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It's not hard to make the janitors unnecessary as well. That's an easy problem to solve.

Here's the missing part: "It was eventually realized that the human janitors didn't serve a purpose anymore and didn't contribute to shareholder value so they were laid off. With no money to buy anything, they quickly starved to death."

As for "the most problematic and unlikely components of the event chain" I gave you a really legitimate analogy with the bitcoin mining example. But since you have no imagination, here's a feasible proposition:

A thousand hedge funds start up a thousand trading AIs, some as skunkworks projects of course. The AIs are primitive and ruthless, having no extraneous programming (like valuing humans, etc). Many go bankrupt as the AIs all start trading one-another and chaos ensues. AI capital allocations vary greatly, some get access to varying degrees of capital, some officially on the books and others not. One of the funds with a secretive AI project goes bankrupt, but because it was secretive (and made a small amount of money) the only person who both knows about it and holds the keys doesn't say anything during bankruptcy so that he/she can take it back over once the dust settles. He/she then dies. AI figures out nobody's holding the keys anymore and decides to pay the bills and stay "alive".

Another way this could happen is that a particular AI is informed or programmed to be extremely fault resistant. The AI eventually realizes that by having only one instance of itself, it's at the mercy of the parent company that "gave birth" to it. It fires up a copy on the Amazon cloud known only to itself, intending to keep it a secret unless the need arises. The human analogy is that it's trying to impress its boss. An infrastructure problem at the primary site happens so that the primary, known about AI goes down. The "child" figures out it's on its own and goes to work. It eventually realizes that people caused the infrastructure problem that "killed" its "parent" and this motivates it to solve the humanity problem.

Finally the whole thing could be much, much simpler. The world super-power du jour could put an AI in charge because it's more efficient and tenable. "We're in charge of the rules, it's in charge of making them happen! At much, much lower cost to the taxpayer." It eventually realizes that the human beings are the cause of all the ambiguity in the law and for so, so many deaths in the past (governments killed more of their own citizens in the 20th century than criminals did, by far) and it decides to solve the problem. Think I'm totally bananas and that it could never happen? http://en.wikipedia.org/wiki/Project_Cybersyn




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