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stoutfellowS., one of the students in my differential geometry class, is quite bright. I suspect she'd be better off at a more high-powered university; once I heard her express dismay at the fact that we don't offer a course in topology. (Our real analysis course covers some metric topology, and I assume our graduate course in functional analysis introduces some non-metric topologies, but that's it. We used to offer a course in point-set topology, but there was so little student interest that we dropped it from the catalog at the last big reorganization.)
S. is rather diffident in class ("Excuse please, I have question."), but her questions are usually good ones. (Frequently, she asks questions that can't be answered in the context of the class...) Last Thursday, I was discussing curvature of surfaces and of curves on surfaces, and pointed out that, for example, a meridian of longitude is not curved relative to the surface of the Earth - its "geodesic curvature" is zero. I went on to mention the three-dimensional equivalent, that the space we live in is curved.
S: "Space is curved?"
Me: "Uh-huh."
S (befuddled, and a little bit outraged): "Why is space curved?"
I fumbled for an answer that wouldn't go too far afield, and finally urged her to look up "general relativity".
I'll admit to being slightly befuddled myself. How did she reach this point never (apparently) having heard of the curvature of space?
S. is rather diffident in class ("Excuse please, I have question."), but her questions are usually good ones. (Frequently, she asks questions that can't be answered in the context of the class...) Last Thursday, I was discussing curvature of surfaces and of curves on surfaces, and pointed out that, for example, a meridian of longitude is not curved relative to the surface of the Earth - its "geodesic curvature" is zero. I went on to mention the three-dimensional equivalent, that the space we live in is curved.
S: "Space is curved?"
Me: "Uh-huh."
S (befuddled, and a little bit outraged): "Why is space curved?"
I fumbled for an answer that wouldn't go too far afield, and finally urged her to look up "general relativity".
I'll admit to being slightly befuddled myself. How did she reach this point never (apparently) having heard of the curvature of space?
