But how do you define the length of a line connect...

2008-05-14T20:41:00.000-07:00

But how do you define the length of a line connecting two points? As the sum of infinitesimal line elements along the line. And what is the length of each line element? Roughly, the time it takes light to traverse the line element.

I doubt that the physical world is actually non-Euclidean in a fundamental way because EPR/Bell experiments may, in principle, make possible a determination of absolute simultaneity. And they definitely demonstrate faster-than-light causation, which indicates that Lorentz symmetry is probably emergent, not a fundamental symmetry. But this takes us into a set of different issues.

You do not use light to define straight lines: you...

2008-05-14T03:01:00.000-07:00

You do not use light to define straight lines: you define a straight line as a geodesic, the minimum distance beetwen two points; and the light always follows the geodesic, so is the easier instrument you can use to find this geodesic/straight line.

There is little doubt about the non-euclidity of the Universe (at least at a local level): General Relativity is today one of the most highly confirmed theories in Science.

Your is a very interesting blog. I'll keep on reading :)

Comments on DanishGold: Some Meta-Geometry

But how do you define the length of a line connect...

You do not use light to define straight lines: you...