Wednesday, May 11, 2005
The Unity of Mathematics
Where a dictionary proceeds in a circular manner, defning a word by reference to another, the basic concepts of mathematics are infinitely closer to an indecomposable element", a kind of elementary particle" of thought with a minimal amount of ambiguity in their defnition.
I think what intrigues me most, is that a world can be fabricated mathematically that is carefully constructed using models of math, to get to a desired visionary culmination? One had to have some culminative effect, from such model thinking, that a vision beocmes clear. In this sense I related Lenny Susskind here, for his developement and contributions to string theory.
Now having spent time delving into parts of this world, the "tidbits" help me to see that such alignmenets of the world of physics have correlations in mathematical design. This has to have it basis set, "in the Rossetta stone you might say," about how we percieve the deveopement of those physics. The math must contrast the physics?
So to set things straight here, in case I gave the wrong link, I thought I should attribute proper link to words in case this mistake was made.
So too, information in blogs can be readily adapted too, where previous articles might have made some feel that the article not worth maintaining in their blog? That it might have been removed? I was thinking of the B-field topic that Lubos had written briefly on, that when I went to look for relevant information pertaining to this current entry, it was no where to be seen.
A VIEW OF MATHEMATICS by Alain CONNES
Most mathematicians adopt a pragmatic attitude and see themselves as the explorers of this mathematical world" whose existence they don't have any wish to question, and whose structure they uncover by a mixture of intuition, not so foreign from poetical desire", and of a great deal of rationality requiring intense periods of concentration.
Each generation builds a mental picture" of their own understanding of this world and constructs more and more penetrating mental tools to explore previously hidden aspects of that reality.
Now many would have to forgive my adventurous heart. I was somehow transported in my thoughts and converted? I don't know when, that such models of the mathematical structure had easily become discernable for me(it's result)? Not it's elemental structure(although I have seen areas of string theory design developed) from basic principals. It had it's culminative effect.
Is my vision always right? Of course not. But I see where such discriptions are necessary. Solid, and in stone, so that such progression can be made. I respect this, and I respect the physics, and it's culminative approach in theoretical developement.
Nature's Greastest Puzzle
Alain Connes refers to "poetic design," much like I see beats to music:?), and artistic adventure, as the play ground of imagination. We hope such songs shared, lyrics or otherwise, will reveal what the most secluded and private individuals might have found in their own world. To seek out, good artistic drawers like Escher? Penrose, needed his help, and the ideas brought forth, interesting results.
Now there is a reason for this post besides setting the record straight. It came up a long time ago with the question of whether mathematics was natural or created.
This may seem simplistic thought to some, but to me, it forced me to consider whether mathematics and physics were directed connected to each other.:) Now as I have said it is not easy for me to follow the matheics of such abtract individuals, but once I catch sight of the world that they allude too, it is somehow easy for me to see the structure of the bubble, or a representative drawing correlated in nodes, and features of a world that is constained in the physics.
This is why I refer back to Lubos and his B-field missing post, or I cannot simply find it. I refer to it, because I made links to mathematical design, that correlated dynkin diagram as shown above, and connects to other blog. Now it was important for me to see this correlation in the archetecture of the picture I linked to its prospective author, in relation to the dynkin diagram. Not the E11 asscoiation, but with that I had linked in image in comments to the B-field post.
My whole blog is based on visionary developement, theoretically, as well as nurturing physics association as best as I can, to show that the envelope is being pushed theoretically.
Interpretations of the magnetic field, in all its desgin is easily comprehensible once we align our thinking to hard fact and design reprsentation. Magnetic field lines on paper, is a child's toy, but easily experimetally done. Much more abstract then, that we see the field created, it's north and south, and a channel through which expression can flow?
Now even this is contained, and a Gausssian representation, highly abtract, relates curvature in away that we would understand this force that nature has created for us.
You must remember I do not have the luxury or life's abilty to move through the higher avenues that scholastic carreers have venture forth in. To preview this branch or that branch in physics, so I am bombarded with information from all angles:?)
I like to wrap the gravitational field, much like we wrap the magnetic field. It's just the way I see, and in it's greater design, that vast gravitational field that is generate through our cosmos? Bubbles become very interesting whenyou wrap somehing and the inside is moving with the outside, and in the vast vacuum of space this is stretching the very fabric itself?
I won't make the mistake of calling it the aether, yet continuity of expression seen in this abstract mode, does not see "tears" and such, so it is allocated to topological relevances. Holes, that look like swiss cheese in the cosmos? Yet I know well the events, that materialize in comsological expression, I wanted to push beyond these material things, to see the greater vision that has been moved by mathematcians.
You can say the rogue man here who speaks, is a wolf cub. Has been raised in a foreign world, without the benefits of scholastic teachers to guide me. So I had to look for them who held sacred some of the vision that I see when this math leads to a comprehensive view.
Reimann lead Einstein, and it was fortunate that Grossman was able to spot Einsteins deficiences. Help him move geoemtical principal beyond the euclidean coordinated world, to one manifested in spacetime, and a new dynamcial feature called gravity. It was beyond billiards and the sound related, and not the clasical discription that now beocmes the analogy of, that strange world we now see in gravitational thought.
Was it enough to speak about theses things and theorectically develope thoughts, to describe ways, in which such sound could ring bars, or influence the flexible arms of LIGO We measure this abstract world mathematcially created, to realize, we are now engaged in something very unique about our visions developement? Kip Thorne progeny will be the new genration that sees in way that were new to bauss and Riemann and now as we see of Einstein. This has a geometrical expression and basis to it, and it leads into projective elements topologically described.
Klein's Ordering of Geometries
A theorem which is valid for a geometry in this sequence is automatically valid for the ones that follow. The theorems of projective geometry are automatically valid theorems of Euclidean geometry. We say that topological geometry is more abstract than projective geometry which is turn is more abstract than Euclidean geometry.
Klien's ordering of geometries were specifc here?