Tegmark's hypothesis is the idea that mathematical structures are physical and thus have physical existence (https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis)

Zuse's thesis says that the universe is fundamentally analogous to a cellular automata (https://en.wikipedia.org/wiki/Calculating_Space)

I found a paper titled "Zuse's Thesis, Gandy's Thesis, and Penrose's Thesis" (https://oronshagrir.huji.ac.il/sites/default/files/oronshagrir/files/zuse_thesis_gandy_thesis_penrose_thesis.pdf) where Zuse's thesis is discussed. At some point of the question, it is discussed how Zuse's hypothesis could be "physically implemented", how would be the "hardware" of that cellular automata.

The authors of the article say that it could consist of an abstract mathematical entity from Tegmark's hypothesis. But they argue that this is doubtful since Tegmark's Mathematical structures would exist timelessly and unchangingly and thus, without time and change, no computation could be done.

Also, in this page (https://physicsworld.com/a/the-unique-universe/), it discusses philosophical/physical theories where time does not exist (and it mentions Tegmark's)

But this confused me a lot and. Tegmark's hypothesis assumes the existence of all mathematical structures. In that set of mathematical entities, all physical theories and "theories of everything" are included. That includes universes based on brane cosmology, string theory, many worlds interpretation...and of course, our own universe. In all of these universes, time and change would exist (as it is obvious in our universe), and thus, computations could exist with no problem (as they exist in our own universe).

So I have to ask, does Tegmark's hypothesis include dynamical mathematical structures? If not, how can computations be done in our universe for example if there would be no time? And, anyways, if time and change can be represented mathematically, wouldn't that mean that they could exist as a mathematical entity in Tegmark's hypothesis?



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