Several years ago, astonishing statistical evidence was published regarding the existence of a hidden code in the Book of Genesis, relating to future events. New research deprives this evidence of its import by proving that the same code can be found in the Hebrew translation of War and Peace.
Maya Bar-Hillel Dror Bar-Natan Brendan McKay
A previous issue of Galileo contained an article by Zvi Atzmon titled: The Torah codes -- The unbearable lightness of the computer. Here we wish to describe the research of Witztum, Rips and Rosenberg1, which Atzmon only touched upon at the end of his article, and to present new research which casts serious doubt on their findings.
If you start from the first T in the Book of Genesis, and skip 49
letters, the 50th letter is an O. Skipping over another 49 letters
brings you to an R, and a final 49 letter skip brings you to A, thus
spelling the word TORA (which in Hebrew has just four letters) in
equal-letter-skips (ELSs). This amusing fact was discovered several
decades ago by Rabbi Weissmandel. What Weissmandel saw with the unaided
eye can nowadays be sought with the aid of computers, spanning much
longer text segments, and much larger letter skips. Such a search shows
that the word TORA can also be found as an ELS in War and Peace (the
Hebrew translation), for example, in the translation of the following
text from chapter one: ' "... said Anna Pavlovna. "You'll spend the
whole evening with me, I hope?" "And the fete at the English
ambassador's? ...", said the prince. '
A computer search for the names of two of the present authors, Maya and Dror, finds them, too, in Genesis (chapter 40, verse 1) as ELSs. Indeed, if a word is not too long (say, up to 6 letters), or its letters not too rare (e.g., in Genesis, the tenth letter yod is thirty times more common than the ninth letter tet), then there is an excellent chance of finding it as an ELS in any sufficiently long text (Genesis, for example, is 78,064 Hebrew letters long). The computer allows an easy search not only for single words, but for pairs of words as well. It can happen that thematically related words (such as the names of the authors) would appear close to each other, as in the phrase just cited.
In the mid '80s, Doron Witztum, a Jerusalemite born-again Jew, started looking for all kinds of words and word combinations in Genesis. His findings are described in his book: The Added Dimension2 (in Hebrew), which was also mentioned in Atzmon's article. The fact that "in any text of sufficient length ... it is possible to find various words as ELSs" (Atzmon, p. 34) did not escape the notice of Witztum and his collaborator in letter skipping, Professor of Mathematics Ilya Rips, another born-again Jew. They decided to run a kind of statistical test, and check whether the letter skips they were finding in the Torah were exceptional, or were merely an artifact of the multitude of letters and possibilities which the letter skipping method allowed. In his article, Atzmon called the results of this test "a line of statistical findings that could really trouble skeptics" (p. 32), and said that it "cannot be ignored, and is certainly disturbing" (p. 38). Atzmon was unaware that meanwhile research had been done which undermines the results that bothered him, and strips them of their significance. But before we describe that research, we should get a grasp of the nature of those statistical findings, which were even published in a scientific journal.
The Encyclopedia of Great Men of Israel, edited by Margaliot, contains short biographies of Jewish Rabbis who lived between the 8th and the 19th centuries. Sometimes the biography contains a death date or a birth date. Witztum and Rips (many regard Rips as the central figure in ELS research, but we shall talk of Witztum and Rips, in the order in which they chose to author their joint paper. Rosenberg only did the programming for them, and will not be mentioned further) listed those rabbis to which the Encyclopedia devotes three columns and upwards of text, and mentions a date of death or birth. They found 34 such rabbis (actually, they erred slightly in composing the list, both in column counting and in missing one rabbi), searched for their names and dates of death or birth as ELSs in Genesis, and computed a kind of distance function between the name of a rabbi and his date (for brevity's sake, we shall talk only of dates of death. There were very few birth dates anyway). Their assumption was that if there is, indeed, a hidden text in the Torah, then thematically related words will appear in proximity, as they do in any meaningful text.
The exact manner in which they computed the distance is technically complicated, and of no importance to the present story. Interested readers can find the details in the original article. Anyway, a list of numbers was obtained, which describes the "distance" between the name of each rabbi and his date of death (in some cases, no ELS was found for a rabbi's name or date, and then, of course, no distance was computed). Here and there some rabbi was particularly close to his date of death. At the same time, many rabbis were actually closer to some other man's date. So to test if there was an extraordinary closeness between the rabbis' names and dates, a statistical significance test was required. "Statistical significance" is the probability of obtaining a certain result by chance. The smaller the significance, the less the probability of getting that result by chance. The question was whether the distribution of distances that was found in the rabbis' list in Genesis was statistically significant.
The original method whereby Witztum and Rips computed the statistical significance of their results was erroneous. Prof. Persi Diaconis, a world reknowned mathematician and statistician who specializes in uses and abuses of statistics to support fantastic claims, was one of the experts consulted by the scientific journals in which Witztum and Rips hoped to publish their results. He suggested a different method, which they used in the Statistical Science article. For the present story, we will assume that Diaconis' method was used all along, and describe no other.
Imagine that each rabbi is paired not with his own date of death, but rather with some other date, sampled at random from the list of dates. It is possible, of course, to compute the distance between the rabbis' names and such random dates. If there is anything special in the Book of Genesis, and the rabbis' names really appear exceptionally close to their dates of death, then the distances between correct name-date pairs should be, on average, closer than between random name-date pairs. Diaconis suggested running a kind of "race". 999,999 permutations of the 34 rabbis were chosen at random. In every permutation, each rabbi was paired with the date against which the permutation pitted him. For each of the 999,999 permutations, the distances between the rabbis' names and the date they happened to be paired with in that permutation were computed. The original, correct, list of distances was compared to 999,999 lists of distances in which each rabbi was paired with a random date. Lo!, the correct pairing achieved one of the first places in this "race"! If there were nothing special in this list or in the Book of Genesis, there would be no reason for it to excel like that. The probability that of all lists, the correct one would excel thus by pure chance is minute. In other words, a latent code was discovered in Genesis, with a very small statistical significance (as said above, the smaller the statistical significance of a result, the greater its actual significance). It is almost impossible that what was found, was found by sheer coincidence.
This and more: Witztum and Rips took various other Hebrew texts, and ran their test on them, too. For example, they took the first 78,064 letters of War and Peace. There, too, the computer searched for the names of the rabbis in ELSs, their dates of death or birth in ELSs, and the distances between names of rabbis and their respective dates. There, too, the list of distances obtained was compared to 999,999 other lists, which were obtained by permuting the names of the 34 rabbis. In War and Peace, the correct list did not at all excel in the race. Its performance was kind of middling. These, then, are the results which Atzmon, and the editor of Statistical Science, found so astonishing.
It is noteworthy that the only thing that Witztum and Rips claimed in their article is that they found in Genesis a phenomenon of extraordinary statistical significance, namely, one whose probability of being sheer coincidence is vanishingly small. They did not offer a possible alternative to chance. But there was no need to say explicitly that which everyone understands: since the rabbis were born and died decades after the Torah was written, only a clairvoyant could have introduced the secret code into it. If you will, Witztum and Rips had discovered a statistical proof of the divine origin of the Book of Genesis.
Now that we have presented - albeit without the technical details - the main essentials of the statistical method whereby Witztum and Rips proved the existence of a secret code in the Torah, it is time to look in detail at the lists they worked with. If hitherto an impression might have been formed that each rabbi was represented by a single name and a single date (or two, if the encyclopedia mentioned his birth date as well), this turns out not to be so. The rabbis were known by many names and appellations, and they entered the list with many names and appellations. For example, Rabbi Yosef Terani appears in the list with 9 names [approximating the Hebrew for the benefit of non-Hebrew speakers: Rabbi Yosef, M'Terani, Yosef Terani, Teraani (another spelling for Terani), M' Teraani, MHRIM"T (an acronym), HMHRIM"T, MHRI"T, HMHRI"T]. Dates also appear in more than one form. For example, The Gaon of Vilna had a birth date and a death date, which are listed under a total of 9 forms. [For the benefit of readers not familiar with Hebrew, we note that Hebrew dates are written using letters rather than numerals, with letters having numerical value, in a manner resembling the use of digits to write numbers. 13 would be written as JC -- J=10, C=3, JC=13. We will not list the 9 date forms here, but we note the following: First, each date was written in three forms, roughly analogous to: June first, on June first, first of June. Second, the 15 and 16 of the month are typically written as 9+6 and 9+7, respectively, rather than 10+5 and 10+6, because of a kind of religious taboo on the letter combinations corresponding to the latter form. Witztum and Rips listed both forms. The Vilna Gaon's 9 forms included a 15th of Nissan date, hence the multiplicity of forms]. What is going on here? Are these, perhaps, ALL the possible names and appellations of the rabbis, or ALL the different ways in which their dates could have been written, and so we simply see a comprehensive list? The answer is: not at all. Indeed, it is in the multitude of possibilities for writing names and dates, and the even greater multitude of possibilities for choosing among them, that the key to the Torah codes puzzle lies.
To demonstrate what is meant by multitude of possibilities, consider January 1. In addition to January first, the frst of January, and on January first, we also have on the first of January, January one, on January one, New Year's day, on New Year's day, etc. If a date has 12 forms (as, for example, 1 of Tishrey does), and one can choose among them, there are almost 4 million ways in which a subset of these 12 forms can be chosen. The 16th of the month of Nissan can be written in as many as 20 forms. How were the particular names and date forms in Witztum and Rips' lists chosen?
Witztum and Rips' article gives a partial answer to this question. Written and oral exchanges with them give a more comprehensive answer: The names and appellations were supplied by Prof. S.Z. Havlin, a bibliographer from Bar-Ilan University, and the date forms were supplied by the late Dr. Yaakov Orbach. It is not quite clear who is responsible for the fact that many of the dates mentioned in Margaliot's Encyclopedia were altered, corrected, discarded, or exchanged, so that the dates in Witztum and Rips' list are not identical to those in the Encyclopedia. Be that as it may, whomever was responsible for the choices made, the end result is that in spite of Witztum and Rips' declared intention of running their statistical test on a "uniform, objective" list, the list they actually ran was neither uniform nor objective: it necessitated the discretionary judgment of experts; judgment which, as we shall presently see, is open to question.
It is worth noting that the objectivity of the list is redundant if the list is a-priori. For present purposes, a list is "objective" if anyone who would try to reconstruct it would get the same list (incidentally, Havlin has admitted in writing that if he were to draw the list of rabbis again, it might look different). On the other hand, a list is "a-priori" if it had been set in advance of any knowledge of how the words in it "perform" as ELSs. For statistical purposes, the importance of being a-priori far outstrips that of being objective, because the significance test described above assumes a-prioricity, but it does not assume objectivity. This can be clarified by the following example: Suppose someone claims to have telepathic powers, which enable him, say, to "read" numbers without seeing them. Suppose he is subjected to a statistical test: he is asked to guess the serial number on a 100NS bill -- and he succeeds. Since there are ten digits in the serial number on such a bill, the probability that the success is mere coincidence is tiny (about 1 in 1010). But suppose that the testee produced the bill out of his own pocket. In this case, one might suspect that the bill was not chosen a-priori; namely, that the chosen bill had been peeked at earlier. In this case, of course, it is impossible to compute the probability of a successful guess from purely combinatorial arguments, as just done. The fact that the bill was not chosen in an "objective" manner is important only insofar as it raises a suspicion that neither was it chosen in a "a-priori" manner; and a-priori choice is important because the computation of the statistical significance assumes it. The probability of successfully guessing the serial number on a bill is not the same whether or not it had been peeked at in advance. Likewise, the probability that a particular list will excel in a race against other lists is not the same whether or not one knows in advance that it contains some "stars" (i.e., rabbis whose name is very close to their date of death).
Was Witztum and Rips' list a-priori? Since it fails the criterion of objectivity, they must be asked. They claim that it was. In particular, they claim that the list of names, and perhaps also of dates, was supplied to them as is by Havlin, with neither them nor him knowing what would happen when they would be subjected to the computerized search described above. It follows, for example, that the eyebrow raising decision to look for the 15th of a month using the unconventional form, was based on a-priori considerations, without knowing that this is a fortunate choice. Should we base our attitude to the Torah codes on Witztum and Rips' claim that their list is a-priori? Here's the irony: if one is willing to take their word for it, one can give up on objectivity all along. Any list at all, constructed any way at all, is acceptable if it is a-priori. Objectivity is meant to remove the need for an act of faith. Lack of objectivity in the list raises suspicion that it is not a-priori, either. Later on, we shall present strong statistical evidence that the list indeed was not a-priori, but first we need to complete another stage in the story.
Out of concern, or out of suspicion, that the statistical significance testing was not carried out in a clean and a-priori manner as required, Diaconis (the same Diaconis mentioned above in connection with the permutation race) recommended a repeat test on a fresh sample. A new list of rabbis was extracted from the Encyclopedia, this time those to whom between 1.5 and 3 columns of text were devoted. 32 rabbis were found this time (there were some errors again). The second list was constructed and tested exactly according to the same rules which governed the first list, and it, too, came almost first in a field of one million contestants.
On the face of it, the second list answered the concerns raised by both the lack of objectivity and lack of a-prioricity of the first list. In other words, all the "degrees of freedom" (a technical term which roughly means "choice possibilities") appear to have been already exploited by the first list, and the second list was bound to the choices made in the first list. Diaconis hoped that the constraints set by the first list would guarantee the objectivity of the second list, and this objectivity was supposed to make it more credible that it was also a-priori. But in fact, we shall presently see that the rules and constraints laid down by the first list left sufficient room for maneuvering in the second list, allowing for the "cooking" of a second list which would be no less successful than the first list. By "cooking" a list we mean playing around with the options it affords until it looks good enough.
Where did any degrees of freedom remain in the transition between the first list and the second? In regard to the date forms, the second list did indeed follow the first list accurately. The same three forms of date writing (e.g., July 4th, on July 4th, 4th of July), and the same two ways of writing the 15th or 16th of a month. But in writing names and appellations, there aren't rules as strict and binding as there are for date writing. For example, Rabbi Yehosef Ha'Nagid was called Yehosef, while Rabbi Yosef Terani was called Yosef. This is not inconsistency in spelling the names -- rather, this is how these names were actually spelled (or so the experts tell us). Rabbi Abraham Saba was also named after one of his books, while Rabbi Abraham the Angel was not. This is not an inconsistency in choosing appellations -- rather, it reflects reality.
Since different people, even if given the same name at birth, may come to be called differently in the course of their life time (a Robert can be Bob, Bobby, Rob, Robby, Bert, Bertie, etc.), allowing nicknames and appellations makes it difficult to specify an "objective" list of names governed by strict rules. The appellations are included because the person who draws the list thinks they should be included. It is a matter of discretionary judgment. Indeed, Havlin, in a written description of his considerations when constructing the list of names and appellations, admitted explicitly that he used a great deal of judgment when constructing the list. It follows, therefore, that the second list did not solve the problem it was intended to solve, namely, gauranteeing that the second list could not be fiddled with and "cooked" to success.
The reader might wonder at this point: Is it really possible to "cook" a second list, following exactly the rules set by the first list, so that it would be as successful as Witztum and Rips' second list actually is? Many of those who readily see that the appearance of words and of word combinations as ELSs, even in proximity, is possible in any text, find it hard to believe that even under the heavy constraints set by the first list of rabbis, Witztum and Rips' results (namely, outstanding performance in a permutation race) can also be replicated in any text. But very recently, this too has been unambiguously demonstrated.
Dror Bar-Natan and Brendan McKay, assisted by Prof. Menahem Cohen of the Faculty of Jewish Studies at Bar-Ilan University, undertook the following challenge: to take some text of the length of Genesis, and cook a list that would excel in a list race run on this text, yet such a list as would follow the guidelines governing Witztum and Rips' first list just as closely as their own second list did. The text chosen for this purpose was War and Peace (the first 78,064 letters), for the simple reason that it played the role of "any old text" in Witztum and Rips' original article, when they tested their second list on it, and it failed. Bar-Natan and McKay's list was constructed as follows:
1. The list of rabbis was chosen by Witztum and Rips' criterion, namely, rabbis to whom the Encyclopedia allotted between 1.5 and 3 columns of text, and whose entry included a date of death or birth.
2. The dates, including their form, were identical to those used by Witztum and Rips.
3. The computational details were the same as those used by Witztum and Rips, with the following exception: Witztum and Rips included two rabbis even though they had discarded the dates given them by the encyclopedia, thus leaving them unpaired in the correct list. Bar-Natan and McKay's list discarded these rabbis, as well as one other who didn't belong in the list in the first place.
4. Only in the list of names and appellations were significant changes made. Out of close to 90 names and appellations in Witztum and Rips' list, twenty were dropped, and 30 were added. For example, the name "Oppenheim" spelled with a single Hebrew letter yod was exchanged for that name with a double yod spelling. The deletions and additions were all based on research, and were governed by principles and consistency considerations to the same extent as Witztum and Rips' list was. Additional detail can be found in Bar-Natan's and McKay's Internet sites.
In a race of ten million permutations, the modified up list came in 12th place! It is possible to summarize matters thus: Except for the "small print", i.e., within the boundaries of trivial changes, all of which are justifiable, consistent and legitimate no less than Witztum and Rips', the astonishing result from Genesis can be replicated in War and Peace.
Of course, from the fact that a list could and was cooked for War and Peace, it does not follow that Witztum and Rips cooked their list for Genesis. They persist in claiming that their list, unlike Bar-Natan and McKay's, was a-priori; that it was chosen in good faith, and the choices were blind with respect to its success probability. Since none of the critics and skeptics were around when the list was drawn up, the decision whether or not to believe the a-priori claim regarding the second list, just like regarding the first one, remains an act of faith. Nonetheless, there are other findings, also statistical in nature, which indicate that if Witztum and Rips' list was not cooked, then its creators enjoyed a fantastic stroke of luck, to say the least. These findings, to be described below, raise serious questions, but we shall leave the readers to draw their own conclusions.
Every researcher in every research must make many methodological choices. So too, Witztum and Rips, or their consultants, faced many choices and decisions. It is convenient to demonstrate this with respect to dates.
1. Witztum and Rips could have settled for dates of death only (they would have lost but one rabbi out of 66), or they could have taken dates of birth as well as dates of death (it would not have been practical to take just birth dates, because only 7 rabbis had them). The choice was between one date, or two (where possible).
2. Witztum and Rips could have written the 15th or 16th of a month by the conventional form only, by both forms, or even just by the unconventional form.
3. There were many degrees of freedom regarding the form of writing dates. Recall, Witztum and Rips chose three particular forms, but they could have added a fourth form; they could have settled on a single form; they could have stuck to the form used by Margaliot; etc.
These are just a sample of the choices presented by the dates. They faced choices in other areas as well, primarily in the form of ELS searching and the distance computation. We cannot go into further detail, due to technical complexity and space limitations, but it is important to note that there were a great many choices.
Suppose, now, that all these choices were made, as claimed, in an a-priori fashion, namely, without knowing how the choice would affect the outcome. It stands to reason that where a choice could have been resolved in one way or another, it would turn out aposteriori that the blind choice was fortunate (i.e., improved the ranking in the race) about as often as it was unfortunate (i.e., hurt the ranking). However, wonder of wonders, it turns out that almost always, if not always, the allegedly blind choices paid off: just about anything that could have been done differently than it was actually done would have been detrimental to the list's ranking in the race. That is the case, for example, with regard to all the date choices listed above. Even the decision on which of the five books of the Pentateuch to carry out the test was fortuitous: in each of the other four books of the Torah, the list does not perform any better than chance. Of course, the probability of blindly choosing so felicitously again and again and again diminishes rapidly with the number of such choices. By the same statistical logic which gave power to Witztum and Rips' results, the results of the present analysis suggest that the chance of drawing up such a successful list blindly is very remote.
This analysis completes the critique of the seemingly astounding statistical results which were published in Statistical Science. A list was presented there which performed most surprisingly and impressively in Genesis. That list perfomed quite poorly in War and Peace, and in several other control texts (though it also performed poorly on Exodus, Numbers, Leviticus, and Deuteronomy). However, another list, as accurate and correct as the original list, did achieve on War and Peace a measure of success as impressive as that of Witztum and Rips' list. So what remains of the "scientific" experiment and the statistical significance testing? We are back to square one. We started by showing that words in ELS form can be found in Genesis -- as well as in any other sufficiently long text. Now we see that even a list of rabbis, whose ELS names were remarkably close to their ELS dates in Genesis -- can be found as well as in any other sufficiently long text. To be sure, the probability that Witztum and Rips' results are due to mere chance is very small. But the alternative to "mere chance" turns out to be not that whomever wrote the Torah inserted the codes into it, but rather that whomever found the codes in the Torah did not find them by mere chance, but rather by diligent tinkering.
Several months ago, Maya Bar-Hillel lectured about this work in the Statistics Department of Tel Aviv University. Doron Witztum was present. At the time, the "cooking" of the War and Peace had not yet been completed, and Bar-Hillel reported that the cooked list was ranked at about 60 in a field of one million. "Only 60?", interjected Witztum mockingly from the audience. "If I were to cook a list for War and Peace, I could get it to perform much better than that". "Indeed you could", replied Bar-Hillel. "I believe him. I suggest you all do, too".
Table of Alterations in Second List
This table lists only the differences between Bar-Natan and McKay's list
and Witztum and Rips' list, in a manner accessible to an English language
reader. The original list appears, in Hebrew, in Witztum, Rips and
Rosenberg's article, and in the Galileo article. + Denotes added
appellations, - denotes deleted appellations.
1. + RAB"D sheni (second Raabad)
3. - H'Malakh (The Angel)
4. Removed, for lack of any date.
6. - Maasey YHVH (the Hebrew spelling for Yahweh); + Maasey H'; Baal Maasey H'
7. - Oppenheim (single yod); + Oppenheim (double yod)
8. Removed, for lack of any date.
10. + MHRX"A, + H'MHRX"A (acronyms)
11. - Benvenesht, + Benveneshty, + H'Rav HBI'B, + H'Rav H'HBI'B (acronyms)
12. - Kafusi, + Kaafusi, - Baal ness, - Baal H'ness
15. + Yehuda Segal
19. + R"Y Terany, + R"Y Teraany, + H'R"Y Terany, + H'R"Y Teraany
20. Removed, doesn't meet inclusion criterion.
21. + Mimongil (family name)
22. - Khaagiz, + R"I Khagiz, + MHR"I Khagiz
23. + Yakov Levi, + MHR"I Levi
24. - HR"I Emden, + R"I Emden, - H"RIEB"C
25. - Horowitz, + Horovitz, + Ytzhak Levi
26. - Krochmal, + Krochmaal
27. - Zacuto, - Zacuta, - Moshe Zacuto, - Moshe Zacuta
30. - AX HE"R, + AHE"XR, + Hon Ashir (book)
31. - Sar Shalom, - Mizrahi, - H'MHR$"$
32. - Xeelma, + Shlomo Xelma
33. Rabbi Meir Eisenstaadt, erroneously omitted from the original second list.
Readers interested in further detail are invited to read Witztum, Rips &
Rosenberg's original article; Atzmon's article; and the following
Internet sites, where some of these res ults appear:
Prof. Maya Bar-Hillel of the Center for the Study of Rationality at The Hebrew University studies biases of judgment and decision making. Dr. Dror Bar-Natan of the Department of Mathematics at The Hebrew University studies quantum algebra and low dimension topology. Dr. Brendan McKay of the Department of Computer Science at the Australian National University studies combinatorics and computational proof.
1. Witztum, D., Rips, I. & Rosenberg, Y. (1994) Equidistant letter
sequences in the Book of Genesis. Statistical Science, vol. 9(3),
2. Witztum, D. (1989) The Added Dimension: On Two-Dimensional Writing in the Torah. Self-published in Israel in the Hebrew language.