Torah Code History
The Early Years
The first documented reference to equal distant letter skips is by Rabbi Bachya ben Asher (1255-1340). He writes of a 4 letter 42 letter skip Equidistant Letter Sequence (ELS) beginning from the first letter of the Torah that relates to the average length of the lunar month. For a complete explanation of how this 4 letter ELS produces an amazingly accurate average length of the lunar month, see the discussion on the first els.
The Ramak, Rabbi Moshe Cordovero, (1522-1570) served as the Head of the Rabbinical Court ("Av Beit Din") in Tzfat, Israel, during the 16th century. This was a time when Tzfat stood as the worldwide center for Jewish scholarship. His book Pardes Rimonim is a voluminous commentary on the Zohar. He writes in the introduction to Gate 30 that there are several ways that there is hidden information encoded in the Torah.
The secrets of our holy Torah are revealed through knowledge of combinations, numerology (gematria), switching letters, first-and-last letters, shapes of letters, first- and last- verses, skipping of letters (Dilugai Otiyot) and letter combinations.
These matters are powerful, hidden and enormous secrets. Because of their great hidden-ness, we do not have the ability to fully comprehend them. Further, to see different angles through these methods is infinite and without limit. On this the Torah says, its measure is longer than the world.
It was the cryptic comment by Rabbi Bachya that influenced Rabbi Michael Dov Weissmandl to engage in his study of the Torah codes. Rabbi Weissmandl was the Slovakian rabbi who developed a smuggling operation near the Slovak-Polish border, which enabled thousands of Jews, at a high ransom price, to reach then relatively safe Slovakia or Hungary. Then Germany invaded Hungary and deportations began in the Spring of 1942. After 60,000 had been sent to Auschwitz, Rabbi Weissmandl succeeded in negotiating with Dieter Wisliceny, Eichmann's assistant, and was able by a $50,000 bribe to halt further deportations. Unfortunately, the deportations were only delayed.
Rabbi Weissmandl was fascinated by Bachya's cryptic comment on the 4 letter ELS. He was certain that there was within the Torah, coded in equidistant letter sequences, divinely ordained information. He wrote out on white cards 10x10 arrays of the entire 304805 letter Torah and studied it for ELSs that were near multiples of 10. After his death in 1957 his Talmud study students edited their notes of Rabbi Weissmandl's teachings, including some of hist Torah codes and published the book Torat Chemed.
In 1976, Rabbi Shmuel Yaniv began working on equidistant letter sequences and associated gematrias, specifically with respect to religious themes. And he began to incorporate this code point of view in his religious lectures. Rabbi Yaniv published his first book צפונות בתורה, Tzefunot Ba'Torah, Volume 1, in 1988, his second book with the title צפונות בתורה, Tzefunot Ba'Torah, Volume 2 in 1989, and his third book with the title צפונות בתורה, Tzefunot Ba'Torah Volume 3,4, in 1990. All his books are in Hebrew. The translation of the title of his 4 volume book is Hidden Things in the Torah.
It was Rabbi Yaniv's teachings in the late 1970's that influenced Professor Eliyahu Rips to examine the Torah from the point of view of codes. It was also Rabbi Yaniv who told Professor Rips about the existence of Rabbi Weissmandl's book Torat Chemed.
The students of Rabbi Weissmandl wrote in the book that they do not remember some findings that Rabbi Weissmandl told them about. For example, they did not know where was the exact location of the ELS Torah with skip -50 at the end of the book of Numbers. Rabbi Shmuel Yaniv told Professor Rips that Avraham Oren had searched for the forgotten findings of Rabbi Weissmandl and was able to restore some of them.
It did not take long for Professor Rips to meet with Avraham Oren who was delighted to show Rips his archive of findings. Most of Oren's work was done using hand-written tables, but in some instances he utilized the then available Apple II computer. Therefore, Avraham Oren must be credited as the first one who used a computer in the search of Torah Codes.
Looking into the archive of Avraham Oren, Professor Rips noticed that there were several tables located in the beginning of the book of Leviticus that contained an ELS of אהרן, Aaron. He was intrigued and decided to check whether there were some more appearances of Aharon in the same passage Leviticus Chapter 1 Verses 1-13. For this, he needed a computer program. This program was written by the late Dr. Boris Zukerman z"l in the very early eighties. Given the number of the letters א ה ר ן in this passage, and assuming the text to be a random shuffling of its letters, with the maximum absolute skip set to 200, the statistical expectation of the number of ELSs of אהרן in the specified passage is about 8.3 The program of Dr. Boris Zukerman found 25 ELSs of the key word אהרן in this passage. This became known as the cluster of אהרן. Professor Rips then checked what happens if the same search were to be made in a random letter permuted text. He also ran some other statistical tests. All of them were consistent with the calculated value 8.3. Under the assumption that the Poisson distribution is applicable, the probability that this event of 25 ELSs of the key word אהרן would happen by chance is about 1 to several hundred thousands. This was the first instance of a scientific study of Torah Codes, or, at least, of an application of statistical methods to the study of Torah Codes. More details of this study can be read about in Michelson's article.
Shortly after Professor Rips first met with Rabbi Yaniv, he met Dr. Moshe Katz who was also aware of Rabbi Weissmandel's findings and planned to study the Torah Codes himself. For some time Rips and Katz worked together.
Professor Rips continued to study the Torah Codes focusing on the beginning of the book of Genesis. He did not have a computerized text of the Torah then, not even of the book of Genesis. He only had the first three thousand letters. He was trying to find some more clusters like the אהרן cluster. It turned out that this passage indeed contains a number of clusters like for the words Makom, Mikve, Eden and some others concentrated near the appearances of these words in the plain text. However, none of them was as statistically impressive as the אהרן cluster. In 1988, the אהרן cluster work was published in the Journal of the Royal Statistical Society, Series A, Vol 151, p165.
In the course of his research Professor Rips made the observation that some words appear as ELSs with small skips near the place where the word appears in the plain text. For example, the word Makom, place, appears with the skip 2 starting with the letter in position 354 of the text while its appearance in the plain text starts with the letter in position 374. A table showing all the ELSs of מקום from the second verse of Genesis through the 2 nearby ELSs that Professor Rips had observed is shown in the table below.
Another instance of clustering was for the key word גלות, Exile. The number small skip ELSs of this key word in the text of Genesis are: 4 skip 1 ELSs, 2 skip 2 ELSs, one skip -3 ELS and one skip 3 ELS. The small skip ELS of גלות that Professor Rips observed is the skip -3 ELS. As there are only two absolute skips smaller than skip 3, each one of the skips having some ELSs, Professor Rips describes this small skip ELS in the cluster he observed as the third minimal skip ELS of גלות. The table below shows the cluster that Professor had observed.
The cluster is in the story of Lot. Recall a mob of men from Sodom tried to grab the angels who were visiting and being sheltered by Lot and take them to the street to sodomize them as they did with all male visitors to Sodom. The last part of the verse Genesis 19:9 says they approached to break the door [ of Lot's house], ויגשו לשבר הגלת. The table below highlights this phrase in the exile cluster table.
This verse and its context struck Professor Rips as being significant. He thought about the many pogroms to which the Jews in exile had been subjected throughout history. In particular, he recalled the pogroms in Russia: in the period of 1881 through 1884, there were over 200 pogroms in the Russian Empire, those in Kiev, Warsaw, and Odessa. From 1903 through 1906 there were pogroms in 64 towns and 626 small towns of the Russian Empire. After 1917, there were an estimated 70,000 to 250,000 Jews who were killed in Russian pogroms. For more details read the wiki article. So he decided to look for ELSs of the key word פוגרום, pogram that might be close to the phrase: they approached to break the door. What he found surpised him: an ELS of פוגרום crosses the phrase ויגשו לשבר הגלת sharing the letter ג. This is shown in the table below.
This is an example where the ELS is not a small skip ELS. There are 7 ELSs of the key word פוגרום and the ELS shown in the table above is the fifth from the minimal skip ELS in Genesis or the third from the maximal skip ELS in Genesis.
In ancient times, the battering ram would be used to break down the door. The earliest Assyrian battering ram dates from about 900BCE. The time of Lot is many hundreds of years before this and we suppose that battering rams were not known in the time of Lot. But the idea that to break down the door you have to hammer at it was certainly known. It is interesting to see that crossing the phrase they approached to break the door is an ELS of the key word פטיש, hammer. This is shown in the table below.
The pogrom experiment led Professor Rips to hypothesize that not just small skip ELS might be important, but large skip ELSs also could be important if they their rank from the minimal skip ELS is not that far.
Later, but still in the early eighties, Professor Rips talked with Doron Witztum who had lived, through 1979, in the same French Hill neighborhood as Professor Rips. Witztum had been a PhD student at the Hebrew University studying and teaching physics. He did his first degree in both math and physics and his second degree in physics, specializing in general relativity. He left his physics studies in 1977 to spend all his time learning Torah. In the spring of 1985 Witztum decided to do some research of his own on Torah codes. Professor Rips gave him a program for searching for ELSs and this enabled him to do his work on the computers at the Jerusalem College of Technology. In the Spring of 1985 Witztum had results he thought interesting and shared them with Professor Rips.
Witztum and Rips tell that they realized that the Torah code phenomena occurred with those ELSs that are minimal on large portions of the text, including even ELSs with very big skips, and excluding short skip ELSs which are minimal skip ELSs on only short portions of the text. This came to be known as the principle of minimal skips: the better ELSs are those which are closer, in rank, to being minimal skip ELSs, even if their skips were large in absolute magnitude.
Witztum suggested focusing on ELSs that are minimal skip ELSs on large portions of the text and examine them for two kinds patterns:
- Meetings between minimal skip ELSs of one expression with a conceptually related expression in the string of letters of the Torah text itself
- Meetings between near minimal skip ELSs of two conceptually related expressions
It was at this meeting that Witztum suggested that the proximity of the two patterns should be measured on two-dimensional arrays. Specifically, for a given ELS with skip s to consider cylinders with circumference s, s/2, s/3 etc.
Witztum called this the principle of two-dimensional writing and it is on such code cylinders that all Torah code tables are shown today. Witztum's ideas were immensely fruitful.
During 1985 through 1987 Doron Witztum produced a stream of remarkable findings. Professor Rips was particularly impressed with Witztum's discovery of the הגאון מוילנא, The Gaon of Vilna, code. The minimal skips for both key words in the book of Genesis have a remarkable meeting in a segment of only 46 letters out of 78064 letters of the book of Genesis. This meeting is shown in the table below.
Witztum's French Revolution Study
One of Witztum's early studies was of the French Revolution, an important historical topic. In a period of three years, the royal monarchy that had ruled France for hundreds of years collapsed. In some senses this was the start of equal rights for all men in the European countries. The first Witztum table we show uses the key words מהפבה הצרפתית, French Revolution. הצרפתית, French, has only one ELS in the book of Genesis and it is therefore the minimal skip ELS.
The second table below shows the meeting Witztum found in Genesis of the smallest skip ELS for the key word בצרפת, In France with the key word מהפבה, Revolution.
The flashpoint of the French Revolution was on July 14,1789 when mobs stormed the Bastille which represented the royal authority in the center of Paris. While the prison only contained 7 inmates at the time of its storming, its fall became an icon for the French Revolution. The table below shows the closest meeting between ELSs in Genesis of the key words Bastille and Revolution. Notice that the ELS for מהפבה, Revolution, in this table and the previous two tables is the same skip 9 ELS. This ELS tightly links together these three tables, tables appearing on very different and non-resonant cylinder sizes.
By the late 1980's Witztum put together his findings in his first Torah code book, המימד הנוסף, The Additional Dimension, which was published in the winter of 1988.
The Great Rabbi's Experiment
In the summer of 1985 Doron Witztum, Eliyahu Rips and Yoav Rosenberg (WRR) decided to investigate convergences between ELSs of the names and appellations of famous rabbinical personalities and their dates of birth and death. This study would be a formal study of the meetings between near minimal skip ELSs of two conceptually related expressions. At that time Yoav Rosenberg was a student at the Jerusalem College of Technology. It was he who wrote the program. Later he went on to complete his PhD in Computer Science at Hebrew University.
To this end a list of personalities was prepared, using the Encyclopedia of Great Men in Israel for the basis of the list. The list was to include only the most famous individuals, i.e. those whose entries consisted of at least three columns of text, and for whom dates of birth and/or death were cited. A list of names and appellations was prepared before the experiment began, by Professor Shlomo Havlin, then head of the Department of Bibliography and Librarianship at Bar Ilan University, following professional guidelines. The rules of orthography and the form of the Hebrew date were also established a priori by the linguist Yaakov Orbach, of blessed memory.
Measurements of the convergences indicated that there is a very strong tendency for the some of the appellations of the personalities to converge with their associated dates. WRR published their results in a Hebrew University report describing their research, in the autumn of 1986.
The report was sent to Professor Diaconis, who is a statistician. Thinking that the experimental results was due to tuning the method to the data, he proposed that a new list of famous personalities be prepared, to be investigated using the exact same program. To compile the new list WRR took those personalities whose entries in the Encyclopedia of Great Men of Israel were between 1.5 and 3 columns of text, and for whom a date of birth and/or death were cited. The dates were written in exactly the same format as was previously established. This time, too, the list of names and appellations was prepared a priori by Professor Havlin, using the same professional criteria. Measurements were made using the same program as in the first experiment. The results were very successful.
A paper describing the two experiments was published as a Hebrew University report in the winter of 1988. A shortened version of this paper was submitted for publication in Proceedings of the National Academy of Sciences by Professor Robert Aumann. Professor Diaconis was one of the reviewers. In a letter to Professor Aumann, dated 3 Aug. '88, Professor Diaconis suggested that a permutation test be used to estimate the p-value of the result. Eventually the details of the test, the number of permutations and the requisite level of significance, were agreed upon by Professor Diaconis and Professor Aumann (as laid down in a letter dated 7 Sept. '90, written by Professor Aumann and approved by Professor Diaconis two days later). Professor Aumann delivered a copy of the agreement to WRR. At Professor Aumann's recommendation a new paper was composed, even before the experiment was run. This version described the new test, leaving out the results, which did not yet exist. This paper was sent to Professor Diaconis and to several other well known statisticians. They approved the test as it was described in the paper, and they stipulated (each one independently) the level of significance that should be required.
The experiment was run in the winter of 1991. The results were very significant: pvalue = 0.000016, well beyond the proposed cutoffs. The results were then incorporated into the paper. The paper was finally published in the journal Statistical Science, Vol. 9 (1994) No. 3, 429-438. The journal article indicates the affiliation of both Witztum and Rosenberg at Jerusalem College Of Technology. That affiliation arose because Jerusalem College of Technology gave them access to their computation facility in return for the agreement to list their affiliations as the Jerusalem College of Technology.
The method designed by Witztum and Rips in the great rabbi's study for scoring compactness is interesting. It involved two independent components. The first component was the compactness of pairs of ELSs in terms of their geometry on the cylinder. The second component involved the quality of the ELSs. The quality of the ELSs itself had two components. The first component was the fraction of the text over which the ELS is minimal. The second component was that in searching for ELSs, the maximum absolute skip was set so that the expected number of ELSs for the key word would be about 10. In later years, Torah code researchers like Professor Haralick did not fully appreciate the need for incorporating the quality of the ELS in terms of the fraction of the text over which the ELS was minimal or in terms of a ELS quality measure like the Rotenberg R-value. All the tables on this site have been created using a protocol that uses area of the table as the compactness for the geometry component and the maximum absolute skip being set on the basis of expected number of ELSs. The resulting compactness measure is undoubtedly less sensitive a detector than the original Witztum and Rips design.
The WRR publication caused a controversy. A discussion of the controversy can be found at http://www.torah-code.org/controversy/controversy.shtml. Some aspects of the controversy are explained in http://www.torah-code.org/papers/icpr98.pdf. Witztum's website is http://www.torahcode.co.il/ and has his extensive remarks on the controversy. The Torah code opponents not only systematically maligned Witztum and Rips as if they were corrupt politicians, but carried on an agenda of doing methodologically incorrect non-apriori experiments to show that compact tables can be found not only in the Torah but in non-Torah books as well. Indeed counterfeit experiments produce counterfeit results. This whole controversy from the counterfeit side, cased in language that has the appearance of mathematical and statistical correctness can be found in the website of Professor McKay, in the writings of Dr. Dave Thomas of Skeptical Inquirer, in the website of Professor Simon, and the website of Avraham Hasofer.
Following publication of the paper in Statistical Science, in March 1994, Professor Rips was invited to give a guest lecture to the Israeli National Academy of Sciences on the subject of: ELS's in the Book of Genesis: the Statistical Significance of the Phenomenon. A paper (in Hebrew) with this title, co-authored by WRR, was submitted to INAS but was not published.
In 1995 WRR published as a preprint an article entitled: Equidistant Letter Sequences in the Book of Genesis: II. The Relationship to the Text . This article dealt with convergences between expressions appearing as ELS's and expressions appearing in consecutive letters in Genesis. One of the samples discussed in the article was the Nations Sample. Measurements conducted on this sample indicated a particularly high level of statistical significance: the p-level for one of the two statistics used, was better then 4/1,000,000,000. In light of criticisms leveled against the composition of this sample and its measurement, by Professor Bar Natan, Professor McKay, and Professor Sternberg, a new and refined study was conducted which led to p-value of 5/100,000,000,000. Thus, a careful analysis of the critics' data and suggestions led to new results supporting WRR research hypothesis with high significance.
Since WRR's experiment using the second list, other experiments involving different lists have been conducted, including several designed to replicate the original second list experiment. A number of works and published papers are found at Witztum's website. At the beginning of 1999, several lists of names and appellations were compiled by Dr. Simcha Emanuel, a specialist in rabbinical history at Tel-Aviv University. He was engaged by MBBK (McKay, Bar-Natan, Bar-Hillel & Kalai), opponents of the Codes' research, and his work was guided by them without WRR's knowledge. One of the lists was intended to "mimic" WRR's second list. Emanuel's new list contains names and appellations of the personalities included in WRR's second list, which he collected without seeing Prof. Havlin's original names and appellations for it. Witztum repeated WRR's original experiment exactly, with one single change: Instead of Havlin's names and appellations, he used Emanuel's. The experiment succeeded with considerable significance. You can read about it in the paper New Statistical Evidence for a Genuine Code in Genesis. In 2004, Witztum published his second book צופן בראשית, The Code of Genesis which describes and explains his research and gives an accurate account of the Torah Code phenomena. As well it also the documents that the complete story of the WRR publication in Statistical Science. Mr. Witztum published a paper The Hidden Birth Dates of Personalities of Genesis at the 2006 International Conference on Pattern Recognition.