Non-Random Equidistant Letter
Sequence Extensions in Ezekiel

By R. Edwin Sherman, FCAS, MAAA, and Nathan Jacobi, Ph.D.

Indications Based on a Conservatively High Discovery Rate

A concern regarding the above analysis is that the 19.4% discovery rate was based on a sample of only 50 initial ELSs from the Islamic Nations Experiment. Consequently, there is a high level of uncertainty as to what the true underlying discovery rate actually is. The question of how the above evaluation of the improbability of the number of lengthy ELSs in the Ezekiel 37 cluster would change if the actual underlying discovery rate were much higher needed to be addressed. A reasonable candidate for an alternative discovery rate that would be viewed as conservatively high is the 27.0% discovery rate indicated from the 50 initial ELSs found in Ezekiel (rather than in the control text),

A one million trial simulation was run to determine the probability that, if the true underlying discovery rate were 27.0%, the indicated discovery rate from a sample of 50 initial ELSs would be 19.4% or lower. That probability is 3.14%. Thus, given that the actual indicated discovery rate was 19.4%, the probability that the actual underlying discovery rate could be 27.0% or higher is only 3.14%.

Table 7 provides the same kind of comparison as displayed in Table 3—using the 27.0% discovery rate for Ezekiel from the Islamic Nations Experiment.

The chi square p-value indicated from Table 7 is 8.75 E -24. The largest p-value indicated by any assumed discovery rate is 7.32 E -20, corresponding to a rate of 30.6%.

One million trials were run of a simulation (based on that model) of the total number of ELSs with three or more extensions, given 295 initial ELSs and a discovery rate of 27.0%. For 480 of those trials the total number of ELSs with three or more extensions was 33 or greater, indicating odds of chance occurrence of 1 in 2,083 of 33 such ELSs in the Ezekiel 37 cluster. Our conclusion was that, even though the chi square p-value was inappropriately small, the null hypothesis should still be rejected at the 0.001 significance level. For 99 trials, the total number of ELSs with four or more extensions was 17 or greater, indicating odds of chance occurrence of 1 in 10,101. In the case of the actual number of ELSs in Ezekiel 37 with five or more extensions (11), none of the 1 million trials produced more than 9 such ELSs, indicating odds of chance occurrence distinctly less than 1 in 1 million.

Although the expected range in the number of ELSs consisting of three (or four or five) or more extensions discovered in the Ezekiel 37 cluster is highly sensitive to the assumed discovery rate, even at the conservatively high assumption of 27.0%, the null hypothesis is still rejected at the 0.001 significance level.

Many code researchers have noted that longer ELSs tend to be topically related to the surface text as well as to one another. If this is in fact the case, it should not be expected that high discovery rates would necessarily persist within every given section of the Bible and every topically related collection of initial ELSs.

In our opinion the content of the long ELSs in Appendix C is much more coherent than that of the Ezekiel ELSs in Appendix A. This is supportive of the claimed correlation of the content of the literal text and of underlying ELSs. Since the ELSs in Appendix C are tightly focused in location, more consistency in their content would be expected.

Commentary on the Content of the Longest ELSs in the Ezekiel 37 Cluster

While the above analysis strongly (if not conclusively) indicates that non-random encoding exists in the vicinity of Ezekiel 37, it is worth noting that the specific content of any single extended ELS is subject to various sources of uncertainty. Key sources are:
1) ELSs do not include attribution, making messages from untruthful sources appear to have equal validity with those from trustworthy sources. If attribution were eliminated from the Bible itself, false statements such as Genesis 3:4 would appear as ostensibly true statements.
2) Copying errors perpetuated over the centuries between the original manuscript of each section of the Hebrew Bible and the finalized Koren version of the Masoretic text (circa 1000 A.D.) could easily result in the elimination of original encoding and the creation of unintended, grammatically reasonable Hebrew ELSs.
3) In the absence of vowel markings, short letter strings often could be interpreted to represent alternative words.
4) The contemporary translator has the freedom to decide where spaces should be inserted to produce intelligible Hebrew. Given such freedom, and 3), significant variation in the "translation" of any given letter string between different Hebrew experts should be expected.
5) It is possible that extinct words from ancient Hebrew would provide a much different translation than usage of extant words from either Biblical or contemporary Hebrew.
6) Short ELSs are abundant in any Hebrew text or sequence of Hebrew letters. Such random ELSs may appear immediately prior or subsequent to, or may be intermingled with intended ELSs.

Given all of these sources of potential corruption of the content of individual lengthy ELSs, it is remarkable that a large differential still exists between the frequency and length of ELSs in the Hebrew Bible and those obtainable from a presumably non-encoded text.

It is surprising that some of the Islamic Nation ELSs from the Ezekiel text are ostensibly prophetic in their content. For example, the extended ELS, "Who of Sudan is alive? Are the poor there not soft and honest?" is reminiscent of the slaughter of over two million Christians by the Sudanese government in recent years.

Several Jewish and Christian books on Bible codes have been published, presenting both strongly positive and negative views. Not uncommonly conservative Jews and Christians have expressed concern that purportedly valid Bible codes might provide a source of new information that could conflict with the content of the literal text. This should not be a substantive concern because of the potential unreliability of the content of any given ELS. The fact is that the extreme improbability of some code clusters, as well as of a broad spectrum of other ELS phenomena, provide a form of objective, verifiable evidence that the Old Testament was not merely authored by human beings.

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Witztum, Doron; Rips, Eliyahu; Rosenbreg, Yoav. "Equidistant Letter Sequences in Genesis." Statistical Science. Vol. 3 (1994): 429-436.
Drosnin, Michael. The Bible Code. New York: Simon and Schuster, 1997.
Satinover, Jeffrey. Cracking the Bible Code. New York: William Morrow & Company, 1998.
Bible Code Digest. March, 2003. Isaac Newton Bible Code Research Society. July 15, 2003
Bible Code Digest. June, 2003. Isaac Newton Bible Code Research Society. July 15, 2003
Bible Code Digest. July, 2003. Isaac Newton Bible Code Research Society. July 15, 2003


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