So here is the crux of my argument. If you believe in an external reality independent of humans, then you must also believe in what I call the mathematical universe hypothesis: that our physical reality is a mathematical structure. In other words, we all live in a gigantic mathematical object - one that is more elaborate than a dodecahedron, and probably also more complex than objects with intimidating names like Calabi-Yau manifolds, tensor bundles and Hilbert spaces, which appear in today's most advanced theories. Everything in our world is purely mathematical - including you.
See Mathematical cosmos: Reality by numbers (requires subscription).
4 comments:
It's an interesting viewpoint, and depending on how you define "mathematics" maybe a tautological one, but it reminds me of this interesting statement that Richard Feynman made:
"It always bothers me that, according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can that all be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one tiny piece of space/time is going to do? So I have often made the hypothesis that ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed, and the laws will turn out to be simple, like the checkerboard with all its apparent complexities."
Feynman's comments resonate with me but you must also know that he made those comments before it was shown that quantum computation and clasical computation were not of equal power (It was his comments that launced interest in Quantum Computing). So in those tiny regions of time and space there are many many quantum computations occuring in parallel and it is of little surprise that a clasical computer can not keep pace.
I think there are a couple of responses to that:
1. While there's promising evidence that quantum computers can more efficiently solve some problems than classical computers, they still can't do an infinite amount of computation in finite time (which is the problem he mentioned).
2. He wanted a coherent Quantum Mechanics, so whether or not Quantum computers can do an infinite amount of classical computation in finite time, there's still the problem of explaining the Quantum computer (e.g.: maybe the problem is just a problem with classical logic). But with the checkerboard reference I think he had this in mind: http://en.wikipedia.org/wiki/Feynman_checkerboard (in any case, a simple logical/mechanical system about which QM statements would fall out as statistical properties)
Yes, of course. It is not logical that an infinite amount of computation be required. However, I don't think Feynman's and Tegmark's views are at odds. A checkboard model or some of the models that Wolfram explores in a NKS are still "mathematical objects". Perhaps that is why you mention "a tautology" - what else could it be if not mathematical. My own view is that the universe IS the evolution of an ongoing computation but one where "the computer" and "the computed" are ultimatly the same thing.
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