home
back
 

Basic Testing

A basic test of Luke 15 corresponding to the author's analysis is presented here, being conducted according to the proposed phrase construction rules.

Apparently arbitrary manipulations of the text were maintained, where the author, in more than a dozen instances, altered the order of certain words, stating, "the conjunction for and or but (de), and one instance of therefore (ouv) had to be moved in the pecking order so that the logic of the computer program could calculate every phrase possibility -- with or without." This was generally at the beginning of a verse where de was preceded by a base word (such as said... eipe). This basic test respected such changes, as well as the omission of the autou reference in verse 14. Thus, the text of the Basic Test is exactly the same as the author's.
 

4-Word Test

The number of 4-word phrases constructed in this test is 683 (shown here). This compares to 763 phrases in the author's (corrected) sample (not 772 since the omission of autou is maintained). Since the author did not publish his phrase pool we cannot explain this difference, however we do note 77 redundant phrase sums in the complete pool of 760 phrases available. It is likely that the author included such redundant phrases in his sample.

The summary table below reports the factors outperforming the author's Theomatic factor (row 0) in descending overall statistical significance. F is the factor, followed by its hits (H), then the expected (arithmetic mean) number of hits (M). The next three columns show the clustering percentages, p-values of hits (P_H) and clustering (P_C), and the joint p-value, P (P_HxP_HC), indicating general statistical significance in the same manner that the author does in Chapter 9, and its associated odds 1 in N. The last column, O, gives the average number of  Theomatic tests needed before seeing results comparable to this factor based on the distribution of the maximum order statistic (MOS). Differences between the author's corrected results and the following results are primarily due to phrase construction. The actual hits obtained by each factor are shown here . Factor 10 is excluded from consideration (greyed out) due to the affect of phrase construction dynamics.

Clearly, one may note that the Theomatic factor identified by the author, 90, is insignificant. All of the valid hits obtained by the author were obtained here: none were missed.

Adhering to fixed phrase construction rules actually yields the same number of hits from a smaller sample (683 vs 765), giving a slightly better P_H value (.0010 vs .0194) than that obtained by the author's phrase construction technique. Clustering significance has deteriorated somewhat (p-value of .6792 vs .4703). The general result is more favorable for the claimed Theomatics factor (1:N is 1:148 vs 1:110 but this difference in O is negligible (both are 1.00). Both results are certainly well below the expected value of the MOS and outperformed by a number of apparently random factors. 90 ranks 4^th among a thousand factors in hit significance in this test, 668^th in clustering, and 21^st overall.

It is significant that 38% of these factors are multiples of 10, and 67% are multiples of 5. If one just looks at the top 10 factors, 50% are multiples of 10 and 80% are multiples of 5. In a random environment these values would tend to be 10% and 20% respectively for the top N factors (regardless of N). This is evidence that phrase construction rules tend to favor small multiples of 5, which violates the assumption of randomness in the test and therefore diminishes any claim of theomatic significance in factor 90 (or, for that matter, factor 10, which would be quite significant otherwise). This non-random property certainly cannot hurt 90's performance, but it evidently has not helped much: there is no Theomatic significance in factor 90 in spite this advantage
 

3-Word Test

The above context was also tested with a max phrase length of 3  to compare with the author's results. The manner of phrase construction would, again, be the only difference between these results and the author's results. This test resulted in 420 phrases, fewer than the 465 in the (corrected) sample of the author's test, and are given here. The actual hits obtained by each factor are given here. Columns are as in the previous table.

The 3-word test gives much different results than the 4-word test. 90 is still insignificant, since it is still being outperformed by the MOS . 90 rank's 3^rd in hit significance, 45^th in clustering, 8^th overall. A much better p-value is obtained for 90 in this test, yet its clustering is poor in comparison with the other top factors.

Again, note that every factor listed is a multple of 5 and 63% are multples of 10. Each factor attains its significance due to an unusual clustering pattern, tending heavily toward direct hits, and smaller factors are nearly always favored to larger ones. Factors 10 and 25 appear remarkably significant. Evidently, the affect of variable manipulation makes this environment very non-random, implying that the resulting probabilities are meaningless. If the environment were purely random we would expect no such patterns as these in the results.

Factor 70, a larger multiple of 10, is mildly interesting due to being bi-polar in its clustering, and very heavy on direct  hits, but it is observed that 70 happens to be the value of the article O, which occurs 17 times in this text, and 70 also evenly divides two other articles, TON and TOU, which appear a total of 15 times in the text and give rise to multiple variations of any successful hit.
 

2-Word Test

The above context was also tested with a max phrase length of 2. This test resulted in 206 phrases, again fewer than the 226 in the author's test, and are given here. The actual hits obtained by each factor are given here. Columns are as in the previous table.

These results show all of the author's 23 hits for factor 90, which appears as the most significant factor for hits among many that outrank it in overall significance, but ranks 3^rd in hit probability overall and 30^th due its clustering qualities. It does finally outperform the MOS in overall significance, but many factors obtain very unusual results in this context due to clustering for some reason.

Again, every single factor is a multiple of 5, and 67% are multiples of 10. The trend observed in the 3-word phrases is extended here, though some larger factors are present. It is reasonable to expect that the combination of phrase construction rules (including and excluding multiple short words that are often multiples of 10), a common subject (with similar wording -- 25% of the reference words used to identify the subject, Son, are divisible by 20, 16% are divisible by 90), and only 2 words per phrase (limiting the number of base words and allowing the phrase construction rules even more impact on the combinations) affects the randomness of the phrase sums in a way that allows certain factors to achieve very unlikely clustering results. This is particularly evident for factors 10, 20 and 30. We therefore do not find any of these unusual results to be statistically convincing, or evidence that Theomatics was designed. Certainly, the factor 90 performs less significantly than many other apparently random factors in this context when both hits and clustering are considered.

Very clearly, the results of the above testing, including all phrase lengths considered by the author, and the exact text that he used in his testing, indicate that 90 does not exhibit significance as a Theomatic factor in either its general hit performance or in the nature of its clustering. In every test conducted there are random factors that outperform it. It is never the top ranking factor in overall significance in any word-length category.
 

Cluster Radius 1 Tests

The above context was revisited with the cluster radius reduced to 1. When divisors are only allowed to be off by one unit, we see the following results with 4-word phrases. 90 is still similarly insignificant, ranking 18^th in overall significance, 8^th in hit significance, and 565^th in clustering significance. No factors appear significant.

Repeating the above on 3-word phrases gives the following:

The 90 factor ranks 3^rd in hit significance, but 249^th in clustering, 3^rd in overall significance. The nonrandom nature of the context for 70, 20 and 30 obscures their results. We think it is appropriate to extend this concept to cover 25 as well, being a small multiple of 5, since it is evidently "energized" by the restricted context but insignificant at the 4-word phrase level. 90 is still insignificant, though it does outperform the MOS whereas it did not in the test using radius 2.

Again, for 2- word phrases, and a cluster radius of 1, we see:

Again, 90 ranks 3^rd in hit significance, but 7^th overall due to poor clustering. Again, we note that with fewer degrees of liberty in the test due to shorter phrases and the smaller cluster radius, very "statistically significant" features appear, all of which are multiples of 10, indicating that the environment has lost so much of its randomness that it is inappropriate to draw any conclusions about Theomatic performance.
 

Restored-Conjunction-Order Test

The Luke 15 test was repeated after restoring the de conjunctions and oun to their original locations and keeping the other factors constant in the author's text. This resulted in 681 phrases, given here, indicating that the swap does not support significant flexibility in consistent phrase construction (implying 2 fewer phrases), as supposed by the author. The actual hits obtained by each factor are given here. Columns are as above. 

The author's mysteriously rationalized rearrangement of the de conjunctions was apparently convenient for the Theomatic factor 90, resulting in 4 additional hits. The rearrangement does not give significantly more combinations to test, but different phrases to test. The reordering appears to have been an inappropriate "maneuver" on the part of the author that happens to have favored the desired outcome of his experiment... at least when consistently following phrase construction rules. It is unreasonable to presume that the author did in fact make this substitution blindly, not knowing that it would improve his results. We infer this simply because he offers no justification for the rearrangement of these words and it violates his principle of taking the text exactly as it is written.

In this new test, 90 is not even in the top ten factors according to its hits (ranks 17^th) and has very bland clustering (506^st). There is nothing interesting about this result
 

Majority Text Comparison

Finally, a similar test to the basic test was made of the author's chosen text in two other versions of the New Testament: the Robinson-Pierpont Majority Text (MT) and the Nestle-Aland 26^th/27^th edition (NA).

The following table shows results for 4-word phrases in MT, maintaining the author's reordering of the conjunctions and excluding the reference in verse 14 as before. This compares exactly with the author's text but in a different version of the same type of biblical text.  Noted differences with the author's text were very minor, generally in the spelling of certain words (11 instances). 682 phrases were formed, given here, and hit results are given here.

The Theomatic factor of 90 ranks 4^th in hit significance, 579^th in clustering, and places 22^nd in overall significance. This compares to 21^st in overall standing with the author's text. Not much is significant here... especially 90.

Test results for the NA text of Luke 15 resulted in 665 phrases, given here, quite a bit fewer than the MT , being a very dissimilar text in a number of respects, and gave factors as follows:

90 ranks 15^th in hit significance, 95^th in clustering, and 13^th overall. Results are again insiginificant.
 

Summary

The above test results demonstrate that the author's claim to have found an unusually significant Theomatic factor in 90 in this Luke 15 context is a false one, in agreement with the conclusions drawn from a mathematical analysis of his claims. The results of the author's own test indicate that this factor is not unusually significant, and every single test above indicates this same fact.

Furthermore, these tests demonstrate that no Theomatic factors exist for this subject and context, at least as the author as defined Theomatics: we have exhausted every single possible factor under a number of different perturbations of the text and found nothing notably significant. Certainly, there is no outstanding factor that clearly shines above the rest in overall standing, that is robust enough to evidence significance under these different scenarios... all of which are reasonable contexts in which to expect to find such a phenomenon if it does indeed exist. As we have observed, the unusual significance of factors 20 and 30 is expected, and can easily be explained by the fact that many of the Greek articles are multiples of 10, which results in a much higher percentage of hits for factors that are smaller multiples of 10. This concludes our general testing of Luke 15.
 

Conclusion

Test results indicate no Theomatic significance of any kind in Luke 15 concerning references to sons in the Parable of the Prodigal Son. All possible factors fail to exhibit general statistical significance in this context. We conclude that this context contains no Theomatic structure.

home
back
top