Bible code

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A Bible code (also Torah code) is the notion that there are information patterns encrypted or coded form in the text of the Bible, or, more specifically, in the Torah, the first five books of the Hebrew Bible.

The existence of such codes has been hypothesized by students of Kabbalah since the Middle Ages, and was endorsed by Blaise Pascal who in his Pensées concluded that "The Old Testament is a cipher." It has no credibility in Old Testament studies today.

Contents

[edit] Overview

Contemporary discussion and controversy around one specific encryption method began in 1994 when Doron Witztum, Eliyahu Rips and Yoav Rosenberg submitted their paper, "Equidistant Letter Sequences in the Book of Genesis" to the peer-reviewed journal Statistical Science[1]. After unexpectedly surviving an unprecedented three rounds of peer review, the paper was published by Statistical Science and the "ELS" phenomenon was "presented as a puzzle" to its readership. A storm of controversy immediately ensued.

Since then the term "Bible Codes" has been popularly used to refer specifically to information encrypted via the ELS method.

Since the Witztum, Rips and Rosenberg (WRR) paper was published, two conflicting schools of thought regarding the "Codes" have emerged among proponents. The traditional (WRR) view of the codes is based strictly on their applicability to the Torah, and asserts that any attempt to study the codes outside of this context is invalid. This is based on a belief that the Torah is unique among biblical texts in that it was given directly to mankind (via Moses) in exact letter-by-letter sequence and in the original Hebrew language.

[edit] Religious Belief Foundations

Hebrew religious, Kabbalaistic and 'Hebraic Sacred Science' traditions hold that the text of the Torah was originally given to mankind in a single long string of 304,805 Hebrew characters. The spaces, punctuation, sentence, chapter and five-book structures were all added later to form the modern Pentateuch. This "Word" of the Creator was, according to this tradition, delivered to mankind in the form of a single 304,805 letter word. It is in this context that the Torah is uniquely, specifically and literally considered by believers to be "The Word".

For this reason, Hebrew tradition dictates that Torah scribes must complete many years of training, much of which has to do with learning the proper meditative techniques, before being allowed to copy Torah scrolls.[1] The tradition holds that not a single "jot or tittle", nor one iota of the Torah must be added, changed or omitted from "The Word".

Believers in this tradition sometimes point to a purely literal interpretation of the first seventeen words of the Gospel of John from the New Testament as evidence for their belief:

"In the beginning was the Word, and the Word was with God, and the Word was God".

In summary, the exclusive application of Bible Codes techniques to the Torah "string" is based in the belief that at the most fundamental level, God is a "Living Word", essentially, an almost infinitely complex information structure that begets all that exists,[2] that the Torah is an information structure analogous to the DNA structure of all creation.[2][3] Some more recent beliefs among various groups suggest that "the Word was made flesh" in a literal sense; that the physical body of Jesus Christ was manifested divinely, that his DNA was somehow perfectly derived from "The Word".[3][4]. Researcher-spiritualist Gregg Braden and others have been exploring the human DNA string and claim to have discovered evidence of "The Word" in human DNA.

Since 1994, more recent (post WRR) views extend the analysis of biblical texts to include Old Testament texts outside the Torah and also to the New Testament, but these are rejected by Kabbalaistic tradition.

The traditional view of the codes further asserts that the "information" encoded in the Torah cannot be used to predict the future, and that at best the codes provide evidence of an all-knowing creator whose knowledge of the Universe and all of its possibilities spans both space and time. In this view, (from an information theoretical viewpoint) the letter-sequence of the Torah is to the Universe as the DNA sequence is to the human body, useful for understanding how the universe works on a macro scale, and illustrative of the "Grand Design" which encompasses all possible events, but nonetheless utterly unreliable for prediction of what specific combinations of micro-scale events will occur to create the 'reality' of human history.

The traditional view conflicts with the more recent and highly sensationalized views suggesting that the Codes may be valuable as tools of prediction. These views of the codes first emerged in popular culture with the book The Bible Code by journalist Michael Drosnin, which suggests that the codes can be analyzed by computer to provide warnings for the future.

A more nuanced and academic view of the Codes was presented in 1997 by Jeffrey Satinover in Cracking the Bible Code. Satinover attempted to present the 'puzzle' in broader historical, mathematical and theological contexts, but this work was overshadowed by the more sensational Drosnin works that fueled the controversy.

[edit] ELS - Equidistant Letter Sequence method

The primary method by which purportedly meaningful messages have been extracted is the Equidistant Letter Sequence (ELS). To obtain an ELS from a text, choose a starting point (in principle, any letter) and a skip number, also freely and possibly negative. Then, beginning at the starting point, select letters from the text at equal spacing as given by the skip number. For example, the bold letters in this sentence form an ELS. With a skip of -4, and ignoring the spaces and punctuation, the word SAFEST is spelled out backwards.

Often more than one ELS related to some topic can be displayed simultaneously in an ELS letter array. This is produced by writing out the text in a regular grid, with exactly the same number of letters in each line, then cutting out a rectangle. In the example below, part of the King James Version of Genesis (26:5–10) is shown with 33 letters per line. ELSs for BIBLE and CODE are shown. Normally only a smaller rectangle would be displayed, such as the rectangle drawn in the figure. In that case there would be letters missing between adjacent lines in the picture, but it is essential that the number of missing letters be the same for each pair of adjacent lines.

center Arrange the letters from Genesis 26:5–10 in a 33 column grid and you get a word search with "Bible" and "code". Myriad other arrangements can yield other words.

Although the above examples are in English texts, Bible codes proponents usually use a Hebrew Bible text. For religious reasons, most Jewish proponents use only the Torah (Genesis–Deuteronomy).

[edit] ELS Extensions

Once a specific word has been found as an ELS, it is natural to see if that word is part of a longer ELS consisting of multiple words.[4] For example, in the middle of the right most column of the boxed matrix above is the ELS "he". After searching immediately above and below this ELS, we see another ELS ("toe") that is right below the "he" ELS. Code pioneers Haralick and Rips have published an example of a longer, extended ELS, which reads, "Destruction I will call you; cursed is Bin Laden and vengeance from the Moshiach." [5]

ELS extensions that form phrases or sentences are of interest. The longer the extended ELS, the less likely it is to be the result of chance.[6]

What it is important to note about the previous examples is that they all seem to be germane to the text in which they begin.

[edit] History

In the last years of his life, French mathematician Blaise Pascal had concluded in his philosophical work Pensees that "The Old Testament is a cipher." [7]

Shortly after Pascal's death, another early seeker of divinely encrypted messages was Isaac Newton, who, according to John Maynard Keynes believed[8] that "the universe is a cryptogram set by the Almighty" and in the structure of the universe, Newton sought the answers to "a riddle of the Godhead of past and future events divinely fore-ordained".

Newton eventually turned his attention to biblical prophecy and "the Revelation, with respect to the Scripture of Truth, which Daniel was commanded to shut up and seal, till the time of the end. Until that time comes, the Lamb is opening the seals." Some sources[9] have attempted to connect Keynes' attribution of the "universe is a cryptogram" quote with Newton's later interest in biblical prophecy, even to the extent of re-wording the quote, substituting the word "Bible" for "universe", but there appears to be no evidence that Newton ever attempted any cryptographic analyses of the Bible, nor any explicit reference by Newton to the text of the bible as a cryptogram or 'cipher', as Pascal had come to believe. Newton's interest in Biblical texts appeared to be in the unlocking of allegorical riddles rather than any mathematical de-coding of texts.

The 13th-century Spanish Rabbi Bachya ben Asher may have been the first[citation needed] to describe an ELS in the Bible. His 4-letter example related to the traditional zero-point of the Hebrew calendar. Over the following centuries there are some hints that the ELS technique was known, but few definite examples have been found from before the middle of the 20th century. At this point many examples were found by the Slovakian Rabbi Michael Ber Weissmandl and published by his students after his death in 1957. Nevertheless, the practice remained known only to a few until the early 1980s, when some discoveries of an Israeli school teacher Avraham Oren came to the attention of the mathematician Eliyahu Rips at the Hebrew University of Jerusalem. Rips then took up the study together with his religious studies partners Doron Witztum and Alexander Rotenberg, and several others.

Rips and Witztum designed computer software for the ELS technique and subsequently found many examples. About 1985, they decided to carry out a formal test and the "Great rabbis experiment" was born. This experiment tested the hypothesis that ELSs for the names of famous rabbis could be found closer to ELSs of their dates of birth and death than chance alone could explain. The definition of "close" was complex but, roughly, two ELSs are close if they can be displayed together in a small rectangle. The experiment succeeded in finding sequences which fit these definitions, and they were interpreted as indicating the phenomenon was real.

The "great rabbis experiment" went through several iterations but was eventually published (1994) in the peer-reviewed journal Statistical Science. Prior to publication the journal's editor Robert Kass subjected the paper to an unprecedented three successive peer reviews by the journal's referees, who according to Kass were "baffled". Though still skeptical,[10] none of the reviewers had found any flaws. Understanding that the paper was certain to generate controversy, it was presented to readers in the context of a "challenging puzzle".

Witztum and Rips also performed other experiments, most of them successful, though none were published in journals. Another experiment, in which the names of the famous rabbis were matched against the places of their births and deaths (rather than the dates), was conducted by Harold Gans, Senior Cryptologic Mathematician for the United States National Security Agency.[11] Again, the results were interpreted as being meaningful and thus suggestive of a more than chance result. These Bible codes became known to the public primarily due to the American journalist Michael Drosnin, whose book The Bible Code (Simon and Schuster, 1997) was a best-seller in many countries.

In 2002, Drosnin published a second book on the same subject, called The Bible Code II. The Jewish outreach group Aish-HaTorah employs the Bible Codes in their Discovery Seminars to persuade secular Jews of the divinity of the Bible and to encourage them to trust in its traditional Orthodox teachings. Use of Bible code techniques also spread into certain Christian circles, especially in the United States. The main early proponents were Yakov Rambsel, who is a Messianic Jew, and Grant Jeffrey. Another Bible code technique was developed in 1997 by Dean Coombs (also Christian). Various pictograms are claimed to be formed by words and sentences using ELS.[12]

Since 2000, physicist Nathan Jacobi, an agnostic Jew, and engineer Moshe Aharon Shak, an orthodox Jew, have discovered hundreds of examples of lengthy, extended ELSs. [13] The number of extended ELSs at different lengths is compared with those expected from a non-encoded text, as determined by a formula from Markov Chain Theory.[14]

[edit] Recent developments

Yitzchok Adlerstein, self described as "one of the most vocal skeptics" about the Bible Codes noted that on October 10, 2005, the Nobel Prize in Economics was awarded to leading Bible Code proponent Robert Aumann for his work in game theory, the same field that led to an earlier award to John Nash. Reviewing Aumann's 2004 concluding remarks in response to the "Gans Committee" study[15] in the context of Aumann's twenty years of codes research, Adlerstein noted that Aumann had come to the conclusion that the codes could neither be proven nor could they be disproven with the scientific methods employed to date.[16]

In 2006, three new Torah Codes papers were published at the 18th International Conference on Pattern Recognition (ICPR'06). Nachum Bombach and Harold Gans presented "Patterns of Co-Linear Equidistant Letter Sequences and Verses,", WRR author Eliyahu Rips and Art Levitt presented "The Twin Towers Cluster in Torah Codes", and Art Levitt published "Component Analysis of Torah Code Phrases".[5] Each of the three works is supported by noted high technology entrepreneur Yuri Pikover, founder of Xylan (acquired in 1999 by Alcatel)[17][18]

[edit] Criticism

 It has been suggested that some of the information in this article's Criticism or Controversy section(s) be merged into other sections to achieve a more neutral presentation. (Discuss)

The primary objection advanced against Bible codes is that information theory does not prohibit "noise" from appearing to be sometimes meaningful. Thus, if data chosen for ELS experiments are intentionally or unintentionally "cooked" before the experiment is defined, similar patterns can be found in texts other than the Torah. Although the probability of an ELS in a random place being a meaningful word is small, there are so many possible starting points and skip patterns that many such words can be expected to appear, depending on the details chosen for the experiment, and that it is possible to "tune" an ELS experiment to achieve a result which appears to exhibit patterns that overcome the level of noise.

[edit] Criticism of the original paper

In 1999, Australian mathematician Brendan McKay, together with mathematicians Dror Bar-Natan and Gil Kalai, and psychologist Maya Bar-Hillel (collectively known as "MBBK") published a paper in Statistical Science, in which they argue that the case of Witztum, Rips and Rosenberg (WRR) is "fatally defective, indeed that their result merely reflects on the choices made in designing their experiment and collecting the data for it."[19] The MBBK paper was reviewed anonymously by four professional statisticians prior to publication.

In the MBBK paper, the authors present the following arguments:

  • The authors argue that because of problems in WRR's test method, the results of WRR's 1994 paper "may reflect (at least to some extent) uninteresting properties of the word list [the appellation-date word pairs] rather than an extraordinary property of Genesis,"[20] and that the test method used by WRR has properties that make it "exceptionally susceptible to systematic bias."[21]
  • The authors argue that WRR had many choices available when selecting the appellations, the dates, and the date forms.[22]
  • The authors argue that, despite the claims by WRR and S. Z. Havlin that Havlin prepared the appellations independently, the earliest available documents on the experiments do not state that the lists of appellations were prepared by an independent expert. Similarly, the authors quote a 1985 lecture by Eliyahu Rips, in which he describes the appellation selection process as taking "every possible variant that we considered reasonable," and makes no mention of Havlin or an independent expert.[23]
  • The authors report that, by adding some appellations and removing some appellations from WRR's list 2, and then repeating the test on the initial 78,064 letters (the length of Genesis) of a Hebrew translation of War and Peace, they achieved a significance level of one in a million. The authors say this shows that "the freedom provided just in the selection of appellations is sufficient to explain the strong result" in WRR's 1994 paper.[24]
  • The authors present a "study of variations," in which they repeated the experiments many times, each time making one or more minimal changes to the test method, the dates, or the date forms.[25] The authors conclude that "only a small fraction of variations made WRR's result stronger and then usually by only a small amount ... we believe that these observations are strong evidence for tuning ... "[26]
  • The authors present experiments they conducted which they say show that some results of experiments by WRR and Harold Gans are "too good to be true." That is, some of the results are statistically improbable even if one accepts that WRR's hypothesis is true, but may reflect the expectations of statistically naive researchers. The authors say that these studies "give support to the theory that WRR's experiments were tuned toward and overly idealized result consistent with the common expectations of statistically naive researchers."[27]
  • The authors present multiple experiments they conducted in which they attempted to replicate WRR's experiments. The authors used an independent expert to prepare the appellations and dates for each of these experiments. The authors report that the results of these attempted replications were negative.[28]
  • The authors argue that the available evidence indicates that the text of Genesis used by WRR is substantially different from its original form, and that ELS's with large skips (which WRR's experiments rely on) could not survive such changes.[29]

From these observations, MBBK created an alternative hypothesis to explain the "puzzle" of how the codes were discovered. MBBK's claim, in essence, was that the WRR authors had "cheated"[30]. MBBK went on to describe the means by which the cheating might have occurred, and demonstrate the tactic as presumed.

MBBK's refutation was not strictly mathematical in nature, rather it asserted that the WRR authors and contributors had intentionally or unintentionally (a) selected the names and/or dates in advance and (b) designed their experiments to match their selection and thereby achieved their "desired" result. The MBBK paper argued that the ELS experiment is extraordinarily sensitive to very small changes in the spellings of appellations, and that the WRR result "merely reflects on the choices made in designing their experiment and collecting the data for it.".

The MBBK paper demonstrated that this "tuning", when combined with what MBBK asserted was available "wiggle" room, was capable of generating a result similar to WRR's Genesis result in a Hebrew translation of War and Peace. Psychologist and MBBK co-author Maya Bar-Hillel subsequently summarized the MBBK view that the WRR paper was a hoax, an intentionally and a carefully designed "magic trick"[31].

[edit] Replies to MBBK's criticisms

Harold Gans has argued that MBBK's hypothesis implies a conspiracy between WRR and their co-contributors to fraudulently tune the appellations in advance. Gans argues that the conspiracy must include Doron Witztum, Eliyahu Rips, and S. Z. Havlin, because all of them say that Havlin compiled the appellations independently. Gans argues further that such a conspiracy must include the multiple rabbis who have written a letter confirming the accuracy of Havlin's list. Finally, argues Gans, such a conspiracy must also include the multiple participants of the cities experiment conducted by Gans (which includes Gans himself). Gans concludes that "the number of people necessarily involved in [the conspiracy] will stretch the credulity of any reasonable person."[32]

Brendan McKay has replied that he and his colleagues have never accused Havlin or Gans of participating in a conspiracy. Instead, says McKay, Havlin likely did what WRR's early preprints said he did: he provided "valuable advices." Similarly, McKay accepts Gans statements that Gans did not prepare the data for his cities experiment himself. McKay concludes that "there is only ONE person who needs to have been involved in knowing fakery, and a handful of his disciples who must be involved in the cover-up (perhaps with good intent)."[33]

Responding to the MBBK allegations of trickery, WRR authors issued a series of detailed refutations of the claims of MBBK, including evidence that no such tuning did or even could have taken place. An earlier WRR response to a request by MBBK authors presented results from additional experiments that used the specific "alternate" name and date formats which MBBK suggested had been intentionally avoided by WRR. Using MBBK's alternates, the results WRR returned showed equivalent or better support for the existence of the codes, and so challenged the "wiggle room" assertion of MBBK. In the wake of the WRR response, author Bar-Natan issued a formal statement of non-response. After a series of exchanges with McKay and Bar-Hillel, WRR author Witztum responded in a new paper claiming that McKay had used smoke screen tactics in creating several Straw Man arguments, and thereby avoided the points made by WRR authors refuting MBBK. Witztum also claimed that, upon interviewing a key independent expert contracted by McKay for the MBBK paper, that some experiments performed for MBBK had validated, rather than refuted the original WRR findings, and questioned why MBBK had expunged these results from their paper.

By 1999, meaningful debate mostly disappeared into personal attacks and diatribes as the participants accused one another of all manner of madness, deceptions and ill intent.

[edit] Criticism of Michael Drosnin

Journalist Drosnin's books have been criticized by some who believe that the Bible Code is real but that it cannot predict the future.[34] Some accuse him of factual errors, claiming that he has much support in the scientific community,[35] mistranslating Hebrew words [36] to make his point more convincing, and using the Bible without proving that other books do not have similar codes.[37]

Responding to an explicit challenge from Drosnin, who claimed that other texts such as Moby-Dick would not yield ELS results comparable to the Torah, McKay created a new experiment that was tuned to find many ELS letter arrays in Moby Dick that relate to modern events, including the assassination of Martin Luther King, Jr. He also found a code relating to the Rabin assassination, containing the assassin's first and last name and the university he attended, as well as the motive ("Oslo", relating to the Oslo accords).[38] Drosnin and others have responded to these claims, saying the tuning tactics employed by McKay were simply "nonsense", and providing analyses to support their argument that the tables, data and methodologies McKay used to produce the Moby Dick results "simply do not qualify as code tables". [39]

Skeptic Dave Thomas claimed to find other examples in many texts, though Thomas' methodology was refuted by Robert Haralick [40] and others. In addition, McKay claimed that Drosnin had used the flexibility of Hebrew orthography to his advantage, freely mixing classic (no vowels, Y and W strictly consonant) and modern (Y and W used to indicate i and u vowels) modes, as well as variances in spelling of K and T, to reach the desired meaning. In his television series John Safran vs God, Australian television personality John Safran and McKay again demonstrated the 'tuning' technique, demonstrating that these techniques could produce "evidence" of the September 11 terrorist attacks on New York in the lyrics of Vanilla Ice's repertoire. Additionally, 'coded' references in non-Torah Bible texts, as for instance the famous Number of the Beast, do not use the Bible code technique. And, the influence and consequences of scribal errors (eg, misspellings, additions, deletions, misreadings, ...) are hard to account for in the context of a Bible coded message left secretly in the text. McKay and others claim that in the absence of an objective measure of quality and an objective way to select test subjects, it is not possible to positively determine whether any particular observation is significant or not. For that reason, most of the serious effort of the skeptics has been focused on the scientific claims of Witztum, Rips and Gans.

[edit] Predictions versus probabilities

Traditional codes scholars and adherents believe that the codes cannot (and should not) be used for "soothsaying". The traditional view that the codes are "useless for prediction", and the basis for it, were described by Jeffrey Satinover in his 1997 book "Cracking the Bible Code"[41]. This view holds that, at best, signs of the existence of encrypted information in the Torah indicate evidence supporting the existence of an all-knowing creator.

Nonetheless, the use and publication of "predictions" based on Bible codes has succeeded in bringing about popular awareness of the codes, most notably based on the work of journalist Michael Drosnin. Drosnin, who says he is "not at all religious" and does not believe in God, has offered speculations on the source of the codes but no answers, saying "I'm a reporter and can't go past the hard evidence. There is a code, therefore there is an encoder. I don't know who or what it/he/she is.[42]

Drosnin's most famous prediction, in 1994, was the 1995 assassination of Israeli Prime Minister, Yitzhak Rabin, using a Bible code technique.[36] Drosnin uses this prediction as evidence for the validity of his bible code techniques.[43] Opponents claim that in the political atmosphere of the time, predicting with no additional details the fact that Rabin would be assassinated is not compelling, though dramatic.[citation needed]. Less political predictions include the 2004 Red Sox World Series victory, and widespread use of hand held communication devices (cell phones).[citation needed]

Drosnin, in The Bible Code II, described the probabilities of nuclear holocausts and the destruction of major cities by earthquakes in 2006, saying "The dangers will peak in the Hebrew year 5766 (September 2005 - September 2006 in the modern calendar), the year that is most clearly encoded with both 'World War' and 'Atomic Holocaust'..."The Bible Code is not a prediction that we will all die in 2006. It is a warning that we might all die in 2006, if we do not change our future." [44]

More recently, Drosnin has refrained from making concrete predictions, saying, "I don't think the code makes predictions. I think it reveals probabilities." Drosnin also said "I think it might tell us all our possible futures."[45]

[edit] See also

Relevant topics:

[edit] References

  1. ^ Doron Witztum, Eliyahu Rips, Yoav Rosenberg (1994). "Equidistant letter sequences in the Book of Genesis". Statistical Science 9: 429-438. 
  2. ^ Primack, Joel; Nancy E. Abrams. In A Beginning...Quantum Cosmology and Kabbalah. Retrieved on 2008-03-14.
  3. ^ Dorey, Shannon (2003-12-22). Dogon Mythology on "The True Origins of Christ". Retrieved on 2008-03-14.
  4. ^ Shak, Moshe Aharon. 2004. Bible Codes Breakthrough. Montreal: Green Shoelace Books. 38
  5. ^ Haralick, Rips, and Glazerson. 2005. Torah Codes: A glimpse into the infinite. New York: Mazal & Bracha. 125
  6. ^ Sherman, R. Edwin, with Jacobi and Swaney. 2005. Bible Code Bombshell Green Forest, Ar.: New Leaf Press. 95-109
  7. ^ Pascal's Pensées by Blaise Pascal - Project Gutenberg
  8. ^ http://www-groups.dcs.st-and.ac.uk/~history/Extras/Keynes_Newton.html John Maynard Keynes on Newton's cryptogram beliefs
  9. ^ As more people consider possible Armageddon during their lifetime, it is little wonder that the Isaac Newton Bible Code Resear
  10. ^ 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, 149.
  11. ^ http://www.aish.com/seminars/discovery/Codes/codes.htm
  12. ^ What are Bible Codes?
  13. ^ http://www.biblecodedigest.com BibleCodeDigest.com
  14. ^ Sherman, R. Edwin, with Jacobi and Swaney. 2005. Bible Code Bombshell Green Forest, Ar.: New Leaf Press. 281-286
  15. ^ “Analysis of the "Gans" Committee Report”, Analysis of the "Gans" Committee Report, 2004-7-19 
  16. ^ Adlerstein, Yitzchok (2005-10-11). Nobel Prize Settles Bible Codes Dispute (almost). Cross currents (web). Retrieved on 2008-02-24.
  17. ^ pikover xylan alcatel billion - Google News Archive Search
  18. ^ http://scholar.google.com/scholar?hl=en&lr=&oi=qs&q=yuri+pikover
  19. ^ B. McKay, D. Bar-Natan, M. Bar-Hillel, and G. Kalai (1999). "Solving the Bible Code Puzzle." Statistical Science, 14, 150-173.
  20. ^ B. McKay, D. Bar-Natan, M. Bar-Hillel, and G. Kalai (1999). "Solving the Bible Code Puzzle." Statistical Science, 14, 154.
  21. ^ B. McKay, D. Bar-Natan, M. Bar-Hillel, and G. Kalai (1999). "Solving the Bible Code Puzzle." Statistical Science, 14, 155.
  22. ^ B. McKay, D. Bar-Natan, M. Bar-Hillel, and G. Kalai (1999). "Solving the Bible Code Puzzle." Statistical Science, 14, 155-157.
  23. ^ B. McKay, D. Bar-Natan, M. Bar-Hillel, and G. Kalai (1999). "Solving the Bible Code Puzzle." Statistical Science, 14, 156.
  24. ^ B. McKay, D. Bar-Natan, M. Bar-Hillel, and G. Kalai (1999). "Solving the Bible Code Puzzle." Statistical Science, 14, 157.
  25. ^ B. McKay, D. Bar-Natan, M. Bar-Hillel, and G. Kalai (1999). "Solving the Bible Code Puzzle." Statistical Science, 14, 157-161, 168-171.
  26. ^ B. McKay, D. Bar-Natan, M. Bar-Hillel, and G. Kalai (1999). "Solving the Bible Code Puzzle." Statistical Science, 14, 161.
  27. ^ B. McKay, D. Bar-Natan, M. Bar-Hillel, and G. Kalai (1999). "Solving the Bible Code Puzzle." Statistical Science, 14, 161-162.
  28. ^ B. McKay, D. Bar-Natan, M. Bar-Hillel, and G. Kalai (1999). "Solving the Bible Code Puzzle." Statistical Science, 14, 164.
  29. ^ B. McKay, D. Bar-Natan, M. Bar-Hillel, and G. Kalai (1999). "Solving the Bible Code Puzzle." Statistical Science, 14, 165-166.
  30. ^ http://www.ma.huji.ac.il/~kalai/aumann.txt
  31. ^ Maddness in the Method at http://www.dartmouth.edu/~chance/teaching_aids/books_articles/Maya.html
  32. ^ H. J. Gans. A Primer on the Torah Codes Controversy for Laymen (part 1). Retrieved April 7, 2008.
  33. ^ B. McKay (2003). Brief notes on Gans' Primer. Retrieved April 7, 2008.
  34. ^ The Bible Code
  35. ^ Torah Codes
  36. ^ a b Review of Michael Drosnin's Bible Code Book 1
  37. ^ Barry Simon on Torah Codes
  38. ^ Assassinations Foretold in Moby Dick
  39. ^ CNN.com
  40. ^ http://www.torah-code.org/papers/skeptical_inquirer_02_15_07.pdf
  41. ^ See "A Talk with Dr. Jeffrey Satinover at http://www.quantgen.com/TALK.HTM
  42. ^ Future News: Nuclear War: A Futurist's View, The Bible Code, Mayan Prophecy and My Vision of World War III
  43. ^ CNN - Meet Michael Drosnin Author, "The Bible Code" - June 4, 1997
  44. ^ Future News: Nuclear War: A Futurist's View, The Bible Code, Mayan Prophecy and My Vision of World War III
  45. ^ CNN - Meet Michael Drosnin Author, "The Bible Code" - June 4, 1997
  • Drosnin, Michael (1997). The Bible Code. USA: Simon & Schuster. ISBN 0-684-81079-4. 
  • Satinover, Jeffrey (1997). Cracking the Bible Code. New York: W. Morrow. ISBN 0-688-15463-8. 
  • Drosnin, Michael (1997). The Bible Code. UK: Weidenfeld & Nicolson. ISBN 0-297-81995-X. 
  • Drosnin, Michael (2002). The Bible Code II: The Countdown. USA: Viking Books. ISBN 0-670-03210-7. 
  • Drosnin, Michael (2002). The Bible Code II: The Countdown. UK: Weidenfeld & Nicolson. ISBN 0-297-84249-8. 
  • Drosnin, Michael (Forthcoming 2006). The Bible Code III: The Quest. UK: Weidenfeld & Nicolson. ISBN 0-297-84784-8. 
  • Stanton, Phil (1998). The Bible Code - Fact or Fake?. Wheaton, IL: Crossway Books. ISBN 0-89107-925-4. 
  • Haralick, Robert M.; Rips, Eliyahu; and Glazerson, Matiyahu (2005). Torah Codes: A Glimpse into the Infinite. Mazal & Bracha Publishing. ISBN 0-9740493-9-5. 

[edit] External links