>> So how *do* you compute the distance between two points in a 
>> non-Euclid space anyway?
> 
> Generally you start with a notion of something like a dot product 
> defined in the tangent spaces of your space and then write out an 
> integral to define the arc length of a curve.  Then the distance between 
> two points can be defined to be the minimum length of any curve 
> connecting them.

Any idea what the hell a tangent space is?

>> For that matter, is there a way to unambiguously refer to a specific 
>> point in such a space?
> 
> Depends on the space.  A relatively general but computationally 
> cumbersome solution is to cover your space will small Cartesian patches 
> which connect together in a "nice" way.  The you can define a point by 
> giving its Cartesian patch and its coordinates within that patch.

Hmm, sounds like kind of a patchy solution...

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