On Feb 15, 2005, at 11:20 AM, Kim Hyatt wrote:
So, how many angels can fit on the head of a pin?
Kim
Angels dancing on the head of a pin... This phrase often triggers a snort of ridicule, but I learned (while a grad student in math) that what was being pondered was the idea of infinity–a useful concept. There are a lot of things that sound silly, while having depth behind them. Topology has a "hairy egg theorem" stating that an egg covered in hair cannot be combed with the hair lying flat everywhere (some might call it the cowlick theorem). It is really a theorem about sections of the tangent bundle of a topological sphere. But "hairy egg" is such an evocative name. I would guess "angels dancing" was a similarly evocative name. The Jordan curve theorem states that a simple closed curve lying in a plane has an outside and an inside. It is surprisingly hard to prove (actually it is easy once the necessary algebraic topology machinery is constructed), though it seems to be so obvious. People used to make fun of medieval medicine's use of leeches. Today, leaches are once again used for treatment. Let us not be too quick to be contemptuous. Jim ---- Jim Cobb james@cobb.name