This essay is an extremely enjoyable read and proposes to help us understand "how a Universe ends up understanding itself."

But using prose to say that the Universe has an "understanding" of something still leaves us with the "mindless mathematics."

I wonder-- would mathematical game theory be the best, or the only, "mindful" mathematics that we have for expressing this statement...

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This essay is an extremely enjoyable read and proposes to help us understand "how a Universe ends up understanding itself."

But using prose to say that the Universe has an "understanding" of something still leaves us with the "mindless mathematics."

I wonder-- would mathematical game theory be the best, or the only, "mindful" mathematics that we have for expressing this statement in a mathematical language?

It's certainly not for me to answer this question. But I can't help thinking about it.

"The Universe was viewed as an infinite space where masses described trajectories determined by forces ruled by immutable laws."

I feel a tacit warning, here, that in the subsequent text, the old-time classical model is going to be wheeled into surgery. "Trajectories," "forces," "immutable laws," it seems, are going to be refined somehow in the balance of the text. OK, that makes me think.

Can we assume that the "laws," or the "regularities" of the Universe are indeed constant, indeed "immutable"?

Maybe not. There might be small exceptions-- too small for us yet to notice, perhaps too small for us ever to observe.

And that-- is enough to outline a game.

The particle in this kind of Universe must be able to adapt. For in this kind of game, it cannot "know" the laws expressed by the Universe because they may subtly, or for very brief periods substantially, change.

Instead of "knowing" the laws of the Universe, in this kind of game the particle would have to "learn" the laws of the Universe. For example, the particle would have to perform a "learning algorithm."

Then--

Would finding such a game-- and finding such a learning algorithm-- in the data, support the following statement?

"The Universe was viewed as an infinite space where masses described trajectories determined by forces ruled by immutable laws. But now-- because of these data (wherein we find a learning algorithm)-- we conclude that the laws of the Universe are Not immutable."

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Dear Jorge, dear Rodolfo,

The first point having impressed me in your essay is your refusal of nihilism, a rare thing in modern philosophy of science. Of course, at first glance, philosophy of science is not directly concerned by nihilism, nor by anti-nihilism, respectively the denial and the defense of values, and even of the pertinence characterizing the notion of value as such. Or,...

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Dear Jorge, dear Rodolfo,

The first point having impressed me in your essay is your refusal of nihilism, a rare thing in modern philosophy of science. Of course, at first glance, philosophy of science is not directly concerned by nihilism, nor by anti-nihilism, respectively the denial and the defense of values, and even of the pertinence characterizing the notion of value as such. Or, in other words, notion of value seems to concerning moral philosophy, perhaps social sciences and so on, but not philosophy of science.

In fact, it is not so simple.

Alexey and Lev Burov – they posted a positive comment on your forum – show in their essay that the current or at least mainstream conception of science reducing the latter to “formal systems” and subsequently denying the value which makes the difference between arbitrary formal things and approaches having a sense, systematically leads to self-refutation Moira and Eileithyia for Genesis by Alexey and Lev Burov . Personally, I am glad to see that the back ground of your essay is the same.

Anyway, to begin, I entirely agree that modern science during a long time-period had been imprisoned by (in?) the mechanism paradigm, and that modern knowledge inciting us to go beyond this paradigm opens up new horizons. Yes, but the mechanism paradigm is not only a path leading to a deadlock. This paradigm, by its nature, denotes something deeper allowing us to transcend a mechanist vision of the world while remaining in a scientific vision of the world. I will try to explain the foregoing. Physical knowledge is characterized by symmetry in prediction and retro-diction. This point makes all the difference between physics and non-physics. Physical time-symmetry without which physics would not be physics is based on group-theoretic foundations. You can find more details in my own essay Daring Group-theoretic Foundations of Biological Evolution despite Group Theory? by Peter Martin Punin. Now, from a physical standpoint – with regard to purely algebraic motivations, it is another story – the epistemic roots of group theory initially, please pay attention to “initially”, are inscribed in mechanics stricto sensu. Consider the watch on your arm. This mechanism expresses a superposition of several expressions of the same rotation group, and this point allows at least ideally to predict as well to retro-dict the passed and future states of the watch from any state chosen as t0-reference. In the same sense, Galileo referred to group-theory avant la lettre, without being aware of it. Nevertheless, that what we call today the Galileo-group is fundamental in Newtonian mechanics. Always from our present-day perspective, we say that the Galileo-group is a subgroup of the Lorentz-Poincare-group in SR, whereas at the RG-level, Riemann manifolds are to be interpreted as a transformations group over a set of local approximations formalized the Lorentz-Poincare-group. So, in macroscopic physics, you find a lot of group-theoretic structures expressed by mechanical systems and vice versa.

Now, saying that quantum physics essentially transcends the mechanism paradigm, you are absolutely right. Of course, quantum entities cannot be reduced to sole “objects”, and even the notion of entity is reducing, but for human minds it is hard to find better. Of course, simplifying bit, a Hilbert space comprises connected potentialities potentially connected beyond their actual (?) realization. And so on, your statement is complete through its compactness; so repeating it would be useless. Well, but how to explain that we are not merely lost at the quantum level?

Here, the answer is compact: it is in turn for group-theoretic reasons. Hilbert spaces, the unique possible “environment” of Schrödinger's wave is a group-theoretic “entity”. Heisenberg's matrix approach equivalent of Schrödinger's approach is based on non-commutative matrix group theory. Top-down causation as you evoke it from a rigorous physical perspective, is formalizable in terms of semi-groups; knowing that the latter, mathematically speaking, require previously given full groups. This point seems paradoxical, but it is not the case: To describe top-down causation to be formalized in terms of semi-groups, you need a Hilbert space being a full group-theoretic entity.

So, on the one hand, I think that the nature of physical laws necessarily comprises group-theoretic foundations, and on the other hand,these group-theoretic foundations allow physics to transcend its initial mechanist limits.

Now, an important point, must be clarified. If group theory funds mechanist as well as non-mechanist physics, it must precede ontologically any form of physics, and “preceding something ontologically” implies “preceding something in an immaterial and eternal way.” The foregoing obviously leads to Platonism which does not please everyone. Well, but since you mention Leibniz, recall that Leibniz precisely says that our physical universe, instead of existing, also could not exist. So its existence is a mystery. The eventual existence Platonist mathematical universe would be mysterious, but not “more mysterious” than the existence of our material/physical one. Subsequently, if the ultimate consistency of physics is better ensured by Platonist presuppositions than by the current refusal of Platonism, there is no reason to reject Platonism at the cost of non-consistency.

In my paper you find certain paths denoting that anti-Platonism encounters serious deadlocks, among others the fact that within an universe considered as a historical process, law appearing “with” the phenomena they govern imply circularity.

Evoking yourselves the turtle paradox, you probably agree with the foregoing. Analogously to the turtle problem, an issue like “Where comes the law XX from?” perhaps receive the answer “From UVU.” Yes, but the answer will be followed by a new question: “Where comes UVU from?” And so on. Ultimately, we have the choice between and endless, infinite series of questions and answers and questions and answers, or self-reference (implying circularity) or the reference to something transcendent/eternal. Reading your non-nihilist essay, and provided I understand well, I think, you are not opposed to a transcendent/eternal solution. Your reference to Leibniz seems to go in this sense.

But now, a real problem arises. Eternity is eternity, whereas aims and intentions are inscribed in time. So, our contest subject has to be reformulated: How can mathematical laws operate such a passage from eternity to temporality?

Or, more basically: given that physical laws are group-theoretic laws, and that biological evolution as such is not formalizable in terms of group theory, how can mathematical laws operate such a passage from group theory to non-group theory?

Even if both questions are not positioned at the same ontological level, they converge, and this interesting. But the answer is hard to find.

Saying that our universe is life-friendly, or fine-tuned for life, of course you are absolutely right. Nevertheless, fine-tuning is a necessary precondition for the appearance of life, but not a sufficient one. Fine-tuning belongs to physics, so to the aspects of our universe being formalizable in terms of groups and/or semi-groups. The next stages, the passage, under life-friendly conditions, from inert matter to living matter, and then evolution, and then the appearance of thought (this is again another story; see the essay of A.& L. Burov and my comment on their forum Moira and Eileithyia for Genesis by Alexey and Lev Burov globally are not formalizable in terms of group theory.

How to resolve this problem?

Have you an answer beyond the fine-tuning precondition?

In my own paper Daring Group-theoretic Foundations of Biological Evolution despite Group Theory? by Peter Martin Punin , I try to find this kind of answer: Given the essentially group-theoretic foundations of physics, evolution theory should be group theory embedded in non-group-theory. Such a model is possible. For the moment, there is a lot of speculation, but perhaps my approach is less speculative than other approaches doing as if physics would not be physics, or as if universal physical laws exceptionally could be forgotten in evolution theory.

Agreeing the essential of your vision, I would be glad to open a discussion with you.

All the best

Peter

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Dear Rodolfo and Jorge,

the hints at a radically new way to look at (and solve) the matter/mind dichotomy that you provide in your text appear to me as very original and attractive, and superior to the majority of the several essays I’ve read. I wrote ‘hints’ because the impression I had is one of a treasure-map in which a considerable amount of effort is still to be made for getting...

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Dear Rodolfo and Jorge,

the hints at a radically new way to look at (and solve) the matter/mind dichotomy that you provide in your text appear to me as very original and attractive, and superior to the majority of the several essays I’ve read. I wrote ‘hints’ because the impression I had is one of a treasure-map in which a considerable amount of effort is still to be made for getting a fully detailed picture. For example, you seem to hint at some intimate connection between the disposition to act that one can attribute to objects under a certain ontological view at quantum mechanics, and the more familiar agency of conscious creatures: how can I decide whether this idea is extremely profound, has practical consequences (up to suggesting specific experiments), or is just a cute remark of purely metaphorical value?

This type of assessment is further complicated, I believe, by the ’regularistic’ choice that you make, which, unlike the ‘necessitarian one’, leaves room (if I understand correctly) for descriptions of some other, non-regular aspects of nature that escape the Galilean grip of mathematical language. How would one then proceed for rigorously assessing similar conjectures? (Please note that this is a genuine question, not a criticism: I think that bold visions of this type are very appropriate for the FQXi Essay Contest, when supported by articulated arguments and competence, as in this case.)

Another idea that I found brilliant is that of viewing the relation between a QM entangled system and its components (the state being defined only for the former, not for the latter) as enabling a form of top-down causation. I never thought of that phenomenon under this perspective, and this is now one of my favourite examples of top-down causation — I wish I knew more, beside the ‘classical’ ones from the biosphere. By the way, I have quickly checked George Ellis’ recent book (‘How can Physics underlie the mind’ - 2016), largely devoted to top-down causation, and I could not find an explicit mention to this case. Was this idea first proposed in Gambini et al. 2015?

Thank you

Tommaso

fqxi.org/community/forum/topic/2824.

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Hello Rodolfo Gambini,

Your essay is the best that I have read. Thank you very much. I am working on the hard problem of consciousness and I have to say that I have learned much from your essay. I have read your essay about 5 times now, and I learn a little more with each read.

My degrees are in astrophysics, and I admire your description of the nature of our universe. Through...

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Hello Rodolfo Gambini,

Your essay is the best that I have read. Thank you very much. I am working on the hard problem of consciousness and I have to say that I have learned much from your essay. I have read your essay about 5 times now, and I learn a little more with each read.

My degrees are in astrophysics, and I admire your description of the nature of our universe. Through hard personal work I had already come to many of the conclusions that I find in your essay, but clarity of your writing has clarified my thoughts. I had come to the Platonist position regarding the mathematical foundations of our universe (I read Max Tegmark’s book), but thinking about causality caused me to think otherwise. You have given me a wonderful label for my current viewpoint – regularist physicalism. I am now regular (sorry, bad pun).

A couple of points and one quibble:

First, the notions of top-down causation can easily be extended into a new argument for the connection between determinism and free will. I think that determinism and free will are flip-sides of the same coin. Free will is a consequence of the loose coupling between deeply complex causal event chains, where causal action in one chain can take action in another causal chain. This is independent action, and where a mind is involved this is free will.

Second, there is a lot more to say about the emergence of semantics. Beyond basic information theory and Turing machines, there are semantics machines that operate with semantics analogous to how computers operate on symbols. Human thought and language are just two examples. This is the leading edge of my current work.

Now for the quibble. It seems to me that in the regularist view, the universe is mindless. Being mindless, the universe isn’t even indifferent. Any purpose in the world is put there by us. We are subjective entities implemented on a physical substrate, and our only experience of the world is through our subjective sensations. Our mental and subjective selves are semantic constructs, and we slather our semantics on the physical universe. We experience the physical world through layers of our semantics. Objectivity and mathematical laws are communally agreed upon semantics that we plaster over the world. The quibble: I think that purpose in the world comes from us and is not already inherently present in the mindless universe – no matter that we live in a Goldie-Lockian just-right universe.

Thanks for the good read.

Cheers,

Bruce Amberden.

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