| 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). |