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"Using your plane analogy, whether you are upside down or not, can be defined by your position in space (instead of the Earth's surface) by using 3-D Euclidian coordinates."
I've read Euclid, but can't recall a reference to coordinates.
Ptolemy has coordinates (spherical at that)
Plane coordinates come with Descartes hence Cartesian coordinates.
Although by carefully choosing the origin (0,0,0) position in space can be defined so that there is an up and a down, it is also possible in every case to have a position in 3D or nD space ( where n is two or more) such that there is no up or down, although there will generally be a "higher"or "lower".
In reference to the ant going from the North pole to the South pole, I can't see that the ant's perception will be different to mine. When I travel to the UK I do not see that i am upside down. Do You?
Last edited by Archy; 10-04-2009 at 10:46 PM.
Reason: clarity
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