Torah Codes Tutorial: 4

Relatively Compact

According to the Torah Code hypothesis, if there is an encoding, then it will manifest itself by one or more relatively compact tables of ELSs of the encoded key words. Relative compactness is measured by statistical significance. If a table has a compactness value that is similar to a compactness value for a table of the ELSs of the same key words and which is easily found in an ordinary text or a monkey text, then the table is not relatively compact. We say that the compactness value is not statistically significant.

By definition, a monkey text is one known not to have the hypothesized Torah code effect. Hence a monkey text is one authored by humans or generated by taking a natural language text and randomizing it in some way such as by randomly permuting letters, words, or verses.

  1. Define a control population of Monkey Texts
  2. Estimate the probability that a text in the monkey text population would have at least as compact table as the one found in the Torah text. This probability is just the fraction of the texts randomly sampled from the monkey text population which produce a best table whose compactness is smaller than or equal to the best table compactness produced by the Torah text.
  3. Estimating a probability requires an experiment

The Experiment

  1. A properly done experiment requires a protocol.
  2. The protocol specifies all the details of the experiment so that another person could repeat the experiment and expect to get the same results.
  3. In Torah code experiments, the protocol specifies the details of the ELS search process, the definition of the compactness measure, the control text population, and the computation of the test statistic.
  4. The experiment with N trials executes the protocol on the Torah text and then randomly samples N-1 texts from the control text and executes the identical protocol on each of the N-1 sampled texts.
  5. The fraction of texts having as compact a table as the Torah text is the estimated probability that a table as compact as the Torah text table would be found by chance.
  6. The probablity is called the p-value of the experiment.


  1. The fraction of texts having as compact a table as the Torah text is the estimated probability that a table as compact as the Torah text table would be found by chance.
  2. When the p-value is sufficiently small it is an indication that something unusual may be going on in the Torah text.
  3. When the p-value is sufficiently small the Null hypothesis of No Torah Code effect is rejected in favor of the alternative hypothesis for the respective set of given key words.
  4. The alternative hypothesis is that there is a Torah code effect for the set of given key words.

Experimental Protocol

In order to do an experiment to determine the probability that as good a table as found in the Torah text would happen by chance, an experimental protocol must be followed. The experimental protocol specifies in an a priori way how the experiment is done in sufficient detail that the experiment with its results can be replicated by other people. A priori means that the protocol is specified before doing any experiments and before looking at the text in any way for ELSs of the key words.

In the case of Torah code experiments involving one set of key words, the exprimental protocol must have: the given set of key words, an ELS skip specification, a cylinder resonance specification, the compactness measure to be used, the control population from which the p-level will be estimated. Torah code experiments involving more than one of set of key words have more complicated protocols.

Key Word Set

The set of key words describing an event or partially describing an event, or making up a sentence about the event, must be specified before looking for any ELSs of these key words in the Torah text and before doing any kind of interactive snooping for ELSs of these key words. The event associated with the key words must have occurred prior to the specification of the key word set.

Torah code critics claim that all Torah code experiments producing small p-values can be explained by hypothesizing that the researcher doing the experiments was not honest and in fact the key words used were not a priori. In that case, the probabilities produced by the Monte Carlo experiments are meaningless.

Skip Specification

The ELS skip specification tells for each key word the minimum and maximum skip permitted. The search process then finds all ELSs from the minimum skip specified for the key word to the maximum skip specified for the key word.

Cylinder Resonance Specification

The cylinder resonance specification specifies the relationship between the cylinder size and the skip of the ELS which qualifies for resonance. For example the maximum row skip and maximum column skip an ELS can have on a cylinder is one way of specifying a resonance criteria.

Compactness Specification

The compactness measure specification indicates the choice of compactness measure, such as area of best table containing one ELS of each of the given key words, or the furthest distance between the pairs of the letters of the ELSs on the the best cylinder size. Compactness measures that attempt to evaluate redundant encoding involve more than just the best table.

Control Population Specification

The control population determines the meaning of the probability that a table of compactness measure better than a given size would occur by chance. The most meaningful group of control populations is a control population of texts. In this case the probability that as good a table would happen by chance means the fraction of texts in the control population whose best table is more compact than the compactness of the best table of the Torah text.

Text populations that are monkey text populations can be created by various random shuffling techniques. These include letter shuffling, word shuffling, verse shuffling, and chapter shuffling. Letter and word shuffling can be done within verse, within chapter, within book, or globally. Verse shuffling can be done within chapter, within book, or globally. Chapter shuffling can be done within book or globally. All these shuffling techniques guarantee that the letter frequency of the text is preserved in all the monkey texts. However, the ELS statistics will change. To keep the ELS statistics the same we favor the ELS random placement monkey text population discussed.

In the ELS random placement monkey text population, the ELSs found in the Torah text are randomly placed. That is their skips are kept and their beginning positions are chosen at random. In this population, the number of ELSs and their skips are kept the same and the only thing that changes from text to text is the placement of the ELSs in the texts.

Website content by: Professor Robert M. Haralick