by Doron Witztum
Twenty years ago, Doron Witztum discontinued his advanced studies and work in Physics at the Hebrew University in Jerusalem in order to dedicate himself to full-time Torah study. In his own words, “motivated by certain sources of our sages, inspired by the findings of Rabbi Weissmandl, zt”l, and encouraged by gedolai Torah,” he spent the past ten years researching Torah Codes. Renowned as the preeminent codes researcher, he is the author of Hameimad HaNosaf (The Added Dimension) published in 1989.
Professor Barry Simon informs us, at the conclusion of his article, “A Skeptical Look at the Torah Codes,” that he hesitated before presenting his doubts about the existence of Torah Codes. Those hesitations were overcome, however, by reminding himself that HaKadosh Baruch Hu’s seal is truth.
Devotion to truth, alas, is not proven by how loudly one proclaims his allegiance, but by one’s exertions in its pursuit. Here Professor Simon’s efforts have fallen short. The arguments he presents against the Codes are a rehash of those made by others over the past year on internet and in other media.
Had Professor Simon approached me before writing his article, I would have provided him with complete and detailed answers to all these claims. In light of the fact that I have been the primary researcher in Torah Codes for the last 12 years, his failure to do so before writing what purports to be an overview of the subject is little short of astounding. (Full responses to opponents of the Torah Codes can be found at internet web site http://www.torahcodes.co.il and in my forthcoming book on the subject.)
Professor Simon did spend a few hours with my colleague Professor Eliyahu Rips of the Hebrew University, but according to Professor Rips the discussion touched superficially on only a few technical aspects of the research. Convinced that Professor Simon did not understand the phenomenon revealed by our research, Professor Rips was eager to meet with him again - even offering to fly to the United States at his own expense to do so — but Professor Simon replied that he was “too busy.”
Not surprisingly, given Professor Simon’s half-hearted search for the truth, his article is rife with factual errors and misinterpretations, misquotations, and mistaken conclusions.
Before detailing his major failings in each of these areas, however, a general discussion of Torah Codes in the mesorah is appropriate.
Torah Codes in the Mesorah
It is axiomatic for all believing Jews that the Torah is the repository of all knowledge. Torah is the blueprint for Creation. As the Zohar puts it, “HaKadosh Baruch Hu looked into the Torah and created the world.” In some sense, everything is included in the Torah. As Ben Bag Bag says, “Delve into [the Torah] and continue to delve into it, for everything is in it” (Pirkei Avos 5:26). According to the Ramban (in his introduction to his commentary on the Torah), the Vilna Gaon, and others, not only are the general outlines of world history contained in the Torah, but the precise details as well. In his commentary on Sifra d’Tzniusa, the Gaon writes: The rule is that all that was is and will be, until the end of time, is included in the Torah from [the word] “Bereishis” to “l’eynei kol Yisrael.” And not merely in a general sense, but including the details of every species and every person individually, and the most minute details of his life from the day of his birth until his death.
Obviously these details are not explicit in the Torah but contained in remazim, “hints,” of various types. One of these types of hints is in the form of Equidistant Letter Sequences (ELSs), words formed by counting at set intervals between letters in a particular text. Rabbeinu Bachya, one of the greatest of the early kabbalists, mentions an example of an ELS in his commentary on Bereishis, and comments that its appearance is the result of intentional design.
Rabbi Moshe Cordovero, one of the leading mystics of Safed, describes in the thirtieth “Gate” of his monumental work Pardes Rimonim the various ways in which the Torah encodes information. Among these, he mentions ELSs.
In our century, Rabbi Chaim Michael Dov Weissmandl, famed for his heroic rescue activities during the Holocaust, discovered many amazing examples of ELSs in the Torah. In perhaps the most famous example, Rabbi Weissmandl found that beginning with the first tav in both Bereishis and Shemos, and counting at 50-letter intervals (50 being the number of the Gates of Wisdom), one finds the word Torah spelled out.
Perhaps even more amazingly, given that Rabbi Weissmandl was operating without benefit of a computer, it is known that he made a number of findings concerning Megillas Esther using skip distances of 12,111 letters, the exact number of letters in Megillas Esther. I was able to reconstruct one of these using a computer. If one starts with the first regular mem (as opposed to “final mem” ) in Bereishis 4:14, where the name Esther (vocalized differently) appears for the only time in the Torah, and counts at intervals of 12,111 letters, one finds spelled out the phrase “Megillas Esther.”1
Prior to the Holocaust, Rabbi Weissmandl showed his findings to the gadol hador, Rabbi Chaim Ozer Grodzensky of Vilna, who was very impressed by them. Years later, the Steipler Gaon described Rabbi Weissmandl’s discoveries as stemming from ruach hakodesh [Divine inspiration].
Modern Research in the Codes
More than a decade ago, Professor Eliyahu Rips of the Department of Mathematics of Hebrew University became aware of some of Rabbi Weissmandl’s research. Rabbi Weissmandl had shown patterns of ELSs that intuitively seemed far too strong to have been accidental. The question that Professor Rips asked himself was: Using modern computers and employing a scientific methodology, can the existence of codes in the Torah formed by ELSs be demonstrated?
After Professor Rips’ early research in the topic, he asked me to join him in this enterprise. I hesitated. I was then learning Torah full time, and had given up my doctoral work in physics to do so. If anything were to come of this project, it would obviously be very time-consuming and distract me from my Torah studies.
I consulted with HaRav Shlomo Fisher, who encouraged me in the strongest terms to engage in this research. One of the questions I asked Rabbi Fisher at our first meeting on this subject was whether our text of the Torah is accurate. He told me that we could fully rely on our text.2 Later, after we had achieved the first promising results, I spoke again with both Rabbi Fisher and Rabbi Shmuel Auerbach, and both insisted that I continue with the research.
Over the years, I also consulted on several occasions (twice together with Rabbi Fisher) with HaRav Shlomo Zalman Auerbach, zt”l, who gave me his blessing to disseminate our findings as widely as possible. We raised a number of issues with him in these meetings. One of these was the potential for others to create counterfeit codes, lacking any scientific foundation, that could be used for a variety of purposes, including by Christian missionaries.3 Rabbi Shlomo Zalman assured us that this would happen, but nevertheless told us to carry on. “Don’t pay attention to scoffers and gentiles,” he said.
Nine years ago, Professor Rips and I visited Rabbi Shlomo Zalman to discuss the criticisms of an Orthodox statistician from Australia, who was concerned about the use of the Torah Codes in kiruv work. Rabbi Shlomo Zalman’s response was the same: He smiled and told us not to worry.
Our initial research in Torah Codes produced some very exciting results. I discovered certain conditions under which conceptually related ELSs appear in close proximity to one another.4 Professor Rips made an important contribution by developing a measure of the statistical significance of the proximities discovered, and Yoav Rosenberg developed the necessary computer software for running the experiments.
After several minor experiments in different subjects, we decided upon a largescale experiment. Professor Rips suggested the idea of testing the proximity between the names of famous rabbis, expressed as ELSs, and the dates of their birth and/or death as expressed as ELSs (the so-called “Famous Rabbis Experiment”).
We created a list of famous rabbis comprised of all those whose biographies take up three columns or more in the Encyclopedia of the Great Men of Israel and for whom there were dates of birth and death. Having compiled our list, we realized that the names of these famous rabbis might be expressed by a number of different appellations. We approached Professor Shlomo Zalman Havlin, professor of both Talmud and Informations Sciences at Bar Ilan University, and one of the world’s leading experts in Hebrew bibliography, and asked him to create a list of appellations for the list of famous rabbis. At the same time, we requested that Yaakov Auerbach, z”l, a linguist, provide a set of spelling rules to be followed.
Using the list created by Professor Havlin and Yaakov Auerbach’s rules, we ran our experiment and obtained statistical results that were highly significant. These results were then sent to Professor David Kazhdan at Harvard University, who in turn forwarded them to Professor Persi Diaconis, one of the world’s leading statisticians. Professor Diaconis challenged us to run a new experiment on a second list of rabbis. This time we chose those whose biographies take up between 11/2 and 3 columns in the aforementioned encyclopedia, and again asked Professor Havlin to prepare a list of appellations. That experiment, too, yielded highly significant results.5
Defense of the Famous Rabbis Experiment
As the best-known verification of the Torah Codes, the “Famous Rabbis Experiment” has attracted the majority of fire from those who reject the existence of Torah Codes.
Those attacks have focused primarily on claims that the data was “cooked” in one way or another, and the experiment was not a true a priori experiment following fixed rules determined in advance. Essentially the claim is that we first ran a multitude of experiments until we achieved statistically significant data, and only then did we develop our rules for the experiment to comport with the data.
Professor Simon follows that approach.6 He is too much the gentleman to say outright that we only reported on our successful results out of a multitude of failures. But that is his basic claim. Indeed, he repeatedly characterizes various aspects of the experiment as ad hoc, i.e., based on rules determined after the fact, rather than a priori.
Professor Simon begins his critique of the “Famous Rabbis Experiment” by charging proponents of the Torah Codes with grossly overstating the significance of the fact that the results of the experiment were published in a respected, refereed scientific journal. We can readily concede his general point that the truth of the conclusions of an article published in a scientific journal are not established just because the article has been subjected to peer review by other experts in the field.
That point, however, has no relevance to the extraordinary scrutiny to which our paper was subjected. When our article was first submitted for publication in the Proceedings of the National Academy of Sciences (PNAS), it had already undergone careful scrutiny by Professor Diaconis, as described above, and we had run a completely new experiment at his suggestion.
Contrary to what Professor Simon alleges, we neither “refined” nor changed our analysis in any way from the first experiment to the second. We ran the new experiment without any changes in the method of measurement. This is fully confirmed by our correspondence with Professor Diaconis. (Even the fiercest opponents of the Torah Codes, psychologist Maya Bar Hillel and mathematicians Dr. Dror Bar-Natan and Dr. Brendan McKay [hereafter “McKay et al.”] admit this.)7 To the surprise of Diaconis, the results of the second experiment were also highly significant.
At the PNAS stage, our article was referred for peer review to six famous statisticians, including Professor Diaconis, each of them a member of the National Academy of Sciences. Because of the amazing claim made by our research, they checked the results very carefully.
After receiving the second preprint, Professor Diaconis had a further request for us. He asked us to employ a new statistical test devised by him on the second list of rabbis to assess the likelihood of our findings appearing at random. He and the other referees were so confident that the new test would completely destroy our results that they required us to sign an agreement that even if the new experiment resulted in failure we would publish the results from the new experiment along with our previous results.
Professor Diaconis and his colleagues were shocked when, employing his measures of statistical significance, we once again obtained highly significant results for the list.
Despite having passed all hurdles set up by Professor Diaconis and the other peer reviewers, they ultimately recommended against publication of the results of our experiment in PNAS on the grounds that there was a “lack of public interest” in the phenomena described. Strangely, they only came to this conclusion after having made repeated demands upon us for years. Their conclusion of a lack of public interest is even more curious when one considers that Michael Drosnin’s pseudo-scientific and sensationalist book on “Bible Codes” was an international publishing phenomenon this past year.
After the rejection by PNAS, we submitted our article, with the results of the Diaconis experiment, for publication in Statistical Science, where it was subjected to further peer review. Only after nearly eight years from the time the paper was first sent to Professor Diaconis, during which time none of the eminent reviewers were able to find any error in the methodology or conclusions, was the article finally published. In his introduction to our article, Professor Kass, then editor of Statistical Science, wrote:
When the authors used a randomization process to see how rarely the patterns they found might arise by chance alone, they obtained a very highly significant result, with p=0.000016 [a probablility of 1/62,500]. Our referees were baffled: their prior beliefs made them think the Book of Genesis could not possibly contain meaningful references to modern-day individuals, yet when the authors carried out additional analyses and checks the effect persisted. The paper is thus offered to Statistical Science readers as a challenging puzzle.
What I have described is hardly the normal process of peer review described by Professor Simon.8
In his concluding section, Professor Simon spells out his “strongest reason” for skepticism concerning the Torah Codes: the sensitivity of the experimental results in the “Famous Rabbis Experiment” to the specific appellations chosen for rabbinic figures whose dates of death and birth are being searched. Here he relies entirely on what he terms the “devastating analysis” of Drs. Dror Bar-Natan and Brendan McKay.
In an article posted on the internet in late Elul entitled “Equidistant Letter Sequences in Tolstoy’s War and Peace,” McKay et al. claim to have reproduced the same phenomenon described in our original paper in a Hebrew translation of War and Peace. Now obviously, they do not think that War and Peace is encoded. Their point is rather that our results do not show an intentional code in Bereishis either.
Far from disproving the existence of the Torah Codes, however, the results of the War and Peace experiment ironically provide strong evidence of the rigidity of our experimental rules. Two points deserve to be highlighted about the McKay’s results: (1) The alleged “success” in War and Peace was produced entirely by breaking the rules. Thus the results are completely lacking in significance; and (2) McKay and company did not demonstrate a single instance in which we deviated from our rules in carrying out the original research.
It is agreed by both proponents and opponents of the Torah Codes that without preestablished rules, it is possible to create the appearance of “success” in any text. That is why the “success” of McKay et al., which was achieved solely by breaking our rules, is without significance.
McKay and Bar-Natan admittedly manipulated the appellations used for the rabbis on the list. They prepared a list of appellations over many months, and went through a number of versions until they found one that worked — the exact opposite of an a priori experiment.
In defense of this procedure, however, they claim that they granted themselves no more leeway than we had in our choice of appellations or, alternatively, that they broke our rules no more frequently than we did. That claim is without foundation.
Though McKay and Bar-Natan admit that before our experiment was run on the second list of rabbis that all the experimental rules were firmly in place,9 they insist, however, that the rules governing Professor Havlin’s choice of the rabbis’ appellations were sufficiently flexible to explain our striking results. On that basis, they proceed to erase many appellations from our list and to add many others.
They have demonstrated no justifications for doing so. With respect to the names erased from the list, they have not shown a single instance in which Professor Havlin departed from his rules for compiling the lists of appellations. Of their additions, no more than five can arguably be said to be justified by Professor Havlin’s rules. Two of these five do not appear as ELSs in Bereishis, and the inclusion of the other two would have improved our results by a factor of 1.5.
Each of their other additions — and remember it is these additions which account for the “success” in War and Peace — border on the absurd: eight are complete fabrications;10 another eight are not pronounced (e.g., Bi is not an appellation for the Bais Yosef); and three violate the spelling rules, etc. These deviations from our research protocols were neither slight, nor legitimate, nor within the rules established by Professor Havlin.11
The reader will no doubt wonder how McKay and Bar-Natan could have relied on a list of appellations so laughable to anyone with even a passing knowledge of gedolai Yisrael and Hebrew. The answer is that their list was not prepared by anyone with bibliographic expertise.12
Since the only flexibility by which McKay and Bar-Natan justify their many erasures and additions was in the choice of appellations, their claim boils down to the charge that there is something “fishy” about Professor Havlin’s choice of appellations. (Let’s make no bones about it, they accuse Professor Havlin of having conspired with us to compose a list of appellations that would achieve successful results.) I have suggested, through an intermediary, to the leading opponents of the Torah Codes that instead of engaging in the parody of producing blatantly counterfeit new “codes,” that we should instead agree upon a mutually chosen bibliographic expert, provide him with Professor Havlin’s rules of choice and have him independently prepare a new list of appellations for the second list of rabbis on the basis of Professor Havlin’s rules. They have not picked up the gauntlet.
They prefer instead to employ tactics more appropriate to warfare than scientific inquiry. In war, it is common for one side to attempt to undermine confidence in the other side’s currency by circulating counterfeit currency. The ease with which the counterfeit code of McKay et al. is discerned, however, only serves to differentiate it from the Torah Codes and to buttress the veracity of the latter.
McKay et al. also charge us with having made biased decisions in formulating the research protocol. But they have shown almost no such choices not dictated by the nature of the experiment. (The decision to use the correct dates of birth and death for the rabbis on the list is, for instance, obviously dictated by the nature of the inquiry.)
At an academic conference last winter, Professor Maya Bar Hillel presented a list of 13 research decisions she claimed were biased in our favor. In a written response, Professor Robert Aumann, winner of the Israel Prize in mathematics and one of the world’s leading mathematicians, stated that he found only one research choice that could be said to be “favorable” that was not clearly dictated by the nature of the research. On the other hand, he found several which had a negative impact on the results.
Many of the “biased” decisions with which McKay et al. charge us, in fact, had the effect of reducing the statistical impact of our findings. For instance, they claim that we miscounted text lines in compiling our lists of rabbis from the Encyclopedia of the Great Men of Israel. But making the exclusions and inclusions in the list that they say should have been made, would have resulted in improving our best result for the second list from a random probability of four in a million to one in five million.
Elsewhere McKay and his colleagues ask why we did not place the preposition “u” before both the day of the month and the month in our expression of the date of birth and death. Yet doing so would have only increased the statistical significance of the results for both the first and second list of rabbis. McKay cites 20 separate decisions in our method of measuring the proximity of ELSs to one another. Yet 11 out of those 20 decisions had a negative impact on our data, and had we changed just one of them we would have improved our results a thousandfold.
Clearly, if we had prepared our research protocol after the fact, as McKay et al. charge, we did a very poor job of it.13
The Seal of HaKadosh Baruch Hu
Professor Simon states that he was guided throughout his inquiry by the statement of Chazal: “The seal of HaKadosh Baruch Hu is truth; Chosmo shel HaKadosh Baruch Hu Emes” (Shir Hashirim Rabbah 1:9). I decided to see whether the concept of Elokim Emes is encoded in ELSs in Bereishis. To do so, I checked whether the expression Elokim Emes appears as an ELSs in proximity to the word “seal” as it appears in Bereishis.
The first step was to list all the ways in which “seal” might be expressed:
- Chatom seal
- Chotam seal
- Hachotam the seal
- Hachotamthe seal
- Chotmo His seal
- Chotmo His seal
- Chotmi My seal (i.e., God writing about His seal)
- Chotmi My seal
Of these possibilities, only 1,2,3,5, and 7 appear as consecutive letters in Bereishis. Each of these words appears in exceptionally close proximity to an ELS of Elokim Emes. Calculating the probability of an ELS of Elokim Emes, in such close proximity to 2,3,5, and 7 (1 was omitted because its success was included in 3,5, and 7), I arrived at an overall probability of less than 1 in 2,500,000.
Indeed, the seal of HaKadosh Baruch Hu is truth.
- It has also been found that the name of Haman’s ancestor, Amalek, is found as an ELS with a skip distance of 12,111 letters in Bereishis. That ELS begins with the first ayin in the first mention of Amalek and ends with the koof in the second mention.
- A full treatment of this issue appears at our web site http://www.torahcodes.co.il, including a discussion of the well-known statement of the Gemara in Kiddushin (30a) that we are not experts in malei and chaser.
- Our concerns on this score have, unfortunately, been realized. Christians have indeed used “codes” in missionary activities. In my forthcoming book, I will demonstrate the various distortions in their use of “codes,” and how far they have departed from any scientific methodology.
- The full details of this discovery are beyond the scope of the present article, but are presented in full in my forthcoming book.
- In addition to the two experiments published as “Equidistant Letter Sequences in the Book of Genesis” by Doron Witztum, Eliyahu Rips, and Yoav Rosenberg in Statistical Science (Vol. 6, No.3), a number of other experiments have been run verifying the existence of Torah Codes. One of these experiments was performed by Harold Gans, formerly a senior cryptologic mathematician in the U.S. Department of Defense, specializing in code-breaking. He has shown in “Coincidence of Equidistant Letter Sequence Pairs in the Book of Genesis” (preprint) a significant correlation between ELSs of the appellations on both lists of rabbis and ELSs of the Jewish communities in which they were born or died.
Another three examples are presented in “Equidistant Letter Sequences in the Book of Genesis II: Relationship to the Text” (preprint) by Doron Witztum, Eliyahu Rips, and Yoav Rosenberg. Four additional examples produced by the same authors were presented in a guest lecture to the Israel National Academy of the Sciences and Humanities on Adar 28, 5756, and are described in “A Hidden Code in the Book of Genesis: The Statistical Significance of the Phenomena” (preprint).
Each of these ten experiments involved a list of pairs of conceptually related terms compiled according to objective and a priori criteria. Of these experiments, eight yielded results that were highly significant statistically, one was significant, and one was judged a failure. Additional examples will be described in detail in my new book. One of these can be found in the last section of this article.
- All references to Professor Simon’s article are to the version published on internet in early November, 1997.
- See their article in the Israeli magazine Galileo (Tishrei 5758). My response appears in the Kislev issue of the same magazine.
- The correspondence with Professor Diaconis will be published in my forthcoming book. I have confirmed that Professor Simon was made fully aware of this correspondence prior to publication of his article.
- They were firmly in place before the first experiment as well.
- E.g.Yitzchak Levi, harav”d sheini.
- These deviations are more fully discussed in my article “A Refutation Refuted” in Galileo (Kislev 5758) and in great detail at our web site.
- McKay et al. credit Professor Menachem Cohen of Bar Ilan University with helping them prepare their list. Professor Cohen’s area of expertise is not in bibliography; his field is Tanach. More importantly, Professor Cohen did not actually compile the list of appellations. That task was left to Aryeh Levitan who has no expert knowledge of gedolai Yisrael and who, as a nonnative Hebrew speaker, is prone to basic Hebrew errors.
- Professor Simon’s criticisms of my other Code experiments carry no more weight than those concerning the “Famous Rabbis Experiment.” For instance, in discussing the “Chanukah Codes,” he notes that there are three or four different ways in which Chanukah could have been spelled. True enough. But as a professional mathematician, Dr. Simon surely realizes that fact does not render it impossible to discuss the statistical significance of the result; it merely alters the result by a factor of 3 or 4. My results were highly significant, and remain so even after this adjustment. See, “Did They Really Find Chanukah Codes in War and Peace?” at our web site.
Dr. Simon makes essentially the same mistake in discussing the Seventy Nations example. He quotes Professor Rips as telling him that if we had used the term lashon instead of safat for “language,” the statistical effect would have disappeared. But Professor Rips told him exactly the opposite: The statistical result remains very highly significant.