61–70 of 183 posts
I like how every time a new technology is invented and becomes big, people start to think it explains everything. Like how in the 16th/17th centuries some people thought the universe was a big clock. Or how in the 19th centuries people thought the universe was like a big steam engine. Or now we think the universe is a big computer. Not saying this is wrong or that I've watched all of the lectures above or anything, b…
There 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…
There 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…
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…
Earlier quoted context omitted.
No Claude was not involved in any way in me writing it, and honestly it's kind of getting depressing how many comments are constantly questioning peoples use of LLMs.
The other day, while reading, my AI-dar triggered on some typical claudisms, but then I remembered I was reading from a paper book that was printed in 1997...
What was the book in 1997? That's about the time of my first UAP sighting.
There 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…
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…
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 physical quantities are information, and on the other hand information is always a large collection of semi-independent semi-stochastic physical objects and can be profitably modelled by some sort of statistical mechanics. Information theory is relevant all over physics because human agents collect all sorts of physical information. The universe "doesn't care" about information in and of itself. Shannon entropy and Boltzmann entropy have similar formulas because they measure precisely the same thing; put another way, a goofy but formally equivalent way to model a gas would be a noisy radio channel communicating each molecule's kinetic energy.
The problem with the black hole information paradox isn't that information is destroyed per se, but that it appears to be destroyed in a way that violates quantum mechanics (destroying quantum state without a measurement). The theoretically predicted destruction of information points to a more general problem.
The Laundauer limit is no more fundamental to the universe than "a mechanical crane cannot violate the laws of pulleys." It says that no matter how you design your binary (or whatever) computer, it must involve an ensemble of binary states, and statistical mechanics puts an absolute floor on how little heat is required to alter such states. Whether these states are gas molecules or the written symbols "0" and "1" is immaterial.
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>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…
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…
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 be hard to figure out which is the correct algorithm, but the Java program is fixed so the algorithm is definitely one of the two.
However, there is no algorithm which can take an arbitrary Java program as input and determine whether it will halt. It's about the class of all possible programs.
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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…
Shannon information, sure.
However, algorithmic information (Kolmogorov complexity, etc.) is based on computation.
Computation 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…
Earlier quoted context omitted.
It can be the case that both: - The physics of the universe can be completely modeled as computation, and - It's possible to pose undecidable problems about the way the universe unfolds This is intrinsic to the idea of undecidability even for Turing machines, e.g. "we equate computation with the functioning of Turing machines, but there are real processes executable in Turing machines that are undecidable".
Of course, if our universe is undecidable it must be the case that computable processes can be executed within it, and it might be the case that all of the processes that are ever executed within it are computable... but it might be that some of the processes that are executed are not computable... because the machine may.. or may not?
For example, if aliens claim their machine solves the halting problem, we could test it on millions of inputs whose halting/not-halting behaviour we already know; but even if it works for all of them, there's no way to know that it works for all inputs. For all we know, it might be a huge lookup table which happens to cover all of those inputs we tried.
Earlier 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…
> Information and computation are not the same thing. Shannon information, sure. However, algorithmic information (Kolmogorov complexity, etc.) is based on computation.