On Thu, Feb 18, 2010 at 1:31 PM, Daniel Fischer <daniel.is.fisc...@web.de>wrote:
> Am Donnerstag 18 Februar 2010 19:55:31 schrieb Nick Rudnick: > > Gregg Reynolds wrote: > > > -- you agree with me it's far away from every day's common sense, even > > for a hobby coder?? I mean, this is not «Head first categories», is it? > > ;-)) With «every day's common sense» I did not mean «a mathematician's > > every day's common sense», but that of, e.g., a housewife or a child... > > Doesn't work. You need a lot of training in abstraction to learn very > abstract concepts. Joe Sixpack's common sense isn't prepared for that. > > True enough, but I also tend to think that with a little imagination even many of the most abstract concepts can be illustrated with intuitive, concrete examples, and it's a fun (to me) challenge to try come up with them. For example, associativity can be nicely illustrated in terms of donning socks and shoes - it's not hard to imagine putting socks into shoes before putting feet into socks. A little weird, but easily understandable. My guess is that with a little effort one could find good concrete examples of at least category, functor, and natural transformation. Hmm, how is a cake-mixer like a cement-mixer? They're structurally and functionally isomorphic. Objects in the category Mixer? > > > Both have a border, just in different places. > > > > Which elements form the border of an open set?? > > The boundary of an open set is the boundary of its complement. > The boundary may be empty (happens if and only if the set is simultaneously > open and closed, "clopen", as some say). > > Right, that was what I meant; the point being that "boundary" (or border, or periphery or whatever) is not sufficient to capture the idea of closed v. open. -g
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