25 Tamuz, 5758
The Seal of G-d is Truth: Supplement
by Doron Witztum
A.
One of the readers, Yosef Beremez [note 1], has made the following comments
related to the measurement of Phenomenon II (described in Part A of the
Appendix):
- Randomization A was done using the same 100 permutations of the expression
")LHYM )MT". This reader suggested that there was a possible dependence
between the permutations. He also suggested redoing the experiment while:
- Using 4 different sets of 100 permutations of the expression
")LHYM )MT".
- Using a larger set of permutations (in such a case the dependence
is negligible).
- Y.B. also inquired - what would be the outcome of Randomizations
B, working with perturbations x, y, z, between -2 and 2 as done in earlier
experiments?
B.
I performed the requisite experiments and the results are as follows:
- 1a. I repeated the measurement described in Part A of the appendix
(section A), with the variation of using 4 different sets of 100 permutations
of the expression ")LHYM )MT".
I randomly drew 4 results as described there, and repeated this process
100,000,000 times. The new rank of P2 was 156 out of 100,000,000.
- 1b. I repeated the measurement described in Part A of the appendix
(section A), with the variation of using all 5039 permutations of the expression
")LHYM )MT" (without the identity) instead of the 100.
I randomly drew 4 results as described there, and repeated this process
100,000,000 times. The new rank of P2 was 454 out of 100,000,000.
It turns out that Yosef' was correct, and I thank him for the correction.
- 2. I repeated the measurement described in Part A of the appendix (section
B), using perturbations x, y, z , between -2 and 2.
The new rank of P2 was 89 out of 10,519,600.
C.
Additional Measurement
Regarding the convergence between ")LHYM )MT" and "XTMY", the function
c showed an exceptionally strong result: the convergences of the ELSs ranked
ahead of all the PLSs. Therefore, we upgraded the program to be able to
work with the domain of perturbation to -20 £x, y, z £ 20. Out of the 68,921
possible perturbations for ")LHYM )MT", 54,825 do appear. The ELSs ranked
first out of all 54,825. It is clear from this measurement, that
in this case we have two types of convergences: the convergence of "XTMY",
which is very strong, and the convergences of the other three words, which
are also successful, but not of the same order of magnitude.
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Note 1. Literary name.