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Why Was The Computer Invented When It Was?

Clearly the modern electronic computer couldn't have been built before electronics existed, but it's not clear why computers powered by steam or clockwork weren't invented earlier. Tom Körner speculates on the historical reasons why computers were invented when they were.
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Mathematical mysteries: The Barber's Paradox

Suppose you walk past a barber's shop one day, and see a sign that says "Do you shave yourself? If not, come in and I'll shave you! I shave anyone who does not shave himself, and noone else." This seems fair enough, and fairly simple, until, a little later, the following question occurs to you - does the barber shave himself?
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Games, Life and the Game of Life

When we finally meet the Martians, John Conway believes they are going to want to talk mathematics. He talks to Plus about his Life game, artificial life and what we will have in common with extraterrestrials.