Level V universes in Tegmark's mathematical universe hypothesis.

[Functor97]

Hello, I have been reading quite a bit about Tegmark's mathematical universe hypothesis. I realize that it is overly speculative in nature, or at least perceived that way. I am unsure if my question is better suited for the philosophy forum as it seems to me inherently unfalsifiable.

Despite this I shall proceed. Tegmark claims that viewing the ultimate ensemble of mathematical universes (possibly Gödel complete ones) is the best basis upon which to base our scientific models. He thus creates 4 levels of the ensemble, the “uppermost” of which is the ensemble of all possible mathematical worlds. My question is, why stop there? Is it not possible for there to be an ensemble of universes with entirely different logic and mathematics, if you could call it such? Does Tegmark’s hypothesis only pertain to universes in which there is order of the form we perceive in our universe? Is a level V any more unscientific than a level IV?

 

[marcus]

I applaud your doubts as to whether Tegmark's speculation is more philosophy, not empirical etc.

Bee Hossenfelder had an effective blog comment on it back in 2007 as I recall, I'll see if I can find the link.

I think what we call mathematics is a human language which evolves by a kind of natural selection by the mathematical community---what they like, what they consider interesting, what they see worthy of imitation and elaboration, what works for physics, what analogies they perceive leading to new definitions, notation, concepts.

Like any human language it has no fixed eternal essence, it grows organically.

Rightly or wrongly, we expect ET's (if any exist in our galaxy) to have languages. But how do we know what their languages might be like? How could we know if they have abstract math in some sense analogous to ours?

Well there is something called CONVERGENT EVOLUTION. It might be that since our math language has evolved to be good at modeling the universe and microscopic nature, and their language was exposed to the same challenges----some similarities? Survival and replication of the fittest concepts, at describing nature? Wave equations, hilbertspaces, selfadjoint operators... It is conceivable that they might have evolved a language in some ways analogous to our math. Because they are exposed to the same universe.
Or they might not have.
And our math language(s) never stay the same. 2000 years ago (Greek) math was different. 2000 years in future (human) math will presumably be different.

It seems silly to take some collection of human and putative ET languages as a model of what exists. And to start drawing conclusions about what must exist, and what it's made of.
Tegmark sometimes strikes me as a glib charmer peddling self-indulgent fantasy.
But brilliant, of course. Understands what appeals to audience imagination. Anyway...

Congratulations on taking a questioning and partially sceptical view. I will get a link to Bee Hossenfelder's "Backreaction" blog on it. You may have seen this already
http://backreaction.blogspot.com/2007/09/imaginary-part.html

 

[czes]

I thought many times how Tegmark uses the math in his Mathematical Universe. We do use it ususally as a language to describe a relation between the matter in the physics.
Is it possible to mimic that relation by a pure math ?
What is a difference between the wave function of Schroedinger and information ?
Both of them are not physical. (in Cramer's interpretation it is a little bit different).
The square modulus of the wave function shows the probability density for finding the system in a given state at a given time.

In mathematical model there is not a particle of a matter at all. There is a description of the particle. A description means a set of the information which relates it toward the environment.
Somtimes it describes an empty space (geometry) and sometimes it describes a particle.

The description changes together with a new relation. Each relation encodes a Planck time delay and therefore there is a description of the flow of the time.
The Planck time delay is not included in Tegmark's MUH but it makes possible the inertia and relative curvature of the geometry (gravity).

The Tegmark's MUH + Planck time delay = Bohm's Interpretation of the QM.

Wheeler wrote that XXI century will search the information and we are on the beginning. How many levels of the description there are is a speculation but the direction as Wheeler said is the quantum information.