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what you need to understand about the halting problem is that at is core it is an epistemological problem. An other expresion of it are Gödel's incompleteness t

what you need to understand about the halting problem is that at is core it is an epistemological problem. An other expresion of it are Gödel's incompleteness theorems. Imagine a blank sheet of paper the area of the paper is what is knowable now start building logic as a data structure. We start with the first nodes which are the axioms now everything derived conects to other nodes etc as it expands as mold its going to cover some of the paper but wont be able to cover all. So the danger here is that computers are living on that fractal dimension and will never be able to see outside of it but us human beings have as kurt said intuition. The fact that we can find this paradoxes in logic means that our brains operate on a higher dimension and that computers will allways have blind spots.

michaelmrose 6y ago
You need to start by proving that brains and all idealized computers we can build are inherently on different levels. Intuitively it seems like intuition is just a probabilistic analysis on incomplete data. For example that shadow is "probably" a predator that may eat me or that sound is probably a prey animal I can kill and eat. Current AI which probably doesn't fit either of our definitions of intelligence can design novel untrained strategies. See for example AlphaGo Zero. It's not even clear exactly how our brains work so its hard to imagine that they couldn't be implemented with a sufficiently powerful computer but more broadly a computer doesn't necessarily mean a silicon chip any more than it meant a vacuum tube. If silicon chips prove an insufficient mechanism there is no particular reason we couldn't somehow use a biological substrate or indeed even one we haven't thought of. Perhaps you simply need to acknowledge our limited understanding of the brain AND expand your definition of the term computer.
- happythomist 6y ago
  > It's not even clear exactly how our brains work so its hard to imagine that they couldn't be implemented with a sufficiently powerful computer... Not commenting on what OP said, but I don't think this is correct. Even in principle, how can any computational process produce conscious experiences, which are by nature subjective and unquantifiable?
  - deleted 6y ago
    [deleted]
  - jkhdigital 6y ago
    Calling consciousness “subjective” feels kind of like calling water “wet”. But anyways, life itself is built on computational processes. Most of these processes are “purpose-built” to accomplish very specific tasks, but in humans the development of a massive cortex created something of a general-purpose computer. Consciousness seems to be the necessary compromise to run such an embodied computer on top of all the other functions of the brain that serve to keep us alive.
    - happythomist 6y ago
      I don't think you can say that life is built on computational processes unless you use a definition of "computation" that is so vague and all-encompassing that it becomes effectively meaningless. The Wikipedia definition of "computation" is "any type of calculation that includes both arithmetical and non-arithmetical steps and which follows a well-defined model". But this only makes sense in the context of a designer or observer external to the computation who can identify what that model is and thereby make sense of the output. So you can't say that brain processes are computational, much less life itself, without committing some variation of the homunculus fallacy. John Searle (famously known for his Chinese Room thought experiment) made this argument in a paper called "Is the Brain a Digital Computer?" [1] He points out that "if we are to suppose that the brain is a digital computer, we are still faced with the question 'And who is the user?'" A related problem is qualia. There is no computational process that will produce the sensations of colour or sound or touch. At best you will have some representation that requires having actually experienced those sensations to understand it. So a computational process cannot be the basis of or an explanation for those sensations, and therefore consciousness generally. [1] https://philosophy.as.uky.edu/sites/default/files/Is%20the%20Brain%20a%20Digital%20Computer%20-%20John%20R.%20Searle.pdf https://philosophy.as.uky.edu/sites/default/files/Is%20the%2...
      - astrophysician 6y ago
        > I don't think you can say that life is built on computational processes unless you use a definition of "computation" that is so vague and all-encompassing that it becomes effectively meaningless. I mean, there's nothing physically stopping us from simulating a brain, right? It's a finite object with a finite amount of physical ingredients, and therefore with a finite amount of computing power we can simulate what it does. To me personally, that's a computational process. Maybe that's an overly broad definition of computation, but I think these debates tend to be about whether there is something fundamentally different about "life" (by which I assume you include consciousness). But maybe that's not what you're saying. > He points out that "if we are to suppose that the brain is a digital computer, we are still faced with the question 'And who is the user?'" What does that question even mean? I think it seems deep because we humans have a tendency to ascribe some sort of supernatural aura to our lived experience. Life is something incredible but that (at least to my knowledge) is not uncomputable... > There is no computational process that will produce the sensations of colour or sound or touch. Got one: the brain! > At best you will have some representation that requires having actually experienced those sensations to understand it. Why does a computer not "experience" something?
- bobthechef 6y ago
  > It's not even clear exactly how our brains work so its hard to imagine that they couldn't be implemented with a sufficiently powerful computer We don't need to know. It suffices to expand "reason" to include not just inference, but properly those things which inference depends on, namely, conceptualization+abstraction and judgement. You could never infer that "all triangles have angles adding to 180 degrees" unless you were in possession of the signified concepts. And here is where the temptation to frame brains in terms of computers becomes plainly, let's say, problematic. Concepts like "triangularity" or "the color green" are abstract in that they do not exist as concrete things in their own right. You can have concrete green triangular objects in the world, but not triangularity or green as such...except in a mind that is able to abstract universals from particulars. So images (including the vulgarized CS sense) won't help you because they're always concrete impressions (one green triangle at the expense of all other possible green triangles). Formal structures expressed in what amounts to some notation won't help you either because they only get their meaning from an interpreting mind. Often, it seems attributions of intelligence to computers stem from a tacit failure to remove ourselves from the picture, projecting our capacities onto a hunk of cleverly arranged metal. > If silicon chips prove an insufficient mechanism there is no particular reason we couldn't somehow use a biological substrate or indeed even one we haven't thought of. Computation is a formalism independent of substrate. You can implement a Turing machine using anything that can maintain the appropriate interpretive correspondence. But even then, a computer is not an objective kind of thing like a tree. Unlike a tree, a computer is only a computer because the observer has chosen to interpret it as such, or to use it as such. (The naive materialists in the room might try to expand that claim to encompass anything, but in the very act they've made things worse. The mind's capacity to comprehend the world is severely crippled if not destroyed, and now you have to explain this mind that somehow can entertain the existence of wondrous things like trees and elephants that the rest of the universe is unable to evince, thus making the mind even more mysterious than it was before the reductionist took to his hatchet.) So if substrate makes a difference, then it's the substrate that matters, not some correspondence with a computational formalism. > You need to start by proving that brains and all idealized computers we can build are inherently on different levels. The burden of proof is on those claiming minds and computers are the same thing.
  - 6y ago
tsimionescu 6y ago
Godel's incompleteness theorems apply to pure mathematics, so even without having any idea how our brains work, we still know for sure that they apply to our brains as well. Even if our brains were able to solve the halting problem, they would still not escape the Incompleteness theorems. And note that it is not that hard, at least in principle, to construct a system that can detect its own incompleteness. As far as we know today, the most likely theory is that our brains are Turing-equivalent computers. There is no other known model of computation, and no scientific argument that would show our vrains/thought processes can't be computers (that is not to say we have proven either of these, they are just the most likely statements, like P!=NP).
adrianN 6y ago
Your brain can store a finite amount of state because it's a finite piece of matter. You are therefore a finite automaton manipulating symbols outside of your brain, e.g. on a piece of paper. That makes you no more powerful than a Turing machine. In fact, since your lifetime is bounded, the amount of paper your can write on is bounded too. You are in thus less powerful than a Turing machine. The fact that you can recognize some paradoxes means exactly nothing about your computational power. There is a sufficiently large lookup table that contains the correct answers to any question you might be able to read during your lifetime. Evaluating it requires nothing more than a finite automaton.

michaelmrose 6y ago

You need to start by proving that brains and all idealized computers we can build are inherently on different levels. Intuitively it seems like intuition is just a probabilistic analysis on incomplete data. For example that shadow is "probably" a predator that may eat me or that sound is probably a prey animal I can kill and eat. Current AI which probably doesn't fit either of our definitions of intelligence can design novel untrained strategies. See for example AlphaGo Zero. It's not even clear exactly how our brains work so its hard to imagine that they couldn't be implemented with a sufficiently powerful computer but more broadly a computer doesn't necessarily mean a silicon chip any more than it meant a vacuum tube. If silicon chips prove an insufficient mechanism there is no particular reason we couldn't somehow use a biological substrate or indeed even one we haven't thought of. Perhaps you simply need to acknowledge our limited understanding of the brain AND expand your definition of the term computer.

happythomist 6y ago
> It's not even clear exactly how our brains work so its hard to imagine that they couldn't be implemented with a sufficiently powerful computer... Not commenting on what OP said, but I don't think this is correct. Even in principle, how can any computational process produce conscious experiences, which are by nature subjective and unquantifiable?
- deleted 6y ago
  [deleted]
- jkhdigital 6y ago
  Calling consciousness “subjective” feels kind of like calling water “wet”. But anyways, life itself is built on computational processes. Most of these processes are “purpose-built” to accomplish very specific tasks, but in humans the development of a massive cortex created something of a general-purpose computer. Consciousness seems to be the necessary compromise to run such an embodied computer on top of all the other functions of the brain that serve to keep us alive.
  - happythomist 6y ago
    I don't think you can say that life is built on computational processes unless you use a definition of "computation" that is so vague and all-encompassing that it becomes effectively meaningless. The Wikipedia definition of "computation" is "any type of calculation that includes both arithmetical and non-arithmetical steps and which follows a well-defined model". But this only makes sense in the context of a designer or observer external to the computation who can identify what that model is and thereby make sense of the output. So you can't say that brain processes are computational, much less life itself, without committing some variation of the homunculus fallacy. John Searle (famously known for his Chinese Room thought experiment) made this argument in a paper called "Is the Brain a Digital Computer?" [1] He points out that "if we are to suppose that the brain is a digital computer, we are still faced with the question 'And who is the user?'" A related problem is qualia. There is no computational process that will produce the sensations of colour or sound or touch. At best you will have some representation that requires having actually experienced those sensations to understand it. So a computational process cannot be the basis of or an explanation for those sensations, and therefore consciousness generally. [1] https://philosophy.as.uky.edu/sites/default/files/Is%20the%20Brain%20a%20Digital%20Computer%20-%20John%20R.%20Searle.pdf https://philosophy.as.uky.edu/sites/default/files/Is%20the%2...
    - astrophysician 6y ago
      > I don't think you can say that life is built on computational processes unless you use a definition of "computation" that is so vague and all-encompassing that it becomes effectively meaningless. I mean, there's nothing physically stopping us from simulating a brain, right? It's a finite object with a finite amount of physical ingredients, and therefore with a finite amount of computing power we can simulate what it does. To me personally, that's a computational process. Maybe that's an overly broad definition of computation, but I think these debates tend to be about whether there is something fundamentally different about "life" (by which I assume you include consciousness). But maybe that's not what you're saying. > He points out that "if we are to suppose that the brain is a digital computer, we are still faced with the question 'And who is the user?'" What does that question even mean? I think it seems deep because we humans have a tendency to ascribe some sort of supernatural aura to our lived experience. Life is something incredible but that (at least to my knowledge) is not uncomputable... > There is no computational process that will produce the sensations of colour or sound or touch. Got one: the brain! > At best you will have some representation that requires having actually experienced those sensations to understand it. Why does a computer not "experience" something?
bobthechef 6y ago
> It's not even clear exactly how our brains work so its hard to imagine that they couldn't be implemented with a sufficiently powerful computer We don't need to know. It suffices to expand "reason" to include not just inference, but properly those things which inference depends on, namely, conceptualization+abstraction and judgement. You could never infer that "all triangles have angles adding to 180 degrees" unless you were in possession of the signified concepts. And here is where the temptation to frame brains in terms of computers becomes plainly, let's say, problematic. Concepts like "triangularity" or "the color green" are abstract in that they do not exist as concrete things in their own right. You can have concrete green triangular objects in the world, but not triangularity or green as such...except in a mind that is able to abstract universals from particulars. So images (including the vulgarized CS sense) won't help you because they're always concrete impressions (one green triangle at the expense of all other possible green triangles). Formal structures expressed in what amounts to some notation won't help you either because they only get their meaning from an interpreting mind. Often, it seems attributions of intelligence to computers stem from a tacit failure to remove ourselves from the picture, projecting our capacities onto a hunk of cleverly arranged metal. > If silicon chips prove an insufficient mechanism there is no particular reason we couldn't somehow use a biological substrate or indeed even one we haven't thought of. Computation is a formalism independent of substrate. You can implement a Turing machine using anything that can maintain the appropriate interpretive correspondence. But even then, a computer is not an objective kind of thing like a tree. Unlike a tree, a computer is only a computer because the observer has chosen to interpret it as such, or to use it as such. (The naive materialists in the room might try to expand that claim to encompass anything, but in the very act they've made things worse. The mind's capacity to comprehend the world is severely crippled if not destroyed, and now you have to explain this mind that somehow can entertain the existence of wondrous things like trees and elephants that the rest of the universe is unable to evince, thus making the mind even more mysterious than it was before the reductionist took to his hatchet.) So if substrate makes a difference, then it's the substrate that matters, not some correspondence with a computational formalism. > You need to start by proving that brains and all idealized computers we can build are inherently on different levels. The burden of proof is on those claiming minds and computers are the same thing.
- 6y ago

tsimionescu 6y ago

Godel's incompleteness theorems apply to pure mathematics, so even without having any idea how our brains work, we still know for sure that they apply to our brains as well. Even if our brains were able to solve the halting problem, they would still not escape the Incompleteness theorems. And note that it is not that hard, at least in principle, to construct a system that can detect its own incompleteness. As far as we know today, the most likely theory is that our brains are Turing-equivalent computers. There is no other known model of computation, and no scientific argument that would show our vrains/thought processes can't be computers (that is not to say we have proven either of these, they are just the most likely statements, like P!=NP).

adrianN 6y ago

Your brain can store a finite amount of state because it's a finite piece of matter. You are therefore a finite automaton manipulating symbols outside of your brain, e.g. on a piece of paper. That makes you no more powerful than a Turing machine. In fact, since your lifetime is bounded, the amount of paper your can write on is bounded too. You are in thus less powerful than a Turing machine. The fact that you can recognize some paradoxes means exactly nothing about your computational power. There is a sufficiently large lookup table that contains the correct answers to any question you might be able to read during your lifetime. Evaluating it requires nothing more than a finite automaton.