From Osher Doctorow
"Uncle Al" in his last typically negative comment (snip etc.) on my
posts (one or two back, as I recall) mentioned 5th or more decimal
places, which gave me an idea.
The coupling strength (alphas) of the strong, EM, weak, and
gravitational forces as exponents of 10 (that is to say, log(alphas))
are:
1) 0 (strong), -4 (EM), -6 (weak), -39 (gravitation)
However, notice that we have:
2) 4 = 1 x 0 + 4
3) 6 = 2 x 4 - 2
4) 39 = 7 x 6 - 3
That is to say, if bi = /log_10(alpha_i)/, where alpha_i is the ith
alpha, then each bi (except 0 which will be considered later) is in
modular arithmetic generated by bi-1 (the i - 1st bj) in the sense
that:
5) bi = k_i bi-1 +/- u_i
where k_i is an integer constant and the u_i are each different
elements of the set {2, 3, 4}. However, (5) says that:
6) bi is congruent to +/- u_i (mod bi-1)
For the case of 0, the strong force bi, Readers can unravel the
situation, noting that the strong force is taken as a "standard" here
conventionally.
Notice that the ui 2, 3, 4, are two of the quantities (2 and 4) which
I have been discussing in this Section and some previous ones as
adding up to 11 dimensions via:
7) 2 + 4 + 5 = 11
So what happened to 3 and 5? Well:
8) u_2 + u_3 = 2 + 3 = 5
Readers can figure out where the 3 went.
Osher Doctorow
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