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

    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

    Dear Mr. Fisher,

    Thank you for reminding us about the uniqueness of various things, from stars to snowflakes, and of course humans. Science, in particular physics, tries to find the things that various entities have in common, since we, as limited beings, don't have the time and resources to understand each unique thing in full depth. It is more efficient for us to focus rather on those things that can be reused in our explorations of various shapes populating the world. Those things we have in common with the others and the universe. The universal. From your phrase, "each real object has a real material surface that seems to be attached to a material sub-surface", I understand that for you this universal is captured in these surfaces. That's an interesting point of view. Good luck in your explorations.

    Best wishes,

    Cristi

    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

      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

      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

        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

        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

          Dear Lawrence,

          I plan to read yours as soon as possible too. Good luck to you too.

          Best wishes,

          Cristi

          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

          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

          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

            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

            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

              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

              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

                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