[Haskell-cafe] Category Theory woes
Gregg Reynolds
dev at mobileink.com
Thu Feb 18 16:15:47 EST 2010
On Thu, Feb 18, 2010 at 1:31 PM, Daniel Fischer <daniel.is.fischer at 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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