Kory Heath wrote:

I greatly enjoyed Tegmark's "Is 'the theory of everything' merely the ultimate ensemble theory?", and there are parts of it that I agree with wholeheartedly (for instance, his arguments against the idea that the AUH is "wasteful"). However, whenever he talks about the testability of the AUH, his views seem unjustifiably physics-centric to me.

For instance, he seems impressed by the fact that versions of our physics with more than 3 dimensions are insufficiently stable to support atoms (and presumably, therefore, self-aware substructures), and those with less than 3 dimensions are insufficiently complex to support SASs. These are interesting facts, but I fail to see their importance when you consider the entire ensemble of possible mathematical structures. For instance, consider the infinitely many cellular automata that exist in the Mathiverse. We know of very simple 1D, 2D, and 3D cellular automata that are computation universal, and therefore (I believe) capable of containing SASs. Undoubtedly there an infinite number of 4D cellular automata that are computation universal and contain SASs that perceive their surroundings as 4D. Ditto for CA with dimensions higher than 4.

Perhaps it's true that within the ensemble of all quantum-physical universes in Mathspace, only those with 3+1 dimensionality contain SASs. But what possible reason do we have for believing that these SASs (or the observer-moments of those SASs) have a greater measure than those in the ensemble of all cellular automata?

1. All cellular automata which are computationally universal are reducible to each other, by the definition of universality, so it doesn't
matter which D the automaton program itself is. The subject matter that they can represent and compute is equivalent.

2. SAS's which are part of a 3+1 space may not have higher measure than SAS's in other spaces, but perhaps the SAS's
in the other spaces wouldn't have "a decent way to make a living". In other words, maybe they'd have a hard time
perceiving the things in their space, existing coherently "physically" in it, being able to "incrementally impact and survival-optimize"
their surroundings in the space etc.
In other words they'd be inhabiting (and trying to perceive and act on)
or of UNRULY, untameable hyperbolic physical laws and functions.

So at the least the 2D or 4 or 5D sentient creatures would be frustrated
(remember, they are SUBSTRUCTURES, they're not computing the space itself, they're
part of the space and perceiving and acting on other parts of it).

At worst, their own "physical" existence in the flat or unruly space would be impossible to define coherently, so
they couldn't BE anything that we would recognize as a perceiving-acting lifeform. Maybe there's still room for some
other ultra-weird form of self-contemplative (4Dimensional navel-gazing) Ent-lifeform thingy, but I don't think so.
I, like Tegmark, believe that the constraints for life, and sentient life in particular, are are EXTREMELY ONEROUS.
There are so many constraints, I believe, that it is possible but only just so, and so expected to be extremely rare even
in a very large universe (note, the universe may be infinite but the event horizon of intercommunicable beings or parts
of beings and their environment is not (at any given time, for a finite-lifetime creature). Each "liveable part" of the universe
is constrained to that subspace reachable by lightspeed interaction.
Within each interreachable event horizon, i.e. each observable universe, life and sentience should be rare because of the
need to satisfy a very large number of constraints simultaneously to get environment-interactive
life and sentience and to retain them.


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