A reliable prediction of artificiality is a relevant but secondary ability of arithmetic. Arithmetic is the only tool for producing information systems of extremely high efficiency. Life, being an information phenomenon, could use arithmetic for control, integrity, and precise alterations of its genetic texts. Gamow (1954) noted this possibility in his pioneering article on the genetic code. He wrote that a long number written in the quaternary system could characterize the hereditary properties of any given organism. In order to convert some DNA base sequence into Gamow's long number one should replace four bases T, C, A, and G with four quaternary digits 0, 1, 2, and 3.

After Gamow, various authors noted the digital nature of the genetic code (e.g. Eigen and Winkler, 1985; Yockey, 2000; Mac Dynaill, 2002; Gusev and Shulze-Makuch, 2004; Negadi, 2004; Rakocevic, 2004; Gonzalez et al., 2006). Ordinary computers use the binary notation and a checksum even parity, i.e. divisibility by 2, as a data integrity control. Similarly, some genetic sequences could be arithmetically arranged using the number system(s). The number system inside the genetic code indicates - besides the code artificiality - a possible arithmetical power on the level of genetic sequences in genomic DNA. One can speculate that some regular arithmetical background may "underlie" genetic sequences without limitation to their biological context. Analyzing its own arithmetic, such background might check, restore, and alter superimposed biological context by means of calculations omitting translation. Is this the essence of the enigmatic meiosis prophase I? For instance, the meiosis prophase I lasts for maximum about 50 years for female humans (Bennet, 1977). Over that long period, homologous chromosomes remain conjugate without visible biochemical activity. It is not unlikely that information analysis - including arithmetical reckoning - prevails over biochemical activity at that time.

Thus, arithmetic residing inside the genetic code forces us to look for its possible analogue inside genomic DNA. We developed a computer code called a Gene Abacus (shCherbak, 2005). This program tool simulates a hypothetical molecular adding machine that slides along a DNA and performs appropriate summations over certain distances as shown in Fig. 14. Let a machine display the checksum 333 accepted as correct on the register in the form of the base triplet AAA. Homogenous digital structure of the register or its absence corresponds to the intact or damaged gene. A routine shape analysis could convert this digital notation into an analogous form and initiate certain biochemical reactions depending on the performed computations. We have used the new code arithmetic as an instruction to equip the Gene Abacus with suitable arithmetic abilities. The Gene Abacus should look for regularities of both arithmetical syntax and quantity in chromosomes. We fully realize that only the discovery of the same arithmetic in genomic DNA gives the strong key to the mystery of the origin of life.

Fig. 14 A hypothetical molecular adding machine working in the quaternary system and a short gene invented for the sake of illustration. The quaternary criterion for divisibility by PN 7 is similar in every respect to the decimal one in Fig. 2 (shCherbak, 1993b, 1994). There are exactly 64 three-digit quaternary numbers in the range from 000 to 333 (decimal 63). The quaternary four digits and 64 three-digit numbers bear a close analogy with the four DNA bases and the 64 base triplets of the genetic code. There is one numbering T = 0, C = 1, G = 2, A=3 of 24 possible ones in the invented gene. The done reckoning shows checksum 333. As before, one needs only three-digit register to establish divisibility by quaternary PN 7 of any number, irrespectively of how large this number would be. Though there is the quaternary numbering, the decimal system was used in the reckoning for simplicity. The same summation performed in the quaternary system results in the same particular notation 333, but in another quantity

Fig. 14 A hypothetical molecular adding machine working in the quaternary system and a short gene invented for the sake of illustration. The quaternary criterion for divisibility by PN 7 is similar in every respect to the decimal one in Fig. 2 (shCherbak, 1993b, 1994). There are exactly 64 three-digit quaternary numbers in the range from 000 to 333 (decimal 63). The quaternary four digits and 64 three-digit numbers bear a close analogy with the four DNA bases and the 64 base triplets of the genetic code. There is one numbering T = 0, C = 1, G = 2, A=3 of 24 possible ones in the invented gene. The done reckoning shows checksum 333. As before, one needs only three-digit register to establish divisibility by quaternary PN 7 of any number, irrespectively of how large this number would be. Though there is the quaternary numbering, the decimal system was used in the reckoning for simplicity. The same summation performed in the quaternary system results in the same particular notation 333, but in another quantity

Almost half a century ago, the idea of chemical evolution determined a stochastic approach to the origin of the newly deciphered genetic code. The molecular machinery of genetic coding revealed however a baffling complexity. It is common practice to criticize the stochastic approach because the likelihood that this machinery could have been produced by chance is extremely low if not negligible. But, on the other hand, the basic premise of the stochastic approach is that billion years and countless natural events could realize, nevertheless, practically impossible things. This vicious circle exists because both these opposing opinions appeal to the same concept - to the assessment of chances of natural events. One needs therefore properties of the genetic code that eliminate any possibility of a dual interpretation or overlapping of the arguments. In these terms, only the facts whose essence cannot be reduced to natural events can solve the original problem. We believe that a part of these facts have been presented and discussed above.

Acknowledgements The work was financed by the Ministry of Science and Education of the Republic of Kazakhstan. Part of this study was made during my stay at Max-Planck-Institute für biophysikalische Chemie, Göttingen, Germany. I am greatly indebted to Professor Manfred

Eigen for his support and express special thanks to Ruthild Winkler-Oswatitsch for her valuable help. I would also extend my gratitude to Bakytzhan Zhumagulov and Alevtina Yevseyeva of National Engineering Academy of the Republic of Kazakhstan who promoted this chapter to see the light of the day.

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