A wonderful paper Christine, very much in line with some of my speculation, in particular taking an approach linking ontology with physical theory, that I completely agree with. When our experimental vices surely end, work in precisely this vein will be the future of a new physics.

Ultimately, in a super-Hilbertian way, we might reach a combined formal language encompassing math, physics and philosophical insight.

I liked this, reminded me of my amalgamated sleuths:

"But this "physical incompleteness" is not just the reflection of a mathematical incompleteness for describing a physical law, but the realization of physical laws that cannot be described mathematically."

Best

Jack

    Christine,

    there are phenomena (e.g. falling apples) and physical theories (e.g. Newton's laws) which according to Gödel are "in HARMONY" with one another. In 1.) you say "The human mind has the ability to disclose intricate mathematical structures, and to use them for DESCRIBING, with a high degree of agreement, the physical world." Then, however, you continue saying that it is not clear why nature follows mathematical laws, which puts in question the assertion that mathematical structures DESCRIBE the physical world. And indeed, nowhere in the philosophy of science you will find clarification what exactly DESCRIPTION is or means. While traditionally the term is associated with reductionism, your essay tries to apply it in the other direction, i.e. emergentism.

    But what if Gödel - knowingly or unknowingly - hit the nail on the head? Could that mysterious relation between nature (the real world) and math simply be HARMONY or, as I call it, orthogonality or Absolute non-falseness?

    Heinz

      "Here, "initial conditions" are understood as the initial (Big Bang) singularity, which we expect to be resolved by a quantum gravity theory ..." (p. 7, "Metadynamics). Is something seriously wrong with Big Bang cosmology? Please google "louis marmet physics".

      I conjecture that the following is a work of genius:

      Pipino, Giuseppe. "Evidences for Varying Speed of Light with Time." Journal of High Energy Physics, Gravitation and Cosmology 5, no. 2 (2019): 395-411

      Am I wrong? I predict that the Big Bang shall soon be replaced by Wolfram's Reset.

        Thank you for your inspiring ideas Christine.

        I like the broad views of your thinking, maybe you like mine too.

        https://fqxi.org/community/forum/topic/3411

        good luck in the cotest

        Wilhelmus de Wilde

          Dear Christine,

          your notion of 'metadynamics' is an intriguing one. The correspondence between logic, physical systems, and computer programs has been remarked upon before, perhaps most well-worked out in Baez' 'Rosetta Stone'-paper (https://arxiv.org/abs/0903.03409), where he proposes a categorical equivalence between Feynman diagrams, cobordisms, proofs in logic, and computer programs. However, I do not recall any attempt, in that paper, to fold the correspondence back in on itself---to find an equivalent to logic talking about itself within Feynman diagrams, for instance.

          I also like your idea that one might get physical laws out of metadynamics---as fixed points, perhaps, of dynamics applied to dynamics, maybe in a way similar to how Löb's theorem (https://en.wikipedia.org/wiki/L%C3%B6b%27s_theorem) can be used to construct modal fixed points, the most famous of which is the Gödel statement itself, equivalent (in this fixed-point sense) to the inconsistency of arithmetic.

          However, I believe the correspondence is usually drawn a bit differently from the way you frame it---one takes the axioms to be something like the initial state of the system (sort of like the input into a program), then proofs as parallel to the dynamics (the computation), with theorems (truths) coming out at the end (final states). This then leads to something like my proposal, in which what 'comes out at the end' may be subject to undecidability---thus leading to the unpredictability of measurement outcomes, as in quantum mechanics.

          Anyway, thanks for an enjoyable essay. I wish you the best of luck in this contest!

          Cheers

          Jochen

            Dr Dantas,

            Very nice work on Metamathematics and metadynamics...

            Undecidability, Uncomputability, and Unpredictability are very much undesirable properties and out-comes of any theory. That theory might have developed by a very reputed person or by a group of well-educated and knowledgeable persons. There is no point of poring resources, money and highly educated man power into that theory when that theory is failing on above three points.

            In my essay just elaborated what should be the freedom available to an author when the " real open thinking" is supported. Have a look at my essay please.

            "A properly deciding, Computing and Predicting new theory's Philosophy"

            =snp.gupta

              Hi,

              If you are replying any of comments I posted on your essay, I request you to post a copy or intimation that you posted reply, on my essay

              "A properly deciding, Computing and Predicting new theory's Philosophy"

              also,so that I can continue discussion....

              Best Regards

              =snp.gupta

              6 days later

              I do not think that my ideas conform to a single philosophical line, but thanks for your comment.

              I do not desire to discuss the paper you mention, but thanks for you comment.

              Thanks, Sabine, and I will be reading your essay opportunely. Good luck too!

              Dear Christine (if I may),

              thanks for a well-written and very interesting essay. The ideas on metadynamics you expounded are quite inspiring.

              I would be most interest if you could find some similarities with your ideas in the general framework I propose in my essay.

              Meanwhile, congrats and good luck with the contest.

              best,

              Flavio

                10 days later

                Hi Christine,

                you developed some deep ideas about the 3 "Uns" and I think your ideas are more than analogies.

                You wrote

                "Hence the limits of provability in formal axiomatic systems would correspond in metadynamics to an associated layer of physical reality which is not mathematically expressible".

                I come to the same inference in my essay. Although some would think this is the end of any proper description of reality, i would think it must not - to the contrary.

                  11 days later

                  Hello Dr Dantas,

                  Very relevant general analysis and innovative extrapolation. I liked your metadynamics like a conceptual space of physical attributes that are self-referential, and symmetries related to these attributes lead to laws.

                  I see so many convergences with the topological spaces, euclidian spaces,and lie Groups and derivatives more the 3D spheres if they are the foundamental mathematical and physical objects of course but I cannot affirm. The points of geometrodynamics or the strings can maybe be conjectured if you analyse deeper the goentrizations and topologies more the rankings of fields and matters. The maths and this metadynamics seem relevant for our physics if they are well harmonised with our pure determinism. Very relevant essay, one of my favorites, you are innovative and it is essential, I wish you all the best in this Contest.

                  Best Regards

                    Thanks! I will be reading your essay opportunely. Good luck with the contest too.