The Project

State of art

Such common ideas as “natural entity” as opposed to “man made entity”, “persistency”, “state”, “system”, “function”, “complexity” are either :

• Merely qualitative¹: such as Qualification, System, Complexity;
• Or operational, dedicated to some specific aim: such as informational Entropy, thermodynamic entropy, function;
• Or imported from mathematics², with their ambiguities: such as Continuity, State

1. Aristote (IV siècle av J-C) La Physique
2. Gabriel Stolzenberg(1988) Une enquête sur le fondement des mathématiques

The goal

Rooting scientific fields, traditionally regarded as various in essence, in a unifying methodological framework, both securing their scientific character and formally integrating human finalities.

A former Schrödinger’s ambition

"Explicitly introducing so much in our knowledge building as in our innovations processes the human finalities which drive our way of tackling Reality, but that, without questioning the principles of generality, of accuracy and of refutability which have fostered our adaptive success, but on the opposite endowing them with new foundations to optimize the control of our destiny³".

3. Freely inspired by Schrödinger, E. (1951) Physique quantique et représentation du monde

The obstacle to overcome

Attempts to scientifically introduce a drastic constructive approach have all come up against a core question:

If any entity is a built concept, how can we consensually refer to what is relatively described ?

Till now, modeling relativized viewpoints has always entailed, on the opposite, to depict in an absolutizing way the “entity-to-be-described”, there and now, to refer to what is described.

Stake : intersubjectivity

Founding: the Method of Relativized Conceptualization (MRC)

Why MRC ?

The Method of Relativized⁴ Conceptualization (MRC) is a method of general scope, radically constructive, which stems from cognitive situations entailed by quantum physics, such as pinpointed by Pr. Mioara Mugur-Schächter underneath mathematical formalism:

• MRC focuses on the intersubjective conceptualization of a preexisting physical Reality;
• MRC conforms to a nearly mathematical formalism, built according to the rules of classical syllogistic;
• Up to now, MRC is the unique method systematically relativized which openly questions the field of so called “hard” sciences.

4. Pr. Mugur-Schächter (2006) Sur le Tissage des Connaissances

Within MRC, any scientific description is relative to:

• Some finality ("building knowledge");
• Some physical field of Reality and a way of operating and qualifying, as consensually conceptualized out of preexisting knowledge;
• A qualification grid to code physical marks.

Any described physical entity is an invariant that springs as a causal node, from the statistical stability of marks resulting from the repetition of a same operational process

• Principle straightforwardly stemming from quantum physic.

Genesis of MCR

The Method of Relativized Conceptualization (MRC) emerges from a long meditation on the very specific cognitive situation entailed by quantum physics where neither the ground on which we operate nor what is qualified are perceptible by our bio psychological senses…

… and where experiments challenge common sense and classical causality.

This reinterpretation puts forth that arbitration between both approaches depends on the conceptualization of what is genuinely qualified by the experiment: one or several entities… what experimental conditions don’t make possible to assert.

5. Mioara Mugur-Schächter, Einstein 1879-1955 (6-9 juin 1979), colloque du centenaire, Collège de France, Editions du Centre National de la Recherche Scientifique

MRC core

We strive to describe something we are an inner part of.

MRC comes as a quasi formal methodological framework.

Pr M. Mugur-Schächter has undertaken MRC as a development of general scope with the intention to apply it then to the specific case of Quantum Physic whence it has originally emerged. This has led to the proposal of a second quantum mechanism, MQ2, endowed with a measure theory.

MQ2 consists in a intelligible reinterpretation of Hilbert-Dirac⁶ formalism

6. Mioara Mugur-Schächter (2017), PRINCIPLES OF A SECOND QUANTUM MECHANICS rooted in factuality and constructed bottom-up,  arXiv:1506.00431v4 [quant-ph]

SR approach

Vision

Individual psyche is the original starting point of any built intersubjectivity.

We postulate a common way of human being.

We conceptualize Reality out of the meaning we project on the interactions localized in space and time we use to delineate the field of Reality we focus on out of the substratum we are part of.

Making this mechanism explicit is bound to optimize the construction of our collective achievements.

We believe this is the key for a brand new scientific approach that substitutes an operationally efficient intersubjectivity for the classic objectivity concept.

RS representation space

RS representation space has shaped up from an interpretation of concepts and dependancies pinpointed underneath MRC formalism.

Three epistemic sites make up the framework to figure out constructive processes.

RS concepts are built within this framework from a unique entity class : The formalization of the MRC concept of transferred or basic description.

Formalism has imposed new conceptual developments to live up to the requirements of the Category Theory :

• To account for the way we conceptualize a starting ground, R_G, on which to operate;
• To set up the conditions which legitimize the postulate that the generated entity and the qualified entity are the same oe_G entity – the described entity;
• To set up a limit to the endless regression mechanism induces by the fact a new knowledge may only emerge from pre-established knowledge : primordial descriptions.

These conceptual developments have required as a prerequisite the setting up of a new definition : the intersubjective description of a psychical entity. It bridges the gap between the imaginative component of any innovative approach and factuality such as it can be described.

• Anticipation : the description of a psychical entity that calls for a physical description;
  • Forecast, project, hypothesis, …
• Realization : a physical description whose modus operandi conforms to the framework given by an anticipation;
  • Description whose epistemic referential is more or less tightly defined by anticipation
• Evaluation whose meaning depends on active finality: comparison between anticipation and conforming realizations.
  • Hypothesis validation, testing of some realization against design documents, knowledge building within a framework shaped up by some intuition, ….

A snapshot of RS formalism:

RS construction of classical concepts

What for ? To avoid conceptual confusion resulting in pitfalls, ineluctable consequences our absolutizing and spontaneous way of conceptualizing reality out of our biopsychical perceptions …

... To better use these “classical” concepts once reintroduce in a controlled and relativized way.

A snapshot of the logic of construction:

To achieve this construction it has been necessary to come up with two operators defined as meta descriptions, operating in a relativized way on transferred or basic descriptions:

• An operator “ᴧ” : descriptional conjunction : set of descriptions co-generated by n-repetitions of the same operating process;
• An operator “ᴠ” : descriptional disjunction : conceptualization of unique entity concept out of separately built descriptions.

These operators are endowed with specific conditions that determine the subsets of descriptions they are applicable to. That feature differentiates them classical operators that may operate on whatever elements of their definition set.

These two operators are associated through the following implication:

RS regards physical State as a modality of existence of an entity. This modality is relative to a viewpoint on the conceivable possible in a future bounded in space and time. Any entity exists only in a given State, relative to the active viewpoint.

The equivalence relation associated with this viewpoint and the considered future formally define a State.

The RS State concept endows the Turing machine with a precise physical meaning which associates calculability and predictability and may be used as a starting point set up a physical Theory of Probability.

Exemple of a car offering a safety feature preventing from releasing the brakes unless the doors are closed and the engine is running:

Exemple of conjunction:

Exemple of disjunction:

RS concept of System

As for any RS entity a System is the product of an explicit generator G that consists in a physical-conceptual operation, which may be purely conceptual, for example when we “recognize” some “pre-existing” entity in given context such as a tree in a wood.

The concept of System emerges when we consider that this entity as made up of persistent “components” whose interactions explain its characteristics as a whole, from a given viewpoint V, in a deterministic or statistical way:

• The acceleration of a bicycle resulting from a force on pedals, pulling the bicycle chain and eventually the wheels (its “components”);
• The pressure of a gas as resulting from collisions between molecules (its “components”).

This is not the case for mayonnaise if we consider it is made up of eggs and oil. But if we consider it is made up of lipid and protein molecules, their chemical bonds may explain mayonnaise consistency which then may be regarded as a System.

Therefore an RS entity may be regarded as a System from a given viewpoint and not from another one, relatively to the way it is conceptualized.

RS concept of complexity

A given entity may simultaneously be regarded as a “component” by distinct Systems.

If the entity qualifications relative to these different Systems are closely correlated and unstable, that if any interaction involving this shared “component” modifies its qualifications relatively to all these viewpoints, ...

... then one may intuitively sense that complexity is maximal: any interaction with this entity that changes a given System characteristic also impacts all the other Systems.

RS makes it possible to quantify an entity complexity relatively to a finite set of viewpoints and to the potentialities of a given context. This possibility results from the way RS considers the relationship between models and factuality, which culminates in the definition of a physical theory of probability.

Modeling versus Reality: the RS proposal

Any “factuality” comes as finite sequences of “events” localized in space and time.

Any attempt to grasp physical Reality basically relies on statistical series of data, either all the same (MRC n-stable description), or different but sufficiently converging to be meaningful, according to adopted criteria.

The stake is therefore to come up with an explicit relationship between these series of data and the a-temporal models we devise to figure out a stable Reality. For this determines the scientifically “objective” (intersubjective) character of our representations.

This amounts to regard the physical meaning of the theory of probability as the key problem yet to be solved.

Indeed, RS postulate leads us to consider that interpreting statistical series of data as different manifestations of the same law of probability amounts to some kind of implicit conceptualization of a physical substratum described by this law of probability.

Once a relativized definition of the concept of probability is achieved, it may be used as a starting point to come up with general definitions of entropy and of complexity.

Theory of Probabilities : shortcomings

Existing definition of the concept of Law of probability is based on the law of large numbers. When used to describe physical Reality, this definition is unsatisfactory in two aspects:

• The definition refers to itself: a Law of probability is defined as the probability that …
• It poses infinite series of events while any physical process is finite.

Furthermore, Kolmogorov’s spaces involve event algebra without any physical definition of the concept of “event”.

Kolmogorov himself was aware of these shortcomings and stated that the Theory of probability could not be used as it is for scientific purposes⁷.

7. Kolmogorov, N.A., (1983) "Combinatorial foundations of information theory and the calculus of probabilities", Russia Mathematical Surveys, 38, pp. 29-40.

RS Probability theory

RS postulate imparts to the concept of Law of Probability the status of a relativized description according to MRC: it is symptomatic of a certain way of conceptualizing Reality inferred from this particular structure of values. This makes it necessary to specify:

• The epistemic referential (G.R_G, V);
• The convergence criteria;
• The postulated conceptual structure imparted to oe_G, the entity whose existence itself is postulated out of the fulfillment of convergence criteria.

The RS definition of the concept of probabilistic description generalizes and formalizes the MRC concept of description of physical entity. It focuses on the kind of conceptualization structure inferred from different kinds of statistical structure of qualifications, what leads to identify three classes of description:

• N-stable descriptions;
• Statistical descriptions;
• Probabilistic descriptions.

RS Probability Theory springs out of a physical interpretation of the Law of large numbers in which the event algebras of Kolmogorov’s spaces emerge as a consequence of several competing viewpoints on the product of a unique generative process, considered together. It relies on the RS relativized concept of physical State.

A Law of Probability is no longer regarded as the limit towards which converge statistics of realization of such or such value. It figures the propensity of a given entity to exist in a given modality (physical State) relative to a given viewpoint that encompasses one or several aspects. This propensity is regarded as a consequence of a conceptualization of this entity generator insufficiently specific relatively to the accuracy of the qualification grid associated to the adopted viewpoint⁸.

• This insufficiency may be wanted (game of chance), it may reflect a limit in our knowledge (causality yet to be figured out), it may also be regarded as an absolute limit of the qualifying interaction (Planck’s constant).

8. Popper’s principle of generality and accuracy - Popper, K. (1935) (2002). The Logic of Scientific Discovery, Routledge Classics.

RS Entropy and Complexity

On the basis of this physical probability Theory, RS has devised a general and physical concept of Entropy. It endows the purely mathematical expression of Shannon’s entropy with a clear physical meaning.

This relativized Entropy measures:

• The stability (based on RS relativized State concept) of a physical entity relatively to a viewpoint and its conceivable interactions with a given context;
• The emergence of “protruding” States.

The RS Complexity concept complements this conceptual construction: it measures the level of entanglement of several viewpoints on the same entity relatively to the conceivable interactions with a given context.

It depends on:

• The Entropy specific to each considered viewpoint;
• Common modes to the generators of the States relative to the involved viewpoints.

We may figure out this concept considering that if any impact on the considered entity that changes some aspect also change all the other aspects then, Complexity is maximal. As mentioned here above, these different aspects are usually associated with roles imparted to this entity by different Systems.

RS developement mapping

The figure here after sums up the constructive dependencies that associate operational developments achieved with the fundamental level at which stands Relativized Systemic.

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