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 17.  Transformations between number-base systems (nb-x) Bases ←→ totals of ams − 5 x ES- numbers − Generative production of the 12-groups 1. Transformations of the codon-bases to the 12-groups of ams: 1.1 All geometrical dimensions should naturally be regarded as present in the cell simultaneously, on different levels, and interdependent through transformations into one another. One simple example is the geometries of proteins, forming linear threads (~ D1), sheets (~ D2) and globular forms (~ D3). The thought that different d-degrees could be associated with different number base systems (nb-x), as nb-10, nb-8, nb-6 for x = 5, 4, 3, led to a first test on mass of codon bases with remarkable results, figure 17-1 below. Further investigation showed also several connections with the ES-series. (Nb-x in text below often written as "-index figure in red. Figures in nb-8 and nb-6 are often rewritten with figures from nb-10.) Fig 17-1: From mass of codon bases to the two 12-groups of ams:   Hence, 4 sets of the 4 bases give the total sum of 24 unbound ams. We find also that 2 x G+C-bases in nb-8 as 768 gives total sum 3276 in nb-6: nb-10      nb-6 768 —> 3276    24 ams R + B, unbound (rewritten from 3320) The sum of the 4 bases in nb-8 = 752 -/+1: nb-10      nb-6 752 —>  2848    24 ams R + B. bound (rewritten from 3252) Fig 17-2. From 752 as sum of ES-numbers 5', 4' and 3' to 2848 in nb-6: 2848 = 24 ams R + B bound 1.2  Some general annotations: However strange the idea surely may seem for scientific "common sense", the many astonishing results here and below are rather difficult to dismiss as only haphazard. If they are not, if they reveal some connections on deep energy levels, they should represent one kind of references, one kind of guiding operators for potential growth - or just what is sometimes in the biochemical field is referred to as "affinities"? All derived numbers shall naturally be regarded as nb-10-numbers, hence transformations as nb-10 →> nb-8 may be repeated, illustrated for instance in the carbon-nitrogen cycle in the sun, from 12C to 14N to 16O, intermediate steps showing one way to perform such transformations. It follows that all operations as multiplications are performed in nb-10. Indexes for x in nb-x are often used below to shorten the text. As mentioned above numbers in nb-8 and nb-6 are often rewritten with figures from nb-10.    A question is of course if such rewritings could be expressed in biochemical processes as for instance 20 equivalent with (~) 18 in nb-8 as -2H or 120 in nb-6 ~ 76 as - 44 (CO2)? Another question is how to interpret nb-16 in many examples below If keeping to the thought of x in nb-x as first three numbers in the elementary chain 5' →> 4' →>3' doubled, should nb-16 be regarded as 2 x 4 doubled or 2(5 + 3) doubled? Fig Ti-1 A general feature may be noted: transformation of sums or whole units give larger numbers in lower nb-systems than their parts transformed and summed afterwards.   1.3   Halves of the 12-groups 770 and 734, -/+1 = 384 and 368: Fatty acids, a first annotation here: Cell membranes are an equally essential part of life as the genetic code. Two of the most common fatty acids give transformed to nb-6 three times these numbers 367 and 385, +/-1, a relation to R-chains of the 24 ams = 3/2 and simultaneously a relation d-degree 3 to 4(nb-6 to nb-8) with the assumed view above. C16H32O2: 256-10 → 1104-6 = 3 x 368 C18H36O2: 284-10 → 1152-6 = 3 x 384, (Note: 1152 = 752 rewritten) Cf. the hexagonal pattern in Table 0 here: fatty acids as a third way to read such a pattern. From the numbers 384 and 368 in nb-10 transformed in two steps to nb-8 we get 2 sets of bases G and A in nb-8, as in opposite direction to the figure above and without C and U: 384 x ½ = 192-10 → 300-8 / 300-10 → 454-8 = 2 x 227 = 2 G-8 368 x ½ = 184-10 → 268-8 / 268-10 → 414-8 = 2 x 207 = 2 A-8 1.4 . Bases → totals: 1.4.1  Four times G+U and A+C to ~ B- and R-chains of total 3276: Sums of R+B-chains together in nb-10:    G1 + U1 = C2 + A2 = 1468    C1 + A1 = G2 + U2 = 1808... Sums of coded amino acids (R + B) With exchanged partners these sums are given from 4 times the bases: Fig. 17-3 In nb-10 we have groups of ams paired in keto-/amino types: Here G- and A-bases have exchanged partners and bases A and U must be multiplied with 4 after transformation. Fig. 17-4 Rewriting 640 to 638 and 828 to 830 gives the right sums B 1772 and R 1504. 1.4.2  Two sets of bases from ES-numbers 5', 4' and 3': Fig. 17-5 Number 416 (2 x 3', 208) is the one which added to 544 gives the A-U-group of ams. Cf. that U-base gets replaced by T-base in DNA, a CH2-group added for inward direction to DNA. (It could perhaps be compared with the interpretation of nb-16 as 2 x (3' + 5'), a step backwards from 3' to 5', equivalent with inwards?   2. The bases in the ES-chain: Fig. 17-6 U 160 + C 157 in nb-8 approximate number 2' = 159 in the ES-series, together 317.    In nb-10 number 385 is the interval 544 to 159. Here G-8 becomes the same interval to both bases U-8 + C-8. Cf. that G-base can bind to both: Fig 17-7: The bases in nb-8 in the ES-chain: These relations could be a reason why G+C-bases get connected with the 12-group 770 of ams in spite of all bases equally represented in this group.   3.  5 times ES-numbers: 3.1 The transformations between nb-10 and nb-8 of main codon groups of ams and 5 times the ES-chain numbers 5' - 4' - 3' are among the most astonishing: Fig 17-8: Main codon groups of ams from 5 times ES-numbers: 816 and 688 is the division of R-chains of total sum 1504 of 24 ams, a division between purine and pyrimidine codon groups, As a division in step 5 - 4 here it precedes the one between complementary pairs G-C and U-A, which are attained from the secondary division of 544 in 336 and 208, a division in step 4 - 3. Note also about 1344, the 24 B-chains bound, included in sum 2848: 1344 in nb-10 = 2500 in nb-8 = ES-numbers 5(292 + 208) These relations seem to support the relevance of both the ES-chain and the thought that nb-transformations could be part of the reference system. Fig 17-9  5 x half of 752, number 688 as an interval:  There is also the feature that divisions stepwise as polarizations of numbers 816 in U1 + C1, separately transformed to nb-8 give 1260, next lower level, and this back to nb-10 and divided G1 and A1 gives 1040 in nb-8: Fig 17-10. Stepwise polarization giving next number x5 in Es-chain: 3.2 About the interval 84 = 292 →> 208 in the ES-chain we have that n x 84 (n = 1, 2, 4) times 10 (1040 ~ 840, 1680 and 3360) in nb-8 gives the groups 544, 960 and 1776 in nb-10:. Fig 17-11.  n x interval 84: 3.3  5 times intervals in the exponent series in nb-8 give ams-groups -/+1: Fig. 17-12  5 x interval in the ES-chain: 3.4  Nb-6:  5 times the ES-numbers 5', 4' 3' in nb-6: It gives the sum of U- plus A-coded ams R and also all C-atoms in R-chains in nb-10, divided on G1 + A1 = 396 and U1 + C1 = 564: Fig..17-13   5 times ES-numbers in nb-6 to 396-564. : 3.5 The parts above of 960 in nb-16 gives the total mass of  bound ams in nb-8: Fig 17-14 3.6  The numbers  U1 + C1 = 816 and G1+ A1 = 688 read in nb-8 rewritten, give in two steps total 24 ams, R + B inbound in nb-8: nb-8 816 ~ 1016 688 ~   710 ... Sum 1726-8./ 1726-10 → 3276-8 4. Generation of the two 12-groups of ams with mixed and non-mixed codons:  4.1  Generative production of sums within 12-groups of ams: 17-15a. The ES-chain, numbers 177 and 208: Cf Table 2,3 in file 02. Numbers 770 and 734 generated from 177 and 208: - From 177 we get 385 in two steps nb-10 to nb-8: - From 208 we get 734 in three such steps: Fig. 17-15b * 318 = 2 z 2', 159, from there only two steps: Fig 17-15c: In group 734 U+A-coded ams = 575, a number given through two steps nb-10 to nb-8, either as sum of 500 + Meth 75 or from 208 + interval 49: Meth that starts the protein synthesis are attained from the middle interval in the ES-chain: Fig 17-15-d: Note too that Meth leaves its outer CH3-goup at start of synthesis, (= -15 +1), which gives R-chain = 61, the intermediate number in the figure above. 575 directly from 208 + 49 = 257 in only two steps: Fig 17-15e: Number 75, R-chain of Meth: In the ES-chain in nb-10 the number 75 = interval 292 - 367 (the sum in the middle of the chain). Transformed in two steps nb-10 to nb-8 it gives the number 159: 75 → 113 → 159  (161 rewritten)     4.2  A- and T-bases give the sum 575 of ams with non-mixed codons: Starting numbers 177 and 208 in transformations, minus 1 in each, are the T- and A-bases in nb-8. With DNA-base T we get the sum 575 in two steps nb-10→>8: (Cf. file 02.) Fig. 17-16: A+T How explain the T-base here, a DNA-base giving A in RNA?   4.3  770-group from 4': It can be added that 2 x 252 (= 4' in the ES-chain) in nb-10 leads directly to 770 in nb-8: 2 x 4' (252) = 504-10 →770-8 4.4  Parts of 12-group 770 from halved ES-chain: The division of group 770 in Cross- and Form-coded ams, 418 and 352, may be derived by dividing the whole ES-chain in step 4'-3' and halving these numbers: Fig 17-17: From halved ES-parts to mixed codon groups 4.5  Derivation of N- and Z-numbers within the two 12-groups of ams: Fig. 17-18:   *

Individual research
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Table 24 amino acids (ams)
R-chsins, A, Z, N

Background model

Files here:
 I. The ES-chain Introduction 3. The exponent 2/3 number series Mass of codon grouped ams 4. Mass division on atom kinds, and on other bases 5. The two 12-groups - details 6. Backbone chains 7. N-Z-division and H-atoms 8. Geometries - Golden section Special arithmetical operations 9. Glycolysis and Citrate cycle: codon grouped amino acids on the basis of origin 10. The bases: - Some annotations 11. Transmitters and the ES-chain

 II. Simpler numeral series 12. Quotients. - Exponents 5-1 13. The 2x2-chain 16. An x3 series?

 III. Transformations between number-base systems 17. First observations 18. Totals and other notable things 20. Additions to files 17-18 21. Triplet series - An alternative series 22. Other substances

 Discussion References

All these files in 3 documents, pdf:
Section I, files 0-11

Section II, files 12-16
Section III, files 17-22
Discusssion, References in section III

The 17 files as one document,
pdf

Latest updating
2018-11-20

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