Subject: Re: [lojban] Re: possible A-F...

From: [email-masked]
Date: Sat, 10 Nov 2001 15:48:37 EST

A collapsed reply to bloke_without_a_ favourite_colour.

First, I want to stress that this is bound to be a merely theoretical 
exercise, that the chances of actually changing the actual numerical notation 
used in the world is less than null in infinity (hyperbole, but only just).
Taht said, the theoretical grounds for preferring one to another of the 
central schemes -- 10, 12, 16 -- come down to the fractions, which are in 
order (with about a halving of frequency at each step) half, quarter, third, 
fifth, eighth, then sixth, seventh, tenth, ninth, twelfth and eleventh, much 
closer together.
The three are equal on half, each requiring one digit
On a quarter, hex and duod require one digit, decimal 2
On thirds, duod still requires only 1, hex and dec need at least 2: the digit 
and the repeater mark
On fifths, decimal needs only one digit, duod needs at least 5; four 
repeating digits and the repeater mark, and hex needs 2, digit and repeater. 
[duodecimalists tend to disregard this result because they take the frquency 
of fifths as largely an artefact of decimal bases.]
On eighths, hex needs one digit, decimal 3 and duod 2.
On sixths, duod needs 1, dec 4, hex 4 (marking the beginning of the 
repetition as well)
Sevenths: dec 7, duod 7, hex 4
Tenths: dec 1, duod 7, hex 3
Ninths: dec 2, duod 2, hex 4
Twelfths: dec 5, duod 1, hex 4
Elevenths: dec 3, duod 2, hex 6
>From this some sort of ordering should emerge. For example, taking the last 
five as worth one per digit and then doubling on up gives dec 186, duod 181, 
hex 179
(somebody please check all these figures -- non-decimal calculations are not 
my forte -- nor is decimal, come tot that).