Points at Infinity I: Projective Geometry

It would … be the number of the point at which Achilles overtakes the tortoise—if he does overtake him—by exhausting all the intervening points successively. Or it would be the number of the stars, in case their counting could not terminate. Or again it would be the number of miles away at which parallel lines meet—if they do meet. It is, in short, a ‘limit’ to the whole class of numbers that grow one by one, and like other limits, it proves a useful conceptual bridge for passing us from one range of facts to another.

-William James, Some Problems of Philosophy

This site is called ‘Point at Infinity’ in part because that is exactly what it attempts to do. Everything we experience directly in life is finite. Infinity fascinates us, but we cannot touch it. The best we can do is ‘point’ at it.

But the phrase ‘point at infinity’…