Would like to think we human are better than what is implied by the course in that we would not mistaken our model of reality as reality itself.
Computation as a universal and fundamental concept
71–80 of 183 posts
Re: Computation as a universal and fundamental concept
#72From my naive pov: Related to computation is the concept of state (I know, functional languages can get away without it, sort of). I always wondered how the universe “knows” the mass of the sun. If there are some underlying functions/computations “running” in the background to keep planets moving and so on, and if the mass of planets is a key element in such computations… then either: the mass is calculated “on the f…
I think it’s easier to conceive of it like this: Each point in spacetime IS storage. Storage can be queried by interacting with it (in a variety of ways), though the process of querying affects the value not only of the querier, but also the queried, which may have side-effects as well. The interaction itself is the computation. A simple example for the computation: It’s like placing boxes next to each other. Yes I c…
Spacetime isn't quantized as far as we know. We don't know since we don't have quantum gravity or ability to probe Planck scale. Quantum fields are continuous, it is excitations in the field, particles, that are quantized.
Re: Computation as a universal and fundamental concept
#73Earlier quoted context omitted.
This is a misconception. It’s more fundamental than that. There’s a fundamental connection between (Shannon) information theory and thermodynamics. The Landau Limit, whether blackholes can destroy information or not, quantum mechanics, etc. Information is actually tangible . It’s not just an analogy or a coincidence that the word “entropy” is a word used in both physics and computer science (information theory). Ther…
Information and computation are not the same thing. I was very specifically talking about Turing machines and other theoretical models of computation. That said, you are still making the same mistake I pointed out, elevating human symbolic information to a higher plateau than it deserves. I think it's because you're being too vague about the connection, when it's fairly mundane. The "fundamental connection" is that p…
I’ve always hated the use of the word “information” in relation to things like spin.
Information and order are effects of human perception and preference. They exist as abstractions in the mind and not in reality.
Re: Computation as a universal and fundamental concept
#74Earlier quoted context omitted.
Information and computation are not the same thing. I was very specifically talking about Turing machines and other theoretical models of computation. That said, you are still making the same mistake I pointed out, elevating human symbolic information to a higher plateau than it deserves. I think it's because you're being too vague about the connection, when it's fairly mundane. The "fundamental connection" is that p…
I’ve always hated the use of the word “information” in relation to things like spin. Information and order are effects of human perception and preference. They exist as abstractions in the mind and not in reality.
Best way to show this is to implement information in multiple physical substrates. Make a book out of paper and make it out of clay. Same information. The physical substrate doesn’t matter.
Re: Computation as a universal and fundamental concept
#75I saw the title and assumed an article by Wolfram. But it's by Tim Roughgarden who I know from algorithmic game theory. Anyway, I'll register my membership in the "it's more fundamental than that" camp.
Re: Computation as a universal and fundamental concept
#76Computation has turned out to be a far more general concept than I think was imagined, up to the point that many computer scientists now seem to equate computation with the functioning of the universe. Recently it's been shown that there are real, physical processes which are undecidable (we cannot know if a latice of atoms has a spectral gap or not, we cannot determine if a specific particle in a fluid flow will rea…
>Recently it's been shown that there are real, physical processes which are undecidable I want to push back a bit on this claim along two dimensions. Imagine a physical Turing machine built out of atoms, gears, levers, and an electron parked on the read/write head and ask whether that electron ever crosses some fixed plane in space, which it does only when the machine enters its halt configuration. That's now a purel…
Agreed, and I'll add: the universe is sufficiently messy and complex that some of the claimed undecidability results may never occur in practice.
For your Turing machine example: even if we built such a machine, it would never truly be giving an answer to the halting problem, because any stray cosmic particle could excite the electron and cause it to cross whatever plane.
For a more realistic example: the ground state of an molecule is a physically relevant quantity, and in theory any molecule alone should lose energy and attain it's ground state, even if finding the ground state electronic configuration is undecidable. But in reality, no molecule is ever truly isolated and so would never actually be guaranteed to enter it's ground state (or if it were truly isolated, it would not be observed at all rendering the question moot)
Re: Computation as a universal and fundamental concept
#77There are a lot of long comments basically saying what I am about to say so I will try to keep this brief: Computation is a metaphysically universal and fundamental concept, since metaphysics is (tautologically) the domain of humans and we use symbolic communication. So of course very general theories of symbolic processes (e.g. Turing machines) are pertinent to the symbolic methodology we use to understand scientifi…
Prove any of this. Or at least provide a cogent argument for it. To me it looks riddled with mistakes, like
> metaphysics is (tautologically) the domain of humans
which is frankly incoherent.
Re: Computation as a universal and fundamental concept
#78Computation has turned out to be a far more general concept than I think was imagined, up to the point that many computer scientists now seem to equate computation with the functioning of the universe. Recently it's been shown that there are real, physical processes which are undecidable (we cannot know if a latice of atoms has a spectral gap or not, we cannot determine if a specific particle in a fluid flow will rea…
Undecidable isn't uncomputable.
"Computable" can mean probabilistic, and classical computers can function over probability distributions just fine.
Re: Computation as a universal and fundamental concept
#79Earlier quoted context omitted.
I think it’s easier to conceive of it like this: Each point in spacetime IS storage. Storage can be queried by interacting with it (in a variety of ways), though the process of querying affects the value not only of the querier, but also the queried, which may have side-effects as well. The interaction itself is the computation. A simple example for the computation: It’s like placing boxes next to each other. Yes I c…
Spacetime isn't quantized as far as we know. We don't know since we don't have quantum gravity or ability to probe Planck scale. Quantum fields are continuous, it is excitations in the field, particles, that are quantized.
Ah, I thought we didn’t have strong evidence either way. Regardless, I shouldn’t have stated spacetime quanta so matter-of-factly. I just have an easier time conceptualizing if I treat everything like hypervoxels and that leaked in.
Re: Computation as a universal and fundamental concept
#80Earlier quoted context omitted.
I may be misremembering Godel's proof or misunderstanding your last paragraph, but I thought Godel's proof actually presented a specific undecidable statement. The hope then was that somehow undecidable statements could be cordoned off from decidable statements, and Turing's result showed that that wasn't possible. Perhaps that's what you mean by "the nonexistence of a single algorithm that correctly answers every in…
There's no such thing as an undecidable statement. A single statement can't be undecidable. Undecidability is a property of a class of statements. For example, you can ask whether a Java program, run with infinite memory, will eventually halt. For any particular Java program, there's obviously an algorithm that says whether it halts or not. The algorithm is a single statement, which says either "yes" or "no". Might b…
That's a different meaning of the word "undecidable". You're talking about undecidable problems [1]. The meaning in Gödel's incompleteness theorem is different and is a synonym with independent [2].
[1] https://en.wikipedia.org/wiki/Undecidable_problem
[2] https://en.wikipedia.org/wiki/Independence_(mathematical_log...