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.

The Succession of thinking

How far indeed the the imagination can be taken to see such processes enveloped in how we percieve these changes all around us. Why is gravity so weak, here and now. I have jumped ahead but will lead into it from the other end of this article.

Never before had I encountered the reasoning of imaging behind the work of "conceptual frameworks" now in evidence. In how a mathmatician, or a scientist, like Einstein or Dirac, had some basis at which the design, of all that we endure, would have its's counterpart in this reality as substantial recognition of what must be done.

I don't think anyone now in the scientific arena needs to be reminded about what it takes to bring theory into the framework of cultural and societal developement, to see how it all actually is working. On and on now, I see this reverberating from Lisa Randall to all scientists that we encounter from one blog to the next, a recognition and developement of this visualization ability.

That Famous Equation and You , By BRIAN GREENE Op-Ed Contributor in New York Times, Published: September 30, 2005


Brian Greene:

After E = mc², scientists realized that this reasoning, however sensible it once seemed, was deeply flawed. Mass and energy are not distinct. They are the same basic stuff packaged in forms that make them appear different. Just as solid ice can melt into liquid water, Einstein showed, mass is a frozen form of energy that can be converted into the more familiar energy of motion. The amount of energy (E) produced by the conversion is given by his formula: multiply the amount of mass converted (m) by the speed of light squared (c²). Since the speed of light is a few hundred million meters per second (fast enough to travel around the earth seven times in a single second), c² , in these familiar units, is a huge number, about 100,000,000,000,000,000.

There are two links here.One by Peter Woit with reference to article and one toSean Carroll who further illucidates the article by Brian Greene.

So here I am at the other end of this referenced article, that other thoughts make their way into my mind. Previous discussison ongoing and halted. To todays references continued from all that we had encountered in what General Relativity surmizes.

That this issue about gravity is very real. So that's our journey then, is to understand how we would percieve the strength and weakness through out the spacetime and unification of a 3 dimension space and one of time, to some tangible reality within this coordinated frame Euclidean defined.

The Succession of Thinking

Mark helps us see in a way we might not of considered before.

Dark Matter and Extra-dimensional Modifications of Gravity

But the issue is much more complicated then first realized if we take this succension of thinking beyond the carefuly plotted course Einstein gave us all to consider.

Plato on Sep 27th, 2005 at 10:23 pm We were given some indications on this site about the state of affairs with Adelberger. Do you think this time span of proposed validation processes, were constructively and experimentally handled appropriately through it’s inception? As scientists would like to have seen all such processes handled in this respect?

So indeed I began to see this space as very much alive with energy that had be extended from it's original design to events that pass through all of creation, then how indeed could two views be established in our thiniking, to have Greene explain to us, that the world holds a much more percpetable view about what is not so understood in reality.

An Energy of Empty Space?

Einstein was the first person to realize that empty space is not nothingness. Space has amazing properties, many of which are just beginning to be understood. The first property of space that Einstein discovered is that more space can actually come into existence. Einstein's gravity theory makes a second prediction: "empty space" can have its own energy. This energy would not be diluted as space expands, because it is a property of space itself; as more space came into existence, more of this energy-of-space would come into existence as well. As a result, this form of energy would cause the universe to expand faster and faster as time passes. Unfortunately, no one understands why space should contain the observed amount of energy and not, say, much more or much less.

All the while the ideas that would leave gravity without explanation in a flat euclidean space, gravity would have been left to that solid response without further expalnatin in a weak field manifestation. But it was always much more then this I think.

While being caution once on what the quantum harmonic oscillator is not, Smolin did not remove my thinking of what was all pervasive from what this "empty space" might have implied, that heretofor "it's strength" was a measure then of a bulk, and what better way in which to see this measure?

Taken in context of this succession, this place where such conceptual framework had been taken too, it was very difficult not to encounter new ways in which to understand how gravity could changed our perceptions.

Thalean views were much more then just issues about water and all her dynamical explanations. It presented a new world in which to percieve dynamical issues about which, straight line thinking could no longer endure. A new image of earth in all it's wander, no less then Greene's analysis to how this famous equation becomes evident in our everyday world. It presented a case for new geometries to emerge. Viable and strengthened resolve to work in abstract spaces that before were never the vsion of men and women who left earth. Yet it all had it's place to endure in this succession that we now have adbvanced our culture in ways that one would not have thought possible from just scientific leanings.

So now I return myself to Einstein's allegorical talk on what concept had taken, when a scientist had wondered on the valuation of time.

On mathematics, imagination & the beauty of numbers

It's always nice to see this kind of infomration, because indeed if one were to start later on in life, then why not learn new things like mathematics. Especially, if it seems to be thta there is some consistancy in thought about geometry, that had been taken hold of, and leads the thinking mind capable.

Dialogue between Barry Mazur & Peter Pesic
Barry Mazur:

I can’t answer that question, but I can offer some comments. A person’s ½rst steps in his or her mathematical development are exceedingly important. Early education deserves our efforts and ingenuity. But also here is a message to any older person who has never given a thought to mathematics or science during their school days or afterwards: You may be ready to start. Starting can be intellectually thrilling, and there are quite a few old classics written in just the right style to accompany you as you begin to take your ½rst steps in mathematics. I’m thinking, for example, of the old T. C.Mits series, or Tobias Dantizg’s wonderful Number: The Language of Science, or Lancelot Hogben’s Mathematics for the Millions. Moreover, one should not be dismayed that there are many steps– there is no need to take them all. Just enjoy each one you do take

.

Make it Fun

Like Alice in Wonderland or views on the Looking Glast, it was not to hard to figure out that mathematicians like to tell stories too. Bring the latest together in a way that the layman can accept at the level societal minds do. It is interesting indeed in facing the strange and wonderful world of scientists and mathematicians in their abstract mood.

The New World of Mr. Tompkins, by George Gamow and Russell Stannard, Cambridge, ISBN 0 521 63009 6
After sending the piece to several large circulation magazines and receiving impersonal rejection slips, Gamow put it to one side until his physicist friend, Sir Charles Darwin (the grandson of the author of The Origin of Species), suggested sending it to C P Snow, then the editor of Discovery magazine, published by Cambridge University Press. The text was immediately accepted and the discerning Snow demanded more.
Mr Tompkins tries valiantly to follow dry science lectures, but easily falls asleep. However, all becomes clear in his vivid dreams. Soon the articles were collected into Mr Tompkins in Wonderland, published in 1940, followed by Mr Tompkins Explores the Atom in 1944. Each was a major success and the two volumes were reissued with additional material as a single volume in 1965. This reissue alone was reprinted some 20 times.

Plectics

Murray Gellman:

The name that I propose for our subject is "plectics," derived, like mathematics, ethics, politics, economics, and so on, from the Greek. Since plektos with no prefix comes from *plek- , but without any commitment to the notion of "once" as in "simple" or to the notion of "together" as in "complex," the derived word "plectics" can cover both simplicity and complexity.

It is appropriate that plectics refers to entanglement or the lack thereof, since entanglement is a key feature of the way complexity arises out of simplicity, making our subject worth studying.

Dirac's Hidden Geometries

I find this interesting because I like to visualizze as much as possible, and I sometimes think the basis of the leading ideas in science would had to follow a progression. Klein's Ordering of Geometries was one such road that seem to make sense. The basis of relativity lead through in geometrical principals?

Such an issue with string theory had to have such a basis with it as well, although how do you assign any views to the very begininngs of the universe below planck length? Well there are images to contend with what are these and how are they derived? Rotations held in context of te progression of this universe and all thoughts held to the very nature of particle creation and degrees fo freedom?

[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.

While I am very far from being the mathematician, I understand that this basis is very important. Such summations in mathmatical design, leave a flavour, for conceptiual ideas to form in images, so I understand this as well. It is a progression of sorts I think, as I read, and learn. Geometry lies at the very basis of all such progressions in science?

So Feynmans toy models arose from the ideas of Dirac?

Professor Shiing-Shen Chern

HOUSTON JOURNAL OF MATHEMATICS
Editorial, Electronic Edition Vol. 28, No. 2, 2002

Shiing-Shen Chern -- famed mathematicianCarrie Sturrock, Chronicle Staff Writer
Thursday, December 9, 2004

He was a great mathematician partly because of the quality of his research as well as his ability to convey it to other people, UC Berkeley mathematics Professor Robin Hartshorne said. Professor Chern turned the once- dormant field of differential geometry, which deals with the mathematical description of geometric figures, into a lively field of study. He had the greatest impact on global differential geometry and complex algebraic geometry, which are fundamental to many areas of mathematics and theoretical physics.

Big Ideas.....To String Theory

Plato said:

yes to Gauss and gaussian coordinates, not forgetting, Saccheri, Bolyai and Lobschevasky along this lineage of geometers

On the Hypotheses which lie at the Bases of Geometry

So A continuation from this, and reference to important papers for consideration.

I was actually looking for papers on S.S.Chern and I have been having difficulty tracking down one of his papers entitled,"Relativity and Post Reimannian Differential Geometry," published in 1980. As I look, I usually come across interesting sites for consideration. They do indeed lead from one spot to another willy-nilly.

So I thought I would show the transition to topics that I compiled for reference in relation to string theory.

So having gone through a list here as follows, I came upon the article from a site called "Big Ideas". It was nice then, that I link to the site in question and the article for consideration. Talk about getting off the beaten path.:)

My intentions was to see how Gauss's and S.S. Chern's work correlated together and developed in line with Reimann. Hence the paper in question I was looking for. If anything had change my perspective, Gauss and Reimann were instrumental here and the understading of the metric. Gaussian coordinates help united much for me into the picture General Relativity had taken me too in see the dynamcial nature of the graviational field.

Big Ideas



It is of course from 2003, but always interesting nonetheless.




I understand Clifford's hesistancy on articles that have come out and some trepidation also seen by P.P. Cook on the issue Horizon of Hawkings in his article here. My focused is well set to this horizon as well, as th e question of blackhole types etc, and how such theoretical positions arise fromthis horizon. This was important to me that I move to the understanding of conformal ideas from tha horizon.

But articles, as best they can, hopefully can bring the lay person up to speed on what these ladies and gentlemen are doing with string theory and such. They help me in the generalized direction, so I hope all things are not to lost for Clifford and Paul in their entrancement of observation. "Disgust" to something fine in the media of consideration.

I noticed Paul's link to Jan Troost's site and have seen that site develope from inception, so it was interesting to continue to see the summation of string theory on his site as well. There are really good sites out there that I have kept track of, to help orientate my thinking in regards to to theoretical thinking at it's finest.

The Total Field

For me this title above strikes a cord somehow in the struggle and regard, leading in our comprehensions to the extension of the standard model. By bringing gravity into the picture and descibing the graviton teaming in the bulk of expression.

The general theory of relativity is as yet incomplete insofar as it has been able to apply the general principle of relativity satisfactorily only to grvaitational fields, but not to the total field. We do not yet know with certainty by what mathematical mechanism the total field in space is to be described and what the general invariant laws are to which this total field is subject. One thing, however, seems certain: namely, that the general principal of relativity will prove a necessary and effective tool for the solution of the problem for the toal field.

Out of My Later Years, Pg 48, Albert Einstein

Well now the reason why this paragraph strikes such a chord with me, has everything to do with the information that I have progressed through, in order to reach this vision Lisa Randall does not think one asa layman is capable of? Now I should be fair here, and I am not judging personalities, but the essence of the statements about "observation" and "vision".

Lisa Randall:

Most people think of "seeing" and "observing" directly with their senses. But for physicists, these words refer to much more indirect measurements involving a train of theoretical logic by which we can interpret what is "seen."

Now in my quest for comprehension, such building has gone on in my conceptual foundations, are ones that we are carefully lead through in theoretical developement. Ah so we see where such extensions have gone beyond th elayan's view then? To have such things of expression, in the computer world, as numerical relativity, is a nice way in which to round out the data and experience. But as she points out, we are talking about Physicists.

Lisa Randall:

Remarkably, we can potentially "see" or "observe" evidence of extra dimensions.

Those Russion Dolls

Well now. I have this strange picture in my head about "time variable images" we seen of the earth in measure, and such a statement above, by Einstein. It is information on the "total field" that struck immediately in my mind about all those things that lead one through to the comprehension of general relativity. It is indeed, about "gravity" and it indeed seen in the larger aspects of the cosmological scale. But then, how would such a thing take us down to scale in our look at quantum mechanical views. Other components of earth that efect time avraiableness and we are indeed driving this image of scale down to the component parts of our earth?



So I have this picture of earth here. I know its not so pretty, but it describes in greater context the world as you have not seen it before. This advancement in observation, is much more inherent in our culture now, that the grade with which we assign physicists and the lay persons, are really never that far apart. What was accomplished, was that leading infomration and theorectical developement paved the way for an "illustrous view" as to those I impart now. They were already there but never seen in context of each other and as a total field.



So now as I think about Lisa's words, I recognize more deeply the sigificance of how far our vision has been taken, not just in terms of the physicists view, but of how far we had been taken in layman terms as well. What then else retains this view about the total field that I had not show and in it writing, other images come to mind as follows.

So developing this sense in terms of relativity and views of Einstein in regards to the total filed had consequences in my mind about how we view things in new ways.

If conceived as a series of ever-wider experiential contexts, nested one within the other like a set of Chinese boxes, consciousness can be thought of as wrapping back around on itself in such a way that the outermost 'context' is indistinguishable from the innermost 'content' - a structure for which we coined the term 'liminocentric'.

Now it has to be understood, that the total field is one which has inclusiveness such as these boxes indicate, that such views of our blue marble earth, do not consider as we lay "one" over the top of another. Such extensions to our views of earth, lead me to understand the complexity of these views in ways that we had not considered before, and with such a synoptical view, what indeed shall this total field say about earth? So that's where I am at. Much like, Glast, in it's own synoptical view about the range of our vision.

So we have this frame of reference now to consider. Our apprehensions about earth(some who share the climatic valuation) that we can now say, that Inverse square law contains information in relation to "these boxes". That if taken to "new heights" our climatic valuations about this new view of earth, how shall we judge now, that such Kaluza Klein modes held in relation to the expanding nature of this point(circle) can have energy valuations assigned right from the supersymmetrical vision ofa beginning, to have phases (symmetry breaking)with which our views have been generated, in what we see of earth now?



While indeed then, "light had been joined to gravity" how shall we wrap again the views of this earth, in what is now a teaming in this new place, where differences exist in our views. Strengths and weaknesses, are measures in this new abstracted view?

So we have this total view in mind, about the "total field" and I have taken us to a a abstracted space within the idealization of what exists here now as earth arose from some beginning point. To what the earth encapsulates.

How we view then such comsological events has a greater story as we look deep into space, and see the valution of those same cosmological events streaming past all things in existance, that such a gravitational view has arrows pointing in a certain direction. To ideas about comsological expansion and such. This has gone to far I think about our place in this new abstracted view of the universe:)

Point--> Line-->Plane <---> Point<-- String<-- Brane

Under the heading of Klein`s Ordering of the 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.

Now the usual thinking here has been placed under intense thinking by the introduction of a new way in which to look at "geometry" that has gone through a "revision" in thinking.

New trigonometry is a sign of the times

Lubos Motl introduces this topic and link in his blog entry and from this this has caused great consternation in how I am seeing. I see Lisa Randall might counter this in terms of what the brain is capable of, in line with this revisionary seeing, and comparative examples of this geometry Lubos links.

Dangling Particles,By LISA RANDALL
Published: September 18, 2005 New York Yimes

Lisa Randall:

Most people think of "seeing" and "observing" directly with their senses. But for physicists, these words refer to much more indirect measurements involving a train of theoretical logic by which we can interpret what is "seen." I do theoretical research on string theory and particle physics and try to focus on aspects of those theories we might experimentally test. My most recent research is about extra dimensions of space. Remarkably, we can potentially "see" or "observe" evidence of extra dimensions. But we won't reach out and touch those dimensions with our fingertips or see them with our eyes. The evidence will consist of heavy particles known as Kaluza-Klein modes that travel in extra-dimensional space. If our theories correctly describe the world, there will be a precise enough link between such particles (which will be experimentally observed) and extra dimensions to establish the existence of extra dimensions.

But first before I get to the essence of the title of my blog entry, I like to prep the mind for what is seemingly a consistent move towards geometry that has it's basis in applicabilty to physics, and move through GR to a vast new comprehsnsion in non-euclidean geometries. Must we now move backwards that we had gained in insight, or was it recognition of the "length scales" that we now say, how could such a dynamcial view ever be assigned to the eucildean discription under the guise of brane world recognitions?

Moving Backwards?

What exactly do I mean here?

Well the idea is that if you move to fifth dimensional views, and there are ways to wrap this within our "Brains":) We then see the dynamcial nature of our neurons have found acceptable ways in which to see this brane feature. As well as, approaches in use of new processes in geometerical considerations as those linked by Lubos.

Dealing with 5D world



Thomas Banchoff is instrumental here is showing us that fifth dimensional views can be utilized in our computer screens, and such comparisons, reduce to a two dimensional frame, makes it very easy to accept this new way in which to attack the dynamcial nature of reality.

How indeed now could our computer screen act a liason with the reality of our world, when see from screen imagery effects, that all the rules of order have been safely applied for inspection and consistancy in physics approaches.

The Earth in Gamma Rays

This is a false-color image of the Earth in three gamma-ray energy bands, analogous to the colors red (lower energy), green (mid energy) and blue (higher energy) in the visible spectrum. The lower right shows a composit image.(Image credit: NASA/CGRO/EGRET/ Dirk Petry)

But Petry created this gamma-ray Earth image to better understand the impact of "local" cosmic-ray and gamma-ray interactions on an upcoming NASA mission called GLAST, the Gamma-ray Large Area Space Telescope. GLAST is planned for launch in 2007. Its main instrument, the Large Area Telescope, is essentially EGRET's successor.