Non-Random Equidistant Letter |
Sequence Extensions in Ezekiel
By R. Edwin Sherman, FCAS, MAAA1, and Nathan Jacobi, Ph.D.
A set of 100 equidistant letter sequences (ELSs) were drawn, equally from the Hebrew text of the book of Ezekiel and a control text (a Hebrew translation of Tolstoy’s novel War and Peace). Each of these initial ELSs (that was the name of an Islamic nation) was reviewed for possible extensions by a Hebrew expert who was blind regarding the source text of each letter string. The number of extensions discovered in Ezekiel was more than 50% higher. A Markov chain model based on the indicated extension discovery rate from the control text (19.4%) was used to determine the expected range in the number of ELSs consisting of three or more extensions that would be discovered from the search for possible extensions around 295 initial ELSs in Ezekiel 37. Although only 5.95 ELSs consisting of three or more extensions were expected, 33 were actually discovered. The greatest number of ELSs with three or more extensions produced from 1 million trials of the Markov chain model simulation was 21. It is evident that the null hypothesis that the Ezekiel 37 findings were due to chance should be rejected.
A similar comparison was made assuming the much higher discovery rate (27.0%) indicated from the Ezekiel text of the Islamic Nations experiment. The null hypothesis was still rejected at the 0.001 level.|
In 1994 the paper, "Equidistant Letter Sequences in the Book of Genesis," was published in the journal Statistical Science. In it three Israeli mathematicians, Dr. Eliyahu Rips of the Hebrew University of Jerusalem, Dr. Doron Witztum and Yoav Rosenberg of the Jerusalem College of Technology, described the results of an experiment in which the proximity of such sequences (ELSs) for related topics tended to be in closer proximity in the book of Genesis than in randomized re-orderings of that text. The ELSs studied were the names of 66 of the most famous rabbis in Jewish history and their dates of death or birth. ELSs are formed by eliminating the spaces between words in the Hebrew text of the Old Testament and then by selecting every n-th letter from the compacted text, where n is the skip of the ELS. For example, within the letter string n e w j e r s e y, "wes" is an ELS with a skip of +2 and "sewn" is an ELS with a skip of –2.
Once an initial ELS such as "wes" has been found at a given skip, an extended ELS can be sought by continuing to extract letters from the literal text at the given skip of the initial ELS. From the sentence, "People say New Jersey was wonderful," the following search string around the "wes" ELS is extracted:
The word "yawn" appears after "wes" in the string, but this is rejected as a valid extension since it doesn’t form a proper phrase in English. If the second to the last letter in this string had been a "d" instead of an "f," "yawned" would have been a valid extension of the "wes" ELS.
In 1997 Michael Drosnin authored the book, The Bible Code, which topped the New York Times best seller list for many weeks. An atheistic Jew, Drosnin claimed that the Bible was filled with ELS codes about numerous current events and that this was proof that some super-human intelligence who knew the future, had written the Old Testament.
Numerous mathematicians have argued heatedly that the Witztum Rosenberg Rips paper was flawed while others have staunchly defended it. Drosnin’s book was repudiated by Dr. Rips, and dozens of mathematicians, since it presents dozens of trivial examples that are so simple that comparable examples could be extracted from any Hebrew book or random sequence of Hebrew letters.
Four years ago Mr. Sherman began examining this phenomenon, strongly suspecting that there was nothing to it. After developing formulae to estimate the probability of chance occurrence of different purported Bible code phenomena, he concluded that virtually all examples from published books were not at all improbable. A few published examples were borderline in terms of improbability, so the help of a Hebrew expert, Dr. Nathan Jacobi2, was sought to enable the search for more extensive ELSs in the same vicinity as the published examples of Hitler codes from Genesis 8 (from Drosnin) and Jesus codes from Isaiah 53 (from Christian author Grant Jeffrey). Dr. Jacobi discovered numerous lengthy ELSs in the Isaiah 53 cluster. Mr. Sherman was forced to reverse his negative position on Bible codes, which he had been presenting on a website, and he changed the site to biblecodedigest.com. During April 2003 this website received 1.3 million hits as the result of interest generated by the war in Iraq and the posting of hundreds of ELSs regarding current events on that site.
In the past two years our research team has located over 120 lengthy ELSs by starting with short initial ELSs of key words about current events, centering on the terrorist attacks and related developments, that are all located in the 37th chapter of Ezekiel. The initial formulae were too simple to gauge the probability of chance occurrence of a code cluster as extensive as the one in Ezekiel 37, so another estimation approach was developed and applied. It is presented in this paper.
The Islamic Nations ELS Extension Experiment
To directly address the question of the purported validity of Bible codes, there has been a clear need for an impartial comparison of a collection of Bible codes with a parallel set of codes from an admittedly ordinary book. This paper presents the results of this experiment. Dr. Jacobi was given 100 pre-defined initial ELSs, equally drawn from the Hebrew text of Ezekiel and from a Hebrew translation of Tolstoy’s War and Peace. Dr. Jacobi searched for extended ELSs around each initial ELS—absent any knowledge of the source of each letter string. The two collections of extended ELSs were then compared and analyzed. This is the first such experiment of this type we have conducted.
Using the Hebrew spellings of a group of Islamic nations3, INBCRS researchers4 located ELSs (with the five shortest skips) of these names of nations in a 78,064-letter portion of War and Peace and the 74,500-letter book of Ezekiel5 provided with Codefinder software6.
Dr. Jacobi was sent five occurrences with the shortest skips from Ezekiel (and five occurrences from War and Peace) of the name of each of the Islamic nations as an ELS. He was asked to document whether letters before and after the terms created longer terms. Throughout the experiment, and up until June 2003, Dr. Jacobi has not known which of the initial ELSs and surrounding letter strings were from which source text.
The experiment was conducted from August 2002 through January 2003 by intermittently including portions of both sets of letter strings. Dr. Jacobi never knew when we started doing so and when we finished. We continued to submit to him our regular supply of letter strings from other parts of the Bible on other topics as part of a number of research projects. His task was always the same—to indicate whether letters before and/or after the terms created longer terms. During that period approximately one-third of letter strings he examined were part of the experiment.
All ELS extensions found around 50 initial ELSs in Ezekiel and 50 initial ELSs in War and Peace were examined and recorded. An extension is a phrase or brief sentence that appears entirely on one side of an existing ELS. The extension must represent a grammatically reasonable continuation of the existing ELS. As such, it could either incorporate part of the existing ELS or be a stand alone phrase or sentence that could reasonably precede or follow the existing ELS. The average extension found in this experiment consisted of two Hebrew words that totaled seven letters. It is of course possible to find several extensions around an initial ELS to form one lengthy final ELS. For example, the following 53-letter-long ELS from Ezekiel 37 was formed by eight extensions found around the initial ELS of the Hebrew word for "combat": 1) The island was restful, elevated 2) and it happened. 3) Where is Libya? 4) And you have disrupted the nation. 5) She changed a word. 6) He answered them with combat. 7) Why the navy 8) and the smell of the bottom of the sea?
Table 1 provides a comparison of the search results on three different bases.
Appendix A provides a listing of all ELS extensions found in both search texts.|
A key statistic estimated in this experiment is the ELS extension discovery rate. It is defined as the ratio of the actual number of extensions found to the number of opportunities available for finding an extension. At the beginning of each search of a new letter string, there are two opportunities to find an extension—one before the initial ELS and one after. If an extension is found, one new opportunity to find yet another extension is created. That opportunity will consist of the new letters that are now next to the extension that had just been discovered. There is no new opportunity on the other side of the ELS where an extension wasn’t found, since that opportunity has already been counted.
The discovery rate in the control text was 19.4% (=24/124). In Ezekiel, it was 27.0% (=37/137), which is 39.2% higher7. A standard statistical test of the null hypothesis that there is no difference in the underlying discovery rates (proportions) indicated that there was a 12.35% probability that the indicated difference could be due to chance. Therefore, the null hypothesis held up at the 0.10 significance level.
It has been our observation in the last four years of investigation that, if anything, the difference in the discovery rates is generally greater than the 8.1 %-age points indicated in this experiment, and appears to be in the range of 10% to 15%. If the 8.1 %-age differential were to hold up under a larger sample of initial ELSs, then the probability of chance occurrence of a differential as large as 8.1 % would drop below standard thresholds. For example, if the names of 82 (rather than 50) Islamic nations were included in the experiment, the differential were to remain at 8.1%, then p would drop below the 0.05 significance level. If the names of 140 Islamic nations were included, p would drop below the 0.01 significance level. This possibility suggests the potential value of expanding the sample size in an enlarged version of this experiment. Of course, it is possible that the addition of more initial ELSs might result in a diminution of the differential.
The possibility that differences in letter frequencies between the two texts might account for some of the difference in discovery rates was considered. A visual comparison of the individual letter frequencies indicated a very strong similarity between the two texts. The correlation between the two sets of frequencies was quite high (0.964827).
The services of another Hebrew expert, Moshe Shak, a Canadian engineer, were retained to investigate the degree to which the indications might be affected by differences in translations between Hebrew experts. The results are displayed in Table 2.
The discovery rate from Shak’s War and Peace extensions (18.7%) was very close to, but somewhat lower than, that from Dr. Jacobi’s extensions (19.4%).|
1 R. Edwin Sherman is a Fellow of the Casualty Actuarial Society and a Member of the American Academy of Actuaries. He received a B.A. and M.A. in Mathematics from the University of California at San Diego, and passed three Ph.D. qualifying exams. He has 30 years of experience as a consulting actuary in serving numerous Fortune 500 corporations, major public entities, law firms and insurance companies in applying probability, statistics and econometric forecasting to risk management problems. He was a Principal with Pricewaterhouse Coopers, the world’s largest accounting and consulting firm, for seven years. He has authored five professional papers in actuarial journals and over 70 articles in trade publications. He directs the biblecodedigest.com website.
2Dr. Nathan Jacobi was educated in Biblical and contemporary Hebrew in Israel. He holds a B.Sc. in Mathematics and an M.Sc. in Physics from Bar-Ilan University. He received a Ph.D. in Physics from the Weizman Institute of Science. He has over 20 years of experience in research, development and scientific computing in applied physics, aerospace and geophysics. He currently teaches an intermediate Hebrew class in Ashland, Oregon.
3Algeria, Abu Dhabi, Bahrain, Dubai, Kuwait, Lebanon, Libya, Qatar, Somalia, Sudan and Yemen. Major islamic nations (Iraq, Iran and Saudi Arabia) were excluded because they had already been the subject of ELS extension searches in the book of Ezekiel. Originally only 10 nations were selected. However, for two of them less than five total ELSs were found, so Somalia was added to bring the total number of ELSs examined up to 50 for each text.
4Isaac Newton Bible Code Research Society. Researchers included Mr. Sherman, Dr. Jacobi and Mr. David Swaney.
5The final search text used extended from Jeremiah 51:52 through Ezekiel to Hosea 1:9. The last chapter from Jeremiah and the first chapter of Hosea were first added to expand the search text, and then as many final verses from the second to last chapter of Jeremiah were added as were needed in order for the Ezekiel Plus search text to have the same size (approximately) as the War and Peace search text.
7The 39.2% differential for the discovery rates is lower than the 54.2% differential in the total number of extensions. This occurs because the denominators of the two discovery rates are not the same. Each new extension opens up a new opportunity to find yet another extension. Hence, there were many more opportunities to find new extensions in Ezekiel because more extensions were initially found in Ezekiel.
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Code Skeptics' Arguments Trashed
Ever since the first Bible codes were announced, skeptics have been saying, "Oh, well, you can also find codes like that in books like War and Peace and Moby Dick."
We took the time to examine this notion and the best example of it that the skeptics have been able to come up with. The results of our research have completely blown away their theory.
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NEW: Second Study Undermines
Skeptics' Main Objection
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