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The Kind of Things a Computer Would Never Be Able To Do

When I was going to university there was a competition with some prize money for anyone who can figure out how to write a program that can recognize text in a photograph - what today is called "optical character recognition" (OCR).
There are a lot of things that people thought is so much so "human" that a computer will never be able to do it; let alone do it better than the best human in the world.
Can you think of such things... before we look at some examples of what has already been done?
Can a computer beat the world champion in chess? Paint a painting? Compose music?