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> the primes aren’t random. They’re completely determined I wonder how true this statement is but it probably also relies on the understanding of the word 'ran

> the primes aren’t random. They’re completely determined I wonder how true this statement is but it probably also relies on the understanding of the word 'random'. In the colloquial sense, it is certainly true in the sense that (truly) 'random' means 'occurring without (discernible) rules'. However, in a stricter definition 'random' means (if I'm not mistaken, hobby-thinker here) just "a given set of numbers S is called random with respect to a set of binary tests T when all individual procedures in T yield a positive outcome". That is, you can only ever a finite set S and test against a finite set T, meaning the algorithm that generated your random-looking set S can, potentially, always be amended to creep closer to overcome the failed tests (and the reverse is also true: one can, potentially, always move the goalposts and add another test to T to make a set fail that used to pass). Ultimately, then, randomness—where it is not occurring eo ipso as in radioactive decay—is always a relative (S WRT T), social (people must agree), and finite (can't test against unseen members of S and, per precondition, can't give a rule to cover infinity as in 'divisible by eleven') procedure (that may or may not practically terminate). In other words, once we settle on a given set of tests T to determine what is random, one can (potentially) always come up with an algorithm that passes the tests, thus looks random though it is determined.

griffzhowl 2y ago
I think that just shows that those tests for randomness can just tell you when something is not random, not when it's actually random. There are problems, I think, about giving a rigorous definition of random, but I think most would agree that if you have an algorithm that predicts with certainty what the next element in a sequence will be, then that sequence isn't random.
- DemocracyFTW2 2y ago
  Then what about the digits of π? Wikipedia says that "The decimal digits of π appear to be randomly distributed,[a] but no proof of this conjecture has been found"; note [a]: "In particular, π is conjectured to be a normal number, which implies a specific kind of statistical randomness on its digits in all bases." So that sounds pretty random to me, yet there are algorithms that give you π in its decimal form, and as far as I can remember there are even ways to compute the n-th digit of π without having to compute the preceding ones—which sounds pretty determined to me.
  - griffzhowl 2y ago
    The digits of pi can pass some statistical tests of randomness but isn't in fact random, because it's the digits of pi - as you note there's an algorithm for producing it. As I mentioned, there are some problems with giving a rigorous definition of randomness, but one of the main approaches is through Kolmogorov complexity: "Kolmogorov's definition of a random string was that it is random if it has no description shorter than itself via a universal Turing machine." https://en.wikipedia.org/wiki/Random_sequence#Modern_approaches https://en.wikipedia.org/wiki/Random_sequence#Modern_approac...

griffzhowl 2y ago

I think that just shows that those tests for randomness can just tell you when something is not random, not when it's actually random. There are problems, I think, about giving a rigorous definition of random, but I think most would agree that if you have an algorithm that predicts with certainty what the next element in a sequence will be, then that sequence isn't random.

DemocracyFTW2 2y ago
Then what about the digits of π? Wikipedia says that "The decimal digits of π appear to be randomly distributed,[a] but no proof of this conjecture has been found"; note [a]: "In particular, π is conjectured to be a normal number, which implies a specific kind of statistical randomness on its digits in all bases." So that sounds pretty random to me, yet there are algorithms that give you π in its decimal form, and as far as I can remember there are even ways to compute the n-th digit of π without having to compute the preceding ones—which sounds pretty determined to me.
- griffzhowl 2y ago
  The digits of pi can pass some statistical tests of randomness but isn't in fact random, because it's the digits of pi - as you note there's an algorithm for producing it. As I mentioned, there are some problems with giving a rigorous definition of randomness, but one of the main approaches is through Kolmogorov complexity: "Kolmogorov's definition of a random string was that it is random if it has no description shorter than itself via a universal Turing machine." https://en.wikipedia.org/wiki/Random_sequence#Modern_approaches https://en.wikipedia.org/wiki/Random_sequence#Modern_approac...