The Egyptian Triangle

The 23 amino acids and one Stop sign form a basis of the calligramme. Lying under own contracted triplet series they arrange them in the cooperative symmetry. Let us consider this basis before we focus on the information content of the calligramme.

The amino acids and syntactic signs - i.e. those divided and set aside by Rumer - produce the numerical symbol of the "Egyptian triangle" and a new block-to-chain balance in Fig. 9. As before, the decimal syntax is exactly superimposed onto equilibrated nucleon sums.

We have interpreted so far the decimal syntax of separate numbers. However, in addition to this syntax, the genetic code displays also a combined symbol composed of three numbers with remarkable proportions. These numbers are 9 + 16 = 25 (32 + 42 = 52). It is worth noting that these numbers can exist as a symbol, say, in Pythagoras' mind, but never anywhere in the outer world. The reasons, which encourage us to interpret this symbol inside the code, are presented in Section 13. One possible interpretation is: "The 'Egyptian triangle'—the world-famous symbol of human cultural medium from ancient to our time." Its possible meaning could be: "Artifactural difference of the genetic code and symbolization of a two-dimensional space, i.e. a plane." Incidentally, the calligramme symbols in Fig. 8 are arranged flatly, but not in a one-dimensional string as we are accustomed.

The new block-to-chain balance at the bottom of Fig. 9 is similar to the previous global balance in Fig. 6, but is contrariwise organized. There, the fixed set of blocks balances all the code chains, whereas here, the fixed set of chains balances all their own blocks. As stated above, the nucleon sum of the standard blocks of the whole code is larger than that of the side chains. Chains are larger than blocks only in 7 out of 24 series. Only a limited set with the number of series less than 24 and containing mostly large amino acids is capable of balancing their own blocks. The new balance composed of large amino acids is located within the degeneracy III, II, and I set, but not within the degeneracy IV set. Such allocation is predetermined by simple algebra in Section 15. As a result, the concentration of small amino acids increases in the degeneracy IV set. Outwardly, this looks like the rough antisym-metrical correlation between the degeneracy and the nucleon numbers noted by Hasegawa and Miyata (1980). Therefore, the calligramme provides a simple explanation for that empirical observation which had been unexplainable till now. There are in addition to Rumer's bisection three more bisections among the contracted series in Fig. 10.

The amino acids of degeneracy IV series

Nucléons of whole molecules: 75

Gly standard blocks: 74

Ala 74

side chains: 1

The amino acids of degeneracy IV series

Ala 74

105

115

117

119

131

Ser

Pro

Val

Thr

Leu

74

73+1

74

74

74

h Çh

h I CH î '

h Çh

h Çh

h Çh

i hÇh

hAHh

hCh

hÇh

ÓH

Ht;

hÇ O

H HC Oh

hChh

hC Ch

31

42-1

43

45

Arg 74

Cys 74

Stop 0

The amino acids of degeneracy III, II, and I series Ser Leu Asn

74

74

74

h Çh

H ÇH

h Çh

hÇh

i hÇh

hCh

ÓH

h4h hC Ch

O hN,

31

57

Asp 74

Gin 74

Lys 74

Glu 74

His 74

Phe 74

Arg 74

Tyr 74

Start Met 74

Trp 74

hCh d 0H

=111+999

Fig. 9 The amino acid's basis of the cooperative symmetry (shCherbak, 1993b, 1994). Pythagoras' images symbolize the squares of the first three Pythagorean numbers, a new standard block-to-chain balance, and their decimal syntax. As before, the arrow near proline (Pro) indicates the virtualization act. The numerical symbol of the "Egyptian triangle" arises when corresponding nucleon sums appear in the parts of the PN 037. Let us consider the nucleon sum 925 as an example. The sought quantity of parts is equal to the quotient of 925 divided by the PN 037, i.e. to 25.

The amino acid's basis is represented by the E. octocarinatus code version; the revealed arithmetic regularities are also true for the universal genetic code

Note that transition from the life-size triplets in Figs. 5, 6, and 7 to the contracted series in Fig. 9, 10, 11, and 12, and vice versa, is a difficult computing task. There are joint contractions or expansions in four different scales in this transition. The arithmetic used should be quite refined to keep intact numerous equilibrations and their decimal syntax at both ends of the transition. This could be considered as one more proof for the great computing skills of the primordial abacus.

13 The Message

The artificial nature of decimalism has encouraged us to suggest a possible semantic interpretation of the four strings of symbols and view them as an intellectual message (shCherbak, 1989d). Evolving Crick's and Orgel's (1973) ideas, Marx discussed a theoretical possibility of such interpretation in 1979. Note that the genetic code is an information messenger with limited storage space. Because of

Fig. 10 Three additional bisections of the contracted genetic code. As before, the bisected series are interconnected by Rumer's and two 50% transformations. The virtualization acts as usual. The total nucleon number of side chains throughout the contracted genetic code is equal to 444 + 999.

(a) The first 5' bisection produces a new standard balance of the block-to-chain type. This balance is composed of contracted series with pyrimidines (Thymine and Cytosine) in the 5' base positions. The initial brace denotes its position in the contracted code. Because of the previous block-to-chain balance in Fig. 9 only this equilibration could be algebraically independent orderliness.

(b) The contracted genetic code (see its initial table in Fig. 3). The second 5' and unique center TG-CA bisection divide the genetic code symmetrically. The framed code series are common parts of both bisections. These parts create balances of the chain-to-chain type. The balanced sums have noteworthy decimal notation. Mitochondria deviate from the universal code. It should be noted that none of the numerous deviations (Jukes and Osawa, 1990) disturbs this balance of the common parts. The bisected genetic code is represented by the E. octocarinatus code version; the revealed regularities are also true for the universal genetic code

Fig. 10 Three additional bisections of the contracted genetic code. As before, the bisected series are interconnected by Rumer's and two 50% transformations. The virtualization acts as usual. The total nucleon number of side chains throughout the contracted genetic code is equal to 444 + 999.

(a) The first 5' bisection produces a new standard balance of the block-to-chain type. This balance is composed of contracted series with pyrimidines (Thymine and Cytosine) in the 5' base positions. The initial brace denotes its position in the contracted code. Because of the previous block-to-chain balance in Fig. 9 only this equilibration could be algebraically independent orderliness.

(b) The contracted genetic code (see its initial table in Fig. 3). The second 5' and unique center TG-CA bisection divide the genetic code symmetrically. The framed code series are common parts of both bisections. These parts create balances of the chain-to-chain type. The balanced sums have noteworthy decimal notation. Mitochondria deviate from the universal code. It should be noted that none of the numerous deviations (Jukes and Osawa, 1990) disturbs this balance of the common parts. The bisected genetic code is represented by the E. octocarinatus code version; the revealed regularities are also true for the universal genetic code this, the message within the code might be a forwarding address to permanent residences of a message body. Message symbols inside the code are recorded in a highly ordered written language. According to the biological standard of reading, we start interpretation from 5' strings.

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