# Experimental Results

This study is one of a continuing number of studies in which we tried to use all the reasonable key word sets relevant to the event in order to have a reasonable possibility of finding all the key word sets that might be encoded. The purpose of these studies is to assemble a sufficient number of data sets so that we can use an automatic optimization process to find the pattern by which encoded key word sets can be distinguished from non-encoded key word sets.

This study involved 2,158 key word combination sets in
order to explore what key word combination sets might be encoded. Because of the large number of key
word sets explored in the study, none of the small p-value key word sets could be said to statistically significant.
Technically, if we were to test the NULL hypothesis of *No Torah code effect*
against the alternative hypothesis that one of the 2,158 key word combination sets was encoded,
we would not be able to reject the NULL hypothesis. And if we were to fix an event category combination
set and test the NULL hypothesis of *No Torah code effect* against the alternative hypothesis
that one of the key word combination sets associated with the event category combination was encoded,
we would not be able to reject the NULL hypothesis.

This does not mean that none of key word combination sets are encoded. It means that if some are encoded, then we cannot detect such an encoding by examining individual p-values. We must look more deeply at the lattice structure of the key word combination sets and their associated p-values. In a different context, with a smaller number of key word sets, the outcome of such an hypothesis test might be different. But to have a different context, we would have to know in advance the pattern of the encoded key word sets themselves. One of our purposes is to discover this pattern.

These kinds of studies need to be repeated multiple times with different random number generator seeds to assure that the differences observed between different runs are just sampling variations. Also these runs are needed to assure that the lattice scoring function we are developing to measure the overall results on a text by text basis is stable under different random number generator seeds. The computer runs are computationally intensive. Using a reasonably fast computer, a 10,000 trial run with 2,158 key word combination sets took about 10 days of running time.

There are two other kinds of experiments that need to be done. The first is to use a word permuted text in place of the Torah text. We wnat to know whether the distribution of p-values for a word permuted text similar to that of the Torah text. If so, then it would provide clear evidence that p-value scores are not sufficient for the efficient detection of encoding. We suspect that this might be the case. Experiments done using a word permuted text in place of the Torah text would provide results that would be useful in helping to determine what is different about the Torah text compared to monkey texts. We are examining this now from the inside using the ELS random placement text population. But these new experiments would examine this from the outside using a monkey text in place of the Torah text and using the ELS random placement text population as the control population to establish p-values.

We have done two sets of experiments in this study. The first set of experiments uses an resonance specification of a maximum row skip of 10 and a maximum column skip of 10. This is the resonance specification that we have been using on nearly all the experiments reported on in this website. The second study, whose results we show following this summary, uses a resonance specification of a maximum row skip and column skip of 5.

Event Category Combination | Number of Key Word Sets | Smallest P-value | Bonferroni Upper Bound P-value |
---|---|---|---|

WHAT | 2 | 825.1/1,000 | 10,000/10,000 |

WHERE | 12 | 147/1,000 | 10,000/10,000 |

WHEN_START | 16 | 462/10,000 | 7,392/10,000 |

WHEN_END | 32 | 336.5/10,000 | 10,000/10,000 |

WHO | 8 | 591/10,000 | 4,728/10,000 |

WHERE WHEN_START | 96 | 223.5/10,000 | 10,000/10,000 |

WHERE WHEN_END | 48 | 171.5/10,000 | 8,232/10,000 |

WHEN_START WHEN_END | 128 | 70.5/10,000 | 9024/10,000 |

WHERE_WHO | 24 | 499/10,000 | 5,184/10,000 |

WHEN_START WHO | 32 | 62.5/10,000 | 10,000/10,000 |

WHEN_END WHO | 64 | 308/10,000 | 10,000/10,000 |

WHERE WHEN_START WHEN_END | 384 | 24/10,000 | 9,216/10,000 |

WHERE WHEN_START WHO | 96 | 103/10,000 | 9,888/10,000 |

WHERE WHEN_END WHO | 192 | 324.5/10,000 | 10,000/10,000 |

WHEN_START WHEN_END WHO | 256 | 16.5/10,000 | 4,224/10,000 |

WHERE WHEN_START WHEN_END WHO | 768 | 50.5/10,000 | 10,000/10,000 |

From a simpler perspective, key word combination sets with
high p-values are certainly not encoded. Key word combination sets with small p-values might be encoded.
To see if the smallest p-value in any event combination category is statistically significant by itself,
we must multiply it by the number of key word combination sets tried in that category. The result is
the Bonferroni upper bound on the overall p-value. If this upper bound is small enough then, we can
reject the NULL hypothesis of *no Torah code effect *. If it is not small enough, we cannot
infer anything. It is clear from these results that
because we tried such a large number of key word combination sets we cannot directly infer from the
individual results of the smaller p-value key word combination sets that there is an encoding
of any of them.

For some time, we have hypothesized that Torah code encoding involves more structure than just p-values of individual key word sets. Technically, this means that when testing the Null hypothesis against an alternative hypothesis our alternative hypothesis must be something more complex than one key word set is encoded among a collection of key word sets. In particular, for this study, we have hypothesized that there is a p-value structure in the event category combination lattice and in the p-values of the lattice of the 2158 key word combination sets. Therefore, the results of this study, as with the previous studies, are going to be used as part of the training set that is required to statistically estimate this structure.

The top layer lattice structure in the event category combination lattice is shown below. Here the smallest p-value from all the key word combination sets that belong to the same event category combination are shown.