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January 13, 2005
quranumerics, randomness and hazard
One fascinating example of borderline-numerological 'quasi-empirical mathematics' (a 'phenomenological law' as this site has it) is Benford's law, which states that in a wide variety of empirical circumstances, "as diverse as the drainage areas of rivers, physical properties of chemicals, populations of small towns, figures in a newspaper magazine, and the half-lives of radioactive atoms" numbers will have "1" as their first non-zero digit disproportionately (about 30% of the time).
This remarkably counterintuitive fact was first discovered a century ago by an astronomer who remarked on the relative wear on the front pages of logarithm table books. It was only in 1996 that mathematician Tod Hill established that the "law" can result from the characteristic types of series produced by amounts being inflated according to compound interest ($1,000 takes a long time to grow past $2,000, and a lot shorter time to make it up to $10,000). However he also proved a more puzzling wider applicability: given any random collection of random data samples, Benford's law seems to apply. (That is, given that the collections are not "truly random" (which would require that they had been artificially created) but are "phenomenological". Randomness is basically an uninteresting fiction. The Hazard of the Real is never featureless and this may be the founding intuition of numerology. You'll notice that we're getting closer here to my repetitious and vague intuition about the convergence of the close-at-hand numero-phenomenological and the 'evacuated' mechanism of materialism [undercurrent,dread & hyperstition passim] ).
The immanent patterning described by Benford's law in real-world numbers has been demonstrated so persuasively that it is used as a fraud-recognition tool for accountants: if a company's accounts do not conform to Benford's law there is likely to have been some tampering going on. Applied in this way, it's an interesting amalgam of mathematical truth and empirical-synthetic principle, which demonstrates that 'exploitation opportunities' in number can often appear causally disconnected, magical or random, being the result of the interplay between number and the use of number, and that in the real world, numbers stubbornly hold on to their peculiarities despite the mathematical drive to indifference.
You may also wish to consult this site for some interesting suggestions on the applicability of Benford's Law to the Quran...
Posted by robin at January 13, 2005 02:00 PM