Euclid's 5th Postulate

In quick and dirty terms, Euclid's 5th has 3 flavours:

Given a line and a point,

1 - Flat/Eucidean - 1 Parallel line through the point

2 - Elliptica/Riemannian - 0 parallel lines throuh the point

3 -Hyperbolic/Lobachevskian - infinite number of parallel line through the point.

1 is always true in the abstraction of 'school' Euclidean geometry and if space is flat.

2 or 3 is true dependoing on how space is curved.

Given that the curvature space is governed by the distribution of mass, it is likely that there are regions of the uniniverse that have space that is flat, 'postively' curved and 'negatively' curved.  That seems to imply which flavour of the 5th is true depends on where you are - ie that 'the truth' varies from place to place!   If we suppose reality to be 'what is true' is it, er, 'true' that there is only one reality?

 

Observations are context sensitive.

Even the laws of physics are temporary.

The nature of space-time was quite different before stars formed and the nature of space-time will be quite different after the last red dwarf blinks out.

False and no evidence for such comments are true.

Energy ergo an occupied space cannot be created nor destroyed is an eternally truth everywhere and everywhen.

The sum of the angles of Euclidean triangle is eternally 180 degrees when the base unity is 360 circle.

The tetrahedron is the minimal 3D enclosure that divides Universe into two ---inside and outside--- is the tetrahedron.