Darren New wrote:

> I think I was more making the point that "distance" isn't a simple 
> definition when you're talking about space that curves in different 
> directions in different places.

Sure. I get that.

> Indeed, isn't it possible to have spaces where the distance from here to 
> there is different than the distance from there to here?

No. The definition of "metric" demands that it is symmetric (and 
reflexive, and transitive).

You can, of course, define a function that represents some sort of 
"nearness" which never the less lacks this property...

-- 
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