tlhIngan-Hol Archive: Wed Oct 01 07:41:06 2014
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Re: [Tlhingan-hol] do any human cultures count like Klingons do?
- From: "De'vID" <[email protected]>
- Subject: Re: [Tlhingan-hol] do any human cultures count like Klingons do?
- Date: Wed, 1 Oct 2014 16:40:51 +0200
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De'vID:
>> The difference becomes more apparently for "larger" numbers: decimal
>> 18 would be written "200" in base 3, but "123" in 3-adic notation.
>> Decimal 33 is "1020" in base 3, but "313" in 3-adic notation.
DloraH:
> It becomes even more apparent when working to the right of a decimal point. (Is it still called a
> "decimal" point when used in a non-base 10 system?)
"radix point" ponglu'.
DloraH:
> Where pi is 3 and some fraction, after borrowing back to fill in those zero place holders, the value
> of pi in Klingon/3-adic ends up being:
> 2.233133312221233133231333333222
>
> base 3:
> 10.010211012222010211002111110222
>
> 3.3333... decimal becomes 3.1 3-adic. (10.1 base-3)
> But then 3.4 decimal, which is more than 3.3333... becomes 2.33121 (10.10121 base-3) because of
> that 0 in the "nineths" position.
nIbbe'chugh pagh mI' je, not mI'vam 'ay'vaD "0" ghItlhlu'.
DloraH:
> Is there another way to handle such numbers?
HIja'. 'ach Qatlh QIjmeH mIw: http://en.wikipedia.org/wiki/Quote_notation
Interesting that such a system requires two place symbols (the radix
point and quote mark), and we know Klingon writing uses upper and
lower triangle punctuation, so that's a good match.
0 (b10) = 2'3 (3-adic) (note that you never need a symbol for "0" in
such a system)
-1 (b10) = 2' (3-adic)
-2 (b10) = 2'1 (3-adic)
-3 (b10) = 2'13 (3-adic)
-4 (b10) = 2'12 (3-adic)
-5 (b10) = 2'11 (3-adic)
... to quote TKD, "and then it got complicated."
1/2 (b10) = 1'2 (3-adic)
1/4 (b10) = 13'21 (3-adic)
1/8 (b10) = 12'2 (3-adic)
You can verify these fractions by multiplying by their inverse to get
2'31 = 1 (since 2'3 = 0).
DloraH:
> Would a Klingon be forced to use fractions instead?
ghobe'. 'ach fractions lo'laHbej je.
DloraH:
> What happens with numbers less than 1 where there is nothing to borrow from to fill those spaces?
> .4 (b10) -> .10121 (b3) -> ?.?3121 (3-adic)
jIQaghbe'pu'chugh:
0.2 (b10) = 1133'2
0.4 (b10) = 1133'1211
Again, you can verify by multiplying by 5 to get 1 and 2, respectively.
DloraH:
> chaq tlhIngan Hol vIlo'nIS. tlhIngan Hol wIlo'taHvIS, chay' [base-n] wI'oS? chay' [adic] wI'oS?
> [place holder] Del nuq?
jISovbe'.
--
De'vID
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