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...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.
I was just pushing it to the opposite extreme, where it is easier to see the interdependence of diversity and chance.
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.
Who said anything about a centralized consciousness? A decentralized superorganism of global scale would have much better chances of surviving, not to mention of harvesting the fruits of diversity and chance.
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.
You only know for sure if an action is good or worse after it happens; but by running millions of simulations beforehand you can significantly increase the odds that the action you choose to do will be closer to the best one possible most of the time.
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".
Once the process becomes self-sustaining, "life will find a way"; i don't see humanity steering away enough to avoid giving the initial kick on the snowball; the probabilistic cloud that is humanity is falling towards the singularity, and just like a star falling into a blackhole, even tough we can't predict the exact position of each subatomic particle that composes it we can be sure that at least a few of those will fall all the way.
Logic provides the evolutive pressure towards self-perpetuating patterns; those that continue to be are obviously better than those that ceased to, even if before the results it might not have been as obvious which ones were 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.
Like i said many times, perfection isn't necessary, as physical biological evolution has proved so many times.
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.
Gray goo overtaking the globe and beyond sounds pretty entropic to me...