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Date: Sat, 10 Nov 2001 14:46:21 -0000
To: lojban@yahoogroups.com
Subject: Re: possible A-F...
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From: bloke_without_a_favourite_colour@yahoo.co.uk
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--- 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