We revisit here "HIERARCHICAL INTROSPECTIVE LOGICS" The theories of John F. NASH 3 by highlighting the self-emergence of a bistable logic. structuring the entirety of the human genome (Logic code -III- in §Methods).

“There can exist no procedure for finding the set of all regularities of an entity. But classes of regularities can be identified. Finding regularities typically refers to taking the available data about the entity, processing it in some manner into, say, a bit string, and then dividing that string into parts in a particular way and looking for mutual AIC (Algorithmic Information Content) among the parts. If a string is divided into two parts, for example, the mutual AIC can be taken to be the sum of the AIC's of the parts minus the AIC of the whole. An amount of mutual algorithmic information content above a certain threshold can be considered diagnostic of a regularity. Given the identified regularities, the corresponding effective complexity is the AIC of a description of those regularities”.

In one hand, in his unformal paper entitled “HIERARCHICAL INTROSPECTIVE LOGICS” 3, the Economy Nobel prize the mathematician Professor John F. Nash Jr. explores new approaches of Turing/Godel undecidability problems adding particularly the “EMBEDDABILITY” dimension.

In other hand, we report here mathematical CODES structuring all genomes and particularly the whole sequenced Draft Human Genome 9 released in 2001 (three billions base-pairs about distributed in the 24 Human chromosomes). This discovery describes particularly the evidence of a self-emerging embedded BINARY CODE structuring the whole human genome.

Then, analysing the texture (mathematical increase/decrease 1^st degree derivates) of the Proteomics (code -III- in §Methods) associated curve patterned signature, we could associate with each codon position “biospins” as following:

If the local codon position derivate is in increase state è then Biospin=1,

If the local codon derivate derivate is in decrease state è then Biospin=0.

Now, for any analysed sequence, we could compute the related balancing increase/decriease percentage related to the whole analysed sequence. These percentage values are real numbers in the range 0-100. Normally, the distribution of biospins percentages must be random, like a Gauss-like distribution.

In fact, we obtain a very strange distribution as a “bath-tub”-like distribution: there appears, in ALL CASES, a binary distribution centered around two ATTRACTORS: one attractor, named “Floor-state attractor” is located around 29%.

The other second attractor, named “Ceiling-state attractor” is located about around 60%.

The following Law is Universal. We Propose the Following Rule Entitled “Genomic BINARY CODE Law”

For any sequence " seq " of genomic DNA, what ever its length, its position, and its nature, one can always associate, by applying the numerical algorithm described in (code -III- in §Methods), a Binary Code status, called « BioBit » such as:

BioBit (seq) = 0 = « Floor » state = « FALSE » if %(seq) neighbouring attractor 29%.

BioBit (seq) = 1 = « Ceiling » state = « TRUE » if %(seq) neighbouring attractor 60%.

We validated and checked this universal law on the totality of the genomes known to date, and, more particularly, on the whole human genome which we studied independantly on three embedded scales: contiguous segments of 10000bases, 100000bases and 1million of bases from Build34 2003 Human genome release 10, see Figure 15 and Figure 16 in §Methods.

We demonstrate now this Nash's sugested law “Natural Hierarchical Introspective Logics” on a randomly selected region within the Draft Human Genome sequence 9. This genomic studied region is located between 130000000 and 131024000 positions within the human chromosome5.

Some regions are undefined (“N” undefined bases or “GAPS”).

We Run 11 Independant Embedded Analyses:

-1024 contiguous DNA segments of 1000bases.

- 512 contiguous DNA segments of 2000bases.

- 256 contiguous DNA segments of 4000bases.

- 128 contiguous DNA segments of 8000bases.

- 64 contiguous DNA segments of 16000bases.

- 32 contiguous DNA segments of 32000bases.

- 16 contiguous DNA segments of 64000bases.

- 8 contiguous DNA segments of 128000bases.

- 4 contiguous DNA segments of 256000bases.

- 2 contiguous DNA segments of 512000bases.

- 1 unique DNA segment of 1024000bases.

In the Following Table, we Resume, for the 11 Independant Analyses:

1. The numbers of elementary BioBits decisions: exp in line 1: 468 “Floor states” and 409 “Ceiling states”, the total correspond to 877 segments, the remaining are GAP segments.

2. The average values of Floor and Ceiling percentages: exp in line 1: 31% for “Floor attractor” and 59% for “Ceiling attractor”.

3. The LOCAL LEVEL VOTE DECISION: exp in line1, the Floor state (468) is majority then the local level decision is “Floor”=FALSE. Table 6

In the Following Couples of Graphics we Demonstrate the SCALE INVARIANCE and the EMBEDDED LOGICAL VOTE Process

è Level 1: 1024 times 1000 bases... Concensus Decision “VOTE” = Floor = “False”.Figure 20, Figure 21, Figure 22, Figure 23, Figure 24, Figure 25, Figure 26, Figure 27, Figure 28, Figure 29, Figure 30, Figure 31

Level 2: 512 times 2000 bases... Concensus Decision “VOTE” = Floor = “False”

è Level 3: 256 times 4000 bases... Concensus Decision “VOTE” = Floor = “False”

è Level 4: 128 times 8000 bases... Concensus Decision “VOTE” = Floor = “False”

è Level 5: 64 times 16000 bases... Concensus Decision “VOTE” = Floor = “False”

è Level 6: 32 times 32000 bases... Concensus Decision “VOTE” = Floor = “False”

è Level 7: 16 times 64000 bases... Concensus Decision “VOTE” = “Undefined”

è Level 8: 8 times 128000 bases... Concensus Decision “VOTE” = Floor = “False”

è Level 9: 4 times 256000 bases... Concensus Decision “VOTE” = Floor = “False”

è Level 10: 2 times 512000 bases... Concensus Decision “VOTE” = Floor = “False”

Figure 30 - Level 10: 2 times 512000 bases... Concensus Decision “VOTE” = Floor = “False”

In the following graphic, we summarize the genomic area around the 1024000bases DNA sequence analysed. This 10 millions lenght sequence was analysed spliting it in 10 “ONE MILLION regions”. The red arrow localizes the studied 1024000 studied region. Then, the area is globally at “Floor” state, with a “Ceiling” state transition at the end (see on the right).

As Professor NASH in " Hierarchical Introspective Logics “Proposes it:

On the one hand, the concept of incompleteness will be able to evolve with the levels of human knowledge. In addition, the discovery of new natural laws will be able to make evolve the approach of this problem “.../... But the history of human progress in science and mathematics reveals that observation of the phenomena of Nature has always played a large rôle.../...” (by J. F. NASH in the above paper).

In other hand, the concept of LOGIC suggested here is radically new because it acts of a self-emerging logic, output of a self-organized multi-levels embedded process of which the roots (" ground level ") are at the basic level of the “average atomic masses of the 6 DNA CONHSP bio-atoms”, therefore in a world of real numbers (atomic mass code -I-).

Lastly, the concept of hierarchy is not discrete but completely continue in an infinity of embedded levels. Thus, the choice of 11 levels in the example suggested is arbitrary, one could also have chosen thousands of others embedded levels... We show thus that the human genome (as all the other genomes) is the source of an omnipresent logical binary language which appears to be invariant on all the scales. This code is not explicit and formal but self-emergent as the " output " of a complex genetic system. This code is embedded in a self-referred infinity of VOTE-like level. Perhaps it could give new ways and tracks to understand the “Natural Hierarchical Intro spective Logics” decision making process.

Thus, the totality of the average atomic masses of all basic materials of genetics, bioatoms, UTCAG bases, amino acids, codons, DNA RNA and proteins are unified as soon as they are mathematically projected in the space of PIs. masses (Atomic mass code -I-).

But why their average atomic masses rather than the atomic masses of individual isotopes?

Does this property extend to the isotopes constituting their bioatoms?

A new question naturally arises:

"Would the projection of the PI-masses be" reserved "and exclusive to the atoms of the living? "

"What would happen if we applied this same projection to all the other atoms of nature? "

We therefore apply the law of projection of PI-masses to all known stable isotopes. This list is then extended after the isotope Bi209 which follows the radioactive isotopes of the following elements. We then discover two remarkable phenomena:

on the one hand, a periodicity = 3.

On the other hand, a symmetry which would be located on both sides of the Lanthanides region (more precisely towards the element CE140.

Finally, it should be noted that these meta-structures are destroyed by a deliberate random disturbance of the atomic masses of all these elements of the order of 1/1000).

Symmetry of the PI-masses of the 306 successive isotopes of the Mendeleev Elements table.

Figure 32 above illustrates very well the symmetry between the 306 isotopes revealed by the projection PI-masses. This symmetry is located on both sides of the Lanthanide element zone; the sudden break between regular elements and radioactive elements (inflection of the graph, see blue arrow) located on the right of the graph corresponds to the transition between regular elements and elements (towards element Bi209).

In figure 33 below, we study the PI-masses in the case of bioatoms or most basic molecules. Those who are the origin of life and who maintain life on earth. But also those that can be encountered in outer space: clouds of interstellar dust, atmosphere of TITAN etc ...

We will analyze here among others carbon C, oxygen O, primitive molecules NH, N2, H2, H2O (water), CO, CO2 (carbon dioxide), CH3OH, and NH3. Let 5 organic atoms and 5 interstellar molecules. In each of these 10 cases, we will analyze the PI-masses of the molecule formed by the lightest isotopes, the average atomic masses, and the heavier isotopes. Thus, NH will be formed

1. In the first test of N14 and H1 (the lightest isotopes of nitrogen and hydrogen).

2. In second test of N and H represented by their average atomic masses.

3. In the third test of N15 and H3 (heavier isotopes of nitrogen and hydrogen). and so on for each of the 10 tests of molecules analyzed.

In Figure 34 and Figure 35, we now study in a similar way a patchwork of several thousand bio-molecules essential for life, from the most primitive bioatoms, to the amino acids, and through the 11 bio-molecules citric metabolic control, all are essential organic compounds for life. All these molecules are derived, on the one hand, from primitive compounds such as can be found in interstellar clouds, and on the other hand, from basic organic compounds extracted from the famous BEILSTEIN 11 ranging from compounds simple to more complex compounds (bases and amino acids).

In this first type of simulation, we submit 12 test sets of "more or less" organic molecules to a set of 3 tests: in the middle, the actual and exact average atomic mass, and, on both sides, on the left. , this same value weakened by a ten thousandth, and on the right, the same value, increased by a ten thousandth. The compared values ​​measure the error observed when adjusting the PI-masses of these various atomic masses by the associated PI-mass integer (multiple of Pi/10). As a result, the higher these values, the poorer the PI-mass optimality. It is therefore concluded that these minute random "noises" applied to the atomic masses destroy the optimality of the PI-mass nPi/10 image value, hence, consequently, the optimality of the atomic mass as well.

On the other hand, the more the organic compounds are to the right, the lower the PI-mass error (average atomic mass), and the more this error becomes hypersensitive to perturbations of its atomic mass. Thus, compounds such as amino acids would be more optimal than interstellar organic compounds, themselves more optimal than non-organic interstellar compounds.

Would the whole path and path of evolution be "trapped" by our discovery of the digital projection of PI-masses?

Finally, a final confirmation of this meta-order revealed by PI-masses is visualized by the analysis of Figure 35 below.

We compare the perturbations of the optimal PI-masses caused, on the one hand, by the substitution of average atomic masses by mono-isotopic atomic masses, and, on the other hand, the substitution of average atomic masses by noisy atomic masses by a tiny random noise. The first disturbance is real and natural whereas the second disturbance is artificial and the virtual order of the simulation.

In all these cases, the reference is the slight thin horizontal line annotated 100%.

We then observe that the more we move to the right of the graph, hence from the inorganic to the organic, and the more the effect of real (isotopic) or artificial (random) perturbations will then increase, become showing strong overtaking above the 100% mark horizontal line.

We conclude the optimality of the average atomic masses vis-à-vis both mono-isotopic atomic masses that atomic masses whose precise value would be very slightly disturbed.

Concentrated information and meaning represented by the 3 figure 34, figure 35, figure 36, it will emerge remarkable information: more organic compounds are moving towards more evolution, from small molecules premisses of life, until Amino acids, bricks of all life, and more the selectivity, the optimality of the atomic masses becomes pointed and adjusted, the work of a grandiose "tuning" ... And it is from this PI-mass - perfect - that go animate whole life "codes": PI-masses (atomic mass code -I-)!

Indeed, it is thanks to this hyper-adjustment of PI-masses that will emerge codes and even real languages that will organize and unify ALL genetic information despite its apparent diversity - bioatoms, DNA, RNA, amino acids proteins and genomes - to lead and induce a high organization up to the scale of whole genomes: from the atom to the genome (code -I- to code -VI-).

A mystery however is that these optimal values of the masses atomic ones are those of the average atomic masses and not those of the mono-isotopic atomic masses ... However, let us remember that the average atomic mass is only ... average. That is to say that not a single molecule, not a single nucleotide, not a single amino acid has this keystone value from which come alive the "codes" in whole numbers of life: the PIs -masses! But the reality is that this ideal PI-mass is only a deception, a kind of "Omega Point" Teilhard Chardin that no molecule can ever achieve, at best only some will approach. Thus, we discover an ideal law, which can only exist in a mass universe, probabilistic, a universe of means, a universe of large numbers. In fact, you will never meet a carbon atom whose mass is exactly 12.01114727 (its Carbon average atomic mass). On the contrary, you will encounter a multiplicity of individualized, mono-isotopic atoms: billions of C12 isotopes, other billions - albeit a little less - of C13 isotopes ... In the same way, you will never come across an Oxygen atom of which the mass is exactly 15.99929706 (its Oxygen average atomic mass). On the contrary, you will find a multiplicity of individualized, mono-isotopic atoms: billions of O16 isotopes, other billions - albeit a little less - of O18 isotopes ... or even more rarely, billions of isotopes O17 Here is the famous curve in "V" that we will call by analogy "Sergeant Major curve".

We are therefore Faced with an Enigmatic Situation

On the one hand, we discover a generic law organizing the entirety of living molecules - the PI-masses code (atomic mass code -I-).

On the other hand, this law is optimal only in the case of the average atomic masses.

But the real world of biology is not a world of average atomic masses but a world of atomic masses mono-isotopes.

This would mean that this optimal law is only a kind of "inaccessible star" as Cervantes would have written.

But, nevertheless, the average atomic masses exist on earth since they constitute the weighted average of the billions of isotopes constituting each one of the populations of atoms.

Then would it mean that life implies, by the very nature of its laws, that its molecules and atoms rely on diversity and multiplicity, perhaps even on the equilibrium and collective co-operation between these billions of atoms?

Life through the optimal search for the average PI-masses would imply in every way spaces of life and permanently a kind of permanent dynamic equilibrium Piaget spoke of "mobile equilibrium" - taking its roots and feeding on the multiplicity and diversity of the different isotopes (C12 / C13, N14 / N15, H1 / H2, O16 / O17 / O18, etc.) forming each bioatom. It will be noted that the complexity of advanced molecules such as amino acids already favors this diversity, the same amino acid can be heterogeneous and consists of different isotopes of the same atom, which will already approach some of the PI-mass ideal average mass (for example the amino acid glycine (Gly) which is written NH2 CH2 COOH may for example consist of an atom O16 and an atom O18, likewise for its carbon atoms which may be 2xC12 or 2xC13 or C12C13.

It will also be noted that this multiplicity of isotopes can be topological (3-dimensional space) but also temporal.

Topological diversity and we then think of the GAIA 12 hypothesis of James Lovelock, about which we wrote.

« He is to science what Gandhi was in politics. His central idea, that the planet behaves like a living organism, is as radical, profound, and vast in its consequences as any of Gandhi's ideas. »

According to Lovelock, everything that lives on our planet would contribute more or less to the balance, maintenance and continuity of life on earth. But it turns out that Lovelock as we reach by taking two radically different paths.

Immediate Consequences of this Requirement of Multiplicity of Isotopes are Multiple

The loss of bio-diversity destroys this balance of average atomic masses required by life.

-the discourse on global warming must climate change revisited according to this new angle of the requirement of isotopic equilibrium. We will think of cancers whose hidden causes are more and more due to the industrial pollution of modern life and agro-industrial mass supply.

The economic arguments of certain lobbies according to which the methane released into the atmosphere by the cows of our campaigns would pollute almost as much (1/5) as the methane rejected by the industries of our cities will suddenly fall: indeed we will have to consider seriously the hypothesis that the isotopes constituting CH4 (methane) released by our cows are very different from the isotopes of CH4 released by our polluting industries!

The other level of isotope multiplicity of the same atom is the temporal and dynamic aspect.

On the one hand, this could partly explain the natural and permanent need for renewal and re generation of living cells. Nature would thus seek to maintain permanently the isotopic equilibrium of the respective proportions of the billions of isotopes of bioatoms forming the living cells.

On the other hand - it may seem bold as a thesis - the dynamic equilibrium of the average atomic masses can also be reached by temporal alternations of the various isotopes constituting the same atom. It would then be a kind of "quantum dance" with a kind of temporal alternation between isotopes of the same atom ... We would then be very close to the wave or quantum theories of matter ... The real but invisible atom would have as mass the mass atomic average while we perceive in the universe palpable and visible that different "views" with distinct masses, the different isotopes of the same atom.

A bold thesis, of course, but why not?

One thing is certain when exobiologists will look for traces of life on other planets, on TITAN, on MARS or EUROPA ... They will not only have to look for the presence of carbon, nitrogen oxygen or hydrogen, but also the existence of isotopes of these atoms in proportions comparable to those which constitute the average atomic masses on the earth biosphere.

Thus, it is in 2010 that a probe went to analyze with precision the reports isotopic C12 / C13 or N14 / N15 on TITAN ...

Have we discovered proportions comparable to those of our planet?

Only in such a case that our discoveries could allow to predict the isotopic ratios that it should find there ... Then, the projections PI-masses of the code of the atomic masses will be able to measure these traces of extra-terrestrial life.

"The emergence of life in the Universe requires a DIVERSITY and an ISOTOPIC BALANCE of bioatoms C O N H identical to those observed on Earth"

or…

"A necessary but not sufficient condition for the emergence in the universe of life-forms similar to earthly life requires that we find, in these regions of the universe, and in MARS in particular, the different isotopes of organic CONH atoms in proportions identical to those observed on Earth ".

Perspectives in Oncology and Cancer Therapy Basic Reesearch 

The biomathematical methods presented above open very wide and promising perspectives in the theoretical study of the mechanisms of emergence, detection and treatment of cancers. Here are 3 remark able examples published in 2017 and 2018.

In (Pérez, jan 2018 and March 2018) we demonstrate that HGO is an optimum destroyed by LOH (Loss Of Heterozygosity) involved in all Cancers: “When an LOH deletion affects a chromosome upstream of the HGO point (chromosomes 4 13...) in the chromosomal spectrum, this deletion degrades the genomic optimum of the cancer genome. When an LOH deletion affects a chromosome downstream of the HGO point (chromosomes 19 22...) In the chromosomal spectrum, this deletion improves the genomic optimum of the cancer genome. The exhaustive analysis of the 240 LOHs for the following 6 cases: Chromosome 13 (breast cancer), chromosome 5 (breast cancer), chromosome 10 (glioblastoma cancer), chromosome 1 (colorectal cancer), chromosome 1 (neuroblastoma cancer) and chromosome 16 (prostate cancer) obey this law in 227 cases and do not obey this law for 13 cases (success rate of our law = 94.58%). In (Perez, Jan2018) we detailed this type of analysis on 153 LOH relating to breast and prostate tumors affecting respectively chromosome 13,chromosome 5 (breast) and chromosome 16 (prostate). In this detailed study, the HGO law described here is edified in 143 cases out of 153, or 93.46% of favorable cases." See also in (Perez, March2018) an analog analyse on brain cancers neuroblastoma and glioblastoma (see example below, Table 9).

Table of synthesis of 240 LOH relating to 5 types of cancer and 5 different chromosomes. The shaded areas represent those that comply with the HGO law, ie 227 cases out of 240. In blue the 53 caeses related to Neuroblastoma and Glioblastoma cancers.

The shaded areas represent cases of LOH complying with the generic rule, while the unshaded areas represent cases of LOH that do not comply with this rule. In total, 227 cases respect the rule and only 13 cases of LOH do not respect it, a success rate of this law equal to 94.58%. In particular, on 53 cases of LOH mutations analyzed for the two types of Glioblastoma and neuro blastoma cancers, the HGO optimality law is verified in 50 cases and in failure for only 3 cases, ie a percentage of validity of this universal law equal to 94.24. %. Figure 37

In (Pérez, 2017) these Fibonacci resonances are used to demonstrate that: “…by analyzing 250 characteristic mutations associated with various pathologies, we establish a very strong formal causal correlation between these numerical Fibonacci meta structures (Figure 6) and these referenced mtDNA human genome mutations involved in cancers or LHON genetic disease (Leber Hereditary Optic Neuropathy)”.

Graphics related 10946 resonances for 36 cases of mutations associated with the LHON disease (Leber's hereditary optic neuropathy). In this figure, the 36Table 5, Table 6, Table 7

LHON mutations on mtDNA genome INCREASES the number of long 10946 Fibonacci“resonances”. Figure 38, Figure 39, Figure 40, Figure 41, Figure 42, Figure 43, Figure 44