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A study in Pythagoreanism
on August 18, 2009
Putting aside Plichta's self-congratulatory style, he does make some interesting points. I liked his discussion of the hemoglobin molecule as a quadrapole magnet (p. 97), and chapter 16, on fractals, chaos, and reciprocal geometry. Plichta's main claim to fame is his discovery of the prime number cross, which is simply a consequence of arranging number in a rings (or shells) of 24 divisions. (The formula 6n (+ or -) 1 that generates the prime numbers above 3 obviously means that they can be derived from multiples of 6 by either adding or subtracting 1. And 24 divided by 6 is 4, so you have the 4 main arms of the cross. The arms are doubled because some numbers are derived by adding 1, as in (6 x 1) + 1 = 7, or by subtracting 1, as in (6 x 1) - 1 = 5). Had Plichta chosen a different number of divisions in his rings (other than 24), then the 4 armed cross would not appear. Arranging data in novel fashions can sometimes lead to new understandings, but I personally don't see anything revolutionary. The cross has two exemptions, the prime numbers 2 & 3 which do not fall on any of the arms. Plichta fudges on this one, and tries to devalue their status as primes. In other ways he elevates the number 3, along with 24, 81, (19 + 1), etc. finding examples everywhere in biology, chemistry,etc. Much of the early part of the book is exploring the "preponderance of threesomes" in science and all aspects of life. He even treats the speed of light as 3 x 100,000 km per second even thought he concedes that it is not exactly, but almost 3. Being a chemist, he should know that while the discovery of elemental triads was initially helpful in grouping elements together according to similar characteristics and multiples of atomic weights, the devotion to threes became a stumbling block to including more members into the same group (comprising the vertical columns of the modern periodic table. All too often, Plichta seems to fudge the facts to fit the numbers--a true Pythagorean. In this regard, he is reminiscent of 19th century scientist, Gustavus Hinrichs, one of the early discoverers of the periodic system of elements (prior to Mendeleev). Hinrich correlated the sizes of the planetary orbits (which produced a series of whole number ratios, the differences among them being multiples of 20) to ratios of atomic spectral line differences and thus atomic dimensions of various elements. He constructed a spiral periodic system with 11 spokes radiating from the center, with the chemical groups lying along the spokes. Whether or not Plichta's prime number cross will similarly advance scientific knowledge remains to be seen.
One of the key chapters seems to be chapter 13, The Law of Empty Space. The sum of the numbers that make up each concentric ring form prime multiples of 300: first ring 1 x 300, second ring 3 x 300, third 5 x 300, and so on. This kind of number play is reminiscent of magic squares and number games. Plichta's main assertion is that the structure of empty space is number: The atomic nucleus is the centre of the Prime Number Cross. (p. 157) And space is arranged around this point in the form of shells. The four prime number twins (primes that flank a non-prime)of the first shell determine the structure of all further shells. Plichta is excluding 3 which also forms a twin: 3 & 5. 3 also is right next to another prime 2 as is the first positive prime 1. So 1 and 3 are unique among the prime number twins, 2 being the only prime flanked by primes. But this doesn't fit his cross structure, so fudge factor glosses over this. Once you acknowledge these discrepancies, you can appreciate the correspondences that Plichta does make. The idea of "prime number space" as four-dimensional space is interesting, but an artifact of the right-angled space mirror imaging.
Other critical reviews focused on Plichta's inept mathematics. One review incorrectly charged Plichta with claiming 25 was a prime number (p. 117). A careful reading will reveal that the statement, "The prime number 25 is above the prime number 5," is a typographical error. The figure 2 shows 29 above 5 and 25 above 1, so the text should have said, "The prime number 29 is above the prime number 5." There are 3 other typos: page 119, third line from the bottom: "number 0 also happened to be occupied by the number 23." The O should be replaced by -1. On page 129, the proportional symbol ~ is missing between E2 and 1/time squared2 at the bottom of the page. On page 196, the 5th line of Pascal's Triangle shows after the -> 14631 and should show 14641. I tend to agree with one reviewer who criticized Plichta for "seeing patterns everywhere and in everything when they have no real significance." Significance was made of multi-scale isomorphisms in our pre-scientific past. It was called the hermetic principal of alchemy: "As above, so below." Their numerical significance was celebrated among the Pythagoreans of ancient Greece and have persisted today in NewAge numerology & astrology. A similar study in isomorphic meaning making can be found in Jose Arguelles' Earth Ascending, where the 64 hexagrams of the I-Ching are linked to the 64 codons of DNA and the numerical patterns of the Ben Franklin Square. For Arguelles, the key to the universe is the binary triplet code, inherent in the Mayan Tzolkin, I-Ching trigrams, and DNA codons. For Plichta, it is the prime number cross. Interestingly, neither Arguelles or Plichta ever mentions the golden ratio and equiangular spiral that was regarded as sacred geometry (the Divine proportion) by the Pythagoreans. If anything deserves the title of "God's secret Formula," then it is the golden ratio.
Seeing numbers everywhere can indeed be delusional as the films "A Beautiful Mind" and "23" aptly depict. One thing both positive and negative reviews indicate about Plichta's book: it is certainly stimulating and provocative. I found it worth the read, even though I disagreed with his conclusions. Read it yourself and you decide.