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**Andrei Kirilyuk**: *on* 4/12/15 at 13:00pm UTC, wrote Dear Vladimir, Thank you for your interest in and the support of my ideas....

**Vladimir Rogozhin**: *on* 4/12/15 at 11:48am UTC, wrote Dear Andrei, Contests FQXi - is primarily a contests of new ideas. You...

**Andrei Kirilyuk**: *on* 4/11/15 at 17:08pm UTC, wrote **Discussion Abstract:** From Complexity Crisis to the New Science Age ...

**Joe Fisher**: *on* 4/7/15 at 15:46pm UTC, wrote Dear Andrie, I think Newton was wrong about abstract gravity; Einstein was...

**Andrei Kirilyuk**: *on* 3/31/15 at 18:25pm UTC, wrote **Discussion Abstract:** Conceptual Mathematics and Causally Complete...

**Andrei Kirilyuk**: *on* 3/23/15 at 18:21pm UTC, wrote **Discussion Abstract:** From Postulated Being to Dynamical Becoming ...

**Andrei Kirilyuk**: *on* 3/14/15 at 17:23pm UTC, wrote **Discussion Abstract:** To Be or Not To Be In relation to the current...

**Andrei Kirilyuk**: *on* 3/13/15 at 19:49pm UTC, wrote Dear Michael, Thank you for your interest and comments. Based on your...

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FQXi FORUM

September 17, 2021

CATEGORY:
Trick or Truth Essay Contest (2015)
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TOPIC: Extended Mathematics of Unreduced Dynamic Complexity: The Exact Image of Unified Reality, from the Electron to Consciousness by Andrei Kirilyuk [refresh]

TOPIC: Extended Mathematics of Unreduced Dynamic Complexity: The Exact Image of Unified Reality, from the Electron to Consciousness by Andrei Kirilyuk [refresh]

The current crisis in exact description of fundamental and applied systems has the well-defined origin and rigorously substantiated resolution in the form of qualitatively extended, unified mathematical framework of unreduced dynamic complexity. It is based on the unreduced universal solution of arbitrary interaction problem revealing the new, extended qualities with respect to traditional mathematical constructions. We describe the origin of the problem, the proposed causally complete solution and its mathematical novelties confirmed by problem-solving applications in fundamental and applied sciences.

Andrei Kirilyuk is a theoretical physicist (since 1979) and Senior Researcher at the Institute of Metal Physics, Kyiv, Ukraine. He also worked in France (Paris, 1991-95). He is the author of the Universal Science of Complexity, the intrinsically unified, causally complete and problem-solving extension of conventional theories.

Could the sequence to complexity be - technology ->new data -> mysteries (data inconsistent with models) ->ad hoc additions to the models (holding on by the fingernails to the status quo) ->`superstitions’ (metaphysics) -> complexity.

Perhaps the solution is a revolution in the concept of the model to encompass the mysteries and the established models. That is, a radically `new’ causality model is required. I had thought this is what the FQXi is seeking.

The Scalar Theory of Everything (STOE) model

started with a concept for one potential field to be the `space’ of general relativity and the medium (plenum) for the quantum mechanical wave. It has addressed many mysteries and corresponds to the Big Bang model and to Quantum Mechanics

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Perhaps the solution is a revolution in the concept of the model to encompass the mysteries and the established models. That is, a radically `new’ causality model is required. I had thought this is what the FQXi is seeking.

The Scalar Theory of Everything (STOE) model

started with a concept for one potential field to be the `space’ of general relativity and the medium (plenum) for the quantum mechanical wave. It has addressed many mysteries and corresponds to the Big Bang model and to Quantum Mechanics

report post as inappropriate

John, a priori there may be two general kinds of "revolutionary novelties" or "problem solutions", one centered on a "new entity" (until now unknown or neglected) and another one on a "new kind of dynamics/behaviour". My "unreduced complexity" and its "extended mathematics" is of the second kind, while your proposal is apparently closer to the first kind. While both kinds of novelties are not...

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Dear Andrei,

From a first reading, I find that your essay offers a very intriguing presentation of ideas, summarizing a rather wide-ranging set of concrete applications. Your approach sounds interesting and certainly novel, and deserves further attention. This will need more time.

I find it very intriguing your term "unreduced" in the context of your dynamic complexity framework. Although I do not have a complete understanding of what you propose at this point, I intuitively have a picture, and I think your point is relevant if related to the fact that we cannot really understand nature, in its all complexity, by using just reducible frameworks (that is, idealizations that are carried all the way "down").

We need a kind of "non-factorizable" dynamics. It is not just a question of how accurate one can describe nature, but the need for not eliminating the essential "ingredients" from the very beginning, because those are what really matter, if we want to make progress beyond models. It is not just a question of "adequacy", but re-analising how we approach our dynamical universe out there in an equally self-dynamical framework. If this is a reasonable interpretation of some of what you propose, even if at a basic level, then it is certainly compatible with some of my points.

Best regards,

Christine

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From a first reading, I find that your essay offers a very intriguing presentation of ideas, summarizing a rather wide-ranging set of concrete applications. Your approach sounds interesting and certainly novel, and deserves further attention. This will need more time.

I find it very intriguing your term "unreduced" in the context of your dynamic complexity framework. Although I do not have a complete understanding of what you propose at this point, I intuitively have a picture, and I think your point is relevant if related to the fact that we cannot really understand nature, in its all complexity, by using just reducible frameworks (that is, idealizations that are carried all the way "down").

We need a kind of "non-factorizable" dynamics. It is not just a question of how accurate one can describe nature, but the need for not eliminating the essential "ingredients" from the very beginning, because those are what really matter, if we want to make progress beyond models. It is not just a question of "adequacy", but re-analising how we approach our dynamical universe out there in an equally self-dynamical framework. If this is a reasonable interpretation of some of what you propose, even if at a basic level, then it is certainly compatible with some of my points.

Best regards,

Christine

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Thank you, Christine, for your kind estimate and keen understanding of my results. Yes, "unreduced" complexity is to make difference from imitative model "complexity" being just mechanistic "intricacy" of basically simple patterns (like entangled one-dimensional thread). The unreduced, "dynamically multivalued" version is indeed about non-factorizable and self-referential dynamics. And, following your hint, it's a kind of intrinsically creative and co-evolution framework, where interaction gives rise to complex-dynamical patterns that give rise to higher-level interactions, etc. That's why it emerges scientifically "as a whole", in the form of intrinsically unified multi-level structure and evolution.

Dear Andrei Kirilyuk,

Your observation and analysis "*shows a strange 'inverted-progress effect', where the number of difficult, 'unsolvable' problems, or 'mysteries', remarkably grows...*" and you note that "usual mathematics does not propose the consistent, unreduced solution to the arbitrary real interaction problem."

I know you are discussing a*far more general problem* when you urge consideration of unreduced reality (i.e., reality not reduced to 1-D or oversimplified models) but in some cases even a 1-D treatment represents progress over a 0-D current treatment. For example, John Bell analyzes the scattering of a particle in an inhomogeneous field by assuming that the field is constant (thus *zeroing out the gradient*) and assumes that the resultant scattering continuum distribution is reduced to a binary result. A less reduced (i.e., simplified) local model of the interaction of the particle with the unreduced field produces exactly the quantum mechanical correlations that are impossible with Bell's oversimplified model.

Thus, while your generalized approach focuses on the mathematics involved in the unreduced solution to the arbitrary real interactions problem, it is also the case that 'de-simplifying" the current approach in specific cases to merely a "less reduced" physically realistic model may pay dividends. I hope you will read my essay with this perspective, and provide feedback to me.

Best regards,

Edwin Eugene Klingman

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Your observation and analysis "

I know you are discussing a

Thus, while your generalized approach focuses on the mathematics involved in the unreduced solution to the arbitrary real interactions problem, it is also the case that 'de-simplifying" the current approach in specific cases to merely a "less reduced" physically realistic model may pay dividends. I hope you will read my essay with this perspective, and provide feedback to me.

Best regards,

Edwin Eugene Klingman

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Dear Edwin, thank you for your interest. I have looked through your essay and I think we have similar attitudes against excessive simplification of physical reality within usual mathematical models. You can find more details in my comment to your paper and the details of my solution to quantum-mechanical problems in respective references in my essay (see also the web outline of my Universal Science of Complexity).

Thanks for your response.

The STOE proposal suggests 2 entities (`space’ and QM wave medium) are only one entity. This is a simplification or replacement of the 2 with the one.

The idea of `correspondence’ is that the successes of the Big Bang and QM are incorporated in the new model. Thus, I don’t deny but affirm the successes. Additionally, the model solves some mysteries that have lead to complexity.

I presume the addition of components such as dark matter, dark energy, etc. is increased complexity. These are the `new entities’ you suggest. Therefore, do you deny them as I do?

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The STOE proposal suggests 2 entities (`space’ and QM wave medium) are only one entity. This is a simplification or replacement of the 2 with the one.

The idea of `correspondence’ is that the successes of the Big Bang and QM are incorporated in the new model. Thus, I don’t deny but affirm the successes. Additionally, the model solves some mysteries that have lead to complexity.

I presume the addition of components such as dark matter, dark energy, etc. is increased complexity. These are the `new entities’ you suggest. Therefore, do you deny them as I do?

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Yes, John, all conventional "dark" entities are but ghosts produced by lacking completeness of usual description (within my approach, I show why exactly, see e. g. [1,2]).

However, pretending for an*extension* of conventional picture, one should start from derivation of *all* usual fundamental entities and laws (hopefully without usual mechanistic "postulates" and contradictions), rather than only solution of *some* conventional problems. So what about electromagnetic, gravitational and other fundamental fields and intrinsic properties or elementary particle nature in your approach? Do you really derive this complete basic set only from your starting entities (even the latter should be somehow justified by real-world properties)? Because if you just add your new entity (at least one) to those usual basic ones, then there will be a new problem - see my previous comment.

However, pretending for an

Dear Andrei Kirilyuk

I am very impressed by your approach to address the issue that underlies the stagnation of results in fundamental science: unreducible states really exist in the world, and they exist in systems across the whole spectrum of science. There-exists a whole class of self-referential systems for which I have proven any physics theory modelling the system components directly...

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I am very impressed by your approach to address the issue that underlies the stagnation of results in fundamental science: unreducible states really exist in the world, and they exist in systems across the whole spectrum of science. There-exists a whole class of self-referential systems for which I have proven any physics theory modelling the system components directly...

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Dear Michael, Thank you for your interest and comments. Based on your description here and your essay and paper, I feel that indeed our attitudes on the incompleteness of standard mathematical and physical framework have much in common. I actually propose a provable version of the necessary completion applicable at all levels of world dynamics, from elementary particles (causally complete quantum mechanics and relativity) to the highest-complexity systems like society, conscious brain dynamics or intelligent communication networks (see my arXiv papers and web page for references). It remains to hope that such extended visions and approaches will finally win and bring fundamental science (otherwise stagnating) to the state of new progress...

In relation to the current situation in fundamental science, the estimates of the role and state of rigorous, mathematical description of reality apparently evolve towards

One of them, the “mainstream mathematical physics”, defends the existing, traditional development of mathematical description of reality by always

In the second attitude, one considers that the truly consistent, not only rigorous, but also

The

That explicit

The transition from the traditional, artificially simplified description to the proposed intrinsically complete mathematical framework corresponds thus to the transition from inevitably separated and often “strangely looking” usual projections to the full-dimensional and

The growing loss of certainty of modern, apparently successful mathematics is largely due to its tacitly increasing departure from the fundamental principle of

In the same way as the elements of physical reality interact and give rise to ever more elaborated structures and phenomena, the “abstract” elements of mathematical framework progressively form respective abstract structures and laws, according to rigorous derivation rules ensuring the result consistency.

However, another, qualitatively more abstract approach to mathematical description of reality has appeared and quickly grown especially in the age of “new physics” starting from the beginning of the 20th century, where the “final”, resulting mathematical structures and laws are somehow heuristically “guessed” and then simply postulated for further direct “confirmation by experiment”, but without the real, consistent derivation and logical understanding of their origin. In particular, their growing number appears even to be quite inconsistent, i. e. incomplete, contradictory and “mysterious” (quantum mechanics, relativity, gravity, “dark matter”, “hidden dimensions”, “broken symmetries”, etc.), but still “unreasonably efficient” and “confirmed by experiment”. This tendency of “mathematical physics” is reduced to never-ending trial-and-error attempts of direct postulation of a new mathematical “language” or “manifold” with its following “adaptation” to a limited set of “experimental observations”. No derivation and solution of a dynamic equation from first principles is involved any more in this now dominating approach (contrary to previous situation of few postulates and the majority of derived features), which strangely and increasingly resembles the ancient

Such kind of mathematical description is the ultimate expression of the “modelling” logic from the previous Discussion Abstract, while the principle of internal consistency can also be formulated as self-referential, autonomous and “automatically correct” nature of the desired truly consistent and complete mathematical framework. The self-referential, “living” and “intelligent” framework of reality-based mathematics should naturally include the intrinsically creative,

Needless to say, the necessary qualitative transition from such postulated “Being” of dead abstract models to dynamically creative, intrinsically complete “Becoming” of consistently derived structures is accomplished with the help of

If mathematics is not only a technical tool or language of knowledge, but is designed for a deeper role of consistent science basis, then it follows that irrespective of details it should contain special foundational directions, or

While particular examples of such kind of fundamentally new features can eventually be found (e. g. non-Euclidean geometry or chaotic dynamics), this quality is rarely emphasized as the

The

As a result of this proper extension of conceptual mathematics, one obtains a whole series of

In order to see the advantages of thus conceptually extended mathematics, one can compare this really emerging unification with the growing serious doubts of conventional science professionals about not only any possibility of unified knowledge (e. g. Gleiser 2010, 2010a, 2011, 2013, Wells, 2013, Noë, 2014), but even the very existence of truly universal and rigorous scientific laws (Kauffman, 2011, 2013).

The resulting ultimate scientific revolution puts therefore an end to usual, “antagonistic” scientific revolutions (Kuhn, 1980) and leads to permanently progressing kind of intrinsically complete knowledge, where the notorious

Dear Andrie,

I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.

All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

Joe Fisher

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I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.

All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

Joe Fisher

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The accumulating “difficult”, practically “unsolvable” and therefore eventually destructive problems of today’s global civilisation, from economical crisis to conflicting interests and missing sustainability, have something deep in common: the “untreatable” dynamic complexity of unreduced multicomponent interaction processes or systems. The same kind of impasse occurs in (traditional) fundamental physics, from the persisting old and growing new “mysteries” (quantum mechanics, unification, dark matter/energy, time, …) to the vital issues of sustainable energy sources and intelligent machines of all levels.

As shown in the

It is important that the same new mathematics of unreduced complexity provides the

In summary, the proposed new mathematics of unreduced complexity, unified by the

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...

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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...

view entire post

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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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