it’s pretty easy, as these things go, to demonstrate random disorder all over the place ~ this is the thesis that God not only throws dice with the universe, He throws them where even He can’t see them.
m, IMHO, what we think of as disorder, or randomness is lack of knowledge of the order of things.
For example, start with a barrel full of lottery numbers (Step A). Turn it by a handle (Step B) (conventional wisdom says this is “randomizing” the numbers), stop (Step C), then a hand reaches in and pulls out a number (Step D).
If one had precise information at Step A, and precise data on Steps B - D, one would know precisely which number was coming out of the barrel.
Randomizing is really just changing the order of a set of things and keeping the result unknown. The order of the set is then unknown.
If we look at the first few elements of a “random” set, and we see a pattern, then we can guess other elements. But if we see no pattern in our sample, we say ew, it’s random.
IMHO, what we really mean is we see no pattern and, since we only have a sample, we can’t infer anything about the overall order of the set.
IMHO, of course, because I’m sure there are rocket scientists who will offer dissertations on randomness (when simply a “no way”, “sorta” or “yeah” would suffice, perhaps with a link to their dissertation, since we can google for dissertations to our heart’s content; I’m just trying to generalize in a few occamesque paragraphs).