[Retra]

Mathematics is a human language for studying the structure of various experiences. To say the universe "is" mathematics without saying what mathematics is doesn't really say much at all. You might as well say it's magic.

And, saying that it's a "mathematical structure" is just saying that it's a structure that humans can apply mathematics to model. So there's really no mechanism for this to be true, except in the trivial "the universe has structure" sense, which also tells you (basically) nothing, because humans can't even perceive things that don't have structure, nor can we reason about them.

[criddell]

> Mathematics is a human language for studying the structure of various experiences

I think you are getting hung up on the semiotics of mathematics which is indeed a human construct. The idea of "1 + 1 = 2" is true no matter how (or if) you represent the idea.

> saying that it's a "mathematical structure" is just saying that it's a structure that humans can apply mathematics to model

That's not what the theory says (AFAIK). The mathematical universe hypothesis says that there is nothing in the universe, it's all just mathematics.

Edit: Think about it this way: if you could simulate a universe and in that simulated universe you modeled people and all the stuff around them, what would you tell those simulated people with their simulated free well what a table is made out of? It's all mathematics, right?

[Retra]

The math universe hypotheses assumes a very strict Platonist POV, which is not really a justifiable position, in my experience.

>The idea of "1 + 1 = 2" is true no matter how (or if) you represent the idea.

That's really a triviality, though. If you have the idea that 1+1=2, then yes, it's true. Usually people say mathematical theorems are true in "all possible universes", but the way they select which universes are possible is... by applying logic that works in this universe. 1+1=2 is only true because it doesn't contradict our experiences. It's useful. In another universe, it may not be useful, and thus wouldn't be true there.

>if you could simulate a universe and in that simulated universe you modeled people and all the stuff around them, what would you tell those simulated people with their simulated free well what a table is made out of?

I would put words in whatever order was most useful to them to employ for the construction and manipulation of tables. Anything else would be meaningless. You might as well just say "magic" if they can't use it.

[nhaehnle]

> 1+1=2 is only true because it doesn't contradict our experiences.

Not quite. In the mathematical sense, 1+1=2 is true because (a) it is a well-formed sentence in a certain formal system and (b) there exists a proof of it in that formal system. The formal system consists of a grammar for well-formed sentences as well as rules for deriving true sentences.

The key point here is that the definition of "true" is part of the definition of the formal system. Unlike in philosophy, we have a clear and unambiguous definition of what "true" means, and its evaluation does not depend on properties of our physical universe.[0]

So when people say that "mathematical theorems are true in all possible universes", they're well-intentioned but I would argue that they are misleading. The deeper (philosophical) truth is that the (mathematical) truth of mathematical theorems is independent of universes[1].

[0] The fact that our minds are drawn to thinking about the specific type of formal systems that are usually considered to be reasonable foundations for mathematics may well be a consequence of the properties of our physical existence.[2] However, if by some magic the definitions of formal systems studied by alien civilizations in a different physical universe were to be transmitted to us, we would be able to arrive at the same conclusions about those systems as the aliens, and vice versa. There would be no disagreement about what sentences are true in such an alien formal system.

[1] Where I use the word "universe" in the physical sense and not in the sense that is found in set theory and its ilk.

[2] However, I personally don't think so. I believe (though I cannot prove it) that something like the Church-Turing hypothesis also applies to foundational formal systems at least up to basic set theory (possibly minus the axiom of choice). It is conceivable that some alien civilization in a much stranger universe would consider a certain extension of our set theory as the natural choice for mathematical foundations, but they would recognize our set theory as a subset of what they're studying.

[Retra]

If you received a formal statement from an alien in another universe, it might not even look formal from your perspective. Mathematical theorems are not necessarily independent of universes, because those factors we consider necessary for formalization may not apply in other universes. You don't know if contradictions in this universe must be contradictions elsewhere.

[criddell]

> I would put words in whatever order was most useful to them to employ for the construction and manipulation of tables. Anything else would be meaningless

Is your objection to the mathematical universe mostly that it's not useful to know everything is just mathematics? That our reality is essentially the same as if it were a simulation is just trivia but doesn't help you make a table?

[Retra]

Pretty much. You say it's all mathematics, I'll say it's a simulation. Or maybe it's a dream. Or a the manifestation of another being's will. Or something completely incomprehensible.

Why should anyone care that it's mathematics? It's certainly not like any mathematics that we know; we can't do it some other way if we don't understand it. It's too big to fit in a brain, and too complex to simplify accurately. Since we don't understand its axioms, how do we know they form a mathematical structure?

[criddell]

> Why should anyone care that it's mathematics?

Well, if the universe is a simulation, then you can start poking around for the limits of the simulation and finding out new things is something that lots of people enjoy.

http://www.technologyreview.com/view/429561/the-measurement-...