I think there's one more deep, interesting (!) question hidden, adjacent to the post and your reply: what exactly makes something
interesting? I feel it's a real question, because the things we find interesting aren't all that arbitrary.
I have only a handwavy notion of it, based on some on-line articles (IIRC one of them might have been a blogpost or a paper by Scott Aaronson), but the general idea is that the things we find interesting exist in the middle between low and high-entropy states.
For example, take matches. A box of matches is relatively low-entropy: they all sit there neatly arranged in parallel rows, pointing the same direction. Matches in a box are boring. Now, dump the box onto the table. The matches are now arranged in a random pattern. This is a high-entropy state, and it's even more boring than the low-entropy one. Now, start putting those matches into some pattern - suddenly, things get interesting. One of the particularly interesting configurations would be a self-supporting 3D structure made of those matches - and that's, in terms of entropy, about half-way between matches in a box, and matches on a pile.
Put in information-theoretic terms, it seems that we find both highly predictable and highly unpredictable configurations boring: the former likely because there is just not much new information to pay attention to - but the latter, seemingly because it's too unpredictable, and we round it up to "pure noise".
So my question is, is there any formal description of this concept? A mathematical answer to why we find both order and disorder boring, and are most interested in things in-between? Some kind of natural quantity that tracks -E² (with E being entropy), and which would be fundamentally useful to maximize?