I have been intrigued by the theory expounded by the MIT physicist Max Tegmark that the universe is composed entirely of mathematical structure and logical pattern, and that all perceived and measured reality is that which has emerged quite naturally from the mathematics. That theory simplifies the question of why mathematics is such a powerful and necessary tool in the sciences. The theory is platonist in essence, reducing all of existence to pure mathematical forms that, perhaps, lie even beyond the realm of spacetime. Mathematics, in fact, may be eternal in that sense. The Tegmarkian scheme contains some compelling arguments. One is that atomic and subatomic particles have only mathematical properties (mass, spin, wavelength, etc). Any proton, for example, is quite interchangeable with any other. And, of course, these mathematical particles are the building blocks of the universe, so it follows that the universe is composed of mathematical structures. Another is that the vastness of the universe is not so vast if composed of math, which can outpace any physical greatness with ease, even when all specie of multiple multiplying universes are in the mix. Tegmark's theory coexists happily and cozily with Hugh Everett's famous many-worlds hypothesis. Dr. Tegmark, by the way, explains our conscious-being status as being the result of the evolution of "self-aware mathematical structures". I have taken a liking to Max Tegmark. His ideas somehow make a lot of sense to me, and I find his theory actually liberating and satisfying. However, it just about makes the case that reality itself is illusory (which in my heart I'm quite okay with). Anyway, given the power of his theory, and it's potential utility, I am surprised it has not been a more visible subject of inquiry and reflection among philosophers. I would be delighted to know the place that such theory has in the philosophy of existence, the philosophy of mathematics, the theory of knowledge, or the philosophy of science. Is Tegmark's theory an active and common subject of debate? (I think it should be.)

I will confess that I don't see the charm of Tegmark's view. I quite literally find it unintelligible, and I find the "advantages" not to be advantages at all.

You suggest a few possible attractions of the view. One is that "atomic and subatomic particles have only mathematical properties (mass, spin, wavelength, etc.) and hence we might as well see them as nothing but math. Any proton, for example, is quite interchangeable with any other." But first, the fact that we only have mathematical characterizations of these properties is both false and irrelevant insofar as it's true. It's false because knowing something about the mass or the spin or whatever of a particle has experimental consequences. It tells us that one thing rather than another will happen in real time in a real lab. If that weren't true, we'd have no reason to take theories that talk about these things seriously; we'd cheat ourselves of any possible evidence. Of course, we may not know what spin is "in itself," and perhaps to that extent, we only have a mathematical characterization of it. But as Bertrand Russell pointed out roughly 100 years ago, it doesn't follow that spin has no intrinsic character; it only follows that we don't know what spin is "in itself."

As for the fact that electrons and whatnot are interchangeable, all that this means is that as far as quantum theory is concerned, they have no intrinsic properties that distinguish them; all electrons have the same mass, the same charge and the same total spin. But they don't all have the same position nor the same momentum, nor the same spin state. (Alice's electron might have spin-up in the vertical direction; Bob's might have spin-down, to take just one possible difference.) And in any case, how would the existence of intrinsically indistinguishable objects count in favor of the view that it's math all the way down?

As for the vastness of space (or space/time), why does this need an explanation? Is it puzzling that the universe is vast and possibly infinite as opposed to finite and small? Why is small less puzzling than big? And in any case, is the view the the universe is nothing but number and the like less puzzling than the idea that the apparently palpable things around us are really timeless mathematical abstractions? How do we account for the unshakeable appearance to the contrary? Something about consciousness, maybe? I don't think we get any help by talking about "the evolution of "self-aware mathematical structures." I'll confess that I have no idea at all how this is supposed to explain consciousness, let alone what it actually means. (Do self-conscious mathematical structures sleep with colorless green ideas? And what are their offspring like?)

I suppose someone might say that my reaction is a sign that I'm hopelessly intellectually conservative. No doubt I'm not the best judge of that. But I think there's a difference between not getting excited by new ideas that really do explain things and pseudo-explanations that give us the illusion of insight without delivering the real goods. Except in my case, I don't even experience the illusion of insight when I'm told that really, everything is nothing more than abstract mathematical structure. I'm inclined to think that we're in the realm of Pauli's "not even wrong."

Finally, please don't take my pique personally. I first encountered a view like Tegmark's roughly 25 years ago, when it was offered by the physicist Frank Tipler. I had much the same reaction then, in spite of my genuine admiration for Tipler's imagination. But nothing I've heard in the intervening two and a half decades has looked like a reason to react differently to the latest incarnation.

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