Since maximal disorder in symbol sequences is computable, it is deterministic, one must conclude that random sources are rather biased - both away from disorder and toward some kind of bias. In that sense, random is not random. Comments?
I can comment on random versus deterministic. Excluding quantum processes, for which (to my knowledge) there is no finalized consensus, what makes something appear random is that its initial conditions are unknown, or that the process is chaotic and the initial conditions cannot be elaborated towards a known endpoint without impossibly high numerical precision. Wolfram's take on discrete cellular automata supports this idea -- a highly deterministic process can act on a simple input to give output that satisfies many criteria of randomness.
So take a maximally disordered sequence and add random noise to it -- it probably becomes less-than-maximally-disordered in the process, but surely it hasn't lost any of its randomness.
Randomness is more about unpredictability or being unknowable. Maximal disorder means that the entropy is maximized. My instinct is that there should be more than one maximally disordered sequence for a given set of symbols.
I think that your algorithm for producing a maximally disordered sequence has some kind of seed value (perhaps implicit to the implementation and hard-coded) which is responsible for some of the quasi-random character. After all, one could reverse your maximally disordered sequence and it would still be maximally disordered (am I right?), so there's at least one equivalently disordered solution that is still being chosen from based on a type of seed value or assumption.
It's the lack-of-knowledge of this assumption that makes your one-million-digit sequence random.
The seed is in the algorithm, not the data; there is an order by which tiles are selected during sequence generation; the ordering is that found in typical permutation generators. My algorithm does not check or generate all permutations however; only those permutations that are maximally disordered are chosen.
- Badges
- Science topic
- Similar topics
- Computer Science
- Computing