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

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

    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

      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

      2 months later

      Thanks, Christine, and congratulations to you too, for your beautiful winning essay!

      Best wishes,

      Cristi

      3 months later

      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

        Dear Steve,

        Thank you very much for your kind and interesting comments.

        Best regards,

        Cristi