Tegmark's Mathematical Universe

[gogins]

Note that Tegmark discusses this when he talks about the bird and the frog on pg 3, ending on pg 4:


He says this because given MWI, everything is deterministic 'from the bird's view'.

I don't see anywhere that he addresses MWI specifically in order to do away with randomness being uncomputable, but it certainly looks like that's what he wants.

Randomness is indeed uncomputable. Note that nonlocality REQUIRES uncomputable randomness. In other words, uncomputable randomness is a central assumption of standard interpretations of quantum mechanics. It can be approached from several angles, but they all have to do with observation.

As far as I know, uncomputable randomness can be banished from Nature only by introducing hidden variables in its place.

The Free Will Theorem was derived just in order to clarify this.

Come on -- admit that Nature is uncomputable. It doesn't mean we can't be scientists any more. It just means that Nature is uncomputable. Uncomputable is not "irrational" in the sense of anti-mathematical or anti-scientific.

This whole discussion reminds me of the ancient Greeks being freaked out by the square root of 2 and other irrational numbers. Since Godel a lot of people are freaked out by uncomputability. OK, we have irrational numbers. We finally got used to that. OK, now we have uncomputable numbers.

Nature is numerical -- that much is clear, right? Why should Nature be numerical, and involve transcendental and irrational numbers, but shrink from uncomputable numbers? What reason is there for such an assumption?

Regards,
Mike Gogins

 

[Q_Goest]

Randomness is indeed uncomputable. Note that nonlocality REQUIRES uncomputable randomness. In other words, uncomputable randomness is a central assumption of standard interpretations of quantum mechanics. It can be approached from several angles, but they all have to do with observation.

As far as I know, uncomputable randomness can be banished from Nature only by introducing hidden variables in its place.

Hi Mike. That's not what Tegmark is saying (ie: you're looking at it from the "frog's" perspective). His reference to MWI being determinate overall is commonly accepted as he states. If you've read his paper, and the portion especially around page 3 and 4, what is it you don't understand?

 

[PF_member_101]

Someone in this thread mentioned an article that I think could lead to something connected to Tegmark's Self Aware Structures (SAS's). Since it may not be directly relevant to THIS particular discussion, I stared a new thread for anyone interested in the math section:

https://www.physicsforums.com/showthread.php?p=1640031#post1640031"

 

[gogins]

Hi Mike. That's not what Tegmark is saying (ie: you're looking at it from the "frog's" perspective). His reference to MWI being determinate overall is commonly accepted as he states. If you've read his paper, and the portion especially around page 3 and 4, what is it you don't understand?

Tegmark uses the word "random" much, much too loosely. He does not appear to address random quantum state transitions, nonlocality, or anything like the Free Will Theorem except by appeal to the MWI. He can do this because he assumes that any mathematical structure that could be a universe has finite computational complexity. So, Tegmark simply begs the question. He is pulling a bait and switch operation. The randomness at stake in uncomputability or in physics has to do with complexity at root, and nothing to do with the MWI. A statistically random temporal sequence MIGHT be random in the sense of computational complexity -- or it might be a pseudo-random sequence. But an incomputable sequence WILL be statistically random.

Actually Tegmark acknowledges the problem here:

"A convincing
demonstration that there is such a thing as true randomness
in the laws of physics (as opposed to mere ensembles
where epistemological uncertainty grows) would therefore
refute the MUH."

Now, let us take the ERH and the MUH seriously by including in it mathematical objects of transfinite complexity. Again, why not? Why stop at finite complexity? This is precisely what is begging the question. If mathematics has omega complexity (and we know it does), and if Nature is mathematics, then doesn't Nature have omega complexity if MUH is true?

Tegmark implicitly acknowledges the problem by distinguishing between the Level IV multiverse which is the union of uncountably many finite computable universes (and so Level IV is incomputable), and our universe (which is a computable universe), but what is it that physically acts to create this distinction? (third man argument). If it acts physically it invalidates the CUH, but if it does not act physically then there is no distinction between Level IV and our universe, which is thus incomputable.

Regards,
Mike Gogins

 

[PF_member_101]

I believe I have a working candidate for a plausibility case for a
structure being literally the universe, assuming the MUH.

It is the structure U(U), where the first U is script and the second
is blackboard bold, on page 3 of the following document, listed under
"conjecture 4."