Geometry Leads us to the Truth?

"The end he (the artist) strives for is something else than a perfectly executed print. His aim is to depict dreams, ideas, or problems in such a way that other people can observe and consider them." - M.C. Escher

I too have always been interested at the idea of what we can see deeper then what we observe on the surface. As if an abstraction in the geometry may be leading when considering Polytopes and allotrope s or even Penrose Tilings as to the Truth?:)

A remarkable mosaic of atoms

In quasicrystals, we find the fascinating mosaics of the Arabic world reproduced at the level of atoms: regular patterns that never repeat themselves. However, the configuration found in quasicrystals was considered impossible, and Dan Shechtman had to fight a fierce battle against established science. The Nobel Prize in Chemistry 2011 has fundamentally altered how chemists conceive of solid matter. See: The Nobel Prize in Chemistry 2011 Dan Shechtman

I do not think one can ever imagine what goes through my mind and I guess that's part of my artistic journey is to better learn how to describe what I am seeing. It goes back some time as to what I learn about myself and how some of these geometers see. I did not ever feel apart from them as I tried to look deeper into reality and see what the basis is and how  we might describe that.

You must also know I now sport an interesting tattoo that I will share shortly. Maybe even consider it as a line break, and as a pointer. You'll see why when I upload picture. So,  that has been my thing when I look at all this science and those espouse the teaching of,  that I tried to find my place in it. I mean I could be so wrong in a long of things.....but isn't that part of the evolution of being?  Learning about those mistakes and dealing with the responsibility of finding that truth within self?

If the heart was free from the impurities of sin, and therefore lighter than the feather, then the dead person could enter the eternal afterlife.

My second tattoo will be as in the picture showing below on this blog site demonstrating and seen above is an ancient idea about "our heart" in relation to "the truth."  How we weight that against one another and how the choices we make will have us asking whether we acted in accordance with that truth. That is "the final judgement" and if this is understood then we can access whether or not we have much more to learn. I know that setting right past mistakes is not an easy thing but if you at least start then that is part of the success of not of having to repeat them. Maybe repeat many times until you finally actually get it.

Well then,how does one simplify that picture of such Judgement in the Hall of Ma'at as to know that this message is alive and well in today's world and just as valid? How well will the tattooist portray this design? I'll have to give it to her  so she has some time to look at it and decipher.:)

 See Also:

• Fulleranes and Allotropes
• Coxeter and Plato's Cave
  

Science and the Mind: Sir Roger Penrose

Above picture, belongs to this article and titled above, of frames that Sir Roger Penrose wrote in 1999.

Roger Penrose, a professor of mathematics at the University of Oxford in England, pursues an active interest in recreational math which he shared with his father. While most of his work pertains to relativity theory and quantum physics, he is fascinated with a field of geometry known as tessellation, the covering of a surface with tiles of prescribed shapes.

Being reminded of Roger Penrose I am actually going to contribute this blog entry to him, and sources that I had collected.

Twistor Theory


The motivation and one of the initial aims of twistor theory is to provide an adequate formalism for the union of quantum theory and general relativity. Twistors are essentially complex objects, like wavefunctions in quantum mechanics, as well as endowed with holomorphic and algebraic structure sufficient to encode space-time points. In this sense twistor space can be considered more primitive than the space-time itself and indeed provides a background against which space-time could be meaningfully quantised.

Twistor Program

http://twistor-theory.rdegraaf.nl/index.asp?sND_ID=436182

R. Penrose and M. A. H. MacCallum, Phys. Reports. 6C (1972) p. 241

pages:

242-243,244-245,246-247,248-249,250-251,252-253,254-255,256-257,258-259,260-261,262-263,264-265,266-265,268-269,270-271,272-273,274-275,276-277,278-279,280-281,282-283,284-285,286-287,288-289,290-291,292-293,294-295,296-297,298-299,300-301,302-303,304-305,306-307,308-309,310-311,312-313,314-315,316-317,318-320,320-322,322-324,324-326,326-328,328-330,330-332

or download the unix tar-ball to get all the pages at once. (WinZip is able to unzip this archive)

Sir Roger Penrose

Science and the Mind

Einstein's Equation and Twistor Theory

Gravitationally Induced Quantum State Reduction

Quantum State reduction as a real phenomenon

Schrödinger's Cat in Space

Fedja Hadrovich
In the past 30 years a lot of work has been done on developing twistor theory. Its creator, Roger Penrose, was first led to the concept of twistors in his investigation of the structure of spacetime and it was he who first saw the wide range of applications for this new mathematical construct. Yet 30 years later, twistors remain relatively unknown even in the mathematical physics community. The reason for this may be the air of mystery that seems to surround the subject even though it provides a very elegant formalism for both general relativity and quantum theory. These notes are based on a graduate lecture course given by R. Penrose in Mathematical Institute, Oxford, in 1997 and should give a brief introduction to the basic definitions. Let us begin with the building blocks: spinors.

R. Penrose, F. Hadrovich
Twistor Theory

The motivation and one of the initial aims of twistor theory is to provide an adequate formalism for the union of quantum theory and general relativity. Twistors are essentially complex objects, like wavefunctions in quantum mechanics, as well as endowed with holomorphic and algebraic structure sufficient to encode space-time points. In this sense twistor space can be considered more primitive than the space-time itself and indeed provides a background against which space-time could be meaningfully quantised.

Lecture I
Lecture II
Lecture III