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It's a harsh, but true reality that with only have finite quantities of time and space, especially in real world computation. The assumption of finite resources
by Valmar 5y ago
It's a harsh, but true reality that with only have finite quantities of time and space, especially in real world computation. The assumption of finite resources is also a harsh, but true reality.
There are many things that fundamentally defy any form of computation. Things which cannot create mathematical formulae to represent, nor create algorithms for.
For a major example, we cannot translate the mental activities of conscious, aware living beings into any sort of computable form, as these activities are not algorithmic in nature. They aren't random, nor deterministic ~ rather, they are indeterministic, following no rigid patterns.
Even the most complex, complicated computer program follows an algorithm, which is ultimately deterministic. Even if you throw in some random inputs at some parts, the algorithm still acts deterministically. Perhaps the only really indeterministic part in an algorithm's behaviour might be hardware level bugs and errata which interfere with the otherwise very predictable algorithm.
- amanaplanacanal 5y ago> For a major example, we cannot translate the mental activities of conscious, aware living beings into any sort of computable form, as these activities are not algorithmic in nature. They aren't random, nor deterministic ~ rather, they are indeterministic, following no rigid patterns. How could you possibly know that? Following no known patterns, maybe.
- skissane 5y agoTrivially, for any finite string (in a finite alphabet), there is a finite program (Turing machine, whatever) which outputs that string given empty input. Hence, "the mental activities of conscious, aware living beings" are trivially computable if there exists a finite string which describes them with perfect accuracy. Furthermore, there obviously are some computable patterns in those activities, so the shortest possible computable program to generate that description will actually be shorter than the length of the description itself. One could respond that a string describing those mental activities, no matter how accurately, is a different thing from the mental activities themselves. I think that is indeed the correct response, but it has nothing to do with any questions of computability. (Another response would be to claim that those mental activities cannot be finitely described because they are actually infinite. Few however will want to claim that human minds are infinite.)
- onethought 5y ago> 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.
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- skissane 5y agoIf 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 agoI 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.