses 13 different digits for representing numbers. Suitable digits for base 13 could be 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, and C, although any 13 characters could be used.

Base 13 in fiction[edit]

In the end of The Restaurant at the End of the Universe by Douglas Adams, a possible question to get the answer "forty-two" is presented: "What do you get if you multiply six by nine?"[1] Of course, the answer is deliberately wrong, creating a humorous effect – if the calculation is carried out in base 10. People who were trying to find a deeper meaning in the passage soon noticed that in base 13, 613 × 913 is actually 4213 (as 4 × 13 + 2 = 54, i.e. 54 in decimal is equal to 42 expressed in base 13). When confronted with this, the author claimed that it was a mere coincidence, famously stating that "I may be a sorry case, but I don't write jokes in base 13." (However, as observed in the Annotated Alice, one of Lewis Carroll's most elaborate jokes featuring the number 42 is a calculation in chapter 2 of Alice's Adventures in Wonderland that breaks down precisely when one multiplies by 13 and attempts to express the answer in base 42.) See also The Answer to Life, the Universe, and Everything.

The Gallifreyan race of "Time Lords", from the science fiction franchise Doctor Who, uses a numeric system based upon thirteen symbols. This was documented in the novelization of "Shada", a story originally written for TV by Douglas Adams and novelized in 2012 by Gareth Roberts:

...a simple enough keyboard with the seven hundred and twenty-three letters of the Gallifreyan alphabet in the centre, the thirteen numerical symbols ranged across the top...

— Adams, Douglas;Roberts, Gareth, Doctor Who: Shada[2]

In The Night Angel Trilogy by Brent Weeks, the Strangers—supernatural antagonists—use a base 13 numbering system, which dictates how many of each hierarchical order can be summoned into the world at once. To summon 13 of any order, one member of the next higher order must be summoned and mastered.

Base-13 calendar[edit]

The Maya calendar used a base system (the trecena), with 13×20 days for the Tzolkin cycle.[3]

Base-13 used in mathematics[edit]

The Conway base 13 function is used as a counterexample to the converse of the intermediate value theorem that is discontinuous at every point.[4]

References[edit]

  1. ^ The Restaurant at the End of the Universe, by Douglas Adams
  2. ^ Roberts, Gareth; Adams, Douglas (26 June 2012). Doctor Who: Shada. Ace Hardcover. p. 285. ISBN 978-0425259986. 
  3. ^ Harvey M. Bricker, Victoria R. Bricker, Anthony F. Aveni, Michael P. Closs, Munro S. Edmonson, Floyd G. Lounsbury and Eric Taladoire (February 1983). Classic Maya Prediction of Solar Eclipses. JSTOR 2742481. 
  4. ^ Willie Wong (2010-07-20). "Conway’s Base 13 Function".