Resonance: Brownian Motion

Now before I go into this I am thinking also if how "weathered effects and chaos" would have allowed quantum probability valuations (let's say spintronic idealization to channel) to have been curtailed to a Professor crossing the room. Brane orientation and fermionic considerations held, while helping to orientate views further out in the bulk?

This encompasses the generalization in terms of bubble dynamics, or how could any singularity too "inside/out" be of value to that same gravitational collapse, regardless of macro or micro considerations?

So one would have to seen how, Langrangian "points" help to view dynamcial situations in relation to the Sun Earth Moon. I would like to have thought of a chaldni plate analogy here, pointing, to a place for consideration of movement of our satelittes with less efffort. It is a vision of geometrical correlations that such idea could have been artistically embued.

Resonance
This is a magazine that Clifford drew our attention too, and while looking in the archive I found reference here below that sort of caught my attention.



Brownian Motion Problem: Random Walk and
Beyond ,

I really find this quite interesting from a "artistic point of view".

While indeed the issue is quite complex in terms of environmental flows and such, this kind of dynamcial valution might seem interesting from the point of view of early plasmatic conditions, would it not?

Now if such supefluid conditions would arise in the collider developements then, this expression would defintiely need to answer the way in which we look at what superpsymmeterical valuation would have ever resulted in symetry breaking valuation sought from these bubble dynamics, fromthe fluid of that early universe.



What constraints would limit you from making such a comparison and the idea of bubbles that form from this bath? To viewing dynamic situations in terms of thermodynamic realization offered from other perspectves. I give some examples shortly. Just know, that gravitational collapse would have signalled a better determination then one how ever discerned, to point to efforts to understand this supersymmetrical valuation. If all grviaational states of collpase are revealled as leaidng indicators to this supersymmetreicla valuation, then the idea to me is that this points to a underlying reality that exists in our moments around us.

While Microstate blackhole would be quick to dissipate, it is equally sufficient to my thinking to see that infomration realease from this "supersymmetrical breaking" would give indictaions as information in UV indications?

Of course it's all speculation from the point of the fluid, because we have evidence of this already. So all I am doing is saying that having the stage set, then how would such relations signal new universes?

So from a geometrical standpoint, having been told that there are no physics and geometry below a certain length (is this a quantum grvaity ascertion since there is no consensus?), this makes it extremely difficult to theoretically deal with how such a issue I am relaying in terms of Brownian motion could have ever spawned those same bubble universes out of such a fluid state.

This gallery was inspired by a lecture of Dr. Julien Sprott and his work.To learn how these are created, check out my Strange Attractor Tutorial. Click on the images to enlarge them.

So my mind is set in this chaotic enviroment, but indeed, the continuity of all these movements and flows seem disjointed from one perspective, that one point over here, might be different in the way a guassian map might reveal of point "p" over there. So we know on the surface, seeing valuation in terms of gaussion coordiantes that we can spell out on the face value of this surface, would have given a ^uv of P a very much different look.


Gaussian Coordinates

We can sum this up as follows: Gauss invented a method for the mathematical treatment of continua in general, in which ?size-relations? (?distances? between neighbouring points) are defined. To every point of a continuum are assigned as many numbers (Gaussian co-ordinates) as the continuum has dimensions. This is done in such a way, that only one meaning can be attached to the assignment, and that numbers (Gaussian co-ordinates) which differ by an indefinitely small amount are assigned to adjacent points. The Gaussian co-ordinate system is a logical generalisation of the Cartesian co-ordinate system. It is also applicable to non-Euclidean continua, but only when, with respect to the defined ?size? or ?distance,? small parts of the continuum under consideration behave more nearly like a Euclidean system, the smaller the part of the continuum under our notice.

Now if such bubble dynamics were to be self revealling, such surface measures would give evidentary features of the shape of this bubble, defining geometrical propensities as a surface valuation. I am thinking here of the "rainbow colors as refractory relevance" that would seem to define heavier color variations over this surface, if using soap bubble as an example.

Plato:

So just to carry on a bit with this point "P" in gaussian coordinated of frame of UV, what realization exists that we could not find some relevance here in the geometry to have further exploited the mind's capabilties by venturing into the Wunderkammern of thinking. By association, of Nigel Hitchin's "B Field manifestations geometries" to realize that althought these might be limited to what Jacque is saying , then what value this geometry if we can not see the landscape as something real in time variable measures?

Now you know you could have never come to this "shape" without the birthing process of expansitory values of a new universe right? So of course there is something troubling about chaotc environments, but also the nice fluidic forms of expression that would seem to reveal the dynamics of nature in overlaid valuation, of motion.

Having come to a surface valution of expansitory features such as a measdure of the earth in a "time variable mode", makes much more sense to me having accumulative histories and use of Grace, that we would now say hey, ourviews of spherical and round earth we live on has a certain new feature about it, that does not seem so pretty. Well, we defined the valuation gravitationally over this whole planet and it is encased. So I see it as a bubble defined to it's mass context and density variations etc.

Mathematical Models

"Backwards" might mean, from a "5d understanding" to a three dimensional fabrication. You had to understand how the 5d world is explained here, before judgement is cast.

While I would like nothing more then to cater to the struggles of good professors, to the aims they had set for themselves, it has come to me, that mathematic modelling is culminative. Where does this point too?

If indeed a good understanding has been established, regardless of string theory or any association for that matter, this stand alone item on Langlands or what ever one might associated it too, would of itself, painted it's own picture and further associations, from a basis and exposition of that mathemtical derivative.

It does not have to be associated it either to historical figures (like Plato), other then the ones we trace to the orignation and factors that brought other areas of mathematics together. This should be readily available, by doing searches which I did. Although I sahl say there is much that needs to be resolved, in our determinations of truth. I am working on understanding this here.

But then to take it further, I wanted to illustrate this point just a little more on imaging.

Thomas Banchoff has set this straight in terms of modelling in computerization and what it can do for us in 5D expressions? While in the Wunderkammern of this site such model although concretize in form have relative associations in computerization value much like the model of the Klein bottle exemplified of itself in acme products.

x = cos(u)*(cos(u/2)*(sqrt_2+cos(v))+(sin(u/2)*sin(v)*cos(v)))

y = sin(u)*(cos(u/2)*(sqrt_2+cos(v))+(sin(u/2)*sin(v)*cos(v)))

z = -1*sin(u/2)*(sqrt_2+cos(v))+cos(u/2)*sin(v)*cos(v)

or in polynomial form:

Yep, no doubt about it: Your Acme's Klein Bottle is a real Riemannian manifold, just waiting for you to define a Euclidean metric at every point.

Felix Klein

When Klein became a Professor in Leipzig in 1880, he immediately started to acquire mathematical models and establish a model collection. Klein was a geometer and used these plaster models in his university lectures. Model collections became very popular in mathematics departments world-wide. When he then moved to Göttingen, Klein, together with his colleague Hermann Amandus Schwarz, expanded his new department's collection of mathematical models and instruments so much that at peak times up to 500 models were on permanent display. When you think that a model could cost about £150, this was a major investment in education.

This idea is and has been lost to the model archives of the Wunderkammern respectively and such a resurgence is making it's way back. Such O ->an outward expression is no less the road taken in artistic expression entitled, "When is a Pipe a pipe," exemplified in the manifestation of mathematical modelling.

Our computer screen although reduced to two dimensional factors, is a fifth dimensional expression, in terms of our visulization capability. The work then is translation of computerization, to imaging.

The "Torso" once mathematically derived, and help enlisted in the Cave, brought mathematical equation through a complete rotation in the Calabi Yau. Until then, the efforts relied on by men/woman whose visualization capabiltes, were equivalent to 5d imaging?

So if I ask, if there is a image of a culminative mathe, without out this the understanding is not complete.

Trademarks of the Geometer II

John g,



Lubos had some claim about Martian ancestry, but we know that he jests?:)

So I do not want to use up to much more of Lubos's blog for this conversation even though he pushes the envelope. Perhaps, you will start your own blog?

Genuis at Work
(Picture credit: AIP Emilio Sergè Visual Archives)

Lastly, I have know certain "trademarks of people" like Dirac as "the geometer" is inherent at the foundations of such psychologies(even I like to dabble in model developement ex: John Venn), with current information Peter Woit brought forward, are key indicators to me of visualization capabilties that are every advanced for this abstract world. Clifford demonstrates like a Rorshach Ink blot as an experiment, with the picture on that "blackboard"?

Wassily Kadinsky

His art and in composition? As a reference made in the comment section of another artist in realtion to Clifford's article, Wassily came to mind.

The term "Composition" can imply a metaphor with music. Kandinsky was fascinated by music's emotional power. Because music expresses itself through sound and time, it allows the listener a freedom of imagination, interpretation, and emotional response that is not based on the literal or the descriptive, but rather on the abstract quality that painting, still dependent on representing the visible world, could not provide.

How would it be possible to extend let's say the idealization to a history of geometries without establishing this basis in thought? There had to be expanded frontiers that would let people develope towards objective goals in science, based on science and herein lies the difficulites with the INKBLOt. As by subjective interpretaion based on current knowledge bases, these views would be very much different then what someone "well trained might see"? Let alone, classify it to any geometric formulation.



Surely inkblot below is a mask? I have one in relation, drawn from the antiquities of evolution. If you ever visit the Drumheller museum, in Alberta Canada, you'll identify it for sure?:) So what is this "projection" based on?



Keep it simple

I like to keep it simple, and fragmentary indications of my blog entries can be accumulative of something deeper and very revealing about such a nature of these geometers I like to talk about. I had to learn this history in order to understand where we had been taken with Einstein's General Relativity. Another one, who understood after Grossman that such geoemters were needed to bring consistancy to the undertanding of theoretical developement.

I would not have gotten this far without bloggists, like Lubos, Peter, Sean, Clifford, Mark and the rest of the Cosmic Variance group, who are most kind in helping us lay people to recognize issues in ways and helping to develope info according to the academic world. This has been truly a grace.

Entries of my own, would have past as incoherent states of unfamiliar words, on a very simple level dealing with the societal world we live in. I now find comfort, that I am not so strange, in this geometer sense.

Have I excelled myself? On the contrary, its about learning about ourselves and who we are, is all. If it past the stage of pure mathematics( towards that center), then why would we not see that this outward development had some psychological model in which to adorn oneself in this mandalic sense.

Sean, makes brief link entree in that blog of Cliffords on Cosmic Variance.

Indeed, this is where such models helped me understand from a Jungian sense, that such a map had to exist, and models built. This can only come from experience, and from the direction of coming from that center. Why I ask Lubos, or anyone for that matter, about where ideas come from. Here you would see such a flavour and distinction in Plato's ideology, about what could manifest in any mind, and not just any one select part of this society.

No doubt, that like any fisherman's hook, you would need to have some valuation and inclination to manifest. As you develope through any model apprehension, where you could add more ideas to the pot. For a further invitation for probilities to manifest in our everyday conversations. Are some of these "inductions and deductions" always right? Of course not, and this is where our education comes in, and the saving grace of bloggists in general.

Who would of thought by using "internet world" the bloggists could have ever reached the "periphery" of this society? I'll intoduce you to another foreigner whose concept defintiely challenges the mind in this bubble sense. In a way I helped him to develope further, and him, I.

UV Fixed Point

Clifford draws our attention to further talks here in his post and directs us to what Jacque Distler has to say.

I must say this is a refreshing look with Jacques contribution to further the layman point of view. Such links are worth while in the advancement of the "sentient being" that Clifford might have thought the computer world could have developed into once we assign our geometries to that world, as we would of numerical relativity and the designs we get from this look. Thomas Banchoff should be commended forthis contribution to fifth dimensional idealism in the computer world, with the notion of graphics design as a whole new approach to this understanding. Who said mathematics guys are a little to abstract for the laymen view?

Jacque Distler:

Yeah. I had hoped I was being clear.

I meant a nontrivial (non-Gaussian) UV fixed point. A Gaussian fixed point would be too much to hope for.

Now you must know that to see what he was saying, "Gaussian coordinates" determined below this post helped me to relate what was being said here. But more then this the statement of Jacques orientates what might be further implied and what had missed in my thinking.

So just to carry on a bit with this point "P" in gaussian coordinated of frame of UV, what realization exists that we could not find some relevance here in the geometry to have further exploited the mind's capabilties by venturing into the Wunderkammern of thinking. By association, of Nigel Hitchin's "B Field manifestations geometries" to realize that althought these might be limited to what Jacque is saying , then what value this geometry if we can not see the landscape as something real in time variable measures?

That we might attribute a globe, that while spherical in it's design, holds much more in it's determination. That while it might issue it's electronmagnetic field of lines, that it too could have found greater relevance in the issues of Quantum gravity, with those same inclinations of time variablenesss, that I allude too?



What am I missing that such events held to the brane in fermion distinction would not find boson production off the brane, as real as, the topic of time variableness that we might issue in geometrical feature of a globe. A globe, that is very bumpy indeed. Is this thinking limited in terms of landscape valuation? Not only in terms of brane and fermionic response, but of the real live correlation of the topic of branes in a more realistic sense, held to these geometries?

While indeed such B Field Manifestation becomes real in tangibles in our arguement of where our UV perspective might be held too, then "P" becomes of value in time variablemess, as a landscape ideology spread throughtout the brane world features? While it is also intriciately linked to our formation of landscape futher out in the recognition of the bumpy world?

So while we might see this landscape in terms of photon calorimetric association with Glast, what value besides gauusian coordinate might be freed, when we see dimensinal sigificance being represented with Glast as well. Is this thinking wrong?

Anomalistic Features of Gold Fish and Ant World?

I was reading Mark Trodden's blog called, "Orange Quark" for reading, and he pointed out the following article. In Praise of Hard Questions, by Tom Siegfried

Geometric basis underlying science? I see this tendency of many to the Halls of records, museums, and whatever you like, to keep current for all us folks outside academia.

These are important historical correlations to draw from. These are wonderful connections to the fathers/mothers of science. Distinctive historical figures who embue science with their particular inflections and bend.

Should we dismiss the motivations of those who are driven by "anomalistic behaviors"? Remember Einstein in his youth and the compass? What are we ignorant of in such a case?

We know well, that such measures, if not supported, cannot be easily removed from the memories. Can be relinguished to subjective interpretations. Should not be ruled inadmissable:)Yet, it can drive the motvation of youth in that case t hard and fsat rules of order?

Had there ever been a time where a scientist had seen something that ran contrary to everything they know? It had to be at the front line, or how would anomalistic valuation had ver been entertained? Had been seen by a reputable scientist and held in the idealization of the Einstein who at his time, "lacked comprehension" but was moved.

Here I point out David Gross's statement and context supplied by Tom Siegfried .

Science's greatest advances occur on the frontiers, at the interface between ignorance and knowledge, where the most profound questions are posed. There's no better way to assess the current condition of science than listing the questions that science cannot answer. "Science," Gross declares, "is shaped by ignorance."

Yes I think we all understand.

So indeed we see then that all the forebears of our science then had something in common as they sought to geometrically express the abstract, and in my line of thinking, runs the Wunderkammer models. These are hard and concrete models in glass cases.

Maxwell understood this in Gauss and Faraday, and Einstein, understood this in Riemann? Sachherri elucidating beyond the limits of Euclids postulates 1-4, paved the way for a new dynamcial world? So how strange indeed that Sean Carroll would give us a sixty second explanation on extra dimensions. Have we eluded to an "aspect of mind" in abstraction?

Extra dimensions sound like science fiction, but they could be part of the real world. And if so, they might help explain mysteries like why the universe is expanding faster than expected, and why gravity is weaker than the other forces of nature.
Three dimensions are all we see -- how could there be any more? Einstein's general theory of relativity tells us that space can expand, contract, and bend. If one direction were to contract down to an extremely tiny size, much smaller than an atom, it would be hidden from our view. If we could see on small enough scales, that hidden dimension might become visible.

Sean, what shall you say to Peter Woit, who might say to you. "We are not Ants?"

So this sixty second explanation now presents itself, for the "mantra induced introspection" that one wonders, what the heck might Sean be talking about? Is there a world somewhere that that exists much like "ant world" in which we take part in?

How strange indeed then that the mind has been taken to Ant World, so that we may see, the angles of perception greatly ehanced for us? Where in the real world, walking straight lines is a "balancing act" when we engage the dynamcial qualites of science, that although engineered, also speak to the dynamcial relation underlying our everyday world.

So how shall such analogies then prepare us for the hard questions of science? Can we see now where such abstractions has moved science and the road shall lead us through to the idea of KLein's Ordering of Geometeries? Have we entered a new dynamcial realm of ant world, and together with Michio Kaku, created the new animated "goldfish world" as well, who see very much different then we see from the bridge?

Who is it that now sees and send our minds into "ants and goldfish?"

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?