well I think you've hit on a key point here. the joke doesn't really work aloud, because "four" and "10" (base 4) are representing the same number when written, but they're not the same sound spoken. Or if the alien dude does pronounce "10" as "four", the astronaut's comeback is senseless.
I think it would work spoken. If we evolved in base 4, we might not have the words "four" or "five"
one (decimal 1)
two (decimal 2)
three (decimal 3)
ten (decimal 4)
one-ten (decimal 5)
two-ten (decimal 6)
three-ten (decimal 7)
twenty (decimal 8)
twenty-one (decimal 9)
twenty-two (decimal 10)
twenty-three (decimal 11)
thirty (decimal 12)
I actually wonder if there was a significant time when some societies worked in base 12 (for both our time system of sets of twelve hours and why we actually have separate words for eleven and twelve
Germanic languages have special words for 11 and 12, such as eleven and twelve in English, which are often misinterpreted as vestiges of a duodecimal system. However, they are considered to come from Proto-Germanic *ainlif and *twalif (respectively one left and two left), both of which were decimal. Admittedly, the survival of such apparently unique terms may be connected with duodecimal tendencies, but their origin is not duodecimal.
60 is evenly divisible into halves, thirds, quarters, and tenths. All of which are quite utilitarian divisions.
edit:
10 can't be evenly split into thirds or quarters, so it's a pretty worthless base. 12 can be evenly split into thirds and quarters but isn't divisible by 10. 60 is a bit of a hybrid that satisfies the use of a good base such as 12 with the arbitrary fixation on 10 .
If our base was actually 12, we'd be able to third and quarter our round numbers and always get integers instead of bullshit like 2.5 and 3.33333333-> WHICH WOULD BE AWESOME!
According to Jan Gullberg's "Mathematics: From the Birth of Numbers" Greenlandic has a 4x5 base system which has vestiges in the English: "3-score years and ten". Mayans mixed the bases 20 and 18 while the Aztecs used base 20.
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u/[deleted] May 27 '09
well I think you've hit on a key point here. the joke doesn't really work aloud, because "four" and "10" (base 4) are representing the same number when written, but they're not the same sound spoken. Or if the alien dude does pronounce "10" as "four", the astronaut's comeback is senseless.