tlhIngan-Hol Archive: Sun Jul 07 23:14:17 2002

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Baseless (ahem) speculation about ternary counting

I was thinking about the old way of counting in Klingon, and
trying to see if we could infer anything about how it may have actually
worked.  Here's what I know that we know so far - am I leaving anything
out?

1. It was ternary (base 3)

2. When it was expanded to base ten, the words for "four" through "eight"
   were apparently borrowed from the names for musical tones.

(It's hard to infer useful information from the TKD description through
 "and then it got complicated"; I'm assuming that the ternary counting
system worked much the same way as the decimal, just in base three instead of
base ten - that is, the way Terran mathematicians would count in base 3.)

Note that <<wej>> was not itself borrowed in this way; it apparently already
existed as the word for "three".   Which implies that wherever <<-maH>> came
from, it wasn't just repurposed from an earlier meaning of "three" instead
of "ten".

This started my wild speculation: What if <<wej>> is actually a contraction of
original ?<<wa'ej>>, with ?<<-ej>> working for threes as <<-maH>> works for
tens?

That would give us old fashioned counting starting like this:

wa'         =  1[3] = 1[10]
cha'        =  2[3] = 2[10]
wa'ej       = 10[3] = 3[10]
wa'ej wa'   = 11[3] = 4[10]
wa'ej cha'  = 12[3] = 5[10]
cha'ej      = 20[3] = 6[10]
cha'ej wa'  = 21[3] = 7[10]
cha'ej cha' = 22[3] = 8[10]

To proceed further, we need to know the old word for "nine".  But we
have a word for nine - <<Hut>> - that must have come from somewhere.
It can't be from the musical scale, which only has eight tone names. Since
the old system would have required words for powers of three, it makes
sense to guess that <<-Hut>> was the old suffix for "nine", used the
same way as modern <<-vatlh>>, "hundred".  Under that assumption, we
can continue counting like so:

wa'Hut	    = 100[3] =  9[10]
wa'Hut wa'  = 101[3] = 10[10]
wa'Hut cha' = 102[3] = 11[10]

And so on all the way up to <<cha'Hut cha'ej cha'>> = 222 ternary = 26 decimal.
But then we run into a brick wall; I can not think of any logical basis for
speculation as to the old word for 27.

I realize this is all wild imaginings, but I tried to stay within the realm
of plausibility, even likelihood.  Any thoughts?

--
marqoS <[email protected]>

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