This and that

Please take a minute to review

/harmonic_entropy/topicId_215.html#215

and

/harmonic_entropy/topicId_267.html#271

Well, I tried the validation exercise mentioned in the first message for the
unreduced-fraction method described in the second message. Unfortunately,
but not surprisingly, it failed -- the simpler the fraction, the more
"probability" there is around it, since one has not only the 1/sqrt(n*d) for
the fraction itself, but also 1/sqrt(2n*2d), 1/sqrt(3n*3d), and so on up
until the limit is reached . . . hmm . . .

Last night I thought of a way of justifying the 1/sqrt(n*d) rule
theoretically rather than empirically, but it would seem to apply to the
unreduced-fraction case and not to the lowest-terms case -- oy! In any case,
it would seem to imply 1/cuberoot(l*m*n) for the triad case, but I suppose
the empirical validation would still appear necessary . . .

Oh well . . .