> [...] In the 19th century it was commonly said that the plane has > (infinity)^2 points; meaning that its points are usually coordinatized > using two real numbers, so in an obvious sense have two degrees of > freedom. Likewise for higher dimensions.
This relates, does it not, to enumerative geometry? I know nothing about the matter but Hilbert & Cohn-Vossen's _Geometry and the imagination_ has a section on it.
-- When a true genius appears in the world, you may know him by this sign, that the dunces are all in confederacy against him. Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting