Abstract
Much of the philosophical and mathematical fun comes from trying to tease the different meanings apart, and deciding which make sense, and why. A clear example occurs in ‘Geometric infinity’, where the discussion takes a sharp turn into a different realm of the infinite: projective geometry. As Euclid insisted in one of his axioms, parallel lines never meet. But the painters of the Italian Renaissance, analysing perspective, stumbled across a rich vein of geometry in which it makes sense to insist that parallels do meet—at infinity. If you’ve ever stood at a railway station watching the tracks converge as they disappear into the distance, you’ve caught a glimpse of geometric infinity.
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