Is there not some categorical difference between a purposefully-built system, which given enough time and effort and expertise and constraints, we can engineer to be effectively secure, and a stochastically-trained black box?
Yes? Kinda? Hard to say tbh. I think the distance between these categories is probably smaller than you're implying (or at least I'm interpreting), or rather the distinction between these categories is certainly not always clear or discernible (let alone meaningfully so).
Go is a game with no statistical elements yet there are so many possible move sets that it might as well be. I think we have a lower bound on the longest possible legal game being around 10^48 moves and an upper bound being around 10^170. At 10^31 moves per second (10 quettahertz) it'd still take you billions of years to play the lower bound longest possible game. It's pretty reasonable to believe we can never build a computer that can play the longest legal game even with insane amounts of parallelism and absurdly beautiful algorithms, let alone find a deterministic solution (the highest gamma ray we've ever detected is ~4RHz or 4x10^27) or "solving" Go. Go is just a board with 19x19 locations and 3 possible positions (nothing, white, black) (legal moves obviously reducing that 10^170 bound).
That might seem like a non-sequitur, but what I'm getting at is that there's a lot of permutations in software too and I don't think there are plenty of reasonably sized programs that would be impossible to validate correctness of within a reasonable amount of time. Pretty sure there's classes of programs we know that can't be validated in a finite time nor with finite resources. A different perspective on statistics is actually not viewing states as having randomness but viewing them as having levels of uncertainty. So there's a lot of statistics that is done in frameworks which do not have any value of true randomness (random like noise not random like np.random.randn()). Conceptually there's no difference between uncertainty and randomness, but I think it's easier to grasp the idea that there are many purposefully-built finite systems that have non-zero amounts of uncertainty, so those are no different than random systems.
More here on Go: https://senseis.xmp.net/?NumberOfPossibleGoGames And if someone knows more about go and wants to add more information or correct me I'd love to hear it. I definitely don't know enough about the game let alone the math, just using it as an example.
