Re: possible A-F...

[bloke_without_a_favourite_colour@yahoo.co.uk]

--- 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