Principles of the General Informotion Theory

by

Jacques Jaffelin, Ph.D.

How to get out of the Mechanical Paradigm and set up a new logic based upon the new concept of "informotion"?

- Axioms and new paradigmatical approach of the notion of "intelligible proposition"

Applications

- Is the metaphor of "genetic code" relevant?

Is the concept of "attraction", as a universal force, an impasse?

- A new view on the Doppler Effect.

January 1992

Preliminary

I would like to invite you to consider this axiomatic as you would a violin or a bicycle. Doing so requires you to learn it in the same way you learn to play or ride it, before allowing your thought to go for a ride. Each of its elements have been thoroughly shaped for it to be an efficient instrument. It would be as much a non-sense to hope to take advantage of any of these elements as, for example, to ride a bicycle with only handlebars, brakes or wheels separately. Its fertility will be appreciated by improvements its users put into it and they will get out of it.

It should be clearly recognized that only axioms and definitions constitute this axiomatic. Other considerations are proposals to render the same logic in "natural" language in order to make easier the comprehension of this latter. Consequently, to make for a more intelligible reading, the reader would better to return to it as often as necessary.

AXIOMATIC

Axiom 1

By general informotion, I mean an irreversible process that intelligibility conceives by creating differential relations called informotion levels.

Axiom 2

The axiom 1 drives intelligibility in a process of coalescing of concepts that should constitute principles or relations of equivalence that would be specified as their creation proceeds.

Axiom 3

The following concepts: acceleration, complexification, selection, differentiation (increasing of variety) and quantification (increasing of quantity), coalesce in an intelligible group spelled "(gI(".

Axiom 4

No informotion level should be integrable.

Axiom 5

1. A relative informotion at the n level i.e. In is formalized as follows:

... ( in-2 ( in-1 ( In ( din-1 ( din-2 ( ... **1

2. and it should be read from left to right, and from right to left on the two sides of In

3. The following symbols: ( In ( din-1 ( ... should be read from left to right, and would mean : In sprung from informotioned  "(gI("  elements of ( din-1 level, and contains ( din-1 ;

4. The following symbols: ... ( in-1 ( In ( should be read from right to left and would mean: In sprung from informotioned "(gI(" elements of the i n-1 level.

5. The symbol "d" from din-1 means that elements from din-1 level expresses an "(gI(" informotion of the in-1 level.

Axiom 6

The list of axioms might not be completed.

Definition 1

The concepts process and irreversibility are analogous. It means that both can be used indifferently with "(gI(" i.e. informotion. See Axiom 2.

Definition 2

The couples of concepts notice thus: space/time, particle/wave, digital/analogical, mass/energy, system/interaction, specie/environment, planet/orbit; etc. (Subject to specification), would be analogous to the general concept form/movement or f/m. That would mean they express the same logical operator depending the In constructed by the intelligibility in the " natural " language. The f/m operator expresses a relation of equivalence between movement and form as also the elements of couples of concepts set forth. That means we could not consider neither form without movement, nor movement without form, and neither wave without particle nor particle without wave, and so forth... See Axiom 2.

Definition 3

The following concepts: frequency, speed, rhythm, constant and threshold, are analogous to In and f/m. See Axiom 2.

Definition 4

An In considered as a " self-duplication ", a " self-reference ", a " self-organization ", an " isomorphism ", a " transfer ", a " transmission ", a " codification ", a " homeostasis ", a " completion ", a " reproduction ", an " integration ", an " identification " or a " vicious circle " **2 would be said impasse, dogma or paradox. See Axiom 3.

Definition 5

The following concepts: gravitation, radiation, calorization, condensation, dissolving, mineralization, organization, predation, metabolization, socialization, sexualization, learning, etc. (Subject to specification), would express different modalities of "(gI(". See Axiom 2.

Definition 6

The concept of transformation would be irrelevant for the prefix trans (like in transference or transmission) connotes a change of space and time without a change of movement (what would be inconsistent since we have postulated space/time and form/movement are relations of equivalence: it would be the same for the following concepts such as transference, transmission or transformation, that connotes a change of form without change of movement or reciprocally; according to our terms such a change would always mean a change of space/time or change of In . Nevertheless for didactic reasons and because of the common sense, transformation could be use in a meaning equivalent to informotion. But to express the passage from a level to another, it would be proposed the concept of trans-form/movementation. See Axiom 1.

We would propose the concept of field, spelt ( I (, or generally speaking, ( I (, to express an non-integrable intelligible group (see Axiom 4) of informotion levels. We would write down **3:

( I ( ij ( Ik ( dij

For example, human beings (not the mechanical **4 set of individuals, but the process or the informotion expressed by the human "history") would make a field: the anthropo/social field (we propose elsewhere definitions of informotion levels of it); planets would make a field: the planetarian field, etc. Fields have the same logical properties than informotion levels. See Axiom 5.

Definition 8

The following propositions: "not any creation of level is foreseeable" and "any created level is single" are equivalent. See Axioms 3, 4, 5.

Definition 9

According to axiom 5, a field ( I ( does not express by no means an hierarchical **5 order; since each level sprung from, contains and is more informotioned "(gI(" than the set of the ( I ( preceding it into "(gI(" which can be said neither finite, nor infinite, nor "transfinite" which can be said neither finite, nor infinite, nor "transfinite" **6.

Remark 1

The difference between ( I ( , f/m and impasse (See Definition 3, 4) does not take place into the logical operation but where the process of intelligibility comes to a deadlock, that is when a ( I ( would be looked upon as a self-reference or an absolute referential.

Thus, the following concepts: the "principle of inertia of Galileo", the "speed of light constant c in vacuum", the "big bang theory" or "logical singularity", the "Planck's constant h", the "hamiltonian of the wave function of the quantum mechanics", the "principle of uncertainty", the "genetic code", the neo-darwinian concept of "adaptation", the concept of consciousness (or knowledge), etc. should be considered as impasses.

Remark 2

The present theory should only use concepts expressing process instead of states of things or closed set or integrable entities. These latter would be called metaphysical, paradoxical or self-referential. Therefore we would avoid concepts such as "system", "structure", "set", "class", "type", "function" and others logical equivalents in their classical meaning; nevertheless they can be used without logical disadvantage only in the same meaning like In or ( I ( . We would also avoid master-concepts such as "absolute origin", "ultimate particle", "universe" and c (as an absolute inertial frame). See Axioms 1, 2, 3,4, 5, 6.

Remark 3

It is not necessary to choose from a "continuous" or a "discontinuous" understanding of the process. Since what it appears "continuous" at one In appears "discontinuous" at another In. It is the same concerning concepts like "individual" and "population". Only mechanical logic generate this controversy. See also Remarks 6, 7.

Remark 4

Axioms 3, 4 and 5 drive intelligibility to conceive only process and not entities, and also to think several concepts jointly and severally. Thus, concepts such as "internal" and "externals" are irrelevant here because of their mechanical connotation. Thus, stating, for example, a gamete is internal or external to an organism, or an idea is internal or external to an individual is just non-sense. The concepts inclusion ("...contains...") and ("...is contained in...") used in axiom five are from now on set free from all mechanical and static connotation, and should be always thought with those expressing jointly generation ("sprung from") and informotion "(gI(".

Remark 5

What we usually call "information flow" in organism, society, etc., should be considered, from the present point of view, as a field that intelligibility should make. The concepts "transfer of information" and "communication" used today in the most of activities and derived from cybernetics and from the "theory of information" should be considered as impasses.

General informotion would be neither "transfer", nor "transmission", nor "communication" nor "duplication" nor, properly speaking, "re-production". These concepts sprung from either an inconsequent distinction or a mechanical confusion between different levels. It would be the same for the concept of "code" that becomes also equivalent to impasse. See Definition 4 and Remark 2.

Remark 6

Also the present theory regards as an impasse the metaphysical concepts (see Remark 2) such as "randomness" and "determinism". The concept of "randomness" is based upon a confusion of levels and that of "determinism" is based upon the same kind of paradox like one of the Russell paradoxes: setting forth the concept of whole never includes that who is setting forth.

Remark 7

Controversies on the previous couple of concepts ("randomness-determinism", "discontinuous-continuous", "individual-population" and "digital-analogical") and also on the common concept of "information" looked upon as a steady and a duplicable content (as in the very well-known proposition: "the genetic code contains the information of whole organism") is due to mechanical conception of the logical operations not got free from the classical cartesian-newtonian paradigm yet.

Remark 8

Scientific activity does only "predict" what it depends on and issues from the practice of the human thought; for "predictability" does not consist in forecasting what it does not exist yet, but in creating some new In. "Predicting" the position of planets is a misuse of that concept indeed. The illusion of the "prediction" comes from the fact intelligibility takes place to a necessarily more informotioned "(gI(" level of general informotion than planets themselves. Generally speaking a "prediction", i.e. intelligibility of lower rhythms than our proper "transformations", concerns only less informotioned "(gI(" phenomena than these concerning the anthropo/social field.

To understand this very important point, just think over this: science cannot predict what the next scientific theory would be, or what the next human events would be. So, we used to concept of prediction in two different meanings:

1. "Prediction" about less informotioned "(gI(" informotion levels than those concerning the anthropo/social field. "Prediction", in that case, does mean we suppose that nothing would change with regard to the frame proposed as an explanation. Ex: the planetarian rhythms; it is not about to pre-dict a change but, on the contrary, to postulate a non-change or a constant rhythm.

2. On the contrary, "prediction" concerning the anthropo/social field occurs as a probable change that, of course, never occurs. See also Definition 8.

Remark 9

The concept of probability is based upon a mechanical confusion of informotion levels; and, furthermore, on a confusion between one field and its levels or again between a field and another field.

Remark 10

A theory would be either an informotion level or a paradox, an impasse or a dogma. Thus, the concept of falsifiability (see Karl Popper), conceived as an impulse toward a "real" postulated true a priori does not make any sense here. Therefore, a theory could not be a "cognition" in the philosophical meaning of knowledge gained through perception, reasoning, or intuition that is to express propositions that would bound to be analogous, isomorphic with "the real": it should be regarded as a proposition of informotion that occurs in general informotion.

Remark 11

The thought defining formalization should not be considered itself as formal. However, this could not be regarded as a guarantee against any self-reference or any paradox. Formalization is necessary in some degree (that degree is not predictable but it is that it comes to a self-reference or to a deadlock), so that it makes theory neither "soft" nor "hard" (as the famous Poincaré's cyclist). Formalization allows also an easier and faster learning (i.e. an informotion) of the theory itself.

Theorem 1

Every informotion level contains (and sprung from) informotioned "(gI(" elements of levels preceding it in the general informotion.

The logical change from a level In to another In+1 should be formalized thus:

if

... ( in-2 ( in-1 ( In ( din-1 ( din-2 ( ... (1)

then

... ( in-1 ( in ( In+1 ( din ( din-1 ( ... (2)

and so forth.

Therefore an informotion would mean a creative process of (informotion) levels that the rhythm of occurrence with the number of levels took into account. That increase expresses the previous principle of equivalence (or the intelligible group) between acceleration, complexification, selection, differentiation and quantification. Let's illustrate this proposition by taking the epigenesis process as an example.

Each of us contains and are sprung from selected/accelerated/complexified/etc. elements during the evolution (or informotion) process: from the electromagnetic field (and, of course, even from less informotioned "(gI(" than it) until ideas, through organs, cells, chromosomes, polypeptidic and nucleic macromolecules, minerals, etc.. And also, each of us contains and sprung from apparently the least informotioned "(gI(" f/m of "life" selected/accelerated/complexified/ etc. "(gI(" during the evolution process (the organic informotion): the gametes.

Gametogenesis, then epigenesis, "reproduces" in accelerated/complexified/selected/etc. "(gI(" way the organic informotion, from the polypeptidic and nucleic sequences until a kind of eukaryotic cells: the gametes. The logical difference between a gamete and an eukaryotic cell belonging to a current species is that the first one is the least informotioned "(gI(" organic f/m contained into the most informotioned "(gI(" f/m of the organic process whereas the latter is a relatively less informotioned "(gI(" informotion level of the organic field. Therefore, a gamete informs informotion level of the organic field. Therefore, a gamete informs **7  "(gI(" (or transforms) according to a very faster rhythm. Thus, it took about 3.6 billion years of trials and errors to create homo sapiens (homo socialis would be a more logical concept) from a certain sequence of nucleotides, while it takes only hours, once the fusion between male and female gametes occurred, to get from an eukaryotic cell to a multicellular organism, then only months to yield a mammal, then years to yield a social being. This general principle must be looked upon as an application of the general informotion to the organic field.

Contrary to current assumptions, general informotion allows to think that "genes" do not contain neither "instruction code" nor "information", for informotion is nothing but the creative process of logical levels. The concept of "code" is based on the confusion between species reproduction and individuals reproduction; and also upon the paradoxical idea that "reproduction" means the very mechanical concept of duplication. That is why genetics uses deceptive concept such as "genetic code" or "genetic program".

In fact, the latter concept is homogeneous to the neo-darwinian (or synthetic) theory; as stated by it, living beings would "reproduce" (i.e replicate) by means of the "genome" separated from the "phenome" by the so-called "Weismann barrier" and would changes by fortuitous mutations. Also, the concept of code is based upon the analogy between what it is coded and the code itself. Therefore there could not be nothing new, no possible "evolution", no informotion (i.e. creation of new f/m), between the code and what it is coding); but this not the case neither among living beings of course, nor among the so-called "physical", "physico-chemical" or "inanimate" nature.

Between two gametes and an old human being there are tremendous informotion "(gI(" sequences. I would just say that these sequences would not be more preconceived in any hidden code into the bottom of cells, than the emerging process of oceans on the earth would have been hidden in a code, hidden in the center of our galaxy, and replicated into the center of the earth or wherever; or that (informotional "(gI(" kinetic sequences of the learning to play the violin would have been hidden in any code somewhere. Not any code determines sequences of the operations (i.e. informotion by creation of logical levels).

Geneticists who are operating on "genes" and high energy physicists who are searching "the ultimate components", still think, no matter they say, in terms of newtonian mechanics. They imagine it stands to reason that "genes" have invariable property in themselves. It is as though one try to search the meaning of a sentence by extracting each word, separately, and quibbling about their own ultimate or specific meaning. Sequences of nucleotides should be seen like words. Their meaning is depending the context (i.e. their relative spatio/temporal situation). Furthermore, since they are "living" molecules, they express a relative very quick evolutionary f/m; so the same sequences belonging to the same chromosome should not be regarded as identical in the fecundated ovule, in the embryo, in a teenager or in an old man.

By the same token, the mechanical thought is still there in the present physics where it is thought that every "atoms" are identical. But in the present theory, each "atom", like any event, is single. They should be considered at first analogously according to their informotion level (gas, liquid, molecular, organic, etc.) and secondly differently while they turn into another f/m from a level to another.

Also, this can be seen as a principle of equivalence between conservation and acceleration of a f/m into a more informotioned one. This can help the intelligibility to catch on the informotion process as shows the following non-cartesian (i.e. without frame of reference) three level curves diagram (see Diagram 1).

The previous theorem can be also formulated so:

Any creation of an informotion level informs "(gI(" relatively informotion levels it contains, whereas it also informs "(gI(" relatively (but with another kind of relativity) informotion levels that contain it.

For example, a new living species expresses relative informotion of the indefinite set of the field that contains it, but, also, any of these elements (i.e. individuals of the species) creates another relative informotion of the levels of informotion it contains (i.e. nucleotides, cells, organs, etc.)

Now, let's see corollaries to illustrate the previous theorem!

First corollary

There could be any level that does not depend on (and that does not issue from) less informotioned "(gI(" level than it.

Human body is made up selected/etc. "(gI(" elements of the organic field that precede it into the organic informotion, but also it is made up chemicals ions, minerals, atoms, electromagnetic radiation, etc. It is the same for any kind of less informotioned "(gI(" field. The earth is made up selected/accelerated/ etc. "(gI(" elements of the sun; the sun ... of the center of our galaxy, and so on.

Second corollary

It would be deduced from the previous propositions that it could not be considered such an insulated intelligible object so-called "the Universe". In fact, since any element of a field issues from an other element of a less informotioned "(gI(", it would just be a non-sense to imagine any intelligible limit at the informotion "(gI(" process whatever the direction of the intelligibility may be (i.e to proceed up the informotion process "(gI(" or to proceed down the informotion process "(-gI(". That is why it is proposed instead of "universe", the concept of general informotion as to express this irreversible process that the thought is just the limit, instead of the center (with the meaning I perceived at the Paragraph 5.6 of the Tractatus logico-philosophicus by Ludwig Wittgenstein: "The limits of my language mean the limits of my own world."). What all this suggests is that intelligibility should be regarded as the moving edge of the general informotion.

Third corollary

There are two intelligible ways to proceed up the informotion process: by going to the relatively "small" or by going to the relatively "large" either. So, according to the previous theorem, levels din (from the relatively "small" are some "(gI(" levels of analogous In levels from the relatively "large".

This point allows to propose a new meaning of the paradoxical concepts such as "outside" and "inside". Those should be conceived as differential relations: the "outside" of an In would be, in fact, the "inside" of an In-1.

For example, the "outside" of the earth would be the "inside" of the solar system; and the "inside" of the earth is the "inside" of the organic species and the societies. This idea is equivalent to the previous theorem. The ancient concepts of "inside" and "outside" sprung from thermodynamics and from the various theories of the systems it generated.

Unfortunately, these theories increased paradoxes. The present theory would consider the relation "outside/inside" or "environment/system", or "environment/species", as we looked upon the relation space/time, i.e. as an informotion level In.

Equally, this corollary can be expressed as much in terms of "time" as in terms of "space". Thus, we can also proceed up the informotion "(gI(" by going to the relatively recent or by going to the relatively ancient. Then the relatively simple "(gI(" form/movements of the relatively recent are some accelerated/etc. "(gI(" form/movements of the simple form/movements of the relatively ancient. That would show, once again, that neither time nor space is transcendental and separable categories.

Fourth corollary

There is no identity, there are only "differences that makes differences", as Bateson would have said. The concept of identity becomes now equivalent to impasse, self-reference or paradox.

The previous concept of field and the present logic shows the deadlock formal logic of identity came to. There is neither reproduction nor duplication, nor two identical form/movements. A mistake in astrophysics, for example, that produces well-known paradoxes, consists to think that "our galaxy is made up billions stars identical to our sun". But in our terms, the sun is the selected/etc. "(gI(" element of the stellar field to have continued the informotional process by creation of planets. In that way, each star is single. The same still recent mistake originated from the idea that planets were all approximately the same in order to engender what we call life. But, according to this axiomatic, each of them has been proved single and the earth must be looked upon as the selected/etc. "(gI(" element of the planetarian field to engender a new field of informotion: the organic field, and so on.

Fifth corollary

The following concepts of analogical and digital can be used to express respectively intelligible differences into an informotion level and intelligible differences into a field of informotion levels.

Thus, the sun seems analogical to other stars of our galaxy, but it would be said the same like a planet to another, or like a human being to another. Analogy should always be defined "inside" a field defined by the selected/etc. "(gI(" element that expresses the threshold of transformation of the field from it originated. Thus, according to the present theory, planets are analogous between them since they all originated from the sun and they depend on it, and so on.

First proposition

Every informotion In is equivalent to an irreversible process of creation of informotion levels that the rhythm of occurrence increases according to the number of levels took into account. This increasing expresses the equivalence between the previous concepts of acceleration, complexification, selection, quantification, differentiation. But that irreversibility has nothing to do with the linear sequence of time of philosophy or physics. Information "(gI(" is neither time nor space, no more than relativistic space-time; it is only process as proposed in the present axiomatic. Information levels do not follow one another neither in time nor in space even nor relativistic four-dimensional space-time. An informotion level could be also said equivalent to a rhythm but there could not be, by definition (see Axiom 4), a rhythm of all rhythms or a level of all levels.

Second proposition

The speed of light in vacuum (or of the electromagnetic radiation) is, as an informotion "(gI(" field and the simplest "(gI(" expression of the visible world, all the same the upper limit of speed and the lower speed limit of all intelligible and observable levels that would be more complex informotion "(gI(" fields and, therefore, more accelerated/selected/etc. "(gI(".

Thus, the whole galaxies or observable stellar objects are all visible; they all sprung from the informotion of the electromagnetic field "(gI(". Therefore, the whole galaxy is borne by the wave/particle that bears this radiation that could be said a big "black hole" (i.e. a simpler field "(gI(" than the electromagnetic radiation itself); this level is non-visible but logically thinkable and it is made up a non-definite set of informotion levels.

Thus, what all this suggests is that the visible world moves at the relative speed of c on regard to this relative simple "(gI(" element whose it sprung from.

It is generally agreed that, according to our calculations, our galaxy moves in space at a relative speed of about 200 km/s in relation to the closest galaxies. But, this calculation is logically analogous to that we would do by measuring the relative speed of the earth in relation to the others planets in order to obtain its speed into the newtonian "space".

Thus, the relative speed of the earth in relation to Venus, for example, is 3 to 5 km/s whereas its relative orbital speed in relation to the sun is 30 km/s. We would have the same logical type of difference if we would compare the relative speed of the sun in relation to the other stars of our galaxy; and its relative orbital speed in relation to the center of our galaxy. I just think that the relative "orbital" speed of our galaxy around the phenomenon that sprung from is nothing but equal to the phenomenon we call speed of light in vacuum. And the whole galaxies gravitate around as it is sprung from it (the two propositions are equivalent).

Nothing beyond "(-gI(" electromagnetic radiation moves faster than it, but all what it is more complex "(gI(" expresses the informotion of that field i.e. its acceleration/complexification/selection/etc. "(gI(".

The following diagrams would illustrate that, and the understanding comes without the rescue of the tensorial calculus that would be irrelevant here:

Then, the increasing of Einstein's "curvature of space-time" would be said as the complexification/acceleration/selection/etc. "(gI(" of elements of the electromagnetic field that contains more informotioned "(gI(" field than it.

Also, this can be looked upon as a new meaning of the Einstein, Podolski and Rosen (EPR) paradox. For example, the field I of an atom Ik and of a particle/wave dij , would be formalized thus:

( I ( ij ( Ik ( dij

where dij expresses: a) a particle/wave belonging to the atom Ik, and, b) an informotion "(gI(" of particle/wave ij analogous to dij , but less informotioned "(gI(". (See Axiom 5 and Remark 13 for further formalization)

Therefore, concepts such as hamiltonian or integration of the wave function is from now on irrelevant for atom cannot be no more considered as a closed (or integrated) energetic system.

Third proposition

Gravitation is one of the expressions of the general informotion. Therefore it cannot be said as an "attractive force" able to reverse the informotion process.

Einstein had claimed that gravitation was not an independent "force" but an acceleration field. According to his considerations, the concept of force, could not be looked upon as a modern scientific one but rather as a magic one. The logic of this great idea leads to assert now that gravitation is no more an independent "attractive force" from form/movements than speed, heath, etc. could be. There is no gravitation but rather kind of gravitation that could be from now on looked upon as informotion levels of general informotion. Thus, gravitation of the planets could be the same that the stars one around the galactic "black hole". Then the classical concept of "black hole" formerly proposed by Laplace is no more to be thought of. Therefore, form/movements of gravitation are also form/movements of acceleration, complexification, etc. "(gI(", according to the present axiomatic.

Gravitation, in its classical sense, is an intelligible expression of the continuation of general informotion concerning relatively simple form/movements: "black hole", electromagnetic radiation, galaxies, stars, planets and their selected/accelerated/etc. "(gI(" elements ("particles", "atoms", etc.). In the case of more complex form/movements, gravitation informs into molecular interactions; then into predaciousness in the case of so-called living form/movements; and into creation of artifacts (including ideas and theories) in the case of human beings, for example. Gravitation is no more an attractive force (i.e. an independent principle from the field, as they were time and space in the classical mechanics and even in four-dimensional space-time of the modern physics); or than predaciousness and sexualization could be independent principles of the organic field; or thought could be an independent principle of the anthropo/social field.

This leads to state that "black holes" are elements of a simpler informotion level whose electromagnetic field is sprung from, and around of which gravitates the whole visible world.

Thus, "black holes" are not "gravitational attractors", since, on the contrary, all visible world sprung from them, in the same logical way we originated from our parents; primates originated from mammals; bacteria originated from ocean macromolecules; the earth originated from the sun; the sun originated from the center of our galaxy; and the latter originated from a kind of "black hole" that it is gravitating around, and so on. Stars would be "attracted" by their "black hole" in the same way we are attracted by food. Thus, the concept of attraction just means a certain modality of interaction between informotion levels and shows the direction of general informotion. Sexual attraction expresses the dependency of individuals on regards of specie that is, according to our logic, at a less informotioned "(gI(" level than individuals " level than individuals **8.

Information, has only one meaning/direction/value, like acceleration, complexification, selection, quantification, differentiation; meaning that the relatively complexified/accelerated/etc. "(gI(" always "gravitates" around the relatively fewer complexified/accelerated/etc. "(gI(". See Axiom 5.

Fourth proposition

The concept of threshold (see. Definition 3) is equivalent to an informotion "(gI(" of an element of a level in order to continue the process by creating a new level. It is also equivalent to an intelligible difference between elements of a level or between different levels.

Fifth proposition

Every informotion level is made up only ONE differential sequence of elements leading to the selection/complexification/acceleration/ etc. "(gI(" of one them in order to create a new more informotioned "(gI(" level. Therefore, other sequences constitute, from the current point of view, impasses or thresholds either. It should be notice that not any sequence could be a priori said "useless" since THE general informotional sequence could not be predicted.

The application of this logic to the anthropo/social level allows to say it is an illusion to claim to control our fate. Nobody can foresee which one of our political constitutions, technological inventions, ideas, theories, are going to come sooner or later to a deadlock that will force us to change the continuation of the process.

Nothing cannot help us from the duty of thinking. But we could recognize sequences of the anthropo/social field that already came to a deadlock. This century allowed to specify some of these.

Some people (scientists or not) are ready to admit that each event is single but they think all the same that it is possible to predict them; what leads to a flat contradiction to the previous statement. The present point of view about the reproducibility of the experiments asserts it is based upon a confusion of informotion levels. let's see why!

Since Galileo, the concept of prediction, and that of reproduction that is joined to it, constitute for some of us the only criterion of the scientific activity. However, nothing of what it happens, or in another hand, of what it is created, has never been predicted. On the contrary, the prediction itself, and more logically, take part into the process of human creativity. To predict does not mean what is going to happen to-morrow but does mean to express a certain proposition of change.

People who express a prediction exclude the emergence of his assertion into the process of prediction whose he is expressing; or more, no one can predict the next prediction. thus, a prediction is necessarily inconsistent tent. Therefore, his prediction is not a prediction in the sense he is thinking; it is merely the statement of a "new", or of a difference - as Bateson would have said -, that claims to be an "old". The scientific activity does not consist to prove whatever it may be, or to express a "truth" that would be there before, or to predict something, but to propose new ideas to the human community in order to continue its process. (Also see Remark 8)

Sixth proposition

The continuation of the same informotional "(gI(" modality beyond the selected "(gI(" threshold comes to a deadlock, a monstrosity, a paradox or a dogma.

After the selection/complexification/acceleration/etc. of a level belonging to an analogical set of levels (or field), the process carries on composing a more informotioned "(gI(" form/movement than the previous one whereas the latter combines with the new one into a more informotioned "(gI(" form/movement; meanwhile the non-selected/accelerated/etc. "(gI(" of the previous one comes to a deadlock (i.e.it could not informotion any more). Five examples:

1. The moon expresses a further gravitation "(gI(" (around the earth) into the planetarian field. However, it composes an impasse since the earth is the selected/accelerated/complexified/etc. element of that field. The reason why the moon appears as a dead star - i.e. as less informotioned "(gI(" than the earth - is that its rotation rhythm on itself is identical to its revolution rhythm around the earth. That could be defined as a confusion since, according to a Bateson's word, there is no difference that makes another difference. Remember the earth has a current difference of about 1/365 between the two rhythms, and that difference produced all the differences we know, included ourselves. Thus, the moon should be considered as an impasse or a paradox (beside our poetic feelings about it). In fact, we don't observe further gravitation, in that sense, around any planetarian satellites except our own artifacts.

2. Invertebrates originated the experiment of a nervous system on the ventral face of their body, not much differentiated from digestive system. Thereby they could not continue the informotion of their organism up to a certain threshold. What we name vertebrates proposed new experiments (internal skeleton associated to the central nervous system) that will be proved (to the best of our judgment today) more fruitful since it allowed a tremendous increase of the learning of individuals.

3. Dinosaurs was the biggest oviparous. Beside the controversy about they are disappearing, they continued the oviparous experiment up to the monstrosity. Thus, organic informotion continued by a new experiment consisting to keep eggs inside the body so that to usher in a new phylogenetic sequence called mammals.

4. Totalitarianism (and all kind of despotism) apparently strong and powerful, as many writers thought during XIXth and XXth centuries, is bound upon an confusion or an identity between organization and socialization. This confusion has just betrayed, by experiment, it was a deadlock to continue what it should be named the socialization process, i.e. the anthropo/social informotion. Reason why a "society" must not be looked upon as analogous to an "organism".

5. The present theory, although it cannot pass judgment on itself without generating self-reference or paradox, however invite to consider theory or idea in general as any other natural process. Thus, whether a theory is selected "(gI(" or not in the anthropo/social informotion does not prove it is true or false (the two are just non-sense for the present theory); that just means it has been selected "(gI(" or not. From this point of view, an idea is neither true nor false; it does allow or it does not allow to carry on the process. For example, to lay eggs or not to lay egg is neither true nor false; but beyond a certain threshold, this patent comes to a deadlock. But it would be absurd to say that, for example, a mouse is more true than a bird. It is just the same with ideas and theories. A theory does allow or does not allow to continue the intelligible process; doing so require necessarily it be selected "(gI(" or not.

Seventh proposition

We would claim, generally, that informotion process is equivalent to an increase of informotional "mass" (or massification if anything) and to a creation of a further informotion level and, in conjunction, a new field. Thus, the relative increase of the informotional sun mass occurred by creating a new field of f/m: the planetarian field, more informotioned "(gI(" than it; the earth increased its informotional mass by creating new informotion levels: the organic f/m; societies increase their informotional mass by creating individuals who are going to create new artifacts, and so on.

Eighth proposition

Information process should be comprehended as a relative increase of the informotion rhythm (i.e. the relative speed of change) jointly as an increase of the complexification/selection/acceleration/etc. "(gI(". See also Axiom 5.

Therefore any In could be also looked upon as the informotional mass of the n level jointly to the relative speed or the relative complexity/acceleration/etc. "(gI(" of that level.

It should be pointed out not to be mistaken with any kind of sophisticated formalism. Formalism must just be taken as an implement of the thought to help it to proceed on its informotion. Not any formula should mean in any case the principle of equivalence between complexification, acceleration, selection, etc. by trans-form/movementional threshold characterizing informotion process. Nevertheless, formalism clearly shows each informotion level In sprung from and relatively depends on those that precede it in general informotion "(gI(": see Diagram 1, Axiom 5 and the new interpretation of cantorian algorithm on next chapter. Also formalism shows that each new level increases the relative informotion according to the given level. For example, the creation on earth of levels such as vegetables, animals, human societies, increased its informotional mass, but it also increased, though in a relatively different way, that of the solar system, and so on, according to the axiom five. In the same way the learning of a child increases his own informotional mass and, also, relatively according to his learning level, and so on.

Ninth proposition

What we call in classical physics inertial mass and gravitational mass whose Einstein showed the equivalence become here a specific property of an informotion level located, in the informotion, at an immediately more informotioned "(gI(" level after the electromagnetic field. Thus, if in a classical point of view, a particle/wave photon cannot have neither inertial nor gravitational mass, however, in the present theory, it expresses a certain informotional mass.

Einstein showed that any increase of "energy", i.e. any mechanical acceleration creates a relative increase of the mass according to the famous formula E = m c2. From the point of view of the special relativity, increasing the mass expressed another way to continue to increase energy without increasing the speed of light (as the absolute speed); that does mean there would be a principle of conservation of energy-mass. In the present point of view the concept of conservation takes a new meaning. In fact, the irreversible informotion process continues by relative complexification/acceleration/selection/etc. Thus, conservation itself becomes relative since what it is conserved at a level changes at another. Therefore the only conservation that can be took into account is that of informotion process itself.

In other respects, the concept of attractive force used by classical theory of gravitation had been replaced, in the relativistic version of it, by the concept of acceleration field. It is proposed now to replace the latter by the concept of informotion. Thus, the concept of attraction must be used to state a local phenomenon.

It has also brought up, in so-called physical phenomena (i.e. form/movements we usually called inert or inanimate), concepts hitherto applied only to more informotioned "(gI(" phenomena: natural selection and transformation threshold. Speed of light and four-dimensional metrical continuum have been also relativised. And the concept of dimension became equivalent to informotion level.

The concept of dimension is a very important one. Modern physics start to question the number of dimensions of the geometric world and also to question the mechanical concept of metric; from three, in the newtonian mechanics, it has been changed into four in the general theory of relativity. These classical concepts of dimension that expressed a constant metric for the whole physical phenomena do not mean nothing in the present theory; as matter of fact each informotion level should be considered as one dimension (or metric) of the general informotion. But that latter cannot be reduced to a general metric or a constant that one could be applied to the whole phenomena without relapsing into paradox or self-reference. There might not be, in general informotion theory, a dimension (or metric) of all dimensions (or all metrics) for it would mean there would be an informotion level of all informotion levels.

Also it would be proposed a new meaning of the non-simultaneity principle stated by Einstein so:

Theorem 2

As any informotion level defines a single and specific space/time there might not be two identical levels or two identical events in different space or time.

Thus, hydrogen, for example, we know on the earth, could not be the same existing in the sun or that close to the center of our galaxy, in other galaxy, etc. It would be the same for electromagnetic radiation and so for all kind of form/movements (or informotion levels). There would be the same logical difference (and the same kind of confusion, too) between, on the one hand, the atmospheric hydrogen and the quasar hydrogen and, on the other hand, an eucaryotic cell and an homo-sapiens's gamete. The two express, inside given fields (galactic and organic) the selection/complexification/acceleration/etc."(gI(" of the simplest "(-gI(" form/movements in the more complex "(gI(" ones belonging to a given intelligible field. Thus, atmospheric hydrogen should be considered as more complex "(gI(" than that of stars and organic hydrogen should be considered as more complex "(gI(" than that of water hydrogen. In the same way, mammal gametes should be considered as more complex "(gI(" than the analogous eukaryotic cells we observe in the organic field, although they would appear alike at first sight.

More precisely, and contrary to the current mechanical genetics dogma, the "genes" **9 of the chimpanzee should be considered as simpler "(gI(" than these of human beings, in spite of their relative analogy. Alike, human baby's "genes" should be considered as simpler "(gI(" than these of human adult and the latter than these of old man.

Remark 12

The theory of general informotion has nothing to do with the philosophical idea of progress, improvement, change for the better or, furthermore, with the darwinian concepts of natural selection and progressive adaptation to an environment. According to the present axiomatic, it is as much a non-sense to state that earth is more adapted than the sun, as a mouse is more adapted than a bacterium or as modern human life is more adapted than that of ancient human. The only value that the general informotion expresses is its own continuity. The concept of impasse, such as defined before, as a deadlock for an informotion level, could be equivalent to meet with a repulse or to suffer a defeat. The consciousness we express after the death of a dear one by: "life goes on", would translate that. Then, moral judgments would be nothing but deduced.

Tenth proposition

No proposition should claim to be an explanation (or a reflection) of what it would be stated.

Eleventh proposition

Each frequency of the electromagnetic spectrum should not be express some different vibrations of a same particle: the photon. According to the present point of view, there would be as much kind of photon as there would be kind of electromagnetic frequencies, i.e. an indefinity, so to speak. Therefore, each frequency would be looked upon as a specific kind of f/m. The way we are going to conceive the frequencies distribution in the spectrum is going to allow a new meaning of the Doppler effect (See Application: on Doppler effect.)

Theorem 3

Any thought about " origin " is, by definition, paradoxical; because it consists to mistake the and of the process (the thought) for the beginning.

One cannot claim in the same time an irreversible principle of irreversibility of unforeseeable creations, and a reversible principle within the same. It is however what we used to do by intending to remake the history of the universe, of the life, of the humanization, of its own life, etc. Thus, the idea of evolutionary process, such as it is practiced by the neo-darwinism, for example, comes to postulate two groups of two contradictory laws in the so-called " nature ". The first group claiming that the nature creates in first moment anything by chance and, in a second moment, selects thoroughly the latter creation; the second group contains a law, say, increasing of complexification (from the big bang to the human being thinking) and another law, of increasing simplification that is the thought of the human being able to wind up the process as a whole.

Thinking to any kind of origin, or telling a story, as much scientific as it may be, is therefore, interpreted, in the present theory, as a human project not, as we make since, say, Plato, as a reminiscence. That's why concepts as, for example, memorization, learning, cognition and informotion coalesced in the present perspective.

We start up from a neither demonstrable nor provable but experienceable irreversible process of our intelligibility, life, generations, techniques, ideas, and so on. The paradox we can see now is engender by realistic conception. This may be claimed as follow: it would exists a real that would be something else that a human concept, capable to undertake a reflection process with itself so as to claim propositions isomorphic to itself. Thus, Einstein believed, at one and the same time, in the second principle of the thermodynamics, in the eternal laws of nature and in the evolution of the scientific ideas. For his part, Karl Popper, for example, in one hand criticized what he called " historicism ", claiming it was " any doctrine based upon the belief in a fortune of human history, that will vow it to reach a goal through a succession of necessary steps ", and in other hand stroke that science is " the quest of the truth ". We can see the same paradox in Kant's assertions; indeed, the a priori forms of the sensibility of its transcendental subject (time, space and causality) are said to be eternal laws (without neither time, nor space, nor causality). And thus, he could assert, seriously, that the human knowledge is temporal, while claiming the eternal laws of the knowledge; that is, its own knowledge is non temporal; or it came to say that his own knowledge was non human. He said too that any knowledge act is a synthetic act that introduces unity in the multiple; and this can be only done in the time. Thus, he could say, a one and the same time that the absolute knowledge (the adequacy of the eternal concept and the eternity) is a temporal task and therefore infinite( " we need time to think ") and to claim the eternal forms, non temporal, of the knowledge.

Critic of the Fractals and of the Cantorian Mechanics

This chapter proposes a non-mechanical answer at the cantorian question: what are the form of statement at which corresponds a class as a unity and what are the form of statement at which corresponds a class as a multiplicity?

The unity (as a segment) of the previous algorithm (see diagram 3) - to illustrate in a mechanical way informotion process - does not stand for a base as in the following Cantor's set (see Diagram 4). The process should be read as following: to create a new level, just duplicate the whole algorithm of the former level; to do so, start by the higher level then go down as showed by arrows. That algorithm is neither finite nor infinite, it is process. It does not work as the Cantor's set that rise from a base (logical singularity). Its construction looks like a spiral without any center and somehow in the opposite way compared to the Cantor's set (see Diagram 4) which is, by definition, transfinite. In the Cantor's set, at the nth operation, the number n of segments is 2n, the length u of these segments is 1/3n. The dimension d of the Cantor's set is defined so:

2n = (3n)d

when

n -> and u -> 0,

hence

d = log 2/log 3 0.65

Should it be observed that in the former algorithm (see Diagram 3) its cantorian dimension remains constant whatever the number of level. That's why the concept of dimension is irrelevant to express the informotion process.

But this mechanic does not allow by no means to express the principle of equivalence between selection/complexification/acceleration/ differentiation/quantification proposed in the present axiomatic. Arrows show the path of the informotion of the algorithm (see Diagram 5).

To get out of this mechanical algebra, that is to say, in order to a new level expresses an informotion, it should square, by definition, with a gI that should be formalized in the following sequence:

... ( in-2 ( in-1 ( In ( din-1 ( din-2 ( ... (1)

... ( in-1 ( in ( In+1 ( din ( din-1 ( ... (2)

... ( in ( in+1 ( In+2 ( din+1 ( din ( ... (3)

and so on...

In fact, it should be well recognized that, in the mechanical algorithm, from a level to another, there could not be seen any kind of acceleration/selection/complexification/differentiation/quantification of the process. Only quantification can be pointed out, and to create a new level it just takes to double the previous level then add a new "base" by trebling the length of the previous level. That's why the cantorian dimension remains constant.

Let's say that a computer works like a Cantor's set. To create a more mechanically powerful computer it is just necessary to increase its clock frequency, but to create a new kind of computer it will take to accelerate/select/complexity/differentiate/quantify: it will take to create something else; a non foreseeable item exactly as the creation of computer was.

Remark 13

It is necessary to realize, in consideration of this sequence, how much the concept of hierarchy is a very important obstacle to comprehend that process (see also: Axioms 2 and 5, Definition 9 and Remark 5 of the Axiomatic). In fact, it is impossible to say a priori whether any level will be or will not be selected/accelerated/complexified/etc. "(gI(" at the time of the creation of a new level. If it will not, the elements of that level seems to "degrade" by returning to their analogous levels. In current use this process is called "recycling". As matter of fact, this "recycling" or this "degradation" expresses the way to continue informotion at the given level.

Also, what it has just called degradation, as a return of a differentiation level contained into I at the i analogous level, corresponds to a new meaning of concepts entropy and death. All this should be formalized so:

This formalization constitutes a new intelligibility of the concept of atom since there is no more possibility of integration of it. Furthermore, each differentiation particle/wave is fed by an analogous i level that does not belong to (in the mechanical meaning) the given atomic level but which does express its interaction with the rest of the "universe". Arrows do not stand for a process of transfer of whatever it can be but would rather show that each di level sprung from informotioned "(gI(" elements of the i level such as definite by the Axiom 5.

Then, what we usually call energy is nothing more that the effect of this permanent renewal of di elements of the atom by the i analogous ones that are "out" of it. Let's make the following mental experiment to get this idea: if one get out this or that atom or this or that any element of the "universe" out of the universe", it would instantaneously loose all its "energy"; i.e. it would became naught. In a less absurd way, and also more generally, if one was shifting it from a place to another, it necessarily will change according to the I informotion level in which it will take place. So, it will grade in a more informotioned level, and will degrade in a less informotioned one.

It is the same when we keep ourselves; The gradation corresponding to what we usually call metabolism of a organism (i.e. feeding); but I would rather say, metabolization. Some i elements are selected/etc. "(gI(" in order to be informotioned in din elements. The degradation expresses either the rejection of the non selected/etc. "(gI(" i elements during the metabolization and recycled in the i analogous elements, or the death of the I level (i.e. the impossibility of continuing the metabolization process).

Those considerations constitute a sort of transformation and generalization of the Einstein's deepest relativistic intuitions (such as I would have understood them). Thus, we completely get out of the formula of the special relativity E=mc2, where energy is strictly defined by the mass, to enter in an new relativistic conception of energy that permit to get out of the paradoxes created by the general relativity theory and quantum mechanics (see also Second Proposition).

Isomorphism, Hologrammism and Logical Fractionnism

The only type of isomorphism, hologrammism or fractionnism the present theory takes into account cannot be by no means illustrated (except words and signs themselves), since it is based on the logical equivalence of the informotion levels (see the previous discussion about the concept of hierarchy, Remark 13). This can be expressed so: every In is equivalent for the intelligibility of general informotion. But, contrary to usual assumptions, the logical equivalence should never be recognized as a description or a model of the world (or the philosophical concept of nature). It is only the necessary condition to continue the intelligible process.

Application: a new view on the The Doppler Effect

The Doppler effect can be stated so:

The change in frequency of a wave is due to the relative motion of the source or of the observer either. If the source is moving toward the observer, the latter will perceive higher frequency than they are being emitted; on the contrary, if the source is moving away from the observer, the latter will perceive lower frequency than they are being emitted.

The Doppler shift of the frequency of light plays a capital role in cosmology for the so-called "red-shift" of the light emitted by galaxies would mean that all galaxies are moving away from us.

I proposed before the constant speed of light observed in vacuum could be seen as the expression of the revolution frequency of the whole visible world around a "big black hole" (that is, according to the previous axioms, a less informotioned "(gI(" phenomenon and with a lower frequency of occurrence, sprung from another itself, and so on. Just like, at an another level, the orbital speed of the sun expresses its revolution frequency around the center of our galaxy.

To consider that the light consists of only one speed forces to read this phenomenon of perceived frequency change as a function of the difference of time the light takes to reach the observer; according as the source is moving away from him or she or moving toward him or she.

However, if only the difference of time was concerned, that should mean a far source, even fixed, should emit a lower frequency light than the same closer source. But this is not the case. Therefore, it is not a simple difference of time. Moreover, this would be inconsistent with one proposition of the general relativity that states that the time cannot be isolated especially when we consider the light.

It is stated so: if the source is moving toward us, when it will emit the next wave, the source will be closer so that the time the wave will take to reach the observer will be shorter. Therefore, as the speed of light is constant in vacuum, the frequency will have to increase. This means that the space between the crest would diminished.

Let's see the following experiment. When a ball is bouncing from our hand to the ground while we suddenly bring our hand nearer the ground, the ball, in order to keep its initial speed, must increase its frequencies of bouncing, its frequencies of oscillation; on the reverse, if we suddenly move our hand away from the ground, the frequencies of oscillation of the ball are going to diminish.

We can illustrate this principle by the following diagrams:

However, to make this effect sensitive, the difference between the speed of the ball and the speed of the hand must be small. This means, in the case of the light, in order to observe the Doppler effect, that the source should move at a speed close to the one of the speed of light (at least 10%).

Each of us has noted the sudden change of tonality of the siren of an ambulance when it meets and passes us. The tonality is increasing while the ambulance move toward us and, on the contrary, it is decreasing while the ambulance move away from us. We used to take this example, to explain the red-shift of the light emitted by galaxies.

I propose now a new meaning of this phenomenon according to the previous axioms.

The siren of the ambulance emits a timbre, not a single frequency. A timbre (of a siren, a flute or a saxophone) consists of a set of frequencies. In fact a timbre is a sound spectrum. Each instrument has a peculiar timbre. This means that while a piano plays a certain frequency, for example, the note A which vibrates at 440 Hz, it is easy to distinguish the same note emitted by a violin or a saxophone; the differences perceived are not differences of primary frequency since beyond those differences we could tune all instruments up this A. Differences we can hear, from an instrument to another is based on differences contained in the peculiar timbre of each instrument. So it is with for the siren of the ambulance.

The timbre of the siren contains a set of peculiar frequencies. So, while it move toward us, we hear high frequencies that the timbre of the siren previously contains but which the relative speeds compared with the one of the timbre (i.e the speed of the sound) corresponds to the increasing rate of the speed of the ambulance. In fact, while the ambulance does not move, the siren emits a set of frequencies carried by the speed of the sound and that corresponds to a certain fundamental vibration of the molecules of the air: 330 m/s.

Whereas the ambulance just meet and pass us we can hear the timbre as though we were sitting by chauffeur side or as if the ambulance were stopped. Then, when the ambulance is going to move away from us, we are going to hear only the low frequencies that the timbre contains i.e. the ones that the speed corresponds to the speed of the whole timbre less the speed of the ambulance.

In fact, the nature of the frequency emitted is not subordinated to the observer. But the observed frequency is subordinated to the relative speed between the emitted frequency and the observer (see Diagram 7).

So it is with the light. The white light we perceive is a timbre of the electromagnetic field that contains an indefinite set of frequencies (from red to violet) that expresses, in fact, the different relative revolution speeds of it, like illustrated in Diagram 8).

1 It would be well recognized that we would use, for the formalization, only open brackets in order to be consistent with the non-integration axiom (see Axiom 4). (return)

2 Henri Poincaré had proposed to think concepts such as "paradox" and "vicious circle" as analogous. For his part, Bertrand Russell had said "self-replicating principle" to express the same analogy. It is all the more amazing as having had to regard concepts such as self-organization, system, structure, which obviously means the same, as a kind of epistemological revolution. (return)

3 Ik should always be understood as the more informotioned "(gI(" intelligible informotion level; and ij and dij as some less informotioned "(gI(" intelligible levels; see also Remark 10. (return)

4 I mean by "mechanics", "mechanistic", "mechanics logic" or "cartesian-newtonian paradigm", logics allowing to think that present theory called properly impasse or self-reference. (return)

5 Definition 9 demands to be specified. In the classical Set Theory, or Theory of Types (see Whitehead and Russell), the intelligible order is based upon a hierarchical system (inferior and superior) by proceeding from an element to a set. Example: it is said that a set expresses an upper logical type than elements of that it is made by. In the present theory,  In or field ( I ( do not express any kind of hierarchy. For example, the molecular level is, jointly, issued from atomic level that is contains it, and issued from and is contained into the general atomic level. The atomic level generates the molecular level while the latter contains selected/accelerated/complexified field/etc. "(gI(" elements of the level that is issued from. Consequently one could not mistake the general atomic level for the elements of it contained into the molecular level. On the other hand, a mineral atom has informotioned "(gI(" in order to become organic, therefore, it belongs to the organic level; so it should be regarded as more informotioned "(gI(" that the analogous one from the organic level; so it should be regarded as more informotioned "(gI(" that the analogous one from the mineral level. However, according to the axioms, it is jointly contained in the organic level while the organic level is contained in general mineral level. The mechanical logic of set cannot render any account of this point. See Remarks 4, 6, 13. (return)

6 That point refers to mechanical set defined by Cantor. In fact, that would propose a new meaning of this "set" so that elements of it would understood in an informotional "(gI(" way, i.e. differentiated in order to have no more "base" or logical singularity (a starting value) in opposition of classical algorithm. See Axioms 2,5; note 5; Remark 13. (return)

7 The verb to inform would express here the intelligible process of general informotion. (return)

8 See Jacques Jaffelin, Pour une théorie de l'informotion générale, Paris, ESF, 1993. (return)

9 The concept of gene is in quotation marks to express the change of meaning, from the current dogma, of nucleotide sequences. (return)