THE BIBLE "CODES": A TEXTUAL PERSPECTIVE

THE BIBLE "CODES": A TEXTUAL PERSPECTIVE

Jeffrey H. Tigay
University of Pennsylvania
October 13, 1999

In the 11th or 12th century, a Jewish woman in Byzantium named Maliha wrote to her brothers in Egypt that she wanted to come visit them, but that when she looked into a Torah scroll she found a bad omen forecasting failure if she were to make the journey.¹ Something in the passage that caught her eye seemed to presage evil. Maliha was practicing bibliomancy, fortune telling by opening the pages of a sacred book at random and spotting a message there -- a practice widely known in the classical, Jewish, Christian, and Muslim worlds.²

In recent years, bibliomancy has been resurrected in a more contemporary form, based on finding hidden patterns and messages in the Hebrew text of the Torah, patterns and messages so sophisticated that most of them can be recognized only by a computer. The method involves finding words formed of letters that are equidistant from each other -- for example, 7, or 53, or 4772, or any other number of spaces apart. These sequences of letters are known as equidistant letter sequences, ELSs for short, and proponents of the method use them to argue that the Torah contains various significant patterns of letters and often alludes cryptographically to historical events that took place long after the Bible, down to modern times.

There are three types of such arguments.

(1) The simplest is to find words of related significance in close proximity to each other. For example, in Exodus 11:9-12:13 (see Fig. 1), the Hebrew title of Maimonides' Code -- Mishneh Torah -- is found by starting with the M in Moshe in 11:9 and counting every fiftieth letter until the word "Mishneh" (M$NH) is spelled out, and then starting with the second T in 12:11 and counting every 50th letter three times until "Torah" (TVRH) is spelled out. Between the first letter of Mishneh and the first letter of Torah there is a gap of 613 letters, equal to the traditional number of the Torah's commandments, which the Mishneh Torah explicates. What is more, one of the verses in this gap, 12:6, mentions the 14th day of the month (of Nisan), Maimonides' birthdate. To top it off, although the following point is not based on an ELS, the last four words of 11:9 begin with the letters R, M, B, and M, which form Maimonides' acronym Rambam (for RABBENU MOSHE BEN MAIMON), and the clause containing the acronym means "that My marvels may be multiplied in the land of Egypt," and 11:3, a few verses earlier, says "Moses was much esteemed in the land of Egypt among Pharoah's courtiers and among the people." These two verses can be taken not only as allusions to the Biblical Moses but to the achievements and public stature of Moses Maimonides, who was court physician in Egypt.³

Fig. 1. "Maimonides" in Exodus

(2) Much more computer-dependent is the discovery of hidden messages and predic-tions in the Torah, spread over such large segments of the text that they cannot be spotted merely by eyeballing the text. For example, the American reporter Michael Drosnin, in his book The Bible Code,⁴ observes that if you look for the name Yitzhak Rabin, you will find it by starting with the first Y in Deuteronomy 2:33 and then reading every 4772nd letter, ending with the first N in Deuteronomy 24:16 (see Fig. 2). If you then lay out all 304,805 letters of the Torah⁵ in an array consisting of 64 rows of 4772 letters, so that the name Yitzhak Rabin appears in a vertical row, it will be found to intersect with a Biblical phrase from Deuterono-my 4:42, ROCEAX 'ASHER YIRCAX, "a murderer who murders." Drosnin, who renders the phrase as "assassin that will assassinate," takes this as a prediction that Rabin would be assassinated.

Fig. 2. "The assassination of Yitzhak Rabin" in Deuteronomy

(3) Finally, the most sophisticated and computer-dependent of all are such phenomena as the "famous sages" experiment, whose proponents -- Prof. Eliyahu Rips of the Hebrew University Mathematics Department, along with Doron Witztum and Yoav Rosenberg -- argue that one can find ELS-coded references to the names of several dozen medieval rabbinical sages and, nearby, in statistically improbable proximity, their dates (Hebrew month and day) of birth and/or death.⁶ For example, the first name and the acronym ("Maharshal") of Rabbi Shelomo Luria and the date of his death (12 Kislev), all composed of ELSs of various length, can be found near each other in an array comprising the text of Genesis 20:9-22:2 (Fig. 3).⁷

Fig. 3. "Rabbi Shelomo Luria" (the Maharshal) in Genesis

To be fair, we should distinguish between what the different proponents of the codes claim. The lecturers at the "Discovery" seminars sponsored by the Aish HaTorah yeshiva; Rips and Witztum in their publications; and Moshe Katz in his book Computorah⁸ hold that the Torah encodes references to persons and events from long after Biblical times, such as Maimonides and the other famous medieval sages, the Holocaust, the 1991 Gulf War, and numerous other events. Some of these proponents use the codes to prove the divine origin of the Torah and thereby win Jews over to Orthodoxy. Others, however, especially Drosnin, have gone much further, arguing that the Torah codes can be used to predict future events. He claims to have warned Rabin of his assassination before it happened, to have predicted Benjamin Netanyahu's election, to have warned of a future atomic attack on Israel by Libya from Jordan, and of numerous other disasters. Rips and Witztum have disowned this soothsaying use of their work.

In what follows I argue that the entire enterprise of the "Bible codes" is specious. It is undercut by what we know about the history of the Biblical text, by flaws in the "famous sages" experiment, and by the arbitrariness of the methods by which the decoders identify which letters belong to the alleged patterns and messages and then proceed to interpret them.

THE TEXT OF THE TORAH

Whatever the purpose for which they use the alleged codes, their proponents depend on the assumption that the text of the Bible on which they base them is universally accepted among Jews and is completely identical to the original text.⁹ It is essential for them to insist on these points because the code consists primarily of finding words formed of letters that are equidistant from each other -- ELSs. What turns these words into messages, or at least mean-ingful patterns, is the fact that when the text of the Torah is laid out in a grid whose dimensions are determined by the size of the ELS that forms these words, they appear unexpectedly close to, and sometimes even intersect in crossword fashion with, other words -- either real words (with no letters skipped) from the Biblical text or other words formed of equidistant letters. This makes it obvious why proponents of the codes must assume that their text is accurate down to the very last letter, for if the spacing between letters in a "message" or in some meaningful pattern formed by equidistant letters is changed by even one letter, the equi-distance, and hence the message or pattern, is destroyed.

The edition of the Hebrew Bible used by the decoders is the popular Koren edition, published in Jerusalem in 1962. It is distinguished by its beautiful Hebrew font. But the history of the Biblical text shows that without special pleading it is practically inconceivable that this text, or any other known text of the Torah, is identical to the original text, letter for letter. While there was an ideal of an unchanging text, identical in all copies, this ideal was not achieved in practice as far back as manuscripts and other evidence enable us to see. ¹⁰

It is not that we lack good texts. All forms of the Tanakh used today are forms of what is known as the Masoretic Text, abbreviated "MT," named after the medieval scholars (the Masoretes) who labored for several centuries to produce the most accurate text they could. The MT in use today is based on Masoretic manuscripts of the ninth and tenth centuries C.E., themselves based on older manuscripts. It has been largely unchanged since late Second Temple times (ca. the third century B.C.E., as reflected in the earliest of the Dead Sea scrolls from Qumran).¹¹ But although the text has been largely unchanged, there is a large number of variant readings, most of which do not materially change the meaning of the text, but drastical-ly affect the number of letters it contains. In fact, in the oldest complete manuscript of the entire Bible, Leningrad Codex B19A which was finished in 1009 C.E., the Torah has some 45 letters more than the 304,805 of the Koren edition.¹² Furthermore, the text of the 3rd century B.C.E. was itself several centuries younger than the original, which was composed over the preceding several centuries -- mostly between the thirteenth and seventh centuries B.C.E., though some books of the Bible were composed a few centuries later. In the centuries between the composition of the Biblical books and the early Masoretic text of the third century, many changes had befallen the text.

These changes are primarily of two types: spelling differences and other types of textu-al variants.

1. Spelling differences. The differences in spelling involve the way the text indicates vowels. As is well known, the Bible contains two different systems for indicating vowels. The fullest and most precise of the two consists of vowel "points" (nequdot), various configurations of dots and lines which stand for the different Hebrew vowels. This system, introduced in the Middle Ages, is used today in printed Bibles where it is superimposed on the older system, the one used in synagogue scrolls. The older system uses the consonants ' (aleph), H, V, and Y to indicate certain similar groups of vowels (e.g. V represents u and o; Y represents i and long e); when functioning as vowels these letters are called vowel letters or matres lectionis (Hebrew 'immot qeri'ah), literally "mothers of reading." These letters are not used with perfect consistency. "David," for example, can be written DVD or DVYD and $omer can be written $MR or $VMR. Spelling with the vowel letter is called "full" spelling," and spelling without it is called "defective" (the latter term does not imply anything erroneous). The use of the vowel letters is attested in the oldest known Biblical manuscripts, the Dead Sea scrolls from the third and following centuries B.C.E., though not always in exactly the same places where they are used in the Masoretic Text of today. Moreover, archaeological evidence indicates that this system of spelling developed gradually; the evidence available indicates that it was not developed until after the time of Moses.¹³ The adoption of this system naturally affected the text of the Bible and the number of letters it contains.

2. Other variant readings. In addition to changes caused by the evolution of the spelling system, manual copying of texts naturally created variants, some by error and some intentional. This happens with virtually all texts. We are not even certain, lehavdil, of the exact wording of the Gettysburg Address which was composed hardly more than a century ago (1863), let alone of the original text of Shakespeare's plays. Even printed Bibles contain typographical errors. Some English printings have acquired humorous nicknames because of the typos: one edition of the King James Version is called "The Printers Bible" because it reads "printers [instead of: "princes"] have persecuted me without a cause" (Ps. 119:161); another, printed in 1631, is called the Wicked Bible because in it the seventh commandment omits one word and reads "Thou shalt commit adultery" (the printers were fined heavily for their mistake!).

In the case of the Hebrew text of the Bible, we can see textual variants clearly enough when we compare texts that appear twice in the Bible. For example, one of the Psalms appears both in 2 Samuel 22 and Psalm 18 with numerous differences: one word is replaced with another, words are present in one version but not in the other, and there are spelling differences (for example, many words that are spelled defectively in 2 Sam. 22 have the fuller spelling, with matres lectionis, in Ps. 18).¹⁴

Ancient manuscripts of the Bible also contain numerous readings that differ from those in the Masoretic Text. These include manuscripts from the Dead Sea region (mostly from prior to 70 C.E.), the Septuagint (the Greek translation of the Torah made from a Hebrew original in the third century B.C.E.), and the Torah of the Samaritans. The vast majority of differences are insignificant variations in spelling and grammar which do not affect the sense of the text but do affect the number of letters in each verse. Most of these readings are scribal errors or revisions made for the sake of greater clarity, particularly in spelling (as mentioned in note 13, the matres lectionis were introduced gradually and without perfect consistency). Some call attention to the fact that certain phrases may have fallen out of the MT, such as the missing "And God saw that this was good" in Gen. 1:7-8 (present in the Septuagint), "the offspring of your cattle" in Deuteronomy 28:18 (contrast verse 4; present in the Samaritan Pentateuch and some medieval Hebrew manuscripts of the Torah), and Cain's words to Abel in Genesis 4:8 (the Samaritan Pentateuch, the Septuagint, and some of the Aramaic targums supply "come let us go out into the field," though they may have guessed these words from the context).

A particularly interesting variant involves Deuteronomy 6:20, in which the child asks: "What are the decrees, laws, and rules which the Lord our God has enjoined upon you ('TKM)?" As is well known, this verse is the basis for the question of the wise son in the baraita cited in the Haggadah shel Pesah. It has caused no end of headaches for commentators because the child's statement that God commanded "you," instead of "us" ('VTNV) makes his question seem as bad as that of the wicked son who asks (following Exodus 12:26) "What is this rite to you (LKM)?" after which the baraita states that the pronoun is the offensive part of his question. In the Septuagint to Deuteronmy 6:20, the son actually says "us," and that is the reading found in the Talmudic sources of the baraita, namely the Mekhilta and the Jerusalem Talmud, as well as manuscripts of the Haggadah.14a In other words, this was the reading found in the Torah texts quoted by the rabbis who first taught this baraita, and with this reading the question of the wise son causes no problems.

The preceding example is one of scores of passages in Talmudic litertature that quote Biblical verses with wording or spelling that differs from the MT.¹⁵ It is conceivable that some of these variants are due either to the rabbis citing verses from memory or to scribal errors in the copying of the rabbinic texts. But sometimes these variants agree with other ancient witnesses to the text, such as the Septuagint or the Dead Sea scrolls, proving that they are based on actual texts of the Bible.¹⁶ And, most significantly, sometimes the Talmud bases laws on the spelling of particular words (e.g., the number of compartments required in the head tefillin),¹⁷ yet the spelling differs from that found in the MT. In such cases, the Talmudic rabbis were obviously confident of the accuracy of the reading they relied on, and none of their colleagues challenged it. This is an important fact: the Koren Bible and all other texts in use today contain readings that differ from spellings which the Talmud was confident were correct.¹⁸ As far as the number of letters and words in the Torah is concerned, it is also worth noting the following: a very puzzling passage in the Babylonian Talmud states that according to the "first scholars," called soferim ("Scribes"), the middle letter in the Torah is a particular letter in Leviticus 11:42 and the middle pair of words appears in Leviticus 10:16. However, in Koren and all the other texts used today, the middle letter appears 4830 letters earlier, in Leviticus 8:28, and the middle words appear 933 words earlier, in Lev. 8:15.¹⁹ There have been numerous far-fetched attempts to explain this descrepancy between the Talmud and the MT. Unless the tradition of the "first scholars" is based on erroneous calculations, it seems to imply that they were referring to a text of the Torah that was either of a different length than today's text or had the pertinent passages in Leviticus in a different order than they are today.²⁰

It is, of course, true that the predominant view in the Jewish tradition is that the Torah has remained completely unchanged, letter for letter, since it was given by Moses.²¹ But this is not the only position that has been considered possible, and several contemporary Orthodox scholars who are critical of the codes acknowledge certain changes in the text of the Torah.²² Earlier, no less a figure than Rabbi David Tsvi Hoffmann, in writing of his conviction of the integrity of the MT, acknowledged that the variants implied in Talmudic sources may indicate that the MT did not completely escape scribal error, although he insisted, against modern emenders of the text, that there is no way for scholars to confidently restore the original reading.^22a

Several traditional sources acknowledge that there have been changes.

a. Talmudic-midrashic and medieval sources list between 7 and 18 Biblical passages containing "corrections of the scribes" (tikkunei soferim). The sources preserve two traditions as to what these corrections involve: some sources describe the corrections as euphemisms in which the Biblical text used a seemingly incongruous phrase to avoid using an expression that might seem disrespectful toward God; other sources hold that the text originally did contain a seemingly disrespectful phrase and that the scribes changed it to avoid disrespect.²³

b. Dots appear above certain letters in the Torah. Avot deRabbi Nathan indicates that the dots were placed there by Ezra the scribe who explained that if Elijah should challenge his having written those letters, Ezra would point out that he had dotted them, and if Elijah should say that he was right to have written those words, he would then erase the dots.²⁴ In other words, Ezra was uncertain whether the letters in question belonged there or not. His practice corresponds to that of Alexandrian grammarians who used dots to indicate doubtful passages.²⁵

c. There is a talmudic report that three scrolls containing variant readings were found in the Temple court.²⁶ The differences were resolved in a mechanical way by adopting the read-ing found in 2 of the 3 scrolls. The need to resort to this method implies that there was no sure knowledge of which readings were correct; hence there is no certainty that following the majority necessarily resulted in restoring the original reading.

d. The MT includes the kere and ketiv system, in which marginal notes indicate that certain words are to be read differently than they are spelled in the text, or that certain words in the text should not be read at all, or that certain words not in the text should be read there. Various explanations have been suggested for this system. The medieval grammarian and commentator Radak (Rabbi David Kimhi, 1160?-1235?) explained that this system was created because Bible texts were lost during the Babylonian exile and the best scholars died. The later scholars who re-established the text found different readings in the surviving manuscripts and accepted the reading found in the majority of manuscripts, but when they couldn't make up their minds about a reading they indicated both possibilities with these marginal notes. Kimhi's explanation of the kere and ketiv system, which like the preceding item (c) also implies that we are not sure which are the original readings, is not the only possibility, but for present pur-poses it is noteworthy that he considered it likely and that his religious faith did not prevent him from holding this view.²⁷

Medieval Jewish authorities were well aware of these textual phenomena.

a. The variant readings in Talmudic quotations of the Bible were well known to Jewish authorities throughout the Middle Ages. As the Tosafists (disciples of Rashi) put it: haShas shelanu xoleq al hasefarim shelanu, "Our Talmud disagrees with our Bibles" (at B. Shabbat 55b, s.v. M^cBYRM). From the 13th through the 19th centuries, major rabbinic authorities insisted that Torah scrolls be corrected to adopt the Talmudic readings, at least in passages where a law was based on a particular reading, but they insisted to no avail. To this day, all Jewish Bibles, including the Koren Bible on which the codes are based, contain the readings that are inconsistent with those quoted in the Talmud.²⁸

b. Discrepancies between good copies of the Masoretic Text were recognized and discussed throughout the Middle Ages and beyond. The Talmudic passage in Kiddushin 30a identifying the middle letter, words, and verses in the Torah concludes with statement that it is impossible to determine whether the middle letter belongs to the first half of the Torah or the second half because "we are not expert on full and defective spelling" (that is, the use of vowel letters). That passage was cited often in the Middle Ages to explain discrepancies between manuscripts and as the reason why a Torah scroll should not be declared unfit for use solely on the basis of discrepancies in full and defective spelling.²⁹ Masoretic treatises such as Minhat Shai (1626) -- which is still commonly printed in rabbinic Bibles (Mikra'ot Gedolot) -- regularly discussed spelling differences between model texts.³⁰ It was only with the rise of printing that greater textual uniformity was achieved, but even today, there is no universally agreed-upon version of the Masoretic Text.³¹ Yemenite Torah scrolls differ from the Koren edition in the spelling of nine words. Their readings are adopted in the edition edited by Rabbi Mordechai Breuer and published by the (Orthodox) Mossad Harav Kook (see Fig. 5a). These readings -- which reduce the total number of letters in the Torah by four -- agree with the Aleppo Codex,³² which Maimonides, in the Twelfth Century, said was considered the most reliable text in his time.³³ This is a point for the decoders to ponder: they are relying on a text that not only disagrees with the Talmud, but also disagrees with the text used by Maimonides, arguably the greatest authority on Jewish law in history.

In sum, apart from the archaeological evidence about the history of Hebrew spelling, and manuscript evidence about the history of the Biblical text, explicit statements in Talmudic and later Jewish sources make it crystal clear that present copies of the Tanakh are not identi-cal to the original text. Even the editors of the Koren edition have stated as much. When this edition was first published in 1962, at a public program celebrating its publication one of the editors who prepared the text stated: "We do not claim that we have established our edition on the basis of the tablets that Moses brought down from Mount Sinai."³⁴ He was absolutely correct.

Of course, one might claim that whatever may be the prehistory of the MT and the computerized version of the Koren text, in the latter the codes do work! Perhaps the Koren editors were miraculously guided to produce the text that does contain the revealed code. It is beyond me why God would have allowed the Talmudic rabbis to base laws on a text that He knew He would eventually change. In any case, whether the "codes" really work is also highly dubious, as we shall see.

THE FAMOUS SAGES EXPERIMENT

Advocates of the codes make much of the "famous sages" experiment in which Witztum, Rips, and Rosenberg (henceforth: WRR) claim to have found ELS-coded references in Genesis to famous medieval sages with their dates of birth and/or death nearby, closer than would be expected by chance alone. They studied two lists of sages, consisting of 34 and 32 individuals, respectively, and published the results, based on the second list, in the journal Statistical Science in 1994. In an accompanying note the editor of the journal stated:

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...readers as a challenging puzzle. (p. 306)

This experiment is controversial among mathematicians and other scientists.³⁵ A refutation has been written by Profs. Brendan McKay, a mathematician in the Department of Computer Science at the Australian National University in Canberra; Dror Bar-Natan, of the Department of Mathematics at the Hebrew University of Jerusalem; Maya Bar-Hillel, of the Department of Psychology and the Center for the Study of Rationality at the Hebrew University; and Gil Kalai, also a mathematician at the Hebrew University (henceforth: MBBK).³⁶ Since I am not a mathematician, I cannot comment independently on the mathematical aspects of the debate, but in all other respects it is clear to me that MBBK's argument is persuasive.

In WRR's experiment, everything hinges on the claim that the sages appear "in close proximity" to their dates. It is noteworthy that "close proximity" does not necessarily mean what laymen are likely to think it means. As Rips states elsewhere:

We have chosen for our analysis a specific pattern, namely, proximity (in a certain technical sense [emphasis mine -- JHT]) of related words appearing as ELSs. Thus, everything is reduced to a statistical analysis of the significance of such proximity patterns.³⁷

Since "proximity" is meant only in a technical sense, readers should not expect to find the names and dates of the sages in actual passages on real pages of the Torah. The letters of their names and dates are drawn from different chapters of the Torah, often many pages apart. Any proximity between them is found only on grids created by computer from ELSs. Perhaps this is why WRR do not show in their article any of the textual arrays in which the sages and their dates appear near each other (an example would be Fig. 3, above).³⁸ Instead, they illustrate the phenomenon of ELSs with a few simple arrays containing words of related meaning (such as the Hebrew words for hammer and anvil and some names that are related to each other) and for the sages experiment they publish the lists of the sages and dates whose ELSs they consider to be unexpectedly close to each other.³⁹ The closeness itself is displayed by mathematical tables and formulas rather than pictorially. It is virtually impossible for non-mathematicians to examine their evidence. In response to my question about this, McKay explained: "The pictorial evidence in the form of letter arrays is irrelevant to the mathematical question. What matters is only the numerical 'distance' computed according to WRR's complicated definition."

Interestingly, however, McKay continued as follows:

WRR don't actually claim that all the rabbis appear close to their dates. All they claim is that they are a little closer than expected on average. This slight statistical trend needs a careful test to detect. Some rabbis are far from their dates...and in fact most of them are closer to the dates of some other rabbi than to their own dates.⁴⁰ Here is a summary I made for WRR's second list, using the smallest distance from any name of a rabbi to any of his dates.

McKay's summary is as follows:

Rabbi Comment

1 Close to many dates but closest to the right date.
2 Closer to at least 8 wrong dates.
3 Closer to at least 3 wrong dates.
4 No date used (claimed to be uncertain)
5 No ELS for the date exists. Not close to anything.
6 Closer to at least 5 wrong dates.
7 Closer to at least 15 wrong dates.
8 No dates used (uncertain). Close to 8 wrong dates.
9 Far from right date, close to 7 wrong dates.
10 Far from right date, close to 9 wrong dates.
11 Far from right date, close to 10 wrong dates.
12 Close to many dates but closest to the right date.
13 Far from right date, close to 15 wrong dates.
14 Far from right date, close to 9 wrong dates.
15 Closer to at least 2 wrong dates.
16 Far from right date, close to 11 wrong dates.
17 No ELS for the name exists.
18 No ELS for either name exists.
19 Closer to at least 19 wrong dates.
20 Closer to at least 7 wrong dates.
21 Closer to at least 9 wrong dates.
(It seems the date is wrong; should be 1st Iyyar.
The right date does even worse.)
22 Good match, equally close to two wrong dates.
23 Close to many dates but closest to the right date.
24 Closer to at least 5 wrong dates.
25 Far from all dates.
26 Closer to at least 7 wrong dates.
27 Closer to at least 12 wrong dates.
28 Closer to at least 9 wrong dates.
29 No ELS for the name exists.
30 Good match, equally close to 1 wrong date.
31 Good match, equally close to 1 wrong date.
32 Far from right date, close to 3 wrong dates.

It is instructive to note that the rabbi contributing most strongly to the Statistical Science result is #27.⁴¹

From a layman's point of view, then, even using WRR's "technical" definition of proximity, the correlation of sages and their dates is actually poor, even though on average it is not quite as poor as one might have expected from chance; that is why mathematicians and other scientists find it interesting. But from a theological point of view, why should one be impressed by correlations that are surprising only "on average," and not in every case?

The same point may be illustrated another way. According to MBBK,⁴² in order to test whether there was an extraordinary closeness between the sages' names and dates, WRR compared the distances in the list of 32 sages and their dates of death to 999,999 alternative control lists in which each sage was paired not with his own date of death but rather with a date chosen randomly from the list (random pairings would more often than not pair a rabbi with the date of some other rabbi). The assumption was that "if there is anything special in the Book of Genesis and the sages' 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." Accordingly, 999,999 permutations of the list were chosen. In each, every sage was paired with the date of a sage chosen randomly from the list, and the distance between the names and those dates was computed. When the original, correct list of distances was compared to the 999,999 random lists, "the correct list achieved one of the first places" (fourth place, according to WRR) in this race among one million contestants. This means that three of the lists in which the sages were mostly paired with the wrong dates did better! In those three lists, the sages and the dates were closer than they are in the correct list. From a mathematical point of view it is interesting that the correct list did as well as it did (better than 999,996 other lists), since there was no a priori reason to expect it to do so. But from a theo-logical point of view, a test in which mostly incorrect lists perform better than the correct one seems meaningless. If God arranged the text so as to pair the sages with their dates, why would He have paired most rabbis more closely with incorrect dates than with correct ones?

Returning to the subject of textual criticism, MBBK re-ran WRR's experiment on the list of 32 sages based on the text of Genesis in the Koren edition and then on six other editions of the MT whose differences from Koren were listed by Prof. Menahem Cohen of Bar Ilan University (Cohen's list is posted on Brendan McKay's website; see note 30). Their results are as follows:⁴³

Differences Rank


Koren 0 6
Yemenite 3 19
Sassoon 11 2308
Venice Mikra'ot Gedolot 15 16608
Leningrad 22 12528
Jerusalem 35 19075
Hilleli 43 6411

"Differences" is the number of places where the other texts spell a word differently than Koren. The numbers under "Rank" mean that if one compares the correct dates to 10,000,000 random permutations of the dates, the correct dates perform 6th best, 19th best, 2308th best, etc. (for greater accuracy, MBBK give the ranks out of 10 million permutations, instead of the 1 million used by WRR). Note that the other texts do much worse than Koren, but that even in Koren the correct dates do not perform best. In other words, there is no known text of the Torah in which the list with the correct dates does best!

Given the fact that all of these editions of the MT are so much later than the original text of Genesis, it is also important to consider the much earlier Hebrew copies of Genesis from Qumran. Fragments from 14 different manuscripts of Genesis have been found at Qumran, from the last two centuries B.C.E. and the first century C.E. They differ from the MT in different degrees. Extrapolating from variants in these fragments, each of the manu-scripts when complete would have differed from the MT by hundreds of letters.⁴⁴ This number of differences is enough to completely obliterate the codes. As MBBK explain:

Clearly an ELS is destroyed if any letter is inserted or deleted within its overall span. The ELSs giving the strongest contribution to WRR's result together span most of the text. Experiments show that deletion of 10 letters in random places is enough to de-grade the result by an average factor of 4000, and 50 letters are enough to eliminate it completely.⁴⁵ Of course, the effect has a very large variance, as it depends on which of a comparatively small number of important ELSs are "hit" by a deletion. WRR's first list [the 34 sages - J.H.T.] is even more sensitive to the effects of corruption, as its important ELSs have greater skips. Ten letters deleted in random places are on average enough to eliminate its significance altogether.

Considering that even the Qumran scrolls are centuries later than the traditional date of the Torah, MBBK conclude:

if the text of Genesis were to be consistently spelled in the style of the inscriptions closest to the time it was traditionally written, the differences would number in the thousands (even without any change of meaning). This conclusion has catastrophic consequences for any theory that "codes" in the original text have survived until today.

MBBK argue that WRR's results, to the extent that they seem interesting at all, are due to flaws in their research methods. There are numerous possible forms of each rabbi's name and acronym that could have been used,⁴⁶ and numerous possible ways to write their dates.⁴⁷ MBBK argue that WRR chose only a limited number from among these possibilities, without any valid scientific reason for their choices, and that this strongly affected the outcome; had the test been run with other, equally valid choices, the results would have been worse. This strongly suggests, they argue, that WRR's choices may have been made not in an unbiased way, but precisely in order to enhance their results.

Much more material is available in MBBK's full article, cited in note 36. Part of that material includes patterns and "codes" found in other texts, such as the Christian Scriptures,⁴⁸ the Qur'an, and Poe's "The Raven." McKay showed that one can also find "encoded" references in Melville's Moby Dick to various political assassinations, such as those of Leon Trotsky, John F. Kennedy, and Martin Luther King, Jr. He and Bar-Natan also ran a version of the "famous sages" experiment on the first part of the Hebrew translation of Tolstoy's War and Peace, equal in length to Genesis. They followed the procedures used by WRR on Genesis, and achieved the same degree of success. That such results can be found in so many texts, including texts for which no one claims divine authorship, is not unexpected. It has long been known that striking pat-terns can be found in all kinds of large masses of data.⁴⁹

INTERPRETIVE METHODS

Apart from the mathematical aspects of the decoders' work, many other aspects of their method are also questionable. The basic method, as mentioned above, consists primarily of finding words formed of ELSs. "Interpreters" such as Drosnin then read the ELS-based words in conjunction with words, or parts of words, that are nearby or that intersect with them crossword fashion. What usually happens is that the computer will be "instructed" to look for a word. When the word is located, it is found to consist of letters spaced at equidistant intervals. As mentioned, the name Yitzhak Rabin is formed by letters appearing 4772 letters apart. Then the computer is instructed to lay out all the 304,805 letters of the Torah (Koren edition) in an array consisting of 64 rows of 4772 letters, so that Rabin's name appears in a vertical row. Then the computer displays the nearest segment of the array, a square consisting of ca. 15-20 rows of letters both horizontally and vertically. This segment resembles the grid of a "Word Hunt" puzzle (see Fig. 6), and the task of the researcher is then to find other phrases nearby that combine with it to form a message. Since the horizontal lines consist of Biblical verses, they can be searched by the naked eye. That's how the phrase "murderer who will murder" was found. But the codes aren't limited to what can be noticed with the naked eye. For example, if one asks ask the computer to find the name of Rabin's assassin nearby, it will do so a mere two lines above -- but with two hitches. As one can see from Fig. 7, the letters of the assassin's name (Amir) are a mere 9 spaces apart, not 4772, and -- they spell his name backwards! What is more, if one changes the width of the array, the phrase "murderer who will murder" will still be found in its place, but Rabin's name will now appear in a diagonal line with the letters separated from each other by two horizontal columns and one vertical (see Fig. 8). And if one does this, one will also find nearby the name of Netanyahu and the phrase "all his people to war," an ominous prediction of what Netanyahu might do. This willingness to change the distance between letters for different parts of the same message, to read words horizontally, vertically, diagonally, upside down and backwards, all within the same message -- procedures that are found on every page of the Bible code books -- gives the impression of arbitrariness and manipulation of the data. Nowhere do the decoders show these choices to be based on any objective, systematic method.

Fig. 6. A "Word Hunt" grid

Fig. 7. "Rabin's assassin" in Deuteronomy

Fig. 8. "Benjamin Netanyahu" in Deuteronmomy

Another key element of the procedures is to ignore the spaces between the words. By running all the letters of the Torah together, they can then be redivided into different words to produce new messages. For example, in Fig. 9, the words "fire, great noise [literally, thunder]" ('E$, RA^cAM, spelled '$ R^cM), allegedly describing a bus bombing in Jerusalem, are produced by redividing the letters of the words "which is near" ('A$ER ^cIM, spelled '$R ^cM) in Genesis 35:4. In an array that spans Exodus 19:12-Deuteronomy 4:48, some letters are lifted from parts of the words in God's declaration "You will be My people. I am the Lord your God" (Leviticus 26:12-13) and are taken to mean "July to Amman" -- Hebrew YULI LE-cAMAN, formed from the last two letters of the Hebrew word for "will be" (YU) plus the word for "My" (LI) and the word for "as a people" (LE-^cAM) plus the first two letters of the word for "I" ('AN) (see Fig. 10); this "phrase" is taken to predict a trip to Amman planned by Netanyahu for July, l996 (it was ultimately delayed until August).⁵⁰ Just how much mischief can be done by this method was shown to me when I was in Hebrew high school by a teacher who pointed out that the words "In the beginning God created" (Genesis 1:1) could be redivided into "At first the god of the sea created himself" (see Fig. 11). Truly, by such methods one can produce messages not only undreamed of by the Torah, but contrary to its most fundamen-tal, monotheistic, teaching.

Fig. 9. "Bus bombing" in Genesis

Fig. 10. "July to Amman" in Leviticus

Fig. 11. "The God of the Sea" in Genesis 1:1

Likewise problematic are other methods used in interpreting these alleged messages. First, the messages consist of disconnected words and phrases with no syntactic connection, which leaves them equivocal. For example, the intersecting phrases "Yitzhak Rabin" and "murderer who will murder" could mean "a murderer will kill Rabin" or "Rabin is a murderer." In fact, since the Hebrew grammatical particle 'ET that usually precedes the direct of object of a verb is not present before Rabin's name, Rabin is more likely the subject of the verb than its object, and the message more likely means that he is a killer than that he will be killed. Another message consists of the phrases "Hitler," "evil man," "Nazi and enemy," and "slaughter." In a somewhat lighter vein we have this message: "Watergate," and "Who⁵¹ is he? President but he was kicked out." And here is a third message: "Einstein," "science," "he overturned present reality," "they⁵² prophesied a brainy person," "a new and excellent under-standing." These disconnected phrases make the author of the codes sound like an incoherent babbler.

Then there are messages that do not come true. In time-honored fashion, they are ra-tionalized or reinterpreted. Near the supposed prediction of Rabin's assassination Drosnin found the words "all his people to war," which he took to predict an atomic holocaust after Rabin's death (pp. 54-58). Eventually, he settled for the 1996 bus bombings as the fulfillment of the prediction "all his people to war" (p. 69). Drosnin found another message with the phrases "atomic holocaust," "Libya," and the date 1995-96, which he took as a warning of a nuclear attack on Israel by Libya in that year; the closest thing he can report to confirmation is the fact that in 1996 the Libyan leader Muammar Kaddafi called on all Arab countries to acquire nuclear weapons. But Drosnin is also protected against this problem because he even-tually "realized" that not all predictions are definite, and that the Hebrew letters that spell out the Hebrew equivalent of 1995-96 (HT$NV) also spell out a word meaning "Will you change (it)?" (HATE$ANNU, pp. 59, 83).

Finally, those parts of the messages produced by reading the letters of the horizontal lines in their actual sequence are not produced by equidistant letter sequences, but by arbitrari-ly selecting certain letters as part of the message and ignoring the rest. This is a very important point: the choice of which letters and words to include in a message is not based on an objec-tive, scientific method, such as considering only words composed of equidistant letters -- it is, rather, subjective and arbitrary. For example, citing again the passage intersecting with Rabin: that passage is from Deuteronomy 4:42, but Drosnin ignores the words immediately following "a murderer who will murder." What comes next is the phrase "unwittingly" (biveli da'at). This is because the verse deals with the cities of refuge where accidental killers can find asylum. In this case, then, the message would refer to an accidental killing of (or by) Rabin and it would therefore be wrong. Another message (p. 71) supposedly contains a "complete" description of the terrorist bombing of a bus in Jerusalem on February 25, 1996. It includes the phrase "fire, great noise," but overlooks the fact that the letters which make up those two words are actually part of a larger phrase from Genesis 35:4 which says: "under the terebinth that was near Shechem." If the phrase does tell of a bus bombing, why not take it to indicate that it would be in Nablus, the site of ancient Shechem?⁵³

Of course proponents of the codes could argue that since Rabin was assassinated and the bus was bombed in Jerusalem, that is what the codes must have meant. But if the very meaning of the messages is apparent only after the fact, of what use are they? What did their author hope to achieve by encoding them? They become no better than the Delphic oracles who told Croesus that if he attacked the Persians he would destroy a mighty empire. When he was defeated and complained to the oracles, he was told that if he had been wise he would have inquired whether the Persian empire or his own was meant; he therefore had only himself to blame for the result (Herodotus 1:53, 91).

* * * * *

As mentioned earlier, there are differences between the work of Rips and Witztum, on the one hand, and Drosnin on the other hand. On a personal level, Drosnin regularly insists that he is not religious and does not believe in God, which puts him in the bizarre position of wanting the Israeli government to act on the disastrous messages that he finds encoded in the Bible while he personally disregards the messages that are stated there plainly! (Perhaps this is connected with Drosnin's suggestion that the true source of the Bible is an advanced alien, extraterrestrial intelligence [pp. 96-98].) Rips and Witztum are religious Jews who at least live in harmony with their theories. Furthermore, they vigorously deny that the Bible codes can be used to predict the future. But all of these gentlemen base their computations on an unreliable textual base which evidence suggests was not the original text of the Torah, and all of them strain the credibility at least of the layman by changing the size of the ELSs for different parts of each message or pattern, and by reading words horizontally, vertically, diagonally, upside down and backwards, giving the impression of arbitrariness and manipulation of the data. Their case, therefore, is not convincing.⁵⁴

NOTES

In transliterating Hebrew, I use the closest English equivalents. Special cases are:

' = aleph ^c = ayin
V = vav C = tsadi
X = het Q = qof
T = tav or tet $ = shin

This paper is based on a lecture delivered as part of a panel on "The Bible Code: Criti-cal Perspectives" convened by Prof. Saul Kripke at the Princeton University Math Department on April 28, 1998. In preparing and revising this paper I benefited from helpful suggestions and information kindly provided by Profs. Moshe Greenberg, Uriel Simon, Emanuel Tov, Shlomo Sternberg, Sid Z. Leiman, B. Barry Levy, Yeshayahu Maori, Alan Groves, Messrs. Scobie Smith and Alec Gindis, my student Shawn Zelig Aster, and my fellow panelists Profs. Brendan McKay and Maya Bar-Hillel.

1. Jacob Mann, The Jews in Egypt and Palestine under the Fatimid Caliphs (reprint New York: Ktav, 1970), 1:241; 2:307.

2. See J. Tigay, "An Early Technique of Aggadic Exegesis," in H. Tadmor and M. Weinfeld, eds., History, Historiography, and Interpretation (Jerusalem: The Hebrew University of Jerusalem. The Institute of Advanced Studies. Magnes Press, 1983), pp. 175-176. See also B.M. Metzger, "Sortes Biblicae," in The Oxford Companion to the Bible, ed. B.M. Metzger and M.D. Coogan (New York: Oxford University Press, 1993), pp. 713-714.

3. Aish HaTorah's Discovery Seminar (no editor, date, or place of publication listed; the cover includes the name of the organization "Arachim" and states that the booklet is "Sponsored by the Dan Family of Canada"), p. 11; M. Katz, Computorah. Dr. Moshe Katz on Hidden Codes in the Torah (Jerusalem: CompuTorah [P.O.B. 23702], 1996), pp. 74-77. According to Katz, p. 74, and J. Satinover, Cracking the Bible Code [New York: William Morrow, 1997], pp. 2-3, 85, this ELS was discovered by Rabbi Michael Dov Ber Weissman-del, while the discovery of Maimonides' acronym is traced, perhaps apocryphally, to the Vilna Gaon.

4. New York: Simon and Schuster, 1997.

5. This is the number of letters in the Koren edition of the Torah (Torah, Nevi'im, uKetuvim [Jerusalem: Koren, 1962 and frequently thereafter]). It agrees with Jacob ben Hayyim ibn Adoniah's colophon in the Pardes edition of Mikra'ot Gedolot at the end of Deu-teronomy.

6. Doron Witztum, Eliyahu Rips, and Yoav Rosenberg, "Equidistant Letter Sequences in the Book of Genesis," Statistical Science 9/3 (1994):429-38.

7. The year of the Maharshal's death (5334 [1573]) also appears in this array, but years were not included in WRR's test.

8. Katz, Computorah, pp. 150-155, 204-208.

9. Katz, Computorah, pp. 12-22; Drosnin, pp. 38, 194-95. Witztum resolved the ques-tion of the accuracy of the text by simply consulting Rabbi Shlomo Fisher, who answered that "we could fully rely on our text" (Witztum, "The Seal of God is Truth," Jewish Action 58/3 [Spring, 1998]:26; on p. 32 n. 2 he claims to have given a full treatment of this issue on his website [http://www.torahcodes.co.il]; however, as of 17 August, 1998 and January 26, 1999, I could find no such discussion in any obvious place on his website, and two e-mailed requests for clarification, sent to the address given on the website, went unanswered). Drosnin states that "all [Hebrew Bibles] that now exist are the same letter for letter" and that "the Bible code computer program uses the universally accepted original Hebrew text." He states that the text "existed at least 1000 years ago, and almost certainly 2000 years ago, in exactly the same form it exists today" (pp. 194-95). In fact, he assumes that it is identical to the text of the time of Moses, since throughout the book he keeps referring to the code's predictions as being from 3000 years ago (e.g. pp. 39, 87, 90). The same assumption of textual accuracy is necessary for a similar reason according to Nahmanides' introduction to the Torah, who refers to a tradition that "the whole Torah is comprised of Names of [God], and that the letters of the words separate themselves into Divine Names when divided in a different manner" (Eng. trans. by C.B. Chavel, Ramban (Nachmanides). Commentary on the Torah [New York: Shilo, 1971] 1:13-15).

10. See Menahem Cohen, "The Idea of the Sanctity of the Letters of the Text and Textual Criticism," in U. Simon, ed., HaMiqra' vaAnahnu (The Bible and Us) (Tel Aviv: Dvir, 1987), 42-69. An English translation under a slightly different title appears on Brendan McKay's website:
http://cs.anu.edu.au/~bdm/dilugim/CohenArt.

11. For the history of the Masoretic Text see E. Tov, Textual Criticism of the Hebrew Bible (Minneapolis: Fortress Press, 1992), 22-79.

12. There are 304,850 letters in the Michigan-Claremont-Westminster (MCW) comput-erized text of Biblica Hebraica Stuttgartensia (BHS), which is the critical edition of the Lenin-grad codex currently in use by most scholars (statistics courtesy of Alan Groves, the final editor of the MCW text). C.D. Ginsburg's edition of the Torah contains 304,807 letters ac-cording to the colophon at its end (C.D. Ginsburg, The Pentateuch [London: British and Foreign Bible Society, 1926; repr. Jerusalem: Makor, 1970]).

13. All known Hebrew Bible texts, ancient and modern, use a system of spelling that is different from the one that was used in the days of Moses. The archaeological evidence shows that Hebrew spelling has gone through three stages.

(1) At first, Hebrew and the other West Semitic alphabets (such as Ugaritic, Phoenician and Aramaic) represented only consonants, and readers were normally left to infer the vowels from the context. This was a problematic system because it left many words equivocal. It would be as if we wrote the English letters r-v-r and left the reader to decide whether they stood for river, rover, raver, revere, or Rivera. On rare occasions, certain long vowels were indicated. To indicate them, a few of the consonants were used as matres lectionis to represent the vowels that sounded like those consonants; the consonant Y, in particular, was also used for the vowel sound /i/.

(2) In the second stage this sporadic use of consonants was expanded and four different consonants were used more frequently to indicate vowels. VAV, originally pronounced like a w, was also employed as a vowel to indicate certain /u/'s and /o/'s (e.g. LNV = LANU; XWRC = XOREC); ALEPH (pronounced consonantly as a glottal stop) represented certain other /o/'s and /u/'s (e.g. R'$ = RO$; H' = HU); YOD repre-sented /i/ and certain /e/'s (e.g. 'DNY = ADONI; BYT = BET); and HEH (pro-nounced consonantally as h) represented /a/ and certain other /o/'s and /e/'s (e.g. HYH = HAYAH; ^cBDH = ^cABDO; ZH = ZEH). This stage began around the tenth century B.C.E. in Aramaic, and later spread to Hebrew. It was a gradual development, used at first for long vowels at the end of words, and later, but less frequently, within words as well. This system was a major help for readers, but it was imperfect for three reasons: first, there weren't enough suitable consonants, so each of them had to represent more than one vowel; second, they were not consistently used -- sometimes a vowel would be indicated, sometimes not ("full" and "defective" spelling, as explained above); and third, those letters continued to represent consonants as well as vowels, creating a certain amount of ambiguity.

(3) Finally, much later, some time between the sixth and eighth centuries C.E., the system of diacritical "points" -- dots and dashes above and below the letters -- was invented to represent the vowels. This created a certain amount of redundancy since the vowel letters of the second stage continued to be used alongside the diacriticals, but it led to greater clarity.

Let me exemplify. In the Gezer Calendar, the oldest known Hebrew inscription from Biblical times, the word meaning harvest, QACIR, is spelled Q-C-R (see the boxed word in Fig. 4). The internal vowel /i/ is not shown. In Masoretic Torah scrolls, it is spelled Q-C-Y-R, with the vowel /i/ represented by Y (see the boxed word in Fig. 5 left). In Bibles with diacritical vowel points, the same letters are used, but the diacrit-ical signs are added above and below the letters (see the boxed word in Fig. 5 right; all three types of spelling are represented in English characters in Fig. 4, lower right).

Fig. 4. The Gezer Calendar and the word QACIR ("harvest")

Fig. 5. Selection from a Torah scroll and a printed Bible
with diacritical vowels and cantillation signs

Now the Gezer Calendar comes from the 10th century B.C.E., approximately three centuries after Moses. Its non-representation of the internal vowel is characteristic of the West Semitic writing that we know from that early period. It is clear that the Bible texts we use today, which usually include matres lectionis to represent long vowels at the end of words and often within the words, reflect a post-Mosaic system of spelling (again, see Fig. 5). The spelling in manuscripts of Moses's time would have looked very different from that in the Masoretic Text of today, which contains thousands of vowel letters that would not have been used in Moses's time.

For the history of the spelling system see F.M. Cross, Jr., and D.N. Freedman, Early Hebrew Orthography. A Study of the Epigraphic Evidence. American Oriental Series 36 (New Haven: American Oriental Society, 1952); Z. Zevit, Matres Lectionis in Ancient Hebrew Epigraphs. American Schools of Oriental Research Monograph Series 2 (Cambridge, Mass.: American Schools of Oriental Research, 1980); Tov, Textual Criticism, pp. 39-49; M. Greenberg, Introduction to Hebrew (Englewood Cliffs, N.J.: Prentice-Hall, 1965), 17-23.

14. The two versions are laid out side by side, with differences highlighted, in Abba Bendavid, Makbilot BaMikra' (Parallels in the Bible) (Jerusalem: Carta, 1972), p. 61-62. Kimhi held that such differences as Dodanim in Gen. 10:4 vs. Rodanim in 1 Chron. 1:7, and Deuel in Num. 1:14 vs. Reuel in 2:14 are due to confusion of similar letters, but he held that the confusion took place in pre-Biblical texts and that the Bible intentionally preserved both forms to show that they referred to the same peoples or persons; there was no confusion in the transmission of the Bible itself (see his comments to Gen. 10:4 and 1 Chron. 1:7, and Uriel Simon, "Ibn Ezra and Kimhi -- Two Approaches to the Question of the Accuracy of the Masoretic Text," Bar Ilan 6 (1968):208-209).

14a. See Mekhilta Pish . a, 18 (ed. Horovitz-Rabin, p. 73; ed, Lauterbach 1:166-167); Yerushalmi Pesahim 10.4, 37d; M.M. Kasher, Haggadah Shelemah 3d ed. (Jerusalem: Torah Shelema Institute, 1967), p. 22; N.N. Glatzer, The Passover Haggadah (New York: Schock-en, 1969), pp. 24-29.

15. Noted in Jacob ben Chaim's introduction to Mikra'ot Gedolot (1525; see C.D. Ginsburg, Jacob ben Chajim ibn Adonijah's Introduction to the Rabbinic Bible...1867; repr. New York: KTAV, 1968; see, for example, p. 42); Minhat Shai (1626); Rabbi Akiva Eiger, Gilyon haShas, Shabbat 55b; S. Rosenfeld, Sefer Mishpahat Soferim (Vilna: Romm, 1883); M.M. Kasher, Torah Shelemah 23 (Jerusalem: American Biblical Encyclopedia Society/Makhon Torah Shelemah, 1969), pp. 113-14 (for Genesis and Exodus); etc. The basic modern study is V. Aptowitzer, Das Schriftwort in der Rabbinischen Literatur (1906-15; repr. New York: KTAV, 1970, with prolegomenon by S. Loewinger), which focuses on Joshua and Judges. See also Y. Maori, "Rabbinic Midrash as Evidence for Textual Variants in the Hebrew Bible: History and Practice," in S. Carmy, ed., Modern Scholarship in the Study of Torah. Contributions and Limitations. The Orthodox Forum Series. A Project of the Rabbi Isaac Elhanan Theological Seminary. An Affiliate of Yeshiva University (Northvale NJ: Jason Aronson, 1996), pp. 101-29. On variant readings in Rashi's commentary, see Shnayer (Sid) Z. Leiman, "Yavneh Studies in Naso," in Yavneh Studies in Parashat HaShavua. Bemidbar (New York: Yavneh. The Religious Jewish Students Association, 1972), pp. 3-7.

16. For example, in Bavli Berakhot 61a R. Nahman bar Yitzhak quotes a passage that is not present in the MT: VYLK 'LQNH 'XRY '$TV, "and Elkanah walked after his wife." This passage, if it existed, would have belonged in 1 Samuel 1 or 2. It is also absent in the Septuagint and in the partially preserved fragments of Samuel from Qumran. However, both of these versions of the text include other extra phrases not found in the MT (in 1 Samuel 1:22 a Qumran fragment reads: "And I shall give him as a Nazirite forever all the days of his life," and in v. 18, after "the woman went her way," the Septuagint adds: "and entered the chamber and ate with her husband and drank"). This suggests that R. Nahman bar Yitzhak was quoting from a text of Samuel known to him. (For the Qumran text see F.M. Cross, "A New Qumran Biblical Fragment Related to the Original Hebrew Underlying the Septuagint," Bulletin of the American Schools of Oriental Research 132 [1953]:15-26.

17. The precept of tefillin is based on Exodus 13:9 and 16 and Deuteronomy 6:8 and 11:18. The word totafot, "frontlets, headbands," referring to the tefillin worn on the head, appears in three of these verses. According to Rabbi Ishmael in the Talmud (Sanhedrin 4b and parallels), the suffix -OT is spelled defectively (that is, without the vowel letter VAV) in the first two occurrences and fully (with the VAV) the third time. This allows the first two to be read "as if" they were singulars, implying one compartment each, and requires the third to be read as a plural, hence requiring two compartments, and thus indicating that the head tefillin must have a total of four compartments. However, in all known copies of the Bible, both ancient (with one exception, in Exodus 13:16) and Masoretic, the suffix is spelled defectively all three times, and this is how Maimonides rules that they must be written (Mishneh Torah, Hilkhot Tefillin 2:7, presumably following the Aleppo Codex). For the ancient manuscripts see J. Tigay, "On the Meaning of totafot," Journal of Biblical Literature 101 (1982):321. For other such examples see Leiman, cited in the next note.

18. Sid Z. Leiman, "Masorah and Halakhah: A Study in Conflict," in Tehilla le-Moshe. Biblical and Judaic Studies in Honor of Moshe Greenberg, ed. M. Cogan, B.L. Eichler, and J.H. Tigay (Winona Lake, Indiana: Eisenbraun's, 1997), pp. 291-306.

19. S. Rosenfeld, Sefer Mishpahat Sofrim (Vilna: Romm, 1883), 34-36, 100, who identifies the middle letter as the ALEPH in the word HU', in Lev. 8:28 (the same is true for the Koren edition), and the middle pair of words as 'EL YESOD in Lev. 8:15. According to the Talmud, the middle letter is the VAV in the word GAXON in Lev. 11:42, and the middle words are DAROSH DARASH in Lev. 10:16. The inconsistency between the Talmudic passage and the MT of today is also noted by Barukh HaLevi Epstein, Torah Temimah, at Lev. 11:42 and M.M. Kasher, Torah Shelemah 28 (Jerusalem: American Biblical Encyclopedia Society/Makhon Torah Shelemah, 1978), pp. 286-289. In the Yemenite text the middle letter is the L of LYHVH in Lev. 8:28; according to Alan Groves, in BHS, which has an even number of letters, the middle two letters are HX in HXZH, also in Lev. 8:28. Witztum claims to have dealt with the passage in Kiddushin 30a on his website but, as noted above in note 9, I could find no such discussion there.

20. For the latter possibility one may compare the Septuagint of Exodus 35-40, which is based on a Hebrew original that had many passages in a different order than in the MT. But if this is the case in the text to which the "first scholars" were referring, it was, without the rabbis realizing it, from a textual tradition other than the one that was current in rabbinic cir-cles.

21. See Maimonides, Introduction to Perek Helek (Sanhedrin 10:1), Eighth Principle; R. Joseph Albo, Sefer haIkkarim 3:22; Abarbanel, Introduction to Commentary on Jeremiah (Tel Aviv: Torah veDaat [n.d.]), pp. 298-99.

22. E.g., Shlomo Sternberg, "Snake Oil for Sale," Bible Review 13/4 (August, 1997): 24-25; "Comments on The Bible Code, in Notices of the AMS 44/8 (September, 1997):938-39. For other Orthodox scholars acknowledging changes in the text, see also Cohen (above, note 10; below, note 30), Leiman (above, note 18) and Levy (below, n. 28). In view of the spell-ing variations in Torah manuscripts, the late Rabbi Yaakov Weinberg, Rosh Yeshiva of Yeshivat Ner Yisrael, wrote:

Rambam knew very well that these variations existed...The words of Ani Ma'amin and the words of the Rambam [in his commentary on Mishnah Sanhedrin 10:1] "the entire Torah in our possession today" [is the one that Moses received from God] must not be taken literally, implying that all the letters of the present Torah are the exact letters given to Moshe Rabbeinu. Rather, it should be understood in a general sense that the Torah we learn and live by is for all intents and purposes the same Torah that was given to Moshe Rabbeinu.

Y. Weinberg, Fundamentals and Faith. Insights into the Rambam's Thirteen Principles, ed. M. Blumenfeld (Spring Valley, N.Y.: Feldheim: 1991), pp. 90-91 quoted by M.B. Shapiro, "Maimonides' Thirteen Principles: The Last Word in Jewish Theology?" The Torah U-Madda Journal 4 (1993):203 (for our purposes R. Weinberg's view is important whether or not Maimonides intended his words to be taken literally). (Ironically, R. Weinberg's book is listed in "Aish HaTorah's Recommended Reading List" http://www.aish.edu/learning/booklist.htm).

22a. See D.Z. Hoffmann, Sefer Vayikra (Jerusalem: Mosad Harav Kook, 1956), pp. 7-8; for an English translation see Hoffmann's "General Introduction to Biblical Exegesis," translated from the original German by Jenny Marmorstein, "David Hoffmann: Defender of the Faith," Tradition Winter 1966, pp. 99-100.

23. See Saul Lieberman, Hellenism in Jewish Palestine (New York: Jewish Theological Seminary, 1962), pp. 28-37; Tov, Textual Criticism, pp. 64-67; Ginsburg, Introduction, pp. 347-363. Examples are in Gen. 18:22 (see also Rashi) and 1 Sam. 3:13, "committed sacrilege at will/for themselves" (LHM), where Radak records a tikkun soferim to avoid saying "com-mitted sacrilege against God" ('L, or 'LHYM), as the Septuagint actually reads (Tanakh [Jewish Publication Society] ad loc., note a-a). Lieberman shows that the views that these readings are original euphemisms (kinnah(u) hakatuv) and scribal corrections (tikkun soferim) are distinct and divergent traditions and should not be harmonized so that one becomes just another way of referring to the other. The view that they are original euphemisms appears in tannaitic sources; the view that the scribes actually changed the original text is first expressed by Rabbi Joshua b. Levi (first half of third century): "It is a correction of the scribes; (the word ^cYNW, 'his eye, in Zechariah 2:12) was (originally) written with a yod (i.e., ^cYNY, 'My eye')" (Shemot Rabbah 13:1). Note also the Masoretic list cited by Ginsburg, Introduc-tion, p. 351 n. 2, which explicitly states that in each case something else "was written" in place of the current reading in the MT.

The Talmud also lists 5 words containing "omissions of the scribes" (ittur soferim) in which the scribes omitted the one-letter conjunction vav (Ginsburg, Introduction, pp. 308-309; Tov, p. 67; see Tosafot, the Geonim, the Arukh and other views cited by Steinsaltz at B. Nedarim 37b).

24. Avot deRabbi Nathan, Version A chap. 34; Version B chap. 37 (pp. 101 and 98 in ed. Schechter; for translations see J. Goldin, The Fathers According to Rabbi Nathan [New Haven: Yale University Press, 1955], pp. 138-39; A. Saldarini, The fathers According to Rabbi Nathan...Version B [Leiden: Brill, 1975], p. 224); see also Bemidbar Rabbah 3:13.

25. Lieberman, Hellenism in Jewish Palestine, pp. 43-46.

26. See Lieberman, Hellenism, pp. 21-27; S. Talmon, "The Three Scrolls of the Law that Were Found in the Temple Court," Textus 2 (1962):14-27.

27. For Kimhi's view on textual criticism see U. Simon, "Ibn Ezra and Kimhi -- Two Approaches to the Question of the Accuracy of the Masoretic Text," Bar Ilan 6 (1968):191-237.

28. Leiman, "Masorah and Halakhah." The struggle is traced in great detail in a forth-coming book by B. Barry Levy, Fixing God's Torah. The Accuracy of the Hebrew Bible Text in Jewish Law, kindly shown to me by the author in advance of publication.

29. Shulhan Arukh, 'Orah Hayyim 143:4, Isserles; cf. Kasher, Torah Shelemah 28:229-30, note 258.

30. For a list of discrepancies cited by Minhat Shai in Genesis and Exodus, see Kasher, Torah Shelemah 23:109-111 (a fuller list of variant readings for Genesis, prepared by Menahem Cohen, is found on Brendan McKay's website at:
http://cs.anu.edu.au/~bdm/dilugim/cohen_heb1.html (see also C.D. Ginsburg, The Massorah, 3:23-36, 106 etc.). Mordechai Breuer presents a list of over 200 orthographic differences between six important versions of the MT (five ancient masoretic manuscripts and the text in Mikra'ot Gedolot); see his The Aleppo Codex and the Accepted Text of the Bible (Jerusalem: Mosad Harav Kook, 1976), pp. 68-94 (in Hebrew).

31. A list of discrepancies in spelling and conjunctions in the first 19 printed editions of the Torah is found in Torah Shelemah 23:111-112.

32. The readings are at Gen. 4:13; 7:11; 9:29; Exod. 25:31; 28:26; Num. 1:17; 10:10; 22:5; and Deut. 23:2. See M. Breuer, Hamishah Humshei Torah (Jerusalem: Horev, 5756/1996), Appendix "haNusah," p. 9; M.L. Katzenellenbogen, ed., Torat Hayyim (Jerusalem: Mossad Harav Kook, 1993), Vol. 5, Devarim, p. 447. The Yemenites regard these dif-ferences seriously enough that they consider non-Yemenite Torah scrolls to be disqualified for public reading. See Y. Kapah, devarim 'axadim, paragraph aleph, in Sefer Keter HaTorah. Ha"Taj" HaGadol, ed. Y. Hasid (Jerusalem, 5730/1970), p. 2. There were three additional variants in the Aleppo Codex not found in the Yemenite text: Exod. 1:19 ('LYHN); Lev. 19:16: R^cYK; Lev. 25:10 (or possibly 11 or 12) (HY'). See Menahem Cohen, Mikra'ot Gedolot HaKeter. Joshua-Judges (Ramat Gan: Bar Ilan University 1992), pp. 55*, 96* nn. 160-161, citing Joseph Offer, "M.D. Cassuto's Notes on the Aleppo Codex," Sefunot N.S. 4 (19) (1989), pp. 309, 335.

33. Maimonides, Mishneh Torah. Hilkhot Sefer Torah 8:4.

34. M. Medan, "Al haNusah beMahadurat Koren," Beth Mikra 3 (15), Jan. 1963:142. It is worth keeping in mind that the decoders do not work directly with the Koren edition, but with a computerized version of its text, which could contain errors. There is at least as much room for human error in typing the text into the computer as there has always been in copying texts manually (and in setting them in type). Anybody familiar with how frequently errors can still be found in Torah scrolls, even though they are written by experienced scribes following exacting procedures, understands this. Rabbi David Greenfield of the Vaad Mishmeret Stam in New York (an organization of scribes that checks Torah scrolls for errors) informs me that errors are found in more than half the scrolls checked, and in more than 90% of those written since World War II (the Vaad now uses computer scanners to check for errors, and when it first received an electronic text of the Torah to use as the standard, 10-15 errors were found in it!). A sobering case in point is an article published in 1981 by Gerard E. Weil, an expert on the Masorah who edited the Masorah of BHS. Weil's article, based on a computerized version of the text that he prepared, gives the total number of letters in the Leningrad Codex's text of the Torah, and the total number of occurrences of each letter of the Hebrew alphabet ("Les decomptes de versets, mots et lettres du Pentateuque selon le manuscrit N 19a de Leningrad," in P. Casetti et al. eds., Melanges Dominique Barthelemy [Gottingen: Vandenhoeck & Ru-precht, 1981], pp. 651-703). But the Michigan-Claremont-Westminster (MCW) text of BHS, prepared independently of Weil's, gives different totals for the whole Torah (304,850 versus Weil's 304,848) and for 14 of the letters of the alphabet. Alan Groves, the final editor of the MCW, text tells me that in every case where a consonantal difference was found between it and Weil's text, Weil's was found to be wrong. Before concluding that the computerized ver-sion of the Koren text reproduces even Koren itself accurately, one would desire some evi-dence of how carefully, and how many times, it was checked against the original Koren text.

35. A critical statement, signed by over 40 mathematicians, is published on the internet at the following website: http://www.math.caltech.edu/code/petition.html.

36. B. McKay, D. Bar-Natan, M. Bar-Hillel, and G. Kalai, "Solving the Bible Code Puzzle," in Statistical Science, 14/2 (1999):150-173. The article is available on McKay's and Bar-Natan's websites at, respectively http://cs.anu.edu.au/~bdm/dilugim/StatSci/StatSci.pdf and http://www.ma.huji.ac.il/~drorbn/codes/StatSci.pdf. An earlier, less technical paper was published by M. Bar-Hillel, D. Bar-Natan and B. D. McKay, "The Torah Codes: Puzzle and Solution," in Chance (A Magazine of the American Statistical Association) 11 (1998): 13-19. For those with the proper software, the paper is available on Brendan McKay's website (http://cs.anu.edu.au/~bdm/dilugim/Chance.pdf).

37. "Dr. Rips Responds to Professor Sternberg," http://www.discoveryseminar.org/rresponse2.htm).

38. A number of arrays are shown pictorially in Doron Witztum, ha-Memad ha-nosaf: 'al ha-Ketivah ha-Du-memadit ba-Torah (Jerusalem: Ka-tamar Yifrah, 5749 [1988-89], pp. 101-131.

39. WRR, pp. 432, 433.

40. E-mail letter of 5 May, 1998. On the same date, Bar-Hillel, responded in a similar vein:

[T]he result WRR published is not really that rabbis are close to their dates, but rather that a large list of rabbis paired with their own dates are closer, on average [my empha-sis - J.H.T.], than lots and lots of lists where rabbis were paired with someone else's dates. So it is a comparative assertion, not an absolute one. To be sure, their rationale requires actual proximity, and they devised a complex measure of alleged proximity, but the "miracle" is not in the absolute proximities, but rather in relative proximities. In other words, even though the rabbis yield very few "pretty pictures" with their own dates, there may be even fewer with other dates. Paradoxically, even that is not the case...but as per the race they ran between lists, the correct list did almost best. Poorly, by the measure of 'pretty pictures,' but almost best."

41. McKay, e-mail letter of 7 May, 1998.

42. Bar-Hillel, Bar-Natan and McKay, "The Torah Codes: Puzzle and Solution," in Chance 11 (1998):15.

43. E-mail letter of 26 May, 1998.

44. 4QGenesis^b is a possible exception. It has one difference in the 1200 surviving letters. If variants were evenly distributed through the entire manuscript, this would imply a difference of about 65 letters in all of Genesis. This would make the scroll quite anomalous among the Qumran fragments, and it may be that the surviving fragments are accidentally closer to the MT than the rest of the manuscript was. But even assuming a mere 65 letters of difference from the MT, that is enough to completely obliterate the codes, as we shall see below.

45. According to cryptographer Harold Gans, 78 deleted letters are necessary to oblit-erate the statistical significance of the codes (Satinover, Cracking the Bible Code, p. 224). For present purposes, this makes no difference.

46. For example, Rabbi Hayyim Benveniste's name can be written: BNBN$TY, HRB HXBY"B, HRB XBY"B, RB XBY"B, or RBY XYYM. Other have even more possible appel-lations, including the names of their major books, sometimes preceded by B^cL, sometimes not.

47. For example, ALEF TISHREI, B'ALEF TISHREI, ALEF B'TISHREI, B'ALEF B'TISHREI, ALEF L'TISHREI, B'ALEF L'TISHREI, ALEF SHEL TISHREI, B'ALEF SHEL TISHREI.

48. Christians have also begun to claim that Christological messages can be found encoded in the Tanakh as well. For example, Grant R. Jeffrey, The Mysterious Bible Codes (Nashville: Word Publishing, 1998), chaps. 6-8, finds ELS-based references to Jesus, Mary, and some of Jesus's disciples in Isaiah 53, Psalm 22, and elsewhere (ref. courtesy of Chanan and Yisrael Tigay).

49. See A.M. Hasofer, "Codes in the Torah: A Rejoinder," in B'Or Ha'Torah 8 (1993/5743), pp. 121-131 (published by "Shamir," the Association of Religious Professionals from the Soviet Union and Eastern Europe in Israel, POB 5749, Jerusalem, Israel).

50. Drosnin, The Bible Code, pp. 157-8. For this and other examples, see R. Hendel, "The Bible Code: Cracked and Crumbling," Bible Review 13/4 (August, 1997), p. 23.

51. Who is "he"? The text never mentions Nixon's name! Actually, the spelling (MHV) would more likely mean: What is he/it?

52. Who? Drosnin never explains.

53. On pp. 58 and 80, Drosnin's rendering "after the death of prime minister" ignores the intervening word 'B, "father," which would make the message mean "after the death of the father of the prime minister" (later in the book, on p. 161, he includes 'B, reading the passage as: "Another will die, Av [i.e., the Hebrew month of Av], prime minister." On p. 54 he ignores what follows "all his people to war": "to Jahaz, and the Lord our God delivered him to us and we defeated him..." (Deut. 2:32-33).

54. Sources of the illustrations are as follows:

Fig. 1. Katz, Computorah, p. 77.

Fig. 2. Drosnin, p. 15.

Fig. 3. Aish HaTorah's Discovery Seminar, p. 5.

Fig. 4. Drawing from J. Naveh, Early History of the Alphabet (Jerusalem: Magnes, and Leiden: Brill, 1982), p. 63; transliteration from R. Hestrin, et al., Ketovot Mesapperot (Inscriptions Reveal). Israel Museum Catalogue no. 100. 2d edition (Jerusalem: Israel Museum, 1973), p. 18.

Fig. 5. Tikkun laKore'im. Revised ed. (New York: KTAV, 1969), p. 87.

Fig. 5a. The upper half of the figure, showing a standard printed text with the Yemenite variant indicated in the margin at Genesis 6:29, is from Sefer Keter ha-Torah. Ha"Taj" Ha-Gadol, ed. Y. Hasid (Jerusalem, 5730/1970), Vol. 1, p. 62; the lower part is from M.L. Katzenellenbogen, ed., Torat Hayyim (Jerusalem: Mossad Harav Kook, 1993), Vol. 5, Devarim, p. 447. [Fig. 5a is not yet loaded on the web version of this paper.]

Fig. 6. Favorite Crossword Puzzles 32/1 (West Springfield, MA: Quinn Publishing Co., February, 1983). pp. 95, 189.

Fig. 7. Drosnin, p. 29.

Fig. 8. Drosnin, p. 76.

Fig. 9. Drosnin, p. 71.

Fig. 10. Drosnin, p. 158.