Grue and Bleen

Brian Greene:

In the late 1960s a young Italian physicist, named Gabriele Veneziano, was searching for a set of equations that would explain the strong nuclear force, the extremely powerful glue that holds the nucleus of every atom together binding protons to neutrons. As the story goes, he happened on a dusty book on the history of mathematics, and in it he found a 200-year old equation, first written down by a Swiss mathematician, Leonhard Euler. Veneziano was amazed to discover that Euler's equations, long thought to be nothing more than a mathematical curiosity, seemed to describe the strong force.

He quickly published a paper and was famous ever after for this "accidental" discovery.

If one did not seek to find a "harmonial balance" where is this, then what potential could have ever been derived from such situations about the possibilties of a negative expression geometriclaly enhanced?

Because the negative attributes have not added up to much in production of anti matter, have we assigned a conclusion to the world of geometerical propensities to not encourge such things a topological maps?

The puzzle to the right(above) was invented by Sam Loyd. The object of the puzzle is to re-arrange the tiles so that they are in numerical order.

The puzzle forms a model of how the positron moves in Dirac's theory. The numbered tiles represent the negative-energy electrons. The hole is the positron. When a negative-energy electron falls into the hole, the hole appears to have moved to another position.

While it would not have seemed likely, such redrawings of the pictures of Albrecht Dürer, this individual might not have caught my attention. I seen the revision of the painting redone, and what was caught in it. You had to really look, to get this sense.

Paul Dirac and Geometrical Thinking?

Into the Antiworld was originally staged at CERN inside the underground cavern that houses the Delphi experiment, in which collisions between electrons and their antiparticles - positrons - are studied. That setting must have been awe-inspiring, particularly as the show closed. The audience would have been whisked from the wonder and novelty of Dirac's theory over 70 years ago to the sophisticated particle physics experiments of today that the discovery inspired. At CERN, the curtain behind the stage ripped apart to reveal the Delphi detector the performance ended - but the gigantic photograph of the Delphi experiment that concluded the show at the Bloomsbury worked surprisingly well.

Oh what fanfare and dance is given these genius's that we find the story ends with where the future begins.

The Quantum Theory of the Electron



Paul Dirac

When one is doing mathematical work, there are essentially two different ways of thinking about the subject: the algebraic way, and the geometric way. With the algebraic way, one is all the time writing down equations and following rules of deduction, and interpreting these equations to get more equations. With the geometric way, one is thinking in terms of pictures; pictures which one imagines in space in some way, and one just tries to get a feeling for the relationships between the quantities occurring in those pictures. Now, a good mathematician has to be a master of both ways of those ways of thinking, but even so, he will have a preference for one or the other; I don't think he can avoid it. In my own case, my own preference is especially for the geometrical way.

Can one distinguish something that is of nature as the basis of reality, and see this before it is algebraically written? Jacques mention where the intuitive lines ends and where the math begins.

So from this statement then, it would have been impossible for Dirac to know what the matrices would look before it was algebraically written?

If there is "no physics" and we are defining things from the horizon or boundary, then what geometry wil be revealing of this nature? Can it be concieved as it was by Dirac?

I was thinking of Lenny Susskinds picture of the rubber band in his mind after working hard to mathematically understand. Did comprehension come by way of his mathe equations or by geometriclaly viewing?

THE LANDSCAPE [12.4.03]
A Talk with Leonard Susskind

Einstein said he wanted to know what was on God's mind when he made the world. I don't think he was a religious man, but I know what he means.

Albrecht Dürer and The Magic Square



So the complexity of geometrical form would have been of value if we had seen the way that it might have taken that vision into the geometrical formations of spin orientated understandings? Isomorphic relations of the orbitals relations in cosmological events?

Trembling, in the Unshakeable?

There is a story on this page that unfolds the more you enter the depth of perception that is offered. If you click on the picture supplied below it takes you into a deeper "cavern of thinking", that relates the depth of ideas that Lubos talks about, with ways in which the standard model might have been used.

I don't say this is the way, but just that in observation, I delved deeper into the meaning of what is not apparent on first look, had me realize that the way history can be rewritten, with a artistic inclination could hold a scientific mind to valuation of what others who demand of this reasoning to be sound.

"But now, almost a century after Einstein's tour-de-force, string theory gives us a quantum-mechanical discription of gravity that, by necessity, modifies general relativity when distances involved become as short as the Planck length. Since Reinmannian geometry is the mathetical core of general relativity, this means that it too must be modified in order to reflect faithfully the new short distance physics of string theory. Whereas general relativity asserts that the curved properties of the universe are described by Reinmannian geometry, string theory asserts this is true only if we examine the fabric of the universe on large enough scales. On scales as small as planck length a new kind of geometry must emerge, one that aligns with the new physics of string theory. This new geometry is called, quantum geometry."

The Elegant Universe, by Brian Greene, pg 231 and Pg 232

On observation alone, who might judge what might issue responsibility, and we have one man's take here. I thought, why waste having hard work deleted, when I can explain myself here:)It always amazes me that such theories were allowed expression and crackpotential meter status recognition, were allowed to live well on, "Not Even Wrong."

New York Times on Toronto Panel Discussion

In Comment Section:

Peter Woit:I’ve always personally felt that the real question is not how to quantize gravity, but how to quantize gravity in some way that tells us how the geometry of space-time is related to the geometry of the standard model.

So Tony Smith opens the door to crackpot alley, and the chances of who might issue forward with possible scenarios, can include, not just the sane in respect of one man's view, but others to comment regardless of the stature with which he might impose a strict recogniton of what is required.

Do they all follow this regiment?

So while this topic was going on I thought about something, or rather someone, who might fit the requirement of Peters statement. Why not my words, and the perspective of another, who saw historically one way, had revisionistic insight, to redraw the picture in a way, that such a view could be extolled in Peter's Comment?

While the Standard Model has been very successful in describing most of the phenomemon that we can experimentally investigate with the current generation of particle acceleraters, it leaves many unanswered questions about the fundamental nature of the universe. The goal of modern theoretical physics has been to find a "unified" description of the universe.

This indeed leaves a "pretty big question mark", but Prof.dr R.H. Dijkgraaf might he learnt to hide this question mark in a place where few with good observational skills might find it? So how lovely indeed, that such a veiw that Peter Woit asks for, might have been embued in artistically thesis of the good professor?

See if this "picture" rings a bell?:)



The dynamical nature of this movement, is the status of what quantum gravity might have brought forward in unseen lines and such, that Prof.dr R.H. Dijkgraaf maybe, just maybe, the answer lies here? What do you think Peter Woit?

Periodic Impingement Orbits:Interference Patterns?

Path through S0(3) Now you must know that the views of this space had association to the >ATLAS, that the paths defined are real intermsof the Calorimetric view, that such appearances are mapped from one state to another by the plate coveringa nd measures of the energy's involved. By taking this covering to symbolize this space? gap we realize how diverse the interactions can be by the implications of the energy used? So we have various idealization here about how the rotational attributes could have been defined in a greater world expression beyond the confines of those same plates

I was looking for the right image to show this rotation and quickly I find Greg Egan's for consideration here, but I had another one as well. When I find it will bring it back for consideration

Shall I call it a real world fantasy that Alice steps into the "mirror world" and we find that exultation of the story again being use to exemplify the world where things enter, and in this strange space/gap, the photon comes out on the otherside?

G -> H -> ... -> SU(3) x SU(2) x U(1) -> SU(3) x U(1). You have to realize that such emergence into the views of universal formulations, has to have some associative response from the quantum world to see that such relevance in the cosmological particpations could have ver pointed to the motivation of these universes coming into being, that it would go through a phase tranasformation relevant to each particle discription? Is this correct? This presented itself iw ay of seeing that stretches the mind imaginations tht I wonder have I indeed gone off the deep end.

Young might have been very happy with this story of Alice in Wonderland, and the wonder of the path integrals, as part of a greater comprehension and revitalization exemplified not just in the feynnmenian toy model production, but of one that enlists a wonderful non-eucldiean world set aside for each and every wonder of entrance and departure into new phase realizations?

It was realized some time ago by Glashow [5] that the orthopositronium system provides one sensitive way to search for the mirror universe. The idea is that small kinetic mixing of the ordinary and mirror photons may exist which would mix ordinary and mirror ortho positronium, leading to maximal ortho positronium - mirror orthopositronium oscillations.

In Albrecht Durer and His Magic Square, I point to what was accomplished in use of an image and artistically rewritten Melencolia II
[frontispiece of thesis, after Dürer 1514]by Prof.dr R.H. Dijkgraaf

Now for me, and I constantly have to remind people that I am junior here in my peceptions, that it would be of my greatest pleasure to expicitly speak to the undestanding of what happens, not only in how we see these lagrange points in space, but also reveal the coming into being of the photon and it's disappearance in a way that involves this complete 720 degree rotation.

I don't know how else to explain what I am seeing other then to find examples and here it would have been most fruitful in looking at what the question mark, where we find the version Melencolia II containing this fundmnantal question about what rises from the standard model and how this is dealt with.

S0 how would define this straight line and measure, but to see it's existnce as a supersymmetrical reality, and as a Calabi Yau model of expression, and find in this same rotational value complete, as a map written, as it is below.

The Photon comes into existance here




The photon is represented here.

So you see this chaos exemplified in a way that the Lorentzian butterfly comes into it's own, that such impngement would find itself relating to each other and trasnferance from state to another? Also, as we look at this, in contrast symmetreical idealization has to have another view reveal itself in the link to the image below where we see this lorentzian butterfly, also mapped in relation to the transferance from one state to another. The Planck Epoch helps here.

How would one mapped unpreditabiltiy in chaos to have seen something grow out of it into a solvable part of some symmetrical views of the gap?

I seemed to have lost the wording that popped into my mind last night. Try as I may, it is one of those times where you repeat it to yourself so that you don't loose it, but being half asleep, this solution was presented for what ever reason.



Is it quite part of what I was looking at, I am not sure. So of course I go looking to see if anything rings a bell?

Wunderkammern

For me this is a wonderful view of abstraction, that had gone into model making, to help those less inclined to "the visonistic qualities of those same abstractions."

Shown here are the models in the mathematical wunderkammer located in the Department of Mathematics at the University of Arizona. Like those in most modern mathematics departments, the collection is a combination of locally-made student and faculty projects together with a variety of commercially produced models. Sadly, a century since their Golden Age, many of the models are in disrepair and much of their documentation has been lost. However, some recent detective work, with the help of the Smithsonian Institution in Washington, has helped the department identify models by the American educators W. W. Ross and R. P. Baker in the collection.

So having been allowed through internet developement to understand the work of fifth dimensional qualites could exist (why Thomas Banchoff must be added below), has far exceeded the understanding of those currently engaged in the mathematics? I do not mean to undermine or cast uncertainty in the direction of those who are helpijng us, but make for recognition of what technology has done for us, in the use of these internet capabilities.

Long before the advent of the World-Wide Web, Tom Banchoff was experimenting with ways of using electronic media to enhance mathematical research and aid in mathematical education. Banchoff helped install one of the first mathematics computer labs in the country, and continues to lead the development of innovative geometric software and curricula for undergraduate mathematics courses. He uses computer graphics as an integral part of his own research, and has used mathematical videos for the last 30 years as a means of disseminating his results.

I have been exploring these issues in regards to the Sylvester Surfaces, and the relationship seen in matrix development. It wasn't without some understanding that "isomorphic images" might have been revealled in orbital images categories, that dealing with this abstract world, didn't require some explanation?

The Magic Square



The picture below was arrived using the applet given from that site. What did you have do to change, in order to get the image I did? We are given possibilties?



But of course I am held by the physics of the world we see. As small as, might have exemplified itself in some larger cosmological imagery of a kind, can it be suited to topological features spoken too in string theory?

We know Max Tegmark has refuted the soccerball universe, and bazeian valuation of a quantum gravity model, that seem to good to be true? PLato, still felt that this soccer ball represented God? So maybe baezian, interpretaion, although derived from archimeadean, was more then the models through which they were precribed in Wunderkammen. Something ancient has been brought forward again for the mind bogglers that like to paly in these abstract spaces?

Mathematical Teaching Tools

Introduction: Lost Geometry

When I was small, growing up in Wisconsin, I loved to walk along the railroad tracks. As I walked, I would watch the steel rails grow from a point in the distance ahead of me, sweep around me, and then disappear again in the distance over my shoulder, converging slowly back to a point. The pure geometry of it was breathtaking. What impressed me the most, however, was the powerful metaphor that it suggested: How wide the present seemed, simply because of my presence there; how small the future and the past. And yet, I could move along the tracks, imagining myself expanding and contracting the infinite timeline of history. I could move ahead until any previous place along that continuum had shrunk to insignificance, and I could, despite the relentless directionality that I imagined moving along the tracks like so many schedule-bound trains, drift backwards as easily as I could let myself be carried forward.

The wonderful stories exemplifed by human experience, places me in states of wonder. About how processes in geometry could have engaged us in a real dialogue with nature's way around us. To see these stories exemplified above. One more that quickly came to mind, was Michio Kaku's view from the bridge, to the fish in the pond. Looking at the surface from two perspective sseem really quite amazing to me.

Such exchanges as these are wonderful exercises in the creation of the historical abstract. A Lewis Carroll in the making? An Abbotsolutely certainty of math structures, that we would like to pass on to our children and extend the nature to matter of the brain's mass?

Albrecht Durer and His Magic Square

Albrecht Dürer(self portrait at 28)

It was important to me that I post the correct painting and one that had undergone revision to exemplify the greater context of geometrical forms. In the Topo-sense? Artistic renditions help and adjust views, where information in mathematical minds, now explains something greater. Melencolia II
[frontispiece of thesis, after Dürer 1514]by Prof.dr R.H. Dijkgraaf

"Two images when one clicked on," shows what I mean.

Melancholia in 1514(the original)

The Magic Square

Like Pascal, one finds Albrecht has a unique trick, used by mathematicians to hide information and help, to exemplify greater contextual meaning. Now you have to remember I am a junior here in pre-established halls of learning, so later life does not allow me to venture into, and only allows intuitive trials poining to this solid understanding. I hope I am doing justice to learning.

A new perspective hidden in the Prof.dr R.H. Dijkgraaf
second rendition, and thesis image, reveals a question mark of some significance?:) So how would we see the standard model in some "new context" once gravity is joined with some fifth dimensional view?

Matrix developement?

Like "matrix developement," we see where historical significance leads into the present day solutions? How did such ideas manifest, and we look for this in avenues of today's science.

In 1931 Dirac gave a solution of this problem in an application of quantum mechanics so original that it still astounds us to read it today. He combined electricity with magnetism, in a return to the 18th-century notion of a magnet being a combination of north and south magnetic poles (magnetic charges), in the same way that a charged body contains positive and negative electric charges.

How relevant is this? How important this history? How relevant is it, that we see how vision has been extended from plates(flat surfaces to drawings) to have been exemplified in sylvester surfaces and object understanding. This goes much further, and is only limited by the views of those who do not wish to deal with higher dimensional ventures?



See:

Topo-sense

The Abstract World