Our purpose is to explore the world of Torah Codes for the purpose of understanding them, their structure, and their content. There are some skeptics, who for various reasons, hold the hypothesis that Torah codes are not real and all that has been noticed is in fact just things that have happened by chance arrangement of letters. We hold a different hypothesis. We hold the hypothesis that the letter arrangements constituting Torah codes are unexpected and do not occur by chance.
The exploration we do in the world of Torah Codes here is not for the purpose of making formal experiments to evaluate the probability that something might happen by chance. Nor is it to formally test the Null hypothesis of no Torah code effect against some alternative hypothesis. Such formal experiments and testing are important and must be done. Our work in that area can be found at torah-code.org.
Rather our purpose on this website is to document our structured exploration as one might do in a research notebook. It is a place where we can write our thoughts and review in some organized format what we have done. We do this to help us think of formal hypotheses to test that will get us to the next level of understanding this phenomena. And we do this in a way that can be shared with others.
In our disciplined exploration, we do in fact use formal tools and do evaluate with Monte Carlo experiments the probability that as good as a table as we have found might occur by chance. These experiments are done in the whole Torah text, also known as the Five Books of Moses. We use the Koren edition. All of our Monte Carlo experiments are done in the ELS random placement text population and the measure of the compactness of a table that we use is table area, the number of rows of the table times the number of columns of the table.
We know that the table area measure is certainly not the most sensitive. In fact, our formal experiments seem to indicate that it is among the least sensitive. But we use it here because it is the easiest for us and others to understand. When we use it we do not need to express what we are doing in technical mathematics.
On the one hand our use of area as compactness may be a major shortcoming because of its lack of sensitiveness. On the other hand it may be a major advantage because it will keep us playing, for now, where the phenomena appears at its strongest. So we have less an issue of distinguishing signal from noise.
Our experimental protocol nearly always has the maximum row skip and maximum column skip for an ELS on a cylinder to be set to 10. We prefer to have the expected number of ELSs to also be set to 10. But it is not unusual to use 20, 30, 50, or even on occasion 100. If we were running formal protocols, we would have to penalize the p-values either in an internal manner or externally by the Bonferroni inequality. However, we do not do that here in our informal work. The requirement that all ELSs be low skip rank ELSs which is what the expected number setting accomplishes, is actually not consistent with the form of the Torah code hypothesis that we hold: that only one or more of the ELSs, particularly the dominant ELS, must be low skip rank. Thus, for now, we regard the setting of the expected number of ELSs to be a nuisance parameter. We believe that when we understand the phenomena better, we will have a protocol that will know how to set it or how to work with various settings automatically and computationally efficiently.