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
You're right, Cristi. I invite you to see my analysis of the philosophical foundations of mathematics and physics, the method of ontological constructing of the primordial generating structure, "La Structure mère" as the ontological framework, carcass and foundation of knowledge, the core of which - the ontological (structural, cosmic) memory, and information - polyvalent phenomenon of the ontological (structural) memory of Universum as a whole. I believe that the scientific picture of the world should be the same rich senses of the "LifeWorld» (E.Husserl), as a picture of the world lyricists , poets and philosophers.
Kind regards,
Vladimir
Dear Christinel,
You are convinced that maths and physics are much related, as in Tegmark's thesis. I suggest you read Leifer's essay and in an another direction the multiverse essay of Laura Mersini-Houghton. As you worked in cosmology and QM, I would be glad to have your view about the multiverse as a possible way to connect these two separate fields. Myself I am quite innnocent on this subject. I am working at this essay by Laura.
I am also rating your essay now.
Thanks in advance.
Michel
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
Hi Christi,
This is a very interesting essay indeed! I have to object on one point though. 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. The point of science is to come up with a useful mathematical model for this. In my essay I explain what I mean with this in more detail. I enjoyed reading your essay, also because it is well structured.
-- Sophia
Sorry for misspelling your name :/
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 Christi,
Thank you for the references. I am interested by the quantum gravity subject but it may take a while before I am able to produce a good idea. These days I was exploring F-theory also because it involves modular group concepts.
Michel
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 Cristi,
Being a fan of the good old Budeanu, I hope you as a new voice of Bucuresti might forgive me my misspelled Cristinel and decide without prejudice which variant is most appealing to you:
1) The late Einstein called the distinction between past and future an illusion. Nonetheless admitting that the now worries him seriously he considered it something outside science. In principle, this is the accepted "spacetime" view of modern physics.
2) Spencer Scoular instead argues for a qualitative theory of physics.
3) Tim Maudlin suggests a notion of number that provides the arrow of time. Spencer and Tim further discussed their views in Maudlin's thread.
4) I gave already in Fig. 1 of an earlier essay of mine an alternative explanation: Only elapsed time is measurable. Only future processes can be influenced. I agree with Tim Maudlin on the good old Euclidean notion of number as a measure, not a pebble.
5) You might have your own idea.
With best hopes and wishes,
Eckard
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 Cristinel,
In your essay you discuss many serious and intriguing topics. I have a question about one matter in particular.
Toward the middle of the essay you ask whether everything is isomorphic to a mathematical structure. I believe that your answer to this question is "Yes." I wonder about the converse question: Is every mathematical structure isomorphic to some physical structure. From your discussion of the mathematical universe hypothesis, I am not quite clear how you would answer this question. I understand that you deny that the mathematical universe hypothesis has been established as true; in other words, for all we know, some mathematical structures might have no application to physical existence. What, then, is the ontological status of the physically irrelevant mathematical structures? Do they have an abstract platonic reality? Are they totally unreal? Do they exist only as mental constructions in human minds? Or something else?
I appreciate also your example of the real number line between 0 and 1, and your discussion of Godel's incompleteness theorem, but I have no specific questions or comments on those parts of your essay.
Best wishes,
Laurence Hitterdale
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 Cristi,
Physics should deal with the conjectured objective reality, not with subjective notions like tomorrow, yesterday, the feeling that time flows, and the like.
What I meant with the objective now is the non-subjective border between past and future. This distinction got lost with the abstraction of theory from reality. Records and mathematical models of processes omit the binding to reality.
I wrote, future events cannot be measured in advance. This should already be a compelling argument although measuring is a human activity, and I intend to stress that the natural border between past and future is something objective. Maybe, you will be better forced to agree on that 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. So the key questions are whether or not a model is bound to real time and it is open to so far not yet given influences.
By writing "slice of spacetime" you denied unpredictable causal influences from reality outside the models. The spacetime by Poincarè/Minkowski corresponds to the monist philosophy of Parmenides.
Best regards,
Eckard
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
Dear Cristi,
You called the past frozen. I see this already contradicting Einstein who denied the objective border between past and future. Einstein didn't object when Popper attributed him to the fatalistic philosophy of Parmenides.
"Einstein's theory of special relativity not only destroyed any notion of absolute time but made time equivalent to a dimension in space: the future is already out there waiting for us; we just can't see it until we get there. This view is a logical and metaphysical dead end, says Smolin."
I am distinguishing between the conjectured reality and anything abstracted from it, including pictures, records, and mathematical models.
You asked: "What would be the problem if each "slice of spacetime" is at some instant the "natural border between past and future"?" Given you are watching again and again a video that shows a tree growing. Then each time there is a slice of time that shows the half-grown tree. This slice is not the original natural border. The whole video was recorded in the past.
What is the problem? The natural border between past and future is worldwide the same. Otherwise, mutual causality did not work. At the basic level of reality, elapsed time cannot be changed. The frozen history grows steadily. Nobody can remain young or even get younger. At the more abstract logical level of usual time as used in the laws of physics, any manipulation is possible: shift, reversal, etc. In other words, the mathematical models seemingly offer a degree of freedom that does not exist in physical reality. The actual border between past and future is a restricting natural reference that got lost with abstraction.
I didn't say that there is no possibility to nonetheless apply mathematics. I merely would like to make aware of the arbitrariness of the conventional point of reference t=0 in contrast to the naturalness of the border between past and future. Models that are based on the usual notion of time work well on condition, relations to this natural border don't matter much, for instance if attenuation can be neglected.
You have to give preference either to the monist concept of a closed in the sense of predetermined by a complete set of influences future or to open models of reality that do not exclude unpredictable causal influences from outside the whole system (including what you called initial conditions) under consideration. As an engineer, I prefer the philosophy of Heraclit and Popper's view.
Best regards,
Eckard
Dear Eckard,
I see that we agree on some points, and you disagree on some, which I discuss now. You say:
"The natural border between past and future is worldwide the same. Otherwise, mutual causality did not work."
Causality works even if the relativity of simultaneity is true.
"Nobody can remain young or even get younger. At the more abstract logical level of usual time as used in the laws of physics, any manipulation is possible: shift, reversal, etc. In other words, the mathematical models seemingly offer a degree of freedom that does not exist in physical reality."
It is simply not true that time in the laws of physics allows one to remain young or get younger etc.
It seems that we understand differently the laws of physics, in particular causality in relativity, and time symmetries. Also, it seems we see differently the role of math in physics. I respect your position and I will not try to contradict you, or to make you see things how I see them.
Best regards,
Cristi
Christinel,
Thanks for the positive assessment of my paper. I gave your paper a pretty high score a few weeks ago. I did this while I was on travel and I don't think I had time to write a post on your blog page. I will try to write a comment, which will probably require rereading your paper.
There is a paper by Schreiber on directly applying HOTT to physics. This is a difficult and in some ways foreign way of doing physics. I am less sure about the role of HOTT directly in physics, but rather that a simplified form of mathematics that connects to HOTT will become more important. It is in much the same way that physicists do not employ set theory a whole lot in theoretical physics. However, behind the analysis used by physicist there is point-set topology. We generally reduce the complexity of this mathematics. If I were to actually engage in this I would study the HOTT, and an introduction to HOTT with physics and related web pages on this site, are worth going through.
To be honest it has been a while since I have studied this. I have been working on a homotopy approach to quantum gravity. I mention some of that in my essay. This concerns Bott periodicity with respect to holography. The connection though is rather apparent. There are also some similarities to C* algebra. This work of mine connects with what is called magma, which constructs spacetimes as the product on RвЉ•V, for V a vector space,
(a, x)в--¦( b, y) = (au + bv, [x|y] - ab)
where the square bracket is an inner product. This is a Jordan product and the right component is a Lorentz metric distance. This is also the basis for magma, which leads to groupoids and ultimately topos. A more convenient "working man's" approach to HOTT is needed.
There is my sense that mathematics has a body and a soul. The body concerns things that are computed, such as what can run on a computer. The soul concerns matters with infinity, infinitesimals, abstract sets such as all the integers or reals and so forth. If you crack open a book on differential geometry or related mathematics you read in the introduction something like, "The set of all possible manifolds that are C^в€ћ with an atlas of charts with a G(n,C) group action ... ." The thing is that you are faced with ideas here that seem compelling, but from a practical calculation perspective this is infinite and in its entirety unknowable. This along with infinitesimals, or even the Peano theory result for an infinite number of natural numbers, all appears "true," but much of it is completely uncomputable.
Cheers LC
Dear Lawrence,
Thank you for the links, and for the explanations.
Best wishes,
Cristi