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> Also, I've said that before, but we already know that brains operate under an irreversible computation model. We don't know that brains operate under any kin

by User23 4y ago

> Also, I've said that before, but we already know that brains operate under an irreversible computation model. We don't know that brains operate under any kind of computational model at all. It's often postulated, but it's not proved. Every attempt I've seen at a proof reduces to begging the question. Edit: To be clear I’m not saying a computational model of the brain can’t be a useful tool. Newtonian physics works quite well quite often even though reality isn’t Newtonian.

sudosysgen 4y ago
To be clear, I'm not saying that everything the brain does can be modelled by a known computation model. All I'm saying is that the interesting part of what the brain does is computation, in that it takes in data, operates on it, and returns data. It does this in an irreversible manner because you cannot determine the input from the output (nor a significant part of it). If there is any model of how the brain works it will be a computational model. Perhaps a new one, and perhaps a radically different one, but it's still going to find the definition of a computational model.
- User23 4y ago
  Ultimately, the open question here is this: are uncomputable functions just a mathematical fancy, or do there really exist processes that can only be fully correctly described by uncomputable functions? Personally I lean towards latter view. I’m the first to admit that I have no proof. It’s just my belief, because I find the metaphysical evidence compelling. I don’t object to investigating the former possibility, but I also don’t care for it just being baldly asserted. If the answer is affirmative, that means that science will probably never be solved and we’ll just have to content ourselves with incremental improvements in our understanding. That’s observably been the case up until now. Granted even if all processes are in fact described entirely by computable functions we might still never discover what they are. I hope it’s clear how all that relates to the concrete problem of understanding human cognition and the brain. I'm nowhere near smart enough to even begin to conceive of a mathematical framework for taming noncomputable functions in a pragmatic way, but I earnestly hope some genius comes along who is, supposing that noncomputable functions are needed to completely describe our reality.
  - sudosysgen 4y ago
    Well, those functions are called uncomputable because, as far as we know, there is no repeatable way of computing them, right? So if the human brain was able to compute functions that Turing machines can't, it doesn't mean those functions are uncomputable, it just means the Church-Turing hypothesis is false.
    - User23 4y ago
      The Church-Turing hypothesis just means that the lambda calculus and Turing machines are isomorphic. It doesn’t actually tell us anything about reality, no matter what enthusiastic misunderstandings might say.
      - sudosysgen 4y ago
        No, it doesn't. The Church Turing hypothesis is much stronger - it states that all real-world computation can be done by lambda calculus or Turing machines. That's why it's a hypothesis and not a theorem - it's pretty easy to prove that lambda calculus and Turing machines are equivalent if you have the mindset of a programmer. Put in other words, the Church Turing hypothesis is that there is no computing model higher in hierarchy than the TM and lambda-calculus. > It doesn’t actually tell us anything about reality Well, of course it doesn't tell is anything about reality. That's because no one managed to prove it, and I suspect no one ever will.
        User23 4y ago
        Ah yes. Fair enough. I confused the thesis with the hypothesis. This comes back to the begging the question I initially objected to. Also, the notion of highest computing model is itself begging the question in the sense that the framing assumes a computational model. So much for undergraduate philosophy. What’s your opinion? Are uncomputable functions just fanciful irrelevancies or are there processes in reality that can’t be described by computable functions? If so or if not can you propose how we might know?

by User23 4y ago

sudosysgen 4y ago

To be clear, I'm not saying that everything the brain does can be modelled by a known computation model. All I'm saying is that the interesting part of what the brain does is computation, in that it takes in data, operates on it, and returns data. It does this in an irreversible manner because you cannot determine the input from the output (nor a significant part of it). If there is any model of how the brain works it will be a computational model. Perhaps a new one, and perhaps a radically different one, but it's still going to find the definition of a computational model.

User23 4y ago
Ultimately, the open question here is this: are uncomputable functions just a mathematical fancy, or do there really exist processes that can only be fully correctly described by uncomputable functions? Personally I lean towards latter view. I’m the first to admit that I have no proof. It’s just my belief, because I find the metaphysical evidence compelling. I don’t object to investigating the former possibility, but I also don’t care for it just being baldly asserted. If the answer is affirmative, that means that science will probably never be solved and we’ll just have to content ourselves with incremental improvements in our understanding. That’s observably been the case up until now. Granted even if all processes are in fact described entirely by computable functions we might still never discover what they are. I hope it’s clear how all that relates to the concrete problem of understanding human cognition and the brain. I'm nowhere near smart enough to even begin to conceive of a mathematical framework for taming noncomputable functions in a pragmatic way, but I earnestly hope some genius comes along who is, supposing that noncomputable functions are needed to completely describe our reality.
- sudosysgen 4y ago
  Well, those functions are called uncomputable because, as far as we know, there is no repeatable way of computing them, right? So if the human brain was able to compute functions that Turing machines can't, it doesn't mean those functions are uncomputable, it just means the Church-Turing hypothesis is false.
  - User23 4y ago
    The Church-Turing hypothesis just means that the lambda calculus and Turing machines are isomorphic. It doesn’t actually tell us anything about reality, no matter what enthusiastic misunderstandings might say.
    - sudosysgen 4y ago
      No, it doesn't. The Church Turing hypothesis is much stronger - it states that all real-world computation can be done by lambda calculus or Turing machines. That's why it's a hypothesis and not a theorem - it's pretty easy to prove that lambda calculus and Turing machines are equivalent if you have the mindset of a programmer. Put in other words, the Church Turing hypothesis is that there is no computing model higher in hierarchy than the TM and lambda-calculus. > It doesn’t actually tell us anything about reality Well, of course it doesn't tell is anything about reality. That's because no one managed to prove it, and I suspect no one ever will.
      - User23 4y ago
        Ah yes. Fair enough. I confused the thesis with the hypothesis. This comes back to the begging the question I initially objected to. Also, the notion of highest computing model is itself begging the question in the sense that the framing assumes a computational model. So much for undergraduate philosophy. What’s your opinion? Are uncomputable functions just fanciful irrelevancies or are there processes in reality that can’t be described by computable functions? If so or if not can you propose how we might know?