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Algorithm for randomness usually use seed, and thus having an unique input it cannot be said to be completely random, so can pure randomness be theoretically computed?

  • Are you referring to things like the statistical bell curve? – Mark Andrews Mar 25 at 18:44
  • Not sure what you mean by that. What I mean by randomness is the output of random numbers. – tefisjb Mar 25 at 18:49
  • I assume "computed" means "generated". Yes, just use a Geiger counter. – Conifold Mar 25 at 20:49
  • Computation is the definitional opposite of randomness, so no. If a sequence of numbers (or decimal digits) is generated by a computation in the sense of Turing, then it is not random. However of course the digits themselves may pass all known statistical tests for randomness; in which case as you note we call it pseudo-random. To be clear I'm equating the meaning of random with what Turing called non-computable. – user4894 Mar 25 at 23:40
  • @JohnForkosh I know, but it was the best I could make of a question that basically asks "can we do X by a process that is, by definition, incompatible with doing X?" – Conifold Mar 26 at 4:08
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As with many questions in philosophy, this hinges on the precise definitions of your words. What do you intend by "pure randomness" and what do you intend by "compute?"

If "compute" means "Apply an algorithm to derive some result" and if an algorithm is "some fixed series of deterministic steps" and if "pure randomness" means "An effect that could not have been predicted more reliably than guessing even if everything about the universe was known beforehand" then the answer to your question is no. Since the algorithm was defined to be deterministic, and all possible starting points to the process are known, simulating the algorithm would be more reliable than guessing.

Of course, that is begging the question. The trick is the word "deterministic." If an algorithm is not restricted to deterministic steps, it could be possible to compute a random number. For example, if a step of the algorithm is allowed to be "measure the output of some pure random physical process." then the algorithm could use that step to generate a random number. It hasn't actually created any randomness: it just stole some and perhaps reshaped the distribution.

It is an open philosophical question whether this universe has any pure random physical processes: the best contender at present seems to be quantum fluctuations but it remains possible that we just don't have a clear enough understanding of physics to work out causality at quantum scales.

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