Originally posted by Lung
Another way to look at it is this:
If you walk along the equator and see a longitudinal line perpendicular to the equator. Just to be sure, you measure the angle, and sure enough, it's 90 degrees. You walk another couple of hundred miles, and you see another. Again, you find it's 90 degrees. You turn and follow the longitudinal all the way to the north pole, only to find the other longitudinal line you passed earlier! However, if they were the same angle, they must be parrallel, right? Wrong. Why? Because you've applied 2 dimnesional geometry to a 3-dimensional world. Applying 3-dimensional geometry to 4-dimensional spacetime will also fail. in other words, your straight line is another dimension's curve.
At least that's my understanding of the geometry of multidimensional spacetime
Another way to look at it is this:
If you walk along the equator and see a longitudinal line perpendicular to the equator. Just to be sure, you measure the angle, and sure enough, it's 90 degrees. You walk another couple of hundred miles, and you see another. Again, you find it's 90 degrees. You turn and follow the longitudinal all the way to the north pole, only to find the other longitudinal line you passed earlier! However, if they were the same angle, they must be parrallel, right? Wrong. Why? Because you've applied 2 dimnesional geometry to a 3-dimensional world. Applying 3-dimensional geometry to 4-dimensional spacetime will also fail. in other words, your straight line is another dimension's curve.
At least that's my understanding of the geometry of multidimensional spacetime

Although your example gives a good explanation on the efects of aplying 2 dimensional geometry to a 3 dimensional world the problem I see is this:
In your example, the two 2 dimensional paralel straight lines are actually two 3 dimensional intersecting curves. Ultimatelly, if I were to walk in a 2 dimensions straight line, forever, I would ultimatelly drawing a circular form.
In time-space we are called to believe that a 3 dimensional elipse is actually a 4 dimensional line which is, exactly, the oposite result.
How can this be?
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