And the math will set you free by Cristinel Stoica

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

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

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

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

Dear Steve,

Thank you very much for your kind and interesting comments.

Best regards,

Cristi