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Supplementary Analyses of the Qur’ânic Initials
You will recall that five of the eight observations about the nature, order, and arrangement of the Qur’ânic initials showed a level of statistical significance suggesting that it inform some aspect of how the initials are to be counted to create the principal data set. One of these (#6) could not be interpreted to generate a unique rule, since such a rule would merely have duplicated one that had already been generated (#4). The four remaining rules generated by those observations are therefore as follows:
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1st Rule (Observation 4): Aggregate sums across identical, uninterrupted sets of initials (first-order groupings).
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2nd Rule (Observation 3): Aggregate sums across all identical sets of initials (second-order groupings).
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3rd Rule (Observation 5): Aggregate sums across quasi-similar sets of initials (third-order groupings).
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4th Rule (Observation 2): Count sums of unique sets individually, and include the aggregate of all initials in the data set.
Purpose of the Supplementary Analyses. The purpose of the supplementary analyses is to test how readily the 19-based code already shown to exist in the principal analysis shows up when one or more of the rules generated from the eight observations are not followed. At the same time, it is important to generate different kinds of data sets to give the other 24 prime numbers below 100 plenty of reasonable opportunity to demonstrate unusual deviation from the random mean, if this really happens in numbers the way it is often claimed.
It is possible to alter the data set either to exaggerate the number of times multiples of 19 appear, or to dilute that number and obscure all evidence of significance. It was for this reason that I chose to assess the nature of the muqaţţa‘ât using statistical tools rather than being content to define the data set subjectively. In the supplementary analyses, however, we want to cover the entire range of possibilities from complete lack of significance to simplified approximations of the principal data set.
In all analyses, we will use simpler definitions than the four-faceted criteria that defined the principal data set. The reason for this is that we want to avoid formulating definitions whose very complexity undermines the value of the test. That is, while we should freely consider definitions that generate data sets that show no evidence of a 19-based code, we should avoid adding any new criteria to our existing definition that are not the product of bona fide observations of the nature of the muqaţţa‘ât. Thus, no rule will be considered if its only reason for existence is its evidenced ability to produce an extra multiple of 19.
Besides establishing how robust the 19-based code is, the supplementary analyses may inform our understanding of the nature of the structure of the Qur’ânic text beyond what we were able to infer from the eight observations. For example, if the inclusion or exclusion of a given criterion does not demonstrate an appreciable difference in significance, then it can be tentatively concluded that the underlying structure of the Qur’ânic text does not depend on that criterion. Using an inductive approach, those variables most closely related to the 19-based code can be brought to light over time, while others that are not related to it can be set aside as probably irrelevant to the code. This kind of process can help people avoid the pitfall of expending excessive time and effort exploring novel configurations of Qur’ânic textual anomalies, while encouraging more in-depth research into those aspects of the Qur’ânic text shown to be relevant to the code.
The links to those supplementary analyses done thus far are as follows:
1st Supplementary Analysis: Chapter-level grouping only.
2nd Supplementary Analysis: Cross-section by individual initials.
3rd Supplementary Analysis: Chapters clustered into groups of identical initials.
4th Supplementary Analysis: Chapters clustered into uninterrupted series of identical initials.
5th Supplementary Analysis: Individual initials by individual chapter (complete fragmentation).
6th Supplementary Analysis: Chapters clustered into quasi-similar groups.
7th Supplementary Analysis: Chapters clustered into quasi-similar, uninterrupted series.
General Conclusions and Implications of the Supplementary Analyses
The 19-based code in the muqaţţa‘ât has been shown to be robust enough to remain clearly evident under all conditions tested thus far, as long as the chapters are grouped together in some fashion based on their identity. If the muqaţţa‘ah sets are reduced to ungrouped, individual chapters or if the letters are examined without regard to their places in the muqaţţa‘ah sets, the code generally disappears.
The most interesting finding among the supplementary analyses is that the arrangement of chapters into quasi-similar groups actually enhances the significance of the number 19, even though only one method of grouping is employed. This might suggest that a variety of grouping methods may be used with the muqaţţa‘ât, each of which could evidence the 19-based structure on its own rather than in a manner dependent on other criteria simultaneously.
Another important finding is that the data may substantiate the contention that the hamzah should not be counted among the alifs. Specifically, whether this is or is not counted among the alifs has no appreciable bearing on the results of most of the analyses, but in the analyses of quasi-similar groups the inclusion of hamzah reduced the number of multiples of 19 in each data set. It will be important in future research to verify the impact of counting hamzah on the 19-based code, but so far the findings from the quasi-similar groups seem to suggest that it should not be counted.
The last issue that should be highlighted is that in none of the analyses did any other multiple emerge as a significant anomaly. The only number to show high levels of significance in any of the analyses was the number 19. No other number even met our one-in-one-thousand rule of thumb (p < .001) for considering a finding significant enough to be worth some attention. In some tests, the number 19 showed so much significance that its graph could not even be contained within the dimensions used for illustrating the results.
The Qur’ân Code:
Home page.
The Mysterious Qur’ânic Initials:
An explanation and chapter-by-chapter count of the Qur’ânic initials.
Use of Statistics: How
statistics can be used to analyze the Qur’ânic text.
Defining the Data Set to be Analyzed:
Overview of the nature of the Qur’ânic initials and definition of the principal
data set.
The Principal Analysis:
Includes links to supplementary analyses.
Implications of the Present Findings:
Discusses the outcome of the principal analysis.
Supplementary Analyses:
Overview, with links to individual analyses.
General Summary of Findings by Statistical Significance:
Compilation of all analyses for comparison of outcomes.
© Copyright Abu Jamil
and The Q Zone
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