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Shut up and calculate: an extreme mathematical universe

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Re: Shut up and calculate: an extreme mathematical universe

#91

Post by Agebor »

placebo wrote: post #76
westoncb wrote: post #49

It baffles me that people ignore the fact that they have subjectivity when making these claims. It makes a certain amount of sense since science itself aims to remove any taint of subjectivity in its practice, so folks who want to be thoroughly 'scientific' in other aspects of their lives (e.g. their personal philosophies of reality) carry over over this ideal. But it's also a contradiction since science scientific m…

You're right, and I also see how this obvious observation is consistently and elegantly ignored in most scientific or philosophical arguments that try and promote some totally "objective" account of reality. However, it's not really that surprising: Science over the centuries has steadily (and for it's time, justifiably) eroded the role of subjectivity in order to uncompromisingly get at what is consistently true (re…

It seems similar to the appeal of platonism over the centuries. The human mind evolved to categorise things to make sense of the world, and to dislike uncertainty. So the concepts of some abstract, ideal essence of things are easily understood and liked.

Re: Shut up and calculate: an extreme mathematical universe

#92

Post by westoncb »

kybernetikos wrote: post #86
westoncb wrote: post #49

It baffles me that people ignore the fact that they have subjectivity when making these claims. It makes a certain amount of sense since science itself aims to remove any taint of subjectivity in its practice, so folks who want to be thoroughly 'scientific' in other aspects of their lives (e.g. their personal philosophies of reality) carry over over this ideal. But it's also a contradiction since science scientific m…

I strongly suspect that I can dramatically affect or entirely 'turn off' your experience of qualia through purely physical means, so I think your objection is much more to do with your skepticism that mathematical or computational processes can generate physical processes than anything to do with qualia. Of course, you only have to have a virtual object thrown at your head in VR to discover that your brain will mista…

Your brain doesn't experience computational processes any more directly through VR: VR works by sending controlled physical sensations to your senses using the same routes as when you ordinarily interact with the world.

Re: Shut up and calculate: an extreme mathematical universe

#93

Post by eref »

otakucode wrote: post #42
eref wrote: post #30

Earlier quoted context omitted.

Tegmark's Mathematical Universe Hypothesis (MUH) is actually pretty much a computational theory of the universe. It basically makes the assumption that there exists somewhere the simplest process imaginable: One that counts through and runs all mathematical formulas which includes all programs, which, in turn, includes all (computable) universes. This assumption explains why our universe is oddly complex: If all univ…

>This assumption explains why our universe is oddly complex That is, to me, a weird mixing of scales. The universe only seems complex to us because of the scale at which we experience it in terms of time and physical extent as well as the convoluted way our own systems of understanding developed and then were later mutated and stretched into different forms to be better suited, etc. By definition the universe itself…

I think the universe could easily be less complex if you would simply remove everything below Newtonian physics and basic chemistry. We would have evolved in pretty much the same way. But our universe is also complex in that the currently most fundamental laws of physics depend on a lot of seemingly arbitrary constants that are finely tuned (i.e. they become incompatible with our observations if they would be set slightly differently). Of course, it could be that we are missing a much simpler unifying theory, but currently it seems to have a quite high entropy such that we cannot explain it by saying it is in some sense canonical, i.e. that it is the only way a universe can be. That is also supported by the fact that we can build tiny universes in our computers (e.g. video games and Convey’s Game of Life).

Re: Shut up and calculate: an extreme mathematical universe

#95

Post by kybernetikos »

westoncb wrote: post #92
kybernetikos wrote: post #86

Earlier quoted context omitted.

I strongly suspect that I can dramatically affect or entirely 'turn off' your experience of qualia through purely physical means, so I think your objection is much more to do with your skepticism that mathematical or computational processes can generate physical processes than anything to do with qualia. Of course, you only have to have a virtual object thrown at your head in VR to discover that your brain will mista…

Your brain doesn't experience computational processes any more directly through VR: VR works by sending controlled physical sensations to your senses using the same routes as when you ordinarily interact with the world.

Sure, but your brain mistakes lights flashing according to a computational process for light flashing according to a physical process. It's not an argument that you are directly experiencing maths, just an example of how easily our brains can get maths and physics mixed up with the hint of a suggestion that if it's so easy, then perhaps there's not as big a distinction as we might think.

Re: Shut up and calculate: an extreme mathematical universe

#96

Post by Phemist »

whatshisface wrote: post #88
Phemist wrote: post #85

Earlier quoted context omitted.

Scott Aaronson wrote a great paper arguing around what you mentioned[1]. He tackles the issue of why a waterfall does not simulate a universe if we transform the waterfall in an appropriate way. He argues that the waterfall would indeed simulate a universe, if and only if the transformation function is of polynomial complexity. However! He argues that it is more likely such a transformation is if exponential complexi…

Aaronson is one of my favorite philosophers. But, what if there's a law of physics inside of the simulated universe that solves exponential problems in polynomial time? You could pack a more limited universe inside of that one, if you didn't want your inhabitants to have access to it. I think that computational complexity absolutely does determine how useful a simulation is to us , but it's not meta-universal enough…

Interesting point! All I have to bring in is that if computational complexity is of no interest to inhabitants of a simulation, very strong assumptions about the nature of the simulating universe still need to be made? This, I think, means that you're saying that time is for all intents and purposes unbounded/unlimited/infinite in the simulating universe. As the law of physics that turns exp->poly problems would still need to be simulated, and likely, if i understand correctly, is not necessarily polynomial in the simulating universe?

If I'm interpreting it correctly it does seem to put some constraints on the nature of the simulating universe, but does not necessarily disprove the existence of it?

Re: Shut up and calculate: an extreme mathematical universe

#97

Post by eref »

gfodor wrote: post #59
eref wrote: post #30

Earlier quoted context omitted.

Tegmark's Mathematical Universe Hypothesis (MUH) is actually pretty much a computational theory of the universe. It basically makes the assumption that there exists somewhere the simplest process imaginable: One that counts through and runs all mathematical formulas which includes all programs, which, in turn, includes all (computable) universes. This assumption explains why our universe is oddly complex: If all univ…

I didn't take Tegmark's argument to be a computational theory. I took it to be an inductive one based upon the trend of the physics over the last decades towards the more and more generified multiverse theories. Ultimately, you land on a model where all consistent mathematical representations of a reality exist. At that level of abstraction, there is no where to go: it is the limit of the induction. There's a rather…

I am unsure now whether he describes the set of mathematical objects by enumeration and evaluation. He definitely describes the set of universes this way, as being “run”, so it is a computation. But you are right that he never discussed the substrate that they are run on. He assumes the existence of that enumeration to be axiomatic, like an uncaused cause, somewhere in the space of all mathematical objects that simply exist. I guess, if we had a proof that all non-computable formal systems are inconsistent then we could also skip one layer and assume the enumeration of all programs as axiomatic in order to be maximally agnostic.

Re: Shut up and calculate: an extreme mathematical universe

#98

Post by Koshkin »

otakucode wrote: post #65
Koshkin wrote: post #53

Earlier quoted context omitted.

> the universe does [predict] But it does not.

That's a very strange quote you did... did you honestly think that I meant the pronoun 'it' to mean 'predict'? I absolutely did not. The universe does it. It executes. It evolves along the pathway and 'calculates' (if you wish) the end result. A thing which no mathematics can, or will ever be able to, do.

> calculates ... the end result

It does not do that, either. (Because there is no "end result" to calculate.)

Re: Shut up and calculate: an extreme mathematical universe

#99

Post by drdeca »

whatshisface wrote: post #71
drdeca wrote: post #61

Earlier quoted context omitted.

Not to say that I think that the world is a simulation or anything like that (I don't), but I think that computational complexity and related things probably do induce a natural notion of "naturality" on the different mappings. Even if there might not be a single most natural mapping, I think it makes sense to say that some mappings are more natural than others. I think there is a natural sense which is independent f…

Computational complexity is an insufficient motivator, because while in our current universe some problems are hard and others are easy, in the hypothetical universe there might be a law of physics that solves NP-hard problems. In fact, if the problem is right, you might even end up in a situation where they can't hook their NP-hard problem solvers together in a way that solves problems that we would consider polynom…

> in the hypothetical universe there might be a law of physics that solves NP-hard problems

I agree with this part.

I wasn't thinking specifically about P vs NP though. (if I was, I think that would be a kind of weak argument because we don't have a proof that P isn't equal to NP ? At least not yet.)

I was thinking more in terms of like, Solomonoff probability and Kolmorogov and things like that.

And even if you suppose that the universe in question has a Turing oracle, I think you would just have to go up enough levels in that hierarchy in order solve that.

Even without that though, looking at the space of permutations on N, I think it is likely that there is a natural way to talk about what things are true of "most" things in that space, and things like that, which could, I think, support at least a weak sense of degrees of naturality between mappings, even without appealing to computational complexity.

Edit: I figured I should respond to this part also:

> In fact, if the problem is right, you might even end up in a situation where they can't hook their NP-hard problem solvers together in a way that solves problems that we would consider polynomial.

I think that whatever process is needed to get the output in a form that can be used as input for other things in general should be considered to be part of the computational process. Maybe that should even be implied by the meaning of "compute".

Like, say that some computation takes a number as input in a binary representation, and outputs a number, but outputs it in ternary. If you are talking about how fast the process is on numbers, it should include the time needed to convert back to the binary representation. (Unless, of course, the computation that you are considering the process to be doing includes the "input is in binary, output is in ternary" part. If it is being considered "on numbers" though, I think it should include the conversion time to and from whatever representation of numbers is being considered to be canonical.)

Re: Shut up and calculate: an extreme mathematical universe

#100

Post by westoncb »

westoncb wrote: post #49

It baffles me that people ignore the fact that they have subjectivity when making these claims. It makes a certain amount of sense since science itself aims to remove any taint of subjectivity in its practice, so folks who want to be thoroughly 'scientific' in other aspects of their lives (e.g. their personal philosophies of reality) carry over over this ideal. But it's also a contradiction since science scientific m…

I'll also add where I see math fitting in: imagine some complex 3d object changing in time. Now imagine it's wrapped in a kind of net, like you see in 'wireframes' in computer graphics. If that complex 3D object is our universe, I see math as like that wrapping wireframe: there is a strong correspondence of some kind, and it covers the full extent of what's out there in some sense, but there are still gaps and extents into other directions etc. which are not math (or any form of human description).
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