Statistical Science

Solving the Bible Code Puzzle

Maya Bar-Hillel, Dror Bar-Natan, Gil Kalai, and Brendan McKay

Full-text: Open access


A paper of Witztum, Rips and Rosenberg in this journal in 1994 made the extraordinary claim that the Hebrew text of the Book of Genesis encodes events which did not occur until millennia after the text was written. In reply, we argue that Witztum, Rips and Rosenberg’s case is fatally defective, indeed that their result merely reflects on the choices made in designing their experiment and collecting the data for it. We present extensive evidence in support of that conclusion. We also report on many new experiments of our own, all of which failed to detect the alleged phenomenon.

Article information

Statist. Sci., Volume 14, Number 2 (1999), 150-173.

First available in Project Euclid: 24 December 2001

Permanent link to this document

Digital Object Identifier

Equidistant letter sequences ELS Bible code Torah code data tuning data selection


McKay, Brendan; Bar-Natan, Dror; Bar-Hillel, Maya; Kalai, Gil. Solving the Bible Code Puzzle. Statist. Sci. 14 (1999), no. 2, 150--173. doi:10.1214/ss/1009212243.

Export citation


  • Anonymous (1999). Equidistant letter sequences in Tolstey's War and Peace: Witztum's "refutation" refuted. M/WNP/Rebuttal. pdf.
  • Bar-Hillel, M., Bar-Natan, D. and McKay, B. D. (1997). There are codes in War and Peace too. Galileo 25 Nov.­Dec. 52-57. (in Hebrew).
  • Bar-Hillel, M., Bar-Natan, D. and McKay, B. D. (1998). Torah codes: Puzzle and solution. Chance 11 13-19.
  • Bar-Natan, D., Gindis, A. and McKay, B. D. (1999). Report on new ELS tests of Torah, revised report. M/report2.html.
  • Bar-Natan, D. and McKay, B. D. (1997). Equidistant letter sequences in Tolstoy's "War and Peace" (draft). M/WNP/draft.
  • Bar-Natan, D. and McKay, B. D. (1999). Equidistant letter sequences in Tolstoy's "War and Peace." M/WNP.
  • Bar-Natan, D., McKay, B. D. and Sternberg, S. (1998). On the Witztum-Rips-Rosenberg sample of nations. M/Nations.
  • Bik, A. (1974). Rabbi Yaacov Emdin Mosad Harav Kook, Jerusalem. (In Hebrew.)
  • Breuer, M. (1976). The Aleppo Codex and the Accepted Text of the Bible. Mosad Harav Kook, Jerusalem. Cohen, M. (1997a). Two letters. M/cohen.html and M/WNP/ CohenLetter2.html. Cohen, M. (1997b). Personal communication.
  • Cohen, M. (1998). The idea of the sanctity of the Biblical text and the science of textual criticism. M/CohenArt. [Translated from the Hebrew original in The Scriptures and Us (Uriel
  • Simon, ed.) (1979). Center for Judaism and Contemporary Thinking and Dvir, Tel-Aviv.]
  • Cross, F. M. Jr. and Freedman, D. N. (1952). Early Hebrew Orthography. A Study of the Epigraphic Evidence. American Oriental Series 36. American Oriental Society, New Haven.
  • Diaconis, P. (1986). Letter of December 30 to D. Kazhdan.
  • Diaconis, P. (1990). Letter of September 5 to R. Aumann. Reproduced with permission at M/witztum/PDtoRA.gif.
  • Dorfmann, D. D. (1978). The Cyril Burt question: new findings. Science 201 1177-1186.
  • Drosnin, M. (1997). The Bible Code. Simon and Schuster, New York.
  • Em Piqchit (pseudonym) (1998). Chanukah candles in War and Peace. M/candles.html.
  • Encyclopedia Hebraica (1988). Society for Publication of Encyclopedias, Jerusalem.
  • Encyclopedia Talmudica (1992). Entry "Iyyar." Talmudit Publishing, Jerusalem.
  • Fisher, R. A. (1965). Experiments in Plant Hybridisation. Oliver and Boyd, Edinburgh.
  • Freedman, D., Pisani, R. and Purves, R. (1978). Statistics. Norton, New York.
  • Gans, H. (ca. 1995). Coincidence of equidistant letter sequence pairs in the Book of Genesis. Preprint.
  • Gans, H. (1998). Public statement of March 24. Available at M/Gans.html.
  • Gedaliah of Siemiatycze, (Rabbi) (1963). Pray for the Peace of Jerusalem 10-11 (in Hebrew). [This disagrees with The Travels of Rabbi Moshe Yerushalmi, Amsterdam, 1769. Hebrew
  • translation in A. Yaari (1946). Travels in the Land of Israel 448. Tel-Aviv, Israel.]
  • Ha-Nagid, S. (1926). Anthology of Poems of Shmuel Ha-Nagid 1, 1 Hebrew Union College Press, Cincinnati. (In Hebrew.)
  • Hasofer, A. M. (1998). A statistical critique of the Witztum et al. paper. M/hasofer s.pdf.
  • Havlin, S. Z. (1996). Statement of opinion. W/havlin.htm.
  • Kaczynski, T. (1995). Industrial society and its future (the Unabomber Manifesto). Washington Post Sept. 19. Copy available at M/unabomber.txt.
  • Kahneman, D. and Tversky, A. (1972). Subjective probability: a judgment of representativeness. Cognitive Psychology 3 430- 454.
  • Kalai, G., McKay, B. D. and Bar-Hillel, M. (1998). The two famous rabbis experiments: how similar is too similar? Discussion paper 182, Center for Rationality and Interactive Decisions, Hebrew Univ. Jerusalem.
  • Kass, R. (1994). Editor's remarks on WRR94. Statist. Sci. 9 306.
  • Kass, R. (1998). Public statement at kass/biblecodes.
  • Khalifa, R. (1992). Quran, The Final Testament. Universal Unity, Freemont. Mabit. (16th century). Responsa I, 1G 103. (In Hebrew.)
  • Margaliot, M. ed. (1962). Encyclopedia of Great Men of Israel Joshua Chachik, Tel-Aviv. (In Hebrew.)
  • McCormack, R. (1923). The Heptadic Structure of Scripture. Marshall Brothers, London. McKay, B. D. (1999a). In search of mathematical miracles. M/index.html. McKay, B. D. (1999b). Torah codes. M/torah.html.
  • McKay, B. D. et al. (1998). Jesus as the Son of Man. M/Jesus.
  • McKay, B. D. (1998). An objective experiment of Doron Witztum. M/witztum/camps.
  • Naveh, J. (1987). Early History of the Alphabet: An Introduction to West Semitic Epigraphy and Palaeography. Magnes Press, Jerusalem.
  • Panin, I. (ca. 1908). Verbal Inspiration of the Bible Scientifically Demonstrated. Privately published.
  • Perakh, M. (1998). Various articles on Bible codes. http://www.
  • Reiner, R. (1997). Rabbenu Tam. Masters thesis, Hebrew Univ. Jerusalem. (In Hebrew.)
  • Rips, E. (ca. 1985). Transcript of lecture. M/ripslect.
  • Rosenthal, R. (1976). Experimenter Effects in Behavioral Research (enlarged ed.). Irvington, New York. Rosenberg, Y. (undated). Two programs, els1.c and els2.c, implementing versions of the function c w w.
  • Satinover, J. (1997). Cracking the Bible Code. Morrow, New York.
  • Schacter, J. J. (1988). Rabbi Jacob Emden: Life and Major Works. Ph.D. dissertation, Harvard Univ.
  • Simon, B. (1998). Various articles on Bible codes. http://wopr. com/biblecodes.
  • Teomim, Y. (1993). New Interpretations by the Author of "Peri Megadim" Machon Sha'ar HaMishpat, Jerusalem, 315-316.
  • (In Hebrew.) [Also see Anthology on Mosaic Law (1988). Kollel Torat Moshe al-shem HaChatam Sofer, 64 (in Hebrew).]
  • Thomas, D. E. (1997). Hidden messages and the Bible code. The Skeptical Enquirer 21 Nov-Dec 30-36.
  • Tigay, J. (1998). The Bible "codes": A textual perspective. http://
  • Tov, E. (1992). Textual Criticism of the Hebrew Bible. Fortress Press.
  • Tov, E. (1998). Personal communication. (Tov is Magnes Professor of Bible at The Hebrew University of Jerusalem and the co-editor-in-chief of the official Dead Sea Scrolls project.)
  • Tversky, A. and Kahneman, D. (1971). Belief in the law of small numbers. Psychological Bull. 2 105-110. Ulrich, E., Cross, F. M., Davila, J. R., Jastram, N., Sander
  • son, J. E., Tov, E. and Strugnell, J. (1994). Qumran Cave 4, VII, Genesis to Numbers. In Discoveries in the Judaean Desert 12. Clarendon Press, Oxford.
  • Vilenski, E. (1949). Biography of Rabbi Immanuel Chai Ricchi. Kiriat-Sefer 25 311. (In Hebrew.)
  • Williamson Hoke, K. (1988). Completely unimodal numberings of a simple polytope. Discrete Appl. Math. 20 69-81.
  • Witztum, D. (1989). The Added Dimension. Privately published. (In Hebrew.) Witztum, D. (1998a). A refutation refuted. W/ref1.htm, W/ref2. htm. Witztum. D. (1998b). The seal of G-d is truth. W/emet hb.htm.
  • Witztum, D., Rips, E. and Rosenberg, Y. (1986). Equidistant letter sequences in the Book of Genesis. Preprint.
  • Witztum, D., Rips, E. and Rosenberg, Y. (1987). Equidistant letter sequences in the Book of Genesis. Preprint.
  • Witztum, D., Rips, E. and Rosenberg, Y. (1994). Equidistant letter sequences in the Book of Genesis. Statist. Sci. 9 429- 438.
  • Witztum, D., Rips, E. and Rosenberg, Y. (ca. 1995). Equidistant letter sequences in the Book of Genesis II. The relation to the text. Preprint. Copy at M/WRR2.
  • Witztum, D., Rips, E. and Rosenberg, Y. (1996). Hidden codes in equidistant letter sequences in the Book of Genesis: the statistical significance of the phenomenon. Preprint. (In Hebrew).
  • Young, J. (1997). Behold Yeshua! For His Glory, Richardson, Texas.
  • Zevit, Z. (1980). Matres Lectionis in Ancient Hebrew Epigraphs. American Schools of Oriental Research, Monograph Ser. 2, Cambridge, MA.
  • Ziegler, G. M. (1995). Lectures on Polytopes. Springer, New York.