Essay Abstract

Physics is described as a Darwinian process, exploring a network of local realities. Mathematical objects, for example Lagrange-functions, are subjected to selection processes similar to DNA in biological evolution. Mathematics plays a fundamental role in this Darwinian process, but without the unfounded assumption of the 'mathematical universe'.

Author Bio

Frank Pohlmann studied physics,mathematics and philosophy in Heidelberg/Germany.....and then turned to the arts. Today he is living as an independent artist in London. You can see his artwork here ( unrelated to this essay) www.holorealism.com

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Dear Frank,

I have studied carefully your very interesting essay a couple of times. It is interesting for me because it discusses the isomorphism between mathematical structures and physical reality. I study all pros and cons.

I agree with your extended Darwinian view as I also implement it in my concept. However, in my opinion, this view does not exclude the isomorphism between mathematical structures and physical reality. The geometrical structures, being parts of elastic fabric of spacetime, naturally evolve. I have coined Geometrical Universe Hypothesis (that makes the testable predictions, what you fairly claim as necessary). The theory is based on the geometrization conjecture, proved by Perelman. It means that it is the theorem (the conjecture, not my GUH). As far, theorems were reserved for math but the isomorphism makes it possible to apply also in physics.

This concept naturally transfers us into more general: the evolution of information. The information, in this view, being a geometrical structure, transferred by wave.

I think that your evolutionary path of theories fits in this general concept as theories are also evolving information. The details in my essay:

http://fqxi.org/community/forum/topic/2452

I have visited your visual art website. As you possess artistic talent and technical means, I encourage you to try to create a visual language, expressing Thurston geometries in 3D as a projection from 4D. That language would be really baggage free and comprehensible even for aliens or future supercomputers.

Best regards,

Jacek

    Dear Jacek,

    thanks for getting in touch and I found your essay very thought provoking.

    Yes, I do agree, I can not completely rule out the possibility of a mathematical structure to be isomorphic to a given physical system. In my essay a stated a sufficient condition for this to be true. As far as I can see no current physical theory fulfills this condition. For that reason the succcess of physics can not be explained by an isomorphism, a faithful representation of reality.

    Dropping the assumption of an isomorphism (in the above sense) leads one to consider a pluralistic view of reality, as opposed to the 'one-reality' of the Greek tradition.

    Thanks for your interest in my artwork. Indeed, I do like to connect science and art in my work and certainly will try to visualize more abstract geometries. Have a look at one of my past projects.Timelab at Royal Institution

    kind regards

    Frank

    8 days later

    Dear Frank,

    I really enjoyed your essay and largely agree with you: that to even approach the "truth or trick" question we have to have some idea of the historical development of physics along with physics relationship to the other sciences. I also like your comparison of mathematical information in physics with the evolution of genetic information.

    Although, I make a very different point, I'd appreciate your thoughts on my essay and your vote:

    http://fqxi.org/community/forum/topic/2391

    Best of luck in the contest!

    Rick Searle

      Dear Frank,

      As I see it, I have a complete skin surface. Every real object appears to have a complete surface of one form or another. 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

      Dear Frank,

      I have been reading many of these essays, and due to the similarity of many of them, it's starting to get a bit boring. The biological insight provided by your essay is a refreshing alternative, one that does not come naturally to most physicists and mathematicians.

      Following this train of thought, could one evolve a mathematical formalism/physical theory that might be locally adaptive, but approaching an evolutionary dead end? Could such a theory be effectively a dodo?

      In my own essay ("Remove the Blinders: How Mathematics Distorted the Development of Quantum Theory"), I propose that the orthodox theory of quantum mechanics is so heavily laden with metaphysical baggage that it should never have gotten off the ground. It was initially successful because there was no acceptable alternative, but its continued success now depends on the active suppression of alternatives even if they are simpler and more elegant.

      Might the time be approaching for the orthodox theory of quantum mechanics to go extinct, to be replaced by a bird that can actually fly?

      Alan

        Hi Frank

        I liked the way you presented your ideas, condensed, yet in a clear systematic way and using a conversational Galilean Q&A method.

        I was attracted to your essay by the use of Darwinian evolution in the title. In the course of reading it I learned a new word isomorphism which exactly fits my idea of why mathematics is so effective - nature is built on the smallest scale in such a way that mathematical concepts and operators could emerge in a direct relation. Human brains evolved out of this Nature experiencing it directly molecule to molecule, and the mathematics that emerged naturally uses concepts that can fit this Nature. You describe a more sophisticated way mathematical physics develops building on what is past, which requires another level of mental sophistication. This 'works' but can lead to convoluted ways. In my theory gravity is a very simple physical effect of twisting of ether nodes (as in a spring) and the required mathematics is equally simple - just a causal direct local accounting of potential and kinetic energy as the lattice energy transfer proceeds.

        Another difference is that I rather prefer thinking in terms of Hamiltonian evolution of systems rather than a Lagrangian. Another is that I write in a rather long-winded wandering manner, but I hope you can read my essay and outline physics theory Beautiful Universe on which it is built.

        With best wishes,

        Vladimir

        Dear Alan,

        I was delighted by your response to my essay. Yes, you do understand me correctly, all physical theories are dead like a dodo, so to speak.

        But first let me comment on your essay. Maybe you are right and it is possible to model quantum mechanical phenomena with solitons. But does that mean that the mathematics is less abstract? You seem to imply that (mechanics of particles/solitons in 'real space') = (mathematics mirroring reality)=(real analysis of differential equations of particles and fields). Likewise you imply (quantum mechanics)= ( abstract mathematics in Hilbert space)= ( no direct correspondence to physics in 'real' space).

        In my opinion this is a false distinction, a false dichotomy. For starters, 'real' physical space is a very abstract concept. It took 2000 years to develop this concept (Greek Atomists to Newton) and since then the greatest physicists try to get rid of this overly abstract concept ( Leibniz, Mach, Einstein,..).In my judgement Hilbert space is far less abstract than 'real' space or concepts such as 'local reality'.

        I am an adherent of Relational Quantum Mechanics (see Rovelli/Smerlak : EPR in Relatinal Quantum Mecahnics)),which is considerably weakens the concept of reality.

        Coming back to the dodo and my thesis that physics evolves in a way similiar way as biological species evolve. All evolution is locally adoptive only.'The survival of the fittest' means the enhanced probability of passing on once genes to the next generation by the individual best adapted( best fitting) to the local environment. As a consequence all evolution, biological or cultural, will approach a dead end. Put differently, there is simply no (biological or otherwise) mechanism to adopt to a meteor impact from outer space. Similarly, all of physics is only local physics, describing local environments, such as classical point particle, quantum particles, fields etc. If this picture is right, there is no such thing as a 'Theory of Everything', but just many 'Theories of Something', connected by an evolutionary tree-structure.

        regards

        Frank

        4 days later

        Dear Rick,

        thank you for your comments and sorry for delay in reply(was moving house).

        I very much enjoyed reading your essay, even if I have to disagree with your main thesis.

        The distinction map/territory or picture/reality ( which can be traced back to Descartes) is a false dichotomy and should be abandoned completely. Mathematics can be useful for physics without being in any way in a one-to-one relation to physical reality.

        Consider the concept of 'absolute Musik', that is music which is emotionally powerful without the use of words. Absolute Musik ( think of Beethoven's 5th) can convey emotions to the listener, without BEING emotion or being in a one-to-one relation to emotions, or having any meaning whatsoever.

        In the same way, mathematics ( without having any meaning), can transmit information about physical systems, without being isomorphic to that physical system.

        regards Frank

        6 days later

        Dear Frank,

        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

        7 days later

        Hi Frank,

        Your essay reminds me to Heisenbergs closed theories: He describes the history of physics as a succession of closed theories (some time before Kuhn), where the newer theory contains the older one as a limiting case. And not only. The older theory is needed to understand the newer theory. This looks like your "paasing on of genetic information from parents to offspring ...".

        As a physicist I never liked the sociological look to our science, since I always felt, physics is uncovering some truth about reality, which is independent from its genesis. So also your essay makes me a bit uncomfortable. However the evolution of science and its success is also an empirical fact and so it should be accessible to scientific analysis. And I think Darwin is a good choice. Although in the biological evolution the evolutionary process leads to a great diversification, whereas if we restrict science to physics we hope for one unified theory.

        I wonder if you know the writings of Carl Friedrich von Weizsäcker. I'm sure you would like his writings as a physicist, a philosopher and as an artist. You may also read my essay as a brief introduction to von Weizsäcker.

        Best regards

        Luca