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I didn't take Tegmark's argument to be a computational theory. I took it to be an inductive one based upon the trend of the physics over the last decades toward
by gfodor 9y ago
I didn't take Tegmark's argument to be a computational theory. I took it to be an inductive one based upon the trend of the physics over the last decades towards the more and more generified multiverse theories. Ultimately, you land on a model where all consistent mathematical representations of a reality exist. At that level of abstraction, there is no where to go: it is the limit of the induction. There's a rather satisfying sense of self-evidence about it, but that doesn't mean it's falsifiable or true.
IIRC there are no arguments about computation or what underlying medium(s) are involved, it seems like a separate question.
- eref 9y agoI am unsure now whether he describes the set of mathematical objects by enumeration and evaluation. He definitely describes the set of universes this way, as being “run”, so it is a computation. But you are right that he never discussed the substrate that they are run on. He assumes the existence of that enumeration to be axiomatic, like an uncaused cause, somewhere in the space of all mathematical objects that simply exist. I guess, if we had a proof that all non-computable formal systems are inconsistent then we could also skip one layer and assume the enumeration of all programs as axiomatic in order to be maximally agnostic.
- naasking 9y ago> Ultimately, you land on a model where all consistent mathematical representations of a reality exist. [...] IIRC there are no arguments about computation or what underlying medium(s) are involved, it seems like a separate question. These are actually related by Goedel's incompleteness theorems and the Curry-Howard isomorphism. Computation and mathematics are inextricably linked. The Computable Universe is a necessary restriction on the mathematical universe hypothesis to avoid accepting inconsistent universes.
- eref 9y agoIt links a certain axiom set with computations, not all of mathematics (i.e. the set of all axiom sets), doesn’t it?
- naasking 9y agoIf you accept that every mathematical structure of interest has an intuitionistic construction (as is currently believed to be the case), then every mathematical structure has an expression as a computer program.