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Trick or Truth Essay Contest (2015)
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And the math will set you free by Cristinel Stoica
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Author Cristinel Stoica wrote on Mar. 5, 2015 @ 01:25 GMT
Essay AbstractCan mathematics help us find our way through all the wonders and mysteries of the universe? When physicists describe the laws governing the physical world, mathematics is always involved. Is this due to the fact that the universe is, at least in part, mathematical? Or rather mathematics is merely a tool used by physicists to model phenomena? Is mathematics just a language to tell the story of our universe, a story which could be told with the same or even more effectiveness using another language? Or quite the opposite, the universe is just a mathematical structure?
Author BioTheoretical physicist. Research interests: foundations of physics, gauge theory, foundations of quantum mechanics, singularities in general relativity. Interested especially in the geometric aspects of the physical laws. ArXiv: http://arxiv.org/a/stoica_o_1 Blog: http://www.unitaryflow.com/ Scholar: https://scholar.google.com/citations?user=aleEOtsAAAAJ
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Edwin Eugene Klingman wrote on Mar. 5, 2015 @ 04:13 GMT
Dear Cristi,
You say "
at least we know that there is room for free will." You know that and I know that, though many dispute it. But free will, in any meaningful sense, is not deterministic, and, although one may draw an analogy with random numbers, I don't think one can draw it in any detail.
Thus I see no reason to contend that free will is isomorphic to math. Even if one...
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Dear Cristi,
You say "
at least we know that there is room for free will." You know that and I know that, though many dispute it. But free will, in any meaningful sense, is not deterministic, and, although one may draw an analogy with random numbers, I don't think one can draw it in any detail.
Thus I see no reason to contend that free will is isomorphic to math. Even if one can, post exercise of free will, or even concurrent with the exercise of free will, find some neural correlates. Free will partakes of
causal and I don't think mathematics reaches causal. So I don't think "everything is isomorphic to a mathematical structure." You seem to think differently. With reference to time, you say, "there is no conflict between mathematics and causal explanations." But I don't believe there is an 'explanation' for free will. I don't see this as in conflict with your arguments about
a theory of everything, to the effect that we cannot be living in a world described by two disconnected sets of laws. That seems to me a self-consistency argument that does not depend upon everything being isomorphic to math.
On another point you note "
if it looks like a duck, swims like a duck, and quacks like a duck, then it is a duck, isn't it?"
My essay analyzes why John Bell thought that "
it looked like Dirac spin, behaved like Dirac spin, and had an eigenvalue equation like Dirac spin, ['it' being the Pauli eigenvalue equation.] I argue that the Pauli equation of Stern-Gerlach is
not the Dirac equation of relativistic QM, and that Bell's oversimplification of this led him to impose what he felt were reasonable constraints that prevent a local model from achieving QM correlations.
I hope you will read
my essay and comment.
My best wishes to you,
Edwin Eugene Klingman
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Author Cristinel Stoica replied on Mar. 5, 2015 @ 07:37 GMT
Dear Edwin,
You say You say "at least we know that there is room for free will." and "Thus I see no reason to contend that free will is isomorphic to math.".
I wrote "at least we know that there is room for free will, whatever this may be", and also, when talking about neural correlates, I said "But by this I don't claim we can explain consciousness,...
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Dear Edwin,
You say
You say "at least we know that there is room for free will." and "
Thus I see no reason to contend that free will is isomorphic to math.".
I wrote "
at least we know that there is room for free will, whatever this may be", and also, when talking about neural correlates, I said "
But by this I don't claim we can explain consciousness, with or without mathematics."
About you disputing Bell's theorem, I may say more after I will read your essay. But I just want to let you know that his theorem is correct and I've seen so many failed attempts to contradict it. If I will find yours is one of them, I will not be interested in insisting to convince you :)
Best wishes,
Cristi
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Edwin Eugene Klingman replied on Mar. 5, 2015 @ 18:31 GMT
Dear Cristi,
I agree with both of your statements about free will and consciousness.
Your attitude toward Bell's theorem is reasonable. If you read my essay and understand it, but find it in error, there is no need to try to convince me. Yet I would appreciate it if you could give a hint of where you find the error.
Please understand that I do not claim his mathematical...
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Dear Cristi,
I agree with both of your statements about free will and consciousness.
Your attitude toward Bell's theorem is reasonable. If you read my essay and understand it, but find it in error, there is no need to try to convince me. Yet I would appreciate it if you could give a hint of where you find the error.
Please understand that
I do not claim his mathematical theorem is not correct. Bell's theorem
is mathematically correct. I claim that his physics is oversimplified and his model does not represent the actual physics that goes on in the inhomogeneous field. He assumes the physics of a constant field, which will produce null results, and so leads to a contradiction. When one analyzes the physics in a non-constant field, one finds new physics, and no contradiction.
My approach is not to deny entanglement as a starting proposition, but to explore Bell's conclusion that
no local model can produce the QM correlation. I have presented
a local model that does produce the QM correlations, unless Bell's constraints are imposed.
This would seem to call Bell's constraints into question, and so I have analyzed the reason why he might have imposed such constraints. My essay offers an explanation, based on his confusion of Dirac and Pauli eigenvalue equations, and assumptions of eigenvalue measurements. If this analysis is valid, then the rationale for entanglement is called into question.
I fully realize that questioning
The Gospel According to Bell almost automatically puts one in the kook category. But if fear of being labeled prevents all attempts to analyze fundamental physics we will never escape any errors that may be built into our fundamental physics.
My very best regards,
Edwin Eugene Klingman
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Author Cristinel Stoica replied on Mar. 6, 2015 @ 05:24 GMT
Dear Edwin,
I completely agree with you that we should question "The Gospel According to Bell" or anything we accept to be true, including classical locality. Bell himself was led to his results by questioning the results against hidden variables accepted in his time (so you are in good company). Reconsidering the foundations should be done systematically, just like one cleans our houses. I...
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Dear Edwin,
I completely agree with you that we should question "The Gospel According to Bell" or anything we accept to be true, including classical locality. Bell himself was led to his results by questioning the results against hidden variables accepted in his time (so you are in good company). Reconsidering the foundations should be done systematically, just like one cleans our houses. I do it myself, so I wouldn't be the one to throw the first stone.
However, I hate to be a party killer, but locality in any classical sense is "deprecated". Bell doesn't assume anything about dynamics, neither that it is Dirac or Pauli. He deliberately resumes the discussion to observables of what today we call qubits. His results are true and apply to any kind of qubit, being it given by electron's spin or photon's polarization.
But like I said, I wouldn't stop anyone for critically analyzing his theorem. I am not
quantum police. I wouldn't stop anyone to study perpetual motion too. This is how we learn, and many important results were found when thinking at impossible things.
Best wishes,
Cristi
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Edwin Eugene Klingman replied on Mar. 7, 2015 @ 03:05 GMT
Dear Cristi,
You claim that Bell doesn't assume anything about dynamics, but on page 141 of 'Speakable...' he states clearly that "
the angular momentum, by gyroscopic action, should stabilize the angle between particle axis and magnetic fields." This is most definitely a dynamic assumption and it underlies his overly-simple model.
The first Letter in the
Phys Rev Letters I received today, (PRL 114, 040401, 30 January 2015) states that
"
To determine if the evolution of the quantum system is governed by one or another Hamiltonian, one must perform measurements on the system and use these outcomes to infer the most likely assumptions."
I don't think Bell should be exempt from that. Nor do I understand why so many physicists are adamantly opposed to investigating a different Hamiltonian than the oversimplified and unrealistic one chosen by Bell to model his local system. I hope that when you read my essay, it might have information that you haven't seen yet. Otherwise there would have been little reason to write it.
My best regards,
Edwin Eugene Klingman
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Author Cristinel Stoica replied on Mar. 16, 2015 @ 17:04 GMT
Dear Edwin,
I've read your essay, and asked some questions
here.
Best regards,
Cristi
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Pentcho Valev wrote on Mar. 5, 2015 @ 07:54 GMT
"But can we find a property of time that can't possibly be described by mathematics? In fact, time was best understood due to mathematics, in relativity and thermodynamics."
This "understanding" is based on postulates that could be false. For instance, Einstein could have mistakenly "taken from the idea of light waves in the ether the one aspect that he needed" - then not only the...
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"But can we find a property of time that can't possibly be described by mathematics? In fact, time was best understood due to mathematics, in relativity and thermodynamics."
This "understanding" is based on postulates that could be false. For instance, Einstein could have mistakenly "taken from the idea of light waves in the ether the one aspect that he needed" - then not only the "understanding" of time, but theoretical physics as a whole would be wrong:
Relativity and Its Roots, Banesh Hoffmann, p.92: "There are various remarks to be made about this second principle. For instance, if it is so obvious, how could it turn out to be part of a revolution - especially when the first principle is also a natural one? Moreover, if light consists of particles, as Einstein had suggested in his paper submitted just thirteen weeks before this one, the second principle seems absurd: A stone thrown from a speeding train can do far more damage than one thrown from a train at rest; the speed of the particle is not independent of the motion of the object emitting it. And if we take light to consist of particles and assume that these particles obey Newton's laws, they will conform to Newtonian relativity and thus automatically account for the null result of the Michelson-Morley experiment without recourse to contracting lengths, local time, or Lorentz transformations. Yet, as we have seen, Einstein resisted the temptation to account for the null result in terms of particles of light and simple, familiar Newtonian ideas, and introduced as his second postulate something that was more or less obvious when thought of in terms of waves in an ether. If it was so obvious, though, why did he need to state it as a principle? Because, having taken from the idea of light waves in the ether the one aspect that he needed, he declared early in his paper, to quote his own words, that "the introduction of a 'luminiferous ether' will prove to be superfluous."
Pentcho Valev
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Author Cristinel Stoica replied on Mar. 5, 2015 @ 09:13 GMT
This is how science works, if a theory turns out to be wrong, we try to find a better one. I doubt that so far relativity and theoretical physics as a whole turned out to be so wrong, but I admit they don't answer everything yet, and they may be replaced by completely different theories someday.
Eckard Blumschein replied on Mar. 10, 2015 @ 19:36 GMT
Cristinel,
After Phipps found better Maxwell's equations, we don't even try and admit what is wrong with Poincaré's Lorentz transformation. This is how science doesn't work.
Everybody persistently uses the expression Michelson-Morley experiment although Morley did definitely not contribute to the concept of Michelson's experiments in Potsdam 1881 and in Cleveland...
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Cristinel,
After Phipps found better Maxwell's equations, we don't even try and admit what is wrong with Poincaré's Lorentz transformation. This is how science doesn't work.
Everybody persistently uses the expression Michelson-Morley experiment although Morley did definitely not contribute to the concept of Michelson's experiments in Potsdam 1881 and in Cleveland 1887.
Pentcho should admit at least the possibility that Michelson's 1881/78 null result does not need an explanation in terms of Relativity if one shares Leibniz' relativity, i.e. the opinion that space is not a medium but just mutual relations between objects.
You wrote to Michel: "it is possible to find for any object a mathematical description that captures everything that can be said about that object, precisely because mathematics is so versatile." Just consider the rather illusory Human Brain Project, or the future of humanity. Perhaps you cannot even calculate how many grandchildren your grandchildren will have.
Regards,
Eckard
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Author Cristinel Stoica replied on Mar. 10, 2015 @ 20:33 GMT
Dear Eckard,
You said "Perhaps you cannot even calculate how many grandchildren your grandchildren will have."
Well, I frankly can't even calculate how many children I will have, let alone the grandchildren of my grandchildren :). But this is not what I said to Michel. I was talking about the power of mathematics to describe the objects we know, not to those we don't know, or which...
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Dear Eckard,
You said "Perhaps you cannot even calculate how many grandchildren your grandchildren will have."
Well, I frankly can't even calculate how many children I will have, let alone the grandchildren of my grandchildren :). But this is not what I said to Michel. I was talking about the power of mathematics to describe the objects we know, not to those we don't know, or which depend on information we can't gather for practical reasons. So I think what I said means something else to you that it meant to me.
Regarding your arguments against relativity, I am sorry, but I am unable to make the conceptual leap required to move forward to Galilean relativity, because my mind is still prisoner of the old paradigm of Einstein's relativity ;). I hope I haven't disappointed you.
Best regards,
Cristi
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Eckard Blumschein replied on Mar. 11, 2015 @ 15:33 GMT
Dear Cristi,
I mentioned the Human Brain Project because I see many participants of the contest sharing the rather naive idea that mathematics is versatile enough as to completely mimic even the brain. Having dealt in detail with auditory function, I would like to explain why this cannot be achieved: Physiological research shows that the biological solution is fundamentally different from any theoretical approach and with respect to aspects like for instance robustness, flexibility, and efficiency still by far superior. Spectrograms that are based on Einstein/Hilbert's denial of the now exhibit ridiculously unreal behavior.
Best regards,
Eckard
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Michel Planat wrote on Mar. 5, 2015 @ 09:36 GMT
Dear Christi,
You try to go very far in the identification of the object and the words/mathematics that describe it. Your map of all sentences to numbers in the segment [0,1] is very illustrative. But you could as well have selected the formalism of QM where epistemological statements are the rule. I understand from your very good essay that you are a platonist, isn'it? What opinion do you have about the ontology of physics? Do you see a cutting edge betwwen the map/description and the physical object? Myself I am reluctant in accepting that physics is just maths and I am not sure that this reluctance can be formalized.
Michel
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Author Cristinel Stoica replied on Mar. 5, 2015 @ 10:09 GMT
Dear Michel,
I am not sure I identify objects with mathematical descriptions. I just say it is possible to find for any object a mathematical description that captures everything that can be said about that object, precisely because mathematics is so versatile. And it is versatile even if our world is not really a mathematical structure, and that's why we can't really distinguish the two. The introductory discussion is just a toy to make a point. To make everything a point :)
I don't consider myself a Platonist. I don't care about abstract mathematical worlds, disconnected from our physical world. But I think that our world is indistinguishable from a mathematical structure, and if we rely on something non-mathematical, this is just provisional.
I think that we should admit
supermathematical* descriptions as final only if we are sure that we exhausted any hope for a
mathematical description. And I don't think this is possible
Best wishes,
Cristi
_______________
*
Supermathematical is to
mathematical what
supernatural is to
natural.
David Brown wrote on Mar. 5, 2015 @ 12:02 GMT
Dear Cristinel Stoica,
In your essay you wrote, "... it may be possible that we will be able to find the fundamental physical laws. The reason is that it seems that the universe seems to be very regular. The physical laws appear to be the same at any point and at any time." Does each universe in the multiverse have precisely the same physical laws? What, in your opinion, might be the explanation for the space roar?
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Author Cristinel Stoica replied on Mar. 5, 2015 @ 12:28 GMT
Dear David Brown,
You ask
Does each universe in the multiverse have precisely the same physical laws?I don't know what's outside our universe, assuming there is something. But if you refer to a particular multiverse theory, it comes with its own answer. For example, in the Many World Interpretation, as well in the multiverse predicted by some theories of inflation, the fundamental laws are the same. However, the laws that are not fundamental and depend on symmetry breaking may be different.
You ask
What, in your opinion, might be the explanation for the space roar?I didn't study the space roar and I don't have an opinion about it.
Cristi
KoGuan Leo wrote on Mar. 5, 2015 @ 15:54 GMT
Dear Cristi,
I always enjoy reading your essay, full of refreshing information and rational, logical and complete argument. I completely agree with you that there must be one coherent theory with one formula that produces only one Integer number normalized one "1" based on one principle derived from one source. I also completely in agreement with your hypothesis that "our universe has to be Turing complete". This is because the universe wants us to know its secret recipe not only for our own survival but also for the survival of Existence (Creator) itself. If not, it is not possible for mere human like us to find this theory and its formula. In other words, this theory of everything not only knows the mind of our Creator but it is the Creator itself, so that Existence, hence the Creator, would avoid its own extinction by allowing us, the avatar Creator, to save ourselves and our Creator. This is because Existence is precariously in the border of collapse and it does need fine tuning to stay on existing. Existence is living dangerously from extinction at any time, because Existence supposed not to exist. If I may plead that KQID might be such theory that would deliver the good.
Best wishes,
Leo KoGuan
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Author Cristinel Stoica replied on Mar. 5, 2015 @ 16:41 GMT
Dear Leo,
Thank you for the interesting comments. As you have noticed, I also tend to adopt the optimistic position that reason can lead us far, because the alternative seems to me that is limiting us, or even makes us focusing on excuses to avoid going deeper. By optimism I don't understand thinking that everything is understood, since this would be as unproductive as thinking we can't understand more.
Best wishes,
Cristi
Anonymous replied on Mar. 6, 2015 @ 00:27 GMT
Dear Cristi,
On the contrary, it is like knowing the rule of the game of Chess, this enabling us to play Chess and the more we play the better we will become. More fun and exciting if we are playing against a grandmaster of Chess, losing and winning is part of the game. Yes, we are in the middle of mathematical game according to FQXI as the creature of Max Tegmark as the creator of this game. Let's continuing on playing as Newton pointed out that the Creator is assumed to help him doing the adjustment to fix the orbits correctly so that our solar system ( our universe at that time) are well behaving and not falling apart. My discovery points me that rather than our Creator is busy in doing so many adjustments in trillions trillions solar systems out there, we as the avatars of our Creator would be the ones doing the adjustments to save ourselves and be the Guardian of Existence.
No bad a job eh, being the guardians of our universe, we will be very busy like in the cartoon,
Leo KoGuan
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Author Cristinel Stoica replied on Mar. 6, 2015 @ 05:34 GMT
Dear Leo,
Then let me dedicate to you and all the guardians
this clip :)
Best wishes,
Cristi
Alan M. Kadin wrote on Mar. 7, 2015 @ 15:08 GMT
Dear Dr. Stoica:
Your essay focuses on the liberating aspect of mathematics: "And the Math Will Set You Free."
In contrast, my essay asserts that mathematics can enslave us and blind us from the truth.
"Remove the Blinders: How Mathematics Distorted the Development of Quantum Theory" questions the orthodox Hilbert-Space Model of QM, and presents a simple realistic picture that makes directly testable experimental predictions, based on little more than Stern-Gerlach measurements. Remarkably, these simple experiments have never been done.
The accepted view of QM is that the physics (and mathematics) of the microworld are fundamentally different from those of the macroworld, which of course creates an inevitable boundary problem. I take the radical (and heretical) view that the fundamental organization is the same on both scales, so that the boundary problem immediately disappears. Quantum indeterminacy, superposition, and entanglement are artifacts of the inappropriate mathematical formalism. QM is not a universal theory of matter; it is rather a mechanism for distributed vector fields to self-organize into spin-quantized coherent domains similar to solitons. This requires nonlinear mathematics that is not present in the standard formalism.
So while mathematics provides essential insights into physics, an incorrect mathematical model that becomes established may be seen as virtually religious dogma which is not to be questioned. That prevents further progress.
Alan Kadin
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Author Cristinel Stoica replied on Mar. 7, 2015 @ 16:09 GMT
Dear Dr. Kadin,
I completely agree with you that insisting on a mathematical model despite contrary evidence may blind us and lead us far from truth. But if someone hurts his finger with a hammer, it's not the fault of the hammer. This doesn't mean we can't make a better hammer. People can make anything into a dogma, and is their fault here, not of that thing. We should question anything.
Best regards,
Cristi
Ed Unverricht wrote on Mar. 8, 2015 @ 02:10 GMT
Dear Cristi Stoica,
Enjoyed your essay. Your comment "there must exist a mathematical structure which satisfies our observations about both the quantum world, and the general relativistic one. Maybe these theories are somehow limits of this theory. But the unified theory must exist, even if we don’t have it yet." was well argued and very believable.
I agree with your comment "The idea that the universe is nothing but a mathematical structure leads to many difficult and interesting questions".
My essay revolves around modelling the mathematical structures of the particles of the standard model. I hope you get a chance to have a look at the modelling I use for the particles of the standard model and look forward to any comments you may have.
Good luck on your essay, you deserve a good rating.
Regards,
Ed Unverricht
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Author Cristinel Stoica replied on Mar. 8, 2015 @ 05:47 GMT
Dear Ed,
Indeed, we need a better understanding of the standard model, and I am happy that there are researchers trying various models. It's a fascinating field, in which geometry plays a major role. Thank you for the comments and wishes.
Good luck to you too,
Cristi
Member Rick Searle wrote on Mar. 9, 2015 @ 02:27 GMT
Dear Cristi,
As always I greatly enjoyed you essay. If I understand you, the position you are taking is that we live in a mathematical structure, but can never express the full intricacy of that structure. The purpose of physics is to express the general laws that describe our universe:
“However, we are just looking for a theory describing the general laws, and not a complete description of this particular instance of the universe, which includes what every human thinks about the universe and themselves. This would not be feasible anyway for practical reasons.”
Is my interpretation of your idea correct? And if so, where would a mathematical structure that failed to match the universe’s general laws be said to exist? Or should we take it that one class of mathematical objects conforms to the real world and another are just humanly constructed?
Also, if you get a chance, please check out my essay where I imagine how a weak version of the MUH might be testable and let me know what you think along with your vote.
http://fqxi.org/community/forum/topic/2391
Best of luck in the contest!
Rick Searle
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Author Cristinel Stoica replied on Mar. 9, 2015 @ 09:01 GMT
Dear Rick,
Thank you for the comments. Yes, I think that the universal laws can be known, but all details of the particular configuration can't be fully accessed by us, which are subsystems of the world, limited in time and space.
> where would a mathematical structure that failed to match the universe’s general laws be said to exist? Or should we take it that one class of mathematical objects conforms to the real world and another are just humanly constructed?
I find more compelling the idea that all mathematical structures have equal existence, but if our universe is a mathematical structure, then the other mathematical structures we know were obviously (re)constructed by us, since I find less likely that we gained some access to worlds outside ours. And if we will find the mathematical structure capturing completely the laws of our world, then we will do it by reason, hence by reconstruction too. However, what I argued is that if MUH is correct, we can't really prove it, not only because we are confined to only one of these structures. I reject Tegmark's attempt of proof on the grounds that if the universe, including us, is computational, then any universe with equal computational power offers the same benefits for the occurrence of intelligent life. But maybe other proofs can work, so I look forward to see your arguments for the testability of a weaker version of the MUH.
Best wishes,
Cristi
Torsten Asselmeyer-Maluga wrote on Mar. 9, 2015 @ 15:26 GMT
Dear Cristi,
welcome and good luck for teh contest.
More later
Torsten
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Author Cristinel Stoica replied on Mar. 9, 2015 @ 17:00 GMT
Dear Torsten,
Thank you, and good luck to you too!
Best wishes,
Cristi
Lawrence B Crowell wrote on Mar. 10, 2015 @ 03:27 GMT
Cristi,
I will get to your essay as soon as possible. I have been on travel, but will be able to read it in a few days. Good luck with this.
Cheers LC
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Author Cristinel Stoica replied on Mar. 10, 2015 @ 06:09 GMT
Dear Lawrence,
I plan to read yours as soon as possible too. Good luck to you too.
Best wishes,
Cristi
Author Cristinel Stoica wrote on Mar. 10, 2015 @ 07:29 GMT
Do we really need math in physics? :)
Member Marc Séguin replied on Mar. 20, 2015 @ 02:21 GMT
Cool T-shirt! It would also work with "Mathematician" and "Physicist" reversed, which proves that math is physics and physics is math!
Marc
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Author Cristinel Stoica replied on Mar. 20, 2015 @ 08:07 GMT
Vladimir Rogozhin wrote on Mar. 11, 2015 @ 11:11 GMT
Dear Cristi,
I read with great interest your depth analytical essays. I totally agree: "So, if we can understand the universe, it is because this immense complexity can be reduced to a small number of laws. And this reduction is made possible by mathematics." The way is simple: Mathematics as constructive ontology should "grab" the dialectic of eidos and logos, the dialectic of absolute forms of existence of matter.
Kind regards,
Vladimir
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Author Cristinel Stoica replied on Mar. 11, 2015 @ 12:27 GMT
Dear Vladimir,
Thank you for the kind comments. We seem to be lost in this complex diversity exhibited by the universe. So having some guiding order principles can help us making sense of the world. I look forward to read your essay.
Best wishes,
Cristi
Vladimir Rogozhin replied on Mar. 29, 2015 @ 14:03 GMT
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
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Jacek Safuta wrote on Mar. 11, 2015 @ 13:24 GMT
Dear Cristi,
In your excellent essay you ask crucial questions in current debate: what is mathematics? what is physics? and linking these: is mathematics merely a tool in physics? Referring also to Tegmark, I agree that everything is isomorphic to a mathematical structure and analogously to MUH I have coined Geometrical Universe Hypothesis. I propose to use the geometrization conjecture, proved by Perelman. We have the set of 8 Thurston geometries. We can treat them as a space-like, totally geodesic submanifolds of a 3+1 dimensional spacetime… and get all interactions and matter.
GUH makes the testable prediction resulting from Thurston geometries.
If you are interested you can find details in my essay
http://fqxi.org/community/forum/topic/2452
I would appreciate your comments. Thank you.
Jacek
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Author Cristinel Stoica replied on Mar. 12, 2015 @ 03:26 GMT
Dear Jacek,
Thank you for the nice comments. If the universe is isomorphic to a mathematical structure, it is my opinion too that this structure should be geometric and topological in nature. I look forward to read your essay.
Best wishes,
Cristi
Joe Fisher wrote on Mar. 11, 2015 @ 16:19 GMT
Dear Dr. Stoica,
Could you please explain to me why you thought that my comment about the real Universe was inappropriate?
You are I hope aware that suppression of the truth is unethical.
Eagerly awaiting your answer,
Joe Fisher
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Author Cristinel Stoica replied on Mar. 12, 2015 @ 03:34 GMT
Dear Mr. Fisher,
I see that your comment, which was rather nice and interesting, along with my reply to it, are missing. I can only assume that someone considered them inappropriate, but it wasn't me that person, so I can't explain why they are missing. Have you tried to ask the administrator to allow them here again, or ask him what happened, rather than accusing me of "suppression of the truth"?
Best wishes,
Cristi
Joe Fisher replied on Mar. 12, 2015 @ 15:42 GMT
I have asked Dr. Foster, the moderator of this competition and he claims that he did not remove it and for me to enquire of the person at the site. I posted a revised comment to your site, and that has been removed. I will repost for a third time.
Ruefully,
Joe Fisher
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Joe Fisher replied on Mar. 12, 2015 @ 15:46 GMT
Dear Dr. Stoica,
You wrote: “Some may hope that there are things in the universe which can't be described by mathematics. But can you name those things?” Thank you ever so much for asking. Please read and try to understand my definitive answer:
Accurate writing has enabled me to perfect a valid description of untangled unified reality: Proof exists that every real astronomer...
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Dear Dr. Stoica,
You wrote: “Some may hope that there are things in the universe which can't be described by mathematics. But can you name those things?” Thank you ever so much for asking. Please read and try to understand my definitive answer:
Accurate writing has enabled me to perfect a valid description of untangled unified reality: Proof exists that every real astronomer looking through a real telescope has failed to notice that each of the real galaxies he has observed is unique as to its structure and its perceived distance from all other real galaxies. Each real star is unique as to its structure and its perceived distance apart from all other real stars. Every real scientist who has peered at real snowflakes through a real microscope has concluded that each real snowflake is unique as to its structure. Real structure is unique, once. Unique, once does not consist of abstract amounts of abstract quanta. Based on one’s normal observation, one must conclude that all of the stars, all of the planets, all of the asteroids, all of the comets, all of the meteors, all of the specks of astral dust and all real objects have only one real thing in common. Each real object has a real material surface that seems to be attached to a material sub-surface. All surfaces, no matter the apparent degree of separation, must travel at the same constant speed. No matter in which direction one looks, one will only ever see a plethora of real surfaces and those surfaces must all be traveling at the same constant speed or else it would be physically impossible for one to observe them instantly and simultaneously. Real surfaces are easy to spot because they are well lighted. Real light does not travel far from its source as can be confirmed by looking at the real stars, or a real lightning bolt. Reflected light needs to adhere to a surface in order for it to be observed, which means that real light cannot have a surface of its own. Real light must be the only stationary substance in the real Universe. The stars remain in place due to astral radiation. The planets orbit because of atmospheric accumulation. There is no space.
Warm regards,
Joe Fisher
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Author Cristinel Stoica replied on Mar. 12, 2015 @ 22:24 GMT
Dear Mr. Fisher,
Thank you for reposting your missing comment, I am happy that you have it.
Best regards,
Cristi
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Mohammed M. Khalil wrote on Mar. 11, 2015 @ 19:13 GMT
Dear Cristi,
What a great essay! I enjoyed reading it very much. The topic of your essay echos that of
mine . However, my collaborator and I take the view that mathematics is invented, and from that we question its accuracy in describing nature.
I particularly liked your arguments for a theory of everything. I agree with you that there must be a unified theory because the universe obeys one set of laws. I used to think Godel's theorem might prevent us from finding that theory, but you provided compelling reasons against that argument. Maybe we can find that theory, and maybe we cannot. Either way, we can only try.
Good luck in the contest.
Mohammed
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Author Cristinel Stoica replied on Mar. 12, 2015 @ 03:38 GMT
Dear Mohammed,
Thank you for the kind and interesting comments. We seem to agree that humans can at least hope to find the theory of everything. Maybe we have different opinions on what it will be, but we agree that we don't know it yet, so maybe it will be as one of us thinks it is, or totally different, who knows. Good luck in the contest!
Best wishes,
Cristi
Torsten Asselmeyer-Maluga wrote on Mar. 18, 2015 @ 14:46 GMT
Dear Cristi,
now I had the chance to read your essay. Very interesting. In many parts, we both agreed (or as Pauli expressed it in a letter to Heisenberg: "boring agreement" ;-)
But at one point I went farther than: in my opinion at the center of modern math is structure (as you explained in one section). Math is not a simple theory to relate one number to another, it is rather a theory of structures. Even this structures will be also important in the future for other sciences. You mention model theory and even this point is crucial: one can change the model (including the logic), i.e. one can change the math completely and only the structure is left.
Maybe an agreement again?
Torsten
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Author Cristinel Stoica replied on Mar. 19, 2015 @ 08:59 GMT
Dear Torsten,
Thank you for the kind comments. Yes, the "boring agreement" between our viewpoints extends to your comments too :) I think math is the science of mathematical structures, and these are beyond models. I started reading your essay, and I will comment on your wall soon.
Best wishes,
Cristi
Torsten Asselmeyer-Maluga replied on Mar. 19, 2015 @ 10:50 GMT
Dear Cristi,
thanks for your words and vote, which I will give back! Other essays concentrated on the close relation between math and physics to forecast experiments. But not yours and I like it (and also your scientific work).
Best
Torsten
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Lawrence B Crowell wrote on Mar. 19, 2015 @ 16:56 GMT
I get a little worried when Goedel comes into the picture. This is not because I don’t think at some point this might rear its head, but because as you say this is misapplied. I think the real question is whether because we are a part of the universe that our attempt to completely codify the universe runs into this sort of incompleteness. We are in a way a piece of the universe that is working to encode its foundations, which is similar to a formal system listing or computing all its Goedel numbers. We may have an issue of this sort with the so called measurement problem and our inability to rectify quantum mechanics and measured outcomes with our macroscopic based thinking.
I am not sure one could say that 19th century physics was a unified theory as such. There were the three main areas of classical-Hamiltonian mechanics, thermodynamics, and electromagnetism. Thermodynamics ran into trouble with classical mechanics over the issue of time reversal invariance. Electromagnetic theory was not able to figure out how an arrangement of charges could be stable in a classical mechanical form. Then of course there was that annoying black body problem. I think physics then was filled with open questions that betrayed any idea of unification. I suppose in many at the time were confident that as Raleigh put it that all would be working once that black body problem is solved.
LC
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Author Cristinel Stoica replied on Mar. 20, 2015 @ 08:39 GMT
Dear Lawrence,
Thank you for the comments. I agree that us being part of the universe makes impossible to us to completely codify the universe. However, I don't think that trying to encode just the foundations is the same as trying to describe the whole, because the fundamental laws probably need a very small amount of memory to encode. Maybe a T-shirt, but even if it would be a book, would not be too much. I can imagine a computer containing a lot of information in it, including the complete specifications of the computer itself. Of course, it would not be possible to contain along with the specifications also a copy of the complete information contained in it, because it would have also to contain a copy of the copy and we regress to infinity. It is true that Maxwell's equations and the black body radiation require relativity and quantum mechanics, but what if these two tensions never appeared? A universe governed only by classical mechanics can easily contain a book of classical mechanics, or at least the page containing Newton's laws, without regression to infinity. I look forward to read your essay, to see your approach to the problem.
Best wishes,
Cristi
Rasjid Chan replied on Mar. 21, 2015 @ 17:36 GMT
Dear Cristinel,
About "And the math will set you free", it may be but only after you have realized the truth - and only "The truth shall set you free".
Man is a created being absolute as he cannot create himself. The Creator is the God of man - the God who divides as well as the God who unites. Everything that we know of as well as things that have never ever crossed our mind are all...
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Dear Cristinel,
About "And the math will set you free", it may be but only after you have realized the truth - and only "The truth shall set you free".
Man is a created being absolute as he cannot create himself. The Creator is the God of man - the God who divides as well as the God who unites. Everything that we know of as well as things that have never ever crossed our mind are all already ready out there - there is not a little one bit more or a little one bit less. Why? Because our God is the One Perfect God who misses nothing.
Mathematics is left only to be discovered. The patterns are all already part of the nature of the universe for our minds to unravel. It is all abstract as it is in harmony with the power endowed with our mind to work with abstract objects and structures. So mathematics is only mental and there is no "physical" reality in mathematics. But there are realms beyond the mental, beyond our endowed mental powers. So with the mind, as well as with mathematics, you cannot understand those unreachable realms.
Time is one realm completely beyond the mental understanding of man and mathematics. Time is only metaphysical. Since ancient time, time is taken to be absolute and its nature is almost as mysterious as the nature of God. To say we know of the nature of time is as good as saying we know the nature of God - which we cannot do. So in Newtonian mechanics time is just the variable 't' - there is no assumption that 't' could have properties that man can understand. It was the case until Einstein's relativity theories which presumed man has the ability to ascribe properties to 't' - that there is a Lorentz factor that have the properties of 't' implied within it. If the Lorentz transformation is "truth" that could describe physical reality, it would mean that man, through his thinking, could understand and give properties to God the Creator - which we cannot. The treatment that Isaac Newton gave to time, just a single variable 't', actually is an acknowledgment that man cannot know God except that "God is God". So there is only absolute time.
"But can we find a property of time that can't possibly be described by mathematics? In fact, time was best understood due to mathematics, in relativity and thermodynamics."
Actually, time cannot be understood;
within physics, there should not be any attempt to incorporate any understanding of time. It is because relativity try to assume that there there is a way to discover some property of time through inventing relative time dependent on the motion of a frame or that of the observer that both the special and general relativity theories can only be invalid.
Any theory of physics founded on the Lorentz transformation can only be invalid as the Lorentz transformation cannot be physical - meaning it can never be a valid physical theory describing the working of our physical universe.
Best Regards,
Chan Rasjid.
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Thomas Howard Ray wrote on Mar. 24, 2015 @ 02:46 GMT
Very nice essay, Cristi -- with the broad range of profound and interesting questions that one has come to expect from you. Well done.
A couple of things:
Being a student of Yaneer Bar-Yam (who by the way was just appointed as visiting professor to the MIT media lab) -- I appreciate your reference to his theory of multi-scale variety, which I regard as one of the most important theoretical advances in science today. It encompasses network-connected phenomena across every scale of physical self-organization, which brings me to the second thing:
Your claim that " ... we can’t prove the mathematical universe hypothesis by Tegmark’s method."
If one is a rationalist in the sense of Karl Popper, no scientific theory is ever proved. That is, no amount of empirical evidence that validates a theory, is proof that the theory is true -- only a falsifiable criterion makes a theory scientific at all. And Tegmark's criterion is very clear and unambiguously stated: if the universe is shown to be fundamentally based in randomness, the mathematical universe hypothesis is falsified.
There is also no ambiguity in Popper's position. Long ago, Popper made an important reversal of himself -- as important as Hawking's reversal in the case of black hole information loss -- that Darwin's theory of common ancestry is a falsifiable theory, after all. Not because we can refute common ancestry by a single experiment, but because biology is incoherent without the theory, and the auxiliary hypotheses that support the theory are clearly falsifiable.
In the same sense, I think that multi-scale variety can be seen as a unifying theory of complex systems, and Tegmark's MUH as a unifying theory of mathematical physics.
All best,
Tom
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Author Cristinel Stoica replied on Mar. 24, 2015 @ 08:29 GMT
Dear Tom,
Thank you for the interesting comments. Sure, Popper is right, "no scientific theory is ever proved". My argument regarding Tegmark's MUH is indeed that it can't be falsified by his criterion. You say that the criterion is "if the universe is shown to be fundamentally based in randomness, the mathematical universe hypothesis is falsified". I am not aware of Tegmark saying this, perhaps I don't get its meaning. I don't see why a mathematical structure can't be fundamentally based in randomness. I think Tegmark's idea is that there is a statistical way to show that our universe is a typical one supporting intelligent life, and this is what I disputed. My argument was that, since he also want them to be computable, most structures are computationally equivalent, for all practical purpose, with ours, so his criterion will fail. I am happy you were a student of Yaneer Bar-Yam, probably was a very interesting professor.
Best wishes,
Cristi
Thomas Howard Ray replied on Mar. 24, 2015 @ 10:59 GMT
Hi Cristi,
I didn't interpret Tegmark's falsifying criterion into existence. He states it explicitly in his book (p.356): "Looking toward the future, thee are two possibilities: If I'm wrong and the MUH is false, then physics will eventually hit an insurmountable roadblock beyond which no further progress is possible; there would be no further mathematical regularities to discover even though we still lacked a complete description of our physical reality. For example, a convincing demonstration that there's such a thing as fundamental randomness in the laws of nature (as opposed to deterministic observer cloning that merely *feels* random subjectively) would therefore refute the MUH. If I'm right, on the other hand, then there'll be no roadblock in our quest to understand reality, and we're limited only by our imagination!"
I explore this falsifying criterion in
my essay.
The question of computability enters because Max approaches the hypothesis the same way that Wigner describes the role of mathematics in physics: discovery of physical regularities leads to discovery of mathematical regularities. I argue that if MUH is true, it has to work both backward and forward -- i.e., discovery of mathematical regularities leads to discovery of physical regularities. MUH is true if, and only if, the hypothetical final theory is mathematically complete.
(By student of Bar-Yam, I didn't mean a classroom student but rather a follower. He is a dozen years younger than I -- showing once again that there's little correlation between age and wisdom.)
Best,
Tom
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Author Cristinel Stoica replied on Mar. 24, 2015 @ 11:36 GMT
Tom, thank you for the clarifications!
Best regards,
Cristi
Christian Corda wrote on Mar. 26, 2015 @ 11:45 GMT
Hi Cristi,
As I told you in my FQXi page, I have read your pretty Essay. Here are some comments:
1) I find the title very intriguing.
2) I think the most brilliant text ever written is Einstein's 1915 paper on general relativity!
3) The idea that all human creation and knowledge is a point in the interval [0, 1] is upsetting!
4) I disagree with Smolin's statement that "there is no mathematical object which is isomorphic to the universe as a whole". I think we merely do not know if such a mathematical object exists or not.
5) Congrats for generalizing the Weyl curvature hypothesis, you know that I am an estimator of your research work.
6) I do not think that you are too reductionist in claiming that there is a mathematical structure which is isomorphic to the universe described by the extended list of propositions. In fact, I agree with you.
7) I am not completely sure of the real existence of a a theory of everything, but it should be a great pity if it does not exist! The same for black holes!
8) Your statement that "if we can understand the universe, it is because this immense complexity can be reduced to a small number of laws" is very intriguing. It I think should have been appreciated by Einstein who claimed that "The most unintelligible thing about the universe is that it is intelligible at all."
In any case, the reading of your intriguing Essay was interesting and enjoyable. It surely deserves the highest score that I am going to give you.
I wish you best luck in the Contest.
Cheers, Ch.
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Author Cristinel Stoica replied on Mar. 26, 2015 @ 14:16 GMT
Hi Christian,
Thank you for the comments and for the kind words! With 2), I think I very much agree with you, but I wanted to connect with most readers, and perhaps upset others. With 3), as well as 1), indeed I wanted to upset the reader. So connect and upset, to make sure what you say will be remembered one way or another :)). About the other points, I think you are right too. I was happy to read your excellent essay, and I hope this edition you will get a well-deserved prize!
Best wishes,
Cristi
Christian Corda replied on Mar. 27, 2015 @ 13:49 GMT
Dear Cristi,
Thanks for your kind words, which honour me. I am happy to see that we are in perfect accord.
I wish you will get a well-deserved prize too! Let us cross our fingers!
Cheers, Ch.
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Armin Nikkhah Shirazi wrote on Mar. 26, 2015 @ 17:05 GMT
Dear Cristi,
The introduction to your essay is very clever. Most people do not appreciate that when going from the rationals to the real numbers, one enters a whole new ballgame, so to say. I did not appreciate it until I began to study some set theory, but your example brings this home very nicely.
I essentially agree with almost everything in the essay, but would like to add the...
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Dear Cristi,
The introduction to your essay is very clever. Most people do not appreciate that when going from the rationals to the real numbers, one enters a whole new ballgame, so to say. I did not appreciate it until I began to study some set theory, but your example brings this home very nicely.
I essentially agree with almost everything in the essay, but would like to add the following comments:
1. I think that at least in part, some of the difficulties pertaining to the metaphysical status of mathematics are linguistic. Specifically, I think "exist" is simply not a good word to apply to mathematical objects (unless one subscribes to the MUH) because it has too much baggage associated with the physical world. There should be expressions which capture subtle ontological nuances, similar to how Eskimos purportedly have over a dozen different words for snow. These nuances might allow us to refer to things like physical objects, feelings, thoughts and mathematical objects in such a way that we can keep separate what it is that we are talking about from everything else, and aid in investigating how they relate to each, if they do. I do agree with you that in the specific sense that you described it, every book, piece of music, etc. is already there.
2. Taking the ability to name something in the real world to entail being able to give a list of propositions that apply to it seems intuitively pleasing, but I still have a lingering feeling that there might be something above and beyond a complete list of propositions that characterizes physical objects. One could of course simply define this relation to be just so, but that seems like a cheap way out to me.
3. I am personally of the opinion that there is no "theory of everything". In fact, I consider the idea that there should be one as one of the last remaining vestiges of anthropocentrism in physics in the following sense: presupposing the existence of such a theory also presupposes that all processes in nature can be described using a small set of laws by one kind of observer of which we are a special example. Who is to say that there are not other kinds of observers whose observations of nature could also be described by a small set of laws but which would be *in principle* inaccessible to us? 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? I often see the argument that it makes no sense to imagine such frames because no spacetime observer can transform to them, but that exactly makes my point: We are observers in spacetime, and to suppose that speaking of such frames makes no sense reflects a very subtle form of anthropocentrism.
Again, yours was a very thought-provoking and well-written essay.
Best wishes,
Armin
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Author Cristinel Stoica replied on Mar. 26, 2015 @ 17:59 GMT
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...
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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
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Eckard Blumschein wrote on Mar. 28, 2015 @ 18:57 GMT
Dear Christinel,
"When physicists describe the laws governing the physical world, mathematics is always involved." This sentence of your abstract is the only one without question mark.
Let me ask you to provide something indispensable but possibly neglected: What about causality and about the border between past and future?
Regards,
Eckard
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Author Cristinel Stoica replied on Mar. 28, 2015 @ 19:44 GMT
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
Eckard Blumschein replied on Mar. 31, 2015 @ 07:46 GMT
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
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Author Cristinel Stoica replied on Mar. 31, 2015 @ 08:04 GMT
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
Eckard Blumschein replied on Mar. 31, 2015 @ 23:45 GMT
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
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Author Cristinel Stoica replied on Apr. 1, 2015 @ 03:45 GMT
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...
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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
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Eckard Blumschein replied on Apr. 1, 2015 @ 17:19 GMT
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...
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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
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Author Cristinel Stoica replied on Apr. 1, 2015 @ 21:02 GMT
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
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Member Marc Séguin wrote on Mar. 28, 2015 @ 19:40 GMT
Dear Cristi,
Thank you for your comments on my essay. I discussed your comment about the paradoxical nature of immortality in the context of a multi/maxiverse in a reply on my page.
Congratulations once again on an outstanding entry to this FQXi contest! I found myself highlighting a lot of your statements that I wholeheartedly agree with. In particular, in the section “Is there...
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Dear Cristi,
Thank you for your comments on my essay. I discussed your comment about the paradoxical nature of immortality in the context of a multi/maxiverse in a reply on my page.
Congratulations once again on an outstanding entry to this FQXi contest! I found myself highlighting a lot of your statements that I wholeheartedly agree with. In particular, in the section “Is there something that can’t be described by mathematics”, you nicely explain that, despite what mathematical universe critcs often affirm, consciousness and the flow of time could very well, in principle, “emerge” from mathematics , even if we don’t understand all of the details yet. I also agree that “emergence”, whatever it is, does not need a non-mathematical explanation (whatever that would mean), even if we, once again, do not understand all the details. There is an interesting parallel between some arguments against a mathematical universe and God-of the-gaps-type arguments : in the same way that some religious believers zero-in on the unexplained details of our scientific theories (for instance, the origin of the first life form on Earth) to see in them evidence that some sort of God is needed for that step, I think that many critics of the mathematical universe hypothesis zero-in on the parts of our understanding of the world that are not quite satisfactory (what is consciousness? why does time appear to flow?) to see in them evidence that the world cannot be fundamentally mathematical.
I agree with your conclusion that Gödel incompleteness and indecidability do not act as “show-stoppers” when one considers the fundamental relationships between mathematics and physical laws, because “to obtain an inconsistency, we should make the physical laws assert their own indecidability, but how could this be done?”
I also agree with you that the statement that our world is isomorphic to a mathematical structure is a “plain truth that doesn’t make predictions at all, and doesn’t explain anything”, and that any universe complex enough for universal Turing machines to exist could sustain our existence: that’s why, in my essay, I argue that we live simultaneously in an infinite number of larger contexts.
As I said in my reply to your comment on my page, I have some questions concerning your affirmation “at least we know that there is room for free will, whatever this may be”. While formulating them, I followed the trail from your reference pages and fallen into a rabbit hole of cross-linked articles… I will continue to think about this and come back to you soon, whether I have free will to do so or not…
Good luck in the contest… I hope you make it to the top this time!
Marc
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Author Cristinel Stoica replied on Mar. 29, 2015 @ 06:33 GMT
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
Michel Planat wrote on Mar. 29, 2015 @ 20:44 GMT
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
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Author Cristinel Stoica replied on Mar. 29, 2015 @ 22:13 GMT
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
Michel Planat replied on Mar. 30, 2015 @ 09:49 GMT
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
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Author Cristinel Stoica replied on Mar. 30, 2015 @ 09:58 GMT
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
Sophia Magnusdottir wrote on Mar. 30, 2015 @ 08:13 GMT
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
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Sophia Magnusdottir replied on Mar. 30, 2015 @ 08:14 GMT
Sorry for misspelling your name :/
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Author Cristinel Stoica replied on Mar. 30, 2015 @ 08:25 GMT
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
Laurence Hitterdale wrote on Mar. 31, 2015 @ 18:20 GMT
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
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Author Cristinel Stoica replied on Mar. 31, 2015 @ 18:55 GMT
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
Lawrence B Crowell wrote on Apr. 1, 2015 @ 21:28 GMT
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...
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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 R⊕V, for V a vector space,
(a, x)◦( 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^∞ 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
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Author Cristinel Stoica replied on Apr. 2, 2015 @ 06:49 GMT
Dear Lawrence,
Thank you for the links, and for the explanations.
Best wishes,
Cristi
Janko Kokosar wrote on Apr. 2, 2015 @ 07:37 GMT
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...
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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
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Author Cristinel Stoica replied on Apr. 2, 2015 @ 09:12 GMT
Dear Yanko,
Thank you for reading and commenting on my essay. I would take this opportunity to make some clarifications, and after that, you will probably feel that we agree more than you thought.
You say "I disagree that neural correlates are enough to explain consciousness." Well, this makes two of us, since I wrote "I don't claim we can explain consciousness, with or without mathematics. My only claim is that its physical manifestations are describable by mathematics, at least in principle."
Also, when I mentioned the duck principle, or "Leinbiz's identity of indiscernibles principle", I did it to delimit the domain of physics and objective science, and not as a claim that this explains also the subjective.
Related to what you said about the relation between quantum and free will, may I point you to some references:
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. Related to what you said about the Turing test,
I wrote something that you might like.
About gravity, I agree with Petkov that it is not a force, at least in general relativity is just inertia on curved spacetime. Make it just a force doesn't seem to me either to be the right way. However, I think that to some extent can still be treated in a quantum manner, given that the other forces are geometric in nature too, and in this case maybe
my own approach to quantum gravity, that singularities help removing the infinities in perturbative QG, may help, even though essentially it is not a force.
I agree very much with your words: "Because foundations of physics should be simple, the task of math is to describe quantum gravity on a t-shirt."
Best wishes,
Cristi
Janko Kokosar replied on Apr. 2, 2015 @ 19:14 GMT
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
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Author Cristinel Stoica replied on Apr. 2, 2015 @ 20:07 GMT
Dear Janko,
You said "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." In the first link I gave you I actually propose an experiment to test whether mind influences the randomness. The experiment is perhaps impossible to perform today, but in the future, who knows. I look forward to read your essay.
Best regards,
Cristi
Sylvain Poirier wrote on Apr. 2, 2015 @ 21:45 GMT
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...
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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.
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Author Cristinel Stoica replied on Apr. 3, 2015 @ 09:08 GMT
Dear Sylvain,
Thank you for reading, and for letting me know that you were bored (my readers seem to be polarized between boring agreement and boring disagreement, I think you are at this latter pole). When I first saw your essay-sized comment, I thought it is just a revenge for me being boring to you. But I wasn't bored by your comments at all, and I am grateful for them. The argument with...
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Dear Sylvain,
Thank you for reading, and for letting me know that you were bored (my readers seem to be polarized between boring agreement and boring disagreement, I think you are at this latter pole). When I first saw your essay-sized comment, I thought it is just a revenge for me being boring to you. But I wasn't bored by your comments at all, and I am grateful for them. The argument with the line being made of atoms seems to me that is just missing the point, since I never claimed that mathematical structures have to be made of atoms. Re. your example with the red color. Here is where you agree with me: "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." Yes, I am talking in this essay about the physical world, and here the neural correlates live, and they can be de described as you said, mathematically. About consciousness, I never claimed that it can be explained by math or physics, nor that it can't. Here is a phrase from my essay, which is missed by many: "I don't claim we can explain consciousness, with or without mathematics. My only claim is that its physical manifestations are describable by mathematics, at least in principle." Now, you mention NDEs. Suppose we are able to supervise all details of the neural activity, and the patient has an NDE. After his brain is rebutted, he will think that he had that NDE, and to these thoughts there will be associated neural activities. Will these neural correlates represent the memory of his feelings and experiences during the death experience, or will they be just the brain filling some gaps by creating compelling dreams? Could the neural correlates distinguish between these? I look forward to see this experiment, together with the irrefutable proof that it was memory and not imagination. Until then, I am thinking to avoid having the NDE myself since I think is a bit dangerous :) Re. Godel, what I said was in the context of Hawking's argument. Also, I don't assume that the laws of physics should be able to express arithmetics, and the quote about Turing completeness is in the context of Tegmark's MUH, which I was discussing. Re. Flowing with a Frozen River, I discuss there both versions of free-will, the standard one, based on quantum randomness, and the delayed initial conditions one, which I proposed merely because should not be excluded by default, and also because has some other advantages. And is not a twisted rewording, you are just being mean :). Also, "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." Sorry, I didn't intend to hide this :)) But I look forward to read your essay. Re. "Modern physics, determinism and free will", you said 'you make a distinction between "branching time" and "choice time".' You seem to understand "branching time" as being in the context of MWI, and it is actually in the context of indeterministic dynamical systems. Indeed, there is such an interpretation of MWI, with which both seem to disagree. The distinction between "branching time" and "choice time" is explained in that article and is not what you think it is. Sylvain, when I first read your comments, I realized they may seem a bit adversarial, but I decided to take them as being honest. Your comments are among my favorites, and although I gave brief answers to them, I will consider them seriously, since I see you invested a lot of time reading not only the essay, but other materials.
Best wishes,
Cristi
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Sylvain Poirier replied on Apr. 3, 2015 @ 20:28 GMT
Sorry for the ambiguity of some of my words that could be perceived more negatively than I meant. I did not mean that you had any intention to twist something. About this, I only meant I saw your interpretation of quantum physics as a sort of more complicated equivalent to other concepts I know. I am aware that when some ideas are discovered, they usually first appear in forms which are not the...
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Sorry for the ambiguity of some of my words that could be perceived more negatively than I meant. I did not mean that you had any intention to twist something. About this, I only meant I saw your interpretation of quantum physics as a sort of more complicated equivalent to other concepts I know. I am aware that when some ideas are discovered, they usually first appear in forms which are not the optimal way they can be expressed.
Of course I am aware that your idea of the line aimed to be interpreted mathematically only, so that physical interpretations of this idea were irrelevant. However, as long as it is about mathematical abstraction, I would consider it more relevant to stay in the vocabulary of abstractions, such as by the idea of encoding texts by numbers, and the idea that all natural numbers exist no matter how big they may be. So I just wanted to insist on the fact that a geometrical view adds strictly nothing to it, unless it gives a wrong intuition.
About NDEs, I think there are enough proofs, the only problem is that it is such a huge field that many people think there is no known proof yet just because they did not take enough time getting informed on what there is. I would just advise you to go explore the field without any preconception about what should a proof exactly look like to be conclusive, because many kinds of things can happen and form different sorts of proofs.
"
Godel, what I said was in the context of Hawking's argument"
I did not check what Hawking's argument is, I just directly know what the incompleteness theorem says and how it can be proven :)
If you don't assume that the laws of physics should be able to address arithmetic then all comments on the consequences of the incompleteness theorem on the laws of physics should be dismissed as inapplicable: then physical laws cannot assert their own undecidability, simply because they are not even able to express the question of their own undecidability, no matter what Hawking might have suggested about it.
About branching time "
in the context of indeterministic dynamical systems" : which indeterministic dynamical systems are you talking about, which can be found in known fundamental physics ? There is one established physical law, that is the unitary quantum evolution, which is deterministic. And there is the measurement problem, with disputed interpretations whether the collapse is due to conscious observation, or a spontaneous one, or none at all (MWI). I think, if you see a branching time somewhere, and you think that the choice operation retroactively modifies the state starting exactly from that branching time, then you make the behavior at that branching time discontinuous, since it does not conform to the unitary character of quantum evolution ; if you try to get a continuous indeterministic behavior from some non-linear differential equations with non-differentiable terms, I will dismiss such equations as having nothing to do with anything that could be scientifically verified about our universe.
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Author Cristinel Stoica replied on Apr. 3, 2015 @ 21:34 GMT
Dear Sylvain,
OK, so you now no longer say that my interpretation is a more complicated version of the standard one, but of some others you know.
Related to the line, I don't think I get what you mean, and how bringing atoms into discussion supported your claim.
About NDEs, you are missing/ignoring my point, which was about distinguishing between remembering and imagination based on neural correlates. Discussing anecdotal evidence will not change this, even if it is true.
About your statement "If you don't assume that the laws of physics should be able to address arithmetic then all comments on the consequences of the incompleteness theorem on the laws of physics should be dismissed as inapplicable", it doesn't make sense. It is like saying that if you don't assume the existence of tooth fairy it doesn't make sense to criticize a viewpoint which assumes the existence of tooth fairy.
Branching time in the context of indeterministic dynamical systems makes perfect sense, because I addressed any possible indeterministic theory, to show that indeterminism doesn't guarantee free-will. Rejecting them because the only one you want to consider is quantum indeterminism is unjustified. And, even if we talk about branching in the context of quantum mechanics doesn't mean MWI, since I was talking about branching in the space of states, the branching of the history into two possible histories, and not into two real worlds.
Best wishes,
Cristi
Sylvain Poirier replied on Apr. 4, 2015 @ 07:56 GMT
I think you are over-interpreting my words. I do think your interpretation of quantum physics is more complicated than the Copenhagen interpretation. What I meant is that you tried to introduce the idea of restoring a continuity, since you criticize the Copenhagen interpretation as introducing a discontinuity. But I consider that we can reach the same "result" of looking at things in a physically...
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I think you are over-interpreting my words. I do think your interpretation of quantum physics is more complicated than the Copenhagen interpretation. What I meant is that you tried to introduce the idea of restoring a continuity, since you criticize the Copenhagen interpretation as introducing a discontinuity. But I consider that we can reach the same "result" of looking at things in a physically continuous way, not by completely different ideas, but by re-interpreting the Copenhagen interpretation :) and more precisely considering the mind makes collapse interpretation as I described, which is not so different from Copenhagen.
I consider that your way of calling "anecdotal evidence" the whole body of existing observations which I guess you did not really care to study, is missing the point of the fact that even though "anecdotal" in some sense, some of these evidences (and even more: the accumulation of them) are nevertheless solid genuine evidence for your question of "distinguishing between remembering and imagination". Thus, I would dismiss the very categorization of evidences between "anecdotal" and some other, supposedly more solid kind of evidence, as meaningless : there is no such boundary. So, as soon as would be established that genuine out-of-body perceptions occurred during the experience (such as by the accurate report of information that could not be accessed by the body), it becomes logically necessary to reject any idea that such memory could be a fruit of the imagination by natural effects of neural activity, as an absolute impossibility, without any need of close examination of the brain activity.
" it doesn't make sense. It is like saying that if you don't assume the existence of tooth fairy it doesn't make sense to criticize a viewpoint which assumes the existence of tooth fairy."
It makes sense, and no it is not "like" what you say. Maybe you misinterpreted my words again, but for what I meant your comparison is just wrong, you are bringing up an example whose structure has nothing to do with the issue of the incompleteness theorem we were discussing. Let me be more precise to avoid any misunderstanding : I meant "Let us split possible cases: either the laws of physics are able to express arithmetic, or they are not. In the first case we can discuss the consequences of the incompleteness theorem on the laws of physics ; in the second case we can't, as it is not applicable". Any issue of personal belief is out of the question here.
" I addressed any possible indeterministic theory, to show that indeterminism doesn't guarantee free-will. Rejecting them because the only one you want to consider is quantum indeterminism is unjustified."
What is the point of discussing "any possible indeterministic theory" ? as if the probability for the mathematically expressible laws of physics of our universe to be as described by quantum physics, was close to zero; my view is to consider that this probability is close to 1. You seem to assume that some abstract general landscape of "all possible indeterministic laws" you nevertheless seem to have somewhat clear ideas of and that excludes quantum physics, should be admitted as much more likely to contain the correct picture instead. I think that my hypothesis has more scientific grounds than yours.
"branching in the space of states, the branching of the history into two possible histories", what the heck is that ? You mean the consistent histories interpretation ? Of course, except that quantum physics could never find anything to explain what may cause such branching, which has to be postulated from the outside of physics, and it makes the evolution clearly discontinuous, which you were claiming to avoid.
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Author Cristinel Stoica replied on Apr. 4, 2015 @ 08:51 GMT
Dear Sylvain,
Thank you for letting me know your thoughts. I read your replies, and I don't recognize my ideas in those that you are attributing to me and criticizing.
Best regards,
Cristi
Author Cristinel Stoica replied on Apr. 4, 2015 @ 12:18 GMT
But let me make one last try.
You said "I consider that your way of calling "anecdotal evidence" the whole body of existing observations which I guess you did not really care to study, is missing the point of the fact that even though "anecdotal" in some sense, some of these evidences (and even more: the accumulation of them) are nevertheless solid genuine evidence for your question of "distinguishing between remembering and imagination"."
First, I said "Discussing anecdotal evidence will not change this,
even if it is true." Did I bother to study it? Well, I read something, including a book by Raymond Moody. But I am also aware of this experiment by Parnia and his colleagues. I did not say for or against this, and I prefer to continue to do so, and if you think I should do something else, that's your problem. In what I write about free will I let this possibility open.
Related to tooth fairy issue. I don't assume the number thing, nor its negation. For the case is false, as you said, Godel's result doesn't matter. For the case is true, you saw my counterargument to Hawking. If I understand well, you claim that I should do only one of these. I think I see where your misunderstanding resides. You think one should discuss only what one believes. But this is not correct. It is perfectly legitimate to discuss different possibilities. In the case X, the solution is A, otherwise, it is B. I don't see here a problem. Discussing alternative cases is not contradiction, and one should not be forced to have an opinion about everything.
The same goes for the "branching" issue. In that paper, I was discussing two possibilities, the world is deterministic or not. Without entering in details about which theories are deterministic and which are not. And the branching was, as I said, in the space of possibilities. You try to label this either as MWI, or as consistent histories, or whatever. This would be incorrect. I already explained this in that article and in the replies.
Sylvain Poirier replied on Apr. 4, 2015 @ 16:24 GMT
"You think one should discuss only what one believes". No I don't. Of course I don't !!!!! How can you imagine that nonsense ????? Again an absurd misunderstanding. What I meant is that any argument should clearly distinguish both cases. So the problem in your essay (or did I fail to read it correctly ?) is that you did not make it clear what are the assumptions under which your argument is written. And this matter of "the assumptions under which an argument is written" is a matter of text and clarified presentation. And this matter of text and clarified presentation, has nothing to do with any issue of personal belief of the author, which is obviously irrelevant. If my reply looks as if your personal belief was the matter, I am sorry I did not mean it. I thought it was your belief since you seemed to take for granted that the incompleteness theorem was applicable, which requires this assumption, but this is ultimately irrelevant. then if it is not your belief, the trouble I found is that your text did not seem to make the needed clarification of the distinction of cases.
I will reply in more details later.
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Author Cristinel Stoica replied on Apr. 4, 2015 @ 17:21 GMT
I thought it is pretty clear that when I discuss Hawking's argument, I discuss it under his assumptions, and if I would want to change the assumption I would state it explicitly. Btw, do you think Hawking makes this assumption explicit? Now, assuming anyway that I was not clear under what assumptions I discuss, I think replying to you four times on the same topic should be enough to clarify this :)
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Harry Hamlin Ricker III wrote on Apr. 2, 2015 @ 22:14 GMT
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.
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Author Cristinel Stoica replied on Apr. 3, 2015 @ 09:11 GMT
Dear Sir,
Thank you for the comment, and for warning me of the fact that "scientists believe in Einstein relativity when the mathematics involved in that theory is completely false". I have in plan to write someday an essay in which I will discuss some misconceptions viz. special and general relativity, but I don't know when I will find time to do it.
Best regards,
Cristi
Alexey/Lev Burov wrote on Apr. 2, 2015 @ 23:21 GMT
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.
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Author Cristinel Stoica replied on Apr. 3, 2015 @ 09:12 GMT
Dear Alexey and Lev,
Thank you for the comment. You made me curious, and I look forward to read your essay, which is on my to do list.
Best regards,
Cristi
Frank Pohlmann wrote on Apr. 4, 2015 @ 16:32 GMT
Dear Christinel,
in your essay you outline clearly the 'isomorphism-paradigm' of the relation between physics and mathematics. I quote from you essay :1. 'If the universe is describable by a list of propositions, then there is a mathematical structure describable by the same propositions'.
And a bit later :2'....the unified theory must exists...because we can not live simultaneously in two disconnected worlds.'
I would like to point out that you make two strong metaphysical assumptions, based upon the ontology of classical mechanics :
1. That it is possible to come up with a complete list of properties of the entire! universe.
This assumption is clearly wrong!Why? Because you leave out the agent compiling the list.According to quantum mechanics it is simply not possible to auto-describe a state to a system.A quantum mechanical state ( even of the 'universe') is always assign by an observer outside the system. In other words, your 'complete' list always has a blind spot.
2.You make the assumption that there is only 'the-one-reality', with all of its parts in mutual 'connection'.
But it is again quantum mechanics which tells us otherwise. The parts of the reality 'to be connected' is not only a logical operation ( like the 'AND'-operator), but also a physical interaction between a system and an observer (another system).During the interaction the system will in general undergo a random change of state.
That means that your 'complete' list of properties not only has a blind spot, but it also undergoes random fluctuations.
As a conclusion, the notion of 'the-one-whole-reality' ( can be traced back to Parmenides) is exposed as a fairy tale.
We should learn to live and do physics without it.
In my essay I describe how physics is better understood as
Darwinian process, instead of a static description of 'the -one-reality'.
regards
Frank
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Author Cristinel Stoica replied on Apr. 4, 2015 @ 17:01 GMT
Dear Frank,
Thank you for reading my essay and for the comments.
1. I agree that a being inside the universe can't get a complete description of the universe. And I agreed also when I wrote the essay: "However, we are just looking for a theory describing the general laws, and not a complete description of this particular instance of the universe, which includes what every human thinks about the universe and themselves. This would not be feasible anyway for practical reasons"
2. I don't see why "it is again quantum mechanics which tells us otherwise", that is, that there is not one connected mathematical structure describing it, given that quantum mechanics is already a mathematical theory about one such mathematical structure, and it includes fluctuations, entanglement, contextuality and all that.
Thank you for pointing me to your essay, which I look forward to read.
Best regards,
Cristi
Donald G Palmer wrote on Apr. 5, 2015 @ 03:55 GMT
Dear Cristinel,
Lots of sweeping statements in this essay and many attempts to refute other arguments without sufficient logic or evidence and more of of attempts to persuade with a general sweeping comment (where is your evidence for "Even if we manage to extend the list with new truths about the universe, there is a mathematical structure which is isomorphic to the universe described by...
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Dear Cristinel,
Lots of sweeping statements in this essay and many attempts to refute other arguments without sufficient logic or evidence and more of of attempts to persuade with a general sweeping comment (where is your evidence for "Even if we manage to extend the list with new truths about the universe, there is a mathematical structure which is isomorphic to the universe described by the extended list of propositions" or "Any phenomenon related to time, for example memory, can in principle be described mathemat- ically.").
The main issue I think you should consider is the evolutionary character of mathematics. Mathematics is not a constant where the universe could or could not be isomorphic to it. Mathematics and physics have grown together. For a couple millennia Euclid's fifth postulate was considered to be True, yet a little over 150 years ago it was shown to be one of a few options (it was only true in certain circumstances, so not all circumstances everywhere). Can we say that the universe was isomorphic to Euclildean geometry in 1800, but not now? Our current physics would not be possible without this fundamental change in mathematics beyond Euclid. Since we are all limited to our current time in history, we are limited in what we know of mathematics, which could be, even today, a very small amount.
You also seem to think mathematics is itself consistent and complete, which is impossible to prove (and Godel's proof indicates otherwise for completeness).
Finally, you appear to think that the universe does not have contradictions in it, something that defies all evidence we have at the moment (if reductionism is correct, why is an intelligent being at our scale needed to understand it and to affect the very small as part of the understanding process?) - so this must be an article of faith on your part, which extends as much to mathematics as to the known universe.
Thank you for your essay, but I an unconvinced by your arguments.
Donald
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Author Cristinel Stoica replied on Apr. 5, 2015 @ 04:46 GMT
Dear Donald,
I read your comments and realized that you did not read with care my essay. Of course our
mathematical representations of the universe evolved together with physics. And these representations change, and I even wrote "We know laws that were never contradicted by our observations, and their validity seems to be eternal, but this doesn't mean they will not be contradicted by experiment someday, or that there are no corners of the universe where they don't apply."
I was talking about the possibility that the physical world is isomorphic with a mathematical structure which
we are still searching. So your argument is not against what I said, but what you think I said.
Also, you call Godel in your defense, but I also discuss this in the essay. Your statement that mathematics is not complete refers to mathematics which include arithmetic, and the incompleteness refers to the incompleteness of a finite set of axioms, in the sense that finite length proofs can't reach any truth. Drawing from this the conclusion that math is some broken toy that can't be fixed is forced. The conclusion, by contrary, is that math is much beyond the limited capacity of humans to express it in finite length proofs based on a finite number of axioms.
I don't understand your last argument, the one that the universe has contradictions and all evidence show this. You mean logical contradictions?
Thanks for your comments,
Cristi
Sylvain Poirier wrote on Apr. 5, 2015 @ 13:58 GMT
Now I more closely examined your article "Modern physics, Determinism and free-will", for properly replying to what you actually put there (sorry I was not careful enough last time). Indeed, I confused between your "interpretation" that you support, and your (incorrect) description of the wave function collapse with the role of free will in wavefunction collapse (that you criticize). I see now...
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Now I more closely examined your article "Modern physics, Determinism and free-will", for properly replying to what you actually put there (sorry I was not careful enough last time). Indeed, I confused between your "interpretation" that you support, and your (incorrect) description of the wave function collapse with the role of free will in wavefunction collapse (that you criticize). I see now they were separate sets of concepts.
About your own "interpretation":
"
even though the states |ψ
j0 〉
were obtained by a unitary operator from the orthonormal states |ψ
j1 〉,
they are not necessarily orthonormal, and may even become dependent. In fact, in our case they all become at t0 equal to |ψ
0 〉.
The operator U is a unitary operator on the total space of |ψ〉|η〉
, but not on the space of |ψ〉
. This shows that it is possible for |ψ〉
to satisfy the constraints of both observations, and still have unitary evolution"
Assuming for a moment that such ideas make sense, then why do you need the evolution to be unitary in the "total space" |ψ〉|η〉 ? After all, this system is only a subsystem of the Earth. So, if all we need is that the evolution is unitary for the Earth system then the evolution of its subsystems do not need to be unitary. By the way, where is the assumption of unitarity in QM ?
Now seriously : according to the rules of established QM, what your claim rigorously means is that the first measurement device (that made the first measurement) keeps physically interacting with the system during the time between measurements, so as to progressively align it with the basis of the second observable. Such a claim of interaction is just plain wrong. In reality, after the first measurement, the system no more interacts with the first measurement device, and even if a little bit of influence might subsist, it would be ridiculous to assume that this interaction systematically manages to align the system to one eigenvector of the second observable. You seem to attribute this coincidence to final causes: you seem to argue that there should exist possible initial conditions that make the evolution fit this condition, so that the presence of the second measurement will retroactively arrange the initial conditions to make all things fit so as to achieve this evolution of the system from the eigenstate of the first observable to the eigenstate of the second observable. I consider this as a mere dream since anyway, in good approximation, there is not supposed to be any interaction between the first measurement device and the system after measurement, so that no fine-tuning of the apparatus can make its non-existing interaction with the system succeed to align it with eigenvectors of the second observable.
"
In UIQM I acknowledge that the observed system is in fact entangled with all systems with which it interacted in the past."
Not entangled, but in continuous physical interaction. You are confusing between (the mathematical expressions of) entanglement and physical interaction.
In conclusion, your "interpretation" of QM is not an interpretation at all but some fantasy, another theory far from what QM actually says. Now since you did not explicitly claim to reject QM to develop your own theory, but kept giving the illusion that you respect it and only try to interpret it by keeping superficial similarities ("unitary evolution"...), it just shows that you have no serious understanding of quantum physics.
Now about your discussion of standard QM and the mind makes collapse interpretation:
"
If humans base their choices on random inputs, then this by itself doesn’t make them free."
Of course but only under the assumption that the inputs are actually random in the case under consideration. As I explained in
my interpretation of QM, I consider that the same process of wave function collapse usually obeys randomness in non-living systems, but departs from it in the cases of brain processes where free will applies. And I explained in length why I see this sort of "discrepancy" between the kinds of outputs of the same physical process of wavefunction collapse (normal randomness in "purely physical systems", vs. free will in the brain), to be not a discrepancy at all but a very elegant, coherent solution. (I also like the explanation by the last reply of
that thread).
"
The configuration after the branching has to evolve, so that the agent can see where it is going"
Where does that idea come from ? I see no reason for it. My view is that the collapse occurs at some time after decoherence, when the different possibilities are meaningfully distinguished by the observer; there is no need to assume any branching to have occurred before that time, nor to assume that the observer has any explicitly conscious perception of the alternative possibilities among which he is actually (more or less) choosing.
"
in the case of quantum mechanics, where the unitary evolution governed by Schrödinger’s equation is interrupted from time to time by the wave function collapse. Assuming that an agent uses this randomness to perform free choices, she must act precisely at the appropriate moment and position where the branching appears."
"
(The discontinuous jump) has never been directly observed. There is no known explicit process leading to the discontinuity. In fact, all interactions we know fit well in the Hamiltonian description, and the measurement devices are made of systems which obey it. So, where does the discontinuity come from?"
Indeed, if taken separately, these 2 issues would be problems. However, taken together they become zero problem as they resolve each other. Indeed, there is no definition of when the collapse occurs ? It looks like a mystery how the time of free choice may coincide with the time of collapse ? No problem : let the "time of collapse" be conventionally defined as given by the time of free choice. Then, there is no more mystery when and how the collapse occurs, and there is no mystery either how the time of choice may happen to coincide with it.
"
It would violate the conservation laws". This is one of my
objections against spontaneous collapse theories. But my interpretation of the collapse is different : I think it occurs not by projection but by selection of a world after decoherence (this is an emergent condition, that fits with my idea of collapse as a non-physical, non-local process) : it is still non-unitary but resolves some defects of the projection postulate. It does not satisfy the conservation laws if taken in a naive sense (expressed by averages) that you wrongly assume to be the necessary form of expression of the conservation laws, but does satisfy a
more subtle understanding of the conservation laws that I explained there.
Generally, my page on the mind makes collapse interpretation replied to all of your objections in your "2.2. The internal tension of quantum mechanics".
"
I find hard to believe that the environment is the cause of selecting the eigen‑states, because these depend only on the measurement device. Change the measurement device, and leave the rest of the environment unchanged, and the eigen‑states change too."
You missed that the role of the environment in decoherence happens by interaction with the measurement device. So, change the measurement device, leave the rest of the environment unchanged, then the environment will interact with the new measurement device to do the decoherence according to the new eigenstates given by the new measurement device.
You speak about the "decoherence interpretation" as if it was an option to accept or reject it. The reality, well-known by all serious participants in QM interpretation issues, is that decoherence is NOT an interpretation but a logically necessary consequence of established QM, completing the picture of what needs to be interpreted.
I stopped reading your article here. I consider that I found enough fatal flaws in it already. And I see it as a big bug in the academic system, to find such an incompetent "physicist" have any position as physicist there.
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Author Cristinel Stoica replied on Apr. 5, 2015 @ 16:22 GMT
Dear Sylvain,
Thank you for keeping your promise that you will "read and refute" my article, and to continue our "dialogue". Unfortunately, you are again missing the point and misinterpreting what I write :)
Let me explain what I am doing in the article you discuss, and in others: I am exploring the consequences of a modification of the standard interpretation of quantum mechanics,...
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Dear Sylvain,
Thank you for keeping your promise that you will "read and refute"
my article, and to continue
our "dialogue". Unfortunately, you are again missing the point and misinterpreting what I write :)
Let me explain what I am doing in the article you discuss, and in others: I am exploring the consequences of a modification of the standard interpretation of quantum mechanics, under the assumption that the unitary evolution is never broken by a discontinuous collapse. Some reasons why I am doing this: 1) there is no direct evidence of a non-unitarity in quantum mechanics, it was only inferred from the outcomes of the measurement, 2) a discontinuous collapse would break the conservation laws, and this also was never observed, 3) a discontinuous collapse introduces a tension between quantum mechanics and general relativity.
One of the consequences of maintaining unitary evolution even during the collapse is that the initial conditions of the measurement device and the observed system have to be correlated in advance (as I proven mathematically
here). Hence, the initial conditions have to be very special, like in contextuality. This may seem for an observer embedded in time, assuming she would know the complete information about the wavefunctions and not only the outcomes of the measurements, as being retroactive. However, by looking at the complete solution from the "outside", as in the block world view, these correlations appear merely as global consistency conditions, pretty much of the kind of consistency condition which Schrodinger used to find the atomic spectra from his wave equation. I explained this viewpoint more in
this talk and
this essay.
Please note that I don't consider that I am the keeper of the absolute truth, I am merely exploring a theory, because I consider it a better alternative for several reasons from which I mentioned some above.
What I do in that paper is that I explain that, if unitary evolution remains unbroken, then a succession of two incompatible measurements still can be explained without discontinuous collapse, if
both of the two measurement devices perturb the observed system in a special way. You misunderstood this, when you said "what your claim rigorously means is that the first measurement device (that made the first measurement) keeps physically interacting with the system during the time between measurements, so as to progressively align it with the basis of the second observable.". No, I don't claim that it keeps interacting with it, only that it perturbed the observed system in such a way I described there. You also said "You are confusing between (the mathematical expressions of) entanglement and physical interaction." You are incorrect, I know very well the difference between interaction and entanglement. What I say is that we can see this as a superposition of composite states (which is entanglement), and each composite state contains a different interaction. So your misunderstanding is clear again.
You quoted my article that "The configuration after the branching has to evolve, so that the agent can see where it is going", and replied "Where does that idea come from ? I see no reason for it.". Well, as I explained there (where I was talking about free will), to make a choice, you need to know what that choice means, some of its consequences. Otherwise what kind of a choice is that? The alternative is letting the randomness choose for you.
I want to point out that my unitary interpretation is compatible with a version of decoherence, and also with relative state interpretation.
If each of the decohered branches is unitary and not plagued with the discontinuous collapse. But usually the density matrix is given a meaning at the beginning (as representing the state), and another one after is diagonalized (as representing a statistical ensemble representing the branches after decoherence), and this amounts for each branch to a discontinuous collapse. Regarding your comment to my statement "I find hard to believe that the environment is the cause of selecting the eigenstates", I suggest you to take a look at the delayed-choice experiment and see if your explanation still holds. Since you called me incompetent for not agreeing that decoherence solves the measurement problem, let me remind you that also Roger Penrose and Anthony Leggett criticized it. Anyway, although I find your personal attacks not conformal to the rules of the contest, I prefer that your comments will not be removed.
Cristi
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Sylvain Poirier replied on Apr. 5, 2015 @ 20:58 GMT
"
to make a choice, you need to know what that choice means, some of its consequences. Otherwise what kind of a choice is that? The alternative is letting the randomness choose for you."
You are talking about fantasy, not about real facts. Of course it would be nice if we were always correctly informed about the consequences of our choices before making them, but this is not how...
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"
to make a choice, you need to know what that choice means, some of its consequences. Otherwise what kind of a choice is that? The alternative is letting the randomness choose for you."
You are talking about fantasy, not about real facts. Of course it would be nice if we were always correctly informed about the consequences of our choices before making them, but this is not how things usually happen in the real world, or anyway the laws of physics do not provide this. I never claimed that freedom never turns out to be a poisoned gift by lack of proper available means to anticipate the consequences of choices (and personally I do feel it as a very absurd poisoned gift in many cases). To anticipate the consequences of our actions we only have our imagination, which is is fallible, and possibly diverse social structures, but such considerations lead us quite far away from physics.
I'm not sure what are all the exact details of your errors, since there are hundreds of possible ways to make mistakes, but I know that your interpretation is incoherent (and if I misinterpret things, then it seems at least that your presentation is very unclear). First, if there is entanglement between the first measurement apparatus and the system after measurement, i.e. the system after measurement is not clearly in one of the eigenstates of the first measurement, then it means that the first measurement never happened (in the sense of its given observable that must be defined independently of the second observation : this first measurement is classified as an interaction and not a measurement). Second, again if there is an entanglement, then the observed system does most surely not evolve into any unique eigenspace of the second observable, so that the second measurement gives random results according to some discontinuous projection. Indeed in the absence of physical interaction between subsystems (as is the case after the first measurement, between the measurement apparatus and the system), the evolution of an entangled state will always lead to another entangled state, i.e. its components cannot evolve into pure states (they keep their shape : dimension of the space of possible values, entropy...).
"
Since you called me incompetent for not agreeing that decoherence solves the measurement problem"
Now you are obliging me to call you illiterate, because you could not even read correctly what I wrote : I never wrote that decoherence solves the measurement problem, only that it is part of the picture that needs to be interpreted. So now I'm done with you, I'll rather comment other essays. Bye.
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Author Cristinel Stoica replied on Apr. 6, 2015 @ 04:20 GMT
"You are talking about fantasy, not about real facts.". Then free will is a fantasy, and that's all. Note that I was not talking about knowing that your choice of lottery numbers is winning or that of you choose to save someone's life, this will not turn out to be a new Hitler. I was talking about being able to perform elementary actions. For example, choosing between going left or right. If the choice is made at the branching, is made by the branching. But randomness is not freedom. If this would be so, then any Geiger counter would have free will.
Joe Fisher wrote on Apr. 7, 2015 @ 15:35 GMT
Dear Cristinel,
I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.
All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.
Joe Fisher
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Member Giacomo Mauro D'Ariano wrote on Apr. 16, 2015 @ 16:38 GMT
Dear Cristi
I really enjoyed reading your beautiful essay.
Here some considerations.
(1)" A universe in a dot". This is a lovely peace of writing. It reinforces my conviction that the principle of finite information density must hold, as Feynman himself believed (see his 1982 Int. J. Th. Phys.) The continuum is paradoxical: you can write the whole history of the universe on...
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Dear Cristi
I really enjoyed reading your beautiful essay.
Here some considerations.
(1)" A universe in a dot". This is a lovely peace of writing. It reinforces my conviction that the principle of finite information density must hold, as Feynman himself believed (see his 1982 Int. J. Th. Phys.) The continuum is paradoxical: you can write the whole history of the universe on a single atom. This is also related to the following point (3)
(2) I totally disagree with Smolin on many things, even if I enjoyed reading most of his books, in particular Time Reborn where he already expresses his new ideas that you can also find in his current essay taken from his last book. The two main things I disagree on are: (2a) the physical laws are not constant; (2b) mathematics cannot describe “particularities”. I think that both assertions are unscientific according to Popper.
(2a) Imagine a physical law that changes every minute, and you don’t know how it does. It is not a law anymore, right? What about if it is valid for a year, or a billion of year, or not valid e.g. two billions light-years from our planet. What should be the validity time (and space) of the law? If we state a law, it is supposedly eternal. This, however, does not protect the law from possible falsification, which will ask for another law, yet supposedly eternal. In particular, the new law maybe a “meta-law“ which regulates the change of the falsified law.
(2b) A theory cannot describe “reality as it is”. It can describe/predict only connections between known conditions/preparations/events and observed facts. Inferring initial conditions in the past needs an increasingly larger knowledge of the current state, the more distant is the past from the now. We can only connects known facts with known facts, or predict facts from known facts: the theory cannot provide the initial conditions. If we want to predict what will happen, we need information about the past. Accounting for the Smolin’s “particularities” requires the knowledge of the initial conditions, otherwise it is not science: it is magic.
I love your ideas about “Is everything isomorphic to a mathematical structure?”. I agree with you that the answer is positive, and I enjoyed very much this part of your essay. I think that the point, however, is another one, and again it is about “what is theory”. A theory is a reduction of complexity of connections between events/observations. Transforming a set of observations (a peace of “reality”) into a list of propositions does not necessarily entail a complexity compression, it is not a theory. Suppose I give you the observation made of the following digits:
3.1415926535897932384626433832795028841971693993751058209749
445923078164062862...
A good theory would be the Plouffe formula that fits in few bits.
Also, as Poincaré says, the power of mathematics stays in the induction method, which produces an infinite compression of true statements. This is also the case of a physical law.
It would be too long to write everything I would like to say ..,
I hope to meet you again very soon and have a long discussion of philosophy of physics at a dinner table.
My best regards
and compliments again
Mauro
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Author Cristinel Stoica replied on Apr. 16, 2015 @ 19:07 GMT
Dear Mauro,
Thank you very much for reading the essay and for the interesting comments. I find myself in agreement with what you say. The continuum seems to allow much more information than it actually uses, so seems to be a waste :). So perhaps the continuum is rather an ordering principle for discrete information. With respect to Smolin's recent philosophy, I think you and I agree again, and your points 2a and 2b are right on the spot. And yes, you are definitely right about a theory being an efficient way to compress information. Indeed, we would have a lot to discuss, and I look forward to see you again at a conference, to discuss in more detail.
Best wishes,
Cristi
ABDELWAHED BANNOURI wrote on Apr. 17, 2015 @ 11:52 GMT
Daer Cristinel
I find your essay very interesting, indeed, I consider mine an extension to it. I agree on almost everything.
I believe, that the universe is "an hyper-equation". "A mathematical structure inside an other, and depends on another external"
"Mathematics and physics are two sides of the same thing. numbers and physical entities in motion”.
Now, I think...
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Daer Cristinel
I find your essay very interesting, indeed, I consider mine an extension to it. I agree on almost everything.
I believe, that the universe is "an hyper-equation". "A mathematical structure inside an other, and depends on another external"
"Mathematics and physics are two sides of the same thing. numbers and physical entities in motion”.
Now, I think we need concrete things from which we can start. For this. I proposed The Paradigm Bi-iterative: a concept that goes beyond quantum mechanics and general relativity.
Quantum mechanics is not enough, General Relativity is not correct. Maybe, that's why it was impossible to combine the two branches of modern physics. Therefore, it was necessary to introduce the mechanics iterative, as the source, to justify the origin of acceleration, force and time. In addition, the rhythm and the polarization.Two mechanics seemingly separate, connected with a constant, only in this way, we can unify them.
I am convinced that reality is made up of thin numbers and geometric shapes. For this, I have proposed a Theorem and various mathematical structures (see Annex), which in my opinion, could be the true universe's mathematics.
The Bi-iterative system's calculation considers reality multi-directional and multi-dimensional. with (1) we mean (1 * 1 * 1). while, the recursive computation and the Fibonacci series uses only the first, the fractal uses the first and the second. So, are wrongly linear, interprets reality on a bi-dimensional sheet. Instead, the system Bi-iterative uses all three.
Let's take an example:
(1 + 5 + 7 + 12) =
= 1 + 5 + 7 + (6 + 8 + 10)
= 1 + 5 + 7 + (3 + 4 + 5) + 8 +10)
= 1 + 5 + 7 + (3 +4 +5) + (1 + 6 - 9) + 10
= 1 + 5 + 7 + (3 +4 +5) + (1 + 6 - 9) + 10
= 1 + 5 + 7 + (3 +4 +5) + (1 + (3 + 4 + 5) - 9) + 10
= 13
= 2197
This structure is compact, inside it could coexist other structures indipendent.
which can be expressed also in a linear fashion:
(1 + 5 + 7 + 12) = 13 = 2197
= (6,5) + (6,5) + (6,5) + (6,5) + (6,5) + (6,5) + (6,5) + (6,5): A straight line.
“A complex and varied reality , can be described only with a structure capable of transforming”.
This sequence is like a clock going always forward, or rather, reflecting itself, coping itself.
( a + b + c + d ) + K
(1 + 5 + 7 + 12) + K
In agreement with the concept of light propagation and the distribution of mass and energy, fairly, K is a constant equivalent to (1) ....... + 1, + 1, + 1, + 1, + 1 ........
"The universe was born so, one bit after another, and continues to do it today."
Sincerly yours
Bannouri
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attachments:
Theorem_1.jpg,
Theorem_345.jpg
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Author Cristinel Stoica replied on Apr. 18, 2015 @ 05:56 GMT
Dear Bannouri,
Thank you for the kind and interesting comments. Indeed, in order to advance toward the understanding of the foundations, we have to go beyond what separates quantum mechanics and general relativity.
Best regards,
Cristi
Peter Jackson wrote on Apr. 17, 2015 @ 12:53 GMT
Christi,
Congratulations on another fine essay, and on hitting the top. Not only do I agree with most of your propositions (I axiomise that maths CAN describe all) but more importantly you set them out and describe them succinctly. I was also pleased to read you agree that a TOE IS possible and that Godel does NOT preclude a mathematical description. Do you agree that recursive higher orders should be able to model that formalism asymptotically?
One thing perhaps 'missing' was any reminder that a mathematical structure may not necessarily precisely model any physical process for which it's developed, though giving apparently correct outcomes. Do you agree this is possible? I assign this 'false proof' issue to much anomaly and paradox in physics and identify an important example in my own essay, confounding logic in QM. My suggestion is that if we say ALL maths must ALL be right if the bottom line proves right then we can be misguided about how nature actually evolves in time (which I agree is 'physical'). I hope you'll read and give your views.
You don't suggest a direction for any new formalism pointing towards a TOE, which is not a criticism as very few do, but again I hope you'll analyse the hierarchical 'rules of brackets' which i suggest does so consistently with your analysis (as far as I can see, but your view?)
I'm not surprised you're in the top group again and hope my score will help keep you there.
Very best of luck in the final judgements.
Peter
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Author Cristinel Stoica replied on Apr. 18, 2015 @ 06:10 GMT
Peter,
Thank you for the interesting remarks. Let me congratulate you as well for your place. Regarding your question "Do you agree that recursive higher orders should be able to model that formalism asymptotically?", I would say maybe.
> "One thing perhaps 'missing' was any reminder that a mathematical structure may not necessarily precisely model any physical process for which it's developed, though giving apparently correct outcomes. Do you agree this is possible?"
I think I addressed the question of models that are not "true" in a section of my essay named "Is mathematics merely a tool in physics?". If you refer to models that give all the correct outcomes, and can't be distinguished by other models by no matter what experiment, I think it is possible. But I think that if these can be related to anomalies and paradoxes, then they can be distinguished and falsified. Regarding "if we say ALL maths must ALL be right if the bottom line proves right then we can be misguided about how nature actually evolves in time", well, correct maths is right, but being right doesn't make it true about our physical world.
"You don't suggest a direction for any new formalism pointing towards a TOE". I think it is too early for such a suggestion.
I look forward to read your essay, which is on my todo list.
Best wishes,
Cristi
Steven P Sax wrote on Apr. 17, 2015 @ 17:46 GMT
Hi Cristinel,
Your excellent essay makes a compelling case for mapping the universe to mathematical structure, and you presented it in an upbeat and enjoyable narrative. Your demonstration of how pivotal topics from relativity and incompleteness do not limit this isomorphism, provides a very persuasive argument. I like that you explained there is no conflict between mathematics and causality, and your discussion on physical explanation and mathematical description was very pertinent. My essay also discusses the strong connection between physics and mathematics, and for example how changing the mathematical representation affects physical explanation. I also show what was considered a limitation on computation due to (Gödel) incompleteness, can in fact be an expansion when attempting to physically model the mathematical structure of indecidability. This may address or at least support points raised in your essay.
Also, I appreciated the wide variety of examples encompassed in your essay, and am motivated to check out your work on the Weyl curvature hypothesis, singularities, and free will.
A very interesting contribution that thoroughly addresses this topic, I give it the highest rating.
Please take a moment to read my essay and rate it as well. Thanks again,
Steve Sax
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Author Cristinel Stoica replied on Apr. 18, 2015 @ 06:24 GMT
Hi Steve,
Thanks for the interesting comments and kind remarks. Indeed, some may qualify my essay as (too) optimistic, and I don't really think there are limitations that should stop us from trying to learn more. By the same criteria, any attempt to understand the universe has to be optimistic. In the same time, I advocate an agnostic and skeptical position regarding the belief in the absolute validity of our theories. And as you said, I indeed see no conflict between mathematics and causality. I think you have a keen eye and understood well my points. Your remarks about how changing the mathematical representation affects physical explanation, and the idea to take advantage from Gödel's incompleteness theorem seem to me very interesting. I look forward to read your essay. Good luck in the contest!
Best regards,
Cristi
James Lee Hoover wrote on Apr. 21, 2015 @ 15:21 GMT
Cristi,
Thanks for being engaged in my essay and for your kind words.
Jim
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James Lee Hoover wrote on Apr. 21, 2015 @ 16:47 GMT
Christi,
I don't know how I missed your essay.
Your essay is delightful, like you have the essence of Socrates on your shoulder, distilling with questions and answers his method of inquiry and discussion. I think the potion you create works. It helps to clarify the mind-numbing. You also throw in helpful progressions of studies, GR beyond Newton, singularities.
Impressive essay.
Jim
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Author Cristinel Stoica replied on Apr. 21, 2015 @ 17:48 GMT
Thank you Jim, for reading and commenting my essay.
Best regards,
Cristi
Alexey/Lev Burov wrote on Apr. 21, 2015 @ 20:28 GMT
Dear Cristi,
Since this comment relates to both yours and our essays, I am reproducing it here, in your blog, with a slight abbreviation.
Thank you so much for your compliments; it is a true pleasure to be highly appreciated by one of the experts!
You underline that your main take away from our essay "is the uniqueness of the laws.” Maybe, our laws of nature are not exactly unique, but they definitely belong to a very special and narrow set of mathematical structures, much more narrow than Tegmark’s multiverse suggests. In other words, our laws are truly beautiful in that deep meaning of mathematical beauty which was professed by Pythagoreans of all times, from Pythagoras and Euclid to Kepler and Newton and to Einstein and Dirac.
In that light the statement of your essay that,
“Mathematics is already there, eternal and unchanging. What we invent is the discovery of mathematics,”
is revealed as having an even deeper meaning than it may at first seem.
Cheers and good luck!
Alexey and Lev
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Member David Hestenes wrote on Apr. 22, 2015 @ 00:37 GMT
I enjoyed your exploratory approach to the essay question, Cristi.
You parse it into many questions. But I get the impression that you are not dogmatically attached to any of your answers. Rather you enjoy the dialectic struggle between opposing ideas.
I would enjoy a joust over a beer with you sometime!
......David
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Author Cristinel Stoica replied on Apr. 22, 2015 @ 06:56 GMT
Thank you, David. I loved very much your essay. I am very pleased and honored that you liked mine. I have the feeling that you understand so well my position. I would be very happy to have a beer with you!
Warm regards,
Cristi
Member Sylvia Wenmackers wrote on Apr. 22, 2015 @ 09:04 GMT
Dear Christi Stoica,
I enjoyed reading your essay. In particular, I liked your approach to include many questions. Most of the competitors (including me) are too eager to give answers, but I think it is an important goal to get the reader to wonder about these questions first.
In addition, I would like to discuss two points.
The idea of illustrating how you can code various texts as numbers in the [0,1] interval seems well chosen for the intended audience. On the other hand, I worry that you may have stretched it a bit too far when you write: "That line contains your entire life". After all, my life is not a text. ;-) And even if it would be narrated, a lot would depend on the wording - in particular: the first word! (If the narrater always starts with "Well,..." then all our lives end up close to 1.)
You write at some that "the fact that mathematics is useful doesn't mean that the universe is mathematical". At a later point, you say that a full isomorphism (unknown so far) between the universe and a mathematical structure would mean that there is no difference between the two. This second part is not so clear to me: could there really be an isomorphism between the universe and a mathematical structure? In my opinion, at best we can find an isomorphism between _the structure of_ the universe and a mathematical structure. This makes all the difference: ascribing a structure to the universe leaves a lot of degrees of freedom, but more importantly, it would leave out the 'substance' of the universe, and it would avoid the conclusion that the universe is mathematical.
Still, my general impression of your essay is a positive one. And the fact that it leaves topics for discussion is a sign of its quality, not a criticism.
Best wishes,
Sylvia Wenmackers - Essay
Children of the Cosmos
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Author Cristinel Stoica replied on Apr. 22, 2015 @ 09:55 GMT
Dear Sylvia,
Thank you for the comments. You raise interesting questions.
One point you make is about my words "That line contains your entire life". You thoughtfully reply "After all, my life is not a text". Well, could you please tell me the part of your life which is not a text? I don't intend to be too curious, rather to ask you a trick question, since if you can tell this, you will make it into a text :) A quick reading of my essay may leave the reader with the feeling that I choose to ignore consciousness for example, but as I wrote, "I don't claim we can explain consciousness, with or without mathematics." What I wrote about this may clarify what I mean: "However, any feeling we may have, there are neural correlates associated to it, and hence, physical correlates. And these physical correlates are in the domain of known physics, which is strongly mathematized." About your excellent remark that you can choose to narrate the same life differently, and make it closer to one number or another, I fully agree, but I can't see why would this be a problem. As you know, there is a bijection between the points on a segment and those in a square, or the entire space, but that bijection can't be continuous. I understand that your remark reveals that representing everything on a segment is counterintuitive, and I like it. I just wanted to make a point regarding whether math is discovered or invented.
Another point you make is "could there really be an isomorphism between the universe and a mathematical structure? In my opinion, at best we can find an isomorphism between _the structure of_ the universe and a mathematical structure." I agree, isomorphism is between structures. For example, there are more isomorphisms between the set of real numbers and other structures. The real line is isomorphic with a square, if we refer to the category of sets, with a line if we refer to the category of topological spaces, with a totally ordered set if we refer to the order, with a vector space, with a metric space, with a group, semigroup, ring, field, etc., it all depends on the structure we are interested in. As I explained in the essay, the structure is captured in the relations, all relations that can be described by propositions. So there's nothing that can be left outside the structure, if we take into account all the true propositions about the world. Saying "ascribing a structure to the universe leaves a lot of degrees of freedom" is not necessarily true, I mean, of course it is true
if we leave outside some of the truths. About the substance, I don't know what you mean by this. Is it something that has effects? Then its properties are captured in the structure. If you think that there are properties of the substance that don't have effects to the structure, then I have nothing to say about it, and anything we would say would be out of our possibilities of verifications. I think the text in a book is what makes a book, and not the paper or the electronic memory used to keep a copy of that text.
It was a deep pleasure to talk with you, and I wish your essay will do well, since I loved it.
Best wishes,
Cristi
Member Sylvia Wenmackers replied on Apr. 22, 2015 @ 10:57 GMT
Dear Christi,
Thank you for your (fast!) response.
If I tell you an episode of my life, my life itself will not turn into words. To keep it simpler, let's talk about colours: mentioning a colour does not produce that colour (at best, it may trigger a memory of it). Even if I would be able to say everything about a particular colour (not just 'red', but the spectrum, possibly partial translucence, etc.) I would still not have reproduced the colour. Sure, I could use the information, in computer graphics for instance, to reproduce it. But I would need some hardware to run it on (part of the universe). With the universe as a whole, I don't see how a full description (for simplicity, let's rely on an outdated materialistic view: some mass here and some mass there) is enough (in the materialistic example: you would still need to get some mass in addition to a mere description thereof).
On your view, can you destroy all copies of a book (including our memories of reading it etc.) without destroying the text?
Best wishes,
Sylvia
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Author Cristinel Stoica replied on Apr. 22, 2015 @ 11:46 GMT
Dear Sylvia,
Thank you for the answer. I think I understand what you mean, but I don't think I made you understand what I mean.
"If I tell you an episode of my life, my life itself will not turn into words." Sure it will not. And even if you give me the complete list of episodes, your life will not turn into words. What I mean is that its structure will be captured in those words. So, going back to my words "That line contains your entire life", I should have said perhaps "That line contains a complete description of your entire life". The main subject of my essay was about the relation between mathematics and physics, and I was careful to mention that I don't aim to explain unphysical stuff, perhaps consciousness being an example.
You give a good example, that of a color. But you answer it yourself, you can reproduce it on a computer (and that information can be expressed if we wish as words, or as a point on a segment). Your worry that there will be not enough room for hardware in the universe to simulate the color is a new element you add. But the proof of principle remains: the possibility to describe that particular color exists. I am talking about the possibility of a description, not a real implementation of it, not of a hardware. I don't think that, in order to prove it, one should effectively build that description. For instance, the number π exists even if its decimals are nowhere written completely, and even if the entire universe is not enough to write it.
"On your view, can you destroy all copies of a book (including our memories of reading it etc.) without destroying the text?" If you destroy all writings containing Pythagora's thereom, you will not destroy it, you will destroy the information about it that we have. It will be soon rediscovered. But if you destroy all books by Shakespeare, I don't expect that we will rewrite them soon. They will still be in that segment, but we will lose the address to retrieve them. Think for example at a computer. When you normally delete a file, you delete a reference to it, but the information remains on the hard drive, and can be recovered by special software, until you overwrite it with other information. When you lose the address, the file is not lost. A home is not lost when you lose the address. But you lose your access to it. In the case of a book, the address is the book.
But when we talk about life, the things are different... I don't think that a complete description of your life values at least 0.000...01% of your life. You may think that this is a contradiction: on the one hand I claim that everything is isomorphic to a mathematical structure, on the other hand, I don't reject the possibility that consciousness or life is more than this. Maybe this is not obvious in my essay of this year (where I focused on the relation between mathematics and the physical world), but perhaps
the one for last year is more on this topic.
Best wishes,
Cristi
Member Sylvia Wenmackers wrote on Apr. 22, 2015 @ 12:29 GMT
Dear Christi,
Yes, it is easier for me to agree with the new formulation "That line contains a complete description of your entire life".
Just a clarification: my point with the color example was not that there isn't enough room in the universe for the hardware. Simply that we need hardware, which presupposes that we already have the universe at our disposal* - and exactly this does not work when it is the entire universe we want to describe. If we have that mathematical description and delete the physical universe, it does not become reality. Our description will at best be isomorphic to the structure of the universe, but still something is missing to be able to bridge the gap from a mere description to reality.
Thanks for your reply to my question about the book text! It was really nice to have this exchange with you.
Best wishes and good luck,
Sylvia
*: It's a bit like the Sagan quote: "If you wish to make an apple pie from scratch, you must first invent the universe" ;-)
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Member Tejinder Pal Singh wrote on Apr. 22, 2015 @ 14:59 GMT
Dear Cristi,
A very enjoyable and easy to read essay, with interesting thoughts and observations. Especially noteworthy for us were your remarks on Godel's theorem.
The duck: for us, a description of the duck is different from the duck; thus we said that mathematics lacks in material substance. Would you agree?
And if pushed, what stance would you take: Platonism, or non-Platonism? :-)
Our best wishes,
Anshu, Tejinder
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Author Cristinel Stoica replied on Apr. 22, 2015 @ 16:59 GMT
Dear Anshu and Tejinder,
Thank you for the kind comments.
"The duck: for us, a description of the duck is different from the duck; thus we said that mathematics lacks in material substance. Would you agree?"
I don't really know what to answer, since I really know neither the nature of mathematics nor that of material substance.
If we call material substance the thing from which things are made, what is that thing? Things are made of atoms, which seem hollow, and made of protons and neutrons, which seem hollow, which are made of quarks. Which are what? and why can't they have independent existence? Are particles waves of some stuff, or waves of probability? Are they fields of what? Can we know about these things more than mathematical abstractions? Are they more than clicks in detectors? You see, I am very confused about all this, and I must admit I don't know what is the substance making all this stuff. I don't want to sound like an ancient oriental wise pondering about the illusion of everything but nothingness, nor like a post modernist cubist surrealist, I just really don't know. What we know are operations from which we infer relations. We know propositions of the form "if we do this we obtain that outcome, with that probability". And we know that in the world there are some regularities, which look like the regularities we find in mathematical structures and nowhere else. So maybe these two things, matter and mathematics, are just one thing, the thread that connects these regularities. Call it the substance making the world, call it mathematical structure, in both cases is just a thread connecting the regularities. So if we say that mathematics lives on a material support, or that what we call material substance is in fact a collection of relations, or of propositions which are true about those relations, or mathematics, would it be a difference? And if there is a substance upon which the regularities are imposed in a way which looks like mathematics, then how can two so different things be so intimatelly connected, if they are not one and the same?
So I agree that "a description of the duck is different from the duck", but we don't have ducks, we only have descriptions of them. We are talking here about two descriptions of ducks. If the descriptions are identical and there is no way to check how the real ducks are (or how real the ducks are), can they be different?
"And if pushed, what stance would you take: Platonism, or non-Platonism? :-)"
None. Should I pick one? If the Platonist view distinguishes between the ideal world and our world, which is just an approximate pale shadow of the former, I clearly am not satisfied with it. Why have an ideal world of shapes and live in the cave? What use would be for that ideal world? And, as you said, how can we know about it, other than by extra-sensorial perceptions, which I don't even know what can be? If non-Platonism means that mathematics is just a secretion of the thinking matter, then again I am not satisfied, because the very source of that secretion is subject to mathematical laws. To avoid circularity, I feel forced to admit identity between the two.
But if I admit the identity of the two, this looks like a mathematical universe hypothesis, or mathematical monism. In this case, what brings the mathematical structure into existence? I don't know, but whatever we would consider to be the reality (including material substance), we face the same question: what brings it into existence? I don't have an answer for this, but I would rather have a single answer about the existence of the two ducks which are one, than two answers about what brings into existence two so different ducks, and another answer about what makes them so similar. Maybe all that there is is just mind, which contemplates an infinite diversity of propositions, which all arise from the principle of explosion (
this essay page 9), and selects from these subworlds which are logically consistent, creating by this all mathematical structures, hence all possible worlds. Maybe. But I don't know :)
Best wishes,
Cristi
William T. Parsons wrote on Apr. 22, 2015 @ 16:05 GMT
Hi Cristi--
I loved your essay! Incredibly well-written, well-structured, and thought-provoking. Your analysis of the applicability of Gödel’s theorems to physics is spot on. Also, I think that you did an excellent job of rebutting Smolin’s objections regarding time and particularities.
Nonetheless, I do not share your view that “the universe is isomorphic to mathematics”. Nor do I believe that “the universe is nothing but a mathematical structure”. Let me ask just one “quick question” to sketch out my objection.
If the universe is isomorphic to math, then why we are unable to analytically solve any of our PDEs in physics? You know what I’m talking about. We are forced to rely on analytical simplifications, numerical approximations, linearizations, and perturbations (to name just a few techniques), every day and in every way, to make progress in physics. Just how isomorphic can mathematics be to the physical world if physicists must typically rely on such mathematical techniques to get the job done? Put differently, if “A Supreme Something” had ordered me to design a physical world—and to do so in way isomorphic to mathematics—I’d like to think that I could have concocted a physical setup far more computationally efficacious than the one we now find ourselves in! And you say?
I firmly believe that constructive criticism, including disagreement, is the engine that drives progress in physics. I may not agree with your overall position, but you did a great job setting it out and getting me to think about our points of agreement and disagreement. Accordingly, I have given you a high rating. (Not that you’ll notice, as you ratings are already very high!). Congratulations.
Very best regards,
Bill.
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Author Cristinel Stoica replied on Apr. 22, 2015 @ 17:31 GMT
Hi Bill,
Thank you for the kind comments.
You ask "If the universe is isomorphic to math, then why we are unable to analytically solve any of our PDEs in physics?"
Why would we be able to analytically solve any of our PDEs in physics? You seem to state it as if it would be an inevitable consequence of the hypothesis that the universe is isomorphic to a mathematical structure.
"if “A Supreme Something” had ordered me to design a physical world—and to do so in way isomorphic to mathematics—I’d like to think that I could have concocted a physical setup far more computationally efficacious than the one we now find ourselves in!"
Why would you do it computationally efficacious? And could you do it like this, and in the same time allow the complexity we observe and we need to exist?
Anyway, our current mathematical models of the physical world are very good approximations. Put it conversely, the universe seems to be able to approximate efficiently our mathematical models, which are indeed not so computationally efficacious. So even if the universe would not be isomorphic to math, it seems to be doing so well the job of a mathematical structure, including these computations.
Thanks again for these interesting questions, and good luck in the contest!
Best wishes,
Cristi
Jonathan Khanlian wrote on Apr. 22, 2015 @ 20:39 GMT
Hi Cristinel,
Turing Machines, Game of Life, Free Will, Godel, Rule 110, etc.?! I think you'd like my
Digital Physics essay, and the actual movie even more so.
Are you fine with using all of mathematics to explain our universe? When using math to describe physical phenomenon, are you fine with incoroporating axioms that are merely known to be independent assumptions or would you prefer axioms to be self-evident? I think the concept of actual infinity, and its different guises (e.g. Axiom of Choice, Continuum, etc.) are the root of many paradoxes in both mathematics and physics. Have mathematicians and physicists forgot that a reductio ad absurdum means we should re-examine our assumptions?
Please check out my essay if you get the chance.
Jon
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Author Cristinel Stoica replied on Apr. 22, 2015 @ 21:16 GMT
Hi Jon,
Thank you for the kind and interesting comments. I am not sure if all mathematics can be used to explain the universe. Maybe there are parts that don't have correspondent in the universe, although they may have in other universes. Also, some mathematical theories are based on opposite axioms. For example, Euclidean and non-Euclidean geometries contradict one another when it comes about parallel lines. But there is a way to incorporate contradiction and use it as a fecundity principle to create mathematical universes, including ours (see
this essay page 9). I look forward to read your essay, in this brief time that remains.
Best wishes,
Cristi
Thomas Howard Ray wrote on Apr. 22, 2015 @ 20:58 GMT
Cristi,
I haven't seen you announce it, though since I have Email confirmation from the Minkowski Institute Press that your PhD thesis has been published, please allow me to extend my congratulations. I note that your acknowledgments include David Finkelstein, one of the Minkowski Institute's founding members (along with Abhay Asktekar whom you also acknowledge, among other highly distinguished academics) -- Finkelstein is one of my favorite scientists.
All best,
Tom
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Author Cristinel Stoica replied on Apr. 22, 2015 @ 21:08 GMT
Dear Tom,
Thank you for noticing. Indeed,
my Ph.D. Thesis appeared yesterday at Amazon. It was
published by Minkowski Institute Press. I wish to thank for this to Vesselin Petkov, the author of
this excellent essay.
Best wishes,
Cristi
Thomas Howard Ray replied on Apr. 22, 2015 @ 21:34 GMT
Christine Cordula Dantas wrote on Jun. 11, 2015 @ 10:12 GMT
Congratulations!
Kind regards,
Christine
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Author Cristinel Stoica replied on Jun. 11, 2015 @ 10:25 GMT
Thanks, Christine, and congratulations to you too, for your beautiful winning essay!
Best wishes,
Cristi
Steve Dufourny wrote on Sep. 3, 2015 @ 09:28 GMT
Hello dear Mr Stoica,
I read your essay, congratulations for your prize. I recognize your analyze of maths.
It is relevant considering the natural automata like the turing machine. That said,if God has inserted mathematical Tools and foundamental laws, so can we utilize the extrapolations without limits. It is important for the prédictions of the evolution.The principle of uniquity is so important considering the entropy and its uniqueness. Of course maths are relevant but can we superimpose all what we want , like we want.I am not sure.
In all case , your essay is interesting in a whole point of vue.
Best Regards
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Author Cristinel Stoica replied on Sep. 4, 2015 @ 15:10 GMT
Dear Steve,
Thank you very much for your kind and interesting comments.
Best regards,
Cristi
Steve Dufourny replied on Sep. 5, 2015 @ 10:16 GMT
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