Daring Group-theoretic Foundations of Biological Evolution despite Group Theory? by Peter Martin Punin

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 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

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

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