US Election 2012
Rabbi Glazerson's table uses the axis key word ברק אובמה Barack Obama. His video discussion of the table can be found at this web page. He has many key words as can be seen in our rendition of his table as shown below.
There is more than one ELS for many of his key words. Rabbi Glazerson typically chooses only one and many of the times the one he chooses is a window minimal skip ELS.
A window minimal skip ELS is the one whose row skip squared plus column skip squared is minimal in the table area.
Two of his key words שניה, Second and ישמעאל, Ishmael have two window minimum skip ELSs. We show both. The ELS he chose for ארהב, US and the one he chose for יבחר, Will be elected, are not window minimum skip ELSs. For these key words, we show both his ELS and the window minimal skip ELS.
Like most Torah code researchers, Rabbi Glazerson uses an interactive technique for developing a table. Without a rigid protocol and a priori key words, associating a p-value with a table is impossible. Therefore, it is easy for there to be semantically meaningful words having ELSs in the table but for which their compactness relationship is not statistically significant. We take one example: the key word נשיא, President, has sixteen ELSs with row skip less than or equal to 15 and column skip less than or equal to 15 in Rabbi Glazerson's table area. Assuming that this behavior is typical for tables of the number of rows and columns his table has, it means that we should not be surprised to find an ELS for נשיא in the table. These ELSs are shown below.
However, this argument is not necessarily a correct argument. Although it may be that it is most surely the case that one ELS for נשיא, president will be in the area of the table, the particular ELS that Rabbi Glazerson chose is minimal in skip and in fact using the axis protocol has the most compact relationship with the ELS for ברקאובמה among all the other ELSs of נשיא. One could even ask a more refined question: what is the probability that an ELS of נשיא would have a better axis compactness relationship than the one Rabbi Glazerson selected? Here we need to know the protocol for the ELS search. If the maximum skip for ELSs of נשיא is set so that the expected number of its ELSs in a random letter permuted text is 200, the maximum skip is 17. The number of ELSs of absolute skip less than or equal to 17 in the Torah is 274. In this case the p-value is about .164. This is not particularly small, but it is certainly not certain. This suggests that instead of summing up the largest squared distance between the letters of the non-axis ELSs with that of the axis ELS, as the axis protocol does now, we should combine p-values instead.
A similar situation occurs with respect to the ELSs of the key word שניה, Second. These twenty-five ELSs are shown below.
On the one hand, it is easy to be fooled into thinking that the ELSs found in a table developed in an interactive way are all statistically significant. On the other hand, the issue is more complex. In any case, this problem does not arise in a protocol that is a rigid a priori protocol and for which there is a Monte Carlo experiment that is done to determine the p-value of the table.
Rabbi Glazerson has many key words. We have selected the nine of his key words closest to the theme of the election: President, US, Cheshvon, (5)773, November, Second, Will be Elected, Threat, O(bama) Barack. These are also the same key words selected by Barry Roffman in his analysis of the Glazerson Table.
We ran three experiments, the first one with our original area compactness protocol and the remaining ones using our newer axis protocol. One experiment uses the axis protocol with the distmax compactness criteria for the compactness between two ELSs and the other uses the axis protocol with the area compactness criteria for the compactness between two ELSs. Our choice of using our original area compactness measure is because that is the compactness measure closest to the kind of analytic calculation that Roffman makes. Of course as we shall see, there is a big difference between the Monte Carlo p-value and Roffmans' analytic calculation.
To do our experiment, we require a specification for the expected number of ELSs for each key word. Then the maximum skip in the search for each ELS is set so that in a random letter shuffle text the expected number of ELSs to be found is what was set. This results in a different maximum skip for each key word. Rabbi Glazerson uses the key word תשעג (5)773, the Jewish year corresponding to an election held in November 2012. The ELS for תשעג has a skip of 22,138. So we had to set the expected number of ELSs to be 10,000 to make the maximum skip for תשעג to be over 22,138.
The results of the area compactness experiment are shown in the table below. Notice that as the protocol changes the p-values change. Using a significance level of 1/100, only the result of the second experiment was statistically significant. It had a p-value of 9.5/10,000.
The axis experiments set the maximum skip for the non-axis ELSs to be the maximum possible. The first table uses the distmax compactness criteria between two ELSs. The second table uses the area compactness criteria between two ELSs.