From bloke_without_a_favourite_colour@yahoo.co.uk Sat Nov 10 06:46:22 2001 Return-Path: X-Sender: bloke_without_a_favourite_colour@yahoo.co.uk X-Apparently-To: lojban@yahoogroups.com Received: (EGP: mail-8_0_0_1); 10 Nov 2001 14:46:21 -0000 Received: (qmail 75464 invoked from network); 10 Nov 2001 14:46:21 -0000 Received: from unknown (216.115.97.172) by m10.grp.snv.yahoo.com with QMQP; 10 Nov 2001 14:46:21 -0000 Received: from unknown (HELO n25.groups.yahoo.com) (216.115.96.75) by mta2.grp.snv.yahoo.com with SMTP; 10 Nov 2001 14:46:22 -0000 X-eGroups-Return: bloke_without_a_favourite_colour@yahoo.co.uk Received: from [10.1.10.94] by n25.groups.yahoo.com with NNFMP; 10 Nov 2001 14:46:03 -0000 Date: Sat, 10 Nov 2001 14:46:21 -0000 To: lojban@yahoogroups.com Subject: Re: possible A-F... Message-ID: <9sjejt+blle@eGroups.com> In-Reply-To: User-Agent: eGroups-EW/0.82 MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Length: 2868 X-Mailer: eGroups Message Poster X-Originating-IP: 62.64.191.187 From: bloke_without_a_favourite_colour@yahoo.co.uk X-Yahoo-Profile: bloke_without_a_favourite_colour X-Yahoo-Message-Num: 12005 --- In lojban@y..., pycyn@a... wrote: > There are two questions here: what would be the most rational base for the > number system, given the sorts of things we use numbers for? and what system > could actually be adopted? > For the second of these, I'm afraid that habit is an enormous obstacle to > overcome. When it is backed up, as decimalism is, but physiology, I don't > see any chance of any new idea working -- certainly in our lifetimes and, I > think, ever until we grow the extra digits. > For the first, a long series of studies have suggested that the most > important uses of numbers are simple counting, for which all the major > contending bases are roughly equal -- small enough to have memorable digits > (60 is out), large enough to give small > numbers for ordinary counts (2 and 4 and probably 8 out); fractions, the > most common of which are half, quarter, third, fifth, eighth, and then the > rest pretty much in a lump (fifth -- and tenth -- seem to be phenomena of > decimalization, since they do't correspond to real-world cases except in > those kinds of contexts); phone numbers and addresses, which may even take > precedence over fractions but are neutral among bases except as in counting. > Hex does actually have a small technical advantage in phone numbers in that > it might allow a more efficient use of switches (at enormous cost -- a factor > in "habit" affecting what changes can actually be made) in the phone system > (which is already set up for duodecimal, note). So, it is fractions that > count most and there duodecimal does better than hex, even though 3 of the > top five fractions are powers of 2. The mess that is 1/3 cancels the > advantages of 2 and 4 and is not nullified by the minor mess of 1/8 > duodecimal. In fact, hex loses out even to decimal on this. (Of course, you > can argue with the weightings, though these have been pretty consistent over > years of studies). I have left out time, since it is so obviously a > duodecimal win, with decimal close behind and hex nowhere in sight. How do duodecimal and decimal do better than hexadecimal with regard to fractions? You said halves, quarters, thirds, fifths, and eighths are the important ones. 12 is divisible by 2, 4, and 3 but not 5 or 8. 10 is divisible by 2 and 5 but not 4, 3, or 8. 16 is divisible by 2, 4, and 8 but not 3 or 5. So duodecimal and hexadecimal have 3 each and decimal only has 2. So it seems to me that duodecimal and hexadecimal are equal with decimal the worst of the three. Even if thirds are more important than eighths, so duodecimal beats hexadecimal, how can decimal possibly be better than hexadecimal here, when decimal only has 5 compared with hexadecimal's 4 and 8, and 4 alone is enough to beat the 5? Sincerely, Robert