Batting 1.000:
An Example of Undeniable ELS Underscoring

Continued

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 1 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 1 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 1 million trials, only 4.07 of the 35 letters appeared in David verses.

In only 1,117 of the 1 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 1 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 1 in 1 million. But, how much less?

Deriving the Odds

How did we come up with odds of 1 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 1 million would be ones where there were 35 David verses, as shown in the following table.

Given that only 0.005 trials out of 1 million would result in 35 David verses, the odds of this occurring by chance were 1 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 1 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 1 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 I 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 %-age is an overall average, some sections of I Samuel 16-II Samuel 24 would naturally have an even higher %-age 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 %-age of David verses in the actual range of text spanned by each of the King David ELSs in I & 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 %-age was 94.81%. So, to be conservative, we replaced the actual %-age 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 %-age 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 1 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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