tlhIngan-Hol Archive: Mon Oct 20 13:52:49 1997

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Re: base 3 (was RE: vIghojqa')




DloraH wrote:
> Klingon was supposedly a base 3 number system
> Both you and MO mention the numbers 1,2,3
> technically that would be a base 4 system
> 
> you have to include the 0
> 
> but MO mentions 1,2,3 in TKD and in the musical scale in KGT.
> base 4?
> 
I see several possibilities:

0: anything weird even I haven't thought of (most likely :)

1: really base 3, assume we have the symbols {Z,O,T} and

1 : O, 2 : T, 3 : OZ, 3+1 : OO, 3+2 : OT, 3+3 : TZ
2*3+1 : TO, 2*3+2 : TT, 2*3+3 : OZZ, 3*3+1 : OZO, 3*3+2 : OZT, 3*3+3 : OOZ

rather implausible given the way Okrand wrote the numbers and also
there'd be no reason to say "then it got complicated"

2: base three, but works more like Chinese etc. numeral system
assume we have the symbols {-,=,+,#} and

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 : #+

although this matches the tlhIngan Hol style of forming numbers better,
the arguments against (1) above still apply

3: something like adding scratches and "collapsing" some of them to
new symbols, e.g.

1 : I, 2 : II, 3 : III, 3+1 : VI, 3+2: VII, 3+3 : VIII
2*3+1 : VVI, 2*3+2 : VVII, 2*3+3 : VVIII, 3*3+1: VVVI, 3*3+2: VVVII,
3*3+3 : VVVIII

this matches the way Okrand writes the numbers. the symbol I represents
a single scratch, the symbol V represents three scratches, but is only
used if there is at least one more single scratch

also it is not quite obvious how to continue after 12, maybe this would
have been done differently depending on profession/discipline/whatever

some possibilities: 

a) the symbol X denotes three V's if followed by at least one more V:

13 : XVI, 14 : XVII, 15 : XVIII, ... 39: XXXVVVIII

b) the symbol L denotes three V's plus three I's if followed by at 
least one more of these symbols:

13 : LI, 14: LII, 15 : LIII, 16: LVI, ... 48: LLLVVVIII

c) a multiplier a la {-maH} represents 13 (I'm writing it as /)

13 : I/, 14 : I/I, 15 : I/II, ... 26 : II/, 27 : II/I, ... 
168 : VVVIII/VVVIII

d) a multiplier represents 12 and must be followed by some other symbol
(I'm writing this multiplier now as \)

13 : I\I, 14 : I\II, 15 : I\III, 16 : I\VI, ..., 25 : II\I, ...
156 : VVVIII\VVVIII


at some point, I would expect some multiplier-like structure
personally I favor the style where you have possibility 3:a)
and a 3:c) type multiplier for 40, with the nice feature that
you have 3 (three) symbols I,V and X which can occur in groups
of one, two or three, giving nine possibilities (and we have
nine words for numbers...)

I wa', II cha', III wej
V loS, VV vagh, VVV jav
X Soch, XX chorgh, XXX Hut

and wa'maH = 40(dec)

(at least I managed to have SOME Klingon in this post)

HomDoq



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