THE EVOLUTION OF MY RESEARCH

Notice

The following presentation is deliberately marked by a subjective tonality of intellectual confession. All the desired neutral information can be found via the joined list of publications as well as via the publications-in-line exposed on this site.

As early as my very first contact with quantum mechanics, as a student, I felt strongly interested by the foundations of this theory, by the singularity of its mathematical formalism, by the cryptic significance of this formalism and the problems of interpretation which it raises. My whole subsequent research, on which a brief account is given below, stems from this initial curiosity.

Invalidation of von Neumann's theorem on impossibility of hidden parameters compatible with the quantum mechanical formalism.

The whole essence of my PhD thesis has been constructed in Bucarest, Roumania, during the period 1957-1960, in a total intellectual isolation; but its final form has been accomplished in France under the direction of Louis de Broglie. This thesis – titled Etude du caractère complet de la mécanique quantique – has been defended in Paris in 1964. Prefaced by Louis de Broglie, it has been published in 1964 by Gauthier-Villars, in the collection Les grands problèmes des sciences (1)¹. The main content of this work consists of the first genuinely proved – and to this day by far the most elaborated – invalidation of the proof of von Neumann's theorem² according to which a theory of microstates more "complete" than quantum mechanics is definitively impossible: this theorem was widely considered to definitively settle the famous question of "hidden parameters", or in other terms, the basic question of the "essential" or "intrinsic" nature of the quantum mechanical probabilities.

I stress that the analyses from my PhD thesis possessed a mainly logical character and related already the quantum mechanical formalism with the human processes of
conceptualisation which subtend it.

Invalidation of Wigner's theorem on the impossibility of a joint probability of position
and momentum compatible with the quantum mechanical formalism

After the publication of my thesis my research continued at the University of Reims, France, where, as a Professor of Theoretical Physics, I founded in 1971 the Laboratoire de Mécanique Quantique et Structures de l'Information, which I headed until 1997.

I first tried to deepen my understanding of the quantum theory of measurements : How does one succeed to measure “mechanical quantities” assigned by hypothesis to microscopic physical entities – states of microsystems – which are for ever non perceptible by human beings and moreover are unstable by their very definition³ ? How, by the help of which cognitive strategy, by the help of which physical operations associated with which organisation of concepts-apparatuses-signs-and-coding, does one succeed to construct, concerning microstates, knowledge, “information”, that leads to probabilistic predictions concerning microstates ?

These questions led me toward Kolmogorov's theory of probabilities and Shannon's theory of communication of information.

Among the works published immediately after my thesis I mention only a second important invalidation, that of Wigner's theorem⁴ on the impossibility of a joint probability of position and momentum compatible with the quantum mechanical formalism (2,3). Again, these works (especially the first one) contain explicit analyses of the connections between the quantum mechanical formalism and the operational-conceptual processes that are involved.

Emergence of a long-term research program

Notwithstanding the mentioned invalidation of Wigner's theorem, the period that followed my PhD seems to me retroactively to have been slow, laborious, disoriented, tinted by a shade of hybrid impotence. By critical opposition I had been able to erect two local dykes in front of the consequences of fallacious reasoning. But I did not genuinely understand what I was defending. Though at the time I already knew very thoroughly the formalism of fundamental quantum mechanics and taught it, the conceptual status of this theory remained obscure in my mind. I did not even know what, exactly, if known, would permit me to claim to have finally "understood" this theory.

This opaque period came to an end only in June 1979. This happened suddenly, in the following way.

The celebration of a centenary since Einstein's birth gave opportunity for a short Colloquium on the problem of "locality" raised by a then recent theorem formulated by Bell and according to which the quantum mechanical formalism would be incompatible with hidden parameters posited to be "local" in the sense of Einstein's theory of special relativity. I had been invited to expose my view on this problem in exactly 20 minutes. Only three days before, in a couple of hours, I had fully written down the 14 pages of my lecture (4). Subsequently, it appeared that in these few pages I had formulated the program of research which since then I never ceased to strive to realise. These pages contained, at last expressed, a detailed sample of the whole structure of curiosity which commands the functioning of my attention, so of my research. I was showing there how, in the particular case of this problem of locality which at that time was shaking the community of theoretical physicists, the words and their designata were associated in an ill controlled manner which generated much confusion. And I was asserting the necessity – which already seemed urgent to me – to reach the very deep buried zone where the roots of logic should somehow merge with those of probabilities, and where still unknown basic epistemological regularities must act, which, implicitly, govern the general organisation of human knowledge and in particular that of the knowledge encrypted in the quantum mechanical formalism.

Starting from that time, 1979, my works began to quite openly assign importance to epistemological features.

Of course, the mathematical structures which I had come to know thoroughly – those of quantum mechanics, of the theory of probabilities and of Shannon’s theory of communication (“information”) – continued playing a major role of reference and orientation, and they even became a permanent object of tentative innovation. But my goal was progressively including a definitely epistemological and constructive character. The invalidation of this or that proof, necessarily circumscribed inside an already constructed mathematical discipline – which, even if it is fundamental, is particular and closed – had ceased to be a sufficient motivation. My objectives had changed by a sort of growth. The experience gained by the elaboration of the proofs of the non-conclusive character of von Neuman’s and Wigner’s impossibility theorems, had displaced my interest on a more fundamental and general level, directing it towards constructive and normative attempts.

From now I knew where and how to search. I was trying to organise a general manner of conceptualising, subjected to definite constraints : to bring into evidence how fallacious representations and reasoning emerge, which afterwards are matter for invalidations ; to suppress a priori the possibility of such fallacies ; to re-construct accordingly to explicit norms, already achieved conceptual structures which, more or less implicitly, bear germs of paradoxes and false problems encapsulated during their natural non regulated geneses.

The functional of opacity : Mathematical unification between the classical theory of probabilities and Shannon’s theory of “information”

For a short time the above mentioned new orientation acted only as a new and explicit instrument, but not yet as a self sufficient independent aim.

For instance, during the period 1979-1982, in a sequence of three works (5,6,7), I concentrated on a problem that was keeping my attention since several years : what is, in mathematical terms, the semantic relation between, on the one hand Boltzmann’s concept of an entropic form Σ_I (n_ij/N)log(n_ij/N) associated to a statistical distribution globally denoted “j”, defined on N realisations of events from a set of λ events distinguished from one another by an index i=1,2,… λ where λ≪N, and on the other hand, Shannon’s “informational” or “probabilistic” entropic form Σ_i p_i log p_i that had been just posited directly for a probability law { p_i } posited to work on that same set of λ events ?

It seemed to me inconceivable that the striking formal similitude between two concepts of which the semantic contents are quite distinct from one another, be a mere coincidence with respect to these semantic contents, as some authors sustained.

In the three works quoted above, the mathematical approach made use of techniques which are rather current in the domains of statistics and of probabilities. But in the global substrate of these techniques there acted already a quite unusual way of separating and stratifying the initial question, in sub-questions treated in succession. This led to a hierarchy of successive partial results. The relation between these partial results was then established via a final mathematical synthesis. These were new features of a conceptual and methodological nature. And, notwithstanding my still very wispy perception of the methodological structure wherefrom they stemmed, only in consequence of these new conceptual-methodological features has it been possible to establish a clear answer to the examined question. This answer was expressed by the following mathematical statement :

lim (N→∞∕ j fixed) (-log P_N (j)⁄N) = Σ_i f _ij log f _ij - Σ_i f_ij log p_i = Ω ( j ⁄{ p_i } ) , i=1,…λ

where :

- j designates a statistical distribution freely chosen a priori on the universe U of λ basic elementary events e_i introduced by the considered random phenomenon (so i=1,…λ), which statistical distribution is maintained fixed throughout the process of indefinite growth of the number N of realisations of the considered basic random phenomenon ⁵ ;

- f ij ≡ n(ei)/N denotes the relative frequency of the outcomes of the elementary event e_i inside the chosen statistical distribution j ;

- P_N(j) denotes the global meta-probability of an effective realisation of the a priori chosen global statistical distribution j, it being supposed that on the universe U is acting a basic probability law { p_i } where p_i is the individual probability assigned by this law to the elementary event e_i ;

- the notation Ω( j∕ {p_i}) designates what I called the functional of opacity of the chosen statistical distribution j, with respect to the basic probability law { p_i }.

So the employed method led to the construction of a new mathematical being : the functional of opacity Ω ( j∕ { p_i } ).

Now, the opacity functional is endowed, by the genesis of its construction, with a quite definite probabilistic significance :

lim (N→∞∕ j fixed) (-log P_N (j)⁄N)

Furthermore, the opacity functional Ω ( j∕ { p_i } ) emerges from the calculations with the form of the difference Σ_i f_ij log f_ij - Σ_i f_ij log p_i between two entropic forms, the first one of which is a statistical entropy (that of the freely chosen statistical distribution j), whereas the second one is an entropic form that mixes relative frequencies f_ij and elementary probabilities p_i. However a rather obvious proof establishes what follows.

In the special case in which the a priori and freely chosen statistical distribution j is that one which is “faithful” to the probability law {p_i} (which means by definition that for any index i one has f _i,j ≅ p_i ⁶ and is pertinently expressed by renoting j=jF, f _i,jF ≅ p_i), the mixture between statistical and probabilistic descriptors from the second term of Ω(j∕ {p_i } ) dissolves – from an exclusively numerical point of view – so the expression of Ω ( j∕ { p_i } ) transmutes into the difference of measure 0

Σ_i f _i,jF log f _i,jF - Σ_i f _i,jF log p_i , i=1,2,…λ

which – again from an exclusively numerical point of view – can be rewritten as the difference Σ_i f _i,jF log f _i,jF -Σ_i p_I log p_i , i=1,2,…λ, where the first one is a purely statistical entropy and the second one a purely “probabilistic entropy”.

Since it is obvious that when the statistical distribution and the probabilistic distribution are posited to (practically) identify numerically, the two corresponding entropic forms will equally (practically) identify numerically, this, at a first sight, might be perceived as a mere
triviality. But in fact, in the present context, this result is very far from being trivial. Indeed :

(a) In the particular case in which the a priori chosen statistical distribution j is “faithfull” to the probabilistic distribution {p_i}, the corresponding opacity functional

Ω ( jF ⁄{ p_i } ) = lim (N→∞∕ j fixed) (-log P_N (jF)⁄N)

assigns an explicitly constructed GLOBAL PROBABILISTIC SIGNIFICANCE to the difference of measure 0 between the two above mentioned entropic forms. Which the theorem of big numbers, that deals with the individual differences ∣ f _i,j - p_i ∣, does not. And notice that the quantity logP_N(j)⁄N) cannot even be separated from the global expression where it is contained, it is organically involved in it. So the assertion

Ω ( jF ⁄{ p_i } ) = lim (N→∞∕ j fixed) (-log P_N (jF)⁄N) ≅ 0

is much more complex than the mere well known statement equivalent to the theorem of big numbers that “the faithful statistics has a probability to be realised which, nearly certainly, is nearly 1”.

(b) The opacity functional defines for ANY statistical distribution j constructible on the universe of elementary events generated by the considered basic random phenomenon, and inside the calculus of probabilities, a numerically estimated “distance” from the probability law that is supposed to act.

(c) The opacity functional brings into evidence the whole conceptual and mathematical genesis – inside the calculus of probabilities – of both entropic forms, that of statistical entropies and that of probabilistic entropies. Thereby it makes perceptible that, while from an exclusively numerical point of view Shannon’s writing Σ_i p_I log p_i is indeed – nearly – founded inside the theory of probabilities, it involves the occultation of the quite essential conceptual distinction between “f_i,jF“ and “p_i“.

(d) And above all, the opacity functional achieves an explicitly understandable UNIFICATION between the theory of probabilities and Shannon’s theory of information, where all the semantic contents are brought into full light. Whereas in Shannon’s approach the concept of a probability law had been only juxtaposed to the specifically communicational (“informational”) approach, and the “entropy of a probability law” had simply been directly posited, in the absence of any probabilistic deduction.

In short : the basic question of the very existence of some relation between statistical entropies and probabilistic “informational” entropic forms, is finally answered positively, while the content of this relation is specified with detail, in probabilistic terms.

The probability tree of a microstate and the first break-through of the goal to build a method of relativised conceptualisation

In 1984 I published the first expression of what I later called the general method of relativised conceptualisation (MRC) (8). This initial expression was still devoid of autonomy and largely implicit. It appeared as a specificity of the conceptual organisation of the quantum mechanical descriptions of microstates, while I drew into evidence the non-classical probabilistic structure cryptically incorporated in the quantum mechanical algorithms, considered globally (9). I called this structure the probability tree of a microstate.

Later, I developed separately the specific consequences which the awareness of the existence of a probability tree tied with any microstate, entails from an epistemological point of view (10,11) and I furthermore established relations between these probability trees, with quantum logic (12), and on another hand, with the classical theory of probabilities and with Shannon’s theory of “information” (13).

While I was achieving these works on quantum mechanics and on the insertion of this theory in the general logical-probabilistic-informational thinking, I found myself caught in a parallel process : I was developing now in explicit terms an independent and self-sufficient GENERAL method of relativised conceptualisation (14,15,16,17). The descriptional essence of this method, materialised in a particular form, had been first isolated out of the quantum mechanical algorithms which concerned exclusively the special case of microstates. But now I was trying to re-express this essence in quite general terms, and I was rooting it into quite general descriptional aims, principles, and constraints.

Thus, starting from 1984, my research underwent a bifurcation. On the one hand I continued to strive to reach a genuine “understanding” of quantum mechanics, accordingly to my own structure of curiosity and my own standards concerning analysis, rigor and global coherence : these standards, compellingly, required a full elucidation of the epistemological organisation that underlies the formalism.

On the other hand I found myself irreversibly engaged in a very long process of elaboration of an independent and self-sufficient general method of conceptualisation, required such as to exclude by construction any ambiguity of significance wherefrom false problems or paradoxes would be permitted to spring.

The general method of relativised conceptualisation (MRC) ⁷

While creating this second, radically constructive direction, it appeared to me more and more clearly that any knowledge susceptible to be communicated without any restriction – in contradistinction attitudes, gestures, exclamations, etc., to which one can pertinently associate significance only if directly perceived, in their context – is DESCRIPTION : unrestrictedly communicable conceptualisation, and “description”, superpose. So, in fact, what I was trying to erect could also be regarded as a general method of norms for describing in a way that should eliminate a priori any source of semantic ambiguity. Step by step, the semantic contents of descriptional conceptualisation subjected to such norms, had to be made precise, stable. And the whole trajectory of the process of conceptualisation had to be kept retraceable so as to offer an uninterrupted possibility of control and retro-modification. Semantic content had to be brought under full domination.

It appeared progressively that the necessary – and sufficient – condition for the possibility of a method of conceptualising under these constraints, consists of an explicit and systematic RELATIVISATION of each descriptional step, to a corresponding triad of basic descriptional elements, namely :

* an operation of generation of the “object-entity” to be described (a radically creative operation, or only an act of selection, or a combination of both) ;

* this “object-(of future description)-entity” itself ;

* a structure which I called a “view”, built in order to qualify the generated object-entity accordingly to, exactly, the nature and characters of the researched data concerning it.

Why the relativisation to such a triad, of each descriptional cell, is indeed a necessary and sufficient condition for the production of a semantically non-ambiguous descriptional cell that corresponding strictly to a well defined descriptional aim, cannot be fully understood without having first decrypted how, on the basis of which quite specific methodological organisation, it has been possible to construct descriptions of these unobservable hypothetical physical entities called “microstates” ⁸.

Indeed, systematic relativisation of each act of description, to a corresponding triad of the sort specified above, induces into the whole volume of the conceptualised, the structure of a network of chains of relative descriptional cells where, in any stage of the process of conceptualisation, any descriptional element can be re-attained, re-examined, its semantic consequences can be checked, and each achieved descriptional cell stays permanently open for retro-active modification. This structure, with its conditions of possibility, re-organises the epistemology into a rigorous and coherent methodology, rooted into the modern scientific thinking introducing explicitly the notion of descriptional aim. Which amounts to a certain technology of communicable and consensual conceptualisation.

The method of relativised conceptualisation structured as indicated above, brings into evidence a fact of fundamental importance.

The very first, the primordial relative descriptions from which any descriptional chain stems, always, are rooted (more or less deeply) into A-CONCEPTUAL PHYSICAL FACTUALITY.

These primordial descriptions possess a very peculiar type of descriptional structure which up to now had remained entirely unknown. I called it basic or TRANSFERRED description (transferred on registering devices of “measurement apparatuses”, natural biological devices, or instrumental artefacts).

Any subsequent descriptional cell from any chain looses this basic structure of a transferred description and acquires instead a structure of radically another type of which the genesis starts by modelisation of transferred basic descriptions. A “modelisation” then evolves by loosing all the ties with the primordial transferred descriptions from which it stems, thereby becoming a “model” which, subsequently, can undergo indefinitely progressive complexifications.

The whole “classical” thinking works with models in which the umbilical cord that connected them with this or that primordial transferred description, has been entirely
suppressed, most often unconsciously, and has got lost for knowledge.

So MRC brings into light what follows.

* At any given time, the whole volume of the conceptualised is entirely traversed by a cut that divides it in a basic layer of – ignored – primordial, non-classical transferred descriptions, and another, increasingly thick stratum of more or less complex classical models.

* These classical models – exclusively these – have commanded the whole organisation of classical logic, classical probabilities, classical science and current thinking.

* The general cut [(transferred descriptions)-(classical models)] includes the famous cut between quantum mechanical descriptions and classical thinking, and it explains it.

* The general concept of transferred description includes the quantum mechanical descriptions of microstates (cf. in 16, 17).

These elucidations lead to major consequences in many respects. But the most important one is a deep unification between logic, probabilities, and information theory.

I cannot get here into details about these quite essential unifications. But I must just mention one result of which the importance, I think, is particularly outstanding : lately (since the years 1980, shortly before his death, Kolmogorov became aware that

« The frequency concept (of “probability”) which has been based on the notion of limiting frequency as the number of trials increases to infinity, does not contribute anything to substantiate the applicability of the results of (the abstract) probability theory to real practical problems where we have always to deal with a finite number of trials »⁹.

So he required that, since nobody knows how to define a factual probability law in a given physical “probabilistic” situation, his abstract theory of probabilities be regarded from now on as exclusively a chapter of the abstract mathematical theory of measure, and that it be banished from any pragmatic use of the concept of probability. Which, for physicists, appears as a conceptual disaster (in so far, of course, that they are acquainted with the problem, which is not frequent at the present time). Now, inside MRC this problem has been solved : an algorithm has been constructed that permits to identify the factual probability law to be asserted in any given physical “probabilistic” situation (17, 21).

As already asserted, the MRC-organisation of the processes of conceptualisation – which from the start on is realised in a qualitative but FORMALISED way – does effectively realise the initially posited aim to exclude a priori, by construction, any possibility of emergence of semantic ambiguities, hence of false problems and paradoxes. This happens in consequence of the fact that an explicit and systematic genetic relativisation of each descriptional action, is equivalent to a precise semantic specification of the obtained conceptual construct. Quite contrary to what language might suggest, descriptional relativisations are directly opposed to “relativism”. “Relativism” stems from an initial ABSENCE of relativisation. Indeed the absence of a rigorous, built-in, explicit and systematic genetic relativisation, carried out on the basis of a method constructed from A to Z in explicit terms, leads to formulations which usually – once they are already produced – are strikingly perceived as devoid of general validity. This is intuitively traced down to a need for specifications. Then these specifications are just superposed a posteriori and in an unorganised way. And this, in its turn, is felt to be arbitrary and therefore it is finally opposed under the verbal label of “relativism”. So “relativism” is a call for genetically incorporated descriptional relativities that should bring forth only descriptions with a well specified semantic content. It is a call for a method of relativised conceptualisation.

MRC constantly assigns a major role to what I called the consciousness-functioning of the observer-conceptor, the human being who observes and conceptualises. It is by actions of this consciousness-functioning that, throughout any process of conceptualisation, are decided step by step and freely, the next descriptional aim, so also the choice of the next operation of generation – constructively, in general – of an object-entity to be produced for subsequent qualification, and of the view to be organised in order to achieve the qualification of this new object-entity, in strict conformity with the observer-conceptor’s cognitive aim. This amounts to asserting that the acting consciousness-functioning constantly decides on the direction of conceptualisation. However the technical modalities of the separate elaboration of each descriptional cell, is entirely dictated by the method.

In consequence of the role played by the consciousness-functioning, a robot or a computer – alone – might never be made able to pass from one descriptional cell, to another one. But a robot or a computer endowed with a program obeying the method and guided by a man who would enter in it, in MRC-language, his own descriptional aims, would work for this man accordingly to MRC, rapidly and accurately.

This might be useful for specialists in the domains of computation and of robotics. More particularly, it might be of interest for all those who try to computerise the human
representations of “complexities” and to define “measures” for these.

Traditionally, the emergence and the elaboration of knowledge are studied from a point of view founded on neurobiological and psychological data and they are researched as a “neutral” description of, exclusively, natural facts. This tradition is continued in modern cognitive science.

MRC involves a radical break with respect to this tradition. Quite deliberately, the aim of MRC is to diverge from the mere description of the natural modes of conceptualising, replacing them by techniques for conceptualising under explicit constraints able to lead to a non natural realisation protected from any semantic ambiguity, of this or that descriptional aim, chosen freely.

All the other techniques drawn from the exact sciences, diverge deliberately from the “corresponding” naturally available processes, in a manner which permits to construct artefacts able to meet objectives tightly specified beforehand. Why should precisely conceptualisation – that which creates any knowledge – be deprived of the right to benefit from technicalities ?

The infra Quantum Mechanics

While the method of relativised conceptualisation was being developed, its roots, hidden in the mathematical algorithms of quantum mechanics, were progressively undergoing a process of elucidation. This process has finally yielded a quite notable global result, linked at the same time to my researches in the domain of physics and to those concerning epistemology :

- on the one hand the mentioned global result founds MRC into fundamental quantum mechanics in a manner which, at last, has become entirely explicit and very detailed ;

- on the other hand, it also constitutes an INDEPENDENT, self-sufficient new discipline which I called Infra Quantum Mechanics (18), the nature of which is unprecedented : it is “a physical-epistemological” theory of microstates.

Infra Quantum Mechanics is a strictly qualitative description of microstates, constructed after having made tabula rasa of the mathematical formalism of quantum mechanics, by proceeding on the basis of the constraints, upon a human being who decides to construct knowledge concerning unobservable “microstates”, that stem from – exclusively – the cognitive situation in which this human being finds himself and the requirements of the general human modes of conceptualising.

Those who know the quantum mechanical formalism can easily recognise in the descriptional form obtained inside Infra Quantum Mechanics, the epistemological essence of this formalism. But they will equally discern features which are hidden by the quantum mechanical algorithms and of which the presence, as well as the importance from various points of view, leap to one’s eyes. Furthermore certain suppositions and ways of reasoning which inside quantum mechanics nurture interpretation problems, come out to be unfounded when these problems are confronted to the genesis and the structure of Infra Quantum Mechanics.

Quantum Mechanics freed of interpretation problems ?

In these conditions it seems permitted to hope that a systematic comparison between, on the one hand, Infra Quantum Mechanics and MRC, and on the other hand the formalism of quantum mechanics, will be able to lead to a coherent elucidation of the set of all the interpretation problems by which quantum mechanics is afflicted since more than 70 years (19).

Junction

So the two directions of research brought forth in 1984 by a bifurcation mentioned before, one contained in the domain of physics and the other one in the domain of
epistemology, might finally join up inside a quantum mechanics of which the way of signifying would be exposed to full sight.

Retroaction of the junction upon MRC

In its turn, this junction is now retroacting upon MRC : it brings into evidence the possibility of a mathematical formulation of the method in terms of multidimensional
description-vectors, which will permit numerical estimations of the results of certain general descriptional operations (comparisons, representations of relative complexities, etc.). For the case of classical descriptions involving models, this formulation will loosen the restrictions involved by the quantum mechanical description of microstates by the help of Hilbert vectors, which, in the case of non-transferred descriptions, in general are not pertinent. (Another mathematical formulation of MRC, in the terms of the theory of categories, has been already sketched out before (16), but, while it permits to expresses certain deep semantic aspects concerning the different sorts of descriptional elements defined in MRC, it seems to be devoid of interest for current pragmatic applications of the method ; whereas a representation in terms of multidimensional description vectors would probably be very useful in this respect and furthermore, it might be able to incorporate into MRC Shannon’s communicational formalism).

The « Centre pour la Synthèse d’une Epistémologie Formalisée » (CeSEF)

In 1994, much before leaving my teaching activity, together with a group of specialists in other domains of research, I founded the Centre pour la Synthèse d’une Epistémologie Formalisée (CeSEF) of which the aim was to construct a modern and formalised epistemological method that would have to take into account the specific normative features from the various nowadays scientific domains of major importance (biology, computer science, cognitive science, mathematics), and also the modern philosophical thinking. This aim has been formulated in a manifest published in the review Le Débat edited by Gallimard (20).

In 2002 the group published with Kluwer Academic Publishers a collective volume (21) where are exposed achievements and views already formed at that time. My own contribution to this book covers 200 pages and it contains the first satisfactory formulation of the (genetic) MRC-logic and the (genetic) MRC-probabilities UNIFIED in ONE whole deeply rooted into physical factuality via basic transferred descriptions.

The CeSEF is still active. However today the formalised epistemological method which since 1979 I never ceased to develop, is fully achieved in its essence (15,16,17,18), accordingly to my own standards and aims.

Program

In my present perspective, what still remains to be achieved, is mainly this :

- the full decoding of the quantum mechanical formalism and – correlatively – its full liberation of interpretation problems (18) ;

- the mathematical re-expression of MRC in terms of a calculus with multidimensional description-vectors, entailing the incorporation into MRC of (a) Shannon’s theory of communications, (b) of the representation and measures of relative complexities accordingly to the features already sketched out in (17), and (c) of the quantum mechanical Hilbert-Dirac formulation (i.e. a representation of fundamental quantum mechanics as a particular instance of a physical-epistemological calculus).

- the development of various rigorous and detailed applications of MRC to pragmatic problems, like for instance the question of management of risks and dangers.

Profession of faith

I am convinced that more or less immediately MRC – drawn from the most basic modern physical theory that roots the knowledge produced by it directly into the still a-conceptual physical factuality – will intimately join with the modern approaches developed in neurobiology, psychology, cognitive science, genetic biology, informatics, robotics. When this will have happened, our understanding and technical domination of our own ways of producing knowledge, will have made a big jump.

Neuilly-sur-Seine, February 2008.