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I am asking myself: Does a probabilistic Turing machines needs aleatory uncertainty? (would have called this ontological but (1) disagrees) Epistemic uncertai

I am asking myself: Does a probabilistic Turing machines needs aleatory uncertainty? (would have called this ontological but (1) disagrees) Epistemic uncertainty would mean her: We don't know which deterministic Turing machine we are running. Right now, I see no way to use this in algorithms. (1) https://dictionary.helmholtz-uq.de/content/types_of_uncertainty.html https://dictionary.helmholtz-uq.de/content/types_of_uncertai...

lisper 2y ago
The whole point of Turing Machines is to eliminate all of these different kinds of uncertainty. There is in point of actual physical fact no such thing as a Turing Machine. Digital computers are really analog under the hood, but they are constructed in such a way that their behavior corresponds to a deterministic model with extremely high fidelity. It turns out that this deterministic behavior can in turn be tweaked to correspond to the behavior of a wide range of real physical systems. Indeed, there is only one known exception: individual quantum measurements, which are non-deterministic at a very deep fundamental level. And that in turn also turns out to be useful in its own way, which is why quantum computing is a thing.
- 11101010001100 2y ago
  Right, the point is that we don't need a solution to the 'measurement problem' to have a quantum computer.
  - lisper 2y ago
    Well, yeah, obviously. But my point is that you do need a solution to the measurement problem in order to model measurements in any way other than simply punting and introducing randomness as a postulate.
    - 11101010001100 2y ago
      And is that solution required to be deterministic? If so, that is another postulate.
      - lisper 2y ago
        You have to either postulate randomness or describe how it arises from determinism. I don't see any other logical possibility. BTW, see this: https://arxiv.org/abs/quant-ph/9906015 https://arxiv.org/abs/quant-ph/9906015 for a valiant effort to extract randomness from determinism, and this: https://blog.rongarret.info/2019/07/the-trouble-with-many-worlds.html https://blog.rongarret.info/2019/07/the-trouble-with-many-wo... for my critique.

lisper 2y ago

The whole point of Turing Machines is to eliminate all of these different kinds of uncertainty. There is in point of actual physical fact no such thing as a Turing Machine. Digital computers are really analog under the hood, but they are constructed in such a way that their behavior corresponds to a deterministic model with extremely high fidelity. It turns out that this deterministic behavior can in turn be tweaked to correspond to the behavior of a wide range of real physical systems. Indeed, there is only one known exception: individual quantum measurements, which are non-deterministic at a very deep fundamental level. And that in turn also turns out to be useful in its own way, which is why quantum computing is a thing.

11101010001100 2y ago
Right, the point is that we don't need a solution to the 'measurement problem' to have a quantum computer.
- lisper 2y ago
  Well, yeah, obviously. But my point is that you do need a solution to the measurement problem in order to model measurements in any way other than simply punting and introducing randomness as a postulate.
  - 11101010001100 2y ago
    And is that solution required to be deterministic? If so, that is another postulate.
    - lisper 2y ago
      You have to either postulate randomness or describe how it arises from determinism. I don't see any other logical possibility. BTW, see this: https://arxiv.org/abs/quant-ph/9906015 https://arxiv.org/abs/quant-ph/9906015 for a valiant effort to extract randomness from determinism, and this: https://blog.rongarret.info/2019/07/the-trouble-with-many-worlds.html https://blog.rongarret.info/2019/07/the-trouble-with-many-wo... for my critique.