Music in Plato's Academy

Academy was a suburb of Athens, named after the hero Academos or Ecademos. The site was continuously inhabited from the prehistoric period until the 6th century A.D. During the 6th century B.C., one of the three famous Gymnasiums of Athens was founded here. Moreover, it is recorded that Hippias, the son of Peisistratos, built a circuit wall, and Cimon planted the area with trees which were destroyed by Sulla in 86 B.C. In 387 B.C. Plato founded his philosophical school, which became very famous due to the Neoplatonists, and remained in use until A.D. 526, when it was finally closed down by emperor Justinian.

Can a different kind of thinking encase the brain's ability to "envision the abstract of space" to know that it's harmonic values can be seen as the basis of experience?

For instance, in Plato's academy, and in contrast, and the revolution of the sixties saw the Beatlemania as subversive? It's lifestyle?



So on the one hand our parents resisting change in the formal art of music and lyrics, might have actually had some values?:) Rap, as a fungal fractorial growth of lyric inspired, emotive rythmics dances around the fire of a most primitive kind, finds an outlet for our youth?

If one thought of the "dissonance of thinking" that Plato saw, could it corrupt youth to it's potential? He saw "sound as instrumental" in moving youth to the farthest reaches, while "bad noise" subversive. This wouldn't have been a cosmological assertion, could it, about the nature of our universe and chaos?

So while beating hearts and rhtymns may have moved the harmonic brain into better retention times( there is some science here), this would not have been known to the revolt against beatle mania. Just that, they wanted to resist corruption of the youth?

I have no script, so I adlib.

An artistic view having grokked paradigmal changes, creates possible artistic pathways for all of us. It takes as little time as asking, "what the future holds."

Ole forms of mathematical construct is a value of mathematical height of abstraction. We common people, would have never understood this loftiness, had we not see their images? But they speak more, about the content, then what little science is known to the public mind. So those who knew better, scoff and make fun?

Feynman as a joker, gave us toy models in which to exorcise our mind of misplaced interactive features of science's theoretical opinion?

The Mathematics Of Plato's Academy: A New Reconstruction(Second Edition)
by David Fowler
Reviewed by Fernando Q. Gouvêa

Greek geometry was not arithmetized. In other words, the way we automatically connect the notion of "length" or "area" to numbers is something completely foreign to Greek mathematics. This is perhaps what makes it so hard for us to think mathematics in the Greek way. The idea that a length is a number is so deeply ingrained in our thought that it takes a conscious effort to conceive of an approach to geometry that does not make such an assumption. It is such an arithmetized interpretation that led historians to describe Book II of the elements as "geometric algebra". Fowler argues that Greek geometry was completely non-arithmetized. The strongest evidence comes from his analysis of the very difficult Book X, where he shows, I think successfully, that the way Euclid (or Theaetetus?) structures the argument precludes an arithmetical approach.

Wunderkammern

For me this is a wonderful view of abstraction, that had gone into model making, to help those less inclined to "the visonistic qualities of those same abstractions."

Shown here are the models in the mathematical wunderkammer located in the Department of Mathematics at the University of Arizona. Like those in most modern mathematics departments, the collection is a combination of locally-made student and faculty projects together with a variety of commercially produced models. Sadly, a century since their Golden Age, many of the models are in disrepair and much of their documentation has been lost. However, some recent detective work, with the help of the Smithsonian Institution in Washington, has helped the department identify models by the American educators W. W. Ross and R. P. Baker in the collection.

So having been allowed through internet developement to understand the work of fifth dimensional qualites could exist (why Thomas Banchoff must be added below), has far exceeded the understanding of those currently engaged in the mathematics? I do not mean to undermine or cast uncertainty in the direction of those who are helpijng us, but make for recognition of what technology has done for us, in the use of these internet capabilities.

Long before the advent of the World-Wide Web, Tom Banchoff was experimenting with ways of using electronic media to enhance mathematical research and aid in mathematical education. Banchoff helped install one of the first mathematics computer labs in the country, and continues to lead the development of innovative geometric software and curricula for undergraduate mathematics courses. He uses computer graphics as an integral part of his own research, and has used mathematical videos for the last 30 years as a means of disseminating his results.

I have been exploring these issues in regards to the Sylvester Surfaces, and the relationship seen in matrix development. It wasn't without some understanding that "isomorphic images" might have been revealled in orbital images categories, that dealing with this abstract world, didn't require some explanation?

The Magic Square



The picture below was arrived using the applet given from that site. What did you have do to change, in order to get the image I did? We are given possibilties?



But of course I am held by the physics of the world we see. As small as, might have exemplified itself in some larger cosmological imagery of a kind, can it be suited to topological features spoken too in string theory?

We know Max Tegmark has refuted the soccerball universe, and bazeian valuation of a quantum gravity model, that seem to good to be true? PLato, still felt that this soccer ball represented God? So maybe baezian, interpretaion, although derived from archimeadean, was more then the models through which they were precribed in Wunderkammen. Something ancient has been brought forward again for the mind bogglers that like to paly in these abstract spaces?

Mathematical Teaching Tools

Introduction: Lost Geometry

When I was small, growing up in Wisconsin, I loved to walk along the railroad tracks. As I walked, I would watch the steel rails grow from a point in the distance ahead of me, sweep around me, and then disappear again in the distance over my shoulder, converging slowly back to a point. The pure geometry of it was breathtaking. What impressed me the most, however, was the powerful metaphor that it suggested: How wide the present seemed, simply because of my presence there; how small the future and the past. And yet, I could move along the tracks, imagining myself expanding and contracting the infinite timeline of history. I could move ahead until any previous place along that continuum had shrunk to insignificance, and I could, despite the relentless directionality that I imagined moving along the tracks like so many schedule-bound trains, drift backwards as easily as I could let myself be carried forward.

The wonderful stories exemplifed by human experience, places me in states of wonder. About how processes in geometry could have engaged us in a real dialogue with nature's way around us. To see these stories exemplified above. One more that quickly came to mind, was Michio Kaku's view from the bridge, to the fish in the pond. Looking at the surface from two perspective sseem really quite amazing to me.

Such exchanges as these are wonderful exercises in the creation of the historical abstract. A Lewis Carroll in the making? An Abbotsolutely certainty of math structures, that we would like to pass on to our children and extend the nature to matter of the brain's mass?

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).

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

"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

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.

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