Why are we so certain in speaking about the decimalism? As shown above, the genetic code is the result of numerous very precise summations. To be performed, these summations must privilege a certain number system over a variety of others. Therefore, that privileged numerical system should leave traces inside the code. Being nothing else but a syntactic rule, such a system indicates its own presence only through syntactic features of arithmetical written symbols. There are several phenomena relevant to the case.
First, a general and the most forcible argument: it has been found that the genetic code is governed directly by the arithmetical symbol of zero. This striking fact is verified simultaneously by several independent orderlinesses - logical, arithmetical, and semantical - in the previous section. Incidentally, such an acting zero alone might be sufficient to assume an artificial nature of the genetic code.
Second: it is obligatory that any place-value number system is preceded by revelation of the zero and that happened in the genetic code. Therefore, one should expect inside the code the traces of some privileged system; such system should have the positional principle and not a very big radix. On the other hand, the inevitability of arithmetical summation for the origin of the genetic code equilibria greatly strengthens this premise.
Third: there is a high number of couplings between balances and divisibility by PN 037 x 3 in the genetic code. Note that a balance is not the cause of certain divisibility and vice versa. Moreover, there are drastic differences among logical conditions that define balanced nucleons throughout the code. Even so, the strange couple - a balance and certain divisibility - remains the regular and immutable phenomenon. Recall that the same strangeness of coupling is inherent to linguistic symbols whose meaning and carrier are coupled for no apparent natural reason. Juxtaposed arithmetic and these couples have revealed a meaning of the couples. There is a complete set of information symbols utilizing the decimal syntax 111, 222, 333, 444, 555, 666, 777, 888, 999 in the genetic code. Each of these symbols consists uniformly of a carrier (balanced nucleons) and a meaning (the decimal syntax).
Fourth: there are no other systems in the neighborhood of the decimal one having similar criterions for three-digit numbers divisible by PN 037 x 3 (shCherbak, 2003). In this respect, the decimal system is a unique one as well, as unique is the above interpretation based on its syntax.
Fifth, indirect arguments: two systems with radixes four and seven precede the decimal system. These systems possess quaternary and septenary criterions for divisibility by PN 7 and PN 19, correspondingly. Both these criterions have affinity to the decimal one in Fig. 2. The quaternary criterion is useful for possible numerical calculations in DNA (see the final section). It seems that there is a syntactic symbol in the genetic code that unites the decimal world of amino acids and the quaternary world of bases. That is the final digital permutation 259 within the numerical symbol of the "Egyptian triangle" in Fig. 9. This number is the product of quaternary PN 7 and decimal PN 037. Incidentally, the canonical pair of the
Thymine and Adenine residues in DNA molecules has the same nucleon number 259 + "0"; the other pair of Guanine and Cytosine has 259 + "1" nucleons. One can speculate that this may be imposed by some standard in binary numbering for the four DNA bases.
Speaking about the septenary system, there are uniformly organized symbols in Fig. 7. These are two balanced sums 703 equal to the product of septenary PN 19 and decimal PN 37.
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