One Light and Life of Truth

[ark]

The ending paragraph from the monograph "Space-Time-Matter" by Hermann Weyl (first published in 1920)

... Whoever looks back over the ground that has been traversed, leading from the Euclidean metrical structure to the mobile metrical field which depends on matter, and which includes the field phenomena of gravitation and electromagnetism; whoever endeavours to get a complete survey of what could be represented only successively and fitted into an articulate manifold, must be overwhelmed by a feeling of freedom won - the mind has cast off the fetters which held it captive. He must feel transfused with the conviction that reason is not only a human, a too human, makeshift in the struggle for existence, but that, in spite of all disappointments and errors, it is yet able to follow the intelligence which has planned the world, and that the consciousness of each one of us is the centre at which the One Light and Life of Truth comprehends itself in Phenomena. Our ears have caught a few of the fundamental chords from that harmony of the spheres of which Pythagoras and Kepler once dreamed.

A beautiful, in my opinion, statement. But do not be misled - the book is loaded with math!

 

[John G]

The ending paragraph from the monograph "Space-Time-Matter" by Hermann Weyl (first published in 1920)

... Whoever looks back over the ground that has been traversed, leading from the Euclidean metrical structure to the mobile metrical field which depends on matter, and which includes the field phenomena of gravitation and electromagnetism... Our ears have caught a few of the fundamental chords from that harmony of the spheres of which Pythagoras and Kepler once dreamed.

A beautiful, in my opinion, statement. But do not be misled - the book is loaded with math!

The math is beautiful even for me without knowing the math (geometric picturing and dimensional patterns can be noticed without knowing the math). Since Newton was here I've been trying to picture/pattern better in my mind what you bring up in that Weyl quote. I'm starting with this from Tony Smith:

Spherical, Euclidean, and Hyperbolic geometries are all
subgeometries of LIE SPHERE GEOMETRIES. Lie sphere geometries are the geometries of hyperspheres embedded in Spherical space, Euclidean space, or Hyperbolic Space. As homogeneous spaces, ordinary spheres Sn are Spin(n+1) / Spin(n)xSpin(1) where Spin(1) is the 2-element group {-1, +1}, and Lie spheres are Spin(n+2) / Spin(n)xSpin(2) where Spin(2) = U(1).

The Lie sphere geometry thus seems conformal group related (the plus two instead of plus one). The part I'm trying to picture/pattern better is that spherical geometry is sometimes referred to as elliptic spherical geometry. I'm currently thinking that the elliptic comes from elliptic as used for modular forms/Mobius transformations/Jordan Algebra and is related to "the mobile metrical field which depends on matter" Is this correct?

 

[ark]

I'm currently thinking that the elliptic comes from elliptic as used for modular forms/Mobius transformations/Jordan Algebra and is related to "the mobile metrical field which depends on matter" Is this correct?

It is a viable idea. Whether it is correct or not depends on the details, where the devil hides. Ane these little devils there are pretty mischievous - they are not helping us at all. We need to WORK, and work hard.

As for me, I do not know what is "elliptic" there, I do not know what are modular forms, I have rather vague idea about Jordan Algebras, as I have never used any advanced form of them. I am not even sure if I know what matter is. The term "mobile metric field" is, as for me, also not quite clear, though I can try to guess what it means. So I have a lot of things to work on. Most of the Tony Smith's writings are well over my head. I may have a rough idea as to what it is about - but I am unable to make any use of it.

The path from an idea to a theory that one can communicate to others in such a form that they understand it and can add it to their own knowledge basis, so that it serves not only the satisfaction of the author, but also humanity, is a long one and a hard one. Sometimes it takes generations, sometimes the ideas do not survive attemts to make them into a rigorous science at all.

My own current project is "Quantum Theory of the Wave". The idea itself is 30 years ago, and I was not able to make it mathematically precise through all these years. Perhaps I will succeed now? Who knows? And how long will it take? A month? A year? A life?

C's used to say: "wait and see". But, in this case, don't just wait! Do it, and THEN see!

 

[John G]

I have rather vague idea about Jordan Algebras, as I have never used any advanced form of them.

Most all of what Tony gets from Jordan Algebras, etc. he also gets (more usefully actually) in his Checkerboard. Thus if you ever need or want to get more into Tony's model, you could begin and end at his Checkerboard. Tony's Checkerboard uses Cl(8) in a way similar to how Wolfram uses it in his cellular automata. For your purposes it may be computationally hard to get all you really want out of a Checkerboard. I could see you creating something using prime numbers along the lines of Matti Pitkanen/the Ulam spiral/what the Cs hint at but I'm not sure you could get all that you want out of that either.