## The Systematization Principle

The systematization principle of the genetic code is a rule that arranges a code calligramme. A "calligramme" was invented in 1914 by the French poet Guillaume Apollinaire (1980). He arranged letters and words of his written texts in the two-dimensional space of a book sheet instead of a traditional line. Thereby he created the so-called calligrammes in which texts, semantics, visual images, and symmetries are joined together. A calligramme surpasses a common text in an information capacity and lucidity. Thanks to ancient calligraphers, Champollion got a ready calligramme of the Egyptian hieroglyphic text. Regarding the genetic code, at first glance there seems to be no recognizable calligramme. The best-known genetic code tabular and circular calligrammes in Figs 3 and 5 have, however, a parameter that people chose voluntarily - the conventional sequence order of four bases T, C, A, and G. Being guided by instructions outgoing from within the code, we should try to reproduce its primordial calligramme. Rumer's bisection in Fig. 4a appears to be a most useful half-finished product in that respect. We present its final upgrade in Fig. 8.

The centrosymmetrical flow chart shows equilibrium of the systematization principle formulation in Fig. 8a. The first object of systematization is the sets of the same degeneracy series. There are exactly four such sets in the genetic code according to four degeneracies IV, III, II, and I. The second object is the synonymic series of the same degeneracy inside each of these sets. Each of these objects is a component part of another one. The crossing arrows symbolize such interplay. There is only one general condition - the objects should be aligned with a monotonic and opposite directed changes of two parameters. These are the degeneracy number of the sets and the nucleon number of the amino acids or syntactic signs. To meet this condition the degeneracy numbers of four sets decrease from left to right in Fig. 8b. A line of variable thickness symbolizes this change. At the same time, the amino acid nucleon numbers - inside each set - are on the decrease in the opposite direction, i.e. from right to left. Diminution in size of amino acid's trigram abbreviations symbolizes this change.

The final calligramme is referred to as the cooperative symmetry of the genetic code (shCherbak, 1988). The calligramme is invariant under mirror symmetry. That means that the calligramme does not change if the opposite directions of the parameter changes were chosen. Note that the principle combines into a single whole Rumer's series bisection and Hasegawa's and Miyata's series alignment.

Fig. 7 (continued) (b) Regularly apportioned triplets of the third set demonstrate the decimal syntax and equilibration of different types. The right balanced arm of the 999-and-999 balance contains the triple balance. Its two of the three symmetrically subdivided arms are a pair of halved lines (a vertical dash-line indicates a halving), the third arm is a complete line (shown by wide bordering). The balances are true for the universal genetic code and its E. octocarinatus version

Fig. 8 The systematization principle and a calligramme of the genetic code (shCherbak, 1993 a). (a) The flow chart of the systematization principle. (b) The principle requires contractions of the life-size series located in Fig. 4a. There are degeneracy-dependent 3' triplet base contraction and 90° turn of the glycine (Gly), isoleucine (Ile), methionine (Met), phenylalanine (Phe), and leucine (Leu) synonymic series as an example. The synonymic series of glycine is contracted four times. The contraction symbol N = {T, C, A, G} substitutes for the four glycine 3' triplet bases. There are also a thrice contraction symbol H = {T, C, A} and a pair of double contraction symbols for pyrimidines Y = {T, C} and purines R = {A, G} in the contracted genetic code. The methionine series retains its life-size. The 90° turn makes contracted series upright. The upright position of the contracted series describes graphically new symmetries of the calligramme. The genetic code is represented by its E. octocarinatus version

Fig. 8 The systematization principle and a calligramme of the genetic code (shCherbak, 1993 a). (a) The flow chart of the systematization principle. (b) The principle requires contractions of the life-size series located in Fig. 4a. There are degeneracy-dependent 3' triplet base contraction and 90° turn of the glycine (Gly), isoleucine (Ile), methionine (Met), phenylalanine (Phe), and leucine (Leu) synonymic series as an example. The synonymic series of glycine is contracted four times. The contraction symbol N = {T, C, A, G} substitutes for the four glycine 3' triplet bases. There are also a thrice contraction symbol H = {T, C, A} and a pair of double contraction symbols for pyrimidines Y = {T, C} and purines R = {A, G} in the contracted genetic code. The methionine series retains its life-size. The 90° turn makes contracted series upright. The upright position of the contracted series describes graphically new symmetries of the calligramme. The genetic code is represented by its E. octocarinatus version

The zero of the Stop signs was previously trivial summands. Now, it forms the calligramme just as an ordinal number does. On that ground, the zero occupies its formally predetermined position at the beginning of the natural series and places its own triplet series at the flank of the degeneracy II set. We shall return to this important point when we discuss the cooperative symmetry.