Appendix E
Determining the Number of Extensions

For some extended ELSs, there is an unavoidable element of subjective assessment involved in determining how many extensions there are around the original search term. Ideally, an extension would consist of a complete new sentence, including a noun and verb and perhaps a few adjectives or adverbs. However, it could consist of a prepositional phrase, if it were lengthy and substantive. In determining how many extensions there were in each extended ELS, one criteria used was the number of letters per extension. Unless there was only one extension, we tried to select a number of extensions such that the number of letters per extension was greater than or equal to 5.0. As can be seen in Appendix B, all of the extended ELSs we discovered are listed in groups according to how many extensions we found. We also display the total number of letters in all extensions around the original search term and the number of letters per extension.

Appendix F
Independence of the Discovery Rate and the
Number of Extensions Previously Discovered

Of the 475 extended ELSs that consisted of one or more extensions, 72.0% (=342/475) of them actually had an additional extension, and so were counted in the 2+ extensions group. Using the formula for the discovery rate,

1.0 – (square root of the %-age of searches where no extension was found),

we have, d = 1.0 – (square root of 28.0%) = 47.1%. The results of this, and parallel calculations for each situation of the number of extensions (or more), are shown in Table 9.

Table 9
Discovery Rate for Different Categories
of Length of Extended ELSs

It is worth noting that the discovery rates in the last column, with only two exceptions, are distinctly higher than the overall assumed discovery rate of 25.6%. The exceptionally high discovery rate of 47.1% for extended ELSs where one extension had already been found is clearly non-random in nature.

A variety of more complex extension models could be constructed by assuming some relationship between d and the number of extensions that have already been discovered. The primary consideration to be reflected in doing so is that the longer an ELS becomes, the more difficult it is to have the entire ELS remain coherent and continue to represent acceptable Hebrew. The previously discovered words and phrases create a context with which subsequently discovered, potentially intelligible phrases in Hebrew, need to be compatible. This effect may be somewhat offset by the possibility that when a Hebrew expert finds one extension, he may try harder to find a second extension, and so forth—since his task is to look for as many extensions as may exist in the letter strings he examines.

Jacobi is of the opinion that he has tended to be motivated to try harder to find yet another extension when the quality of the Hebrew in the existing extended ELS was particularly good. This was more motivating to him than the mere fact of the actual length of the extended ELS. Given that the quality of the Hebrew of an ELS tends to deteriorate as the ELS becomes longer, this would suggest that he would generally become less motivated to search for yet another extension as the existing extended ELS became longer. All of these considerations, taken together, indicate that the simple assumption of the independence of d may tend to overstate the expected number of long ELSs of different lengths from a non-encoded text.

Appendix G
Dependence of the Conclusions
on Variations in the Discovery Rate

We tested the sensitivity of our findings to variations in the assumed discovery rate from a non-encoded text. As noted previously, the chi-square probability of random occurrence of the results presented in Table 2 is 1.373 E -277, assuming a discovery rate of 25.6%. If the assumed discovery rate is lowered, the probability of random occurrence rapidly becomes even more remote. Table 10 shows how the chi-square probability changes as the assumed discovery rate is varied.

Table 10
Impact of Changes in the Assumed Discovery Rate

When the discovery rate is assumed to be 37.7%, the chi-square probability of random occurrences reaches its maximum. However, that indicated probability (1.086 E -39) is so infinitesimal that the null hypothesis should still be rejected.

Appendix H
Commentary on the Content of Extended ELSs

While this analysis conclusively indicates that non-random encoding exists in the Hebrew Bible, it is worth noting that the specific content of any single extended ELS is subject to many 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 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 point (3), some 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.

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 significant concern because of the 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 authored by a super-human intelligence.

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