Fascinating! So, are those locally-annealed subjective opinions about how the universe really works? Or global, objective assessments about how you think the universe works?

No it is logic.
For example, Godel's incompleteness theorem is somewhat related-- a computable system can't be both complete and consistent.
...
...Chance and diversity require each other. It is a very interesting conceptual discovery. I would expect some other scientists or philosophers had this discovery, but I am not aware of who they are.
That is borderline tautological (in the sense that is self-evident). To have infinite possibilities but having the odds always lead to just one of them is pretty much the same as having only one possible outcome but the odds being the same for any possible outcome.
That doesn't make any sense. The orthogonal probabilities in a free market means many different things are possible and occurring. If there was only one, the entropy is minimized not maximized. Even the Second Law of Thermodynamics says the entropy of the universe trends to maximum.
But still, nothing in that prevents machines from having access to both enough diversity and enough random values.
Sigh. Please reread what I wrote in reply to you upthread. For example, to be diverse requires that they can't think as one, and that the information doesn't move in real-time to a centralized consciousness (decision making) for a groupwise superiority over humans.
Perhaps CoinCube can help explain. I really have to do some other things.
Sure, chaotic systems are hard to manipulate towards any specific goal in the long term; but machines can do it better than humans. Perfection is unattainable, i agree; but machines don't need to be perfect, they just need to be better than humans.
I already explained upthread that is no measurement of "better", only there exist different subjective choices that different actors make.
And i don't see how anything short of extinction of the human species could prevent humanity from eventually giving birth to a self-improving AI that improves itself better than humans could. Such a life-form would be more adaptable than anything Earth has ever seen; capable of trying more simultaneous evolutive routes than the whole organic biome combined.
Because you still don't admit that there is no such metric for "more adaptable" or "better".
Everything is chance and local gradients towards local choices about optimums. There is no global, omniscient God and if there was then for that God, the past and present are already 100% known, i.e. for God there is no more chance nor probabilities less than 1.
Remember entropy is maximized when the orthogonal probabilities are minimized and spread among the most possible diverse orthogonal outcomes. Not when there is only one result.