And the math will set you free by Cristinel Stoica

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 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 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 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

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 Cristi Stoica

Your essay is clearly written and you included all the essential notions, which are important at explanation, for instance, consciousness. I also look on physics from reductionical view. But, I disagree that neural correlates are enough to explain consciousness. Not only me, Tononi and Koch also claim for panpsychism. Thus neural correlates only explain consciousness in brain, but not panpsychism, primary consciousness everywhere. Thus Duck is not a Duck if everything looks like the same. I think from reductional view that various qualia in brain should be explain from one qualia. Thus despite of all, I agree that everything is isomorphic to mathematical structure of physics, because primary consciousness is only extremely reduced element, which in principle does not disturb this isomorphism. Thus, if the duck is completely the same, it is maybe not duck, but the difference is not important.

In the prolonged version of my essay [reference 1], I describe Turing experiment, which tries to distinguish conscious ''duck'' from unconscious one. The principle is:''Let us suppose that Turing experiment gives distinct answers of a duck versus computer. (Otherwise free will does not exist.) If we respect non-quantum physics, then explanation of free will needs new physics. But a quantum computer always gives distinct answers than a duck, thus free will does not need new physics.''

It is important for me, that consciousnes does not exist without free will.

I agree with you, that theory of everything thus not need two independent set of laws. But Petkov has an interesting idea that gravitational force does not exist. I gave one answer to him, but what is your answer to him?

One good example of precise words of Maluga are: ''Without abstraction, our species with a limited brain is unable to reflect the world.''

Thus math is a process of abstraction. Thus, my conclusion is that the essence of math in physics is to be abstract and simple as much as possible. Because foundations of physics should be simple, the task of math is to describe quantum gravity on a t-shirt.

Because of this reason, and because of intuition I am reductionist also.

Best Regards

Janko Kokosar

Dear Cristi,

About interrelations among consciousness, math and physics, we are close, we only need to see details. But you do not mentioned a word ''Panpsychism'' and not many about ''quantum consciousness''. Thus maybe you can give some words about this. I looked two your links about free will, but here are clear differences.

If you wish you can read my essay. The main speculation in my quantum consciosness is that quantum randomness is free will, thus that the human mind MAYBE sometimes changes randomness of quantum phenomena.

Best regards

Janko Kokosar

Very boring essay. Such a filling of the maximum allowed length for so little... maybe I'm just already too familiar with the fact that mathematics is the study of structures to have any interest reading it again, but...

Despite your try to develop a visual metaphor to illustrate the question of discovered vs. invented, you did not even come up with any decent answer to this question. Your illustration by points of a line is more confusing than explaining, since if you take a physical line made of aligned atoms, a physical point in this line as defined by a particular atom can only encode a few words, not even an ordinary sentence. To encode whole texts you need a mathematical line, far from anything concrete or visual (would you qualify this as visual ? I don't). There are not even enough atoms in the visible Universe to be in bijection with all possible meaningful texts of 1 page length. But a decent answer is possible as I explained in my essay : by making the difference between mathematical existence (where all possibilities exist but can be lost in a huge pool of alternatives as soon as they are a bit complex) and the conscious act (or contingent event) of pointing out a particular possibility here and now (which is what the notion of "brilliant text" is actually about).

"Some may hope that there are things in the universe which can't be described by mathematics. But can you name those things? To name them, you would have to provide a list of their properties, of propositions which hold for them. If the universe is describable by a list of propositions, then there is a mathematical structure describable by the same propositions. But then, couldn't we find something to say which is true about our universe, but not about the mathematical structure? The answer is no."

Example : the sensation of the red color. I can name it (as I just did). I can list its properties : this is the empty list, since it does not have any mathematical structure. Or maybe I can say that I do not like this color : would you classify it a property of this sensation ? We can also say that it is the color of blood. However, if the sensation of the red color is a property of the sight of blood, I doubt the relevance of this link as a description of the sensation of red itself. So, some things can be said about the sensation of the red color, which does not mean that it admits any mathematical description as a mathematical structure.

"If we can't [describe it completely by a list of true propositions], it's only because of practical limitations."

Disagree: if I can't describe the sensation of the red color completely by a list of true propositions, it is not because of any practical limitations, but on the contrary because the list of mathematical structures it is made of is trivial: an empty list.

"We know what a feeling is: some chemistry of the brain"

Disagree. The sensation of the red color surely has neural correlates which can be described mathematically, however these mathematical structures will never account for what this sensation actually is. And it is found in NDEs that many feelings occur far away from any chemistry of the brain. As for the idea that a feeling is some chemistry of the brain, it is still pure speculation from a scientific viewpoint. Feelings must have correlates in the brain of course, but these concepts of chemical correlates in the brain did not achieve any actual scientific understanding of what feelings are and how they work, and I think they never will (if psychiatrists think they do, they are just hallucinating).

"any kind of world, as long as it is free of contradictions, is isomorphic to a mathematical structure"

Unfortunately, this claim looks much less like an expression of amazement at how deep mathematical concepts are involved in physics, than like an expression of lack of imagination to consider any other possibility. In my essay I explained how I consider the world as not a mere mathematical structure since it includes the non-mathematical component of consciousness, even if mathematics takes a large part in it.

"...maybe the universe obeys two or even more sets of laws. This doesn't make much sense, since if the universe obeys two or even more independent sets of laws, there must be two or more disconnected mathematical structures modeling them. But we can't live simultaneously in two disconnected worlds."

Looks like you never heard of any intermediate possibility for 2 sets between being equal or disjoint. I see no contradiction in having a world made of a combination of the fundamentally different ingredients of maths and consciousness, as I described in my essay.

You don't even seem to understand what is Godel's incompleteness theorem actually saying. You wrote: "To obtain an inconsistency, we should make the physical laws assert their own undecidability". What the incompleteness theorem says, is that "To obtain an inconsistency, we should make a mathematical theory able to express arithmetic, stating (among its theorems) its own consistency". I admit that your claim is rigorously correct, since, actually, and still according to this incompleteness theorem, the claims of consistency and incompleteness (in a theory able to express arithmetic) are logically equivalent. But... the reason for the correctness of your formulation is so indirect that it makes things even more twisted to figure out than they basically are. Especially given your previous sentence: "If a man states the undecidability of some problem in physics, would this introduce an inconsistency in the universe? No, since the statement can simply be wrong". If consistent theories able to express arithmetic are unable to prove the claim of their own undecidability, it is not because this claim can be wrong, but on the contrary because it is right: these theories are undecidable, which is why they are unable to prove some true facts, such as the fact of their own undecidability.

And I see no justification for your implicit assumption that the laws of physics should be able to express arithmetic, as I disagree with this claim (see my essay).

"the only prediction made by the mathematical universe hypothesis is that our universe has to be Turing complete"

I answered about the issue of predictions of the MUH in reply to Marc Séguin's essay.

In your previous essay "Flowing with a Frozen River" you described a possibility for free-will in a way that seems to be the same as I support, except that you seem to attribute free will to a retroactive effect on the initial conditions. Maybe because you use your own variant of quantum mechanics, "Smooth quantum mechanics", while I accept quantum mechanics in its standard formulation, and I attribute randomness to the event of wavefunction collapse by conscious observation, which I qualify not as a physical event but a metaphysical one (so that the discontinuity is not something physical, it is not located in the physical space-time). It looks like your interpretation is just a twisted rewording of the "discontinuous collapse of the wave function" into a "retroactive discontinuous collapse of the initial conditions" from which the present state would be a posteriori re-determined by the continuous quantum evolution, and which is just mathematically equivalent to the former, but only coming as an illusory way to deny that anything here is discontinuous.

So it looks like, your special way of wording your interpretation through this mathematical reformulation is just hiding the fact that we have essentially the same interpretation, which I invite you to read in my essay.

But... no, there is still a difference, by which I would qualify your version as incoherent: the problem I see with your interpretation is that the new observations do not just complete the previous ones, but can also be incompatible with them (in the sense of non-commutation). Thus, the new initial conditions are turning past states into thermodynamically incoherent states (such as with the story of "liar states" which I commented there), retrospectively changing past clear observations into indeterminate ones, and finally, changing the big bang into a combination of initial conditions mixing the smooth big bang that normally explains things (the thermodynamic time arrow) with highly chaotic initial states with multiple singularities and so on, where the thermodynamic time arrow cannot be found anymore.

In your text "Modern physics, determinism and free will", you make a distinction between "branching time" and "choice time". But what is the role of a "branching time", that would not be the same as "choice time" ? I cannot see a role for it. Nothing in the formalism of quantum physics, speaks about "branching" as a fundamental event. Proponents of the Many-worlds interpretation saw it well, as they just dismissed the existence of any branching, to conclude that different possible measurement results keep coexisting, not really as branches from any specific branching event (as might be intuitively said for approximative descriptions), but as emergently separable components of the unitarily evolving state, which remains a unique physical state that only happens to be equal to a combination of these practical measurement results (without being directly affected by this fact). As David Wallace wrote : there is no such a thing as a well-defined "number of branches". Instead, in my view, all what plays the role of a branching time, is what you call the choice time; it needs not be retroactive, but only non-local (see details). So, since other interpretations (Bohm and Many-worlds) just deny the existence of any special measurement times at all, I think that introducing 2 different special times, one for branching, the other for choice, is a bit too much.

Dear Sir, I was not convinced. Your argument that mathematics is not a human invention was not convincing. I am more interested in the problem of why scientists believe in Einstein relativity when the mathematics involved in that theory is completely false. We are supposed to believe it because experiments validate it. So we believe in a false mathematical theory because the experiments say it is correct. Pretty funny.

Dear Cristinel, conclusion of your essay "So we can't prove the mathematical universe

hypothesis by Tegmark's method" provokes me to let you know that in our essay this hypothesis of Tegmark is refuted.

Best regards,

Alexey Burov.