Batting 1,000:
An Example of Undeniable ELS Underscoring



We are completely astonished at the most recent results of our King David codes research, which we began covering in our September and November 2002 issues. These are mosaic patterns of seven-letter ELSs and their appearances in portions of the Old Testament where David is either the subject or the writer of the surface text, along with extensions of these seven-letter ELSs into much longer ones.

As we have compiled additional data on the codes for analysis, we have seen some of the most amazing results we have ever encountered during our study of codes in the Tanakh, with breath-taking numbers that we may be reporting on for many issues to come.

Code researchers have often noted that the subject matter of ELSs "tends" to relate to that of the surface text. We call this "Underscoring" or an "Echo Effect." Skeptics have often been unmoved by such claims, often with fairly good reason. The tendencies that code researchers have noted have often been based on subjective summaries of scattered anecdotes. Demonstrating anything statistically using evidence of this type is inherently questionable.


One in 200,000,000

This article presents an example of Underscoring where the odds of chance occurrence of the noted phenomenon are one in 200,000,000. Since this was determined using very strict definitions and procedures, it is a strong enough piece of evidence that it should cause skeptics to reconsider their position. Even when we made some of the assumptions harshly demanding, the calculated odds were still one in 20,000,000.

The example presented in this article is only an introductory one that is representative of much more extensive and improbable examples of the same type. We are using this example (involving only five ELSs) in part to more simply introduce some new concepts and some new ways of analyzing ELS phenomena. There is much more to come. The claim of skeptics that there are no valid codes is destined to fall from the sheer weight of a continuing flood of compelling evidence.

In the November 2002 Digest, we included an article on the general textual locations of King David () codes. This article works with a subset of that data. It focuses on very precise ways of categorizing the verses where each of the letters of the five King David ELSs with the shortest skips appear in the Tanakh. This provides an example of a way of rigorously evaluating the likelihood that purported links between the content of the surface text and key underlying codes could be due to chance.

What caught our attention about these King David ELSs was that all five appeared in obvious David passages. Furthermore, eight of the ten King David ELSs with the shortest skips were in David contexts. Was this just a fluke or was it solid evidence of intentional encoding? How could we determine the odds?

We also noted that one of the top ten King David ELSs that didn't appear in a passage where David was literally mentioned was in a messianic prophecy (Daniel 2). That chapter could be seen as pertinent because David is portrayed in the Bible as a type of the messiah. In designing a way of statistically testing things, however, this kind of subjective observation had to be excluded from any tallies. The accusation of stretching things could be raised reasonably.

It is essential to define criteria for strictly and unambiguously labeling any verse as a "David verse" versus one that is not in order to complete a proper tally and apply statistical tests in a truly scientific manner.

In looking at the specific verses where the individual letters of each King David ELS appeared, it was evident that there were several different possible ways that David was either mentioned or clearly involved. We will refer to these ways by letter coding and color coding:





The following table documents application of these criteria to each of the specific verses where the letters of the five King David ELSs with the shortest skips in the Tanakh appeared.






What is truly astonishing is that every one of the 35 letters of the top five King David ELSs appears in an unambiguous David verse (type D, 1D, K or 1K). As documented in the Technical Addendum to this article, the odds of this happening by chance are one in 200,000,000.

To get a visual idea of how extremely unusual it is for all 35 letters to appear in David verses, the following graph provides a comparison of how often different total numbers of letters appeared in David verses in a computer simulation of 1,000,000 trials involving random placement of five King David ELSs.

What the graph shows is that in 178,003 trials out of one million, not a single one of the 35 letters appeared in a David verse. This is not surprising since over 70% of the text of the Old Testament does not contain any, or only very infrequent (e.g., less than 1.5% of the verses) mention of David.

For more than 90% of the one million trials (912,121), fewer than 10 of the 35 letters in the five King David ELSs with the five shortest skips appeared in a David verse. On average only 4.07 of the 35 letters appeared in David verses. In only 1,117 of the one million trials did 20 or more of the 35 letters appear in a David verse. And in only 9 of those trials did 27 or more of the 35 letters show up in a David verse. Not once in one million trials did more than 30 letters appear in David verses. Batting a thousand (i.e., 35 out of 35) is by any definition an extremely unlikely event. And yet that is what happens in the Old Testament.





The significance of such calculated odds is further supported by some interesting anecdotal observations:

  • A 29 letter-long code surrounds the 73 skip occurrence of the King David code. It reads, Bow the palm, Master of King David. Where is my light and the holy ghost of God? Fully 27 of the 29 letters of this ELS appear in David verses (19 D's, 6 K's, 1 1D and 1 1K). In the text it is clear there is a Master of King David. It is Saul.

  • A 21 letter-long code surrounds the 1,095 skip occurrence of the King David code, and it reads, What is present? From whom in him is he King David? One of the letters of this lengthy code appears in the key verse (the exact word where the letter appears is shown in bold italics and highlighted in yellow below) where David is introduced as the future king of Israel:

    Jesse had seven of his sons pass before Samuel, but Samuel said to him, "The LORD has not chosen these." So he asked Jesse, "Are these all the sons you have?"

    "There is still the youngest," Jesse answered, "but he is tending the sheep."

    Samuel said, "Send for him; we will not sit down until he arrives."

    So he sent and had him brought in. He was ruddy, with a fine appearance and handsome features.

    Then the LORD said, "Rise and anoint him. he is the one."

    So Samuel took the horn of oil and anointed him in the presence of his brothers, and from that day on the Spirit of the LORD came upon David in power.


The first six letters of this 21 letter ELS appear in verses just before David is introduced. After his introduction, every one of the 15 remaining verses is a David verse (9 D's, 2 K's, 2 1D's, and 2 1K's).

  • The ELSs with the 7th, 8th and 9th shortest skips were also direct hits on David passages. So eight out of 10 of the ELSs with the shortest skips appear in "David" texts.

TECHNICAL ADDENDUM

Calculating the Odds

How did we determine what would be expected by chance? In short, we used a computer to generate the letter positions of randomly occurring King David ELSs. Then, we determined which section of the Tanakh each letter appeared in and attached the probability that it would fall in a "David verse." For each letter, we generated a random number between zero and one and, if that number were less than the probability that the letter would appear in a David verse, we tallied it up as an incident where that letter so appeared. If the random number were greater than the probability, we did not count it as appearing in a David verse. After doing that for each of the 35 letters of the five King David ELSs with the shortest skips, we tallied up the total number of letters appearing in David verses. Each time the computer performed this exercise, we treated it as one "trial." We had the computer do this over and over again one million times, and it compiled how many trials each given total number of David verses occurred. The results appear in the next table.





From the above table we see that for more than 90% of the one million trials (912,121), fewer than 10 of the 35 letters in the five King David ELSs with the five shortest skips appeared in a David verse. On average, over all one million trials, only 4.07 of the 35 letters appeared in David verses.

In only 1,117 of the one million trials did 20 or more of the 35 letters appear in a David verse. And in only nine of those trials did 27 or more of the 35 letters show up in a David verse.

Not once in one million trials did more than 30 letters appear in David verses. And yet in the Tanakh all 35 letters appeared in David verses. So it was evident that the odds were substantially less than one in one million. But, how much less?


Deriving the Odds

How did we come up with odds of one in 200,000,000 that all 35 verses would be David verses? We fit a curve to the number of trials resulting in each of 19 or more letters being in David verses, and optimized its "goodness of fit." We then used this curve to estimate how many trials out of one million would be ones where there were 35 David verses, as shown in the following table.






Given that only 0.005 trials out of one million would result in 35 David verses, the odds of this occurring by chance were one in 200,000,000. Such odds are so small we should properly conclude that at least some of these King David ELSs were intentionally encoded in David verses.


Running the Trials

How did we generate the letter numbers of the 35 letters for each trial? First, we used a random number generator to produce the skip size of each of the five King David ELSs, assuming that all skip sizes fell in the range between one and 1,100. We picked 1,100 as the maximum skip because the actual King David ELSs with the ten shortest skips appear with skips up to 1,095, as may be seen by referring back to the first table in this article.

Next, we had the random number generator produce a letter number for the first letter of each King David ELS, where that number was equally likely to be between one and the total number of letters in the Tanakh (1,196,921), less six times the skip size of the given ELS. We did this so that all of the generated letter numbers would fall within the range of the entire Tanakh.

With these two generated numbers, the seven letter numbers of each randomly generated "King David ELS" were determined. We then determined the probability that each of these letters appeared in a David verse. To do this, the text of the Tanakh was segregated into logical subsets where the frequency of David should be expected to be quite different.





For each section of the Tanakh, the calculated probability is based on a precise tally of the total number of David verses. As expected, the probability that a given verse will be a David verse varies dramatically between these different sections of the Tanakh. In the first account of David's life (I Samuel 16 to II Samuel 24), 87.09% of the verses were David verses. This contrasts with only 1.38% of the verses in books in the "all other" category, and 0.0% in the lengthy text prior to David's introduction (Genesis to II Samuel 15). These latter two categories of text comprise over 70% of the verses in the Tanakh. Given that, it is easy to understand why it is true for so many trials that the total number of letters in David verses is quite small.


Addressing A Potential Issue

It could be argued that it was just good luck that four out of the five King David ELSs with the shortest skips just happened to occur in I Samuel 16 II Samuel 24, where the probability of any letter appearing in a David verse is very high (87.09%). Since that percentage is an overall average, some sections of I Samuel 16 II Samuel 24 would naturally have an even higher percentage of David verses, so if the ELS appeared in one of those sections, having all of its letters appear in David verses wouldn't be that big a surprise. To consider this, we calculated the percentage of David verses in the actual range of text spanned by each of the King David ELSs in I and II Samuel (including one verse immediately prior to the first letter of the ELS and one verse immediately after the last letter of the ELS). The results appear in a table.





As may be noted, for these four King David ELS texts, the percentage was 94.81%. So, to be conservative, we replaced the actual percentage for the entire range of text of I Samuel 16 II Samuel 24 of 87.09% with 95% something slightly higher than is actually the case. In other words, we assumed that if the ELS appeared anywhere in that text, it must appear in a section with a particularly high percentage of David verses. We re-ran the simulation. The trial with the most David verses had 32. We again fit a curve and calculated odds of chance occurrence of all 35 letters in David verses of one in 20,000,000. Having done this, confidence was increased that it should be concluded that King David ELSs were intentionally embedded in the Tanakh in key David passages. Consequently, we have very hard evidence that such Bible codes are not coincidental.



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