Projective Geometries

Action at a Distance

Now ths statement might seem counterproductive to the ideas of projective geometry but please bear with me.

In physics, action at a distance is the interaction of two objects which are separated in space with no known mediator of the interaction. This term was used most often with early theories of gravity and electromagnetism to describe how an object could "know" the mass (in the case of gravity) or charge (in electromagnetism) of another distant object.

According to Albert Einstein's theory of special relativity, instantaneous action-at-a-distance was seen to violate the relativistic upper limit on speed of propagation of information. If one of the interacting objects were suddenly displaced from its position, the other object would feel its influence instantaneously, meaning information had been transmitted faster than the speed of light.

Test of the Quantenteleportation over long distances in the duct system of Vienna Working group Quantity of experiment and the Foundations OF Physics Professor Anton Zeilinger

Quantum physics questions the classical physical conception of the world and also the everyday life understanding, which is based on our experiences, in principle. In addition, the experimental results lead to new future technologies, which a revolutionizing of communication and computer technologies, how we know them, promise.

In order to exhaust this technical innovation potential, the project "Quantenteleportation was brought over long distances" in a co-operation between WKA and the working group by Professor Anton Zeilinger into being. In this experiment photons in the duct system "are teleportiert" of Vienna, i.e. transferred, the characteristics of a photon to another, removed far. First results are to be expected in the late summer 2002.

One of the first indications to me came as I looked at the history in regards to Klein's Ordering of Geometries. Now I must admit as a layman I am very green at this understanding but having jumped ahead in terms of the physics involved, its seems things have been formulating in my head, all the while, this underatnding in terms of this "order" has been lacking.

In Euclidean geometry, the basic notions are distances and angles. The transformations that preserve distances and angles are precisely the rigid motions. Effectively, Klein's idea is to reverse this argument, take the group of rigid motions as the basic object, and deduce the geometry. So a legitimate geometric concept, in Euclidean geometry, is anything that remains unchanged after a rigid motion. Right-angled triangle, for example, is such a concept; but horizontal is not, because lines can be tilted by rigid motions. Euclid's obsession with congruent triangles as a method of proof now becomes transparent, for triangles are congruent precisely when one can be placed on top of the other by a rigid motion. Euclid used them to play the same role as the transformations favored by Klein.

In projective geometry, the permitted transformations are projections. Projections don't preserve distances, so distances are not a valid conception projective geometry. Elliptical is, however, because any projection of an ellipse is another ellipse.

So spelt out here is one way in which this progression becomes embedded within this hisotry of geometry, while advancing in relation to this association I was somewhat lifted to question about Spooky action at a distance. WEll if such projective phase was ever considered then how would distance be irrelevant(this sets up the idea then of probabilistic pathways and Yong's expeirment)? There had to be some mechanism already there tht had not been considered? Well indeed GHZ entanglement issues are really alive now and such communication networks already in the making. this connection raised somewhat of a issue with me until I saw the the phrase of Penrose, about a "New Quantum View"? Okay we know these things work very well why would we need such a statement, so I had better give the frame that help orientate my perspective and lead to the undertanding of spin.



Now anywhere along the line anyone can stop such erudication, so that these ideas that I am espousing do not mislead. It's basis is a geometry and why this is important is the "hidden part of dirac's mathematics" that visionization was excelled too. It is strange that he would not reveal these things, all the while building our understanding of the quantum mechanical nature of reality. Along side of and leading indications of GR, why would not similar methods be invoked as they were by Einstein? A reistance to methodology and insightfulness to hold to a way of doing things that challenegd Dirac and cuased sleepless nights?



Have a look at previous panel to this one.

While indeed this blog entry open with advancements in the Test in Vienna, one had to understadn this developing view from inception and by looking at Penrose this sparked quite a advancement in where we are headed and how we are looking at current days issues. Smolin and others hod to the understnding f valuation thta is expeirmentally driven and it is not to far off to se ehosuch measure sare asked fro in how we ascertain early universe, happening with Glast determinations.

Quantum Cryptography

Again if I fast forward here, to idealization in regards to quantum computational ideas, what value could have been assigned to photon A and B, that if such entanglement states recognize the position of one, that it would immediately adjust in B?

Spooky At any Speed

If a pair of fundamental particles is entangled, measuring an attribute of one particle, such as spin, can affect the second particle, no matter how far away. Entanglement can even exist between two separate properties of a single particle, such as spin and momentum. In principle, single particles or pairs can be entangled via any combination of their quantum properties. And the strength of the quantum link can vary from partial to complete. Researchers are just beginning to understand how entanglement meshes with the theory of relativity. They have learned that the degree of entanglement between spin and momentum in a single particle can be affected by changing its speed ("boosting" it into a new reference frame) but weren't sure what would happen with two particles.

So there is this "distance measure" here that has raised a quandry in my mind about how such a projective geometry could have superceded the idea of "spooky things" and the issues Einstein held too.

So without understanding completely I made a quantum leap into the idealization in regards to "logic gates" as issues relevant to John Venn and introduced the idea around a "relative issues" held in my mind to psychological methods initiated by such entanglement states.

As far a one sees here this issue has burnt a hole in what could have transpired within any of us that what is held in mind, ideas about geomtires floated willy Nilly about. How would such "interactive states" have been revealled in outer coverings.

The Perfect Fluid

Again I am fstforwding here to help portray question insights that had been most troubling to me. If suych supersymmetrical idealizations arose as to the source and beginning of existance how shall such views implement this beginning point?

So it was not to unlikely, that my mind engaged further problems with such a view that symmetry breaking wouldhad tohave signalled divergence from sucha state of fluid that my mind encapsulated and developed the bubble views and further idealizations, about how such things arose from Mother.

What would signal such a thing as "phase transitions" that once gauged to the early universe, and the Planck epoch, would have revealled the developing perspective alongside of photon developement(degrees of freedom) and released information about these early cosmological events.

So I have advance quite proportinately from the title of this Blog entry, and had not even engaged the topological variations that such a leading idea could have advanced in our theoretcical views of Gluonic perceptions using such photonic ideas about what the tragectories might have revealled.

So indeed, I have to be careful here that all the while my concepts are developing and advanced in such leaps, the roads leading to the understanding of the measure here, was true to form and revalled issues about things unseen to our eyes.

It held visionistic qualities to geometric phases that those who had not ventured in to such entanglement states would have never made sense of a "measure in the making." It has it's limitation, though and why such departures need to be considered were also part of my question about what had to come next.

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.

John Venn

The early historical work can be derived from personages. Helps sometimes to illucidate the avenue and abtractions that seem only fitted for the abstract mind?

Do people like to deal with such issues? I am finding that as I am learning, I am tryng to find the means with which to express myself, so that such a basis is understood when I bring togehter the thoughts I like to do, into other areas. So it is necessary to see how such abstract avenues play their role in my "fantasy journey's" and then introduce the deepr pursuate to explain myself more coherently.

A painting of John Venn by Charles E. Brock. Photograph by Christopher Hurst, Hamilton-Kerr Institute, University of Cambridge

John Venn (August 4, 1834 - April 4, 1923), was a British mathematician, who is famous for conceiving the Venn diagrams, which are used in many fields, including set theory, probability, logic, statistics, and computer science.

He was born in Hull, Yorkshire. He entered Gonville and Caius College, Cambridge in October 1853 and graduated in 1857. Shortly after graduating he was elected a fellow of the college. He was ordained as a deacon at Ely in 1858 and became a priest in 1859. In 1862 he returned to Cambridge as a lecturer in moral sciences.

So having lead one to the esence of this individual I wanted to introduce a journey that combined a few different avneues, and how I go to that point. But before I do this, the image with which I wanted to supply, will do wonders on the unification idea manifesting in my own mind.

Thomas Young's Double Slit Experiment

The double-slit experiment consists of letting light diffract through two slits producing fringes on a screen. These fringes or interference patterns have light and dark regions corresponding to where the light waves have constructively and destructively interfered. The experiment can also be performed with a beam of electrons or atoms, showing similar interference patterns; this is taken as evidence of the "wave-particle duality" explained by quantum physics.

Society and all it's function might have seemed beyond the approach of a method to determination that could underlie it's very existance by functions that would have never made sense had they not been curtailed to a way of seeing. I exploit this ability to see underneath society and its basis, by bringing together perspective, hopefully in a sound mangagement style and artistic endeavor, no less then the work of Lewis Carroll and his fictous name sake, that will be revealled soon enough.



This image below will serve it's purpose when it comes time, so being part of this overall post, this directs us to the amazing value of mathematicians as they exercizes their creatve abilities beyound the abstract frames they have give themself.

Lewis Carroll's fame is universal. I can easily cite a couple dozen books that mention him or quote from his books. Temptation to quote from Alice's experiences with which so many people can identify, is indeed great. But the trend may be reversing. In the introduction to a book I have recently come across, the author found it necessary to mention that in the whole of the book there is not a single reference to either Alice in Wonderland or Through the Looking Glass - the two books that made the name of Lewis Carroll a household item the world over. However, his other works are either forgotten or known far less. In real life he was a mathematician C. L. Dodgson with deep interest in symbolic logic and logical reasoning. I have described elsewhere one of his probability and the doublets puzzles.

Now for some, the Feynmen diagrams become a useful toy model for defining the interatcive phases, and for me, being Junior in these aspects, I come with a lot of speculation, but no less the need for something to hang my hand on. It was interetsing for me to see that such defintions and pathways would have been exemplified by such drawings to hold the perspectve to specific interactve phases.

Now a given wide a berth to my speculation, from Young to Feynmen, I saw this content from Dirac's early work, as example used the matrice design? The work of Feynmen, leading from this. Now not to spread the willy nilly fate of wrong information, I would have to qualify this statement, and I wil do so at a later date. I will watch for such statements in my journeies and draw from them for support, if given. I would not lesson this view, by stating the topological pathway would have been incorporated into a design of strings no less held to such views of feynmen lines, that it would have explained these interactve phases as well. I think peope do not understand this very well?

So the work her ehas been lead nto a area of math that defnes the thinking process I have in a way that might not have been considered before? I wil expound even greater to confuse the masses, by introdcution of other areas that I found explicable by uniting avsion of such phase as to ask what value would GHZ entnaglement serve, but to have found the questions of the like sof Gerard t' hooft haunting when it comes to the questions also posed by Penrose. Do we need a new quantum mechanical view?

This highlighted my thinking and of course directed it too the state of examination given by Smolin and others, as we expound greatly on the essecne of Thomas young and his expeirment, and the basis bneeded for detrmination of the Trigger?:) I bet some see the principals now shown as I lead into other areas soon?:)

You had to understand, that Alice and Bob serve their purposes in a strange wonderful way. That one asks where had the photon gone, in it's illustrous journey of possibile pathways, that we did not wonder what intiatied this process? Would such a signature have highlighted the view with the question of the rigger signifying some deeper inherent basis of existance. That signalled other views to manifest into the world of gravtonic perceptions, no less dictating our understanding of time variable measures?

The Looking Glast