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How doesn't it? Modern AI use algorithms for problem solving and reasoning. The more complex the puzzle, the more time and memory a computer requires to solve it. Right now that is a problem because complex things take monumental amounts of both of them, but if in the future processing speeds are blindingly fast, then this would not be an issue.
No. It doesn't mater how fast the computers are. The development of AI, or any software program, isn't connected to the speed of computers. AI wouldn't need fast computers to operate. An AI could perform on slow computers, it would just take longer.
Similarly, the rendering of an animated motion picture is unconnected to the speed of the computers. The movie Toy Story 3 wasn't rendered in real time. It didn't need to. Rendering took weeks, if not months to complete. Rendering was done on massive server farms over long periods of time. It doesn't matter how fast the computers were. The rendering got done when it got done.
Windows 7 and Maya 3D can run on a Pentium I. Just don't expect it to be very fast.
The problem in Artificial Intelligence isn't a hardware problem. There is no reason why an Artificial Intelligence program couldn't exist and operate on existing super computers and server farms.
The problem with Artificial Intelligence is a software problem. No one has figured out how to do it. Throwing fancy new computer hardware at it won't solve an intelligence problem.