Subject: Re:HEX advert... (Don't know what it was)

From: [email-masked]
Date: Sun, 30 Sep 2001 02:24:26 -0000

--- In lojban@y..., "G. Dyke" <gordon.dyke@b...> 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