> Is time real? Kurt Godel investigated that question very seriously. His > contribution is published in a special event organized for Einstein around > his 70th birthday, "Library of Living Philosophers, Vol VII", Paul Arthur > Schlipp editor. > > FYI, the Karl Menger essay on Geometry of Lumps, mentioned previously in this thread , is in this same series.
Menger was a Vienna Circle dude, like Godel, like Wittgenstein. Menger's geometry feel's like a ray tracer's tool (e.g. povray.org) in that if photons won't reflect or emit from it, "it" might as well not exist, not that we need to define "photons" (just an analogy).
Points, lines and planes all get to be volumetric, just rolled differently as cookie dough (so more like topology where donut = coffee cup). "What's the cookie dough made of though?" We don't need to worry. This is mathematics. It's not "made of" it's just "a synonym for" so-called res extensa, that which extends in space presenting a convex or concave aspect vis-a-vis the viewpoint.
This essay is in the same book volume even: 'Modern Geometry and the Theory of Relativity', in Albert Einstein: Philosopher-Scientist , The Library of Living Philosophers VII, edited by P. A. Schilpp, Evanston, Illinois, pp. 459-474.