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?

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?

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

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