Essay Abstract

Thanks to its group-theoretic foundations, physical knowledge is time-symmetric. Now, by definition, systems formalizable by group theory "always function in the same manner" through the transformations they express. So it seems hard to expect that mathematical laws may play an analogous role within systems supporting any form of evolution. Until further notice, biological evolution confirms this point. Whereas there are highly convincing models of the history of our physical universe, the evolution having led to human self-awareness giving meaning to concepts like aims or intentions remains the subject of speculation. Contrary to time-symmetric physics ideally escaping irreversibility, evolution falls under the irreversibility it apparently violates. Certainly, Neo-Darwinism claims to resolve this problem by the notion of cumulative selection. But the present paper proves that cumulative selection, far from circumventing irreversibility, confirms its generalized diktat. Since only systems formalizable by group theory escape irreversibility, while group theory and evolution do not go together, a deadlock seems unavoidable. In fact, perhaps there is a group-theoretic approach conciliating evolution and irreversibility. In order not to attribute to evolution any form of determinism, this model must be conceived as a potentiality where several factors comprising chance can realize an infinity of paths. Now, a group-theoretic potentiality must ontologically precede the actually realized evolution, and this point leads to intrinsically controversial Platonism. However, the present paper shows that without Platonist presuppositions, even an explanation of the history of our physical universe would encounter circularity. So, why not dare for evolution an explicit extension of Platonism, implicitly - perhaps unconsciously - assumed by physics?

Author Bio

Holding two french M.Phil. degrees (D.E.A), one in philosophy of physics, and another in cognitive sciences, lecturer at Pôle Universitaire Léonard de Vinci and at IPECOM, Paris, France, I am focusing on mathematical Platonism and physical reversibility/irreversibility. More precisely I argue that in a material world universally subjected to irreversibility, no organized material or partially material entity could manifest/maintain itself without the intervention of essentially immaterial, eternal, and immutable principles existing objectively.

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Dear Mr. Punin

I agree with: "Our physical universe is governed by mathematical laws giving physics an extraordinary epistemic power characterized by symmetry between prediction and retro-diction. "

At 1.3 you brilliantly, deny the physical universe as a historical process. How it works, mathematically presented, you can see in my essay. From the formula follows the conclusion of the unsustainability of the physical universe as a historical process and conclusion "matter dominant Universe" and "radiation dominant Universe" coexist in every point in time. Do you agree?

I would be grateful if you would have found a mistake in my formulas or methodology.

Terms multiverse and "parallel universes" are very confusing (see my discussion in Mr. Gibbs place). It is possible that there are bubbles without interaction between them, but there is the same math in bubbles of Universe.

Best regards,

Branko Zivlak

    Dear Peter,

    First of all, I am happy to see you among the participants of this contest!

    I wish to stress that I highly appreciate your courageous attempt to suggest a Platonist paradigm for scientific explanation for the origin and evolution of life. If I understand you correctly, it is another way to suggest reductionism, isn't it? As I see it, the only difference of your approach from the conventional reductionism consists in the idea of a special set of timeless laws, responsible for life, but negligible for the dead matter. Am I right? If yes, I'd like to suggest to you a couple of my arguments against reductionism.

    As you have already read in our essay, we do not believe it possible that thinking can be reduced to fundamental laws of nature. Since life is a bridge between the mental and physical worlds, there must be something important in life, which cannot be expressed by the atemporal laws either.

    My second argument against reductionism focuses on the tremendous complexity of living beings. Nothing close is generated by elegant physical laws. Physical structures are very simple compared to living beings. Hence, the related laws of evolution, were they to exist, must be extremely complicated. If so, they would be very different from the simple physical laws, resembling rather a long and detailed set of instructions than laws.

    Having said that, I'd like to repeat my great respect for your heroic efforts in understanding the limits and possibilities of reductionism. The question is very important and any step here is very valuable.

    Good luck with your essay!

    Yours,

    Alexey.

    Dear Peter,

    Thank you for your interesting essay. I'm still not very sure I understand you very well, however, so I'd like to summarize your thoughts here. Please correct me, if I'm too wrong.

    First, to try boiling down your thesis to a sentence: if a research that has even a small part of the epistemic power of physics is at all possible in the study of evolution, some of the same, minimal metaphysical assumptions are necessary, namely, the existence of immaterial, atemporal and reversible laws, which are to be sought out. You defend this by showing a two-fold contradiction in the alternative scenario: either we decree out of the blue that biology escapes the tendency of nature to move from order to disorder, or we suppose the "emergence" of new laws alongside new phenomena, which is circular reasoning.

    What this paper is not, in my understanding, is an attempt at refuting the thesis that life randomly emerged, even though you refute some of the main justifications thereof.

    All the best,

    Lev

      Dear Mr. Zivlak,

      Thanks for your interest in my paper. I will carefully read your article and your reply to Mr. Gibbs before answering your substantive questions.

      Here just some details concerning the controversial multiverse theory (theories?).

      Perhaps we have to go back to the initial motivation of string theory. The latter was seen as an extremely promising way for the unification of the 4 fundamental forces, before encountering a serious problem. String theory certainly founds physics as we know it, but also would go with a quasi-infinity of otherwise configured physics. Now Weinberg and others think that the forgoing, far from being a deadlock, opens new horizons. These authors propose a synthesis of eternal inflation and assumed sring-theoretic multi-physics implying a multiverse comprising a quasi-infinity or even a potential infinity of parallel universes each one characterized by specific physics different from those you could find in any other parallel universe.

      YOU RIGHTLY SAY THAT PARALLEL UNIVERSES OR "BUBBLES" - terminology is not so important - EXPRESS THE SAME MATHEMATICS. But on the basis of the same mathematics, an infinity of potentially possible physics can be expressed. So, string theory combined to eternal inflation COULD found found a certain type of multiverse theory.

      According to Weinberg and others, THIS type of multiverse represents a plausible solution to the fine-tuning problem. IF there is a quasi-infinity of parallel universes, one among them, "by chance ours" can be configured in a way allowing at least locally the occurrence of life.

      All this is more than speculative and subsequently controversial, but in the context of my own paper, this point is not so important. Fine-tuning is a necessary but NOT sufficient precondition for the occurrence of life. So, even if the above-mentioned multiverse theory is true, it misses the essential of evolution. Whereas string theory has group-theoretic foundations, it is very different for evolution.

      I will see you soon on your own forum.

      Best regards

      Peter Punin

      Peter,

      There are some things I liked a lot and some I was uncomfortable with. Starting with what I liked a lot was the use of group theory. That has some promise as an analysis tool, but one wonders why you are working only with groups. They are not very powerful in themselves, and need to be combined to create algebras. I noticed that some writers in this contest proposed some very complex groups and noted that as the groups went up the hierarchy they lost some structure. So it needs to be stated what axioms are needed. In my opinion the most important property of a group is the unique identity property that produces uniqueness. Without that what do you have? You focus on the property of inversion in time which is interesting, but maybe not the only property we need to consider important.

      I am skeptical regarding the Platonic hypothesis since Aristotle refuted the idea that nature is mathematics, and the current reappearance of that idea is not convincing to me. However, the idea of group extensions does seem to have a useful role in describing nature as we go from simple to complex systems.

      There is a lot in your essay that is worth exploring in more detail and so I recommend that people read it and try to understand the concepts involved as I am trying to do.

      Harry Ricker

        • [deleted]

        • Post #7

        Hi Peter,

        In Section 1.3, you mention that natural law, must first exist in an immaterial manner, "...preceding its first 'materialization' not only temporally but also ontologically".

        Agreed that the notion of Scientific Platonism -- the idea of an objective immaterial reality -- is controversial. At first, identifying the 'objective immaterial' as mathematics, and that in turn as 'being objective' makes good sense, insofar we -- multiple diverse people -- experience mathematics in a way that is both repeatable and surprising (ie, it feels scientific).

        However, there is also implication that the mental (ie, the idealism of mathematical models, etc) ontologically precedes the physical realism (ie, an actual 1st person experience of material causality, reality, etc). That latter aspect seems invalid -- to not be the case -- insofar as the experience of the physical consistently includes elements that we could not have predicted in advance, on the basis of any deterministic theory currently available, or even on the basis of *any* possible/potential future theory that could be proposed, even in principle.

        The idea that 'reality' 'consistently includes inherently unpredictable measurement aspects' is well modeled by QM, as a theory of evolving potentials, as long as we do not attempt to go too far and moreover posit a 'determinism' of 'hidden variables' -- re-introducing the same old problems all over again by continually trying to model all that is real with only mathematics.

        ~ ~ ~

        In section 2.1, you write "Irreversibility cannot be reduced to the sole fact that the corresponding system never returns to its states occupied in the past".

        This is a claim. Why is it true? Why *not* posit a basic and irreducible asymmetry in the relation between observer and observed, when measuring -- gaining information about -- some inherently random process, as a axiom?

        Perhaps the actuality of objective potentiality -- unpredictability -- is the very thing that separates that which is completely model-able in system terms and that which is real, in actual terms.

        You might want to see my one page summary of why a basic fundamental temporal state asymmetry might be "built in".

        ~ ~ ~

        In section 3.2, the notion of 'potential' and 'energy degradation' both refer, inherently implicitly, and moreover inevitably, to an entropic arrow of time. However, this in itself, in turn, depends on a notion of 'randomness' as being inherent in the 'real', even though there is no corresponding characteristic in the lawful substrate of the platonic ideal (ie, the symmetrically reversible mathematics, models, etc). As such, the dis-connect is actually between how the 'real world' cannot not have some type of embedded randomness, (potentiality) whereas the group theory models simply/ultimately do not.

        As such, it can be argued that the ontology of the real is actually based on the mixture of the random and the pure, rather than just on the basis of what can be fully and completely predicted as an outcome of theory, no matter how modeled, what mathematical forms are used, etc.

        The notion of 'ordered to disordered' (as entropic arrow of time) is considered as 'objectively meaningless', insofar as fully/absolute lawful causation/determinism can contain no new information (no novelty). This is in clear contrast with, and distinct from 'life', 'alive', etc, insofar as the notion of 'choice' is regarded (subjectively at least) as 'meaningful' in direct proportion to the degree that it is novel, contains new information not derivable from prior states, etc, (ie, it in at least some irreducible way is in-deterministic, non-rational, random).

        Thanks,

        Forrest

          hi peter,

          as a software engineer i appreciate that functional programming languages (such as haskell, hope or miranda) are required to produce exactly the same answers based on exactly the same inputs, and thus it becomes possible to carry out formal proofs. i notice from the following sentence (and its surrounding context) that it would appear that your essay is from this same perspective:

          "Or, if you prefer, through all its operations or transformations, Σ always functions in the same manner."

          i have a question for you: how, then, is pure randomness (as an input and also an output) of both a system and its state taken into account? what can we infer from either massive replication of a system (with the implication that each copy would encounter entirely different inputs from all other copies), or prolonged exposure (of a single system) to wildly different (random) inputs?

          also i thought you might be interested to know that TN3.1 is the fundamental basis (the underlying algorithm) behind DHTs - Distributed Hash Tables. each "letter" is considered to be one axis along a hypercube. the target node is reached by enquiring throughout the network of closest neighbours if they know of one of *their* neighbours that is closer to the target hash. it's quite funny to see that same algorithm occur as "pseudo-evolution"

            Dear Lev,

            Thanks for your first comments.

            Concerning the refutation of the thesis that life has emerged randomly, well, there is a purely contingent problem:the length of our essays is limited to 25000 characters. If I could, I would have evoked more things, but in fact, probably like everyone among us, I was obliged to cut a lot of things in principle useful. This is not a criticism of the fqxi policy - in the context of permanent discussion too long essays would be counterproductive - but it is a constraint.

            Now I am sure that most of people seriously working in/on/about physics do agree that allegedly scientific theories requiring the actual occurrence of quasi-infinite improbabilities cannot be credible. Alexey's and your article shows that that this problem, far from being an exclusively probabilistic one, results from a lot of other - also logical, ontological ... ... - factors. For this reason, I think that our papers are highly complementary, and coming discussions will confirm it.

            But in my own paper,the sole - per se obvious probabilistic refutation must be the principal basis for the global approach. It is not only a question of contingent space constraints, but also of a fundamental problem. The current neo-Darwinist discourse is the following. "Of course, the random occurrence of life is too improbable to be envisaged. But non-specialists do not know the difference between single-step selection and cumulative selection. So, we neo-Darwinists have to teach cumulative selection to non-specialists (like physicists and/or philosophers of physics). And so on.

            Physicists and/or philosophers of physics have to reply: Even if "biology is not physics", any system apparently violating irreversibility is embedded in a wider system where irreversibility is reestablished, and in terms of a bit advanced probability theory, cumulative selection does confirm generalized irreversibility.

            All the best

            Peter

            Dear Harry,

            Thanks for your comments; I am glad that you share my conception of the group-theoretic foundations of physics. Of course, the purely formal notion of mathematical group has to be expressed by adequate algebras, but the interesting point is (i) that mathematically speaking, formal group theory does exist in a consistent way, and (ii) that there are natural phenomena formalizable in terms of group theory. Without this point, physics would be an uncertain thing like social sciences. Or, if you prefer, without the group-theoretic foundations of physics, internet would not exist, and we could not communicate in this way.

            Saying "In my opinion the most important property of a group is the unique identity property that produces uniqueness", you are absolutely right, and I also share your idea that, absolutely speaking, time-symmetry is not the only remarkable property of group theory. Yes, but concerning the subject of this contest, "intentions" and/or "aims" are inscribed in time. So, in the context of this subject, the issue of time-symmetry within physics and non-time-symmetry outside physics - even the notion of "asymmetry" would not be adequate non-group-theoretic fields - is essential.

            One among the potential interpretations of the subject concerns the fact that the mathematical foundations of physics conferring to the latter the extraordinary power we know, apparently are meaningless in theory of biological evolution and that beyond appearances, there could be a solution. Working in this area, I spontaneously adopted this interpretation which in turn is entangled in time-symmetry/non- time-symmetry issues.

            Now, there remains the question of Platonism. Personally, I think that philosophy is the confrontation of standpoints with regard to given issues which do not allow a definitive answer. Concerning metaphysics, the latter even is sure. By definition, metaphysical propositions are neither provable, nor refutable. Subsequently, it is the same for the negation of a metaphysical propositions.

            So, Platonism cannot be "refuted by Aristotle", while Aristotle in turn could not be "refuted" by anyone. Platonism as well as anti-Platonism is metaphysics. All we can do is comparing Platonism and anti-Platonism under criteria currently carried by philosophy of science. And, concerning physics, such a comparison denotes the following: Platonism certainly encounters difficulties I would not deny, whereas anti-Platonism leads to untenable positions. Perhaps retake my argument on the basis of our physical universe considered as a historical process, where any conception denying the existence of immaterial physical law preceding ontologically the occurrence of material/energetic phenomena would lead to circularity. And there are many supplementary argument I had not the space to evoke.

            (竊' http://philsci-archive.pitt.edu/11465/;

            竊' https://fermisocietyofphilosophy.wordpress.com/2016/12/01/scientific-platonism-without-metaphysical-presuppositions-talk-by-peter-punin/ (clic on presentation notes

            竊' https://fermisocietyofphilosophy.wordpress.com/2017/01/08/peter-punins-answers-to-presentation-questions/

            If I understand well, you agree that a group-theoretic extension to biological evolution could be a new path to follow. Well, but as I tried to explain it in the paper, in order not to attribute to evolution deterministic foundations it manifestly does not have, this extension must be considered as a set of potentialities the actual evolution very partially can realize. Now, to be realizable by the actual evolution, the potentialities in question have to precede ontologically any path the actual evolution could express, and this presupposes Platonism.

            Best regard; thanks again

            Peter

            Dear Forrest,

            To begin, I entirely agree your one page summary I carefully read. There is a non-entropic time arrow, and even a time arrow non-reducible to the sole order/improbability 竊' disorder/probability, knowing that the latter does not necessarily, nor exclusively concern energy degradation. There also are other ways to reach the same result: time-symmetry presupposes metrical spaces, knowing that the latter are specifications of topological spaces. Now, any mathematical model needing simultaneously a metrical space embedded in a topological space which, as such, does not specify the metrical space it is embedding ipso facto generates an arrow, and when the metrical space in question is space-time, the corresponding arrow has to be interpreted as a time-arrow.

            Anyway, any arrow generating factor implies symmetry 竊' non-symmetry and so the passage from phenomena formalizable in terms of group theory to phenomena which are not, and such a passage from group theory to non-group-theory does not necessarily concern entropy, nor energy degradation. Concerning QT you evokes, the Schrﾃｶdinger equation inscribed in a group-theoretic Hilbert space is reversible and deterministic. Quantum indeterminism and irreversibility comes from the interaction between the considered quantum phenomenon per se covered by the Schrﾃｶdinger equation and the observer or observation device who/which is not.

            Well, but the subject of the contest concerns among other the question of how biological evolution can go against irreversibility in the sense of order/improbability 竊' disorder/probability transition. Focusing on biological evolution, I necessarily have to point out order/improbability 竊' disorder/probability transitions, without considering entropy as the principal problem.

            From this perspective, my paper can be summarized as follows: (i) until further notice, no phenomenon non-formalizable in terms of group theory allows any knowledge comparable to the extraordinary epistemic power of physics; (ii) for phenomenon formalizable in terms of group theory, a meta-group mathematically can be envisaged as potentiality. So (iii) such a meta group could be a less speculative way than - for example - "chaos theory" leading to contradictions, "fractal theories" here leading no where, and finally "cumulative selection" which, far from circumventing generalized irreversibility, does confirm it.

            Best regards, thanks again

            Peter

            Dear Dear Ajay Pokhrel,

            Please excuse me for I have no intention of disparaging in any way any part of your essay.

            I merely wish to point out that "Everything should be made as simple as possible, but not simpler." Albert Einstein (1879 - 1955) Physicist & Nobel Laureate.

            Only nature could produce a reality so simple, a single cell amoeba could deal with it.

            The real Universe must consist only of one unified visible infinite physical surface occurring in one infinite dimension, that am always illuminated by infinite non-surface light.

            A more detailed explanation of natural reality can be found in my essay, SCORE ONE FOR SIMPLICITY. I do hope that you will read my essay and perhaps comment on its merit.

            Joe Fisher, Realist

            Dear Luke,

            This is highly interesting - and so philosophically controversial - question.

            A first attempt to answer a simplified version of your question goes back to the 19th century, to Boltzmann:

            Already the precursor formulation of the Second Law of Thermodynamics due to Sadi Carnot says that even under ideal conditions, each form of energy can be converted into heat, whereas only a part of given heat can be converted in another form of energy. So, even an ideal engine always produces residual heat.

            Subsequently, trying to explain irreversibility by statistical mechanics, Boltzmann encounters a serious problem. Within an ideal system, say an ideally rigid box containing ideally elastic - or if you prefer, ideally rigid - molecules, the trajectory of any molecule would be governed by Newtonian reversible mechanics. So, the system would not produce residual heat, contrary to Sadi Carnot's engine Boltzmann try to explain in a statistical way after Clausius' phenomenological formalization. On the other hand, with regard to an ideal molecular system, a statistical approach is meaningless. So, to consider an irreversible molecular system from a statistical standpoint, Boltzmann necessarily has to accept irreversibility generating imperfections within the system, but this leads to a "statistical explanation of irreversibility by irreversibility."

            This genuine circularity never found a convincing solution, and the controversy whether irreversibility is a "law-like" or "fact-like" phenomenon - the formulation is from Mehlberg - still is continuing today.

            Now it is analogous for n replications of a "same" system (n 竊' infinite雞･), or the interaction between n "identical" systems (n 竊' infinite雞･). Ideally such replications/interactions remain reversible, in practice not, but any explanation of this problem finally remains an explanation of irreversibility by irreversibility.

            Concerning your remark about "pseudo-evolution", there was a subsection in a former version of my paper distinguishing biological evolution as history and the "history" of our physical universe as "pseudo-history."

            Best regards

            Peter

            Nice essay Dr Punin,

            Your ideas and thinking are excellent about gap between Group theory and Biological systems... For eg...

            "deep gap between (i) the group-theoretic foundations of physics allowing the latter to escape irreversibility, and (ii) evolution theories constrained to decree ad-hoc and a posteriori some mysterious suspension of the irreversibility necessarily entangled in their essentially non-group-theoretic investigation field.

            Now, by definition, biological evolution can not belong to this category of systems. So a gap seems to open up between physics and evolution theory.

            If this infinity of different "parallel universes" exists - for the moment it is a highly

            speculative hypothesis - then it may be plausible to say that there is at least one "fine-tuned" universe, by chance ours. Well, but even if we accept this hypothesis - "parallel universes" are not observable - the problem of evolution is not resolved: fine-tuning is a necessary but not sufficient"

            For your information Dynamic Universe model don't support "Multi-verses" and is totally based on experimental results. Here in Dynamic Universe Model Space is Space and time is time in cosmology level or in any level. In the classical general relativity, space and time are convertible in to each other.

            Many papers and books on Dynamic Universe Model were published by the author on unsolved problems of present day Physics, for example 'Absolute Rest frame of reference is not necessary' (1994) , 'Multiple bending of light ray can create many images for one Galaxy: in our dynamic universe', About "SITA" simulations, 'Missing mass in Galaxy is NOT required', "New mathematics tensors without Differential and Integral equations", "Information, Reality and Relics of Cosmic Microwave Background", "Dynamic Universe Model explains the Discrepancies of Very-Long-Baseline Interferometry Observations.", in 2015 'Explaining Formation of Astronomical Jets Using Dynamic Universe Model, 'Explaining Pioneer anomaly', 'Explaining Near luminal velocities in Astronomical jets', 'Observation of super luminal neutrinos', 'Process of quenching in Galaxies due to formation of hole at the center of Galaxy, as its central densemass dries up', "Dynamic Universe Model Predicts the Trajectory of New Horizons Satellite Going to Pluto" etc., are some more papers from the Dynamic Universe model. Four Books also were published. Book1 shows Dynamic Universe Model is singularity free and body to collision free, Book 2, and Book 3 are explanation of equations of Dynamic Universe model. Book 4 deals about prediction and finding of Blue shifted Galaxies in the universe.

            With axioms like... No Isotropy; No Homogeneity; No Space-time continuum; Non-uniform density of matter(Universe is lumpy); No singularities; No collisions between bodies; No Blackholes; No warm holes; No Bigbang; No repulsion between distant Galaxies; Non-empty Universe; No imaginary or negative time axis; No imaginary X, Y, Z axes; No differential and Integral Equations mathematically; No General Relativity and Model does not reduce to General Relativity on any condition; No Creation of matter like Bigbang or steady-state models; No many mini Bigbangs; No Missing Mass; No Dark matter; No Dark energy; No Bigbang generated CMB detected; No Multi-verses etc.

            Many predictions of Dynamic Universe Model came true, like Blue shifted Galaxies and no dark matter. Dynamic Universe Model gave many results otherwise difficult to explain

            So I request you to please have a look at my essay on Dynamic Universe Model and its blog also where all my books and papers are available for free downloading...

            http://vaksdynamicuniversemodel.blogspot.in/

            Best wishes to your essay.

            For your blessings please................

            =snp. gupta

            15 days later

            Peter,

            You are the Platonist! I recall your excellent essay from the last contest.

            You have applied the rigorous mathematical logic of groups and sets to the problem of apparently irreversible evolution, and you have found an idealized group existing in Platonic space. Well done.

            The meat of your work really begins with section 2 with subsection 2.2 stating the problem very clearly. I had never considered the Noether Theorem is this way, but it is certainly true. Many Thanks!

            I think that many in the FQXi community will struggle with the mathematical formalisms you use. But the precision of those formalisms is essential to making the logic work. Well done.

            Lastly, the use of some type of selective mechanism such as Maxwell's Demon is a component of many of the essays in the contest. So that is a major point of agreement with other essays.

            All in all, this was an excellent effort.

            Best Regards and Good Luck,

            Gary Simpson

            Dear Gary,

            It is a real pleasure to meet you again! Thanks for your comments.

            Concerning the Noether theorem - its intuitive formulation is "If a physical system has a continuous symmetry property, then there are corresponding quantities whose values are conserved in time." - the quantities to be conserved if you want continuous symmetry are either energy as such, or intrinsically related to energy.

            Now, ideally speaking, symmetric physical systems - except thermodynamics - conserve their quantity of available energy. If there are irreversible effects within a non-thermodynamical system, then the quantity of available energy diminishes, and ideal - group-theoretic symmetry becomes something non-formalizable in terms of group theory.

            With regard to the global structure of my paper, there is some speculativity I entirely assume. But I think there is no other way. There is nothing against generalized irreversibility. A system apparently violation irreversibility in fact is included in a wider system where irreversibility is reestablished. A physicist claiming to be able to build an operating perpetuum mobile would not be taken seriously. So the synthetic theory of biological evolution claiming that "cumulative selection" can go against irreversibility is in turn not very serious, and we have to find other solutions.

            I just see just a first path to explore, and no more. Please could you just tell me what you do think about the outline of the project, summarized as follows:

            Since only systems formalizable in terms of group theory escape irreversibility, there must be something like this behind evolution. Now, group theory as such and evolution by definition are incompatible. On the other hand, it would not be acceptable to attribute to biological evolution deterministic characteristics it does not have. But we can envisage a potentiality comprising a great number of group-theoretic systems - in fact a superposition of groups and semi-groups - where contingent factors like chance make the actual choice between potential paths. Such a potentiality implies Platonism. Nevertheless, since a non-Platonist conception of the history of our physical universe leads to circularity allowing to prove anything and the contrary, there is no reason to exclude Platonism behind our biological history.

            Well, what do you think about?

            Thanks again,

            Best regards,

            Peter

              Peter,

              The question you ask at the end of the above post is interesting. There could be a Platonist set that contains all possible solutions and there could be a subset of solutions within that set that avoids irreversibility. Those solutions might be determined by the random events associated with the environment that you mention. So, each random event might push towards a different solution. And there might be a generic solution that is favored by many paths. For example, a four legged creature becomes bipedal so that it can use two limbs to use tools.

              So ... it sounds like a very interesting and very lengthy and difficult problem. It makes me think of a series of books titled "The Hitch Hikers Guide to the Galaxy".

              On a different note, if you have not already done so, you should read the essay titled "A Tale of Two Animats" by Larissa Albantakis. She uses a set that contains both the history and the future of the species.

              Best Regards and Good Luck,

              Gary Simpson

              Dear Gary,

              Great thanks. Sometimes feeling torn between the desire not to lose myself in unbridled speculation and the necessity to find new paths instead of decreeing things which cannot be, your answer reassures me.

              Concerning Larissa Albatakis, I read carefully her highly interesting paper, before posting a detailed reply and some questions, a week ago. Well, she prefers to ignore my post; that's her good right.

              All the best,

              See you soon on your own forum,

              Peter

              11 days later

              Peter,

              FYI, I have responded to your post in my forum.

              Best Regards and Good Luck,

              Gary Simpson

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