The Entropy Argument

Randall Ingermanson has a PhD in Physics, is an excellent programmer, enjoys writing fiction, and is currently working for Vala Biosciences. In his book Who Wrote the Bible Code he makes the following entropy argument against the existence of Torah codes.

If the Torah contains so much information embedded as ELSs in the text, then the entropy of the skip texts containing these ELSs must be lower than we would ordinarily expect. p 70.

"If the believer's [of the Torah code hypothesis] are right, then the ELSs in each skip text taken from the Bible will be measurably different from those you'd predict in a random text." p 86.

"If their [the believer's] interpretation is correct, the Torah must be chock-full of ELSs at many different skips. No matter which skip we consider, we ought to see many more meaningful ELSs than random chance predicts. This means that every skip-text must contain many more meaningful words (spelled both backward and forward) than you'd expect to see in a random text. The digram and trigram frequencies of intentionally encoded words are different from those you'd expect by random chance, and they result in different digram and trigram entropies than those you'd get by random chance." p 86-87.

"If the skeptics [of the Torah code hypothesis] are right, we expect that skip-texts taken from the original will have the same distribution of words, on average, as random skip-texts provided the skip is large enough." p 87.

Ingermanson then makes the entropy calculation for digrams and trigrams of Torah skip texts and finds that for skips greater than around 50 the Torah skip text digrams and trigrams have the same entropy as randomized texts. He concludes that there is no more structure in the Torah skip text ELSs than expected by chance and, therefore, the Torah code hypothesis must be false.

In summary, Ingermanson argues that if the Torah code hypothesis is correct, [this is the premise] there ought to be more words occurring as ELSs and if there are more meaningful word ELSs there will be more statistical structure or order in the skip texts and therefore, the entropy of Torah skip texts ought to be lower than the corresponding entropy of randomized Torah skip texts [this is the consequence].

He makes the measurements and finds that the entropy of the Torah skip texts are not lower than the corresponding entropy of randomized Torah skip texts. Having provided evidence that the consequence is not correct, he concludes that the premise is false.

The argument is fallacious because Ingermanson does not understand the Torah code hypothesis. The Torah code hypothesis is that there are some domains of logical/historical relationships where if one collects together clusters of key words that are logically/historically related from the domain, then there will be a higher probability that there are more corresponding clusters of ELSs of these key words that are more compact (spatially close) in the Torah text we have today than expected in a population of randomized Torah texts.

The Torah code hypothesis does not imply as Ingermanson argues that if the Torah code hypothesis is correct, there ought to be more semantically structured ELSs with lower entropy skip texts. The Torah code hypothesis is completely consistent with a condition that the number and kind of ELSs are exactly what would be expected by chance. The Torah code hypothesis states that the placement of the ELSs in the Torah text is skewed in such a way that there is a higher frequency of ELSs of related key words that appear closer together than expected by chance.

Basically, what Ingermanson has done is to restate the Torah code hypothesis in a way that is not equivalent to the true Torah code hypothesis, and then he provided evidence that his restatement of the Torah code hypothesis must be false. His evidence has no bearing on the correctness or incorrectness of the true Torah code hypothesis.