From mark@kli.org Sat Sep 29 19:24:39 2001
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Subject: Re:HEX advert... (Don't know what it was)
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From: mark@kli.org
--- In lojban@y..., "G. Dyke" wrote:
> Apart from the beauty of it, why have better divisibility ?
whether I have
> IIIIIIIIIIIIIIIIIIIIIII , 10111, 27, 23, 1#, or 17 people, you
still won't
> share IIIII cakes fairly between them with any ease.
Ah, no divisibility is important in a number system! Consider some
simple, common fractions.
ju'u re ju'u dau ju'u gai ju'u vaisu'ipa
One-half: li pipa li pimu li pixa li pibi
One-third: li pira'enopa li pira'eci li pivo li pira'emu
One-quarter: li pinopa li piremu li pici li pivo
See? Any fraction whose denominator's prime factorization has only
primes in the base's prime factorization can be expressed as a
*terminating* radix fraction (you can't well say "decimal" in this
context). So base-2 and base-16 will allow *only* fractions whose
denominators are powers of 2 to have terminating representations.
Base-10 allows for halves (and powers of two, with more digits),
fifths (and its powers), and tenths and so on. Base-12 will give
you all the powers of two, but with fewer digits (1/4 only needs
one-digit precision), *and* the extremely common 1/3 (fifths are
much less commonly used). That's what makes the dozenal people foam
at the mouth. There's a *reason* all those old systems of
measurement went in 12s and 60s: so you could *easily* find 1/3 or
1/4 of a foot, without having to start fracturing your inches.
Now, does this really matter all that much in Lojban? After all, we
have ra'e for repeating digits, and we even have fi'u for explicit
fractions. Hard to say. It feels like it still might matter; there
are all kinds of settings, maybe there'll be limited digit precision
someplace. Granted, not really likely, but if we're talking about
*thinking* in the language, thinking in terms that allow for easy
thirds and fourths can be handy.
I *am* a computer geek, and I still see no plusses to using
hexadecimal anywhere I don't actually need to.
~mark