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Computation as a universal and fundamental concept

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Re: Computation as a universal and fundamental concept

#81

Post by andsoitis »

jibal wrote: post #77
Diogenesian wrote: post #49

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…

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.

Metaphysics operates one level up from physics or the sciences, asking what reality has to be like for anything, including the sciences, to be possible or meaningful at all.

Re: Computation as a universal and fundamental concept

#82

Post by unknown_user_84 »

kaashif wrote: post #57

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…

It strikes me that this is a kind of an escalating pattern though I don't suppose it has to be. Clock -> Steam Engine -> Computer -> AGI -> Skynet -> Throw rocks at robots -> Judgement Day. Also very not serious commentary.

On I suppose a slightly more serious note it also strikes me that there will eventually, probably, maybe be _something_ that fits best; though we are not promised to find it. And it seems wild to say that about a model because all models are fundamentally wrong, but they are usually group-able by less-wrongness, so probably fundamentally feasible.

Re: Computation as a universal and fundamental concept

#83

Post by rdtsc »

BirAdam wrote: post #73
Diogenesian wrote: post #65

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…

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.

It’s not as simple as for example degrees of freedom and the states for a system is “information” and those one can argue are physical.

Re: Computation as a universal and fundamental concept

#84

Post by spragl »

sgt101 wrote: post #2

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…

Both P and NP are computable. That is, a Turing machine can compute both of them.

Those quantum processes are interesting. Take the random numbers generated from radioactive decay. They are (after some cleanup) truly random. That is what we think. But how could we tell the difference from pseudorandom numbers, generated by a sufficiently advanced algorithm? We couldnt. So particles could simply be Turing Machines running sufficiently advanced algorithms that we cant reverse engineer. If so, quantum mechanics is computable even if we cant compute it.

(Particles being TMs doesnt mean they are FAs with an infinite tape, but that they are computationally equivalent to TMs.)

Re: Computation as a universal and fundamental concept

#85

Post by jibal »

Robotbeat wrote: post #60
Diogenesian wrote: post #49

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…

> 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).

Shannon asked von Neumann what to call it, and von Neumann said "You should call it entropy, for two reasons: In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name. In the second place, and more important, nobody knows what entropy really is, so in a debate you will always have the advantage."

Re: Computation as a universal and fundamental concept

#86

Post by jibal »

andsoitis wrote: post #81
jibal wrote: post #77

Earlier quoted context omitted.

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.

Metaphysics operates one level up from physics or the sciences, asking what reality has to be like for anything, including the sciences, to be possible or meaningful at all.

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.

Re: Computation as a universal and fundamental concept

#87

Post by jstanley »

jojogeo wrote: post #9

Something has always nagged me about the halting problem, might be my mis-understanding of the problem space but; - You have a piece of software - That software does in memory compute only - The software does not touch any peripherals, networking, or any other external source which introduce unpredictability (x) I'm convinced that somehow this can be solved/proven whether the execution will halt or not. (x) The secon…

The standard argument is:

Assume H(P,i) to be a program that tells you whether the program P will halt on input i. Returns true if it halts and false if it doesn't.

Define a new program G(x) that halts if x does not halt on itself as input and loops forever if x halts on itself as input:

  def G(x):
    if H(x,x):
      while True:
        pass
    else:
      return
Does G(G) halt?

If G(G) halts then H(G,G) is true so we end up in the infinite loop, a contradiction. If G(G) does not halt then it returns without looping, also a contradiction.

So our halting oracle H does not exist, so there can not be a function that tells you whether another function will halt on itself as input, so there can not be a function that tells you in the general case whether some other computation will halt, QED.

Re: Computation as a universal and fundamental concept

#88

Post by dchftcs »

Diogenesian wrote: post #65
Robotbeat wrote: post #60

Earlier 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…

A more concise explanation is that, computation is the transformation of information. Any transformation of information is computation, and is thus subject to some theory of computation. A physical process involves the transformation of information, so can be studied with a theory of computation.

Re: Computation as a universal and fundamental concept

#89

Post by jdw64 »

jojogeo wrote: post #43
jdw64 wrote: post #32

Is 'computation' really universal and fundamental? Turing machines, lambda calculus, algorithmic notations, they're all human-made formalisms. Are the halting problem and the limits of computability actually constraints that exist only within these human-made formal systems? When we constrain a formalism to reduce complexity, it feels like necessity emerges from within those constraints. For example, when we say 'CRU…

Ahhh this is fantastic thank you; it _is_ hard to reconcile whether problems come with the original topic or whether they are introduced by the abstraction that we _need_ to make in order to quantify a thing/explain it to ourselves and others. Regarding the downcast/upcast; I think it _can_ be possible to do this successfully; > I have a glass, I throw it at a hard surface. What will happen? Well (duh) the glass will…

You're right. But consider this: the geocentric model perfectly predicted planetary positions for centuries, and it was certainly useful. But could we say it was the essence of the universe? In the end, it's a useful model within limited cognition, but whether it's 'fundamental' is a separate question.

I think the key is that different phenomena require different approaches, and even if you interpret a single phenomenon through multiple mental models, none of them necessarily captures its essence. Ultimately, it's about which mental model is shared by a 'group'—not about what's fundamentally true.

We currently share the model of computation, but whether that makes it fundamental is a different story.

As a programmer, I'd put it this way: no matter how well an API describes the backend, the backend itself is not the API.

Here, the API is human knowledge, and the backend is the world

Re: Computation as a universal and fundamental concept

#90

Post by jdw64 »

amavect wrote: post #56
jdw64 wrote: post #32

Is 'computation' really universal and fundamental? Turing machines, lambda calculus, algorithmic notations, they're all human-made formalisms. Are the halting problem and the limits of computability actually constraints that exist only within these human-made formal systems? When we constrain a formalism to reduce complexity, it feels like necessity emerges from within those constraints. For example, when we say 'CRU…

You sound like you believe in philosophical skepticism. Tell me: can a map ever properly describe the territory? When would a map properly describe the territory? (Can a theory ever properly describe reality? What does a theory need to properly describe reality?) We know that universal Turing machines can emulate other Turing machines. Weirdos like Wolfram believe that a universal Turing machine can emulate reality.…

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