fancier way of saying that is that in general, it's okay to model the space around us using the Euclidean metric. But the Euclidean model stops working when gravity becomes strong, as we'll see later. The Euclidean model for space
The magic square of "Albrect Durer" located in my index on the right is fascinating from the point of view that such a symmetry can be derived from the view of moving in an abstract space.
Trying to understand the implication of what is happening in a stronger gravitational field is an abstract journey for me as well, while I hold "thoughts of lensing" in my mind as a accumulative effect of something that is happening naturally out in space.
The move to Lagrangian points out in space is also an accumulative effect of thinking in this abstract way.
I not only think of the "magnetic field as as an associative value for that abstractness," it is a geometry that is the same for me, as I try to unravel the energy valuation of points(KK Tower) of any location in space. While the valuation of a circle on a 2 dimensional screen sees a string vibrating, I am moving this perception to valuations onto mathematical models.
I have nobody to help this way I have to push forward, knowing there will be mistakes, and that hopefully I am grasping the full scope of seeing in a abstract way.
Figure 2. Clebsch's Diagonal Surface: Wonderful.
We are told that "mathematics is that study which knows nothing of observation..." I think no statement could have been more opposite to the undoubted facts of the case; that mathematical analysis is constantly invoking the aid of new principles, new ideas and new methods, not capable of being defined by any form of words, but springing direct from the inherent powers and activity of the human mind, and from continually renewed introspection of that inner world of thought of which the phenomena are as varied and require as close attention to discern as those of the outer physical world, ...that it is unceasingly calling forth the faculties of observation and comparison, that one of its principal weapons is induction, that it has frequent recourse to experimental trial and verification, and that it affords a boundless scope for the exercise of the highest efforts of imagination and invention. ...Were it not unbecoming to dilate on one's personal experience, I could tell a story of almost romantic interest about my own latest researches in a field where Geometry, Algebra, and the Theory of Numbers melt in a surprising manner into one another.
Dr. Kip Thorne, Caltech 01-Relativity-The First 20th Century Revolution
It was the beginning of what might be called (and in fact is called) Stringy Geometry. The point is that strings are not points, and specifically, their extended nature means that in addition to being able to see the usual geometrical properties of a space that the theory like General Relativity can see, the strings can see other, intrinsically stringy, data. There is a quantity in the theory that is called the Kalb-Ramond field (or just the “B-field”) that can be used to measure how much the string can winds on or wraps a piece of the geometry, in essence. The parameter a that measures the size of a piece of the space that collapses when the geometry becomes singular, is essentially joined by another parameter, b, that sort of measures how much the strings have wound or smeared themselves on that piece of the space. The upshot is that a and b naturally combine themselves into a complex parameter that naturally describes the resolution process, solving the puzzle that the Mathematicians faced.Beyond Einstein: Fixing Singularities in Spacetime
I am always trying to get the "visual models" of such proposals in terms of the B Field. Nigel Hitchin
Can you tell me, if the Dynkin diagrams and the points on a Sylvestor surface/ Cayley model have some value when looking at this subject?
Also, if it would be wrong to see "UV coordinates of a Gaussian arc" can be seen in this light as well?
I am recording this to help me understand how energy windings of the string may be seen as points on the Sylvester Surface?
See: What is Happening at the Singularity?