[duaneb]

Why do you (and others) tend towards arguments suggesting simulations?

To me, the language here is important. Both simulation and computation imply (to me) a tool and a user of the tool. Even a broader interpretation of computation as, umm, the efficient transfer of precise information through spacetime in certain shapes (which is easily providable by our understanding of physics today) requires an observer to extract the computation from the otherwise non-semantic system.

It definitely makes sense to think of the universe as a projection of a higher dimension, or a holograph, or however you want to look at it, but that's a far cry from implying a simulation.

EDIT: hologram -> holograph

[madaxe_again]

A simulation doesn't mean that there is a simulator - just that what we consider real may be a projection of something else. As you say, the holographic universe principle can equally answer this.

That said, the simulation argument strongly pushes in favour of a simulated reality - particularly when you consider that there is no need for it to be real time, or of the entire universe. In short if we ever gain the capability to accurately simulate a small corner of the universe, then it stands to reason that someone further up the hylaean flow (apologies to Stephenson) also has.

Hell, maybe the rotation of distant galaxies is off because they're just sprites ;)

[padobson]

Hell, maybe the rotation of distant galaxies is off because they're just sprites

So there's probably some other simulation of our universe where they tried to do models, but it was too slow.

If not, then the simulator introduced a pre-mature optimization. The existential ramifications of such a development inefficiency are palpable!

[criddell]

What do you feel about the mathematical universe hypothesis[1]? If I understand it correctly (and I probably don't), it says that the universe is literally mathematics. Not that it's a manifestation of mathematics or can be modeled by mathematics, but is 100% mathematics.

I think that fits the computation model and doesn't require an observer or operator.

[1]: https://en.wikipedia.org/wiki/Mathematical_universe_hypothes...

[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?

[duaneb]

I actually love that theory because it makes me feel warm and fuzzy. However, it is.... Highly hard to defend, to say the least.