Showing posts with label Gauss. Show all posts
Showing posts with label Gauss. Show all posts

Saturday, April 15, 2006

On Gauss's Day of Reckoning

A famous story about the boy wonder of mathematics has taken on a life of its own -Brian Hayes

Illustration by Theoni Pappas

In a fanciful drawing done in the manner of a woodcut, the young Carl Friedrich Gauss receives instruction in arithmetic from the schoolmaster J. G. Büttner. As the story goes, Gauss was about to give Büttner a lesson in mathematical creativity.

To me the historical significance of this research is important to me. People could chastise me for saying that the research I do has no quality, then what should be assumed with scientific credentials? Still the romance I have for such abstractions and development of thinking is important just the same. It is about creativity to me, and looking back to the ingenuity of thought, is something I can see in everyone. One doesn't have to consider them self less then, just by being the student that would solve the problem, while insight and acute perception, might have been revealed in one who could throw down the slate the quickest.

The story is fascinating tome on a lot of different levels and to tracking down the essence of what we see passed from one hand to another, and how this ambiguity might creep in and additions make there way for added material.

I understand this in our response to writing science, with what language is supposed to be. Sure talk about chinese , Italian, Latin of ole, and we want to know what the truest expression of the language should be?

Of course this is the responsibility of math, that a common basis be found, between all languages, that the source would have described it so abstract/yet closest to the center of the circle) that all would understand and could work the abstract nature of this math.

I feel guilty, that I cannot contribute so well to this math language, that I strive to listen very good to the concepts espoused, as close as possible to the development of this Algebraic way of seeing.

Yes, it is as important, as the geometrical seeing that it be inherent in the way things abstractly can be seen. That both would have supported the continued work fo science.

Mine then is the student's plight in a vast world that I exist away from, yet, try and stay as close as I can to learn.

Do I sanction everyones abilities away from this in character, is no less then the character I assume, and has been treated. That respect be given, might have found the truer calling of sharing the insights, be as truthful as possible. We should all strive to this of course.

What is Swirling in my Mind

As I lay there many things float through my mind about how we are seeing things now.

So the article above sparked some thoughts here about Sylvestor surfaces and B field understandings, that also included Lagrangian perspective along with WMAP polarization mapping. All these things seem so disconnected?

I keep finding myself trying to wrap all of this in a gravitational perspective as it should , no less important then gauss contributions, hidden for a time, while the student of his brings the perspective for us all to see. So how familiar is protege as Riemann that his Hypothesis is so much the like of the numbers apparent, as in the youthful gaze of the student challenged.

Thursday, April 06, 2006

Hyperbolic Geometry and it's Rise

Omar Khayyám the mathematician(6 april 2006 Wikipedia)

He was famous during his lifetime as a mathematician, well known for inventing the method of solving cubic equations by intersecting a parabola with a circle. Although his approach at achieving this had earlier been attempted by Menaechmus and others, Khayyám provided a generalization extending it to all cubics. In addition he discovered the binomial expansion, and authored criticisms of Euclid's theories of parallels which made their way to England, where they contributed to the eventual development of non-Euclidean geometry.

Giovanni Girolamo Saccheri(6 April 2006 Wikipedia)

Saccheri entered the Jesuit order in 1685, and was ordained as a priest in 1694. He taught philosophy at Turin from 1694 to 1697, and philosophy, theology, and mathematics at Pavia from 1697 until his death. He was a protege of the mathematician Tommaso Ceva and published several works including Quaesita geometrica (1693), Logica demonstrativa (1697), and Neo-statica (1708).

Of course the question as to "Victorian" was on mind. Is non-euclidean held to a time frame, or not?

Victorian Era(wikipedia 6 April 2006)

It is often defined as the years from 1837 to 1901

Time valuations are being thought about here. In regards too, non euclidean geometry and it's rise. Shows, many correlations within that time frame. So that was suprizing, if held to a context of the victorian socialogical time frame. But we know this statement is far from the truth?

Seminar on the History of Hyperbolic Geometry, by Greg Schreiber

We began with an exposition of Euclidean geometry, first from Euclid's perspective (as given in his Elements) and then from a modern perspective due to Hilbert (in his Foundations of Geometry). Almost all criticisms of Euclid up to the 19th century were centered on his fifth postulate, the so-called Parallel Postulate.The first half of the course dealt with various attempts by ancient, medieval, and (relatively) modern mathematicians to prove this postulate from Euclid's others. Some of the most noteworthy efforts were by the Roman mathematician Proclus, the Islamic mathematicians Omar Khayyam and Nasir al-Din al-Tusi, the Jesuit priest Girolamo Sacchieri, the Englishman John Wallis, and the Frenchmen Lambert and Legendre. Each one gave a flawed proof of the parallel postulate, containing some hidden assumption equivalent to that postulate. In this way properties of hyperbolic geometry were discovered, even though no one believed such a geometry to be possible.

History (wikipedia 6 April 2006)

Hyperbolic geometry was initially explored by Giovanni Gerolamo Saccheri in the 1700s, who nevertheless believed that it was inconsistent, and later by János Bolyai, Karl Friedrich Gauss, and Nikolai Ivanovich Lobachevsky, after whom it is sometimes named.

Sunday, March 26, 2006

On Gauss's Mountain

You must understand that any corrections necessary are appreciated. The geometrical process spoken too here must be understood in it's historical development to undertand, how one can see differently.

Euclidean geometry, elementary geometry of two and three dimensions (plane and solid geometry), is based largely on the Elements of the Greek mathematician Euclid (fl. c.300 B.C.). In 1637, René Descartes showed how numbers can be used to describe points in a plane or in space and to express geometric relations in algebraic form, thus founding analytic geometry, of which algebraic geometry is a further development (see Cartesian coordinates). The problem of representing three-dimensional objects on a two-dimensional surface was solved by Gaspard Monge, who invented descriptive geometry for this purpose in the late 18th cent. differential geometry, in which the concepts of the calculus are applied to curves, surfaces, and other geometrical objects, was founded by Monge and C. F. Gauss in the late 18th and early 19th cent. The modern period in geometry begins with the formulations of projective geometry by J. V. Poncelet (1822) and of non-Euclidean geometry by N. I. Lobachevsky (1826) and János Bolyai (1832). Another type of non-Euclidean geometry was discovered by Bernhard Riemann (1854), who also showed how the various geometries could be generalized to any number of dimensions.

These tidbits, would have been evidence as projects predceding as "towers across valleys" amd "between mountain measures," to become what they are today. Allows us to se in ways that we are not used too, had we not learnt of this progression and design that lead from one to another.

8.6 On Gauss's Mountains

One of the most famous stories about Gauss depicts him measuring the angles of the great triangle formed by the mountain peaks of Hohenhagen, Inselberg, and Brocken for evidence that the geometry of space is non-Euclidean. It's certainly true that Gauss acquired geodetic survey data during his ten-year involvement in mapping the Kingdom of Hanover during the years from 1818 to 1832, and this data included some large "test triangles", notably the one connecting the those three mountain peaks, which could be used to check for accumulated errors in the smaller triangles. It's also true that Gauss understood how the intrinsic curvature of the Earth's surface would theoretically result in slight discrepancies when fitting the smaller triangles inside the larger triangles, although in practice this effect is negligible, because the Earth's curvature is so slight relative to even the largest triangles that can be visually measured on the surface. Still, Gauss computed the magnitude of this effect for the large test triangles because, as he wrote to Olbers, "the honor of science demands that one understand the nature of this inequality clearly". (The government officials who commissioned Gauss to perform the survey might have recalled Napoleon's remark that Laplace as head of the Department of the Interior had "brought the theory of the infinitely small to administration".) It is sometimes said that the "inequality" which Gauss had in mind was the possible curvature of space itself, but taken in context it seems he was referring to the curvature of the Earth's surface.

One had to recognize the process that historically proceeded in our overviews "to non-euclidean perspectives," "geometrically enhanced" through to our present day headings, expeirmentallly.

Michelson interferometer(27 Mar 2006 wikipedia)

Michelson interferometer is the classic setup for optical interferometry and was invented by Albert Abraham Michelson. Michelson, along with Edward Morley, used this interferometer for the famous Michelson-Morley experiment in which this interferometer was used to prove the non-existence of the luminiferous aether. See there for a detailed discussion of its principle.

But Michelson had already used it for other purposes of interferometry, and it still has many other applications, e.g. for the detection of gravitational waves, as a tunable narrow band filter, and as the core of Fourier transform spectroscopy. There are also some interesting applications as a "nulling" instrument that is used for detecting planets around nearby stars. But for most purposes, the geometry of the Mach-Zehnder interferometer is more useful.

A quick summation below leads one onto the idea of what experimental validation has done for us. Very simply, the graduation of interferometer design had been taken to astronomical proportions?

Today the Count expands on this for us by showing other information on expeirmental proposals. How fitting that this historical drama has been shown here, in a quick snapshot. As well the need for understanding the "principal inherent" in the project below.

VLBI is a geometric technique: it measures the time difference between the arrival at two Earth-based antennas of a radio wavefront emitted by a distant quasar. Using large numbers of time difference measurements from many quasars observed with a global network of antennas, VLBI determines the inertial reference frame defined by the quasars and simultaneously the precise positions of the antennas. Because the time difference measurements are precise to a few picoseconds, VLBI determines the relative positions of the antennas to a few millimeters and the quasar positions to fractions of a milliarcsecond. Since the antennas are fixed to the Earth, their locations track the instantaneous orientation of the Earth in the inertial reference frame. Relative changes in the antenna locations from a series of measurements indicate tectonic plate motion, regional deformation, and local uplift or subsidence.

See:

• Apollo Moon Measure
• Wednesday, January 04, 2006

KK Tower

Like many people who devote their time to understanding the nature of the cosmo and the micro perspective of the world around us, these things have their own motivational packages which move to further rquired comprehensions. In that, one needs to further educateas to what they are talking about.

It's definitiely not easy, but I am trying, and devote a lot of time to this regardless of what schooling is required, it is not my intent to send people down the wrong paths, or, no paths at all, before I have investigated the terrain as best I can.

Mountains can give persepctive where sitting in the valleys circumspect what the greater can be?

KK Tower

What is it?

Kaluza-Klein theory(Wiki 4 Jan 2006)

A splitting of five-dimensional spacetime into the Einstein equations and Maxwell equations in four dimensions was first discovered by Gunnar Nordström in 1914, in the context of his theory of gravity, but subsequently forgotten. In 1926, Oskar Klein proposed that the fourth spatial dimension is curled up in a circle of very small radius, so that a particle moving a short distance along that axis would return to where it began. The distance a particle can travel before reaching its initial position is said to be the size of the dimension. This extra dimension is a compact set, and the phenomenon of having a space-time with compact dimensions is referred to as compactification.

Kaluza-Klein theory is a model which unifies classical gravity and electromagnetism. It was discovered by the mathematician Theodor Kaluza that if general relativity is extended to a five-dimensional spacetime, the equations can be separated out into ordinary four-dimensional gravitation plus an extra set, which is equivalent to Maxwell's equations for the electromagnetic field, plus an extra scalar field known as the "dilaton". Oskar Klein proposed that the fourth spatial dimension is curled up with a very small radius, i.e. that a particle moving a short distance along that axis would return to where it began. The distance a particle can travel before reaching its initial position is said to be the size of the dimension. This, in fact, also gives rise to quantization of charge, as waves directed along a finite axis can only occupy discrete frequencies.

Kaluza-Klein theory can be extended to cover the other fundamental forces - namely, the weak and strong nuclear forces - but a straightforward approach, if done using an odd dimensional manifold runs into difficulties involving chirality. The problem is that all neutrinos appear to be left-handed, meaning that they are spinning in the direction of the fingers of the left hand when they are moving in the direction of the thumb. All anti-neutrinos appear to be right-handed. Somehow particle reactions are asymmetric when it comes to spin and it is not straightforward to build this into a Kaluza-Klein theory since the extra dimensions of physical space are symmetric with respect to left-hand spinning and r-hand spinning particles.

So in order to get to the summation, views of hidden dimenisons had to be mathematically described for us, so a generalization here would suffice in the following diagram.

Now, not having the room to explain, and having linked previous information on extension of KK theory, I wondered about the following. If we understood well, the leading perspective that lead us through to the dynamical realizations, then the road Gauss and Reimann lead us to would help us to understand the visualization materializing by the calorimeter disciptions of each energy placement harmonically describing each particle's value? Even in a empty space, there seems to be something of a harmonical consideration?

If one understood well enough about the direction of discernation of early universe consideration and microstates, then such questions would have been of value in the ideas of topological considerations?

Friday, October 21, 2005

Resonance: Brownian Motion

Now before I go into this I am thinking also if how "weathered effects and chaos" would have allowed quantum probability valuations (let's say spintronic idealization to channel) to have been curtailed to a Professor crossing the room. Brane orientation and fermionic considerations held, while helping to orientate views further out in the bulk?

This encompasses the generalization in terms of bubble dynamics, or how could any singularity too "inside/out" be of value to that same gravitational collapse, regardless of macro or micro considerations?

So one would have to seen how, Langrangian "points" help to view dynamcial situations in relation to the Sun Earth Moon. I would like to have thought of a chaldni plate analogy here, pointing, to a place for consideration of movement of our satelittes with less efffort. It is a vision of geometrical correlations that such idea could have been artistically embued.

Resonance
This is a magazine that Clifford drew our attention too, and while looking in the archive I found reference here below that sort of caught my attention.

Brownian Motion Problem: Random Walk and
Beyond
,

I really find this quite interesting from a "artistic point of view".

While indeed the issue is quite complex in terms of environmental flows and such, this kind of dynamcial valution might seem interesting from the point of view of early plasmatic conditions, would it not?

Now if such supefluid conditions would arise in the collider developements then, this expression would defintiely need to answer the way in which we look at what superpsymmeterical valuation would have ever resulted in symetry breaking valuation sought from these bubble dynamics, fromthe fluid of that early universe.

What constraints would limit you from making such a comparison and the idea of bubbles that form from this bath? To viewing dynamic situations in terms of thermodynamic realization offered from other perspectves. I give some examples shortly. Just know, that gravitational collapse would have signalled a better determination then one how ever discerned, to point to efforts to understand this supersymmetrical valuation. If all grviaational states of collpase are revealled as leaidng indicators to this supersymmetreicla valuation, then the idea to me is that this points to a underlying reality that exists in our moments around us.

While Microstate blackhole would be quick to dissipate, it is equally sufficient to my thinking to see that infomration realease from this "supersymmetrical breaking" would give indictaions as information in UV indications?

Of course it's all speculation from the point of the fluid, because we have evidence of this already. So all I am doing is saying that having the stage set, then how would such relations signal new universes?

So from a geometrical standpoint, having been told that there are no physics and geometry below a certain length (is this a quantum grvaity ascertion since there is no consensus?), this makes it extremely difficult to theoretically deal with how such a issue I am relaying in terms of Brownian motion could have ever spawned those same bubble universes out of such a fluid state.

This gallery was inspired by a lecture of Dr. Julien Sprott and his work.To learn how these are created, check out my Strange Attractor Tutorial. Click on the images to enlarge them.

So my mind is set in this chaotic enviroment, but indeed, the continuity of all these movements and flows seem disjointed from one perspective, that one point over here, might be different in the way a guassian map might reveal of point "p" over there. So we know on the surface, seeing valuation in terms of gaussion coordiantes that we can spell out on the face value of this surface, would have given a uv of P a very much different look.

Gaussian Coordinates
We can sum this up as follows: Gauss invented a method for the mathematical treatment of continua in general, in which ?size-relations? (?distances? between neighbouring points) are defined. To every point of a continuum are assigned as many numbers (Gaussian co-ordinates) as the continuum has dimensions. This is done in such a way, that only one meaning can be attached to the assignment, and that numbers (Gaussian co-ordinates) which differ by an indefinitely small amount are assigned to adjacent points. The Gaussian co-ordinate system is a logical generalisation of the Cartesian co-ordinate system. It is also applicable to non-Euclidean continua, but only when, with respect to the defined ?size? or ?distance,? small parts of the continuum under consideration behave more nearly like a Euclidean system, the smaller the part of the continuum under our notice.

Now if such bubble dynamics were to be self revealling, such surface measures would give evidentary features of the shape of this bubble, defining geometrical propensities as a surface valuation. I am thinking here of the "rainbow colors as refractory relevance" that would seem to define heavier color variations over this surface, if using soap bubble as an example.

Plato:
So just to carry on a bit with this point "P" in gaussian coordinated of frame of UV, what realization exists that we could not find some relevance here in the geometry to have further exploited the mind's capabilties by venturing into the Wunderkammern of thinking. By association, of Nigel Hitchin's "B Field manifestations geometries" to realize that althought these might be limited to what Jacque is saying , then what value this geometry if we can not see the landscape as something real in time variable measures?

Now you know you could have never come to this "shape" without the birthing process of expansitory values of a new universe right? So of course there is something troubling about chaotc environments, but also the nice fluidic forms of expression that would seem to reveal the dynamics of nature in overlaid valuation, of motion.

Having come to a surface valution of expansitory features such as a measdure of the earth in a "time variable mode", makes much more sense to me having accumulative histories and use of Grace, that we would now say hey, ourviews of spherical and round earth we live on has a certain new feature about it, that does not seem so pretty. Well, we defined the valuation gravitationally over this whole planet and it is encased. So I see it as a bubble defined to it's mass context and density variations etc.

Friday, October 14, 2005

Art and Science

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

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

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

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

The new willingness to consider what might have happened before the big bang is the latest swing of an intellectual pendulum that has rocked back and forth for millenia. In one form or another, the issue of the ultimate beginning has engaged philosophers and theologians in nearly every culture. It is entwined witha grand set of concerns, one famosly encapsulated in a 1897 painting by Paul Gauguin: D'ou venons? Que sommes-nous? Ou allons-nous?
Scientific America, The Time before Time, May 2004.

Sister Wendy's American Masterpieces":

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

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

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

Art Mirrors Physics Mirrors Art, by Stephen G. Brush

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

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

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

The Search for Extra Dimensions
OR Does Dzero Have Branes?

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

Issues with Dimensionality

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

And who could not forget Salvador Dali?

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

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

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

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

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


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

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

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

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

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

Who in Their Right Mind?

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

Penrose and Quanglement

Order and Chaos, by Escher (lithograph, 1950)

Saturday, September 24, 2005

Big Ideas.....To String Theory

Plato said:
yes to Gauss and gaussian coordinates, not forgetting, Saccheri, Bolyai and Lobschevasky along this lineage of geometers

On the Hypotheses which lie at the Bases of Geometry

So A continuation from this, and reference to important papers for consideration.

I was actually looking for papers on S.S.Chern and I have been having difficulty tracking down one of his papers entitled,"Relativity and Post Reimannian Differential Geometry," published in 1980. As I look, I usually come across interesting sites for consideration. They do indeed lead from one spot to another willy-nilly.

So I thought I would show the transition to topics that I compiled for reference in relation to string theory.

So having gone through a list here as follows, I came upon the article from a site called "Big Ideas". It was nice then, that I link to the site in question and the article for consideration. Talk about getting off the beaten path.:)

My intentions was to see how Gauss's and S.S. Chern's work correlated together and developed in line with Reimann. Hence the paper in question I was looking for. If anything had change my perspective, Gauss and Reimann were instrumental here and the understading of the metric. Gaussian coordinates help united much for me into the picture General Relativity had taken me too in see the dynamcial nature of the graviational field.

Big Ideas

It is of course from 2003, but always interesting nonetheless.

I understand Clifford's hesistancy on articles that have come out and some trepidation also seen by P.P. Cook on the issue Horizon of Hawkings in his article here. My focused is well set to this horizon as well, as th e question of blackhole types etc, and how such theoretical positions arise fromthis horizon. This was important to me that I move to the understanding of conformal ideas from tha horizon.

But articles, as best they can, hopefully can bring the lay person up to speed on what these ladies and gentlemen are doing with string theory and such. They help me in the generalized direction, so I hope all things are not to lost for Clifford and Paul in their entrancement of observation. "Disgust" to something fine in the media of consideration.

I noticed Paul's link to Jan Troost's site and have seen that site develope from inception, so it was interesting to continue to see the summation of string theory on his site as well. There are really good sites out there that I have kept track of, to help orientate my thinking in regards to to theoretical thinking at it's finest.

Saturday, August 27, 2005

On the Hypothese at the foundations of Geometry

I am trying to make my case on the greatest physics paper over at Cosmic Variance. One notices the slight misinterpretation I assigned, "geometical propensity to physics" that the case is more then just physi,s but the limmerack added envisioned, over such a paper that leads into physics.:) I see no difference now. So I refer to it as the greatest physics paper!

The title of this thread is attributed to Bernhard Riemann and a paper he wrote that revolutionized our concept of space with geometry of distances(the metric). With Gauss's tuteluge on curvature that was being developed, Reimann moved to understand how such changes now would be considered, where space is no longer flat. He moved Pythagorean thereom from:

c2=a2+b2 to c2=a2+b2-2ab cos Æ

where the right angle is no longer right but has magitude Æ then the above theorem has been generalized

The function that measures the instantaneous distance between two points was later used by Einstein where m and n vary over the intergers 1 and 2

ds2=gmndxmdxn

On the Hypothese at the foundations of Geometry

By use of similar triangles and congruent parts of similar triangles on the Saccheri quadrilateral, ABDC with AC = BD and ‚A = ‚B = p/2, he establishes his first 32 theorems. Most are too complicated to be treated in a short paper, but here some examples are merely stated, some are illustrated and some are proven. For those proofs which are brief enough to show here, the main steps are indicated and the reader is invited to fill in the missing details of the argument. A century after Saccheri, the geometers, Lobachevsky, Bolyai and Gauss would realize that, by substituting the acute case or the obtuse case for Euclid's postulate Number V, they could create two consistent geometries. In doing so they built on the progress made by Saccheri who had already proven so many of the needed theorems. They were able to create what we recognize today as the "elliptical" and "hyperbolic" non-Euclidean geometries. Most of Saccheri's first 32 theorems can be found in today's non-Euclidean textbooks. Saccheri's theorems are prefaced by "Sac."

How far advanced our thinking has become, that we can move quickly here to other avenues of consideration? How much "inbetween" the leading thinking of Riemann that we can have gotten here in our "physics of geometries?" Is it a suttle generalization in words and limmerack that such a physics view could have seen nature at its finest, and explained in a mathematical way.

Gaussian Coordinates
We can sum this up as follows: Gauss invented a method for the mathematical treatment of continua in general, in which ?size-relations? (?distances? between neighbouring points) are defined. To every point of a continuum are assigned as many numbers (Gaussian co-ordinates) as the continuum has dimensions. This is done in such a way, that only one meaning can be attached to the assignment, and that numbers (Gaussian co-ordinates) which differ by an indefinitely small amount are assigned to adjacent points. The Gaussian co-ordinate system is a logical generalisation of the Cartesian co-ordinate system. It is also applicable to non-Euclidean continua, but only when, with respect to the defined ?size? or ? distance,? small parts of the continuum under consideration behave more nearly like a Euclidean system, the smaller the part of the continuum under our notice.

Yes so easy now that we can see this space in ways that the average person without the physics comprehension would have never found that the fancy brane worlds held to perspective on the developing sciences and recognition of such physics processes had been elevated.

Would the likes of a Peter Woit be stagnated on what he sees if such limitation to the math endowed creator of mind, would see that such limitations to spintronic value added, would only partake of the events held to this brane and that a wider audience would now see that such dynamicsi n this universe would be greatly enhanced by entering a whole new world of abstraction.

According to Einstein's general theory of relativity, the gravitational potential due to an isolated source is proportional to rho + 3P, where rho is the energy density and P is the pressure. For non-relativistic matter the pressure is negligibly small, whereas for radiation P = rho/3. Therefore, for the same value of the energy density, radiation produces a deeper and more attractive gravitational potential (left) than non-relativistic matter (centre). If rho + 3P is negative, as in the case of quintessence ­ in this example P = ­2rho/3 ­ the sign of the gravitational field is transformed from attractive to repulsive (right).

Sunday, July 03, 2005

Anomalistic Features of Gold Fish and Ant World?

I was reading Mark Trodden's blog called, "Orange Quark" for reading, and he pointed out the following article. In Praise of Hard Questions, by Tom Siegfried

Geometric basis underlying science? I see this tendency of many to the Halls of records, museums, and whatever you like, to keep current for all us folks outside academia.

These are important historical correlations to draw from. These are wonderful connections to the fathers/mothers of science. Distinctive historical figures who embue science with their particular inflections and bend.

Should we dismiss the motivations of those who are driven by "anomalistic behaviors"? Remember Einstein in his youth and the compass? What are we ignorant of in such a case?

We know well, that such measures, if not supported, cannot be easily removed from the memories. Can be relinguished to subjective interpretations. Should not be ruled inadmissable:)Yet, it can drive the motvation of youth in that case t hard and fsat rules of order?

Had there ever been a time where a scientist had seen something that ran contrary to everything they know? It had to be at the front line, or how would anomalistic valuation had ver been entertained? Had been seen by a reputable scientist and held in the idealization of the Einstein who at his time, "lacked comprehension" but was moved.

Here I point out David Gross's statement and context supplied by Tom Siegfried .

Science's greatest advances occur on the frontiers, at the interface between ignorance and knowledge, where the most profound questions are posed. There's no better way to assess the current condition of science than listing the questions that science cannot answer. "Science," Gross declares, "is shaped by ignorance."

Yes I think we all understand.

So indeed we see then that all the forebears of our science then had something in common as they sought to geometrically express the abstract, and in my line of thinking, runs the Wunderkammer models. These are hard and concrete models in glass cases.

Maxwell understood this in Gauss and Faraday, and Einstein, understood this in Riemann? Sachherri elucidating beyond the limits of Euclids postulates 1-4, paved the way for a new dynamcial world? So how strange indeed that Sean Carroll would give us a sixty second explanation on extra dimensions. Have we eluded to an "aspect of mind" in abstraction?

Extra dimensions sound like science fiction, but they could be part of the real world. And if so, they might help explain mysteries like why the universe is expanding faster than expected, and why gravity is weaker than the other forces of nature.
Three dimensions are all we see -- how could there be any more? Einstein's general theory of relativity tells us that space can expand, contract, and bend. If one direction were to contract down to an extremely tiny size, much smaller than an atom, it would be hidden from our view. If we could see on small enough scales, that hidden dimension might become visible.

Sean, what shall you say to Peter Woit, who might say to you. "We are not Ants?"

So this sixty second explanation now presents itself, for the "mantra induced introspection" that one wonders, what the heck might Sean be talking about? Is there a world somewhere that that exists much like "ant world" in which we take part in?

How strange indeed then that the mind has been taken to Ant World, so that we may see, the angles of perception greatly ehanced for us? Where in the real world, walking straight lines is a "balancing act" when we engage the dynamcial qualites of science, that although engineered, also speak to the dynamcial relation underlying our everyday world.

So how shall such analogies then prepare us for the hard questions of science? Can we see now where such abstractions has moved science and the road shall lead us through to the idea of KLein's Ordering of Geometeries? Have we entered a new dynamcial realm of ant world, and together with Michio Kaku, created the new animated "goldfish world" as well, who see very much different then we see from the bridge?

Who is it that now sees and send our minds into "ants and goldfish?"

Tuesday, June 21, 2005

Thematic Resolutions

It is of course with some concern that any scientific mind, held to the established rules of his organizational, "motto of acceptance of the stringent rules of science" would allow such room, as to embue the human being with qualities greater then, the value assigned to subjective valuations. A church of reason that finds itself distasteful to the inquiry of life, and sanction it to the discourse of valued scientific principals that those of Strings and LQG fight back and forth with.

It's okay, we won't be fooled:)

Is it a coming to terms with the features we see in our own makeup as children, that we might sight the significant memory of that same childhood. What stuck, that you would have seen this course of action, no less then what held a Einstein in the mystery of the world, to understand it is a real and wonderful world of the forces that we do not readily see, yet we know well it directs the sciences in our world.

Nuances

The Alchemy of Creativity and the Social Artist.

Briggs speaks of themata as informing the lives of many geniuses. Beginning with themata for example --what are they, what is their deeper purpose and meaning? I see them as patterns of creation for which we are specially tuned, each of us tuned differently by the special sense organs in ourselves which pick up variations on these themes throughout the world. The famous example of the child Einstein and his fascination with the magnetic operation of the compass which then influenced his entire life of looking for the electromagnetic field in the unified field of reality. Each of us then is given as our gift a kind of guiding visionary theme which recurs throughout our life, and when we attend to it as an ally and helper, it gives us unique perspectives on working with reality.

God's Equation, by Amir D. Aczel, Pg 14

From a early age, young Albert showed great interest in the world around him. When he was five years old, his father gave him a compass, and the child was enchanted by the device and intrigued by the fact the needle followed a invisible field to point always in the direction of the north pole.Reminicing in old age, Einstein mentioned this incident as one of the factors that perhaps motivated him years later to study the gravitational field.

Is there some deeper force that evades our thinking, that it could have transcended the world of science, to know that envisioning the capabilities beyond those we enlist in our psychological reasoning, has real physical results manifest. It has been the direction and question that has existed most in my mind, that the world of the discrete, had many explanations before such solidification could have ever existed in the mind of concrete things.

So while such a view is held to a space beyond the limitations of math's design, such views revealled in the Wunderkammer were realistic abilties of the mind to incorporate the envisioning abilites beyond the euclidean defintions. "Straight lines and course of measure," that there could exist other forms beyond the limitations Einstein sought to describe for us in the gravity explanation given in General relativity.

It is well understood that the adventures lead too here were very instrumental in the realization that the noneuclidena geometires were very well adpatable to the view of Faradya, Gauss and Riemann in further defining ths geometric tendency a sa basis of exploration that today we are taken inot the abstract space of mind.

So what was the motivating force and we find that the culminative effect of a life exists, for those who by name are defined. Where is this basis that we can call forth eth elemental table of Mendelev to say that al things arise and her eare the concrete constructs of mind embellsih in the material world?

The light behind, in the analogy of Plato's cave, sets up the thinking in how issues from the source[the fire]( and here it might be referred to the fifth dimension)shines in its radiation. How is form realized?

Betrayal of Images" by Rene Magritte. 1929 painting on which is written "This is not a Pipe"

The jest here recognizes, that a picture of, and the real pipe are very different indeed. How is "form" percieved from perspective. The picture of the pipe and the real pipe are different things? And yet in this comparison, there is a third aspect as the idea?

It was a attempt to define this emergent property of existance that all of it could have been derived from some basis? Background dependant/ independant and two views that enlist the funcitonabiltiy to discourse, the thoughts held?

So it is well understood that such motivations that drive the character have some motivating force beyond what we had understood in the complete individual, called a "Peter Woit" or a "Lubos Motl", to find that such forces govern one or the other in it's drive for expression. One the justice that would not milead scoiety from someintelligent design feature to have gauaged society to a standard of being, better undertsood with a greater idealism set? Or of th efire that instigates a lubos Motl to question and position and valid it no less then the "peacemaker" might have revealled in the just and reasonable society?

So we have exposed a greater potential relaization that not only is motivated from perspectve, to find the creation of the universe is no less the creative adventure of the soul in i';s own design, for fruitation. So where exists this idea who find itself of the universe, as it unfolded in it's own motivation?

Saturday, May 07, 2005

The Use of Language, over Geometric Design?

One must realize that to further develope scenarios for the mind had to consider, created conversation. To use this to formulate new steps and expansion of thought. One needs to create the situation?

So what if, Plato in this case, is not real, and "the dialogues," using this figurative object, was used to create the dialogues? Can he have ever produced further thoughts for us to consider in dramas, without a bouncing board?

So is the situation real below?

Kansas Board Holds Evolution Hearings By JOHN HANNA

TOPEKA, Kan. (AP) - As a State Board of Education subcommittee heard more testimony Friday on how evolution should be taught in Kansas classrooms, one member acknowledged that she hadn't read all of an evolution-friendly draft of science standards proposed by educators.

Kathy Martin of Clay Center made the comment while attempting to reassure a witness who said he hadn't read the entire proposal, just parts of it. Russell Carlson, a biochemistry and molecular biology professor at the University of Georgia, said he had reviewed an alternate proposal from intelligent design advocates.

Islamic Creationism In Turkey

Sometime in the mid 1980s, the Turkish Minister of Education, Mr. Vehbi Dinçerler [. . .] placed a call to ICR. [. . .] he wanted to eliminate the secular-based, evolution-only teaching dominant in their schools and replace it with a curriculum teaching the two models[.] As a result, several ICR books which dealt with the scientific (not Biblical) evidence for creation were translated into Turkish and distributed to all Turkey's public school teachers.

You have to wonder too, about thedistrust of and motivations seen in the Templeton foundation and the list of scientific personalities that contribute or those thinking of contributing?

This mistrust is seen by some as instigating such concerns as revealled in the issues above? Motivating society with fasle idealizations? I do not quite understand this. This is not a position I take, but was one of observance that I witnessed and relay here.

The whole issue around the Sokal Affair:
The essay you have just seen is completely meaningless and was randomly generated by the Postmodernism Generator. To generate another essay, follow this link. If you like this particular essay and would like to return to it, follow this link for a bookmarkable page
.

Is it intentional, or are people easily fooled?

Is there a greater design behind and leading people into falsehoods? Is this what everyone fears could happen to them?

It's strange, but this post of yours sets up a complex scenario. About shadows and light? :)

That the tenable position would be, "the earth they stand on," some how intrudes on the surface of the moon, and from behind the earth, the sun.

A classic Plato story? :)

Not just the plain ideals of observance.

Might one believe beyond the scope of our scientific valuations? To see, that it might have some other answer to why life is the way it is. What is it's motivator? It's energy?

A higher perspective on what we know about earth is summed up in an overview of the globe. Are not the intricacies of earth's design, much more complex, then it's mere shadow causing presence?

The expansitory thinking beyond straight euclidean thinking, is much more versatile? Reveals geometrical design much more intricate then just two dimensional observances?

Thought and observance, is now telling us to think beyond the hard fact realities? You can still be a scientist and believe in God. :)

A tesserack or hypercube is a four dimensional analogue of a cube. See the figure on the left for a 2-D representation of this 4-D object. More information about these can be seen and found. Many people have difficulty believing such can exist which is why such books as Flatland (Abbott, 1884), Sphereland (Burgers, 1983), and Flatterland (Stewart, 2001) were written.

I tried to show leading indicators in this trial, further expanding it's boundry into todays world. No less than, "climate exchanges on Kyoto," and scientist to scientist, "battle for supremacy of ideology?" Intelligent design?

More abstract, the inclinations of the quote selected provided a opportunity. About what few people will ever understand? Are the roads leading to complex scenarios about the particle world.

The way Arthur Miller quote might have sufficed might be to say, "that we need to think differently about reductionistic processes."

These are all governed by geometrical consistancies although we rely on experimental process. The progression to topological forms, as abstract processes. These are relevant to our "dynamical way of thinking." If lead to fifth dimensional scenarios, you are beyond the limitations of our solid world, becasue it arose from some place else first?

The "Calorimetric view," addresses this. We create the scenario of particle collisions and measure, particle production.

None of you would know this, but the inherent "opera of image," leads you to ask, "what is a tesserack?" Non?

The last two picture gaves views from a fifth dimensional element, where gravity and light have been joined. Dali's painting, and relation to the wonder of God's son. Are these related to these higher geometrical figures and wonder about God?

We are not simple machines. As well, the computer screen is a work and play on fifth dimensional imagery. Some might assume a atheist approach to life and settle on proofs, and a s a scientist this is expected logic to validation.

Yet there is still room for thinking that within the spaces of thought, the inherent suttleness of God might pervade all things? That such thoughts could lead us to higher pinnacles above the solid world, and what is present around us now?

Why should we allocate such spiritual thinking to classes of religions like Islam and the Turkey scenario? You hurt the quest for theoretcial endeavors by limitations of ideology? When the world requires innovative thinking, "to push the boundaries of our envelope."

Without leading to these realization of the electromagnetic principles, Gauss and Maxwell relations, might we ever understand the simple visionistic world of the magnetic field?

Tuesday, March 22, 2005

Quantum Jitter

When you look at the spacetime fabric the cosmological views makes it nice and neat for us, when we are tryng to comprehend the ripples and waves that are generated.

So how, you might ask, can multiple strings make up a proton if each has a mass of ten billion billion times that of a proton? The answer has to do with quantum jitter. According to the uncertainty principle in quantum mechanics, nothing is completely at rest. Quantum jitter actually has negative energy that cancels out much of a string's mass. In the case of the graviton, the cancellation is perfect, yielding a particle with zero mass. This is what was predicted since gravitons travel at the speed of light.

The microscopic view of gravitatinal wave generation asks that we look much closer at how we perceive the actions of the turbulence and uncertainty as we move closer for a introspective view of the compact spaces that the genration of graviton in place of the views such uncertainty might be generated.

Reviews Georg Riemann's view of curved spaces, which is the mathematical core of general relativity. Quantum geometry is the mathematical core of string theory, though it is not as ready-made as was Riemann's geometry for Einstein. Riemann drew on Gauss, Lobachevsky, Bolyai etc. and evaluated the measure of distances in curved space. Einstein concluded the curvature of space is gravity.

Larry Summers Issue Reveals Deeper Implications

All the informtaion is gathered material, that held the Larry Summers issue in context. I was revealing aspects of this issue on another level, that many would not have understood. I wanted to bring it together here because the understanding of rhythmns, is at the core of my belief system. I have expounded on this greatly throughout this blog. It is not altogether clear sometimes even for myself.:)

So I hope the suttle implications here are understood not only from a psychological point of view, but also from a scientific one as well. It is a strange thing when the mind has jumped in model apprehension about how it might look at the world in a new way(Quantum Harmonic Oscillators).

I don't know when it happened, and how, it's just that I don't look at the world in a normal way anymore.:) Model apprehension if adopted, will color one's thinking. If life was so simple as the circle would have implied, then it's varying attributes topologically would be listed deeply embedded within our thinking? Thinking that extends far beyond the earth and it's solid form, to the far reaches of the cosmo to all of our suns and balckholes, in our thinking?

Without this cyclical nature, the universe does not make much sense to me. Of course I have to bite my tongue here, so that I do not loose many good minds that are speaking to the finer details of our views theoretically developing at the forefront of the physics and theoretic examination of those same "fields" of endeavor.

Anyway to the below information gathered.

For some who wanted to know? Have a good look at what took place today in a Harvard vote. Of course this is date dmaterial so looking back one should look forward, to what is presented today here.

I present on the one hand, material for revealing a closer views of the "source material." I have refrained from commenting as well, until now.

I tend to look at the ideas here as more inclined to questioning the dynamics of geometry. Male and female, as a dynamical expression, not only in the cosmos(Friedmann equations) but in how this may be deeply inserted in our psychological processes.

I inserted previously, the subject of Liminocentric structures under the title of PI day, as part of this comprehension and expression.

Maybe see a ole rerun of the movie PI and wonder if the Show Numb3rs was based on it?

Or think about the Perimeter Institute(PI) for those less familiar.

....or even contemplate John Baez's Fool's Gold PHI and the golden ration begininng from some sort of mandalic interpretation, coming from a psychological model based on Liminocentric structures? :)

This might seem a little kookish as well? :)

I try to reserve judgement on characters, while maintaining a view of the situation as it is reported. I do not look at the character of who is reporting but maintaining awareness of the bend they might have to that same reporting.

European attitudes, are they different then Canadians views on men and woman?

So I try and move past these stereotyping behaviors to look deeper in the process of the human structure of thinking. You know, right brain left brain? :)

In looking past to the origins of expression, to undertand, what it is that both sexes use to express either of these nurturing, or abstract tools of mathematics? As moving beyond the home, where the ability is quite feasible in either sexes, when implored.

If you wanted to understand democracies, first principles this is where I began my journey.

Matter condensed physics under the likes of Robert Laughlin and his buildings blocks of matter, or a deeper look into the structure of our universe? Some reject the Mother principle of M theory,and preferred to stay in the coordinates of a euclidean world.

This does not reject, what we could apply in our non-euclidean thinking. Maxwell and Gauss and Riemann are all part of this process in enlighened thinking? Einstein moved it further, in the use of GR with the help of Grossman? Now there is this attempt to join the cosmological world of the very large with the very small(reductionism views).

You just had to know how to get there in the expression using the Fifth postulate. Emmy Noether and others tell me that we can all use this faculty for inductive/deductive processes in our expressions?

Even Thales, recognized the Arche of reason? Parts of this picture, are pasted throughout this site linked above.

Thales might of called it the primary principal and used water. It is a very defining I think that we understand this fluid nature as a contiuity of expression, while we like discrete things as well. Plato solids eventually lead to a defintion of what God might be? :)

Discrete things could be viewed as solidification processes, we like to see consolidating in the shadows of things, while the sun can be a very abtract thing topologically in revealing the energy that we can use? :)

I tend to look at the ideas here as more inclined to questioning the dynamics of geometry. Male and female, as a dynamical expression, not only in the cosmos(Friedmann equations) but in how this may be deeply inserted in our psychological processes.

One may tend back to philosophical questions about these differences, but they are innnate features in all of us? Jung's determinations, in the animus or anima, and the response's too, the male and female that seeks balance in it's life?

The distinction may be domineering at one point or another, but there is this balance contained, much as we would define the relationship of Maxwell in electric/magnetic fields? That one would ask where good common sense should rule?

The humanities in science should then beg the question, that neither of these things should ever be considered separate, or not equal, for they would be interchangeable and contained deeply in our extensions and consolidations of expressive thought?

That these distinctions are never really separate issues contained in the brain's alternating features of the brain's capacity to Babble, left/right? :) Topologically it would be difficult to distinction of the inner from the outer, but this is not to say that this can't be done in perspective.

....or even contemplate John Baez's Fool's Gold PHI and the golden ration begininng from some sort of mandalic interpretation, coming from a psychological model based on Liminocentric structures?

The mind, all the time engaged in heavy thought can easly recognize, when it has all come together in model apprehension. It's own image, for complete acceptance, we then undertand well the forays the mind has ventured through to come to such forms of consolidate thought and image reproduction? :)

It is not until well into the high school years that males begin to close the gaps in terms of Language and social skills. Unfortunaly the boys, society, and educators continue to view boys as poor communicators and as doing poorly in L.A., therefore boys don't view their language skills as strong.

There are just plain busy elsewhere? It's the primal words spoken of beating drums and far off places? :)

Maybe, the educational system is not intune with the developing scenarios of male/female attributes??

I was reading the other day a opening in regards to Plato's academy for learning. Although this was in context of early historical developement, I couldn't help be drawn to the the views that were developed alongside of, perspective. I will have to go back and look at this.

One thing that attracted my interest was the role music would play in developing rythmns of youth that were conducive to awareness and steady developement? Now I don't like to be called ole fashion, but the rhythms in youth were attractive to me because they might have taught the basis of movement in life, much like, and in concert with, the expansion and contraction scenarios of thinking and developement. Now remember focus on the rhythm

Of course I always come back to the regress of reasons to explain this intuitive leap that developed trends found in new realities emerging. Arche means elements, and any reductionistic system asks us to delve into the reasons why, even though on large scale media observation, the Summers might have had issue with deeper implications to consider?

Not fully understanding the emotive developement and differences between both, mental enhancement through age aggression to advance thinking, these rhythmns would have helped to place, societal thinking above the aggressions of war, our own human struggle to rise above those things that would hold us to the earth? :)

Monday, March 21, 2005

Power of Symmetry Allows Us to Unify Disparate Pieces?

You know it is very frustrating sometimes when the paradoxal is presented to the mind through obsevration, to have it sloughed off as some speculative point that might be less then what the Doctor ordered?

In this case, the cause of the observation posts, what a three brane wrapped blackhole can mean? Here we see where the issues of Space-tearng conifold transitions are presented in a theoretical approach and quickly discarded by some, because it contained the brane word and would imply some kind of Brain world, ( Brane world.)

Well if you do not catch it the first time, there is hope that the theoretic applied will speak to what Hawking radiation might have in regards to the gravitational collapse initiated.

What is this physics doing here? This is not some free jaunt down memory lane, but a advancement in what is proposed? Very difficult to do this, if the environment is not translated in and by other ways, to see what the outcome of such a gravitational collapse can do. What is transmitted back into the space?

So I leave this here for a minute, and draw a quote from someone who is a good writer and has a good comprehension of the world as it sits. He might have been targeted as some wonder seeker by some, but his position to me has presented inquiring minds with the knowledge and basis, from which we must think.

So here is his quote, and I shall not name him. So that those who think he is some "wonder seeker" who has bastard the science who sold out his values, might wonder about their own position in the developing world of theoretics. To wonder, why such a message might not be important, when they think they can propose their own views about what the world should be.

Should what they have to say be held in any less contempt, that we should not only apply these same rules to those who hold a position about the harmonious whole, that we should even take the time to listen what they have to say?

To be quickly dismissed as verbiage not worth seeking because of some entertainment value as though one might he have sold out his profession? Any one, who uses this medium and blogging, can now consider themself part of the evil they think has manifested and sold out on. I refuse to even name this individual because he is advanced in his thinkng and is courting the world of theoretics.

For the first time, physicists appreciate the power of symmetry in their equations. When a physicist talks about “beauty and elegance” in physics, what he or she often really means is that symmetry allows one to unify a large number of diverse phenomena and concepts into a remarkably compact form. The more beautiful an equation is, the more symmetry it possesses, and the more phenomena it can explain in the shortest amount of space Pg 76

And again here so that we see know less the value of these inisghts, I place this final quote of his as well.

Rotating in four dimensional space unifies the concept of space and time

You had to know, that the pre-existing set of cicumstances would highlight the accomplishements of what Maxwell had done, as well as, learn to see into what the world Gauss and Reimann sought to exemplify beyond our normal comprehensions modes.

Moving into such realms dones not as far as I see it lessen the impact of what theorectic has done by way of descrbing the physics, but cautiously asks us to see what is happening in those compacted spaces.

Friday, March 18, 2005

Space-Tearing Conifold Transitions

Many years ago in my doodling, I created some comparisons to what I would have percieved in describing a point, line and plane. To me, I wanted to find a way to describe this point amidst a vast background of all points, so by constructing this diagram, and by realizing coordinates, intersection of lines and planes seemed a interesting idea to get to this point.

This brought some consideration to what was being shown by Greene below.

The Elegant Universe, by Brian Greene, pg 326

Now at the time, this being far removed from the stories that are developing in string theory, learning that having moved to brane considerations we can see where three brane world wrapped around a sphere could produce wonderful things for us to further ponder. That such emissions, from the gravitatinal collapse could all of a sudden produce, massless vibrating strings. We know then that such strings can be a photon or a other massless particles?:)

The Elegant Universe, by Brian Greene, pg 327

Part of the problem then for me is to figure out the stage of the developement of the cosmo what stage followed which stage, and the scheme within the cosmological display, the torus that had to become a sphere, or sphere collapsing to a torus? Concentrations of gravitonic expressions?

There were geometrical consideration here to think about.

Physicists found that a three-brane wrapped around a three-dimensional sphere will result in a gravitational field bearing the appearance of an extremal black hole, or one that has the minimum mass consistent with its force charges. Additionally, the mass of the three-brane is the mass of the black hole and is directly proportional to the volume of the sphere. Therefore, a sphere that collapses to a point as described above appears to us as a massless black hole, which will return to the discussion later.

Now as you know from my previous thread on the Flower considerations, color is a wonderful thing, but if my view was to be consistent, then how could there be any tearing in the use of a topological structure? The flower became very symbolic to me of what we see in the universe unfolding in these galaxies?

Two-dimensional strings trace out two-dimensional worldsheets. Since strings, according to Feynman's sum-over-paths formulation of quantum mechanics, simultaneously travel by all paths from one point to another, they are always passing by every point in space. According to physicist Edward Witten, this property of strings ensures that six-dimensional figures called Calabi-Yau spaces (theorized to be the shape of the other dimensions of our universe) can be transformed by certain topology-changing deformations called flop transitions without causing physical calamity. This is because strings are constantly sweeping out two-dimensional worldsheets that shield the flop transition point from the rest of the universe. A similar thought process goes toward the ability of Calabi-Yau spaces to undergo more drastic changes called space-tearing conifold transitions.

In order for me to consider the comlexity of the question certain insights about the nature of our universe has pointed out that there always had to be something existing, even in face of what any of us might thought of as a singularity in that blackhole collapse. But it is not that easy.

One had to assume that the bulk represented the continuance of some kind of flunctuating field of endeavor, that could hold our thoughts to dimensional attributes shared in the presetnation of Reimann's sphere. Gauss saw this early and gaussian coordinates also help to unite Maxwell into the glorifed picture of a dynamcial world?

The replacement of a 1-D sphere ( a circle ) with a 0-D sphere ( two points ) can create a different topological shape. A do-nut has a circle, round its lesser diameter, which is pinched to nothing. The do-nut turns into a cresent or banana-shape, with the two end-points repaired by the two points of a zero-dimensional sphere. The torus cum cresent can now transform into a ball, without further tearing.

This is as if Klein's hidden extra dimensions of space transformed from the one curled-up shape to another, comparably to the normal extended three dimensions changing the shape of the universe from a torus to a ball.
The evolution of the universe may involve such transmutations between curled-up Calabi-Yau spaces.

Equations governing the 'branes' showed that, from our limited three-dimensional view-point, the three-brane "smeared" around a three-dimensional sphere, within a ( curled-up ) Calabi-Yau space, sets up a gravitational field like a black hole.
The space tearing conifold transition from three to two dimensional sphere happens to increase the number of holes by one. These holes determine the number of low mass particles, considered as low energy string vibration patterns. The shrinking volume of the 3-D sphere goes with a proportionate mass decrease to zero: a massless black hole.