tea.mathoverflow.net - Discussion Feed (concrete isomorphisms)

Michael Hardy comments on "concrete isomorphisms" (18283)

2012-02-04T12:05:02-08:00

The Hercules-versus-the-jury example merely illustrates the concept of cardinality, which, as I said, everyone is familiar with by the time they're five years old. The concept of cardinality is not frivolous, and all basic examples of it look just like that.

If there will be a lot of silly answers, it's because the question will be misunderstood.

Tic-tac-toe is not a really good example in some ways.

I'll work on rephrasing it.

Andy Putman comments on "concrete isomorphisms" (18271)

2012-02-03T21:14:39-08:00

I do not think this is a good question. The example given (Hercules vs the jury) strikes me as being entirely frivolous and without content (mathematical or otherwise). If the OP cannot give a serious example of what he is looking for, then I don't think we will get any worthwhile answers. But I expect that we will get a lot of silly answers, like the ones there right now.

Joseph O'Rourke comments on "concrete isomorphisms" (18270)

2012-02-03T17:37:10-08:00

I voted to reopen. Michael raises an interesting, almost philosophical question. In fact, John Searle, a well-known philosopher, has written on precisely this point. In so far as MO is appropriate for mathematical philosophy, I feel this question is appropriate. As quid say, "it will always be a bit hard": Yes, it will be difficult to articulate these issues. Which does not imply they should not be explored.

quid comments on "concrete isomorphisms" (18269)

2012-02-03T17:00:18-08:00

I do not understand the question at all. In particular, how is this tic-tac-toe iso (though nice) related to this; neither of the things involved is particullarly part of the 'physical world'. And, what is the example in the original question. Right, there are twelve. And? In particular since then it is dicussed this is not just about cardinality. Like, two arms, two feet, two eyes, two ears, two kidneys,...with some canonical iso given by left to left and right to right.

I could imagine there being something if some 'structure' or 'relation' is preserved. But to be direct I doubt this question itself is salvageable as it will always be a bit hard to communicate what is asked for and then if there is some sort of false start the thing is lost. So if anything I could imagine that after some discussion OP reasks something along these lines but clearer.

Sidenote: the fact that there is a tag implies that somebody with nonminimal rep once typed this in the tag field and it was not yet deleted. That being said I have nothing against pedagogy or education questions, but this one is unclear to me.

Michael Hardy comments on "concrete isomorphisms" (18268)

2012-02-03T15:36:30-08:00

There's a tag for pedagogical questions, I think. Does the existence of a tag imply something?

I'm not sure pedagogy is the only thing that this bears upon (unless it's the only thing that all questions here bear upon).

darijgrinberg comments on "concrete isomorphisms" (18267)

2012-02-03T15:21:10-08:00

It looks like a valid pedagogical question to me. Do we have a policy on pedagogical questions?

Michael Hardy comments on "concrete isomorphisms" (18266)

2012-02-03T15:09:52-08:00

Can someone explain why my "concrete isomorphisms" question was closed?