Revising Space Time Geometry: A Proposal for a New Romance in Many Dimensions by Renate C.-Z. Quehenberger

Just in case

My advice to read

http://www.galiulin.narod.ru/ufn022f.pdf

http://www.galiulin.narod.ru/crys03_6.pdf.pdf

Dear Rick,

many thanks for your link to your fascinating essay!

Now I guess, I understand why octonionic algera exceeds he Hilbert space ...

Here you might find the preliminaries for a geometry of a diecrete space using grid Z5 which should support the geometric visualisation octonions (- work in progress).

www.researchcatalogue.net/view/22616/22617

I wish to proceed far enough to visualize one day soon your complex field equations;-)

Best wishes !

Renate

Dear Renate,

I enjoyed reading your essay! The historical context is very interesting. It's nice to have this all in one place. A couple of questions and remarks.

1. I think Maxwell's poem was referring to the fact that all (one-dimensional) knots come undone in four-dimensional space. Is this what you were referring to on page 8?

2. The quaternions and octonions (defined by Cayley) are related to Hopf fibrations, which are geometrically beautiful and also physically relevant (for instance, in quantum information theory).

3. You mention Klein's program in regard to covariance (i.e. "Lorentz invariance.") I think it's interesting to consider the possibility that this is only an approximate concept. This is one of the topics I discuss in my essay On the Foundational Assumptions of Modern Physics.

4. Another interesting thing to consider is non-integer dimension (fractal dimension, emergent dimension, etc.). This is particularly relevant in discrete models.

Thanks again for the interesting read! Take care,

Ben Dribus

Dear Ben,

many thanks for your interesting remarks:

ad 1) yes and I described it why,- ) Yes, one-dimensional strings if you like, but you may also take a thick rope which can be considered as a 3d dimensional knot, but if you make a knot into a 2D surface you get a pentagon and if you try to make a knot into a pentagon you get an epitahedron ...

ad 2 ) Here you may watch a 3-sphere, where the circle bundels of the Hopf fibration became hemispheres: http://quantumcinema.uni-ak.ac.at/site/

ad 3) I guess Kretschmann meant what you call: "The properties of Minkowski spacetime impose external symmetries described by the Poincaré group.

If you embed 4D space into a discrete higher dimensional space stucture, all problems with the socalled "incompatibility of general relativity with Quantum Mechanics "are vanishing.

ad 4) Higher dimensional spaces are complex configurations of 3 dimensional spaces, therefore I don't think we have to consider fractal dimensions as relevant for discrete space models, because usually they serve as the measure of a certain space-filling capacity in 2D patterns.

Best wishes!

Renate

Thank you so much for this invaluable links, Yuri!

Dear Quehenberger,

In the conjecture of Tetrahedral-branes in Coherently-cyclic cluster-matter paradigm of universe, reductionism of extra-dimensional expressions is by the non-descriptive complexity of the coordinates of configuration space, in that its generalized coordinates are time, string-length and the central angle of transformed eigen-rotation. Thus in this scenario of dimensionality, three-dimensional structures emerge with fractals.

With best wishes

Jayakar

Hey Renate, love the prose and historical intertwines. Great piece. A nice example of ScienceArt, both with capitals. Although to my personal taste there's a bit to much geometry here and a bit too little topology here. :) We all meanwhile know where babies come from, but where do dimensions come from? Where do lines come from?

If you do not understand why your rating dropped down. As I found ratings in the contest are calculated in the next way. Suppose your rating is [math]R_1 [/math] and [math]N_1 [/math] was the quantity of people which gave you ratings. Then you have [math]S_1=R_1 N_1 [/math] of points. After it anyone give you [math]dS [/math] of points so you have [math]S_2=S_1+ dS [/math] of points and [math]N_2=N_1+1 [/math] is the common quantity of the people which gave you ratings. At the same time you will have [math]S_2=R_2 N_2 [/math] of points. From here, if you want to be R2 > R1 there must be: [math]S_2/ N_2>S_1/ N_1 [/math] or [math] (S_1+ dS) / (N_1+1) >S_1/ N_1 [/math] or [math] dS >S_1/ N_1 =R_1[/math] In other words if you want to increase rating of anyone you must give him more points [math]dS [/math] then the participant`s rating [math]R_1 [/math] was at the moment you rated him. From here it is seen that in the contest are special rules for ratings. And from here there are misunderstanding of some participants what is happened with their ratings. Moreover since community ratings are hided some participants do not sure how increase ratings of others and gives them maximum 10 points. But in the case the scale from 1 to 10 of points do not work, and some essays are overestimated and some essays are drop down. In my opinion it is a bad problem with this Contest rating process.

Sergey Fedosin

good text

Cheers Reni.

Like the Nietsche quote.

Many thanks for your personel review, Prof. Bob!

Indeed, one could easily draw a line of thoughts from the abolished Limbo, via the abandoned ether and Plato's forgotten „order of heavens" to the hierarchy problem.

A topologist, could take a bundle (F) of hyperbolic spaces with some handles and loopholes in it, apply the Fourier transform, arrive in 6D and - wait for the babies.

A geameter exists already there,- in Plato's ideal world, filled with (Maxwell's and Faraday's) interfering lines of forces, forming triangles over and over, entangled towards manifolds of all possible higher order.

Didn't Klein tell, that all geometries and topology are merging in higher dimensions?

Good question; - can we realy explain „dimensions" with "degrees of freedom" only ?

I guess they are necessary to avoid Hilberts trap and mix up a beer mug with ...