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.

Krauss Speaks, People React? :)

We understand that Alice is just part of the developing perspective we have about interactions? THis is consistant with Glast, as well as any calormetrical understanding, from an interaction?

That we had not explain the extra energy should still be held respective positions in mind if incoming and outcoming energy calculatins do not match? That left room in mirror world for other possibilities and had not explain all "sum over paths?"

Lubos:

My understanding is that the very main point of his latest book, Hiding in the mirror, is to present the idea of extra dimensions as an essentially religious idea in order to diminish the credibility of the research of modern high-energy physics - because he knows that most of the readers are anti-religious.

Everyone who has ever worked in phenomenology or string theory knows very well that this research has nothing to do with religion. The link is an invention of Krauss' - one that is intended to politicize things and to encourage his readers to think about completely irrational relations between different ideas.

Foot, R., and S.N. Gninenko. 2000. Can the mirror world explain the ortho-positronium lifetime puzzle?

(belongs to another article words that follow within link)
Welcome to the mirror world, in which every particle in the known universe could have a counterpart. This cosmos would hold mirror planets, mirror stars, and even mirror life.

While Alice in Wonderland may be a fictional story and pervasive in terms of many paths taken, the consequence of the photon in this enviroment and under gravitational influences, is well understood I think?

Lubos's first paragraph quoted is a questionable one to me, "on character," as I have understood Krauss to be.

Startreking explanatory on the understanding of reality, to make sure we understand what is going on, as well as, explaining the idea's of scientists who write for the public, in the movie production scenario's?

Kip Thorne and Brian Greene?

Would the normal public understand the evolution of Abbott and flatland, or the develomment of non-euclidean geometries?

You have taken the word geocentrism in vain Lubos:)

As a "liminocentric structure" wholeness is important to me, not just as some circle, a sphere, or how a genus figure is move from one form to another, but that other things are happening as well, when this happens? If it happens many times microscopically will this have satisfied our viewing of Coleman de Luccia Instanton?

It's just another way of "toposeeing" is all" ( many microprocesses make for many new physics to emerge?), and as far I understand it, it is necessary back ground with which to develope a consistant picture of what is going on with our universe, macroscopically, as well as microscopically, continously? Wmap polarization is topolgical driven by perpective sound valuations, blendings so that sucha 2d pciture measured is much more dynamcially seen?

Yes I know, no one knows what geometry this is in the blackhole or what new physics will emerge, so we needed to look for this consistancy beyond the standard model?

How could one not attempt to join this with quantum and cosmological views?

This just may mean that "uncertainty" is encapsulated?

I am glad to have "information" that would maintain my current hold on reality, as I expand the brain's coverings.

As we project our "evolutionary mind in projective geometries" further into the strange world of high energy, as well as reducing to a weak field measure, some hope of a consistant picture.

Okay, I have not forgotten what string theory has already done in regards to bulk pespective:)

So the bulk perspective is "nothing," or does it act as a catelysct?

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

Modulating Phases States:Neural Correlates to Consciousness

J. Metzinger Le Gouter/Teatime 1911

Dynamical triangulation

I added the wording below picture to encourage you to click on the picture. While discretization may have been thought endorsed, I still believe in continuity and flow, yet, I could not help think about how the mind is wanting to speak about that confined space, and the simplest discription of it. So in this sense, there are a lot of us asking what geoemtry/physics is involved in those spaces?

Lets be kind to each other.

I was just thinking about how, if I can so easily shift into the ways of non-euclidean realms, how perception had been changed from my current state of writing, how would I convey that?

Classically Shifting Gears maybe?:)

Such vast insight into how we see the universe with it's "analog in nature," sound was considered to extend our thinking by such relations, as well as, point to current WMAP data and the way it is being percieved. I introduce this here, in this blog after travelling through much information.

But it is more then this, with which I have been enthralled about, how we see that situations arose, where my not getting the message across , had me think about what was going on. About the ways in which I like to be creative. Use words, in a multidimensional way, as to poke fun. I am not saying I have what Kandinsky has, but as I thought about it more, I wanted to undertand this creativity, as well as, what the seed bed of each of our experience might manifest to the way it would in our role in who we today.

A High School Tutorial

Something to consider before we move into todays world of science. How I am seeing the data:)



While some of what I might be saying has been relegated to our senses, I would take it further, in that model apprehensions could , and do change current life positions, about which future possibilties arise.

We know this intellectually is a simple assertion about all life and it's changes, that from day to day, new insight, would make the new tomorrow very different.

Signs within Society

Can I say, that peppered throughout society, that the adventurous in science, could have been attributed with skills that could vary according to the modulation states of the mind, with which it had been gifted?

That it would know no race, gender, and human being that what ever the conditon, such skills applied, will be creativitly used in developing science alongs it's routes. Along what ever road it took in life.



IN the one sense "gifted with" might have implied a "given ability" as is the case in Kandinsky's, while in other's I see those whose same wirings had "crossed paths" and created such points, as modulation of the thinking brain. Ths is not held to any one person. Yet if you were to take the "senses away" would imagery have still be functionable in the mind?

In a similar manner, in string theory, the elementary particles we observe in particle accelerators could be thought of as the "musical notes" or excitation modes of elementary strings.
In string theory, as in guitar playing, the string must be stretched under tension in order to become excited. However, the strings in string theory are floating in spacetime, they aren't tied down to a guitar. Nonetheless, they have tension. The string tension in string theory is denoted by the quantity 1/(2 p a'), where a' is pronounced "alpha prime"and is equal to the square of the string length scale.

This is a bold idea I am stating in conjunction with how deveopement is taking place in science, and wondering about, as, "sign's of creativity."

Wonder about what is hidding behind the "facades" we had built up in our lives. That a truer seedbed existed, for life to be expressed in you. You, are the modulator.

Phase shifting(wikipedia 23 Feb 2006)

Phase shifting describes relative phase shift in superposing waves. Waves may be of electromagnetic (light, RF), acoustic (sound) or other nature. By superposing waves using different phase shifts the waves can add (0° shift = "in phase") or cancel out each other (180°). A modulation of the relative phaseshift while superposing waves thus causes an amplitude modulation.

There are so many things that I am trying to bring together from what I see, it is very hard without all the science undertsood ,to the degree that any consistent picture sould ever come forth. The picture(yet fuzzy and foggy) is there, and it holds ideas about holography, about the map of the universe supplied, and it's phase changes. Also that such an idea would have been held in relation to a "troubled mind" who might be exposed to Kandinsky's troubles, or, how society had been changed in a way, by such ideas being put forth in modulation idealizations.

I won't lie to you here, my mind is whirling with all these things in relation to how we are developing along in society as well as what is taking place in our universe. Such a large contrast to each other for sure. Almost like saying the microperspective view had some relation to evidence int he cosmo as we know it today.

I know it is not that easy, and the whole story about uncertainty, is really a baffling one to me. Yet, for some strange reason in face of this uncertainty there seems to be ways in which we can speak abstractually about the effects on the horizon issues, in relation to conformal theories.

So how would such transformative changes allow us to speak to what might be happening inside that blackhole would be as challenging as describing the length measures and what signal planck length according to some time clock measure? Yes i understand that this is important because the limits had been set as to what point quantum gravity effects come into play. How fine our measure that we can know the depth of dynamical situations.

See:

Links Philosophical and Conjectural?

More on Wassily Kandinsky

"Wholeness and Creativity" under the Guise of Synesthesia

Books for the Dead are Really, Books for Life?

Mendeleev's Table in a New Light

Links to More Speculated Science?

Ways IN which To Percieve Landscape?

If it's Not a Soccer Ball, What is it?

Singing Bowl

If it's Not a Soccer Ball, What is it?

Timaeus concludes

And so now we may say that our account of the universe has reached its conclusion. This world of ours has received and teems with living things, mortal and immortal. A visible living thing containing visible things, and a perciptible God, the image of the intelligible Living Thing. Its grandness, goodness, beauty and perfection are unexcelled. Our one universe, indeed, the only one of its kind, has come to be.

WMap currently expressed, has some explaining to do. While they talk about ekroptic universe and such, such cyclical natures need some reference with which to speak, in order for such idealizations and perspective form around the information WMap has currently released.

The fifth element, i.e., the quintessence, according to Plato was identified with the dodecahedron. He says simply "God used this solid for the whole universe, embroidering figures on it". So,I suppose it's a good thing that the right triangles comprising this quintessence are incommensurate with those of the other four elements, since we certainly wouldn't want the quintessence of the universe to start transmuting into the baser subtances contained within itself!

Higher abstractness, in the case of leaving euclidean perspective, are part of the realization when you look at the WMAP, that is being presented. While sound implications are being implied, they are necessary if it is understood the role they will play in such analogies of a larger global pewrspectve then the one seen in how gaussian coordinates and curvatures are implied, in Omega features, and critical density.

A Finite Dodecahedral Universe

According to the team, who published their study in the 9 October 2003 issue of Nature, an intriguing discrepancy in the temperature fluctuations in the afterglow of the big bang can be explained by a very specific global shape of space (a "topology"). The universe could be wrapped around, a little bit like a "soccer ball", the volume of which would represent only 80% of the observable universe! (figure 1) According to the leading cosmologist George Ellis, from Cape Town University (South Africa), who comments on this work in the "News & Views" section of the same issue: "If confirmed, it is a major discovery about the nature of the universe".

So having a greater perspective on this kind of mapping is necessary. While I reference tunneling and such, implicate bee's travelling or satelittes using pathways of least resistance, how does such states have been reached, if you did not have the perspective that is necessary in seeing how the universe is laid out geometrically?

Scientists Get Glimpse of First Moments After Beginning of Time by DENNIS OVERBYE

"If this holds up to the test of time, it's a real landmark," said Max Tegmark, a cosmologist and cosmic microwave expert at M.I.T. "I really feel like the universe has given up one more clue," he said.

The quantum gravity issues implored, and speculated, have a diverse model selection with which to talk about? John Baez's view came up when I seen the model in which he choose for such understanding. Having seen the "membrane" idealizations used in qauntum gravity models, helped with the perspective that he used, but like Plato his definition fell short to me of the substructure(a discrete meaasure in bubble facets) of the cosmo that would relegated some model, to perfect our view microscopically, as well as macroscopically.




Tegmark and others disproved this, so what is the nature of the cosmo in question, and it's shape? So having understod the idealization of flat gemetries of the universe, how could such negative features be understood as the hyperbolic understanding became part and parcel of GR in our understanding of the gravity issues?

With the discovery of sound waves in the CMB, we have entered a new era of precision cosmology in which we can begin to talk with certainty about the origin of structure and the content of matter and energy in the universe.-Wayne Hu

Such analogies were very important in raising our understanding of what might have been seen in the membrane ideals of how gravity could act in bubble boundaries conditions. While such faces might have been understood in such analogies of John Baez's, a spherical harmonics would have had to been much smoother in our understanding?

Imploring the analogies and models in this respect made it much easier to see on another level, in non euclidean realities. Further then, the understanding of gaussian coordinates. You knew this was part and parcel of a larger picture understood in GR?



The Sound of Gravitational Waves

We can't actually hear gravational waves, even with the most sophisticated equipment, because the sounds they make are the wrong frequency for our ears to hear. This is similar in principle to the frequency of dog whistles that canines can hear, but that are too high for humans. The sounds of gravitional waves are probably too low for us to actually hear. However, the signals that scientists hope to measure with LISA and other gravitational wave detectors are best described as "sounds." If we could hear them, here are some of the possible sounds of a gravitational wave generated by the movement of a small body inspiralling into a black hole.

So there is a culmination in my views as I now look at the new WMap presented. A greater understanding implored in geometric realization, that had to be taken down to the microscopic where quantum gravity existed, yet, the geometry used, what new math would this be? It was encapsulted in the overall understanding of cyclical natures.



Is there such a thing, as isometrical relations of orbitals, in cosmological designs? A Classical definition of the Quantum World perhaps?

Some patterns are telling to me of the way in which the universe, and the galaxies in which had formed, would have followed some geometrical all inclusive pattern, that we see unfolding from place to place, and assigning, specific polarization points within the view of the WMAP.



Now, look at the map below.

The WMAP (Wilkinson Microwave Anisotropy Probe) mission is designed to determine the geometry, content, and evolution of the universe via a 13 arcminute FWHM resolution full sky map of the temperature anisotropy of the cosmic microwave background radiation. The choice of orbit, sky-scanning strategy and instrument/spacecraft design were driven by the goals of uncorrelated pixel noise, minimal systematic errors, multifrequency observations, and accurate calibration. The skymap data products derived from the WMAP observations have 45 times the sensitivity and 33 times the angular resolution of the COBE DMR mission. The WMAP mission characteristics are summarized in the table below.

So by using information in the Chladni plate exhibit within this site, it becomes a interesting picture when such "spectrum analysis" make themselves representable in "color" as a variation of the landscape.

The temperature fluctuations of the Cosmic Background Radiation may be decomposed into a sum of spherical harmonics , much like the sound produced by a music instrument may be decomposed into ordinary harmonics. The "fundamental" fixes the height of the note (as for instance a 440 hertz acouctic frequency fixes the "A" of the pitch), whereas the relative amplitudes of each harmonics determine the tone quality (such as the A played by a piano differs from the A played by a harpsichord). Concerning the relic radiation, the relative amplitudes of each spherical harmonics determine the power spectrum, which is a signature of the geometry of space and of the physical conditions which prevailed at the time of CMB emission.

But if you are really interested in the way we see the universe how would such patterns illustrate what is being shown in the WMAP. A Chladni plate perhaps as spoken in reference. I needed a model with which to work the whole geometrical picture.

If you sprinkle fine sand uniformly over a drumhead and then make it vibrate, the grains of sand will collect in characteristic spots and figures, called Chladni patterns. These patterns reveal much information about the size and the shape of the drum and the elasticity of its membrane. In particular, the distribution of spots depends not only on the way the drum vibrated initially but also on the global shape of the drum, because the waves will be reflected differently according to whether the edge of the drumhead is a circle, an ellipse, a square, or some other shape.

In cosmology, the early Universe was crossed by real acoustic waves generated soon after Big Bang. Such vibrations left their imprints 300 000 years later as tiny density fluctuations in the primordial plasma. Hot and cold spots in the present-day 2.7 K CMB radiation reveal those density fluctuations. Thus the CMB temperature fluctuations look like Chaldni patterns resulting from a complicated three-dimensional drumhead that

See:

Plato's Defintion of God

Sound of the Landscape

B Field Manifestations

Resonance:Brownian Motion

The Singing Bowl

One harmonious possibility is that string enthusiasts and loop quantum gravity aficionados are actually constructing the same theory, but from vastly different starting points-Page 490, Fabric of the Cosmos by Brian Greene

What would such gravitons in the bulk concentration mean, to those whose value might have seen sound expressed, as low and rumbling, while energy would have been freer to implement the expression of higher pitched notes?



Some might have never gotten the greater significance, or the relation to the Kernel of Truth, but hidden behind all the facades of humanities thoughts about sound, it was with the understdanding of Joseph Weber's work, that I too, became intrigued with the cylinder bars and sound.

In the late 1950s, Weber became intrigued by the relationship between gravitational theory and laboratory experiments. His book, General Relativity and Gravitational Radiation, was published in 1961, and his paper describing how to build a gravitational wave detector first appeared in 1969. Weber's first detector consisted of a freely suspended aluminium cylinder weighing a few tonnes. In the late 1960s and early 1970s, Weber announced that he had recorded simultaneous oscillations in detectors 1000 km apart, waves he believed originated from an astrophysical event. Many physicists were sceptical about the results, but these early experiments initiated research into gravitational waves that is still ongoing. Current gravitational wave experiments, such as the Laser Interferometer Gravitational Wave Observatory (LIGO) and Laser Interferometer Space Antenna (LISA), are descendants of Weber's original work.

Now what does sound mean in this case? How far shall we go back with Kip Thorne, or John Wheeler? Would a good scientist know that the roots of these thoughts about string theory began long before the mathematical struggles became known in current day thoughts. That the roots began in relativity, and what relativity means geometrically as a gravitational force in consideration?

It required a graduation in thinking. Views in the abstract spaces that were less then understood, that without understanding how such thoughts lead from the classical world, would now move perspectve to it's strengths and weakeness as part of a larger view established from the standard model and beyond. It had to include all the fundamental forces and ultimately it's carriers?

The activity in string theory and quantum gravity is aimed at developing a quantum theory that incorporates the physics of gravity and is valid down to the smallest length scales, where conventional quantum field theory can no longer be applied. There has been rapid progress in this area in recent years, in part due to work of Princeton faculty and students, and it continues to be a fertile source of research problems.

Would These good scientists might have forgotten maybe, or because of the failure of Joesph Webers experiments, the very ideas of LIGO today, would not support the greater depth of seeing? In ways such structures would ring with the gravitational expansion and contraction, and allocated sound value in analogy? What use?

Might I have missed the nature of the bubble in geometric views, as we looked at the sonofusion idea manifested in the way that "time and the bubble's membrane," elastic in it's measure, might have symbolized a larger global view of all the things that it would contained within it. Even, it's magnetic field?



So some were better equiped to see spheres whithin spheres, and all bubble membranes as some topological derivation of Sklars's quandry of what line is a 5 or 1, in relation to the torus. How diffiuclt to undertand that then, inner bubble/line might have encapsulated the expression of Maxwell and all the equations, as being defined within the context of General Relativity and it's completion, as th eenvelope on the outer sphere called earth in space. Some might never have resolved such thinking to sucha bumpy world but it does indeed happen. Not only there, but in how such energies would have made themselves known as we turned this inside out, like some Klein bottled?



I know I have much to learn in the geometrical perspective, but I am trying.

Recognition of a Sphere that is Not so Round

Gravity is the force that pulls two masses together.

Since the earth has varied features such as mountains, valleys, and underground caverns, the mass is not evenly distributed around the globe. The "lumps" observed in the Earth's gravitational field result from an uneven distribution of mass inside the Earth. The GRACE mission will give us a global map of Earth's gravity and how it changes as the mass distribution shifts. The two satellites will provide scientists from all over the world with an efficient and cost-effective way to map the Earth's gravity field.

The primary goal of the GRACE mission is to map the Earth's gravity field more accurately than has ever been done before. You might ask, how will GRACE do this? Two identical spacecraft will fly about 200 kilometers apart. As the two GRACE satellites orbit the Earth they are pulled by areas of higher or lower gravity and will move in relation to each other. The satellites are located by GPS and the distance between them is measured by microwave signals. The two satellites do not just carry science instruments, they become the science instrument. When mass moves from place to place within the Earth's atmosphere, ocean, land or frozen surface (the "cryosphere"), the gravity field changes.

So while I was quite aware of what the earth contained in it's views as a planet on which we live, it was not without some understanding that such mass considerations woul have also included the "view of bubbles"? AS rings around this planet.

The way in which they can work to help push perspective inside/out? Is this wrong? Can no undertanding that leads to electrognagnetsm and gravity joined in the fifth dimensional perspective, lead to the dynamcial understanding of nature in accordance with the spacetime fabric and it's orientations?



Why then lagrange coordinates, and how we see the "hole in space" as satelittes that might choose the most easiest route to travel and least fuel to burn? What say the equillibrium status, had not been reached in the blackhle interior, as a anomlie of perception, in regards to the formation of the superfluid through such collidial events?

The Z Machine

There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world.— Nikolai Lobachevsky

Sandia’s Z machine exceeds two billion degrees Kelvin

Z’s energies in these experiments raised several questions.

First, the radiated x-ray output was as much as four times the expected kinetic energy input.

Ordinarily, in non-nuclear reactions, output energies are less — not greater — than the total input energies. More energy had to be getting in to balance the books, but from where could it come?

Lubos Motl

Janice Granhardt has pointed out a press release that is two days old and arguably much more serious and potentially far-reaching than the news about "sonofusion" we described yesterday.

http://motls.blogspot.com/2006/03/two-billion-kelvins-at-z-machine.html

I reference current article information that I had been working through here and here for obvious reasons. I would like to expand on this.

I am writng this article because of the references Lubos Motl offered on his blog about the need for, "energy production." The whole context of any model has to have understood that the current situation in gravitational perspective will have it's two extremes (weak and strong) held in thought, and ending within this context? A cyclical process maybe like thinking about Steinhardt maybe? :)

I know the idea of free energy machines is a quacks realm, if, the imput energy and output energy is not held in consideration. That a greater output must be sustained. How?

Klein's Ordering of Geometries

A theorem which is valid for a geometry in this sequence is automatically valid for the ones that follow. The theorems of projective geometry are automatically valid theorems of Euclidean geometry. We say that topological geometry is more abstract than projective geometry which is turn is more abstract than Euclidean geometry.


So on what conditions, could you map the process consistently and geometrics, to have been all inclusive?

While one may discuss these alternatives, it might require that we see this process at work on a cosmological scale, and having reduced it to the quantum realm, the questions about the geometries, becomes held under the auspice of "new physics,". That we might ask, "what new geometries?"

The natural process then would have to acknowledge the need for many microstate blackholes to have further the context of the standard model and it's extension?

Is this not a fair statement? Even though we may talk about one event, the recogition is that, this happens many times in regards to high energy articles in a collidial region. This had been answered in Risk assessment, as to why the process developed naturally, in the production of microstate blackholes, we might have created in LHC.

This did not discount, the understanding of what "extra dimensions meant" when we were understanding the "new physics." Reference here, neutrino or strangelets. It was just part and parcel of a greater understanding that John Ellis had pointed us too, is our recognition of the poor man's accelerator.

See:

The Unity of Mathematics

Spacetime 101

Here's some basic background covering how mathematical models of space and time have evolved since ancient times, from the Pythagorean Rule to Newtonian mechanics, Special Relativity and General Relativity.

For the roads leading to one's view of the strange world of non-euclidean views had to offer, I of course needed some model from which to work. As I looked at the model above and the transfer of higher dimensional thinking, the very idea and contrast to the lower image represented, how would you associate gravity in the diagram but watch the circle valution along side of gravity that emegres from the 2d discription as a energy valution, and relationship to gravity, evolving from mass, energy interconnectivity. I have to apologize as I was developing and am developing.



I do not know if this is right to assign my view above, while one did not know the evaluation of 1R as I watch DRL assessment of what can no longer be considered as valid, I have to wonder why such observations are not thought about more intricately as the valuation of that circle is considered. The comparison was drawn between the two pictures of the spacetime fabric above here, and below.

Let's now start analysing a 2D case, that of the classic Flatland example, in which a person lives in a 2D universe and is only aware of two dimensions (shown as the blue grid), or plane, say in the x and y direction. Such a person can never conceive the meaning of height in the z direction, he cannot look up or down, and can see other 2D persons as shapes on the flat surface he lives in.

So if you follow the dimensional analysis, there is a systemic procedure that one has to follow, that does not have to be held in context of KK interpretation to this point, but it does help if you think about the very basis of this graduation that certain statements make themself known.

Degrees of freedom(Wiki 24 Jan 2006)

Zero dimensions
Point
Zero-dimensional space
One dimension
Line
Two dimensions
2D geometric models
2D computer graphics
Three dimensions
3D computer graphics
3-D films and video
Stereoscopy (3-D imaging)
Four dimensions
Time (4th dimension)
Fourth spatial dimension
Tesseract (four dimensional shapes)
Five dimensions
Kaluza-Klein theory
Fifth dimension
Ten, eleven or twenty-six dimensions
String theory
M-theory
Why 10 dimensions?
Calabi-Yau spaces
Infinitely many dimensions
Banach space (only some have infinitely many dimensions)
Special relativity
General relativity

Would you dimiss a comment by Greene because of the speculation you have felt about him that you might not recognize, what is being said as you watch that circle develope alongside of the sphere, as it moves through the 2d discription? Here's what mean, as I had focused on Brian Greene's words.

Angular momentum can twist light cones and even make time travel possible in theory if not in practice.

The familiar extended dimensions, therefore, may very well also be in the shape of circles and hence subject to the R and 1/R physical identification of string theory. To put some rough numbers in, if the familiar dimensions are circular then their radii must be about as large as 15 billion light-years, which is about ten trillion trillion trillion trillion trillion (R= 1061) times the Planck length, and growing as the universe explands. If string theory is right, this is physically identical to the familiar dimensions being circular with incredibly tiny radii of about 1/R=1/1061=10-61 times the Planck length! There are our well-known familiar dimensions in an alternate description provided by string theory. [Greene's emphasis]. In fact, in the reciprocal language, these tiny circles are getting ever smaller as time goes by, since as R grows, 1/R shrinks. Now we seem to have really gone off the deep end. How can this possibly be true? How can a six-foot tall human being 'fit' inside such an unbelievably microscopic universe? How can a speck of a universe be physically identical to the great expanse we view in the heavens above?

( Brian Greene, The Elegant Universe, pages 248-249)

Fifth dimension(wiki 24 Jan 2006)

Abstract, five dimensional space occurs frequently in mathematics, and is a perfectly legitimate construct. Whether or not the real universe in which we live is somehow five-dimensional is a topic that is debated and explored in several branches of physics, including astrophysics and particle physics.

Five dimensions in physics(Wiki 24 Jan 2006)

In physics, the fifth dimension is a hypothetical dimension which would exist at a right angle to the fourth dimension

Radius of the Universe

HUBBLE DIAGRAM AND ITS CONSTRAINTS ON COSMOLOGYBradley Schaefer

A Hubble Diagram is presented based on 172 distance measures involving 52 Gamma-Ray Bursts out to redshifts of 6.3. The observed shape of the Hubble Diagram is a measure of the expansion history of the Universe, which will include the effects of the 'Dark Energy' that dominates over matter. Gamma-Ray Bursts can be seen to high redshift, and this uniquely allows for tests as to whether the Dark Energy changes with time. If Einstein's Cosmological Constant is a good representation of cosmology, then the equation of state of the Dark Energy won't change in time over the age of the Universe. The observed Hubble Diagram can be compared with the shape predicted by various models, including the model where the Cosmological Constant is a constant. The result is that the Cosmological Constant is rejected at a moderate confidence level. That is, apparently, Dark Energy changes with time. As with all such results, a consensus final conclusion can only be reached after the result is duplicated by independent experiments. To this end, over the next two years, the satellites Swift and HETE will discover another ~50 bursts that can be placed on the Hubble Diagram and this will serve as an independent test of the claim. The result also highlights the Gamma-Ray Burst Hubble Diagram as a new front-line technique to measure Dark Energy and the high-redshift Universe.

As I relay in the earlier part of the thread containing responses to the Evolving Dark Enery of Sean Carroll's, certain insights that had been gained along the way raise the issue of how such a dark energy would have influenced, how we gain information from the luminousity of standard candles, and how we would gain from that information.

Lubos Motl:

The corresponding equation of state would give "w" (the pressure/energy_density ratio) smaller than "-1" (much like in models of phantom energy) which would violate the dominant energy condition - and potentially allow superluminal signals. This sounds highly suspicious. Gamma ray bursts had to be used for the analysis - and they are sufficiently poorly understood - and independent experimental astrophysical sources at Harvard also recommend you to ignore the news.

Of course we are going to want to know why Lubos.

This set the stage for me in wonder about gravitonic concentrations, and how these woudl have been indicators of the strengths and weakeness, which would influence this information gained. I guess, it is in understanding better how such information could be "skewed" that I am looking at the answers given as a further response by Brad is illucidated upon.

So what is "dark energy" in relation to what gravitonic considerations might have on how we see such expasnion process say to us, the unievrse is indeed expanding.



It is always interesting to me to see how the cosmological values contained in the universe could have ever held to "GR curvature indicators" and that such values if held in regard to Einsteins and Riemann's spherical relations, then how indeed could we have siad that the nature of the universe is

As mentioned earlier, the value of is a measurement for the density of the universe. The definition of is such that,




where is the critical density of the universe. A critical density is associated with an "Einstein de Sitter Universe" for which equals 1. It has the property that the curvature is zero, the universe is spatially flat. Light will travel in a straight line and the angles of a triangle add to 180 degrees (space is Euclidean). The other possibilities are an open universe ( ) in which space will expand forever, and a closed universe ( ) in which gravity will halt the expansion and force the universe to contract, eventually leading to a "big crunch". The consequence could possibly be an oscillating universe, which gives a kind of continuity to the model. Figure 2 illustrates the three cosmological models.


Figure 2: The three cosmological models of the universe: open (), closed ( ) and flat ( )

Part of my exercise is to see the underlying geoemtries that are evolving thriugh time as we keep our universe in perspective. Do we know where this center is? And if so can we see whwere such expansiotry calculations would have given some indication? Are we always looking to the furthest edge so that we can help understand this red shifting that is going on tohelp us determine this value of the open uinverse?



Well within context of all this, the move to a higher lensing implications is most puzzling becuase it will shape the nature and kinds of infomration that is needed in order to make these determinations about unibverse values. Thus being inclined to pass by such galaxies in the forming state, as influencing the viability of the information given to us. So to me "Luminousity" is very important here as to the ejection of infomration that may reach us, and information that will held in context of those galaxy formations. So it is as if we are giving, an image in mind of these holes geoemtrically induced, along side of matter formation from causes that would influence the very nature of the repsonses we get.

Critical density

Sean Carroll:

Last time we talked about dark energy and its equation-of-state parameter, w. This number tells you how quickly the dark energy density changes as the universe expands; if w=-1, the density is strictly constant, if w>-1, the density decreases, and if w<-1, the density actually increases with time. (In equations, if a is the scale factor describing the relative size of the universe as a function of time, then the density goes as a-3(1+w).) For comparison purposes, cosmological "matter" (slowly-moving massive particles) has w=0, and "radiation" (relativistic particles, including photons) has w=1/3

So if we are to look for this center how would we find the valuation of what began?



You would have needed to see a time when critical density would have said to you that the infomration that is being propelled from the center, and here, critical density would have partaken of this value, because gravity would have been very strong? Strong enough that for any infomration to be propelled from that center, to have continued on to this day as a expansitory consideration. So that we may still hold it in considertaion as to exactly what this universe is doing now.

Once you have then held the unierse in a certain way you have to ask these question based on what you understood by implicating Lagrange points in your assesment of how the univere became the way it is. YOur lensing has created these holes for light to travel, and in those spaces, satelittes have found easier ways to have manueverd without expending a lot of energy.

We can still tap the greater reserviors of energy and radiation, to help these vehicles continue their journeys. But it is more then that, that we might have sent this vehicle to collect the stardust to help shape our perspective on what constituted that beginning of the universe, as we sent our probes out for further material in which to judge?

Tiny Bubbles

AS a child, Einsten when given the gift of the compass, immediately reocgnized the mystery in nature? If such a impression could have instigated the work that had unfolded over timein regards to Relativity, then what work could have ever instigated the understanding of the Pea as a constant reminder of what the universe became in the mind of a child, as we sleep on it?

Hills and Valley held in context of Wayne Hu's explanations was a feasible product of the landscape to work with?

'The Princess & The Pea' from 'The Washerwoman's Child'

If Strings abhors infinities, then the "Princess's Pea" was really a creation of "three spheres" emmanating from the "fabric of spacetime?" It had to be reduced from spacetime to a three dimensional frame work?

Spheres can be generalized to higher dimensions. For any natural number n, an n-sphere is the set of points in (n+1)-dimensional Euclidean space which are at distance r from a fixed point of that space, where r is, as before, a positive real number. Here, the choice of number reflects the dimension of the sphere as a manifold.

a 0-sphere is a pair of points
a 1-sphere is a circle
a 2-sphere is an ordinary sphere
a 3-sphere is a sphere in 4-dimensional Euclidean space

Spheres for n ¡Ý 3 are sometimes called hyperspheres. The n-sphere of unit radius centred at the origin is denoted Sn and is often referred to as "the" n-sphere. The notation Sn is also often used to denote any set with a given structure (topological space, topological manifold, smooth manifold, etc.) identical (homeomorphic, diffeomorphic, etc.) to the structure of Sn above.

An n-sphere is an example of a compact n-manifold.

Was it really fantasy that Susskind was involved in, or was there some motivated ideas held in mathematical structure? People like to talk about him without really understandng how such geometrical propensities might have motivated his mind to consider conjectures within the physics of our world?

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

You had to realize that working in these abstractions, such work was not to be abandon because we might have thought such abstraction to far from the tangible thinking that topologies might see of itself?


Poincaré Conjecture Proved--This Time for Real
By Eric W. Weisstein

In the form originally proposed by Henri Poincaré in 1904 (Poincaré 1953, pp. 486 and 498), Poincaré's conjecture stated that every closed simply connected three-manifold is homeomorphic to the three-sphere. Here, the three-sphere (in a topologist's sense) is simply a generalization of the familiar two-dimensional sphere (i.e., the sphere embedded in usual three-dimensional space and having a two-dimensional surface) to one dimension higher. More colloquially, Poincaré conjectured that the three-sphere is the only possible type of bounded three-dimensional space that contains no holes. This conjecture was subsequently generalized to the conjecture that every compact n-manifold is homotopy-equivalent to the n-sphere if and only if it is homeomorphic to the n-sphere. The generalized statement is now known as the Poincaré conjecture, and it reduces to the original conjecture for n = 3.

While it is very dificult for me "to see" how such movements are characterized in those higher spaces, it is not without some understanding that such topologies and genus figures would point to the continuity of expression, as "energy and matter" related in a most curious way? Let's consider the non-discretium way in which such continuites work, shall we?

From one perspective this circle woud have some valuation to the makings of the universe in expression, would identify itself where such potenials are raised from the singular function of the circular colliders. Those extra dimensions had to have some basis to evolve too in those higher spaces for such thinking to have excelled to more then mathematical conjectures?

We can also consider donuts with more handles attached. The number of handles in a donut is its most important topological information. It is called the genus.

It might be expressed in the tubes of KK tower modes of measure? That such "differences of energies" might have held the thinking to the brane world, yet revealled a three dimensional perspective in the higher diemnsional world of bulk. These had to depart from the physics, and held in context?



Clay Institute

If we stretch a rubber band around the surface of an apple, then we can shrink it down to a point by moving it slowly, without tearing it and without allowing it to leave the surface. On the other hand, if we imagine that the same rubber band has somehow been stretched in the appropriate direction around a doughnut, then there is no way of shrinking it to a point without breaking either the rubber band or the doughnut. We say the surface of the apple is "simply connected," but that the surface of the doughnut is not. Poincaré, almost a hundred years ago, knew that a two dimensional sphere is essentially characterized by this property of simple connectivity, and asked the corresponding question for the three dimensional sphere (the set of points in four dimensional space at unit distance from the origin). This question turned out to be extraordinarily difficult, and mathematicians have been struggling with it ever since.

While three spheres has been generalized in my point of view, I am somewhat perplexed by sklar potential when thinking about torus's and a hole with using a rubber band. If the formalization of Greene's statement so far were valid then such a case of the universe emblazoning itself within some structure mathematically inclined, what would have raised all these other thoughts towards quantum geometry?

In fact, in the reciprocal language, these tiny circles are getting ever smaller as time goes by, since as R grows, 1/R shrinks. Now we seem to have really gone off the deep end. How can this possibly be true? How can a six-foot tall human being 'fit' inside such an unbelievably microscopic universe? How can a speck of a universe be physically identical to the great expanse we view in the heavens above?

(Greene, The Elegant Universe, pages 248-249)


Was our thoughts based in a wonderful world, where such purity of math structure became the basis of our expressions while speaking to the nature of the reality of our world?


Bubble Nucleation

Some people do not like to consider the context of universe and the suppositions that arose from insight drawn, and held to possibile scenario's. I like to consider these things because I am interested in how a geometical cosistancy might be born into the cyclical nature. Where such expression might hold our thinking minds.


Science and it's Geometries?


Have these already been dimissed by the physics assigned, that we now say that this scenario is not so likely? Yet we are held by the awe and spector of superfluids, whose origination might have been signalled by the gravitational collapse?

Would we be so less inclined not to think about Dirac's Sea of virtual particles to think the origination might have issued from the very warms water of mother's creative womb, nestled.

Spheres that rise from the deep waters of our thinking, to have seen the basis of all maths and geometries from the heart designed. Subjective yet in the realization of the philosophy embued, the very voice speaks only from a pure mathematical realm, and is covered by the very cloaks of one's reason?

After doing so, they realized that all inflationary theories produced open universes in the manner Turok described above(below here). In the end, they created the Hawking-Turok Instanton theory.

The process is a bit like the formation of a bubble
in a boiling pan of water...the interior of this tiny
bubble manages to turn itself into an infinite open
universe. Imagine a bubble forming and expanding at the
speed of light, so that it becomes very big, very quickly.
Now look inside the bubble.

The peculiar thing is that in such a bubble, space and time
get tangled in such a way that what we would call today's
universe would actually include the entire future of the
bubble. But because the bubble gets infinitely large in
the future, the size of 'today's universe' is actually infinite.
So an infinite,open universe is formed inside a tiny, initially
microscopic bubble.

Xtra dimensions

In the Beginning.....

The field of cosmology has experienced an explosion of activity since the discovery of ripples in the energy of the primordial light of the big bang. Cosmology is the study of the origin, evolution, and fate of objects in the observable universe. These include galaxies like our Milky Way, a vast collection of stars spanning many thousands of light years. The key to the birth and evolution of such objects lies in the primordial ripples observed through light shining through from the early universe.

Having learnt from Wayne Hu and his CMB info study, it help me see where the hills and Valleys might have attained some recognition in how one landscape might have been seen in relation to Wayne Hu's.

Cosmologists actually run computer simulations to track how matter collects into valleys. For example, here is a simulation running forward in time which shows how particles collect and enhance small initially small wrinkles

Thank you Wayne Hu to opening the doors to the realizations that I had formed in the ideas of the supersymmetrical Universe. Little did you know that Andrey's picture would set the course for how I saw the Cosmic string arise from such a background.



Develope our views into the CSL Pictures here. I wanted to take this time to thank Lubos Motl for his continued efforts in this direction.

CSL-1 cosmic string gravitational lens and 2 more, with many views of the Capodimonte Deep Field OACDF2 with subtle background features, similar to recent Millennium Simulation of evolution of structure in our Universe. Identical stereo pairs are introduced.

So to then, if such a trail leads us to what that geometical propensity is, how so from such a tale of quantum gravity? It had to lead from something, so from the beginning.......? :)

Modification To GR

Sean Carroll:

Why three dimensions of space just aren't enough?

What does General Relativity say in terms of a simple word to describe it? "Gravity?"

“This is what’s happening all the time within us, we have these little lava lamps,” said Frank Wilczek in his Nobel lecture in 2004 when he showed this QCD animation created by Derek Leinweber. The animation illustrates the fluctuations of the quark and gluon fields over time, revealing a lumpy structure that Leinweber dubbed the QCD lava lamp.

So modifications to Gr bring perspective to lead us to other views in terms of xtra-dimensional analysis(degrees of freedom at a gluonic level)? Can I say this in regard to such things as xtra dimensional analysis?

Of course mine is a generalization spoken from the idea of what Eric Aldeberger might find, but this did not limit the scope of vision that would have moved us beyond the fifth postulate. Non euclidean geometries, were very hepful here and so too, hyperdimensional thinking?

Relativistic Jets: The Common Physics of AGN, Microquasars and Gamma-Ray Bursts

Reimann then thought there would come a time to see such thinking expressed beyond just the positive expressions in spherical relations? Jets, in relation, to Anti-matter creation? A whole new abstract way of thinking in the mathematical realms?

So what had radiation and CFT showed us from Bekenstein bound, as we peered into the inside of the blackhole construction? What geoemtries existed? Was there a emergent geometric principal. Of course, that is in question, and the degrees of freedom would spell the depths to what we were able to see? That did not stop us from talking about the substance of quantum Geometry as Greene explained to us.

What value did the temperatures play in our assessment of the internal dynamics of what would have happpened from a the grvaiational collapse generated and the radiation, that would hav been emitted. Acoustic radiation helps to a degree.

Thank you Smolin for such a responsible attitude of the science position of Glast, but it now has to induce new insight by adopting other theoretical positions?

Religious Convictions and Belief

I as a layman do operate from a biased position, and one that would have asked for a better respect of the scientific procedure, as Peter Woit and those of science would ask us as layman in our demonstrations.

Would I accept the responsibilty of Sean atheistic valuations, in our determinations of what we can be held accounatble as to the repercussions of our very actions. In our thoughts, that would ripple ever wider, as a consequence of our choices?

Yes I think deeply about these things, and they are far distant from the responsibilities of science, but I needed to show this, so it is understood that I accept that responsibility, even though I too might have had a belief about God and and our roles in choosing to evolve?

I quickly generalized Relativity above, and so too, did my journey to have been thinking about a simplification in general conceptualizations of those extra dimensions.

Was it wrong to do so in light of the need for sound thinking right now? I have to apologize for that too, as this is biased in my views from such a simplifcation.

There is a result in thinking about the measure of those extra dimensions, and what had been missing from the initial energy determinations calculated. Where is that missing energy?

Did such a simple logic not recognize that associated in this energy valuation, to reductionist principles, that this would be sent off into some other dimensional recognition of the values of that energy along side of modification to General relativity?

There had to be a consistancy lead from to incorporate such thinking to simplfications in general concepts and views I have about the psychological prospects of causes of our thought processes. To have ramifications beyond the border of our own brains. But this is just me right now. So I don't want to mislead anyone.

Further Speculations

Sometimes I can't but help think that we currently in a blackhole that driven to expansitory values and curent CMB temepratures made me think, that if we saw the expansion process as inhernet in this universe, then why is it not that we see we are in such a Blackhole? Is this wrong?

Then what value these Suns that still burn within this context, and such distance between the objects of space seen in a cosmological distance? More speculation that I send such thoughts of mine to the beginings of the universe and what interactive features sent this universe into it's expansion process? What stage are we atthen, to have been held at a certain process in the blackholes status, to have thought about the big crunch signal by the very initial response and distance of the schwarzchild radius that preceded this expansive view?

Inverse Square law, to explain the value of these determinations, as to what would exist on our horizon?

Forgive me as I lost myself in such thoughts.