[99502] in tlhIngan-Hol
[Tlhingan-hol] do any human cultures count like Klingons do?
daemon@ATHENA.MIT.EDU (De'vID)
Thu Sep 18 04:12:42 2014
Date: Thu, 18 Sep 2014 10:12:25 +0200
From: "De'vID" <de.vid.jonpin@gmail.com>
To: tlhIngan-Hol <tlhingan-hol@kli.org>
Errors-To: tlhingan-hol-bounces@kli.org
In The Klingon Dictionary, Section 5.2, the Klingon numbers are
enumerated as follows:
1, 2, 3;
3+1, 3+2, 3+3;
2*3+1, 2*3+2, 2*3+3;
3*3+1, 3*3+2, 3*3+3; etc.
Mathematicians would immediately recognise this as 3-adic notation
(see 3-adic under
http://en.wikipedia.org/wiki/Bijective_numeration#Properties_of_bijective_base-k_numerals).
This system is interesting, because while it's a base-3 or ternary
notational system, "3" is not written as "10", but as its own symbol.
"6" is not written as "2 times 3" (or 2 shifted by one position), but
as "3+3".
This is how you'd count in 3-adic notation, if we allow the "tens"
position to represent 3 and the "hundreds" position to represent 9):
0, 1, 2, 3, 11, 12, 13, 21, 22, 23, 31, 32, 33, 111, 112, 113, 121,
122, 123, ...
So decimal 12 is written as "33" (what TKD would call "3*3+3"), and
decimal 18 is written as "123" (or "3*3+2*3+3" using TKD notation).
Everyone is aware that Marc Okrand chose OVS grammar because it's rare
among human languages. He apparently pulled something similar off with
Klingon mathematics. Does any human culture count like this? (Simple
tallying, of course, is 1-adic notation, but that's always used
alongside a decimal or base-20/30/60 system. Ignoring simply tallying
and advanced mathematics, do any human cultures even use p-adic
notation in any base?)
I couldn't find anything with a quick Google search, but then
anthropologists probably wouldn't use a term like "p-adic notation",
and mathematicians wouldn't usually be writing about ancient human
cultures. I figured someone on this list would know, though.
--
De'vID
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