tlhIngan-Hol Archive: Tue Jul 07 08:14:03 1998
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Re: Question from a newbie
Terrence Donnelly wrote:
> '(2 x 10^2) + (3 x 10^1) + (4 x 10^0)'. Zero is absolutely necessary in
> place-holder notation, to hold the place of powers of the base without
> a value: '101' = '(1 x 10^2) + (0 x 10^1) + (1 x 10^0)'. There is no need
> for more than (base)-1 actual digits (plus 0) in a placeholder system, since
> the value of the base itself is accounted for by the next column over. So,
> base-10 has '0,1,2,3,4,5,6,7,8,9', base-2 has '0,1'.
>
> MO says in TKD "Klingon originally had a ternary number system; that is,
> one based on three. Counting proceeded as follows: 1, 2, 3, 3+1, 3+2, 3+3;
> 2x3+1, 2x3+2, 2x3+3; 3x3+1; 3x3+2; 3x3+3; and then it got complicated." 8+)
>
Then 1x9+1x3+1, 1x9+1x3+2, etc. If you remove all the x this and x that you get 1,
2, 3, 11, 12, 13, 21, 22, 23, 31, 32, 33, 111, 112, etc.
> This is clearly not place-holder notation. If Klingon had a true base-3
> placeholder notation system, it would run '0, 1, 2, 10 (i.e. 1 x 3^1 = 3),
> 11 (1 x 3^1 + 1 = 4), 12 (1 x 3^1 + 2 = 5), 20 (2 x 3^1 = 6), 21 (2 x 3^1 +1
> = 7)',
> etc. Okrand may be right in calling it ternary, since it has only 3 basic
> numbers,
> but it is not base-3 as I understand the term.
>
You're right, not base three the way WE think of it, but it looks like place-holder
notation to me. Simply that each place MUST have a value, no zeros.
> I can't imagine how Klingons actually formed the number words, but
> presumably they
> were based on the basic {wa', cha', wej}. If they used numerals at all, they
> would
> not have been things like 1,2,3,11,12, etc., because that only makes sense
> in place-
> holder notation. More likely, each numerical value would have had its own
> symbol.
>
> I can see that zero isn't needed for simple counting, but I can't see any
> culture doing higher math without it. This is probably why the Klingons
> switched to the base-10 system; I'd expect the sero was adopted then.
>
> -- ter'eS
-- tuv'el pach puqloD