


the focus of a New York Times best seller, The Prayer of Jabez. Though Jabez is mentioned only four times in the literal text of I Chronicles, his name appears as an ELS in the surrounding text 80% more often than expected by chance (53 times vs. 29.45). One could think of this as a sort of encoded “halo effect.”
This kind of finding naturally begs the question of whether a similar effect might exist around passages about the leading figures in the Hebrew Bible. We first checked this out for Moses and found a moderately unusual mosaic for him. Upon turning to our next search candidate, David, and checking out as a first guess the text in I Samuel where David first breaks into written history, we encountered a mosaic so massive and dramatic we immediately suspected that there must be some natural explanation for its enormity.
While natural causes quickly emerged for the extreme shape of the mosaic at the highest skip sizes, no such similar rationale has surfaced for the highly exceptional excess of David ELSs at short skip sizes in I Samuel 1420. We completed an extensive statistical analysis to derive the odds that this David mosaic could be as unusual as it is. The results: less than 1 in 600 billion. We suspect that this new mosaic may well prove to be one of the most daunting challenges to code skeptics who might attempt to explain it away.
After searching through I Samuel 1420, which surrounds David’s first mention in I Samuel 16:19, the David ELS appeared 2,323 times more often than expected by chance with skips between 11 and 3,000. This is 17.3% greater than expected, which is an exceptionally large difference given the large number of expected appearances (13,420). According to the Law of Large Numbers, the larger a sample, the closer (percentagewise) it should be to expectation. If the David ELS showed up less than 5% more often than expected, the David mosaic would be a natural phenomenon. However, as the next graph shows, for 22 of the first 23 skip bands of width 100 up to 2,300, the David ELS typically appears at least 10% more often than expected. Typically David appears between 10% and 30% more often than expected by chance.

To get a handle on how unusual this was, we checked for David mosaics with skips of 113,000 in 40 different randomly selected texts in the Tanakh and measured how strong the mosaic effect was. The results are shown in the following graph.

While our “mosaic effect index” fell within the range of 0.02 and 4.68 for these 40 texts (with an average of 2.21), the David mosaic in I Samuel 1420 scored an exceptionally high 9.88. After extensive statistical analysis, we determined that the odds of this happening by chance were less than 1 in 600 billion (see Technical Discussion for details).
So the search began for natural explanations. The leading candidate for that is large variations in letter frequencies between different sections of the text, and these certainly exist within I Samuel 1420. The bulk of these differences are due to the fact that David bursts onto the scene of the literal text an exceptional number of times. Since David’s name includes two Dalets, the frequency of Dalets in I Samuel 16:1920:42 (4.8%) is much higher than in I Samuel 14:116:18 (2.0%). This fact largely explains why the David ELS appears far less often than expected for very high skips (for example, 4,296 actual appearances versus 5,694 expected for skip sizes of 4,001 up to the maximum of 8,085). Such ELSs must be comprised of a Dalet from the early part of the text (where Dalets are relatively scarce).
While this rationale explains away the dramatic shortage of David ELSs with large skips in I Samuel 1420, it literally does nothing to explain the nonrandom behavior of short skip David ELSs. We checked another section of the Tanakh where David is suddenly mentioned a large number of times (I Chronicles 814), also causing a dramatic increase in the frequency of Dalets (from 2.2% to 3.9%). For most skip bands, the David ELS showed up quite a bit less often than expected.

So much for the hypothesis that a sizeable increase in the frequency of Dalet’s due to David appearing frequently in the literal text would naturally cause the David ELS to appear much more often than expected. So, if differences in letter frequencies are to be an explanation, it will need to be on a much more complex and subtle basis than the obvious.
Technical Discussion of David Mosaic Analysis
We constructed a mosaic effect index by comparing the actual versus expected number of appearances of the David ELS within three skip bands: 111,000, 1,0012000, and 2,0013,000. For each of these the absolute value of the number of naïve standard deviations was calculated (as the ratio of the difference between the actual and expected number of occurrences and the square root of the expected number of occurrences). and these were added up to get the index. The following table displays this process for I Samuel 1420.

By way of comparison, the next table displays the calculations for II Kings 1925, which had an average mosaic index among the 40 we checked.

Notice that the standard deviations in the second table are all less than 3, staying within the typical boundaries of a bellshaped curve, while the standard deviation for the skip bands of I Samuel 1420 are all well beyond the bellshaped curve that depicts the behavior of random occurrences.
The next table discloses the mosaic effect index and the transformed index for I Samuel 1420 as well as each of the 40 passages we checked. The passages appear in descending order of the magnitude of the index.

It was clear that the straight indices followed a distribution that was skewed toward larger values, so we searched for a logical way to transform those indices so that they would conform as closely as possible to a normal distribution. To get the transformed mosaic index, we optimized the variable A in (LN(mosaic effect index))^A so that the skewness of the resulting transformed indices was 0.0, which is the skewness of a normal distribution (bellshaped curve). The resulting value of A was 1.816764. We then determined the probability that the transformed index for I Samuel 1420 of 9.88 could be the result of chance, given a normal distribution with mean of 2.21 and standard deviation of 1.2953, these values being determined from the 40 transformed indices of the randomly selected passages. That probability was 1 in 600 billion, since 9.88 was 5.916 standard deviations above the mean.
To further check the reasonableness of fitting a normal distribution to the transformed indices, we made a comparison of the actual versus expected number of transformed indices within different numbers of standard deviations above and below the mean. That comparison is shown in the following table:

Since the actual number of indices within different standard deviations around the mean were quite close to the expected number, the above comparison supported the hypothesis that the distribution of transformed indices was approximately normal, lending support to the calculated probability of chance occurrence of 1 in 600 billion. A chi square pvalue for goodness of fit indicates that there is a 96.8% probability that the above differences between expected and actual are due to chance. This confirms how well the normal distribution fits the transformed indices. We also fit 20 different probability distributions to the set of 40 transformed indices and the normal distribution had the best fit, based on the chi square statistic for goodness of fit.
(For more information on mosaic codes, please see articles in past issues of Bible Code Digest listed on the Subscribers page.)
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