Quote:
Originally Posted by Archy
"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?
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Since the Earth is not sufficently massive to cause space-time to curve, the surrounding space is flat and the geometry
must be Euclidean.
With this in mind one can have the origin at the centre of the Earth, and the Z-axis along the polar axis. A person standing at the North Pole is at position (0, 0, R), at the South Pole (0,0, -R) where R is the Earth's radius.
A coordinate transformation from (0,0,R) to (0,0, -R) is equivalent to an upside down reflection.
If you are travelling in a plane at a constant velocity you are in an plane's inertial frame of reference not the Earth's frame of reference. Your position and velocity is relative to the plane's frame of reference.
If your upside down it means the plane has turned upside down.
In the Earth's frame of reference, an observer on the ground can definitely perceive the Earth's curvature. The ancient Greeks were aware of it buy noticing that ships disappeared below the horizon.
Steven