Art and Science

This is going to be quite the blog entry because as little a response might have been from Clifford's links to artistic imagery and it's relation to science. I definitely have more to say.

So being short of time, the entries within this blog posting will seem disjointed, but believe me it will show a historical significance that one would not have considered had one not seen the relevance of art and it's implications along side of science.

Did Picasso Know About Einstein

Arthur Miller

Miller has since moved away from conventional history of science, having become interested in visual imagery through reading the German-language papers of Einstein, Heisenberg and Schrödinger - "people who were concerned with visualization and visualizability". Philosophy was an integral part of the German school system in the early 1900s, Miller explains, and German school pupils were thoroughly trained in the philosophy of Immanuel Kant.

Piece Depicts the Cycle of Birth, Life, and Death-Origin, Identity, and Destiny by Gabriele Veneziano
The Myth of the Beginning of Time

The new willingness to consider what might have happened before the big bang is the latest swing of an intellectual pendulum that has rocked back and forth for millenia. In one form or another, the issue of the ultimate beginning has engaged philosophers and theologians in nearly every culture. It is entwined witha grand set of concerns, one famosly encapsulated in a 1897 painting by Paul Gauguin: D'ou venons? Que sommes-nous? Ou allons-nous?

Scientific America, The Time before Time, May 2004.



Sister Wendy's American Masterpieces":

"This is Gauguin's ultimate masterpiece - if all the Gauguins in the world, except one, were to be evaporated (perish the thought!), this would be the one to preserve. He claimed that he did not think of the long title until the work was finished, but he is known to have been creative with the truth. The picture is so superbly organized into three "scoops" - a circle to right and to left, and a great oval in the center - that I cannot but believe he had his questions in mind from the start. I am often tempted to forget that these are questions, and to think that he is suggesting answers, but there are no answers here; there are three fundamental questions, posed visually.

"On the right (Where do we come from?), we see the baby, and three young women - those who are closest to that eternal mystery. In the center, Gauguin meditates on what we are. Here are two women, talking about destiny (or so he described them), a man looking puzzled and half-aggressive, and in the middle, a youth plucking the fruit of experience. This has nothing to do, I feel sure, with the Garden of Eden; it is humanity's innocent and natural desire to live and to search for more life. A child eats the fruit, overlooked by the remote presence of an idol - emblem of our need for the spiritual. There are women (one mysteriously curled up into a shell), and there are animals with whom we share the world: a goat, a cat, and kittens. In the final section (Where are we going?), a beautiful young woman broods, and an old woman prepares to die. Her pallor and gray hair tell us so, but the message is underscored by the presence of a strange white bird. I once described it as "a mutated puffin," and I do not think I can do better. It is Gauguin's symbol of the afterlife, of the unknown (just as the dog, on the far right, is his symbol of himself).

"All this is set in a paradise of tropical beauty: the Tahiti of sunlight, freedom, and color that Gauguin left everything to find. A little river runs through the woods, and behind it is a great slash of brilliant blue sea, with the misty mountains of another island rising beyond Gauguin wanted to make it absolutely clear that this picture was his testament. He seems to have concocted a story that, being ill and unappreciated (that part was true enough), he determined on suicide - the great refusal. He wrote to a friend, describing his journey into the mountains with arsenic. Then he found himself still alive, and returned to paint more masterworks. It is sad that so great an artist felt he needed to manufacture a ploy to get people to appreciate his work. I wish he could see us now, looking with awe at this supreme painting."

Art Mirrors Physics Mirrors Art, by Stephen G. Brush

Arthur Miller addresses an important question: What was the connection, if any, between the simultaneous appearance of modern physics and modern art at the beginning of the 20th century? He has chosen to answer it by investigating in parallel biographies the pioneering works of the leaders of the two fields, Albert Einstein and Pablo Picasso. His brilliant book, Einstein, Picasso, offers the best explanation I have seen for the apparently independent discoveries of cubism and relativity as parts of a larger cultural transformation. He sees both as being focused on the nature of space and on the relation between perception and reality.

The suggestion that some connection exists between cubism and relativity, both of which appeared around 1905, is not new. But it has been made mostly by art critics who saw it as a simple causal connection: Einstein's theory influenced Picasso's painting. This idea failed for lack of plausible evidence. Miller sees the connection as being less direct: both Einstein and Picasso were influenced by the same European culture, in which speculations about four-dimensional geometry and practical problems of synchronizing clocks were widely discussed.

The French mathematician Henri Poincaré provided inspiration for both Einstein and Picasso. Einstein read Poincaré's Science and Hypothesis (French edition 1902, German translation 1904) and discussed it with his friends in Bern. He might also have read Poincaré's 1898 article on the measurement of time, in which the synchronization of clocks was discussed--a topic of professional interest to Einstein as a patent examiner. Picasso learned about Science and Hypothesis indirectly through Maurice Princet, an insurance actuary who explained the new geometry to Picasso and his friends in Paris. At that time there was considerable popular fascination with the idea of a fourth spatial dimension, thought by some to be the home of spirits, conceived by others as an "astral plane" where one can see all sides of an object at once. The British novelist H. G. Wells caused a sensation with his book The Time Machine (1895, French translation in a popular magazine 1898-99), where the fourth dimension was time, not space.

The Search for Extra Dimensions
OR Does Dzero Have Branes?

by Greg Landsberg

Theorists tell us that these extra spatial dimensions, if they exist, are curled up, or "compactified."In the example with the ant, we could imagine rolling the sheet of paper to form a cylinder. If the ant crawled in the direction of curvature, it would eventually come back to the point where it started--an example of a compactified dimension. If the ant crawled in a direction parallel to the length of the cylinder, it would never come back to the same point (assuming a cylinder so long so that the ant never reaches the edge)--an example of a "flat"dimension. According to superstring theory, we live in a universe where our three familiar dimensions of space are "flat,"but there are additional dimensions, curled up so tightly so they have an extremely small radius

Issues with Dimensionality

"Why must art be clinically “realistic?” This Cubist “revolt against perspective” seized the fourth dimension because it touched the third dimension from all possible perspectives. Simply put, Cubist art embraced the fourth dimension. Picasso's paintings are a splendid example, showing a clear rejection of three dimensional perspective, with women's faces viewed simultaneously from several angles. Instead of a single point-of-view, Picasso's paintings show multiple perspectives, as if they were painted by a being from the fourth dimension, able to see all perspectives simultaneously. As art historian Linda Henderson has written, “the fourth dimension and non-Euclidean geometry emerge as among the most important themes unifying much of modern art and theory."

And who could not forget Salvador Dali?

In geometry, the tesseract, or hypercube, is a regular convex polychoron with eight cubical cells. It can be thought of as a 4-dimensional analogue of the cube. Roughly speaking, the tesseract is to the cube as the cube is to the square.

Generalizations of the cube to dimensions greater than three are called hypercubes or measure polytopes. This article focuses on the 4D hypercube, the tesseract.

So it is interesting nonetheless isn't it that we would find pictures and artists who engaged themselves with seeing in ways that the art seems capable of, while less inclinations on the minds to grasp other opportunities had they had this vision of the artist? They of course, added their flavor as Salvador Dali did in the painting below this paragraph. It recognize the greater value of assigning dimensionality to thinking that leads us even further had we not gone through a revision of a kind to understand the graviton bulk perspective could have so much to do with the figures and realization of what dimensionality means.



So while such lengths had been lead to in what curvature parameters might do to our views of the cosmos, it wasn't to hard to envision the realistic valuation of graviton as group gatherings whose curvature indications change greatly on what we saw of the energy determinations.

Beyond forms
Probability of all events(fifth dimension)
vvvvvvvvvvvvv           Future-Time
vvvvvvvvvvv                  |
vvvvvvvvv                   |
vvvvvvv                    |
vvvvv                     |
vvv                      |
v                       |
<<<<<<<<<<<<>>>>>>>>>>>now -------|
flash fourth dimension with time     |        
A                       |
AAA                      |
AAAAA                     |
AAAAAAA                    |
AAAAAAAAA                   |
AAAAAAAAAAA                  |
AAAA ___AAAAA                 |
AAAAA/__/|AAAAA____Three dimension          
AAAAAA|__|/AAAAAA               |
AAAAAAAAAAAAAAAAAAA              |
|
___                      |
/__/ brane--------two dimension
\ /              
.(U)1=5th dimension

I hope this helps explain. It certainly got me thinking, drawing it:)

Similarly a hypercube’s shadow cast in the third dimension becomes a cube within a cube and, if rotated in four dimensions, executes motions that would appear impossible to our three-dimensional brains.

So hyperdimenionsal geometry must have found itself describable, having understood that Euclid's postulate leads to the understanding of the fifth. A->B and the field becomes a interesting idea, not only from a number of directions(Inverse Square Law), dimensional understanding of a string, that leads from the fifth dimensional perspective is a point, with a energy value that describes for us the nature of curvature, when extended to a string length(also becomes the point looking at the end, a sphere from a point, and at the same time a cylinder in its length).

In looking at Einsteins fourth dimension of time, the idea of gravity makes its appearance in respect of dimension.

So how is it minds like ours could perceive a fifth dimensional perspective but to have been lead to it. It is not always about points( a discrete perspective)but of the distance in between those points. We have talked about Gauss here before and Riemann.

Who in Their Right Mind?


Penrose's Influence on Escher
During the later half of the 1950’s, Maurits Cornelius Escher received a letter from Lionel and Roger Penrose. This letter consisted of a report by the father and son team that focused on impossible figures. By this time, Escher had begun exploring impossible worlds. He had recently produced the lithograph Belvedere based on the “rib-cube,” an impossible cuboid named by Escher (Teuber 161). However, the letter by the Penroses, which would later appear in the British Journal of Psychology, enlightened Escher to two new impossible objects; the Penrose triangle and the Penrose stairs. With these figures, Escher went on to create further impossible worlds that break the laws of three-dimensional space, mystify one’s mind, and give a window to the artist heart.

Penrose and Quanglement


Order and Chaos, by Escher (lithograph, 1950)

Information on Entanglement

Atomic dance

What the teams at the University of Innsbruck and the US National Institute of Standards and Technology (Nist) did was teleport qubits from one atom to another with the help of a third auxiliary atom.

It relies on a strange behaviour that exists at the atomic scale known as "entanglement", whereby two particles can have related properties even when they are far apart. Einstein called it a "spooky action".

Lots of people haven't a clue what entanglement is all about. That's why this site is most helpful

To understand quantum entanglement, several ideas and words must be explained, especially the idea of a photon. The photon is a key concept in physics, and so critical to entanglement that its behaviours must be fully understood. Yet before delving into the details of photons, we need to understand the world of the very tiny, beginning with waves and atoms.

I would like to thank the person for giving this link, as it can helps others as well as myself understand the entanglement issues much more easily through generalization.

I would like to respond in kind.

The History of Dark Matter Theory

The existence of dark matter was first suggested in the early 1930's by the Swiss physicist Fritz Zwicky who calculated that the radial velocities of eight galaxies was 400 times greater than that expected by the shared gravity of luminous matter in those galaxies. The explanation given by Zwicky to his extraordinary find was to suggest the existence of what he called "dark matter", or matter which cannot be directly observed but can be inferred indirectly by its gravitational influence on visible matter. Analogously, imagine a caveman, who never saw a modern city, looking at New York at night. Naturally he will assume that New York is just a collection of light sources since all he can see is a variety of bright dots. Just like New York, space has much more then meets the eye.

Microstate Blackhole Production

I thought it important that some clarity be brought to this subject. So by bringing some information together that I had been thinking about, I would blog it.

Horatiu is referring to a mathematical similarity between the physics of the real world, which govern RHIC collisions, and the physics that scientists use to describe a theoretical, “imaginary” black hole in a hypothetical world with a different number of space-time dimensions (more than the four dimensions — three space directions and time — that exist in our world). That is, the two situations require similar mathematical wrangling to analyze. This imaginary, mathematical black hole that Horatiu compares to the RHIC fireball is completely different from a black hole in the real universe; in particular, it cannot grow by gobbling up matter. In other words, and because the amount of matter created at RHIC is so tiny, RHIC does not, and cannot possibly, produce a true, star-swallowing black hole.

Unfortunately, all of this is overstated. At RHIC we don't make a "real" black hole, in the sense envisioned by Einstein's General Theory of Relativity. Rather, Nastase's point of view is that RHIC collisions can be described by a "dual" black hole. But what does "dual" mean in this context? It's not "two-ness" in any sense, but rather indicates that one can write down a theory which describes the collision as a black hole, but in a completely different world than that we see around us. To make his model work, he (and many other researchers who are exploring this direction) make a calculation of a black hole in 10 dimensions in order to describe difficult (but gravitationally benign) aspects of the strong interaction in 4 dimensions.

This is not to undersell how interesting RHIC collisions are: if we in fact can use this "dual black hole" language to describe the collisions we are making daily, this may be a real advance in our understanding. But no-one I have ever spoken to has suggested that this black hole can or does act like a traditional black hole in our observed universe (although this possibility has been considered, and has been generally discounted as an implausible scenario).

Missing Energy

Given the dearth of knowledge about gravity in the subcentimeter range, the group is looking for any kind of deviation from expectations, not just extradimensional effects, he says. Nonetheless, the excitement about extra dimensions helps spur the group on, Price says.

If the strength of gravity takes a sharp turn upward at around 1 TeV, as the Stanford-Trieste scenario implies, an opportunity opens for testing this theory also in accelerators. Collisions at such energies could produce gravitons in large numbers, and some of these particles would immediately vanish into the extra dimensions, carrying energy with them. Experimenters would look for an unusual pattern of so-called missing energy events.

This and more subtle effects of extra dimensions could show up at existing accelerators, such as LEP and the Tevatron at Fermilab, only if the dimensions have scales nearly as big as a millimeter. The powerful LHC will greatly improve the chances for detecting missing energy events and other prominent extradimension effects.

In 1930 Wolfgang Pauli proposed a solution to the missing energy in nuclear beta decays, namely that it was carried by a neutral particle This was in a letter to the Tubingen congress. Enrico Fermi in 1933 named the particle the "neutrino" and formulated a theory for calculating the simultaneous emission of an electron with a neutrino. Pauli received the Nobel Prize in 1945 and Fermi in 1938. The problem in detection was that the neutrinos could penetrate several light years depth of ordinary matter before they would be stopped.

Dissident:

If you perform an experiment in which some of the energy you put in seems to disappear somewhere, unaccounted for, then yes, you have some explaining to do. Conservation of energy is not something we’d give up lightly; rewriting all those textbooks would be exhausting… but large extra dimensions would certainly not top the list of things to consider.

First of all, “missing energy” is a normal feature of collider experiments, since you can’t expect to catch all the stuff that comes out of them. You have two particle beams banging into each other inside a tunnel of finite width; any decay products flying off into the tunnel are lost. Around the collision point, you have detectors which, while huge and most impressive, also have blind angles and - most importantly - finite size.

Stanford’s Savas Dimopoulos: New Dimensions in Theoretical Physics

Our new picture is that the 3-D world is embedded in extra dimensions,” says Savas Dimopoulos of Stanford University. “This gives us a totally new perspective for addressing theoretical and experimental problems.

The machine, dubbed ATLAS (A Toroidal LHC ApparatuS), is one of four facilities to be located at a powerful accelerator, the Large Hadron Collider (LHC), now under construction near Geneva, in Switzerland

Some Distant Bounding Surface

I mean when I referred to fifth dimensional views you know that the computer screen includes not only it's functionability in relation to science, but adds that bit of extended flavour to model construction we call imaging right?

a) Compactifying a 3-D universe with two space dimensions and one time dimension. This is a simplification of the 5-D space­time considered by Theodor Kaluza and Oskar Klein. (b) The Lorentz symmetry of the large dimension is broken by the compactification and all that remains is 2-D space plus the U(1) symmetry represented by the arrow. (c) On large scales we see only a 2-D universe (one space plus one time dimension) with the "internal" U(1) symmetry of electromagnetism.

Remember Brian Greene's is from 2001. What might have change since then with Brian Greene and his views about about that distant bounding surface. Of course to many of us it is a brane world recognition.



If we did not recognize what advancements might have been accomlished with mathematics and the fifth dimensional views on our computer screens? Could we ever really talk about such idealizations, without understanding that there are ways to look at this, and reductional valuations taken from fifth dimensional views down to 2? Our computer screen. Of course Brian Greene has included the thickness of the bounded surface, so, time had to be inclusive here would it not?:)

The Edge

Physics and everything we know in the world around us may really be tied to processes whose fundamental existence is not here around us, but rather exists in some distant bounding surface like some thin hologram, which by virtue of illuminating it in the right way can reproduce what looks like a 3-dimensional world. Perhaps our three dimensional world is really just a holographic illumination of laws that exist on some thin bounding slice, like that thin little piece of plastic, that thin hologram. It's an amazing idea, and I think is likely to be where physics goes in the next few years or in the next decade, at least when one's talking about quantum gravity or quantum string theory.

So how can such a thing as Brian calls a Bounded surface and relate it's thinness to a vast capability? Also in the cosmic perspective, to have brane collisions illustrated by Steinhardt, become much more then our views held to the surface mathematically inclined. To be revealled, in stringy dynamics, at the basis of our viewing?

Such creation slotted into the time frames of this beginning, is stil questioning the valuation of what existed before stringy ideas manifest, so what pray tell, could have ever been "the sun" in behind, that illuminates "shadows" on the wall?

The Randall-Sundrum braneworld model is characterized by ordinary matter being confined to a hypersurface embedded in a higher-dimensional manifold through which gravitational signals may propagate

Physics strings us along by Margaret Wertheim of LAtimes.com

In the latest, hottest Big Science tome — the delightfully titled "Warped Passages" — Harvard physicist Lisa Randall describes the idea that the universe we see around us is but one tiny part of a vast reality that may include an infinite number of other universes. Randall is an expert on both cosmology and that arcane branch of particle physics known as string theory. By marrying the two fields, she and her colleagues have formulated a picture in which our universe may be seen as a soap-film-like membrane (a "braneworld") sitting inside a much larger space: the bulk. According to general relativity, the universe we live in has four dimensions: three of space and one of time. Randall's work extends this framework and posits the existence of a fifth dimension. The fifth dimension is the bulk, and within its immeasurably expanded space, there is no reason to assume that ours is the only cosmos.

So there are amazing leaps here then to new world recognitions of ideologies that formed from where?

John Ma Pierre:

What is remarkable is that much of the recent progress in understanding non-perturbative aspects of string theory and supersymmetric gauge theories has been made in parallel, using each to gain knowledge and insights about the other. There are various reasons for this intimate connection between supersymmetric gauge theories and string theory. One is that supersymmetric gauge theories arise as low energy effective descriptions of compactified string theories in limits where gravity decouples. Another reason is that superstring theories can be formulated in backgrounds that contain D-branes, and supersymmetric gauge theories serve as effective world volume theories for these D-branes. In addition to these direct examples, it is sometimes the case that intuition about non-perturbative physics that is gained in one area can be directly applied to the other. An example of this is the guiding principle that singularities in the quantum moduli space of a low energy effective theory signal the appearance of new massless states. This was seen to be a generic phenomena in supersymmetric gauge theories and was subsequently applied to the resolution of conifold singularities by massless black holes in string theory.

Wow! More then five!:) Okay reference was made by Sean on a one liner about magic and his meeting in a bar. Where a sister as the science teacher explains this statement. Well it has been gathered up for consumption in other areas, so of course we have to explain this as now this conversation is leading other talks to consider more issues about what began as a mystery has no place in the developement of science.

I am a little dismayed by this, because anomlistic features without explanation would seem as such, while it is true, that it can be expalined afterwards, once we understood how something from the 21st century dropped into our laps for consideration:) We know what this means right? It had to be coisstent and logicall so repeatability can hav eother hands , for verification. How did you expalin it and lead them hwere one had not gone before?

That sounded like Startrek for a minute there:)

A Supersymmetrical Valuation of Where things Began

Of course "phase transitions" and "asymmetrical realizations" had to arise from developmental processes in the universe? One had to know, in what sphere such developemental would take place, and if we circumvented all these chinese boxes or Russina dolls to exemplifed allegorical comments about consciousness. It had to follow a Gr perspective, and, a quantum mechanical one? "Topo-sense" as to developing topolgical models within consciousness, as a well as, models in the developing universe as a GR sense? IMagine to then such toposense further develped from theidealizatin of quantum views such physicla actions taken from cosmological proportions and reduced to probability functions entailed in our mental structure, then indeed we had transgressed our limitation to a feeling?:)

The theory of relativity predicts that, as it orbits the Sun, Mercury does not exactly retrace the same path each time, but rather swings around over time. We say therefore that the perihelion -- the point on its orbit when Mercury is closest to the Sun -- advances.

Imagine for a moment about that such a "momentus occasion", as well we learn to see the developmental process of circles(orbits) and Mercuries orbital patterns (a daisey) and got this general sense of reduced orbital pattern decay of rotatng binary pulsar systems as revealled by Taylor and Hulse.

We got to know "information release" from the distances involved, and could calculated when they would combined? This is a "prediction then" based on, a viable measure, not only in terms of that distance valuation, but of how we might arrive at it other then in astronmical viewing. What would be revealled in LIGO application?

Atiyah's comments are important here I think.

If theory is the role of the architect, then such beautiful proofs are the role of the craftsman. Of course, as with the great renaissance artists, such roles are not mutually exclusive. A great cathedral has both structural impressiveness and delicate detail. A great mathematical theory should similarly be beautiful on both large and small scales.

Assymetrical views would have revealled mandalic interpretations very distinctive of conscious awareness, and unfoldment in design. This had to have a geometric and foundational perspective that arose from the expansitory valution of brane world idealizations? As well as, the deeper recesses of our own minds?

Finally, we also hope that this series furthers the discussion regarding the nature and function of 'the mandala'. In the spiritual traditions from which Jung borrowed the term, it is not the SYMMETRY of mandalas that is all-important, as Jung later led us to believe. It is their capacity to reveal the asymmetry that resides at the very heart of symmetry. By offering a new view about how consciousness itself is structured - in a fundamentally paradoxical fashion - and how these structurings are reflected in principles according to which the mandala is organized, we are able in this series to show how personality itself may be thought of as having an essentially 'liminocentric' design.

One had to be able to recognize this "model apprehension" and speak to it directly in experience. I could do that because of my explorations. Am I adapting to new methods of model developements? For sure. :)



"Luminousity" as enlightenment could possibly help push back the veil, if we could probably do this?

Bubble World and Geometrodynamics

As I related in the blog entry comments of "trademarks of the geometers II" it was from that perspective the relation developed on plate 47 and indications of YING Yang interconnectivity to oriental philosophy that I encouraged bubble idealizations.



I think he(meaning site linked on new views) understood immediately the reference I made to the "Taoist symbol" and the relation to the Calabi Yau, in terms of the rotation being complete. No singularity, but the turning inside out of the state of the current universe to expressions detailed in the culmination of such gravitational collapses. I had to look for examples like this.

This idea was based on example lead from geometrical insight, I had encouraged from the understanding of that same gravitational collapse. This was derived from correlative attempts to encourage such "geometrical dynamics" revealled in sonoluminence examples, set out in experimental fashion, that physics might have encouraged, and then related back to the maths.

I never really understood this inclination of myself, but drawing examples in society seemed to be the way of it, so that the understanding could have found examples. It couldn't be that abstract that we could not find some relation, could it?

It seems I cannot locate my list references to the idea of gravitational collpase so I will have to refill this article with links to help direct the attention I gained from observing this inherent geometrical inclination .


The glass cell used by Fink and colleagues, surrounded by the eight high-frequency sound generators

The team believes this method can be modified to make the bubble collapse even faster, which would lead to greater light intensities. This would allow physicists to study the relationship between pressure, light intensity and temperature in sonoluminescence in more detail

So the point here is not to take sonoluminece as "the process" but of looking deeper into the geoemtrical design that ask blackhole creation, to give indicators as to the depth and contact glast might reveal from a inception point, with viable measures detailled through "calorimetric evidence" and design.

From a cosmological standpoint, this helped me to see the values of the curvature parameters that exist at the outer most edge of our cosmos. Is it right I am not sure?

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.

Langlands Duality

Appointed to Princeton as an instructor after completing his doctoral studies, Langlands taught there for seven years and was promoted to associate professor. He spent 1964-65 at the University of California, Berkeley as a Miller Foundation Fellow and an Alfred P Sloan Fellow. Then in 1967 he returned to Yale University as a full professor. However Langlands spent 1967-68 visiting in Ankara, Turkey having an office next to that of Cahit Arf. After five years at Yale he returned again to Princeton, this time as professor of mathematics at the Institute for Advanced Study. He has remained at the Institute for Advanced Study since his appointment there in 1972.

In 1967 he wrote a letter to Weil which contains profound mathematical ideas which continue to drive a whole area of mathematical research. The letter was 17 pages hand-written and sent in January 1967. It sketched what soon became known as "the Langlands conjectures". Weil had the letter typed and this typed version circulated widely among mathematicians interested in the topics. Casselman writes in [3] that the letter contained:-

... a collection of far-reaching and uncannily accurate conjectures relating number theory, automorphic forms, and representation theory. Theses have formed the core of a program still being carried out, and have come to play a central role in all three subjects.

The work of Robert Langlands

....is currently a Professor at the Institute for Advanced Study in Princeton. He has won several awards recognizing his outstanding contributions to the theory of automorphic forms, among them an honorary degree from the University of British Columbia in 1985.

Letter to André Weil from January, 1967

Dear Professor Weil,

While trying to formulate clearly the question I was asking you before Chern’s talk I was led to two more general questions. Your opinion of these questions would be appreciated. I have not had a chance to think over these questions seriously and I would not ask them except as the continuation of a casual conversation. I hope you will treat them with the tolerance they require at this stage. After I have asked them I will comment briefly on their genesis.

It might be good to begin from statements made from Weil and this letter circulated. It might help set up early history and thoughts and ideas lead into the Langland Duality Lubos has renamed. References made by Lubos today and following correspondance by Peter Woit. Lubos Motl, opens his blog entry with following link.

Gauge Theory and the Geometric Langlands Program by Edward Witten
August 10th, 2005 Based on notes by Ram Sriharsha

Introduction
The Langlands program of number theory, or what we might call Langlands duality, was proposed in more or less its present form by Robert Langlands, in the late 1960s. It is a kind of unified scheme for many results in number theory ranging from quadratic reciprocity, which is hundreds of years old, to modern results such as Andrew Wiles’ proof of Fermat’s last theorem, which involved a sort of special case of the Langlands program. For today, however, I will not assume any prior knowledge of the Langlands program.

Langlands duality , by Lubos Motl

I am using Witten's favorite word "duality" instead of "program" because it is a bit more concrete; it's puzzling why the mathematicians haven't realized that their terminology can be sharpened. I encourage everyone to respect that the official terminology has changed to a "duality" right now.

Notes for Witten Lecture by Peter Woit

Witten gave a lecture on the beach at Stony Brook on the topic of gauge theory and the Langlands program two months ago, and lecture notes are now available. Lubos Motl has a posting about this, where he promotes the idea that people should stop referring to the “Langlands Program” and just refer to “Langlands duality”.

Langlands Program and Physics by Peter Woit

One of my minor hobbies over the years has been trying to understand something about the Langlands conjectures in number theory, partly because some of the mathematics that shows up there looks like it might be somehow related to quantum field theory. A few days ago I was excited to run across a web-page for a workshop held in Princeton earlier this year on the topic of the Langlands Program and Physics. Notes from some of the lectures there are on-line.

Geometric Langlands Program

This program is dedicated to the investigation of the geometric Langlands, its relationship to other areas of mathematics, and its relationship to physics;

THE LANGLANDS PROGRAM AND PHYSICS NOTES BY MATT SZCZESNY

The following are notes from the workshop on connections between the Langlands correspondence and Physics that took place at the Institute for Advanced Study at the beginning of March, 2004. Its purpose was to bring together researchers in representation theory and string theory to explore the question of whether it is possible to give a physical perspective on the geometric Langlands correspondence. Certain parts of geometric Langlands make use of tools arising in Conformal Field Theory (CFT), and so provide a point of contact between the two fields.

Raphael Rooms

Room of the Segnatura

Virtual Tour of this Room

The Room of the Segnatura contains Raphael's most famous frescoes. Besides being the first work executed by the great artist in the Vatican they mark the beginning of the high Renaissance. The room takes its name from the highest court of the Holy See, the "Segnatura Gratiae et Iustitiae", which was presided over by the pontiff and used to meet in this room around the middle of the 16th century. Originally the room was used by Julius II (pontiff from 1503 to 1513) as a library and private office. The iconographic programme of the frescoes, which were painted between 1508 and 1511, is related to this function.

Room of Constantine

Room of Heliodorus

Room of the Segnatura

Room of the Fire in the Borgo

The four rooms known as the Stanze of Raphael form part of the apartment situated on the second floor of the Pontifical Palace that was chosen by Julius II della Rovere, the Pope. as his own residence and used also by his successors. The picturesque decoration was carried out by Raphael and his pupils between 1508 and 1524.

The Raphael Rooms (also called the Raphael Stanze) in the Palace of the Vatican are papal apartments with frescoes painted by Italian artist Raphael.

The Rooms were originally intended as a suite of apartments for Pope Julius II. He commissioned the relatively young artist Raffaello Sanzio and his studio in 1508 or 1509 to repaint the existing interiors of the rooms entirely. It was possibly Julius' intent to outshine the apartments of his predecessor (and rival) Pope Alexander VI as the Raphael Rooms are directly above Alexander's Borgia Apartment.

The Rooms are on the third floor, overlooking the south side of the Belvedere Courtyard. Running from East to West, the rooms are called:

This picture by Raphael is very important to me, as you must be aware, by the opening at the very head of this blog, and by the picture I cut from Raphael's painting. It shows myself(Plato:) and Aristotle.

I mentioned that ">one thing" before remember. How this insighted Curly 's touching philosophy about that "one thing" and the search for Gold.

Well, such depictions taken I gathered from the painting, as well as, what I gathered from what I thought Raphael was saying. You noticed of course that they are all under this Arche? Yes, this was very symbolic to me.

So indeed, what is truth?

Justified true belief

The Theaetetus account of Plato further develops the definition of knowledge. We know that, for something to count as knowledge, it must be true, and be believed to be true. Plato argues that this is insufficient, and that in addition one must have a reason or justification for that belief.

Plato defined knowledge as justified true belief.

One implication of this definition is that one cannot be said to "know" something just because one believes it and that belief subsequently turns out to be true. An ill person with no medical training but a generally optimistic attitude might believe that she will recover from her illness quickly, but even if this belief turned out to be true, on the Theaetetus account the patient did not know that she would get well, because her belief lacked justification.

Knowledge, therefore, is distinguished from true belief by its justification, and much of epistemology is concerned with how true beliefs might be properly justified. This is sometimes referred to as the theory of justification.

Well to help direct the truth to bare on what these sources are, I thought it important to continue to bring perspective not only to the tidbits of images that are floating around this site, and those of others, but brings the significance of such "gatherings" to Raphael's painting and the place it rests.

So anyway, a little more clarity, with a "slight twist" of my humour.