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Re: Non Euclidean parallelsPosted by MaddenL3 on October 06, 2002 at 14:45:01: In Reply to: Non Euclidean parallels posted by DickT on September 25, 2002 at 08:13:16: Forget parallels. Forget "lines". All we have in nature are unit line segments where the connecting line segments go off in "60 degree" directions (dimensions) from each other (no right angles allowed!). The basic units of space are tetrahedrons. What we see at the large scale as a line is a series of these unit line segments continually changing direction (dimension). The three "apparent" dimensions at right angles to each other is an illusion helped along by the following error in mathematical reasoning: The Phythagorean Conjecture is (and always was) false, the simplest counterexample being the right triangle with unit sides. Since the sum of the two unit sides squared is two and no number existed that was (or is) the square root of two, normal mathematical logical reasoning requires that one or more of the assumptions is false. I contend that the assumption that right triangles (or right angles) exist is in error. I believe that Richard Dedekind suspected this when he concluded an irrational almost has to be accepted as a primitive concept even if "nature itself turns out to be discrete". He probably thought that mathematics itself would be imperiled without the irrationals. But given the falsity of right angles, in other words, the three commonly accepted spatial dimensions, what dimensions are logical? How can we survive without Cartesian Coordinates? It turns out that unit tetrahedrons are basic and extra dimensions are created in putting together these unit tetrahedrons (remember! no right angles!). The number of these dimensions is at least 11. A "Tetrahedronal Coordinate System" is very complex, but at least it has a rock-solid logical foundation.
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