Madness in the Method
Maya Bar-Hillel and Avishai Margali
December 1999

"How often have I said to you that when you have eliminated the impossible, whatever remains, however improbable, must be the truth?" (Sir Arthur Conan Doyle).

The Torah, like the Freudian dream, has always been believed by some of its interpreters to have a latent content in addition to its manifest content. Throughout many generations, mystics devoted great efforts to discovering what they thought were divine secrets or messages encoded in the Torah. In 1994, Statistical Science, a peer reviewed journal of the American Institute of Mathematical Statistics, published what appeared to be statistical proof, based on a scientific experiment, that the bible contains a hidden code, in the form of words spelled by equal-sized letter skips (ELS, for short).1

Here is an example of an ELS: In the book of Genesis, the first appearance of (the Hebrew letter corresponding to) T is followed 50 letters later by an O, which is followed 50 letters later by R, and yet another 50 letters later by H, thus spelling the word TORH (which in Hebrew has just these four letters).

This curious anecdotal discovery is one of several that were made a few decades ago by the Slovakian Rabbi Weissmandel. Apparently, no similar discoveries were made until the 1980s, when some people realized they could search the Torah for meaningful ELSs much more effectively with the aid of computers. Computers allowed reliable counts of skips much larger than 50 -- 500, 1000, 5000, etc., thereby expanding the scope of the search beyond ordinary human capacity.

Around 1984, Doron Witztum, an Orthodox Jew from Jerusalem, conceived the idea of writing the entire book of Genesis as a single extended page consisting only of letters (deleting punctuation marks and closing up spaces). This huge rectangle of letters could have any width one likes. For example, since Genesis consists of about 78,000 letters, it can be written as a page of 78 rows, each 1000 letters wide, or as a page of 780 rows, each 100 letters wide, etc. ELSs cn be read horizontally, vertically, or diagonally, and in any direction: left to right or right to left, top down or bottom up.

An example in an English text is shown in Figure 1, which is a piece of a huge page on which the entire text of Moby Dick was written. It displays various words relating to the assassination of Martin Luther King written as ELSs (e.g., MLKING, TENN, GUN). In this case, the size of skip between adjacent rows is over 26,000 letters (since that is exactly the width of the full page).

Figure 1. Martin Luther King was fatally shot
in Tennessee on April 4,1968. 2

Playing around with his computer, and using the book of Genesis as his text, Witztum noticed that sometimes thematically related words (e.g. "HAMMER" and "ANVIL") both appeared as ELSs within the same small letter array -- as in Figure 1. Other times, an ELS seemed to be related to an ordinary word sequence in the text in a striking way, as is also shown in Figure 1.

A much trumpeted later example is Figure 2, taken from the jacket of a 1997 best-selling book by Michael Drosnin. 3 The text in the rows is from the Pentateuch (the books of Numbers and Deuteronomy). The eight letters in the column spell "Yitzhak Rabin". They are separated from each other by almost 5000 letters in the original text. Rabin's name intersects a string of words which Drosnin (who doesn't speak Hebrew) translated as "an assassin who will assassinate" (the Jerusalem Bible translates these words as: "a man ... who had killed"). This letter array was found by Drosnin in 1994, a full year before Israel's Prime Minister Rabin was assassinated. He was sufficiently impressed by his own discovery to try to bring it to the attention of Israeli security forces and Rabin himself. When Rabin was assassinated a year later, an impressive centerpiece for Drosnin's book had been established.

Figure 2. Drosnin predicts the assassination of Israel's Prime Minister Rabin.

By now Witztum had teamed up with Ilya Rips, another Orthodox Jew and a professor of mathematics at The Hebrew University. Rips realized that in a sufficiently large text interesting patterns of ELSs can be found in proximity as the result of mere chance. After all, there is a large number of possibilities to exploit: What words to search for, where to start the search, how many letters to skip, etc. Convinced nonetheless that something extraordinary was happening in the book of Genesis, he sought to subject his hunch to a systematic quantitative test.

For their test, Rips and Witztum wanted a list of related word pairs, constructed according to objective, well-defined criteria. They decided on a list of famous Jewish rabbis, along with their dates of death or birth. They drew the rabbis from an encyclopedia which gives brief biographical sketches of Jewish rabbis who lived between the 9th and 18th century AD. 4 To be included, the rabbis had to have a sufficiently long entry (over 3 columns of text for the first list, over 1.5 columns of text for a later list) and a date of death. A computer program searched Genesis for ELSs corresponding to the names of the rabbis and their dates of death (in Hebrew, dates are written with letters only, requiring no digits). Where the search was successful (some names and some dats were not found as ELSs at all), the program also measured how "close" a rabbi's ELS name was to his ELS date.

The rabbis' names and their respective dates did not form any neat or regular pattern in Genesis. Readers who can verify on their own, without needing a computer, how TORH is spelled out as an ELS in the opening phrases of Genesis, cannot, practically speaking, see for themselves how close the rabbis names and dates are found in Genesis. Even with the aid of a computer, a rabbi's name and his date are rarely both found in the kind of small letter array shown in Figures 1 and 2. Moreover, most names of rabbis are closer to some other rabbi's date than to their own. In fact, the measurement of distance between names and dates was so complicated and unintuitive, that only statistical analysis could determine whether they really were closer to each other than could be expected by chance.

Witztum and Rips were not statisticians, and their early attempts at such analysis were fraught with errors. They ended up following a suggestion of Prof. Persi Diaconis of Harvard, which we shall not describe here. The analysis very strongly indicated that whatever was going on could hardly be attributed to mere chance. If what Witztum and Rips found was not due to chance, it can only be described as a miracle, because the rabbis lived millenia later than the time the Torah was written. Since they could not have been deliberately coded into the text by an ancient scribe, the code could only be the work of a clairvoyant, presumably divine, intelligence.

The study, which came to be known as The Famous Rabbis Experiment, was carried out between 1986 and 1988. It took until 1994 for the results to be published in Statistical Science. In the eyes of many, the Torah Codes had graduated from the realm of esoteria, populatd by the likes of tea-leaf reading, to the hallowed halls of Science.

What could have moved a statistical journal to even review, let alone publish, such an outlandish experiment, in which even the then-editor, Prof. Robert Kass of Carnegie-Mellon, put no credence? The answer, as is often the case, lies in the human element more than in the experiment itself.

Ilya Rips, a soft-spoken cherubic man sporting the long white beard and black skullcap worn by Ultra Orthodox Jews, was born in the USSR. In 1969, when he was a young secular Communist of about 20, he made headline news by setting himself on fire in the Riga town square, in protest of the Russian invasion of Czechoslovakia. He was put in a mental institution for three years, and then allowed to emmigrate to Israel, where he acquired both a doctorate in mathematics, and a new identity as an Orthodox Jew. His unworldliness is exemplified in the following story: In 1973, during Israel's Yom Kippur War, Rips volunteered to pump gas in a gas station which was short of manpower, due to the mobilizatin of all reserve soldiers. Long after the war had ended, he was still pumping gas voluntarily, to the owner's delight. To friends trying to persuade him to resume his own life he said that the landlord had not released him yet. Only when someone argued that Rips was taking the job from someone who needed it for his living did Rips leave the gas station.

Doron Witztum has an MSc in Physics from The Hebrew University, acquired before his conversion to Orthodoxy, but has never held an academic position. But for about 15 years he has devoted much of his time to Codes research. Oft heard claims that he holds an academic position are untrue. There is a third author, Yoav Rosenberg, then a young student who helped with the programming, and has avoided the limelight. Drosnin, and the media, largely credit Rips with discovering the codes. Rips' reputation lends more credibility to the codes than the unknown Witztum could have ever mustered alone. However, Rips himself credits the codes to Witztum, who is also listed first of the three authors of their joint paper, in spite of conventions favoring alphabetical ordering of authors.

When Rips and Witztum made their Torah Codes discoveries, Rips described them to colleagues at The Hebrew University. One, Robert Aumann, a well known game-theorist and also an Orthodox Jew, took a particular interest in the work. He played a prominent role in bringing it to the attention of the scientific community. Being more fluent in English than Witztum and Rips, he rewrote their research report, turning it into the dry, tight, and lucid version that was later published in Statistical Science (and is reproduced in full in The Bible Code). He also arranged for Rips to give a public lecture in the Israeli Academy of Sciences, an event that caused much embarassment and furor in the Academy. Perhaps most significantly, Aumann, also a member of the American National Academy of Sciences, attempted to have the paper published in the prestigious journal of the Academy, the PNAS. This journal will only publish a paper that is sponsored by an Academy member. Aumann was willing to sponsor the paper, and sent it for peer review to a bevy of world reknowned statisticians, among them Harvard's Persi Diaconis.

Diaconis was a perfect choice for the job. As well as being a MacArthur Prize winner for his work in mathematics and statistics, he is also a first class magician and an expert on how statistics is used -- or rather, misused -- in support of ESP research, and other fantastical claims. Diaconis had been introduced to Torah Codes research earlier by his Harvard Math Department colleague, David Kazhdan, an old friend of Rips' from their early years in Russia, who, like Rips, had also become an Orthodox Jew. When Diaconis was first approached, only the first list of rabbis existed. Diaconis had suggested that a fresh sample be constructed, and this is what prompted the second list of rabbis mentioned above. Diaconis also suggested a different and ingenious way of calculating the statistical significance of Witztum and Rips's results. He was quite sure that the results of the famous rabbis experiment wouldn't survive the statistical significance test, and wouldn't be repeated in the new sample.

Being a magician, Diaconis should have known better. His own audiences also often believe that they can uncover his tricks, only to be even further baffled when the tricks survive the scrutiny and suspicions. How Diaconis was foiled will be described later. But, being a statistician as well as a magician, he knew that the implications of the experiment depended more on the integrity of the researchers, than on the reported numbers. A clever and unscrupulous researcher can manipulate the numbers. Again and again Diaconis asked: Are these people reliable, are they honest? Again and again he was assured of the absolute integrity of Rips. No one he asked, however, could vouch for Witztum.

Impressed by the evidence, but quite unconvinced of the existence of the codes, Diaconis ultimately recommended against publication of the work in the PNAS, much to Aumann's chagrin. However, he assisted in getting the paper published in Statistical Science, hoping that this "would give statisticians a chance to say out loud what they thought was wrong" with it. As we shall see later on, figuring out what was wrong with it, and especially being able to prove it, only happened several years later.

It is appropriate to remark here that -- contrary to common lay perceptions -- the decision to publish a scientific paper is by no means an endorsement of its findings or conclusions. Some philosophers of science, most notably the late Karl Popper, even argue that science progresses strictly by refutation: conclusions and results are meant to be refuted. Aumann's anger at Diaconis was not for refusing to believe Rips and Wiztum's results, but only for refusing to recommend their publication in the PNAS. Moreover, though Aumann has been this work's most ardent advocate in the academic world, he claims that he himself is still not convinced of the existence of codes. He is only convinced that the case for codes is strong. Both Aumann and Diaconis believed that even if the results were flawed, the flaws had a better chance of being exposed after publication, simply because they would draw more and wider attention. Indeed, according to the Treasurer of the Institute of Mathematical Statistics, the journal issue in which the codes paper was published is far and away the best-selling issue Statistical Science ever published.

But although Statstical Science, in its own words, offered the paper to its readers "as a challenging puzzle", for several years, the paper elicited no critical response. Apparently, readers who assumed that there was something wrong with the results, couldn't be bothered to take the time to figure out what it was. Those who didn't personally know Rips were probably not even much intrigued. Three years were to pass before the puzzle was tackled.

While Torah Codes research was being largely ignored by scientists, it was warmly embraced by a quite different group, Jewish proselytizers. Judaism does not encourage missionary attempts to recruit non-Jews. The Talmud states that "... the proselytes are as burdensome to Israel as leprosy". 5 But in Israel, in the US, and in other countries, there are many outreach seminars and other forums intended to convert secular, non-believing Jews into Orthodoxy (both Rips and Witztum are such born again Jews). Aish Ha'Torah ("The flame of the Torah") is a Jerusalem-based group that operates "Discovery seminars", designed to encourage such conversions by a "rationalistic" approach. The Torah Codes are the jewel in the crown of their seminars, offered as objective, scientific proof that the Torah is of divine origin, and targeted primarily at educated, sophisticated Jews who respect numbers, science, and rational thinking. According to an article in The Wall Street Journal, in 1996 alone, "about 240 Jewish community centers, schools and synagogues [in the US] eager to expand their membership - have paid Aish Ha'Torah ... about $1000 to put on each Discovery seminar. Aish HaTorah ... has put about 60,000 people worldwide through the seminar since 1987 - more than one-third of those just in the past two years". 6

The apparent seal of approval conferred by the publication in Statistical Science played an essential role in this use of Codes research, as did the Foreword to a book which Doron Witztum had self-published in Hebrew a few years earlier, 7 which was signed by four prominent mathematicians: Furstenberg, of The Hebrew University, I. Piatetski-Shapiro of Yale, and D. Kazhdan and J. Bernstein, of Harvard. Although the Foreword only said that the work was "serious" and "sufficiently striking to deserve a wide audience", many saw it as an endorsement by the most respectable and knowledgeable authorities. These authorities all happen to be Orthodox Jews, and personally familiar with Rips.

Their sentiment, however, is hardly widely shared. The very quest for objective proof of the divine origin of the Torah or for the existence of God is anathema to many Orthodox Jews, who regard belief as necessarily a pure act of faith. The triviality and puerileness of the codes increases these people's disdain for the attempts to prove their existence. An outspoken voice in this camp is that of Shlomo Sternberg, who in addition to being a professor of mathematics at Harvard is also an ordained Orthodox rabbi. He has written that the very notion of the codes research is a disgrace for Judaism, as well as for mathematics. Prof. Barry Simon, the Orthodox Jewish chairperson of Caltech's Math Department, has gone so far as to draw up a formal statement, that can only be signed by professional mathematicians and statisticians, attesting to the flaws and follies of the famous rabbis experiment. Scores have signed it. The network of personal contacts between various mathematicians in Israel and in the US has drawn into the fray a sizable number of mathematicians. Many are from the previous USSR. Many are Orthodox. Personal friendships have been forged around the codes. Others have foundered.

Another concerned group consists of some Israeli Orthodox rabbis who were debating the value of Codes research, and its possible religious and theological significance. They had reason for concern. Some time ago, several hundreds of thousands Israelis received in the mail a little black book published by the Christian Mission, which makes extensive use of Torah Codes to prove that Jesus is the Messiah (for example, in Numbers chapter 21 verse 10, where instructions are given to the priests who sacrifice the sacrificial lambs, taking every third letter from the first H on spells "Hence the blood of Jesus", an expression which in the vowelless Hebrew takes up three words totalling eight letters). 8 However, outside of some religious circles and a small circle of people around Rips and Witztum, codes research was still a completely marginal and esoteric phenomenon.

And then came Drosnin's book. On May 29, 1997, Simon and Schuster took out a full page ad in The New York Times announcing its debut, with the following caption: "In all of history, few books have completely changed the way we view the world. The Bible was one. The Bible Code is another". Within a week, the book had been featured in all seriousness on CNN, The New York Times, TIME magazine, and Newsweek (in the Religion section). In short order, it was featured in other leading newspapers, in the Today Show, the Oprah Show, etc. . It went into translation, and topped bestseller lists all over the world. A year later it was released with renewed fanfare in paperback. A 1999 movie, The Omega Code, is predicated on the existence of the codes, and plays primarily to Christian audiences. On the other hand, Harvard, by awarding Drosnin its annual Ignobel prize in literature for 1997, interjected a rare note of humor.

In a nutshell, the book tells of how Drosnin, a journalist and writer, had met with Rips and learned about the Torah Codes and how to look for ELSs. It shows a great many letter arrays he found, in which various ELSs are highlighted for the reader's benefit. Drosnin's arrays resemble those in Witztum's earlier book. The boldest departure between the books is in Drosnin's attempt to read into his letter arrays predictions of the future. His only "success" (he admits to some failures) is the "prediction" of Rabin's assassination, verfiably found before the assassination actually occurred. How impressive is this prediction?

The skeptic may note the following: 1. The possibility of an attempt on Rabin's life was not only raised by many at the time, but was actually promoted by some extremist rightwing circles. 2. Drosnin's memo to Israel's chief scientist at the Israeli Ministry of Defense stated: "I think Rabin is in real danger, but that the danger can be averted" (p. 187). This much, however, was not only a common concern, but would have been confirmed whether Rabin had been assassinated or not. 3. That the ELS for "Yitzhak Rabin" crossed the words (under the Drosnin's dubious translation) "assassin who will assassinate" no more predicts that Rabin will be assassinated than that Rabin himself will assassinate. Moreover, there is no indication which Yitzhak Rabin is referred to (this is a not uncommon name in Israel). As with the Delphic Oracle, the interpretation of the Bible Code depends on what the interpreter wants it to. The success of Drosnin's prediction is only in the eyes of the beholder.

More impressive by far is the fact that Drosnin has made much more money and fame out of the Torah Codes than all codes researchers put together ever have. Not surprisingly, there are suits pending against him, for example, for failing to credit the writers of the software he used to look for codes). Also impressive is Drosnin's unique position in simultaneously claiming to believe in Codes -- but not in God.

In spite of this success, or perhaps because of it, Rips and Witztum have made public statements to the press repudiating the book and distancing themselves from it -- an oddity in itself, considering that The Bible Code extols and extends their work. Drosnin's book, much more than the Statistical Science paper, let the Bible Codes genie out of the bottle, and brought it to the world's attention.

Creative magicians love to amaze and baffle their peers with a new trick they've invented, challenging them to figure out the secret of the trick on their own. An important psychological element in this task is strict adherence to what you know with certainty to be impossible. Suppose you see a magician cutting the pretty lady in two, separating her smiling face, upper torso and all, from her twitching toes, long-booted legs and all, and then putting them together again. It is wrong to ask: "How can the lady be cut in half and glued back together again?", because the obvious answer to that question is: She cannot! But you are on your way if you ask: "How can one appear to be cutting the lady in half and then putting her together again?".

The codes research raises the obvious question: "How could the names of rabbis and their dates of death have been encoded in a text written millenia before the rabbis were even born?" For the skeptic, this is the wrong question. Compelling evidence that such a code truly exists is the stuff of The X-Files. A committed skeptic does not ask how the Codes got into the Torah, but rather how did they appear to get there. Interestingly, this should be the question even for those who literally believe that the Torah was dictated by God letter for letter on Mt. Sinai, because there is little disagreement among biblical scholars that the many different texts of the Torah that we have today differ much more from the original text of antiquity than they do from each other -- which is by quite a lot. Witztum and Rips ignore the problem of conducting research on an artificial publisher's version called the Koren edition, which is known to be hundreds if not thousands of letters different than the original of antiquity. Drosnin falsely claims that "every Hebrew Bible that now exists is the same letter for letter", and that the text used for the codes research "has not changed in at least a thousand years" (p. 38). In any case, it had two thousand years to change before this millenium. And it did.

We ourselves became interested in the codes after attending a colloquium at The Hebrew University's Center for the Study of Rationality, in which Aumann presented the work of Witztum and Rips (oddly, Witztum and Rips presence in the audience was unacknowledged). At that talk, as at others, a common reaction was: "How does the list of rabbis fare in other books?". In fact, Witztum and Rips had tried out their list on several other texts, among them, at some referee's suggestion, War and Peace (in the Hebrew translation). 9 In the parlance of methodology, these texts serve as a kind of "control" against the possibility that some result that appears unique or remarkable actually might crop up anywhere. But just as Witztum and Rips hoped, the rabbis list did not fare well on any of these texts. Genesis was clearly special.

Recall that in addition to checking other texts, Witztum and Rips were also asked by Diaconis to check another list. This is called in the parlance of methodology replication, or cross-validation. Notably, though Witztum and Rips seemed willing to check a large number of control texts, they were only willing to perform a single replication. That replication was the second list of rabbis mentioned earlier. The usual function of replication is to demonstrate an effect's reliability, stability, or generalizability. But where "miracles" are involved, replication serves another purpose: it subtly guards against methodological or other wrongdoing, in a manner we shall elucidate.

Without having said so in so many words, Diaconis, Kass, and other skeptics, clearly suspected that in spite of Witztum and Rips' self-declared goal of "uniformity and objectivity with regard to the choice of the pairs" (p. 431), indispensable in so delicate an inquiry, they had perhaps -- deliberately or inadvertently -- drawn the target only after shooting the arrow, so to speak. In other words, they may have had some advance knowledge of some rabbis whose names were close to their dates, and used that knowledge to construct the rules for drawing their lists.

Checking a new list according to the same rules or protocol which governed the first list can be viewed as tantamount to removing the first arrow, and requiring the authors to shoot a fresh arrow into the same target, with no opportunity for adapting its position. That is why Diaconis insisted on a fresh sample. Witztum and Rips were well aware of the suspicions regarding their experimental procedure. Their paper states: "In order to avoid any conceivable appearance of having fit the tests to the data, it was later decided to use a fresh sample, without changing anything else [e.g., the distance measurement, the spelling rules, etc.]" (p. 43, our emphasis).

When the second list proved as successful as the first, the referees were stumped. Short of saying: "We simply don't believe it", the referees had taken their mandate as far they could. Referees are not, nor are they meant to be, detectives. Their job is to evaluate a manuscript on the presumption that it is truthful, and to check its theoretical and methodological integrity -- not its veracity. In an interview given in 1995, Kass said: "I don't think anyone ended up believing it. They still think there's some kind of flaw, but they don't know what it is". 10 The flaw turned out to be that the target had after all been drawn around the arrow in the second list too. Later analysis revealed statistical traces of how this legerdemain feat was achieved. We shall outline this analysis.

A close look at the list of famous rabbis suggests where "uniformity and objectivity" had been departed from, and where "fitting the tests to the data" might have occurred, even in the second list. Readers may be forgiven for assuming hitherto that each rabbi in the lists was represented by a single name and a single date, perhaps forgetting for a moment that a person's "name" or even a person's "date of death" is not a unique and well-defined sequence of letters. Say one is born on July 4. Should the letter sequence one looks for be: JULY4 (recall that 4 in Hebrew is represented by a letter)? or JULY4TH? how about 4THOFJULY? Is the name of the present American president Bill Clinton? Mr. Clinton? Mr. President? Or just Clinton? Bill?

It seems that Witztum and Rips could have elected to do one of two things: use a single, predefined, way of writing dates -- e.g., just JULY4TH, and a single predefined way of writing names -- e.g., just first initial and family name (BCLINTON). They chose not to do that. Or they could have used all possible ways of writing names and dates. This is problematic. Regarding dates, do "all possible ways" include "AMERICANINDEPENDENCEDAY"? Regarding names, note that at birth, Mr. Clinton's first intial was not B, and his family name was not Clinton -- he was named William Jefferson Blythe IV. How does one define "all names" -- and how does one verfiy that a list is complete? Witztum and Rips' odd solution to this crucial matter was to fail to acknowledge it as a problem. They used some, but not all, names, and some, but not all, date forms. Later -- but not in the paper -- they stated that the choices were made by experts they had consulted, according to apriori rules. In the opinion of other experts, however, their list is "arbitrary", "unscientific", even "appalling".

To give an example of one of many inconsistent choices, suppose some name has become accepted as the family name of a rabbi even though he did not use it himself. Should it be used? In the case of one rabbi, the name Emden was included, even though it had been explicitly disowned by that rabbi. Yet in the case of another rabbi, the name Chelma, long accepted as his family name, was rejected on the grounds that it was no so used in the life-time of that rabbi.

Most important for assessing the statistical claims, however, is not so much the quality of the list as its flexibility. The very possibility of selecting what to include in it and what not allows, if not fitting the tests to the data, then fitting the data to the tests. Indeed, in a September 1997 interview with The Jerusalem Report, Furstenberg (the author of the Foreword to Witztum's book) conceded that "Five years ago, [the experiment] looked fairly foolproof. You put the data in the computer and it comes up with remarkable results. But there was a greater choice of names than one realized. I would now be more hesitant to write even that quasi-endorsement which appeared in Witztum's book" (p. 18). 11

As it turned out, several quite different skills were required to turn suspicions of data fitting, or tuning, into statistical proof. Some were not part of the experise of the statisticians who had reviewed the research for PNAS and Statistical Science. Math and computer skills were required for the checking and the analysis of the quantitative parts of the work. Hebrew and Talmudic expertise was required to evaluate the choice of dates, appellations, and forms, and to uncover the unchosen possibilities. That these different skills were brought to bear on the codes is largely thanks to the persistent interest of Alec Gindis, a Jerusalem-based businessman. Gindis has a summer house near David Kazhdan in the Catskills, and had often discussed the codes with him. His curiosity was aroused, but his religious sensibilities were offended. His God, he felt, was not one to play around with primitive, childish codes.

Through Kazhdan, Gindis contacted Dror Bar-Natan, Dror Bar-Natan, a young Israeli mathematician who had met Kazhdan while a post-doc at Harvard, to look into the matter. Bar-Natan was eventually joined by his dpeartment colleague, Gil Kalai. Through one of the Internet Torah Codes discussion groups, they discovered and began a collaboration with Brendan McKay, a mathematician from Australia's National University, with a previous history of debunking numerological sci-fi. McKay had begun his own critical examination of the codes, and was delighted to discover that he was not alone. In June 1997 McKay came to Jerusalem to meet both the advocates of the codes, and the local skeptics. The meeting, which had been set months in advance, happened to right after the publication of Drosnin's book. Thus McKay, a much sought-after commentator on the codes, happened to be interviewed in Israel for TV stations the world over.

One such interview was taped at the Western Wall by Italian TV. Drosnin, in Rome, was confronted by McKay, in Jerusalem. McKay countered Drosnin's letter arrays with letter arrays of his own. Drosnin relates how he had found in the book of Isaiah (which Witztum and Rips, ironically enough, had used as a control text, namely one which should not have codes) a letter array relating to the 1994 collision of the Shoemaker-Levi comet with the planet Jupiter, and also including the collision date. McKay noted that Drosnin, perhaps unaware that Jewish dates change at sundown rather than at midnight, had an incorrect date. To the glee of the studio audience, McKay produced his own letter array of the cosmic explosion, but with the correct date! The coup de grace was that McKay's array was found in the Hebrew translation of War and Peace...

In a Newsweek interview, 13 Drosnin had stated: "When my critics find a message about the assassination of a prime minister encrypted in Moby Dick, I'll believe them". Not one to shirk a challenge, McKay found a letter array in Moby Dick, containing an ELS message "predicting" the murder of Drosnin himself. He also found arrays "predicting" many of the major assassinations of the century, includingTrotsky, John Kennedy, Robert Kennedy, and the Reverend King's (Figure 1). In spite of notable differences between the two languages, these arrays (in English) closely mimic the Rabin assassination array (in Hebrew), allowing the English speaking reader to appreciate how tenous these predictions are. Of course, McKay's discoveries in Moby Dick, like Drosnin's in the Torah, don't really "predict" anything specific. Figure 3 shows an array from Moby Dick relating to Princess Diana's fatal car accident.

Figure 3. Lady Diana, a member of the British royal family, died in a car accident
together with her boyfriend Dodi and the driver Henri Paul. 14

Far from being frivolous, McKay's letter sequences go to the heart of the matter by showing that anecdotal messages like those which Drosnin and Witztum find in the Bible can be found anywhere. But can even the famous rabbis experiment be replicated anywhere? We already know that letter for letter, the rabbis list failed in War and Peace. But could success be achieved within the "wiggle room" which the choice of names allowed?

To demonstrate this, McKay and Bar-Natan, with the scholarly help of some others, constructed a list whose "performance" in War and Peace matches or surpasses the performance of the original list in Genesis. The criteria for choosing the rabbis, the dates used, letter for letter, the various calculations -- all are the same. Only the list of chosen names and appellations have been slightly altered, tuned explicitly to work well on War and Peace. This was done by systematically writing down many permissible names, appellations and spellings of some rabbi, and preferring those that are felicitous for War and Peace to those that are not. Remarkably, the adjusted list overlaps the original list by about 80%. Some of the changes are as trivial as changing Horovitz to Horowitz (in the case of a rabbi documented to have been spelled both ways). Far from being, or claiming to be, perfect, the list nonetheless is as historically accurate and internally consistent as the original list.

As a complement to this work, McKay and Bar-Natan also checked how Witztum and Rips' lists, letter for letter, worked on the four other books of the Pentateuch (Exodus, Leviticus, Numbers, and Deuteronomy), all five of which together comprise the holy Torah. In not a single book did they find the slightest statistical evidence for anything that could not be attributed to mere chance. A title for their results could very well mimic the Statistical Science title: Equidistant letter sequences in the book of War and Peace.

In 1999, Statistical Science published a paper by McKay, Bar-Natan, Bar-Hillel and Kalai called Solving the Bible Code Puzzle. 15 It contains details of the War and Peace tuned experiment described above, as well as much other material, some highly technical. It underwent the same rigorous review process that the original work had undergone, in part by the same experts. It is an embarrassment, at best, to that work. Engaging the services of a law firm, Witztum and Rips sought to halt publication of the critical paper, by threatening Statisitcal Science with a libel suit if they published it. In response, the 1994 editor of Statistical Science was invited to write a preface to the article. Kass wrote that "there is good reason to think that the particular forms of words [Witztum and Rips] chose effectively "tuned" their method to their data, thus invalidating their statistical test", and concluded that "it indeed appears ... that the puzzle has been solved" 16 (p. 149). The present editor, Prof. Leon Gleser of the University of Pittsburgh, accompanied the publication of the article with an unprecedented press release. In the scientific world, if not in the religious one, it is safe to say that the Bible code has been laid to rest.

In the aftermath, one might ask how so many prominent mathematicians apparently come so close to accepting the genuineness of Codes? Many people believe mathematics to be the very embodiment of rigor, logic, precision and sheer brainpower. In fact, however, mathematics demands less common sense and street-smarts from its practitioners regarding the possibility of bias, fraud, or evasiveness than any other science. In mathematics, a written proof is wholly self-contained. Either it can be confired, or it cannot. It is irrelevant how the proof came about, who the mathematician is being paid by, and whether there is anything that is not being disclosed. Nothing need be taken on faith, and a gullible mathematician is not at a disadvantage.

In contrast, in all empirical sciences, everything about the reported results depends crucially on the manner in which they were obtained: the protocol, the methodology, the tools, the assumptions, the measurement devices, even the motivations. Without some degree of trust, nothing in empirical science can be believed.

Of the four mathematicians who endorsed Witztum's book, not one is willing to speak out today in support of the codes. When The Discovery Channel recently produced a program on the codes, they could not find a single academic of any discipline who was willing to defend the codes. As to statisticians -- not even the referees who finally endorsed the article for publication were ever swayed by it. They just gave up on finding the flaw, or, more accurately, on being able to prove it. Kass, who had made the editorial decision to publish Witztum and Rips' work, said in an interview following the publication of Drosnin's book: "Rips is not a statistician. They wouldn't be doing this if they were statisticians. Statisticians are professional skeptics. I'd be very surprised to see any statistician believe any of this." 17

Einstein is quoted as having said: "God is subtle, but He is not malicious". That is to say, the physical world is difficult to understand, but it is not deliberately evasive. That is why natural scientists, too, are often ill prepared to consider deception in the phenomena they study. In contrast, people, and their creations, are often deliberately evasive, misleading, and deceptive. They sometimes go to great lengths to avoid being found out. Hence, the people best equipped to detect deception are often those who practice it: magicians, politicians, and used-car salesmen.

The well-known Argument from the Design takes the facts of the world being so orderly, and its creatures so purposeful, to prove the existence of a divine designer. The Torah code is, in fact, a similar argument for the existence of God. It is a "proof" meant to convince skeptics, who doubt the existence of God, and to strengthen the believers in their belief. By testing features of the text that are supposedly explainable neither by human design nor by chance, it begs the inference that their only explanation is divine authorship of the text. It takes as powerful a theory as the theory of evolution to show how, given world enough and time, the universe could be an outcome of mere chance processes. It takes a simple computer program to show that the codes, those pretty letter arrays with the ELSs relating to future events in them, are likewise the outcomes of chance processes. Sadly, it is not the codes themselves, but rather the alleged "proof" that the codes cannot be due to chance, that nec

essitates the inferring of design -- an all too human design.

Aumann has stated, on more than one occasion, that the codes, if they are genuine, are the most important religious event since the Torah was given to Moses on Mt. Sinai. Far from being the discovery of the millenium, however, the codes may well be the folly, if not the hoax, of the decade.


  1. Witztum, D., Rips, I. & Rosenberg, Y. (1994) Equidistant letter sequences in the book of Genesis. Statistical Science, vol. 9(3), p. 429-438.
  2. Letter array courtesy of Brendan McKay. Source: H. Melville, Moby Dick. From the Internet version, complied by Prof. Eugene Irey from the Hendricks House edition.
  3. Drosnin, M. (1997). The Bible Code. New York: Simon and Schuster.
  4. Margaliot, M. (1961) Encyclopedia of Great Men in Israel: A Bibliographical Dictionary of Jewish Sages and Scholars from the 9th Century to the End of the 18th Century, vols. 1-4. Joshua Chachik, Tel Aviv (in Hebrew).
  5. Tractate Yebamoth 47b.
  6. Wall Street Journal, Monday, November 11, 1996.
  7. Witztum, D. (1989) The Added Dimension: On Two-Dimensional Writing in the Torah. Self-published in Israel in the Hebrew language.
  8. HaShalom (1997) POBox 5554, Herzeliya 46100, Israel (in Hebrew).
  9. Tolstoy, L. (1953). War and Peace. Hebrew translation by Leah Goldberg. Sifryat Poalim, Merhavya.
  10. National Weekly Edition, November 20-26, 1995.
  11. The Jerusalem Report, September 4, 1997, p. 18.
  12. Newsweek, June 16, 1997, p. 50-51.
  13. Letter array courtesy of Brendan McKay. Source:
  14. McKay B, Bar-Natan, D., Bar-Hillel, M. & Kalai, G. (1999) Solving the Bible code puzzle. Statistical Science, 14 (2), p. 150-173.
  15. Kass, R.E. (1999) Introduction to "Solving the Bible code puzzle" by Brendan McKay, Dror Bar-Natan, Maya Bar-Hillel and Gil Kalai. Statistical Science, 14(2), p. 149.
  16. Eastside Week, July 16, 1997.