Authors: Miloje M. Rakocevic
According to my best knowledge, for the first time here is presented a hypothesis, that the one and only accompanying diagram in Darwin famous book On the Origin of Species contains, may be, a hidden code. Direct inspection reveals that the Diagram, viewed as built of four parts [(two upper and two lower / two left and two right); (two with more and two with less branches / two with multiple and two with single branches)], corresponds to the logical square of the genetic code. When, however, viewed as built of two parts (upper and lower), then it corresponds with Shcherbak diagram (Shcherbak, 1993, 1994) of four-codon and non-four-codon amino acids; not only by the form but also by the number of elementary quantities. The number of nucleons in the upper part of Shcherbak diagram (four-codon amino acids) is determined by the Pythagorean law, meaning that the total number of nucleons makes the product of the number 25 and Prime quantum 037 (925); and the number of branches in the lower part of Darwin diagram is determined by the law of Plato, meaning that the total number of branches makes the product of the number 216 and First quantum 01 (216). On the other hand, in the lower part of the Shcherbak diagram there are 60 of Prime quantum 037 (2220), while in the upper part of the Darwin diagram there are 60 of First quantum 01 (60). There are 216 + 60 = 276 branches (in total), and this number is also the number taken from a specific and unique arithmetical system. Furthermore, it is shown that Darwin, starting from the basic structure of the Diagram, formed a sophisticated structure which strictly corresponds to the arithmetical and /or algebraic structures that also appear to be the key determinants of the genetic code.
Comments: 96 Pages. This is a pre-print form for a booklet with the same title; the suggestions are welcome! As new, in relation to V3, here are Appendices H & K, and Remark 4.2.
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