Dear Andrei,

Contests FQXi - is primarily a contests of new ideas. You have given a deep analysis of the modern fundamental science and offered new ideas: "new mathematical basis for the causally complete and intrinsically sustainable scientific knowledge, in the form of extended unified mathematics of unreduced dynamic complexity."

I fully agree with you that the problem of modern fundamental science - this is a problem of knowledge base, especially mathematics:

"Usual mathematics does not propose the consistent, unreduced solution to the arbitrary, real interaction problem, while it is the development of such many-component interaction processes that gives rise to all observed phenomena and structures (of increasingly complicated configuration for modern tasks). "..."Any real interaction in the three-dimensional world, including large numbers of interacting components and their eigenmodes for real cases of interest, falls far outside of those limits of "integrable" problems within which that kind of explicit solution provides the adequate picture of reality. "

I agree with your conclusions:

"The outlined crisis in today's exact sciences and knowledge system in the whole suggests only one kind of "really good" solution: the new, explicitly extended and now intrinsically complete content of rigorous, mathematical description of reality, leaving no place for postulated supernatural mysteries, arbitrary guesses and impasses of development."

"The critically acute modern problems of "complexity crisis" in both fundamental science and real world development find thus their universally applicable solution within the framework of extended mathematics of complexity presented above, and we also show why exactly they cannot be solved within the artificially restricted unitary science paradigm."

I think your concept of "new mathematical basis" is very urgent and requires a broad discussion among mathematicians and physicists.

I have only one question for clarification(like "lyricist"): how you present "consciousness" mathematically?

I invite you to see my analysis of the philosophical foundations of mathematics and physics, the method of ontological constructing of the primordial generating structure, "La Structure mère" as the ontological framework, carcass and foundation of knowledge, the core of which - the ontological (structural, cosmic) memory and information - polyvalent phenomenon of the ontological (structural) memory of Universum as a whole. I believe that the scientific picture of the world should be the same rich senses of the "LifeWorld" (E.Husserl), as a picture of the world poets and philosophers.

Kind regards,

Vladimir

    Dear Vladimir, Thank you for your interest in and the support of my ideas. Me too I hope that eventually the objective, most consistent truth will prevail. As to the rigorous description of consciousness within the proposed framework, it emerges as a particular, high enough and well specified level of the same, universal and rigorously defined dynamic complexity. Specifically, it starts with the level of "bound", i. e. locally quasi-fixed structures (in the conscious brain) representing those of external world, while lower-level, unconscious intelligence can contain mainly "free", unstable high-level structures. You can find more details in my recent book available on line (actually since 2004). I'll have a look at your essay, which apparently deals with a yet deeper origin of reality.

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