# Torah Codes Tutorial: 7

## Technical Discussion

Let us simplify the Torah code hypothesis for our discussion.

Words that are conceptually related to each other, such as key words of an historical event, are more likely to have relatively compact meetings of their equidistant letter sequences (ELSs) in the Torah text than expected by chance.

This statement has three levels:

- If (A) the words are conceptually related, then (B) they have relatively compact meetings of their equidistanct letter sequences;
- relatively compact meetings; and
- relatively compact meetings is modified by more likely than chance.

Let us leave (2) and (3) alone for the moment and concentrate on (1).

Clearly, even if A implies B holds, it does not imply that B implies A holds. For example, if (A) something is gold, then (B) it glitters. This is generally true. On the other hand, if (B) it glitters, then (A) it is gold is obviously false. Thus, the folk wisdom: "All that glitters is not gold". The problem is that although it is true that gold glitters, there are many other things that glitter too.

Likewise, (B) a relatively compact meeting of equidistant letter sequences does not imply (A) that their corresponding words are conceptually or historically related. Simply stated, there are many relatively compact meetings of equidistant letter sequences whose corresponding key words are not related in any meaningful way, let alone correspond to some historical event.

To summarize: the statement "If words are related to each other via an historical event then they have relatively compact meetings of their equidistant letter sequences, while true, does not imply the truth of its converse If some words have equidistant letter sequences that are in a relatively compact meeting, then they are related to each other through some historical (or future historical) event. Thus, the concept of using codes to predict the future is logically flawed.

Now let us take up (2), relatively compact meetings. How does one evaluate whether or not some ELSs of some key words are in a relatively compact meeting?

Relatively compact does not mean that there are ELSs of each of the key words that all fit in some small size table, say 10 rows by 10 columns, a size that easily fits on a single page. For suppose that we sampled 100 modern Hebrew novels and each time we found the smallest area table having at least one ELS of each of the same given key words, and this smallest area table was larger than 10x10=100 characters. In that case, we would argue that the 100 character table was in fact relatively large. For out of a sample of 100 texts, each had a smallest area table that was smaller than 100 characters.

On the other hand suppose we found that of the 100 Hebrew novels, 99 of them had smallest area tables larger than 10x10=100 characters and one of the had a smallest area table smaller than 100 characters. In that case we would infer that the 100 character table produced by the Torah text was in fact relatively compact because the probability that a modern Hebrew novel text would have a smaller table than 100 characters was about 1/100. In summary, relatively compact is measured by the fraction of texts from a monkey text population that have a more compact meeting than that found in the Torah text.

Finally, let us take up (3) more likely to have. Let us put this into context. Suppose that we choose 100 different major historical events. And for each historical event we determine a set of three or four key words that are the most central key words that describe the historical event. The Torah code hypothesis is not that all the major historical events have key words whose ELSs have relatively compact meetings. Rather it is that more of these major historical events have key words whose ELSs have relatively compact meetings than expected by chance.

In this setting the Torah text produces 100 tables and associated with each table is the fraction p of texts from a monkey text population having tables as compact or more compact than that produced by the Torah text. So we have 100 fractions.

Now we go to the monkey text population and sample say 999 monkey texts. Each of these 999 monkey texts also produces 100 fractions.

To determine if the Torah text produces smaller fractions with a probability higher than expected by chance we have to define an appropriate test statistic. Just for the sake of simplicity, suppose we choose for our test statistic the product of the 100 fractions. This kind of test statistic has especially small values when a handful of the terms in the product are small fractions. So we take the product of the 100 fractions for the Torah text and for each of the 999 monkey texts. This results in 1000 products. We count the number of products in these 1000 products whose value is less than or equal to the product associated with the Torah text. If the number of small products is say 2/1000 then we know that it is not likely that a monkey text will have a set of 100 fractions that are especially small. Or to say it another way, the Torah text is producing its 100 fractions more likely than expected by chance to be small values.

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