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> Even the most complex, complicated computer program follows an algorithm, which is ultimately deterministic. Gödel's work proved this statement false. To gi

> Even the most complex, complicated computer program follows an algorithm, which is ultimately deterministic. Gödel's work proved this statement false. To give an example, what if the algorithm is to generate the correct algorithm? What if the correct algorithm ends up being the original algorithm? That is not deterministic.

deleted 5y ago
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skissane 5y ago
If a machine is deterministic, all programs for the machine must be deterministic. Gödel’s theorems don’t contradict that. If you think they do, you’ve misunderstood them.
Rioghasarig 5y ago
>> To give an example, what if the algorithm is to generate the correct algorithm? That's not a description of an algorithm. You've stated a "problem". An algorithm, by definition, is an actual deterministic procedure.
- skissane 5y ago
  > That's not a description of an algorithm. You've stated a "problem". I wanted to say the same thing, but you managed to find the words I couldn't. > An algorithm, by definition, is an actual deterministic procedure That's not necessarily true. There are non-deterministic algorithms: https://en.wikipedia.org/wiki/Nondeterministic_algorithm https://en.wikipedia.org/wiki/Nondeterministic_algorithm
  - Rioghasarig 5y ago
    I guess you're right. But I was trying to defend Valmar's statement which I still think is basically right in this context. Computers can't really implement non-deterministic algorithms.
    - skissane 5y ago
      > Computers can't really implement non-deterministic algorithms. Well they can. Quantum computers are inherently non-deterministic. Even for a classical computer, access to a true randomness source (such as a sufficiently good hardware RNG) is enough to make a classical computer non-deterministic, and hence programs that rely on that true randomness source are classified as non-deterministic. In practice, we sometimes classify a program as nondeterministic even if it only has access to pseudorandomness, provided that pseudorandomness is "random enough". If a program uses a high quality PRNG seeded with the current time, that might be practically considered non-deterministic, even though strictly speaking the program's behaviour is a deterministic function of the current time (and other inputs).
- onethought 5y ago
  Where do neural networks fall? Are you tautologically saying “determinism is determinism” because you define an algorithm as a “deterministic procedure”.
  - skissane 5y ago
    Artificial neural networks can be either deterministic or non-deterministic. Biological neural networks are non-deterministic. (You can debate philosophically whether apparent non-determinism is actually fundamentally non-deterministic or ultimately reduces to some hidden determinism. It depends on one's choice of interpretation of quantum theory – many worlds and hidden variables both claim that reality is fundamentally deterministic, other interpretations do not. But, whether or not non-determinism ultimately exists, it certainly apparently exists, both in biological and technological systems.)
  - Rioghasarig 5y ago
    Yes I was asserting that algorithms are by definition deterministic. But I guess you can technically consider non-deterministic algorithms but those aren't really relevant here. Computers don't behave non-deterministically. Every program in your computer describes a deterministic process.

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skissane 5y ago

If a machine is deterministic, all programs for the machine must be deterministic. Gödel’s theorems don’t contradict that. If you think they do, you’ve misunderstood them.

Rioghasarig 5y ago

>> To give an example, what if the algorithm is to generate the correct algorithm? That's not a description of an algorithm. You've stated a "problem". An algorithm, by definition, is an actual deterministic procedure.

skissane 5y ago
> That's not a description of an algorithm. You've stated a "problem". I wanted to say the same thing, but you managed to find the words I couldn't. > An algorithm, by definition, is an actual deterministic procedure That's not necessarily true. There are non-deterministic algorithms: https://en.wikipedia.org/wiki/Nondeterministic_algorithm https://en.wikipedia.org/wiki/Nondeterministic_algorithm
- Rioghasarig 5y ago
  I guess you're right. But I was trying to defend Valmar's statement which I still think is basically right in this context. Computers can't really implement non-deterministic algorithms.
  - skissane 5y ago
    > Computers can't really implement non-deterministic algorithms. Well they can. Quantum computers are inherently non-deterministic. Even for a classical computer, access to a true randomness source (such as a sufficiently good hardware RNG) is enough to make a classical computer non-deterministic, and hence programs that rely on that true randomness source are classified as non-deterministic. In practice, we sometimes classify a program as nondeterministic even if it only has access to pseudorandomness, provided that pseudorandomness is "random enough". If a program uses a high quality PRNG seeded with the current time, that might be practically considered non-deterministic, even though strictly speaking the program's behaviour is a deterministic function of the current time (and other inputs).
onethought 5y ago
Where do neural networks fall? Are you tautologically saying “determinism is determinism” because you define an algorithm as a “deterministic procedure”.
- skissane 5y ago
  Artificial neural networks can be either deterministic or non-deterministic. Biological neural networks are non-deterministic. (You can debate philosophically whether apparent non-determinism is actually fundamentally non-deterministic or ultimately reduces to some hidden determinism. It depends on one's choice of interpretation of quantum theory – many worlds and hidden variables both claim that reality is fundamentally deterministic, other interpretations do not. But, whether or not non-determinism ultimately exists, it certainly apparently exists, both in biological and technological systems.)
- Rioghasarig 5y ago
  Yes I was asserting that algorithms are by definition deterministic. But I guess you can technically consider non-deterministic algorithms but those aren't really relevant here. Computers don't behave non-deterministically. Every program in your computer describes a deterministic process.