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Shut up and calculate: an extreme mathematical universe

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181–190 of 191 posts

Re: Shut up and calculate: an extreme mathematical universe

#181
post #180

Earlier quoted context omitted.

> a Subset cannot have greater cardinality than the set it derives from. I am not completely certain in the subtleties of non-standard set theory, but at least if we replace the axiom of Choice (AC) by the axiom of Determinacy (AD) - which is perfectly fine, though it is less common to do mathematics in this system - we can partition the real line R by an equivalence relation that has more equivalence classes than el…

> we can partition the real line R by an equivalence relation that has more equivalence classes than elements of R That's not surprising, since an equivalence relation is a function of two elements of the set, i.e. O(N^2), and a subset is a function of a single element, i.e. O(N) . The OP mentioned subsets, and an equivalence relation is not a subset of the original set--it doesn't even typecheck.

> That's not surprising, since an equivalence relation is a function of two elements of the set, i.e. O(N^2), and a subset is a function of a single element, i.e. O(N) . The OP mentioned subsets, and an equivalence relation is not a subset of the original set--it doesn't even typecheck.

I don't understand your reasoning. Every equivalence relation partitions the set S on which it is defined on into subsets - these are called equivalence classes. Every equivalence class contains at least one element of S. So I find it quite surprising that there are more equivalence classes than elements of S (in this case S are the real numbers) if we assume AD.

Re: Shut up and calculate: an extreme mathematical universe

#182

Earlier quoted context omitted.

AI in general (whether via RL or whichever new development that will surface) opens up a fascinating new arena for learning about how agents operate, and investigating the soft problem of consciousness (i.e, what are the type of processes and the complexity involved that is required for having an inner experience), but I stand by my assertion that it will never explain the hard problem of consciousness, and no concep…

By saying "no conceptual explanation ever will" you put consciousness in a category of its own, supernatural or mysterious, like Chalmers. That's just a soft form of dualism. You have sense organs and sensory cortex that creates representations. Those representations are evaluated subjectively for their utility, thus, generating emotion. This is qualia. What else is there? The fact that it feels like something to see…

>By saying "no conceptual explanation ever will" you put consciousness in a category of its own, supernatural or mysterious, like Chalmers. That's just a soft form of dualism.

I think you just pointed out the very paradox which illustrates my point: In which category do you place something that cannot belong to any category?

At this point you might want to say that I'm just making up an artificial nonexistent construct that has no bearing on reality and my task would be to show that not only does it exist, but it is the very basis necessary for all categories to exist. This thread would probably not suffice to achieve that :-) And by the way, I don't see it as supernatural - if anything, the process of concepts and objects created by an agent to approximate reality and then taking these approximations to be reality is what I find to be supernatural. It amazes me how evolution managed to pull this off...

>The fact that it feels like something to see red or blue? That's just sensation + emotional response.

I'm suggesting that "just sensation" is a placeholder for "I have no idea what that is"... There's a big difference between the explanation of a process and the experiencing of a process. We are so quick to categorise experiences into concepts and relationships between them that we overlook the fact that the sensory experience exists before any conceptualisation and categorisation, and in a way is much more real than any story we mould it into some milliseconds later (i.e "this is red", "this is cold" etc.)

>So the substrate of consciousness is not the brain, but the "game".

By now you probably realise (though I assume still disagree with me) that I see it the other way around: i.e that no concept can exist without knowing it. This is not the same as saying nothing exists without our knowledge, but it does mean that what exists before our knowledge of it remains by definition undefinable and inscrutable.

Re: Shut up and calculate: an extreme mathematical universe

#183

Earlier quoted context omitted.

I did not mean to imply that subjectivity is irreducible, but rather to say that it a mistaken belief that is the flip side of another mistaken belief (i.e reality is the objects/concepts we use to describe it). > it still leaves us with the question of the nature of subjectivity, a term you use with impunity but without definition! I didn't try to promote or define subjectivity, I challenged you to define an object…

> I didn't try to promote or define subjectivity, I challenged you to define an object without making any references to something subjective I can easily posit an ontology that references no subjects. Just because I formulated said ontology from sense perception doesn't entail that it references subjective concepts. > Mind you, I'm not saying objects and subjects are real, but that they are co-created by the mind and…

>Just because I formulated said ontology from sense perception doesn't entail that it references subjective concepts.

My point is that calling it sense perception will not make the subjective pre-conceptual experience of it go away. I'm not advocating a ghost in the machine here, but trying to show that neither the ghost nor the machine can survive as primitives when put under deep scrutiny, but I first need to demonstrate how neither can independently exist as a valid concept.

>this sort of skepticism necessarily presupposes the very knowledge that it attempts to undermine, and therefore it contradicts itself and is literally false.

Not sure I follow how this relates to the quoted sentence, but the problem with any explanation (physical or philosophical) is that it is always limited to discussing concepts and relationships between them and can never break the boundaries of what can be grasped by thought (this explanation not excluded). My attempt is to show that thought (and thus any object derived from it) is not the pristine reality, but something that comes after reality is processed. At most, thought can point in the right direction (e.g, understand it's own limitations).

Re: Shut up and calculate: an extreme mathematical universe

#184

Earlier quoted context omitted.

By saying "no conceptual explanation ever will" you put consciousness in a category of its own, supernatural or mysterious, like Chalmers. That's just a soft form of dualism. You have sense organs and sensory cortex that creates representations. Those representations are evaluated subjectively for their utility, thus, generating emotion. This is qualia. What else is there? The fact that it feels like something to see…

> By saying "no conceptual explanation ever will" you put consciousness in a category of its own, supernatural or mysterious, like Chalmers. That's just a soft form of dualism. I think you just pointed out the very paradox which illustrates my point: In which category do you place something that cannot belong to any category? At this point you might want to say that I'm just making up an artificial nonexistent constr…

> In which category do you place something that cannot belong to any category?

How could something created by a body not belong to any category? It belongs to the category of self-regulated systems adapting to their environment.

Creating concepts has been demonstrated since 2012 (Google 'cat detector' https://www.wired.com/2012/06/google-x-neural-network/). In natural language processing, Andrej Karpathy demonstrated in his char-RNN blogpost the emergence of neurons specialized in various concepts (http://karpathy.github.io/2015/05/21/rnn-effectiveness/). It happens naturally in deep networks, as lower layer features are combined into higher level features.

> I'm suggesting that "just sensation" is a placeholder for "I have no idea what that is"...

Ah sorry, I didn't mean "sensation" as in "placeholder for no idea". I meant it as a neural net, the kind we have in our vision system, or the kind used in Deep Learning. They are made of millions of neurons and trained on millions of images to distinguish and localize objects and object relations in images. We have had thousands of papers optimizing on this kind of architecture - Convolutional Neural Network (CNN) - arguably the most successful part of deep learning. Not only that "sensation" was a neural net, but "emotional response" is also a neural net that computes scores of utility of states and actions.

So I was referring to concrete concepts. That's what I like about RL compared to philosophy - it replaces vague concepts with concrete models.

Re: Shut up and calculate: an extreme mathematical universe

#185

Earlier quoted context omitted.

> By saying "no conceptual explanation ever will" you put consciousness in a category of its own, supernatural or mysterious, like Chalmers. That's just a soft form of dualism. I think you just pointed out the very paradox which illustrates my point: In which category do you place something that cannot belong to any category? At this point you might want to say that I'm just making up an artificial nonexistent constr…

> In which category do you place something that cannot belong to any category? How could something created by a body not belong to any category? It belongs to the category of self-regulated systems adapting to their environment. Creating concepts has been demonstrated since 2012 (Google 'cat detector' https://www.wired.com/2012/06/google-x-neural-network/ ). In natural language processing, Andrej Karpathy demonstrate…

It looks like we share a similar enthusiasm for the potential of artificial neural networks (and I also assume a similar distrust in the ability of philosophy to answer these questions), and I agree that NNs are currently the best candidate to eventually create self-conscious machines (though unlike some prominent celebrities, I believe it's still in the far future). The point we depart is that you seem to be saying there is no real difference between the hard problem and the soft problem of consciousness.

We obviously mean different things by "sensation": I've implemented neural nets to solve problems using ML, I understand the theory and certainly impressed with the results . I assume that by "sensations" you are referring to the process of inputs entering the input layer of the neural net. This is exactly part of a model for solving the soft problem of consciousness. What I'm getting at is that you know what a sensation feels like before you give it any label - it has a certain "is"ness to it that no equation or concept can convey. I'm saying this becomes possible when a system becomes complex enough to be self-conscious and it is usually attributed as some sort of emergent property that is created by the system, whereas I claim it is much deeper than that, and in fact it is the other way around.

Obviously this correspondence format is not really suited to dive deeper, but I'm always happy to discuss this to find if and where I'm mistaken.

Re: Shut up and calculate: an extreme mathematical universe

#186
post #93

Earlier quoted context omitted.

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 sli…

I understand that perspective, but to me it seems a failure of history. If we had simply thrown out all of our previous knowledge when we discovered 'lower level' understandings and reformulated them in those terms, we would see no 'special values'. Those values would be 1. And all else would be derived from them, and the things at our scale would look complex and maddening. Temperature measured in Kelvin, velocity m…

What I gather from discussions about fine-tuning, it would not be enough to define all the constants as 1 to simplify the picture. In fact, this is already often done in physics. The universe still appears to be oddly fine-tuned.

Re: Shut up and calculate: an extreme mathematical universe

#187
post #141

Earlier quoted context omitted.

If my understanding is right, a bijective function won't change the entropy of the strings it acts on. So, as long as I can find enough states in my grain of sand (quite possibly undoable, so imagine I'm talking about a few photons in space instead!), I can map them on to my universe and be no worse-off, from an information entropy standpoint.

A mapping is a computation. If your mapping is very complex compared to the ostensible simulator, then the mapping is actually doing most of the simulation. So the simulation is not mostly running when the ostensible simulator runs, it is running when you perform the mapping. If you are inside the universe being simulated and think you can do that mapping, it seems unlikely that there exist enough time and space for…

Right, but if the role of the mapping is just to make the status of the simulation make sense to you, (after all, that's the only thing you would be able to observe it doing), then the inhabitant wouldn't care if the mapping was ever computed. So, it's fine if the mappings would be ridiculously impossible to compute. (Extra note: it is extremely hard to simulate the chaotic motion of nearly every physical system. Does that mean they are doing lots of hard computation? If so, does that make them "more likely" to be interpretable as simulating universes?)

Re: Shut up and calculate: an extreme mathematical universe

#188
post #96

Earlier quoted context omitted.

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 stil…

Well, I can try to lay it out more formally:

We can divide up the task of running a physical simulation into the part where the state is computed, and the part where the results are made visible to us in a way we understand.

We can also divide computation up into the same two pieces: the actual solving of the problem, and then the task of reading symbols off the Turing tape. Usually, we set up our definitions so that a program isn't thought to "solve" a problem unless the reading-the-answer part is trivial.

Now, for a person living inside a simulation, the reading-the-answer part would become insignificant. Why do they care if we can see in to their universe?

So, if all we want is to make a world for simulated people to live in, why not stuff all of the computational complexity into the reading-the-answer part, and then not do it? They would be perfectly happy with a jumbled-up, uninterpretable state in our world, because they would be living on the inside where it made sense.

So, if that is convincing, then allow me to pitch my universe simulating computer:

Launch two photons into space. The distance between them is the state of the simulation. If you want to look in to the state, you have to solve an incredibly hard exponential problem to map the distance to a certain corresponding wavefunction that you could make sense out of.

However, the inhabitants wouldn't care about whether or not you interpreted their state. So, as far as the simulated are concerned, two photons flying apart do make a simulation!

In my opinion the easiest way to make this reductio-ad-absurdum go away is to reject the idea that the simulated is real.

Re: Shut up and calculate: an extreme mathematical universe

#189
post #6
post #2

I like the idea that the reality is just mathematics, I thought about it independently, but it gets weird really fast. I yet to have read this essay, but I had two thoughts: 1. Similar to Turing completeness, actual physical reality might not matter for the internal observer. All Turing-complete machines can calculate same things and observer from the inside of the machine cannot determine on what hardware the machin…

If you like the idea of thinking about physical space in computational terms give one of the classics a try, Calculating Space by Konrad Zuse.

https://en.wikipedia.org/wiki/Calculating_Space

ftp://ftp.idsia.ch/pub/juergen/zuserechnenderraum.pdf

http://www.mathrix.org/zenil/ZuseCalculatingSpace-GermanZeni...

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