Professor Rips has maintained that long ELS phrases is one of the most promising research areas in Torah Codes. He has asserted that meaningful long ELS phrases "can be found [in the Torah text] with relative ease." And indeed he has a large collection of them. We are hopeful that he will organize them and give us permission to show them on this website.

Testing the hypothesis that meaningful long ELS phrases occur more often in the Torah text than in monkey texts is not an easy hypothesis to test. The problem centers around computing maximally long ELS phrases, each of whose ELSs is a word in a given lexicon of tens of thousands of words, and evaluating the degree to which an ELS phrase is meaningful. Some research work has been done in the evaluation of meaningfulness of an ELS phrase. Unfortunately, the methodology is very labor intensive and it is too costly to run many experiments. The Long ELS phrase reported here uses an automated way of trying to differentiate the Maximal ELS phrases coming from the Torah text from those coming from a monkey text without any direct linguistic evaluation of meaning or semantic connectedness.

We have developed a special fast algorithm to be able to find all the maximal ELS phrases in a text using a lexicon of even some tens of thousands of key words. Using this tool we can examine the maximal ELS phrases from the Torah text and see if there is any statistic by which they are different from those of monkey texts. The statistics we use are the best ones we can think of for which there is a simple algorithm to compute them. However, what they measure is most certainly a weak derivative of meaningfulness and they in fact may not be powerful enough to capture what they really need to measure.

We have begun this examination using two statistics of an ELS phrase: a feature called difficulty class and the Conditional Entropy per letter. The difficulty class of an ELS phrase is defined by Professor Rips as the phrase length (not including spaces between words) minus three times the number of words in the phrase. The conditional entropy per letter is the average number of bits it would take to guess the next letter of the ELS phrase given the previous K letters. In our experiments we take K to be 4.

Our entropy feature is different from that used by Dr. Ingermanson. He only used entropy of digrams and trigrams, letter subsequences of two successive letters or three successive letters on entire skip texts without reference to any lexicon. By contrast, we only consider maximal ELS phrases composes of words from a lexicon. And our entropy statistics are computed from subsequences of five successive letters, rather than two or three. We estimate the distribution of subsequences of 5 letters at a time, including the space character, from a Hebrew Corpora composed from a variety of sources. Our Hebrew corpora has about 60 million letters so far. Our maximal ELS phrase is composed of equal distance letter sequences at a uniform skip formed of words in our lexicon and in which we put the space character between each pair of successive words. Maximal means that the ELS phrase cannot be extended either from its beginning or from its end.

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