tlhIngan-Hol Archive: Mon Jul 06 16:01:56 1998

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Re: Question from a newbie

At 12:24 PM 7/6/98 -0700, Tuv'el wrote:
>
>
>Quvar muHwI' wrote:
>
>> >What "error" about the number system?
>> >Ternary is correct.  1,2,3 is correct.   What's wrong?
>> Well, when I was on the list last year, there was a big discussion on that.
>> The thoughts were:
>> - the binary system is based on 0 and 1
>> - a ternary; shouldn't it be on 0, 1 and 2 ?
>
>Why would ternary HAVE to be based on 0,1, & 2.  If you don't acknowledge the 0
>(sorry pagh), then you have 1, 2, 3, 11=4, 12=5, 13=6, 21, 22, 23, 31, 32,
>33=12, etc.
>

nuqjatlh?  I think we're getting confused between simple counting systems and 
place-holder notation.  In place-holder notation, each subsequent column 
(starting from the left) represents the value of one greater power of the 
base.  In arabic notation (our own), base 10, the first column
is 10^0 (or 1), the next is 10^1 (10), then 10^2 (100), etc.  The actual 
digit found at that location is the multiplier for the particular power of 
10 at that position.  The number '234' for example, can be read as 
'(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+)

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.  

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

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