From mark@kli.org Sat Sep 29 19:24:39 2001 Return-Path: X-Sender: mark@kli.org X-Apparently-To: lojban@yahoogroups.com Received: (EGP: mail-7_4_1); 30 Sep 2001 02:24:39 -0000 Received: (qmail 87532 invoked from network); 30 Sep 2001 02:24:39 -0000 Received: from unknown (10.1.10.26) by l10.egroups.com with QMQP; 30 Sep 2001 02:24:39 -0000 Received: from unknown (HELO n15.groups.yahoo.com) (10.1.1.31) by mta1 with SMTP; 30 Sep 2001 02:24:38 -0000 X-eGroups-Return: mark@kli.org Received: from [10.1.1.35] by ml.egroups.com with NNFMP; 30 Sep 2001 02:24:28 -0000 Date: Sun, 30 Sep 2001 02:24:26 -0000 To: lojban@yahoogroups.com Subject: Re:HEX advert... (Don't know what it was) Message-ID: <9p5voq+jj20@eGroups.com> In-Reply-To: <002d01c148d5$cc58f360$b42203d5@oemcomputer> User-Agent: eGroups-EW/0.82 MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Length: 2075 X-Mailer: eGroups Message Poster X-Originating-IP: 162.33.229.2 From: mark@kli.org X-Yahoo-Message-Num: 11201 --- 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