|Bible Code Digest: November/December 2006 Continued
Precipitating a Moment of Truth |
Is there validity to the alleged phenomenon of Bible codes, or not? In the last two months, BCD again submitted this question to extensive testing. The results: Without a doubt, the phenomenon is real. How can we be so certain? After all, there are some highly intelligent and respected scientists who have vehemently asserted that the entire thing is a hoax. Yet, if you carefully examine their arguments, they do not address the real question at hand. What they say, in effect, is that people can find such codes in any text. Yes, that is a solid half-truth. But, it is only half of the truth.
How do we find out the other half of the truth? It all depends on whether or not those short equidistant letter sequences (ELSs) of the type that Drosnin has presented are part of longer ELSs in good Hebrew, or not. And if they are, how long are these extended codes, and what is the rate of discovery of extensions to the shorter ELSs previously found? Yet prominent code skeptics won't even check this out, or if they have, they aren't disclosing their results. We challenged them to do so some time ago. There has been no response, and we don't expect one — because they know full well that the discovery of lengthy codes in non-encoded texts is a rare occurrence. So whatever they could come up with would not begin to compare with the high frequency of lengthy codes discovered by Bible code researchers.
The key question is: "Is the short ELS I have found only a part of a (much) longer ELS, or not?" Suppose a code researcher has found a search term as an ELS with a skip of +10. He then collects every tenth letter before and after his six-letter-long ELS. He has two opportunities to find an extension (a phrase or sentence in good Hebrew) to the original ELS, one before and one after the original search term. If he finds an extension, this presents an additional opportunity to discover another extension beyond the one that has just been found.
In the past two months, we examined 54 original search terms about Jesus (from a list of two-Hebrew-word terms that had already been discovered in the vicinity of Isaiah 53, and that was previously published on page 63 of Bible Code Bombshell). The discovery rate was 50.0%, an exceptionally significant excess over the non-encoded discovery rate of 19.4%. And the content of most of these codes is clearly on topic.
Let's take a specific example. Four years ago when we were looking for ELSs in Isaiah 53, the two Hebrew words meaning "living water" were searched for and two occurrences were discovered. The first had a skip of -2,976 and the second a skip of +3,277. When Dr. Jacobi examined the string of Hebrew letters before and after the "living water" ELS with a skip of -2,976, he found three coherent phrases within that string, as illustrated in the following table:
The above extensions, and the original term, make up a 25-letter-long code.
When Dr. Jacobi examined the string of Hebrew letters before and after the "living water" ELS with a skip of +3,277, he found one coherent phrase right before "living water."
When Jacobi examined the string of Hebrew letters before and after the "who is the messiah?" ELS with a skip of -5,760, he found five coherent phrases before that ELS, and four coherent phrases after it.
The very high density of lengthy on-topic codes in this collection is well beyond anything we had thought possible, based on prior investigations. In a scientific paper we presented a few years ago, we submitted a series of 50 letter strings around original search terms (the names of Islamic countries) to our Hebrew experts, without them knowing that any were from a non-Biblical text. The discovery rate from the non-Biblical text (a translation of Tolstoy’s War and Peace into Hebrew) was 19.4%, demonstrating that extended codes can be found in a non-encoded text — at a certain rate. The discovery rate from the book of Ezekiel was 27.0%, 39.2% higher. This was a sizeable difference, but not enough to be conclusive regarding the potential reality of the phenomenon of Bible codes.
We have since examined three different groups of search terms for possible extensions and have consistently observed discovery rates that were noticeably greater than the 19.4% from the non-encoded control text of War and Peace. The chart below provides a comparison of these discovery rates.
The discovery rates from the two Isaiah 53 searches were so dramatically greater than that from the non-encoded control text that either one, by itself, provides conclusive proof of the validity of the phenomena of Bible codes.
The chart below discloses the specifics behind the above graph.
We developed a Markov chain computer model in Appendix B of the scientific paper to determine what the chances were that discovery rates as high as those observed in the Biblical texts could be the result of chance variation. If the underlying discovery rate from a non-encoded text is 19.4%, then what is the probability that the second Isaiah 53 search we had just completed would result in a 50% discovery rate? We ran 100,000 trials of an examination of 54 initial search terms, and compiled the number of trials that resulted in each possible number of extensions. The results all fell within the bell-shaped curve on the left side of the graph below, with an average number of 26 extensions and a maximum number of 54 extensions. This was in stark contrast to the 108 total extensions discovered during the second Isaiah 53 search (noted at the far right of the graph below).
The table below shows the full results of this computer simulation. Out of 100,000 simulations of an examination of 54 original search terms for possible extensions, none resulted in 55 or more total extensions.
From the above, it is appropriate to conclude that the odds that chance could result in the discovery of 108 or more extensions are essentially zero. The rational conclusion is that the phenomenon of Bible codes has substantive validity.
We fit a mathematical curve to the results from the above table that very closely followed the number of trials for results with 40 or more extensions, and estimated the odds of chance occurrence of 108 or more extensions as less than one in a trillion times a trillion.
Code Skeptics Evade the Real Issue
Code skeptics obscure the real issue by making statements that implicitly assume that all ELSs are comparable in terms of their probability of random occurrence. They would have people believe that a three-letter-long ELS of a Hebrew word is no more likely to be due to chance than a 200-letter-long ELS consisting of eight sentences in good Hebrew that are highly coherent in their content. Yet, it is obvious that the latter would naturally be far more rare than the former. The first is like a dandelion, the second like an extensive, well-tended botanical garden. The first is an everyday accident, the second is the result of a great amount of planning, planting and maintenance. The first is like anyone who first picks up a golf club to try playing the game, the second, like Tiger Woods.
Just how rare or common a given ELS is depends on its length and content. Based on previous analysis done by BCD, given any collection of original search terms, we have a very clear definition of how many extended ELSs of different lengths we might expect to find in a non-encoded text. These expectations can then be compared with the results of searching a group of original search terms for possible extensions.
Focusing on the Real Issue
In our latest investigation, we examined 54 original search terms for possible extensions. The five longest extended codes we found were 75, 64, 59, 55 and 54 letters, respectively. We know, approximately, how long the five longest extended codes would be if we had been searching in a non-encoded text, because we have done such searches, with the Hebrew expert not knowing that the search text wasn't the Bible. From a non-encoded text, we would expect that the five longest extended codes would be 25, 22, 19, 17 and 16 letters long, respectively. Or something quite similar to that. In short, the longest extended codes found in this new Isaiah 53 search are three times as long as those expected from a non-encoded text. How could they be three times as long? It is because they were intentionally encoded. Chance cannot explain this large a difference in the length of the longest ELSs discovered from examining 54 original search terms for extensions.
From this most recent search for extensions, we would expect that 17.7 of these search terms would have one or more extensions. We actually found 33, or 87% more than expected. We would also expect that 4.6 would have two or more extensions. Yet, we actually found 26 with two or more extensions, or 463% more than expected. Furthermore, we found 15 with three or more extensions, 1,277% more than expected by chance. And the percentage excess rapidly gets bigger as we only look at the ELSs with the most extensions. The next table summarizes these comparisons.
Comparison of Actual vs. Expected
ELS Extension Search Results
From the above table, we see that the expected number of final ELSs with eight or more extensions that could be found from searching 54 original search terms in a non-encoded text is 0.0005. That means that, on average, you would have to examine 2,000 different sets of 54 search terms to find just one extended ELS with eight or more extensions. And, on average, you would have to examine eight billion different sets of 54 search terms to find three extended ELSs with eight or more extensions. However, we didn't check out eight billion different sets of 54 search terms. We only checked out one such set. So you can begin to get some idea of how improbable the new set of Isaiah 53 findings actually is.
Continue to Hebrew Alphabet: Lesson Three
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