Pages

Tuesday, May 31, 2005

Coulomb Interactions, Thomson Scatterings



I think most people understand this stuff, and that experiment is the most efficient way of dealing with this issue. Even if we understand the matrix developemental view it's shortcoming are well expressed by others in that field of quantum grvaity. That could have easily helped orientate further constructive processes in that same respect.

John Ellis:
To my mind, one of the most plausible extensions of the Standard Model is supersymmetry (just look at the subjects of my research papers!), so could the minimal supersymmetric extension of the Standard Model have created the matter in the Universe?


John Ellis and the views about the supersymmetrical are really more in depth then the suttle words listed and spoken about by some. String Theorists knew how far this went?:)

Peter Woit said,
Certainly some people should be working on quantum gravity, especially if they are doing it in a non-overhyped way, trying to really seriously understand the technical issues involved. The LQG community appears to be doing this. But, personally, I don't have any ideas about how to start from thinking about quantum gravity and get to particle physics, whereas I do see some hope that if one better understands the structure of the standard model, one may be able to get to quantum gravity from there.
Posted by Peter Woit at May 30, 2005 05:22 PM


While some people are looking for consistant means of determinations, others apply "conceptual situations" and bring forth comprehension of a kind. Now to this degree, that "gluonic perception is being adjusted" to see these values. The Smolins and others understood well the limitation of these views? Are there any?

It becomes extremely difficult, as reductionistic processes are further detailed. So how far will this informtaion take us in terms of early universe understanding? Througha comsic interactive theme in the expeirments lead by situation in particle interaction in our atmosphere we can direct same particle interaction?


The calorimeter design for GLAST produces flashes of light that are used to determine how much energy is in each gamma-ray. A calorimeter ("calorie-meter") is a device that measures the energy (heat: calor) of a particle when it is totally absorbed.


What will glast do for this comprehension, understanding well the Calorimetric view of information given to us about those early universe situations?


Remember that the age is determined by the dark matter density. Mathematically, the length is roughly the geometric mean of the mean free path and the distance light can travel without obstruction (the horizon scale).


Monday, May 30, 2005

Microstates and Gravity


Strominger: That was the problem we had to solve. In order to count microstates, you need a microscopic theory. Boltzmann had one–the theory of molecules. We needed a microscopic theory for black holes that had to have three characteristics: One, it had to include quantum mechanics. Two, it obviously had to include gravity, because black holes are the quintessential gravitational objects. And three, it had to be a theory in which we would be able to do the hard computations of strong interactions. I say strong interactions because the forces inside a black hole are large, and whenever you have a system in which forces are large it becomes hard to do a calculation.



I was scanning over at Sean Carroll's blog and noticed his current article. It seems he is doing some kind of exorcism?:)

Entropy and intelligence


Consider the following system: a rectangular container filled part way with tiny spheres, some of them made of glass and some of brass. All the spheres have equal size, but the brass ones are heavier than the glass ones. Okay, now please tell me which of these configurations has the lowest entropy (or highest order, or greatest complexity, or whatever it is that you think only intelligence can bring into existence):


Now what was appealing to me here is the question of arrangement, and how chaotic systems might have been ruled by other consequences? Like gravity. So troubled by the analogy presented and distancing myself from some satanic feature of intelligent dsign, I wonder, what is going on here?


The animation shows schematically the behavior of the gas molecules in the presence of a gravitational field. We can see in this figure that the concentration of molecules at the bottom of the vessel is higher than the one at the top of the vessel, and that the molecules being pushed upwards fall again under the action of the gravitational field.


Now if I was to wonder about what would govern these thoughts, then indeed the question is raised that such intelligence is governed by a organizational ability that evolved from a better understanding of these graviational influences?

I am a junior here so the idea that such a exorcism would have been dispelled in this attempted has me wondering. Is there some greater design here in elminating the abilities of capable good thinking people and spooky actions, that have defied explanation?

A nice airplane ride is always fruitful to higher forms of thinking here? Time clocks, still exemplify some characteristics on molecular arangements? As well as Einstein and liethe impulsive qualites that such characters appeal to the scolastic heroes of our time, we are drawn by some inexplicable force to wonder about natures way?

Self Organization of Matter

Likewise, if the very fabric of the Universe is in a quantum-critical state, then the "stuff" that underlies reality is totally irrelevant-it could be anything, says Laughlin. Even if the string theorists show that strings can give rise to the matter and natural laws we know, they won't have proved that strings are the answer-merely one of the infinite number of possible answers. It could as well be pool balls or Lego bricks or drunk sergeant majors.


See:

  • Quantum Microstates
  • Sunday, May 29, 2005

    "Lightening," as Strings, Strike?



    With a "supersymmetrical realization" capable of being disemminated in the brain? What could have manifested from it's beginning? To have nature exemplify this greater potential "for new airs to breath life " into other possibilties of minds constructs "real objects" and "things"?

    Are the brain matters limited in terms of this new math? A perspective on the origination of what this universe was before it settled into "the cosmic bands of creation," we know as matter constituents of a galaxy kind.

    Flower representation (plank epoch and guth's expansnonary universe) as a torodial expression of form? As the basis of this supersymmetrical realization, seen in mathematical enlightenment? Makes it hard ,to see how expansionistc views could have been missed in gaining this toposense?

    Mind Over Matter: Brain Waves Guide a Cursor's PathBy Rick WeissWashington Post Staff WriterMonday, December 13, 2004; Page A08


    Wolpaw's "thinking cap" sports 64 sensors (the polka dots) that detect electroencephalographic (EEG) signals generated by neurons. With a software program analogous to those used in voice-recognition programs, which "learn" people's verbal quirks over time, people can gain control over a cursor's movement in two dimensions by modulating signal intensities in certain regions of the brain, Wolpaw and co-worker Dennis McFarland reported in last week's early online edition of the Proceedings of the National Academy of Sciences.


    Now it's never easy to see how such tomographical initiatives of the brains complex firings, might have a issue with the way we do things? So early work here, and the ideas of cursor control stimulation from human contact rhythmns could exemplfy the greater complexity of control that the minds likes to extend from itself?

    No less the idea that calorimetric views would measure some event in particle reductionistic views, about how things work. As a picture, is taken. Views condensed into greater meaning from a huge outlay of supersymmetrical issues, into this crazy bands that streak across our mind sky?

    Here we have gone to extremes to say, "that the brain has a third arm" and we know how it works and we can use it?

    Monkeys Adapt Robot Arm as Their Own


    Image: Miguel Nicolelis, M.D., Ph.D., professor of neurobiology and co-director of the Center for Neuroengineering, Duke University Medical Center, with robot arm. PHOTO CREDIT: Duke University
    "In our new experiments, the idea is that by using vision and touch, we're actually going to create inside the brains of these animal a vivid perceptual image of what it is to have a third arm," he said.


    The greater complexity of a system would have known that the physiological coordination of views, could have, "photosynthesis processes"? Used chemcial derivatives endocronologically reduce to the euclidean view. While it existed, within this massive torodial view of the human body? Reduced it, to viable means of expression?


    So why is it so difficult to accept the idea "that if a Professor is walking across the room, that many of his students would congregate.:)" Just as they would in any other attempts at defining the nature of this reality?

    Hooft, Witten and now Lauglin himself understands, that we have face to face with a problem? By arguing "stuff", would we have divested ourselves of recognition of this Third Superstring Revolution? Of course not.:)



    BrainInfo Site

    Saturday, May 28, 2005

    Mathematical Enlightenment

    This enlightenment experience is a realization about the nature of the mind which entails recognizing it (in a direct, experiential way) as liminocentrically organized. The overall structure is paradoxical, and so the articulation of this realization will 'transcend' logic - insofar as logic itself is based on the presumption that nested sets are not permitted to loop back on themselves in a non-heirarchical manner. 11




    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.


    While it is has become evident that the perspective I share and the wonders of mathematcial endowment, this basis has pointed me in the direct relationship between, brain matter and mind? Mind and mathematics?

    In the West we tend to think of 'enlightenment' itself as an exceptional mental state, outside of (or separate from) ordinary states. But in many of the spiritual traditions of the East, enlightenment is described as, in essence, a 'realization' 9 about the ultimate nature of the mind. Enlightenment is really nothing but the 'ordinary' state, as seen (and experienced) from a somewhat wider perspective, as it were. This is not unlike how the Newtonian frame which describes events in the material world at a HUMAN scale can be conceived as enclosed within a wider frame of explanation that is Einsteinian.


    So is there some cosmological embodiment of brain matter, once it has realized the mathmatics, that it will issue from that brain has somehow traversed, all laws of nature and transcended itself away from the curent standards set for itself. Mind, is limited by the brain matter we have?


    In this metaphor, when we are seeing the donut as solid object in space, this is like ordinary everyday consciousness. When we see the donut and the hole at its center, this is like a stage of realization in which 'form' is recognized as 'empty'. When we zoom in extremely closely and inspect the 'emptiness' at the center, or zoom out an extreme distance away from the object and the donut seems to disappear and we have only empty space - this is like certain 'objectless' states of awareness that can occur in meditation. But the final goal is not to achieve the undifferentiated state itself; it is to come to the special perspective that allows us to continue to see all three aspects at once - the donut, the whole in the middle, and the space surrounding it - this is like the 'enlightened' state, in this analogy. 10 The innermost and outermost psychological 'space' (which is here a metaphor for 'concentrated attention' and 'diffused attention') are recognized as indeed the same, continuous.


    So imagine the eire I could raise when I say that string theory has transcended the current status of mathematics, "brain matter controlled." That any attemtps to side swipe this new emergent quality of mathematics (what is it that has materialized?)and now we see that what lies in the cosmo is not limiteed to cosmlogical endeavors of General Relativity alone, but the deepr significance and recognition of the reductionist views of those same matters around us?

    Who is going to argue with this?

    I have set the standards well, that brain matters and functions if stood by, have revealled that mathematics is embodied by the brain matter with which we are dealt?

    Then how shall any new mathematics form and become the responsive road to recogniton of the physics we have endured by experimentation, to say, that new roads are now to be considered? Our brain status will not allow this, because the brain matter has not be readied for this new transcendance of thinkng. We are limited by the very matters with which we like to deal?

    So if string theory is to be considered in context, of the way in which the brain deals, then how could transcendance and twenty first century thinking ever prepare society for this new transcendance and viability for change in the way humanity has always seen?




    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)




    One had to be able to maintain this positon between the inner and outer and a consistent feature of the brains ability to unite, the world outside, with the one inside?

    Did we not see the ability of Time variable measures on the basis of how we see earth not mean, that we should place less significance to how Persinger asked the question, and ran contray to Lakoff and Damasio's views? One in which I postulate now too, as evidence of the transcendance needed to incoporate a much more palatable feature of the 21st century.

    My evidence is, and although speaking to some ideal of enlightenment, has shown that such graduations needed to see the "Work of Iscap" as a fundmental progression of this new feature of the brain's compacity? This is part of it's evolution.

    Oh, I have no views on intelligent design, so any comparisons seen, are coincidence.

    Friday, May 27, 2005

    Liminocentric structures and Topo-sense

    I hope I don't loose a lot of people on this one. This article is also closely associated to the thread on models of math that are constructed. Here Topo-sense is being referrred here.

    I like to think, and if I didn't, I wouldn't exist? So who's going to move this lump of matter? If it isn't motivated....will I exist?

    What moved the types of neurons to exist?



    "The Mind is Inherently Embodied"

    Our brains take their input from the rest of our bodies. What our bodies are like and how they function in the world thus structures the very concepts we can use to think. We cannot think just anything - only what our embodied brains permit."

    Without some path mapped out by the brain, what use are neurons that follow behind it?



    If we did not think "the lifeforce" as something just outside the body, what would we assign matter distinctions like our bodies? Lumps of clay? :)



    Damasio's First Law
    The body precedes the mind.

    Damasio's Second Law
    Emotions precede feelings.

    Damasio's Third Law
    Concepts precede words.



    So Lakoff and Damasio present points of view from one position. So how shall we see life, if it did not have some motivation? No spark?

    So is there a physiological consequence for many who see this "light at the end of the tunnel" would have been no less the descent through what we used in the beginning?

    This presents all kinds of possibilties? What is the essence of each of us if we had preassigned determinations besides our personalities, with which we can grow and mould. While, distinctive attributes have been initiated with the growth of the body? I mean, I am speculating here?

    Wednesday, May 25, 2005

    Greg Egan Visualizations

    Thanks to Lubos Motl and John Baez for bringing these views for perspective to us. These visualizations have helped me greatly, and have alowed me to see what other see in this abstract world, written, or computationally described.



    Many of Greg Egan's animations have served many to see, what he is seeing. I guess by saying I had no teachers, I had somehow missed those who bring these images to us. So I apologize for saying I had no teachers when they are abound in these blogs written or otherwise.

    Blaise Pascal


    Blaise Pascal (June 19, 1623 – August 19, 1662)

    Born in Clermont-Ferrand (France), the young Pascal was introduced to mathematics and physics by his father. So precocious was his talent in these disciplines that he published his innovative Essai pour les coniques [Essay on conics] in 1632, at only sixteen. In 1631, he moved to Paris, where he frequented the intellectual circle of Marin Mersenne (1588-1648)—a forum for the discussion of the most topical scientific and philosophical questions. In 1644, he became interested in the technological aspects of scientific research, devising a calculating machine that could perform additions and subtractions. In 1646, he conducted path-breaking research on the vacuum and fluid dynamics. He devoted two major works to fluids—Équilibre des liqueurs [Equilibrium of liquids] and De la pesanteur de la masse d'air [On the weight of the mass of air]—written in 1651-1654, but not published until 1663. In 1653-1654, he composed some brief but seminal papers on combinatory calculus, infinitesimal calculus, and probability. Pascal repeated Evangelista Torricelli's experiment, using various liquids and containers of different shapes and sizes. This research, in addition to the publication of Expériences nouvelles touchant le vide [New experiments on the vacuum], culminated in the famous experiment performed in 1648 on the Puy-de-Dôme, in which he demonstrated that atmospheric pressure lessens with an increase in altitude.

    In parallel with his scientific pursuits, Pascal displayed a deep and abiding concern with religious and moral issues. In his youth, he espoused Jansenism and began to frequent the Port-Royal group. These contacts form the background to the Lettres provinciales (1656-1657) and the Pensées (published posthumously in 1670).


    I had to lay this out before I continued to speak to the world Lubos motl directs us too. In a way, these mathematical pursuance and comprehensions, are revealing, when they speak to the greater probability of discovering the root systems mathematically as well as philosophically. Cases in point, about compaction scenarios are self explanatory when it comes to energy determination and particle reductionism . This relationship to idealization of supergravity, points thinking to a vast overall comprehension suited to the culminations of a model employed such as string theory?

    But back to the point of focus here.

    Earlier derivation of Pascal's thinking, "are roads that even he was lead too," that we have this fine way in which to speak about the root of mathematical initiative, and these roots leading to mathematical forays into the natural world.


    Diagram 6. Khu Shijiei triangle, depth 8, 1303.

    The so called 'Pascal' triangle was known in China as early as 1261. In '1261 the triangle appears to a depth of six in Yang Hui and to a depth of eight in Zhu Shijiei (as in diagram 6) in 1303. Yang Hui attributes the triangle to Jia Xian, who lived in the eleventh century' (Stillwell, 1989, p136). They used it as we do, as a means of generating the binomial coefficients.

    It wasn't until the eleventh century that a method for solving quadratic and cubic equations was recorded, although they seemed to have existed since the first millennium. At this time Jia Xian 'generalised the square and cube root procedures to higher roots by using the array of numbers known today as the Pascal triangle and also extended and improved the method into one useable for solving polynomial equations of any degree' (Katz, 1993, p191.)



    See I am somewhat starting with a disadvantage because buried in my head is the reasons for describing math more then it's intuitionist valuation in computer generated idealizations. It all of a sudden brings into perspective a deeper sense of the possibilities and probabilities?

    Here I am quickly reminded of Gerard t'hooft, and the thinking, about reductionistic views of information in computerized versions. Philosophically how can we have reduced information to such sizes and find the world a much more complex place. Would we not realize that such intuitionist attempts too have to undergo revisions as well?

    A Short History of Probability


    "A gambler's dispute in 1654 led to the creation of a mathematical theory of probability by two famous French mathematicians, Blaise Pascal and Pierre de Fermat. Antoine Gombaud, Chevalier de Méré, a French nobleman with an interest in gaming and gambling questions, called Pascal's attention to an apparent contradiction concerning a popular dice game. The game consisted in throwing a pair of dice 24 times; the problem was to decide whether or not to bet even money on the occurrence of at least one "double six" during the 24 throws. A seemingly well-established gambling rule led de Méré to believe that betting on a double six in 24 throws would be profitable, but his own calculations indicated just the opposite.


    Shall we quickly advantage to a age of reason where understand well the beginnings of mathematical systems and lead into Boltzman? But before I do that, I wanted to drawn attention to the deeper significance of this model appreciation.

    Discovering Patterns



    While we get some understanding here of what Pascal's triangle really is you learn to sense the idea of what culd have ever amounted to expressionand this beginning? Did nature tell us it will be this way, or some other form of expression?

    So overall the probability of expressionism has devloped the cncptual basis as arriving from soem place and not nothing. True enough, what is this basis of existance that we would have a philosphical war between the background versus non background to end up in stauch positional attitudes about how one should approach science here?

    So to me, I looked for analogies again to help me understand this idea of what could have ever arisen out of string theory that conceptually mad esense . Had a way in which to move forward, with predictable features? Is their sucha things dealing with the amount of information that we have in reductionsitic views. These views had to come to a end, and I will deal with this later.

    Of course now such idealization dealng with probabilties off course, forces me to contend with what has always existed and helps deal with this cyclcial nature. You have to assume soemthing first. That will be the start of the next post.

    But back to finishing this notion of probability and how the natural order of the universe would have said folow this way young flower, that we coud seen expansionism will not only be detailled in the small things, but will be the universe, in it's expression as well?


    The Pinball Game


    The result is that the pinball follows a random path, deflecting off one pin in each of the four rows of pins, and ending up in one of the cups at the bottom. The various possible paths are shown by the gray lines and one particular path is shown by the red line. We will describe this path using the notation "LRLL" meaning "deflection to the left around the first pin, then deflection right around the pin in the second row, then deflection left around the third and fourth pins".

    So what has happened here to force us to contend with certain issues that the root numbers of all things could have manifested, and said, "nature shall be this way?"


    Ludwig Boltzmann (1844-1906)

    In 1877 Boltzmann used statistical ideas to gain valuable insight into the meaning of entropy. He realized that entropy could be thought of as a measure of disorder, and that the second law of thermodynamics expressed the fact that disorder tends to increase. You have probably noticed this tendency in everyday life! However, you might also think that you have the power to step in, rearrange things a bit, and restore order. For example, you might decide to tidy up your wardrobe. Would this lead to a decrease in disorder, and hence a decrease in entropy? Actually, it would not. This is because there are inevitable side-effects: whilst sorting out your clothes, you will be breathing, metabolizing and warming your surroundings. When everything has been taken into account, the total disorder (as measured by the entropy) will have increased, in spite of the admirable state of order in your wardrobe. The second law of thermodynamics is relentless. The total entropy and the total disorder are overwhelmingly unlikely to decrease


    So what has happened that we see the furthest reaches of our universe? Such motivation having been initiated, had been by some motivator. Shall you call it intelligent design(God) when it is very natural process that had escaped our reasoning minds?

    So having reached it's limitation(boundry) this curvature of the universe, has now said, "such disorder having reached it's reductionistic views has now found it's way back to the beginning of this universe's expression? It's cyclical nature?

    This runs "contray to the arrow of time," in that these holes, have somehow fabricated form in another mode of thought that represents dimensional values? This basis from which to draw from, had to have energy valuations missing fromthe original expression? It had to have gone some place. Where is that?

    But I have digressed greatly, to have missed the point of Robert Lauglin's principals, "of building blocks or drunk sergeant majors", and what had been derived from the energy in it's beginning? To say the complexity of those things around us had to returned our thinking back to some concept that was palitable.

    Why the graduation to ISCAP, and Lenny's new book, is the right thing to do

    (LEONARD SUSSKIND:) What I mostly think about is how the world got to be the way it is. There are a lot of puzzles in physics. Some of them are very, very deep, some of them are very, very strange, and I want to understand them. I want to understand what makes the world tick. Einstein said he wanted to know what was on God's mind when he made the world. I don't think he was a religious man, but I know what he means.

    The thing right now that I want to understand is why the universe was made in such a way as to be just right for people to live in it. This is a very strange story. The question is why certain quantities that go into our physical laws of nature are exactly what they are, and if this is just an accident. Is it an accident that they are finely tuned, precisely, sometimes on a knife's edge, just so that the world could accommodate us?

    Monday, May 23, 2005

    Albrecht Durer and His Magic Square


    Albrecht Dürer
    (self portrait at 28)

    It was important to me that I post the correct painting and one that had undergone revision to exemplify the greater context of geometrical forms. In the Topo-sense? Artistic renditions help and adjust views, where information in mathematical minds, now explains something greater. Melencolia II
    [frontispiece of thesis, after Dürer 1514]by Prof.dr R.H. Dijkgraaf


    "Two images when one clicked on," shows what I mean.

    Melancholia in 1514(the original)

    The Magic Square

    Like Pascal, one finds Albrecht has a unique trick, used by mathematicians to hide information and help, to exemplify greater contextual meaning. Now you have to remember I am a junior here in pre-established halls of learning, so later life does not allow me to venture into, and only allows intuitive trials poining to this solid understanding. I hope I am doing justice to learning.



    A new perspective hidden in the Prof.dr R.H. Dijkgraaf
    second rendition, and thesis image, reveals a question mark of some significance?:) So how would we see the standard model in some "new context" once gravity is joined with some fifth dimensional view?

    Matrix developement?

    Like "matrix developement," we see where historical significance leads into the present day solutions? How did such ideas manifest, and we look for this in avenues of today's science.


    In 1931 Dirac gave a solution of this problem in an application of quantum mechanics so original that it still astounds us to read it today. He combined electricity with magnetism, in a return to the 18th-century notion of a magnet being a combination of north and south magnetic poles (magnetic charges), in the same way that a charged body contains positive and negative electric charges.



    How relevant is this? How important this history? How relevant is it, that we see how vision has been extended from plates(flat surfaces to drawings) to have been exemplified in sylvester surfaces and object understanding. This goes much further, and is only limited by the views of those who do not wish to deal with higher dimensional ventures?



    See:




  • Topo-sense





  • The Abstract World
  • Saturday, May 21, 2005

    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
  • Thursday, May 19, 2005

    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)