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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

#61

Post by drdeca »

whatshisface wrote: post #54
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 know of a nice argument against simulationism that I think applies here: If simulated universes can be "real," then we're assuming that there's a mapping between patterns of electrons in a computer (or provable theorems, if you're brave enough), and the real universe they represent. (Say, interpreting two numbers that may be stored very far apart on the chip as the positions of two particles that are, in the univer…

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 from human perception and intent, in which a computer running, say, a graph coloring algorithm, is doing that more than a waterfall is.

Even if there is a bijection between a collection of initial states of the waterfall with the input of program, that fits together with one between the outputs and the results of the waterfall.

Re: Shut up and calculate: an extreme mathematical universe

#62

Post by jcmoscon »

hackinthebochs wrote: post #32
jcmoscon wrote: post #14

Math works because reality works. Not the opposite. Reality is bigger than math. Math is just a tool that models reality.

On the contrary, reality works because reality cannot contain contradictions. But the set of possible structures without contradiction is a superset of what is physically realizable. And mathematics is just discovering and cataloging the set of structures without contradiction. So reality works because math works.

Also, Aristotle invented logic while studying cats (reality). That's what I am telling you: reality is amazing, not math!

Re: Shut up and calculate: an extreme mathematical universe

#63

Post by otakucode »

lou1306 wrote: post #34
Koshkin wrote: post #18

Earlier quoted context omitted.

Not really. Berkeley's idealism contests the objectivity of reality, while here we are presented with another view of the foundation of the (objective) material world.

This is true, but: > When we derive the consequences of a theory, we introduce new concepts — protons, molecules, stars — because they are convenient Couldn't matter itself be just another "human", "convenient" concept? Indeed the author writes: > our external physical reality is assumed to be purely mathematical Why should a purely mathematical reality also be material? Doesn't this lead to the logical conclusion th…

>Sure, in this case ideas are objective and not subjective, but Berkeley's "mind of God" argument also leads to an objective, albeit immaterial reality, doesn't it?

No, it leads to a subjective inability to know anything at all. It's a difficult philosophical view to talk about, because the people espousing it can not possibly actually believe it and usually don't even understand it. The non-existence of a shared, knowable, objective reality means that, even in a totally solipsistic model, inductive reasoning can not be applied. You can not assume that attempting to breathe in the next moment will extend your life rather than extinguish it. You can not conclude that the air in your lungs will not suddenly become ants. You certainly can not leap to the extensively complex chain of reasoning necessary to believe that between this sentence and the next the English languages will turn into French. It introduces aggressive, pervasive, impossible-to-dismiss inconstancy in all things, including ones self.

A true believer in a subjective universe would remain still in their bed, doing nothing, until they died. Any action whatever beyond automatic biological functions instantly betrays their belief that they know their body, know the environment they are in, and know how the mental activity necessary to cause the action will elicit a change in the environment which is not likely to destroy them. And that is a thing they can never know in a subjective universe.

The 'mathematical universe' on the other hand is simply discussing how the shared, knowable, material universe we live in came to be or is best understood. I happen to think it is factually wrong on a few points (the author just off-hand claims that if we had a big enough supercomputer we could exactly calculate the future development of the universe which is fundamentally untrue for one) but it certainly doesn't amount to subjectivity.

Re: Shut up and calculate: an extreme mathematical universe

#64

Post by kybernetikos »

whatshisface wrote: post #54
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 know of a nice argument against simulationism that I think applies here: If simulated universes can be "real," then we're assuming that there's a mapping between patterns of electrons in a computer (or provable theorems, if you're brave enough), and the real universe they represent. (Say, interpreting two numbers that may be stored very far apart on the chip as the positions of two particles that are, in the univer…

Not sure why this is an argument against simulationism. As far as I can tell, you're just making the point that any system could be regarded as simulating any other system given a sufficiently complex mapping. This seems more like an argument for simulation than against it. In fact, I first heard this argument a long time ago in high school as part of a discussion on panpsychism - the speaker claimed that a cup of tea was sentient because interpreted in a particular way, its thermal states could represent a self aware entity.

The fact that you have to consider the complexity of the encoding scheme and not just the input and the output bit patterns is well understood in information theory. If I have an encoding scheme that has included in it a complete simulation of the universe, I can encode any video into 0 bits since the decoder will always know what I am about to request of it. The more the mapping is customized to the information you're searching for, the less complexity is needed in the input bit patterns to produce the desired output. If you go searching PI for a message, it'll probably take you longer to find it if you use the ASCII values of characters than if you use base64. You'll find it even quicker if you specify that 3='h' 1st 1='e' 4='l' 2nd 1='l' 5='o'.

This all ultimately comes back to Ockham and parameters on a model. Models with more parameters can fit more things spuriously, so you want the model with the fewest parameters that can do the job. Minimum Description Length (and MML) is a great concept https://en.wikipedia.org/wiki/Minimum_description_length

Re: Shut up and calculate: an extreme mathematical universe

#65

Post by otakucode »

Koshkin wrote: post #53
otakucode wrote: post #50

Earlier quoted context omitted.

No, that is not true. Their intractability has absolutely nothing to do with the precision of measurement. Assume the initial condition with infinite precision and the further evolution of the system is still intractable. Ignoring the Heisenberg Uncertainty Principle for a moment and getting to the heart of chaos theory the problem is the production of information at a rate faster than any existant (and I believe, th…

> 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.

Re: Shut up and calculate: an extreme mathematical universe

#66

Post by jcmoscon »

malkarouri wrote: post #33
hackinthebochs wrote: post #32

Earlier quoted context omitted.

On the contrary, reality works because reality cannot contain contradictions. But the set of possible structures without contradiction is a superset of what is physically realizable. And mathematics is just discovering and cataloging the set of structures without contradiction. So reality works because math works.

Why wouldn't reality contain contradictions?

The contradictions is not in reality but in your ideology/agenda. Everybody has an agenda nowadays...

Re: Shut up and calculate: an extreme mathematical universe

#67

Post by agumonkey »

followmeon wrote: post #38

If our reality consists of mathematical programs and the multiverse theory holds, then the theory of everything is a simple incrementing binary counter. Every possible binary string is ran on a Turing machine in a different universe. The halting problem (endless loops) is sidestepped by being contained to a single universe. Also, apparently our universe got lucky as we get to live in an ordered universe, and not diss…

can we rollback that tape ?

Re: Shut up and calculate: an extreme mathematical universe

#68

Post by otakucode »

klank wrote: post #45
otakucode wrote: post #37

A purely mathematical universe immediately brings to mind a question: Since chaotic systems evolve in a way provably intractable to calculation, how could any system based solely upon calculation address, well, almost everything that exists?

That's an odd definition of chaotic systems you are using. It's not so much that chaotic systems can not be calculated but instead that enough precision of starting conditions can't be obtained to ensure an accurate result (for example, highly non-linear systems). The double pendulum system is a perfect example where computation is simple yet the system is still chaotic.

I think it's an odd definition you are using. Chaos depends upon the sensitivity to those initial conditions, not what those initial conditions ARE. You do not need actual physical objects to see this. Conjecture that a double-pendulum system starts in a perfectly real-number-valued mythical reality where spacetime is perfectly continuous (a fiction). Now predict what state the system will be in at a bunch of 'close together' states. Then try to do some 'closer together' states. See if you can ever get them to line up. Do it on pencil and paper, of course, since you want to capture the full real-number-infinity effect.

Of course, you can't write down the real-number result with infinite precision, can you? You'll have to chop it off at some point. That's OK. That's what error bars are for. Just keep going and keep track of your error. Oops, you'll find that your error grows larger than the prediction itself with remarkable speed! THAT is the chaos. It doesn't matter if you measured the starting conditions with literal infinite perfect precision. The error bars on your predictions are going to explode like a busy beaver function. You're not going to catch that. Nothing can. (I imagine the actual physical limit would be that your predictions can be accurate within a distance equivalent to the radius of a sphere expanding at the speed of light from the initial position but I haven't actually read anything suggesting that, it just seems sensible.)

Then you've got stupid simple cellular automata like rule 31 1D systems. Totally discrete. Totally basic. No precision even needed anywhere. And yet, you can't predict it. Not without accumulating an error greater than the state in the system itself if you skip even the slightest act of computation necessary to evolve the system as a whole from one step to the next.

Re: Shut up and calculate: an extreme mathematical universe

#69

Post by [deleted] »

otakucode wrote: post #50
tzahola wrote: post #39

Earlier quoted context omitted.

Chaotic systems are only intractable if you measure the initial conditions with finite precision.

No, that is not true. Their intractability has absolutely nothing to do with the precision of measurement. Assume the initial condition with infinite precision and the further evolution of the system is still intractable. Ignoring the Heisenberg Uncertainty Principle for a moment and getting to the heart of chaos theory the problem is the production of information at a rate faster than any existant (and I believe, th…

[deleted]

Re: Shut up and calculate: an extreme mathematical universe

#70

Post by hackinthebochs »

namelost wrote: post #51
hackinthebochs wrote: post #41

Earlier quoted context omitted.

I mean in the logical sense. If reality could contain logical contradictions then that would mean reality isn't rule-based, which means unconstrained randomness, no information, no meaning, etc.

But the contradiction is in the mathematical model not reality. Even a totally random universe follows some kind of distribution, which can then be modelled (which is exactly what QM is).

>But the contradiction is in the mathematical model not reality

So then you're saying reality can't have a logical contradiction? Seems like you're agreeing with the original statement.

>Even a totally random universe follows some kind of distribution

Which is just a kind of rule.

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