Orchid XP v8 wrote:
> 
> That's a whole crapload of jargon, right there.
> 

Those are all very basic terms for dealing with non-Euclidean spaces. 
Since we're talking about non-Euclidean spaces, I don't think it's 
uncalled for.

That said, you do have something of a point there, so I'll rephrase:

I thought we were assuming that the spaces we were talking about come 
with a pre-defined notion of distance, so why is there a need to 
explicitly define it ourselves?

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