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Computation as a universal and fundamental concept
111–120 of 183 posts
Re: Computation as a universal and fundamental concept
#112There 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…
A related question might be, what's the difference between mathematical (Godel), computational (Turing,) and physical (Yang-Mills) undecideabilty/computability?
Re: Computation as a universal and fundamental concept
#113Earlier quoted context omitted.
I know what metaphysics is (and your description isn't accurate--science is a knowledge-producing method that doesn't depend on metaphysics in order to be meaningful), but that has nothing to do with my statement. And it's called "metaphysics" because Andronicus placed that volume after the "physics" volume when he organized Aristotle's writings.
I asked for proof of claims and I just get "it absolutely does" and a bunch more assertions, and word salad like "the validity of the scientific method is ultimately a metaphysical extension of our intuitions about inductive reasoning and causality" -- there's nothing "metaphysical" about it ... the scientific method is a disciplined application of an effective process of discovery. And '"Our intuitions" is why I sai…
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Re: Computation as a universal and fundamental concept
#114Earlier quoted context omitted.
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?
There's no way to empirically spot an uncomputable process, since it would require infinitely-many observations. 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 whic…
No, you can prove things hold in the abstract mathematically, don't need to resort to physical systems.
Re: Computation as a universal and fundamental concept
#115Computation 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…
The infinite lattice doesn't represent a "real" physical processes, it's just mathematical technique for closing a (fundamentally) quantized combinatorial sum over millions of interacting elements. The gap problem exists in the limit. For real systems the spectrum can be measured (in principle) by probing the ground state. The computational paradigm is incredibly general but only within what's apparently a pretty aty…
In this case quantum thermo.
Re: Computation as a universal and fundamental concept
#116Earlier quoted context omitted.
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 stat…
A quantum Turing machine would be needed to simulate a truly quantum process. Stochasticity exists in classical systems, but that's an entirely different type of randomness.
Quantum computation is not super-Turing: anything you could solve with a quantum Turing machine you could also solve with a classical Turing machine, albeit sometimes a lot slower. We know how to emulate quantum systems in classical systems.
Re: Computation as a universal and fundamental concept
#117Earlier quoted context omitted.
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…
> 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". This isn't true. In general, if a program hasn't halted yet you don't know if it will. In particular, consider the Collatz conjecture. You can't even tell if your Java implementation of it will halt for a particular input, until it does. https://en.…
And yet there is a correct algorithm — it's either the const yes algorithm or the const no algorithm.
We don't _know_ which algorithm it is, but that's not relevant to the definition of undecidability, which only requires that the algorithm exist.
Re: Computation as a universal and fundamental concept
#118Earlier quoted context omitted.
> 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". This isn't true. In general, if a program hasn't halted yet you don't know if it will. In particular, consider the Collatz conjecture. You can't even tell if your Java implementation of it will halt for a particular input, until it does. https://en.…
And yet there is a correct algorithm — it's either the const yes algorithm or the const no algorithm. We don't _know_ which algorithm it is, but that's not relevant to the definition of undecidability, which only requires that the algorithm exist.
Cheers, I had missed the nuance.
Re: Computation as a universal and fundamental concept
#119Earlier quoted context omitted.
> up to the point that many computer scientists now seem to equate computation with the functioning of the universe. Do you think that's a kind of tunnel vision? If the only thing you focus on is computation, you'll probably end up seeing computation everywhere - it became a way of seeing the world.
It is a common accusation. There's a somewhat famous quote I've seen a few times: "It's interesting to look back through history on this one. Each age has its pinnacle of technology, and each age uses that technology as a metaphor for nature, for the universe. In ancient Greece, the technological marvels were musical instruments and the ruler and compass. The Greek philosophers tried to build an entire cosmology from…
The universe as a computer/computation has been explored by many (e.g., see John Wheeler and Seth Lloyd). However, the laws of physics give us a lot more predictions, so their explanatory power tend to be greater. For example, the nature of space and time.
Re: Computation as a universal and fundamental concept
#120Earlier 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…
You can say things like, “In the domain of physics, X,” “Assuming the scientific method, X,” or “Assuming the premises of logic, X.” But “computation is a fundamental aspect of the universe”, in the way it's being understood in this thread (as opposed to the article) does not remain within any of those frameworks. It makes a claim about reality as a whole. Once you make that kind of universal claim, all the assumptio…
The Heisenberg Uncertainty Principle and the Laws of Thermodynamics are pretty d*mn fundamental.