I Ching and Information Theories (1/ 2)

""When one has well understood that experimentation depends of an anterior intellectual construction, one looks for proofs of the consistency of concrete in the abstraction." " _Bachelard, "Le nouvel esprit scientifique"_ (extract translated from French)


  • I. - Epistemology and scientific patterns.

  • II. - Patterns, analogy and isomorphism.

  • III. - Auto organisation Theories

  • IV. - Chaos Patterns

  • V. - Auto referential patterns

  • VI. - Incompleteness Theorems

  • I. - Scientific Epistemology and patterns.

    "The scientific progress consists to find to the founding apories (*) some temporary solutions of which posteriors progresses will show soon the illusory character. _René Thom, magazine "Autrement" No102, November 88_ (extract translated from French).

    The complex systems are those which number of control parameters is infinite. The reductionism vision recommended until then to break the "black box" in order to reduce this complexity... that could be not the most adequate method, especially about living systems! (even if Claude Bernard's experimental method duly made his proofs...)

    Issued from formal logic and cybernetic, the powerful theories of information are able to make a pattern for complex systems : systemic and auto organisational patterns, auto referential and catastrophist patterns (chaos theory).

    (*) Apories: dead ends, meaning problems founding each scientific disciplinary.

    II. - Patterns, analogy and isomorphism

    ...It's in improving our understanding of the analogy that one will have chance to resolve or limit these founding apories, and to reveal thus a best intelligibility of real."" _ René Thom, op. cit._

    While specifying the idea of analogy, the concept of isomorphism (1) induces the idea of scientific pattern.

    An isomorphism designates the identity of structure between two groups (algebraic, topologic, etc.) between whom exists a bi-univoque correspondence who maintains invariant the relations characterising the structure.

    So the DNA (2) of one living cell is isomorph to the complete organism...

    In the human sciences, the sense of isomorphism is made tasteless, because excessively assimilated to any correspondence.

    Douglas Hofstadter (1980) will react to it in attempting to distinguish between "prosaic isomorphism" and "mannered isomorphism." When the first are only a correspondence from element to element, that is to say a simple bijection, the second assumes a reciprocal correspondence between the internal relations between these elements, defining an identity of structure between two sets..

    Math. sample :
    Cantor, in demonstrating the existence of an isomorphism between the subset of real numbers between 0 and 1 and the all group of real numbers, showed that parts of a set could possess the same number of elements and the same structure that the all set.

    Other examples :

    - In psychoanalysis, between the psychic bases of the individual, and (the hypothesis of) a collective unconscious.

    - In social psychology, between human institutions having a history and a consistency.

    - In data processing: between the Unix core and the Internet network architecture.



    (1) One calls isomorphism of an E set, supplied with an internal T law of composition, toward an E' set, supplied with a T' internal law of composition, a f bi-univoque correspondence element to element of E toward E' and who makes also correspond the T and T' internal laws of composition.

    (2) Desoxy ribo Nucleic Acid : discovery by Watson and Crick this biochemical molecule supports genetic code (Lwolf, Monod and Jacob, 1972)



    III. - Auto-organisation theories

    Theories of auto organisation are issued from various and apparently distant disciplines :

    - Cybernetic (Norbert Wiener);

    - Thermodynamic of irreversible processes and of systems far of the balance (Ilia Prigogine);

    - Biochemistry and Biophysic (Mr. Eigen);

    - Neurophysiology (H. Maturana);

    - Immunology (François Varela);

    - Artificial intelligence (H. A. Simon, A. Newell);

    - Experimental and natural epistemology (H. Von Foerster);

    - Sciences of organisation, communication and complexity (C. Shannon, H. Haken, Henry Atlan, Isabelle Stengers, Edgard Morin, Jean Jean-Louis The Moigne, E. Jantsch, Paul Vendryes, Jean Pierre Dupuy, Douglas Hofstadter, Abraham Moles, etc.).

    Since Von Bertalanffy (1925, 1947) and his General Theory of Systems (G.T.S.), the notion of auto-organisation is present. As capacity for a system to grow toward more organisation and complexity, it is melt to "the aperture" inherent to all living system, that is to say to his capacity of maintaining unceasing exchanges of matter, energy and information with his environment, and to regulate in the most adapted way, his metabolism.

    For Henry Atlan, these "noises" become events of the proper history of system, by the effect of auto-organisation.

    Since the system is able to reacting such a way to don't disappear; it modifies himself by integrating these noises to his own organisation in a sense who he assures his survival. Then, saw from inside the system, these "noises" lose a little their perturbing character and become factors of auto-organisation...

    But "noises" induced in the system by uncertain environnement factors constantly perturbing the shaky balance of living, threaten the maintain of homeostasis. However all elements and relations who constitute a living system cannot be known : the observer is necessarily outside to the system. It is the famous Shannon idea of "black box".

    Observation of the system from outside allows to deduct the inside point of seeing, to modelise what happens in the "black box", taking account of eventual noise or interference produced by the presence of the observer or by observation devices.

    (for example in animal ethology).

    Auto organisation is considered like a phenomenon of increasing complexity (structural and functional) by a process where new information, integrated to a level of weaker redundancy, becomes inherent to the system.

    Example: accommodation and assimilation in genetic epistemology (J. Piaget)



    (*) It is the reaction of system itself that makes that external events are considered like perturbing ("noises") or on contrary belong to its organisation, its history, its information.



    Summary of this page

    Next Page