Sylvester's Surfaces

Figure 2. Clebsch's Diagonal Surface: Wonderful.

We are told that "mathematics is that study which knows nothing of observation..." I think no statement could have been more opposite to the undoubted facts of the case; that mathematical analysis is constantly invoking the aid of new principles, new ideas and new methods, not capable of being defined by any form of words, but springing direct from the inherent powers and activity of the human mind, and from continually renewed introspection of that inner world of thought of which the phenomena are as varied and require as close attention to discern as those of the outer physical world, ...that it is unceasingly calling forth the faculties of observation and comparison, that one of its principal weapons is induction, that it has frequent recourse to experimental trial and verification, and that it affords a boundless scope for the exercise of the highest efforts of imagination and invention. ...Were it not unbecoming to dilate on one's personal experience, I could tell a story of almost romantic interest about my own latest researches in a field where Geometry, Algebra, and the Theory of Numbers melt in a surprising manner into one another.

I had been looking for the link written by Nigel Hitchin, as this work was important to me, in how Dynkin drawings were demonstrated. Although I have yet to study these, I wanted to find this link and infomration about James Sylvester, because of the way we might see in higher dimensional worlds.His model seem important to me from this perspective.

Sylvester's models lay hidden away for a long time, but recently the Mathematical Institute received a donation to rescue some of them. Four of these were carefully restored by Catherine Kimber of the Ashmolean Museum and now sit in an illuminated glass cabinet in the Institute Common Room.

The reason for this post is th ework dfirst demonstrated by Lubos Motl and th etalk he linked by Nigel Hitchin. The B-field, which seems to no longer exist, or maybe I am not seeing it in his posts archived?

In 1849 already, the British mathematicians Salmon ([Sal49]) and Cayley ([Cay49]) published the results of their correspondence on the number of straight lines on a smooth cubic surface. In a letter, Cayley had told Salmon, that their could only exist a finite number - and Salmon answered, that the number should be exactly 27

.

There had to be a simplification of this process, so in gathering information I hope to complete this, and gain in understanding.

James Joseph Sylvester (September 3, 1814 - March 15, 1897) was an English mathematician and lawyer.

Now as to the reason why this is important comes from the context of geometrical forms, that has intrigued me and held mathematicians minds. Sometimes it is not just the model that is being spoken too, but something about the natural world that needs some way in which to be explained. Again, I have no teachers, so I hope to lead into this in a most appropriate way, and hopefully the likes of those involved, in matrix beginnings, have followed the same process?

The 'Cubics With Double Points' Gallery




f(x,y,z) = x2+y2+z2-42 = 0,

i.e. the set of all complex x,y,z satisfying the equation. What happends at the complex point (x,i*y,i*z) for some real (x,y,z)?

f(i*x,y,z) = x2+(i*y)2+(i*z)2-42
= x2+i2*y2+i2*z2-42
= x2-y2-z2-42.

Has it become possible that you have become lost in this complex scenario? Well what keeps me sane is the fact that this issue(complex surfaces) needs to be sought after in terms of real images in the natural world. Now, I had said, the B-field, and what this is, is the reference to the magnetic field. How we would look at it in it's diverse lines? Since on the surface, in a flat world, this would be very hard to make sense of, when moved to the three coordinates, these have now become six?

fancier way of saying that is that in general, it's okay to model the space around us using the Euclidean metric. But the Euclidean model stops working when gravity becomes strong, as we'll see later.

Now what has happened below, is that what happens in quark to quark distances, somehow in my mind is translated to the values I see, as if in the metric world and moved to recognition of Gaussian curves and such, to decribe this unique perspective of the dynamics of Riemann, lead through geometrical comprehension ad expression. No less then the joining of gravity to Maxwells world.

Like the magnetic field we know, the lines of force represent a dynamcial image, and so too, how we might see this higher dimensional world. Again I don't remember how I got here, so I am trying hard to pave this road to comprehension.



"Of course, if this third dimension were infinite in size, as it is in our world, then the flatlanders would see a 1/r2 force law between the charges rather than the 1/r law that they would predict for electromagnetism confined to a plane. If, on the other hand, the extra third spatial dimension is of finite size, say a circle of radius R, then for distances greater than R the flux lines are unable to spread out any more in the third dimension and the force law tends asymptotically to what a flatlander physicist would expect: 1/r.

However, the initial spreading of the flux lines into the third dimension does have a significant effect: the force appears weaker to a flatlander than is fundamentally the case, just as gravity appears weak to us.

Turning back to gravity, the extra-dimensions model stems from theoretical research into (mem)brane theories, the multidimensional successors to string theories (April 1999 p13). One remarkable property of these models is that they show that it is quite natural and consistent for electromagnetism, the weak force and the inter-quark force to be confined to a brane while gravity acts in a larger number of spatial dimensions."

Now here to again, we are exercising our brane function(I mean brain)in order to move analogies to instill views of the higher dimensional world. The missing energy had to go somewhere and I am looking for it?:) So ideas like "hitting metal sheets with a hammer", or "billiards balls colliding", and more appropriately so, reveal sound as a manifestation of better things to come in our visions?

See:

Unity of Mathematics

The case for discrete energy levels of a black hole

Jacob Bekenstein

Download for Lecture

The Bekenstein Bound, Topological Quantum Field Theory and Pluralistic Quantum Field Theory

An approach to quantum gravity and cosmology is proposed based on a synthesis of four elements: 1) the Bekenstein bound and the related holographic hypothesis of 't Hooft and Susskind, 2) topological quantum field theory, 3) a new approach to the interpretational issues of quantum cosmology and 4) the loop representation formulation of non-perturbative quantum gravity. A set of postulates are described, which define a (\it pluralistic quantum cosmological theory.) These incorporates a statistical and relational approach to the interpretation problem, following proposals of Crane and Rovelli, in which there is a Hilbert space associated to each timelike boundary, dividing the universe into two parts. A quantum state of the universe is an assignment of a statistical state into each of these Hilbert spaces, subject to certain conditions of consistency which come from an analysis of the measurement problem. A proposal for a concrete realization of these postulates is described, which is based on certain results in the loop representation and topological quantum field theory, and in particular on the fact that spin networks and punctured surfaces appear in both contexts. The Capovilla-Dell-Jacobson solution of the constraints of quantum gravity are expressed quantum mechanically in the language of Chern-Simons theory, in a way that leads also to the satisfaction of the Bekenstein bound.

Spheres Instead of Circles

This is a torus (like a doughnut) on which several circles are located. Unlike on a Euclidean plane, on this surface it is impossible to determine which circle is inside of which, since if you go from the black circle to the blue, to the red, and to the grey, you can continuously come back to the initial black, and likewise if you go from the black to the grey, to the red, and to the blue, you can also come back to the black.

Reichenbach then invites us to consider a 3-dimensional case (spheres instead of circles).





Figure 8 [replaced by our Figure 2] is to be conceived three-dimensionally, the circles being cross-sections of spherical shells in the plane of the drawing. A man is climbing about on the huge spherical surface 1; by measurements with rigid rods he recognizes it as a spherical shell, i.e. he finds the geometry of the surface of a sphere. Since the third dimension is at his disposal, he goes to spherical shell 2. Does the second shell lie inside the first one, or does it enclose the first shell? He can answer this question by measuring 2. Assume that he finds 2 to be the smaller surface; he will say that 2 is situated inside of 1. He goes now to 3 and finds that 3 is as large as 1.

How is this possible? Should 3 not be smaller than 2? ...

He goes on to the next shell and finds that 4 is larger than 3, and thus larger than 1. ... 5 he finds to be as large as 3 and 1.

But here he makes a strange observation. He finds that in 5 everything is familiar to him; he even recognizes his own room which was built into shell 1 at a certain point. This correspondence manifests itself in every detail; ... He is quite dumbfounded since he is certain that he is separated from surface 1 by the intervening shells. He must assume that two identical worlds exist, and that every event on surface 1 happens in an identical manner on surface 5. (Reichenbach 1958, 63-64)

Topo-sense?

Michael Persinger has a vision - the Almighty isn't dead, he's an energy field. And your mind is an electromagnetic map to your soul.

Persinger's research forays are at the very frontier of the roiling field of neuroscience, the biochemical approach to the study of the brain. Much of what we hear about the discipline is anatomical stuff, involving the mapping of the brain's many folds and networks, aperformed by reading PET scans, observing blood flows, or deducing connections from stroke and accident victims who've suffered serious brain damage. But cognitive neuroscience is also a grab bag of more theoretical pursuits that can range from general consciousness studies to finding the neural basis for all kinds of sensations.

IN a materialistic sense I wanted to show how matter constructed phases and brain thinking, could be exemplified. Just as mathematics can, and this requirement of models of math, somehow need it's inception to arise from that same brain?

Rafael Núñez and George Lakoff have been able to give an elaborate first answer to the questions: How can advanced mathematics arise from the physical brain and body? Given the very limited mathematical capacity of human brains at birth, how can advanced mathematical ideas be built up using the basic mechanisms of conceptual structure: image-schemas, frames, metaphors, and conceptual blends?

Now I have done some home work here to say, that the thinking is leading from a brain orientated perspective, although this evidence is overwhelming, I have countered it with another thought.


Stanislas Dehaene
Like Lakoff, I am convinced that cognitive studies of mathematics will ultimately provide beautiful examples of the limits that our brains impose on our thoughts. As I tried to show in The Number Sense, we have very strong intuitions about small numbers and magnitudes, which are provided to us by a specific cerebral network with a long evolutionary history. But one could probably write another book describing the limits on our mathematical intuitions. Take topology, for instance. At home, I have a small collection of extremely simple topological brainteasers. Some of them (essentially made from a metal ring and a piece of string) are strikingly counter-intuitive ‹ our first reaction is that it is simply impossible to remove the ring, but of course it can be done in a few moves. Thus, our sense of topology is extremely poor. Yet it's easy enough to imagine a different species that would have evolved a cerebral area for "topo-sense", and for which all of my brain-teasers would be trivial

This intuitive feeling that is generated once math processes are understood are realized in dynamical movement revealled in the brains thinkng? Had to arrive from lessons it learnt previously? Pendulums, time clocks, great arcs, and gravity?

"What's Your Law?"

Damasio's First Law The body precedes the mind.

Damasio's Second Law Emotions precede feelings.

Damasio's Third Law Concepts precede words.

What if the condensation of the human brain was the reverse, of Damasio's First Law. I mean we can train the neuron pathways to be reconstructed, by establishing the movements previously damaged by stroke?

What is the evolution of the human brain, if mind is not leading its shape?

In Pioneering Study, Monkey Think, Robot DoBy SANDRA BLAKESLEE

Monkeys that can move a robot arm with thoughts alone have brought the merger of mind and machine one step closer.

In experiments at Duke University, implants in the monkeys' brains picked up brain signals and sent them to a robotic arm, which carried out reaching and grasping movements on a computer screen driven only by the monkeys' thoughts.

The achievement is a significant advance in the continuing effort to devise thought-controlled machines that could be a great benefit for people who are paralyzed, or have lost control over their physical movements.

In previous experiments, some in the same laboratory at Duke, both humans and monkeys have had their brains wired so they could move cursors on computer screens just by thinking about it. And wired monkeys have moved robot arms by making a motion with their own arms. The new research, however, involves thought-controlled robotic action that does not depend on physical movement by the monkey and that involves the complex muscular activities of reaching and grasping.

Now the direct connection, is self evdient once the brains mapping is understood and connections made. In computerization the mathematical structure is very importan,t so such a math mind and the computer persons would excell if the equaitions would demonstrate the math as a model constructed. In this sense, if we think of the Torso, rotation turns 360 degrees, or 720, would somehow bring it back to it's original position.

Monkey Moves Computer Cursor by Thoughts Alone, By E.J. Mundell

Going one step further, her team then trained the monkey to simply think about a movement, without reaching out and touching the screen. A computer program, hooked up to the implanted electrodes, interpreted the monkey's thoughts by tracking flare-ups of brain cell activity. The computer then moved a cursor on the computer screen in accordance with the monkey's desires--left or right, up or down, wherever ``the electrical (brain) pattern tells us the monkey is planning to reach,'' according to Meeker.

So I must put here some information to show the counter proposal.

Lets say my own brain did concieve a process within it's own structure that I had been able to identify as a process of continuity and called it a inductive deductive process, according to that shape? Would this reveal something about my own brain, but of others as well? Hw el have tunnels served to help the mind engage a physiolgical process, to find it self decribing the math, in experience?

The counter proposal I am making, is disguised in Persingers own words. That such a field manifested in the brain dynamics, as neuronic developmental pathways? Could this have been initiated from thinking structured born in mind and as a model assumption, somehow transformed the process of the whole brain?

A Paradigm Change? Penetrating the unpenetrable?



This plate image is a powerful one for me becuase it represents something Greene understood well. His link on the right hand side of this blog is the admission of "cosmological and quantum mechanical readiness," to tackle the cosmological frontier.

How do you classify some experience where mind might have projected ahead of itself, while the neurons would become the basis of thinking. Something had to exist before a personality could develope. Personality is our man made, while deeper is the essence of that flows through to expression? How would you have concieved of this in a physiological processes? Einstein crossing the room, and in this, "higgs will have found it's comparison?" "Neurons," that fall in behind the projected mind?

Brian Greene:

it turns out that within string theory ... there is actually an identification, we believe, between the very tiny and the very huge. So it turns out that if you, for instance, take a dimension - imagine its in a circle, imagine its really huge - and then you make it smaller and smaller and smaller, the equations tell us that if you make it smaller than a certain length (its about 10-33 centimeters, the so called 'Planck Length') ... its exactly identical, from the point of view of physical properties, as making the circle larger. So you're trying to squeeze it smaller, but actually in reality your efforts are being turned around by the theory and you're actually making the dimension larger. So in some sense, if you try to squeeze it all the way down to zero size, it would be the same as making it infinitely big. ...

So you look for the topological equivalent.The sphere and the torus? So there is this struggle of sorts. Where energy can flow through, in and out, and how had it changed, and this field becomes the image of gaussian curvature easily expressed in Maxwells delivery as part of some greater whole?

But it is more then the relationship of that same cosmological partnership to reductionistc attempts at defining the beginning of the universe, will somehow have found it's relevance through the expression of the mind? The universe 's beginning?


Melencolia II
[frontispiece of thesis, after Dürer 1514]


Historically this development of the geometry of consciousness was working hard to bring itself to light? The manifested realization, of those early universe indications.

A Model for Thought?

Bernhard Riemann once claimed: "The value of non-Euclidean geometry lies in its ability to liberate us from preconceived ideas in preparation for the time when exploration of physical laws might demand some geometry other than the Euclidean." His prophesy was realized later with Einstein's general theory of relativity. It is futile to expect one "correct geometry" as is evident in the dispute as to whether elliptical, Euclidean or hyperbolic geometry is the "best" model for our universe. Henri Poincaré, in Science and Hypothesis (New York: Dover, 1952, pp. 49-50) expressed it this way.

See:

Science and Hypothesis

Rasmus said:

If you accept mathematical platonism, which is by far the prevalent philosophy of mathematics, at least among mathematicians, then you accept that to say that "x exists" is not necessarily to posit a single way of "existing": this very much depends on the x that is being spoken of.

This is a difficult one. The basis of existance arrived from nothing? What is nothing, and as soon as you do this, you have no frame work?

So one percieves that there is always something and from it? So we postulate X ?

In this platonist are discretism people, while the people who believe there is always something, an expression of the continuity of something called X? The true vacuum? The Quantum harmonic oscillator?

This all might be "abtraction to some" but it goes to the heart of any logic. In my case, I have to assume something always existed. So how do you deal with that logically?

Now you might be better educated then me, yet to me, numbers reveal a strange world of things we can't see yet we know exist. We have ways to measure it, and numbers in which to express it.

Now it would be very hard to assume that the average person, that scienitific progress can ever have any basis in what I just say above, but they are articluated from real issues that pervade thinking.

Now real things discrete as they are reveal matter constitutions, and the basis of this dealing with the likes of a Robert Mclauglin, or the likes of those who wish to expound on the continuity of expression. Leading into the understanding of Genus figures, this becomes a interesting analogy to way such continuity can be expressed?

Let me just say here that topologically this wold have arisen from a euclidean based perspective and move dynamically into revelations of curvature and such. So we know that above euclidean perspective and coordinated frames of reference this is discretism's way?

Dynamically the non-euclidean world condensing into a box? Some of us like things this way, but there are higher realms of thinking, that are transcendance to a platonist like me. :)

This is not a "superiority wording," but the true recognition of higher forms of mathematical derivation that the lay person would not understand. This intellectual was moved too, as I developed away from material things? :)

Here I am respective of the lineage of geometries, and anyone could interject in this consistancy. Some will be better equiped to move past the abstraction, while others perfectly comfortable with what I just said.

Is it transcendance? IN a way it is. In that we had moved intellectual academia into and away from emotive causations that might have ruled our thinking?

Is this feature absent from our intellectual developement, or is it more well defined? "Better perspective," as we move away from articulated matter constitutions and speak about "the finer things" above those same material things?

As one knows, one can become very abstract to the lay individual. While any who deal intellectually and emotively from the lay people, are not removed from and have perfected the emotive causes of memory inducement:?) Your history. Although we know of prospective change, as viable opportunites in the future. Continuity of expression.

Rasmus

But many are those who say that this is NOT what they mean when they say they believe in God. If atheists wish to argue against THESE religionists, then first they must reckon with what they are arguing against
No doubt.

How far can science go here? So they look for this beginning.

It's not easy if you assume nothing in the beginning and it is always much easier to change the models of perception. Adjust the view point, to see that a new model can change the way we always viewed things. That what model assumption does when you grokked it.

So like I said in the beginning, and where if such a continous nature is implied, can we deal with the idealization in science?

So if you took a look at calorimentric views and encapsulte this action you would find the point to which this beginning spoke? So a blackhole, is just not some sinkhole, but a transformation of a kind that we hope we can measure finding some means.

Energy in energy out if unbalanced leaves some room for questions? This dimensional perspective is very relevant in math, yet soe do not like to infer this and deem it unrealistic.

Early universe and glast determination have detailed discretism in interactions, as a viable means to measure. Yet we understand well the photon is massless, yet it can be indicative too. Thanks LIGO for engrandizement of the interferometer.

Artists such as M. C. Escher have become fascinated with the Poincaré model of hyperbolic geometry and he composed a series of "Circle Limit" illustrations of a hyperbolic universe. In Figure 17.a he uses the backbones of the flying fish as "straight lines", being segments of circles orthogonal to his fundamental circle. In Figure 17.b he does the same with angels and devils. Besides artists and astronomers, many scholars have been shaken by non-Euclidean geometry. Euclidean geometry had been so universally accepted as an eternal and absolute truth that scholars believed they could also find absolute standards in human behavior, in law, ethics, government and economics. The discovery of non-Euclidean geometry shocked them into understanding their error in expecting to determine the "perfect state" by reasoning alone.

Discretized 2D quantum gravity

Ancient Comparisons for thought

Now in itself, and of itself, the triangle when hit produces sound. IN this we understand the vibrational field that is generated. Hold your finger to a spot and where will the resonances slow down and come to a stop?

The chaldni plate is a easy experiment in using sound, "as an analogy of this higher quality." Some like the magnetic field, and its demonstration. Gaussian arc?
Imagine that the "earth based square," as the basis of mass considerations. Call it iron if you like.

Now in light of the triangle, or "trinity," what ever, lets say that the vibrational nature can be associated to this triangle.

That low notes that are slow in vibrations, also can reveal the mass considerations at the base , with greater vibration intensity at the peak? You now have a scale and iron as the core/base? We know there are certain energy values to elemental consideration?

How would you apply this to the chaldni plate? How would this apply to the world at large. How would you apply this in yourself?

A recipe for making strings in the lab

All you educated people must forgive me here. I do not have the benefit, of the student and teacher relationship, yet I rely heavily on my intuitive processes. I cannot say whether for sure these are always right. IN this sense, I would not have been liked to call a Liar, or one who had ventured forth to spread illusionary tactics to screw up society.

On the contrary, my ideal is set in front of my mind, and all things seem to gather around it most appropriately. A place and time, where good educators have watched out for the spread and disemmination, that could lead society away from, good science? I will give credit to Peter Woit in this sense. Lubos Motl for staying the course. As to those who excell these views for us as well. We are your distant cousins in need of education and for those, in the backwoods of isolation.

Fixations on Objective Design

This is far from the truth of my goal, and "fixations on objective design" of reality, are not what I was hoping to reveal. More, the understandng, that to get there, there are some considerations to think about.

The idealization in theoretcial developement should show this. The physics must accompany the development of this lineage of mathematics, as well as the lineage of physics must lead mathematics? What is the true lineage? Could any mathematican tell me or are they limited to the branches they deal with in physics?

Now back to the topic of this thread.

When I was a kid, I liked to take buttons and place a thread through them. Watching Mom, while I prep the button, she got ready to sew. I would take both ends of the thread and pull it tightly. I liked the way the button could spin/thread depending on how hard I pull the thread.



Now for some of you who don't know, the pythagorean string tension was arrived at by placing gourds of water on strings, to dictated the harmonical value, "according to weight?"

It is said that the Greek philosopher and religious teacher Pythagoras (c. 550 BC) created a seven-tone scale from a series of consecutive 3:2 perfect fifths. The Pythagorean cult's preference for proportions involving whole numbers is evident in this scale's construction, as all of its tones may be derived from interval frequency ratios based on the first three counting numbers: 1, 2, and 3. This scale has historically been referred to as the Pythagorean scale, however, from the point of view of modern tuning theory, it is perhaps convenient to think of it as an alternative tuning system for our modern diatonic scale.

So we see the nature spoken too, in a much different way?

KakuIf strings are to be the harmony then what music do such laws of chemistry sing? What is the mind of God? Kaku saids,"According to this picture, the mind of God is Music resonanting through ten- or eleven dimensional hyperspace which of course begs the question, If the Universe is a symphony, then is there a composer to the symphony."

Simply put, superstring theory says all particles amf forces are manifestations of different resonances of tiny one dimenisonal strings(or possibly membranes) vibrating in ten dimensions.


Artist's impression of the setup.

The disks represent the bosonic condensate density and the blue balls in the vortex core represent the fermionic density. The black line is a guide to the eye to see the wiggling of the vortex line that corresponds to a so-called Kelvin mode, which provides the bosonic part of the superstring

(image and text: )arXiv.org/abs/cond-mat/0505055.

Now I will tell you why this elementary experiment is very good for fixing the mind around some potential idea? Now, when I look at it, and look at the ball placings on each disk ( are they in the same spot....hmmm yes this could be a problem), each disk will automatically spin according to the placement of the ball, in relation to it's edge. Now when you place this in line, like a one dimensional string, as if you see this string vibrate, imagine how you would get these waves to exemplify themself and the disk placement acccordingly.

Now it is most important that you see the tension of this string vibrate, in relation to how we see the disks spin. Pull tightly on the string and you get a wonderful view of a oscillatory nature, that is dictated by the respective placement of the balls on the disk. Good stuff!

In brackets above, the exploration of artistic rendition is very good, because it allows you to further play with this model and exhaust it's potential. Would it be incorrect to say, that ball placement and vibratory placement can be related to string harmonics? In this case, how would KK tower and circle allocation to disk identify this string, but to have some signature in the way these disks spin,,individually and as a whole(one string)

The link below was 2000 but it is effective in orientating thoughts?

To find extra dimensions of the type studied by the CERN group, experimenters are on the alert for what they call Kaluza-Klein towers, which are associated with carriers of the nongravitational forces, such as the photon of electromagnetism and the Z boson of the weak force. Excitations of energy within the extra dimensions would turn each of these carriers into a family of increasingly massive clones of the original particle—analogous to the harmonics of a musical note.

For me, nodal impressions at spots, serve me well to see the vibratory nature of the reality that we live in. Balloons with dyes spread around it, and sound application help us see where such nodal point considerations would settle themself to these distinctive notes. You take the sum(it harmical value, in order to distinctively classify the partcle/object?

Maybe we can have experts describe this in a most genaral way, where I might have complicated the picture:?) What I did want to say about artistic rendition, is like the work of Penrose. It is very important it culminates the vision, to real things? As I showed in Monte Carlo effect. Or, John Baez's view of Plato's God?

Ultracold Superstrings byMichiel Snoek, Masudul Haque, S. Vandoren, H.T.C. Stoof

Supersymmetric string theory is widely believed to be the most promising candidate for a "theory of everything", i.e., a unified theory describing all existing particles and their interactions. Physically, superstring theory describes all particles as excitations of a single line-like object. Moreover, the bosonic and fermionic excitations are related by supersymmetry. A persistent problem of string theories is the lack of opportunity to study them experimentally. In this Letter, we propose and analyze a realistic condensed-matter system in which we can create a non-relativistic Green-Schwarz superstring in four space-time dimensions. To achieve this, we make use of the amazing tunability that is now possible with ultracold trapped atomic gases. In particular, for the creation of the superstring we consider a fermionic atomic gas that is trapped in the core of a vortex in a Bose-Einstein condensate. We explain the tuning of experimental parameters that is required to achieve supersymmetry between the fermionic atoms and the bosonic modes describing the oscillations in the vortex position.

Now what is very interesting to me is the way such harmonical value can be seen in in relation to particle identification. It is not always easy to see how such disks and toys could exemplify this for us, but I am trying. If we wanted to see the new toy and the relations that I will show how would this all relate to the disk and the ball on it?



I wanted to look at what you were saying to "try," and understand.

One of the most exciting predictions of Einstein's theory of general relativity is the existence of a new type of wave, known as a gravitational wave. Just as in electromagnetism, where accelerating charged particles emit electromagnetic radiation, so in general relativity accelerating masses can emit gravitational radiation. General relativity regards gravity as a curvature of spacetime, rather than as a force, so that these gravitational waves are sometimes described as `ripples in the curvature of spacetime'.

This mode is characteristic of a spin-2 massless graviton (the particle that mediates the force of gravity). This is one of the most attractive features of string theory. It naturally and inevitably includes gravity as one of the fundamental interactions.

By looking at the quantum mechanics of the relativistic string normal modes, one can deduce that the quantum modes of the string look just like the particles we see in spacetime, with mass that depends on the spin according to the formula

Remember that boundary conditions are important for string behavior. Strings can be open, with ends that travel at the speed of light, or closed, with their ends joined in a ring.

See:

Quantum Harmonic Oscillators

Distinctions of Holographical Sound

Visualization: Changing Perspective

I give some perspective on "image use and artistic expression." But such journeys are not limited to the "ideas of a book" or "a painting" in some form of geometric code.

Some will remember Salvador Dali picture I posted. I thought it okay, to see beyond with words, or how one might see a painting and it's contribution to thoughts. Thoughts about a higher dimensional world that is being explained in ways, that we do not generally think about.

So while it is not mysterious, there is some thought given to the ideas of moving within non-euclidean realms. In the one hand, "discrete forms" have us look at how such a model in terms of quantum gravity is built, and these images and paintings, accordingly?


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.


Click on image for a larger view

On page 65 of Hyperspace by Michio Kaku, he writes, "Picasso's paintings are a splendid example, showing a clear rejection of the perspective, with woman's faces viewed from several angles. Instead of a single point of view, Picasso's paintings show multiple perspectives, as though they were painted by someone from the fourth dimension, able to see all perspectives simultaneous

Talk of the Nation, August 20, 2004 · How did Leonardo da Vinci use math to influence the way we see the Mona Lisa? And how does our visual system affect our perception of that, and other, works of art? A look at math, biology and the science of viewing art.

This idea of dimension seemed an appropriate response to what I see in the Monte Carlo effect. I mean here we are trying to dewscibe what dimenison might mean in terms of a gravity issue. Is there any relevance?

What are Surfaces and Membranes?

Surfaces are everywhere: the computer screen in front of you has a smooth surface; we walk on the surface of the earth; and people have even walked on the surface of the moon.

By surface we mean something 2 dimensional (*). Clearly objects like a coffee cup or a pencil are 3 dimensional but their edges - their surfaces - are 2 dimensional. We can put this another way by seeing that the surface has no thickness - it is just the places where the coffee cup ends and the air or coffee begins.

Surfaces can be flat, like a table top, or curved like the surface of a football, a balloon or a soap bubble. The surface of water can be either flat without ripples, or curved when it has ripples or waves on it.

We use the word membrane to mean a sheet-like 2 dimensional object, an object with area but very little or no thickness. Good examples are sheets of paper or a piece of plastic food wrap. Just like surfaces, membranes can be flat or curved; rough or smooth.

Quantum Gravity Simulation

P. Picasso
Portrait of Ambrose Vollard (1910)
M. Duchamp
Nude Descending a Staircase, No. 2 (1912)
J. Metzinger
Le Gouter/Teatime (1911)

The appearance of figures in cubist art --- which are often viewed from several direction simultaneously --- has been linked to ideas concerning extra dimensions:

Dimensionality


Cubist Art: Picasso's painting 'Portrait of Dora Maar'

Cubist art revolted against the restrictions that perspective imposed. Picasso's art shows a clear rejection of the perspective, with women's faces viewed simultaneously from several angles. Picasso's paintings show multiple perspectives, as though they were painted by someone from the 4th dimension, able to see all perspectives simultaneously.

Art Mirrors Physics Mirrors Art, by Stephen G. Brush

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.

Piece Depicts the Cycle of Birth, Life, and Death-Origin, Indentity, 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 with a grand set of concerns, one famously 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.

"

The Unity of Mathematics

Alain Connes

Where a dictionary proceeds in a circular manner, defning a word by reference to another, the basic concepts of mathematics are infinitely closer to an indecomposable element", a kind of elementary particle" of thought with a minimal amount of ambiguity in their defnition.

I think what intrigues me most, is that a world can be fabricated mathematically that is carefully constructed using models of math, to get to a desired visionary culmination? One had to have some culminative effect, from such model thinking, that a vision beocmes clear. In this sense I related Lenny Susskind here, for his developement and contributions to string theory.

Now having spent time delving into parts of this world, the "tidbits" help me to see that such alignmenets of the world of physics have correlations in mathematical design. This has to have it basis set, "in the Rossetta stone you might say," about how we percieve the deveopement of those physics. The math must contrast the physics?

So to set things straight here, in case I gave the wrong link, I thought I should attribute proper link to words in case this mistake was made.



So too, information in blogs can be readily adapted too, where previous articles might have made some feel that the article not worth maintaining in their blog? That it might have been removed? I was thinking of the B-field topic that Lubos had written briefly on, that when I went to look for relevant information pertaining to this current entry, it was no where to be seen.

A VIEW OF MATHEMATICS by Alain CONNES
Most mathematicians adopt a pragmatic attitude and see themselves as the explorers of this mathematical world" whose existence they don't have any wish to question, and whose structure they uncover by a mixture of intuition, not so foreign from poetical desire", and of a great deal of rationality requiring intense periods of concentration.

Each generation builds a mental picture" of their own understanding of this world and constructs more and more penetrating mental tools to explore previously hidden aspects of that reality.

Now many would have to forgive my adventurous heart. I was somehow transported in my thoughts and converted? I don't know when, that such models of the mathematical structure had easily become discernable for me(it's result)? Not it's elemental structure(although I have seen areas of string theory design developed) from basic principals. It had it's culminative effect.

Is my vision always right? Of course not. But I see where such discriptions are necessary. Solid, and in stone, so that such progression can be made. I respect this, and I respect the physics, and it's culminative approach in theoretical developement.

Nature's Greastest Puzzle



Alain Connes refers to "poetic design," much like I see beats to music:?), and artistic adventure, as the play ground of imagination. We hope such songs shared, lyrics or otherwise, will reveal what the most secluded and private individuals might have found in their own world. To seek out, good artistic drawers like Escher? Penrose, needed his help, and the ideas brought forth, interesting results.

Now there is a reason for this post besides setting the record straight. It came up a long time ago with the question of whether mathematics was natural or created.

This may seem simplistic thought to some, but to me, it forced me to consider whether mathematics and physics were directed connected to each other.:) Now as I have said it is not easy for me to follow the matheics of such abtract individuals, but once I catch sight of the world that they allude too, it is somehow easy for me to see the structure of the bubble, or a representative drawing correlated in nodes, and features of a world that is constained in the physics.

This is why I refer back to Lubos and his B-field missing post, or I cannot simply find it. I refer to it, because I made links to mathematical design, that correlated dynkin diagram as shown above, and connects to other blog. Now it was important for me to see this correlation in the archetecture of the picture I linked to its prospective author, in relation to the dynkin diagram. Not the E11 asscoiation, but with that I had linked in image in comments to the B-field post.

My whole blog is based on visionary developement, theoretically, as well as nurturing physics association as best as I can, to show that the envelope is being pushed theoretically.



Interpretations of the magnetic field, in all its desgin is easily comprehensible once we align our thinking to hard fact and design reprsentation. Magnetic field lines on paper, is a child's toy, but easily experimetally done. Much more abstract then, that we see the field created, it's north and south, and a channel through which expression can flow?



Now even this is contained, and a Gausssian representation, highly abtract, relates curvature in away that we would understand this force that nature has created for us.

You must remember I do not have the luxury or life's abilty to move through the higher avenues that scholastic carreers have venture forth in. To preview this branch or that branch in physics, so I am bombarded with information from all angles:?)

I like to wrap the gravitational field, much like we wrap the magnetic field. It's just the way I see, and in it's greater design, that vast gravitational field that is generate through our cosmos? Bubbles become very interesting whenyou wrap somehing and the inside is moving with the outside, and in the vast vacuum of space this is stretching the very fabric itself?

I won't make the mistake of calling it the aether, yet continuity of expression seen in this abstract mode, does not see "tears" and such, so it is allocated to topological relevances. Holes, that look like swiss cheese in the cosmos? Yet I know well the events, that materialize in comsological expression, I wanted to push beyond these material things, to see the greater vision that has been moved by mathematcians.

You can say the rogue man here who speaks, is a wolf cub. Has been raised in a foreign world, without the benefits of scholastic teachers to guide me. So I had to look for them who held sacred some of the vision that I see when this math leads to a comprehensive view.

Reimann lead Einstein, and it was fortunate that Grossman was able to spot Einsteins deficiences. Help him move geoemtical principal beyond the euclidean coordinated world, to one manifested in spacetime, and a new dynamcial feature called gravity. It was beyond billiards and the sound related, and not the clasical discription that now beocmes the analogy of, that strange world we now see in gravitational thought.

Was it enough to speak about theses things and theorectically develope thoughts, to describe ways, in which such sound could ring bars, or influence the flexible arms of LIGO We measure this abstract world mathematcially created, to realize, we are now engaged in something very unique about our visions developement? Kip Thorne progeny will be the new genration that sees in way that were new to bauss and Riemann and now as we see of Einstein. This has a geometrical expression and basis to it, and it leads into projective elements topologically described.

Klein's Ordering of 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.


Klien's ordering of geometries were specifc here?

Gamma Ray Detection

A important point here is that there should be coincidental features in gamma ray detection, that should align with LIGO detectors?

Why are two installations necessary?

At least two detectors located at widely separated sites are essential for the unequivocal detection of gravitational waves. Local phenomena such as micro-earthquakes, acoustic noise, and laser fluctuations can cause a disturbance at one site, simulating a gravitational wave event, but such disturbances are unlikely to happen simultaneously at widely separated sites.

Lubos said::

The LIGO collaboration informed that the second science run did not detect any gravitational waves. The results follow from 10-day-long observations in early 2003 (two more science runs have been made ever since)

A current blackhole has been detected and so should LIGO detect it. So how long should we wait if findings are only now being conisdered from 2003 run?

Scientists have detected a flash of light from across the Galaxy so powerful that it bounced off the Moon and lit up the Earth's upper atmosphere. The flash was brighter than anything ever detected from beyond our Solar System and lasted over a tenth of a second. NASA and European satellites and many radio telescopes detected the flash and its aftermath on December 27, 2004. Two science teams report about this event at a special press event today at NASA headquarters.

Journey to a Black Hole

A direct image of gravity at its extreme will be of fundamental importance to Physics. Yet imaging a black hole requires a million times improvement over Chandra. That's a big step. Over the next 20 years, the Cosmic Journeys missions will take us closer and closer to a black hole though the power of resolution. Each successive mission will further us in our journey by 10- or 100-fold increases in resolution, step by step as we approach our goal of zooming in a million times closer. And each stop along the way will bring us new understandings of the nature of matter and energy.

GLAST is a gamma-ray observatory mission that will observe jets of particles that shoot away in opposite regions from a supermassive black hole at near the speed of light. We do not fully understand how a black hole, which is known for pulling matter in, can generate high-speed jets that stretch out for billions of miles. Galaxies that harbor black holes with a jet aimed in our direction are called blazars, as opposed to quasars, which have their jets aimed in other directions. GLAST, up to 50 times more sensitive than previous gamma-ray observatories, will stare down the barrel of these jets to unlock the mechanism of how the enigmatic jets form. The Constellation-X mission will probe the inner disk of matter swirling into a black hole, using spectroscopy to journey 1,000 times closer to a black hole than any other mission before it. With such resolution, Constellation-X will be able to measure the mass and spin of black holes, two key properties. This X-ray mission will also map the distortions of space-time predicted by Einstein. Constellation-X draws its superior resolution by pooling the resources of four X-ray satellites orbiting in unison into one massive X-ray telescope. The ARISE mission will produce radio-wave images from the base of supermassive black hole jets with resolution 100,000 times sharper than Hubble. Such unprecedented resolution can reveal how black holes are fed and how jets are created. ARISE will attain this resolution through interferometry. This technique is used today with land-based radio telescopes. Smaller radio telescopes spread out on land -- perhaps one mile apart -- can work together to generate a single, huge radio telescope with the collecting power of a one-mile radio dish. ARISE will utilize one large radio telescope in space with many other radio telescopes on Earth, bringing what is now a land-based technology to new heights.

New NASA Satellite to Study Black Hole Birth and Gamma Ray Bursts

The Swift observatory comprises three telescopes, which work in tandem to provide rapid identification and multi- wavelength follow-up of GRBs and their afterglows. Within 20 to 75 seconds of a detected GRB, the observatory will rotate autonomously, so the onboard X-ray and optical telescopes can view the burst. The afterglows will be monitored over their durations, and the data will be rapidly released to the public.

See:

Longitudinal and Transverse Information about the Energy Deposition Pattern

The Calorimetric View?