At 34:00, he describes mathematical truth.

At 35:00, he describes mathematical Platonism.

At 40:30, he says physical theories are approximations to truth.

I can accept all of that, but then at 40:50 he says:

"The one hypothesis that underlies every viable physical theory is that the Universe is a mathematical object."

Here is where I differ. I don't think that our Universe is a mathematical object, or that any of our theories assume that it is. Our physical theories are mathematical approximations to a non=mathematical object.

This puts me at the opposite extreme from Tegmark's hypothesis. While he says all mathematical objects are universes, I say that none of them are.

My skepticism is based primarily based on:

(1) All of the interesting mathematical statements are about infinities, but there are no infinities in the physical universe.

(2) We don’t really even have any candidate for the Universe as a mathematical object. There are those who talk about having a quantum wave function of the Universe, but they end up talking about many-worlds and other ideas that have never made any sense or had any predictive value.

(3) Attempts to realize the world as a mathematical object are what led Bell to believe in local hidden variables. We now know that local hidden variables are impossible, so maybe the assumptions that led to that belief are also wrong.

Penrose has given lots of interviews, and will probably give some more now that he is a big-shot Nobel prize winner. I don't remember him giving an opinion on this issue, but it is possible. He is as close to being an authority on this as anyone.

Roger,

ReplyDeleteTegmark is confusing an abstract logical overlap with an actual physical overlap. The actual basis of mathematics is logic... applied to numbers. When we 'count' something, we are replacing an actual thing with a number, and then logically operating on the number NOT the thing itself. When we measure something like a wall, we use a ruler or some other measuring device which approximately converts the dimensions of the wall into numbers we assign labels of lengths to, we then operate on the numbers, NOT the wall.

In any case you can think of which involves anything with any actual physical extension in our reality, NONE of it can directly be operated on mathematically whatsoever. Everything must first be measured approximately and then represented numerically, and then it is those numbers which can be operated on mathematically. I dare you to try to apply numbers or mathematics directly to anything real. You can't. You must first construct your measured numerical model, then putz around with that, so you are always at least one level of approximated abstract representation away from the reality of what you are measuring.

Reality is actually the opposite of what Tegmark imagines, he gets the horse and cart badly confused. It is strange that one supposedly so brilliant exhibits such a poor understanding of the logic of causation, and can not discern between the difference between the abstract and the actual. Abstractions do not inform reality, reality informs abstraction.

All numbers only exist within peoples heads as ideas connected to symbols we use to represent them with. If you examine the computation of an abacus or an arithmetic logical unit, neither uses actual numbers at all, only physical things easily differentiated (like beads or higher and lower voltages, there are no 1's and 0's in binary computation) that we then abstractly group and label as numbers (once again, we convert the actual to the numerical abstract then logically operate on the abstract).