And the math will set you free by Cristinel Stoica

Dear Armin,

Thank you for reading my essay and for the comments. You raised interesting points, and I will address them.

1. As you know, in mathematics the term "exists" is the same as in logic. For example, "there exists a field which extends the field of real numbers and is algebraically closed". This doesn't have the meaning of physical existence, but rather of logical consistency. Whenever I used "exists", the sense of mathematical existence or physical existence follow from the context, otherwise, I specified that I was talking about mathematical existence or physical existence. To change the terminology would be unnecessary and would introduce confusion. You are right that they can be identified in the context of MUH. You are, of course, right, that the standard terminology is not the most fortunate, but I hoped that my precautions were enough.

2. Probably the reason why you feel that there is more to existence than relations is that one considers more existent the things with which we have a relation, directly or indirectly. But this is relation too. If you could be more specific about that property that escapes the relational viewpoint, that would be helpful. Otherwise, I think my statement is not merely a way out, but is the only way which avoids reference to things which don't have observable effects by themselves.

3. I agree with you about the necessity to avoid anthropocentrism. This is why I wrote "Being able to guess them and then test them would mean either that we are that lucky, or that the universe wants to be completely understood by us, who are just tiny waves on its surface." As you could see, I did not claim that this theory must exist with certainty, and certainly didn't claim that, even if it exists, we can find it. But I think that it is likely that it exists, and even that we find it, simply because we are so close. Most of the physical laws are contained already in general relativity, quantum theory, and the standard model, which really are a small set of laws accessible to us. Of course, this doesn't ensure us that TOE exists and can be found. You also said "To give a specific example, who is to say that it is not possible to formulate a theory of nature from the frame of reference of an observer associated with null geodesics in spacetime?" Well, you are right, physical laws can be described very well in coordinates whose constant surfaces are lightcones. Also, in Finkelstein coordinates and Kruskal-Szekeres coordinates, and also in Penrose-Newman formalism and Penrose-Carter diagrams, null coordinates are used. There is no need for an observer to travel at the speed of light, this is simply the diffeomorphism invariance of laws in general relativity. So the problem of antrhopocentrism introduced by reference frames was solved in general relativity, for other reasons. I think this was a good point you raised, because it could lead to the diffeomorphism invariance, or at least is another good reason to use them.

Thank you for the excellent points you raised, they allowed me to clarify some perhaps unclear elements, and to see some things I knew in a different light.

Best wishes,

Cristi

Dear Eckard,

Thank you for the questions, but I would like to ask you to be more specific. Could you please describe the specific features or instances of causality and present which you refer to, and why you consider that math is not involved in them? Or if this wasn't what you meant, could you please explain me the question?

Best regards,

Cristi

Dear Marc,

Thank you for the kind and interesting comments. You said "I found myself highlighting a lot of your statements that I wholeheartedly agree with." I had the same feeling while reading yours! There is a perfect harmony and complementarity between our essays :)

You wrote "I have some questions concerning your affirmation 'at least we know that there is room for free will, whatever this may be'." Yes, I gave some citations to previous essays and other works. I think a place to start are these two, Flowing with a Frozen River (pages 4-7) and Modern physics, determinism and free-will, both used in Aaronson's The Ghost in the Quantum Turing Machine. My arguments come from quantum mechanics, and the conclusion about free-will is very close to Hoefer's Freedom from the Inside Out. Also in "The Tao of It from Bit" I discuss a bit the issue. Please let me know what you think, or if you have questions. The bottom line is that I think free will is compatible with both determinism and indeterminism (indeterminism alone anyway doesn't guarantee it, because If quantum randomness would equal free will, then any Geiger counter would have free will.. But I only say there is room from free will, I don't know what it is :)

Best wishes,

Cristi

Dear Michel,

Thank you for the comments. Indeed, I tried to bring some arguments supporting/explaining the connection between math and physics. The essays by Matt and Laura are on my to do list, I hope to get there soon. Regarding the connection between cosmology and QM, if you refer to the connection between inflation and QM, as advocated by Sean Carroll, I am not sure what to say about this. If you refer to Quantum Gravity and Quantum Cosmology, I think that it is premature the standard view that perturbative methods fail for Quantum Gravity. I have a paper on the connection between singularities and dimensional reduction in perturbative quantum gravity (Metric dimensional reduction at singularities with implications to Quantum Gravity, Annals of Physics 347C (2014), pp. 74-91). Many researchers found that various dimensional reduction effects may help quantum gravity. I argue that we don't need to put by hand these various dimensional reductions, since they occur already due to singularities in GR. But I also hope there is a better, nonperturbative way to quantize gravity, yet to be found.

Best wishes,

Cristi

Dear Sophia,

"Just because you can list certain properties about a system doesn't mean you know that there must exist a mathematical structure describing what the system does. It is trivially true that if you collect certain quantities that describe some system, then that is some kind of table, which you can call a "mathematical structure" if you wish, but this is just data collecting."

Well, I didn't refer to data collecting. I meant that if you have all the propositions that are true for a system, then there is a mathematical model which makes these propositions true. You have an axiomatic system (the collection of true statements), and there is a mathematical model of it (in the sense of model theory). It would be ridiculous to think that collecting some numbers that follow from a series of measurements would give a mathematical model. So I agree with you that "The point of science is to come up with a useful mathematical model for this.". I was not talking about collecting data from experiments, but about the existence of a mathematical model of a system which can be described by propositions and is free of logical inconsistencies.

Best wishes,

Cristi

Dear Michel,

I too tend to focus more where the previous research leads me. I was not interested in perturbative Quantum Gravity, but the singularities which I studied turned out to have dimensional reduction effects, so this is how I become interested. To make a parallel, I move from one field of interest to another rather by analytical continuation, than by jumps :) So I guess for you is more natural to explore F-theory, given that it involves modular group concepts.

Best wishes,

Cristi

Dear Eckard,

Thank you for the clarifications.

I explained how I think time may be both appear to flow and be frozen here. The point is that whatever one may feel in the present, it has neural correlates and is recorded in the state of the universe at that point. Each instant contains the feelings that we have at that time, including the feeling of "now". And there is no need to be a highlight of one moment of time, since each of them contains the feeling that it is highlighted in its own present. I see no problem here. I agree that some may disagree, and this is why you can find as many references as you want. But no matter what property of time one may consider that it is characteristic to the now, it is part of the instant, of the slice of spacetime at that time, and each instant contains such thoughts. Yesterday you considered that that time was now, tomorrow you will say the same. Today you may say that yesterday isn't now, but yesterday you didn't. So I don't think it is so easy to find something that distinguishes now from other instants, except the fact that our instances in that moment call it now. Regarding endowing time with an arrow, this is done by the thermodynamical arrow. We don't know why the universe started with such a low entropy, but we do know that solving the problem for the big bang solves it for the other times too. Adding by hand an arrow, like Tim does, doesn't solve the issue, since to each of his structures there is a dual structure in which the directions are reversed, and there is no way to distinguish one from its dual. You can ask him, I am sure that this is what he will answer too.

Best regards,

Cristi

Dear Laurence,

Thank you for the comments, your raise an excellent question: " Is every mathematical structure isomorphic to some physical structure?". It may be, but I think that not all mathematical structures are isomorphic to physical structures from our universe. For any mathematical structure A, it is possible to find another mathematical structure B which is not isomorphic to a substructure of A. Hence, if there is a mathematical structure isomorphic to our entire universe (including its past and future), there have to be mathematical structures not isomorphic to physical structures from our universe. But maybe there are other universes with which they are isomorphic. I find appealing MUH, precisely because it removes the distinction between mathematical structures that have physical counterpart, and those that don't. Simply, according to MUH, each mathematical structure is a physical structure, and this is the physical structure isomorphic to it. But, as I argued in the essay, this maybe is impossible to prove, and is not falsifiable.

I look forward to read your essay, and I wish you good luck in the contest!

Best wishes,

Cristi

Dear Eckard,

Thanks again for the clarifications. It seems that I keep missing your point. So I will ask you to clarify even more, otherwise I will answer you to something else than you meant.

You mentioned

"the non-subjective border between past and future"

and

"I intend to stress that the natural border between past and future is something objective"

What would be the problem if each "slice of spacetime" is at some instant the "natural border between past and future"?

Again, if you say it is objective, please show me that exists and is not mathematical, as you claim. I understand that you imagine it somehow, but for some reason either I don't get it, or you don't get what I said, or both.

You said "anything that already happened for sure is an effect of a preceding causal influence definitely belonging to the past. What happened cannot be changed while future processes are still open to influences except for a closed mathematical model."

If anything that already happened is an effect of preceding causes, then, at that time, would you have said that it have to be free of preceding causes, so that it is still open? Either I don't understand what you said, or it is a contradiction, or perhaps you think that the outside cause that makes the future open becomes inside, so that it is in the past. I mean, you seem to accept that past is determined by its own past, but future not.

Let me try to explain what I said and I think you misunderstood. You claim "you denied unpredictable causal influences from reality outside the models". I don't see how I deny it, and why I should take care not to deny it, and why this would be a problem. The proof that I did not deny it can be found in the same essay I gave you the link. There, you can find how it is possible to have free will even in this context, and how mathematics and even determinism doesn't exclude it.

You say that you want the future to be open. Mathematical structures are not necessarily deterministic, as you seem to imply. So, if you think indeterminism means open future, then it is not excluded. Also, as I explained in that essay, determinism doesn't exclude open future and free choice. The key point here is the idea of delayed initial conditions. Even in a deterministic mathematical structure, if the initial conditions are not fully specified from the beginning, but you add them with each choice of the observable you make, the future is open (of course, because you get to choose now initial conditions which were not specified before, the past is open in a sense too, so long as it doesn't contradict the records of previous observations).

So I don't see what you claim it escapes any mathematical description. If I am missing something, please explain what that thing that escapes is, and the proof that it can't be described mathematically. Maybe it is that thing about which I wrote in my essay "I don't claim we can explain consciousness, with or without mathematics."?

Best wishes,

Cristi