Monday, September 11, 2006

Donald Coxeter: The Man Who Saved Geometry

"I’m a Platonist — a follower of Plato — who believes that one didn’t invent these sorts of things, that one discovers them. In a sense, all these mathematical facts are right there waiting to be discovered."Harold Scott Macdonald (H. S. M.) Coxeter

Some would stop those from continuing on, and sharing the world behind the advancements in geometry. I am very glad that I can move from the Salvador Dali image of the crucifixtion, to know, that minds engaged in the "pursuites of ideas" as they may "descend from heaven," may see in a man like Donald Coxeter, the way and means to have ideas enter his mind and explode in sociological functions? Hmmmm. what does that mean?

Geometry is a branch of mathematics that deals with points, lines, angles, surfaces and solids. One of Coxeter’s major contributions to geometry was in the area of dimensional analogy, the process of stretching geometrical shapes into higher dimensions. He is also famous for “Coxeter groups,” the inversive distance between two disjoint circles (or spheres).

It is not often we see where our views are shared with other people?

I was doing some reading over at Lubos Motl's blog besides just getting the link for Michio Kaku article, I noticed this one too.

You might think the loss of geometry | like the loss of, say, Latin would pass virtually unnoticed. This is the thing about geometry: we no more notice it than we notice the curve of the earth. To most people, geometry is a grade school memory of fumbling with protractors and memorizing the Pythagorean theorem. Yet geometry is everywhere. Coxeter sees it in honeycombs, sun°owers, froth and sponges. It's in the molecules of our food (the spearmint molecule is the exact geometric reaction of the caraway molecule), and in the computer-designed curves of a Mercedes-Benz. Its loss would be immeasurable, especially to the cognoscenti at the Budapest conference, who forfeit the summer sun for the somnolent glow of an overhead projector. They credit Coxeter with rescuing an art form as important as poetry or opera. Without Coxeter's geometry | as without Mozart's symphonies or Shakespeare's plays | our culture, our understanding of the universe,would be incomplete.

Now you know what fascination I have with the geometries, as they have moved us towards the comprehension of GR and Reimann? Could Einstein have ever succeeded without him?

Michael Atiyah:
At this point in the development, although geometry provided a common framework for all the forces, there was still no way to complete the unification by combining quantum theory and general relativity. Since quantum theory deals with the very small and general relativity with the very large, many physicists feel that, for all practical purposes, there is no need to attempt such an ultimate unification. Others however disagree, arguing that physicists should never give up on this ultimate search, and for these the hunt for this final unification is the ‘holy grail’.

Without stealing the limelight from Donald, I wanted to put the thinking of Michael Atiyah along side of him too. So you understand that those who speak about the "physics" have things underlying this process which help hold them to the very fabric of thinking.

Some do not know of "this geometric process" I speak, where such manifestation arise from the very essence of the thinking soul. If you began to learn about yourself you would know that such abstractions are much closer to the "pure thought" then any would have realized.

Some meditate to get to this essence. Some know, that in having gone through a journey of discovery that they will find the very patterns sealed within each of the souls.

How does it arise? You had to follow this journey through the "muddle maze" of the dreaming mind to know that patterns in you can direct the vision of things according to what you yourself already do inherently.

Now some of you "know," don't you, with regards to what I am saying? I spoke often of "Liminocetric structures" just to help you along, and help you realize that the sociological standing of exchange houses many forms of thinking that we had gained previously. Why as a soul of the "thinking mind" should you loose this part of yourself?

So you begin with the "Platonic Forms" and look for the soccer ball/football? THis process resides at many levels and Dirac was very instrumental in speaking about the basis of the geometer and his vision of things. Along side of course the algebraic way.

(Picture credit: AIP Emilio Sergè Visual Archives)

This is very real, and not so abstract that you may have departed form the real world to say, you have lost touch? Do you think only "in a square box" and cannot percieve anything beyond the "condensive thoughts and model apprehensions" which hold you to your own design?

Maybe? :)

But the world is vast in terms of discovery, that the question of mathematics again draws us back too, was "Mathematics invented or discovered?" So "this premise" as a question formed and with it "the roads" that lead to inquiry?

Al these forms of geometrics leading to question about "Quantum geometry" and how would such a cosmological world reveal to the thinkingmind "the microscopic" as part of the dynamical world of our everyday living?

Only a cynic casts the diversions and illusions to what is real. Because they cannot inherently deal with the "strange language of geometrics" that issues forth in model apprehensions. This is the basis from which Einstein solved the problems of his day.

But the question is what geometrics could ever reside at such a microscopic level?

No comments:

Post a Comment