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.

Quantum Mechanics: Determinism at Planck Scale

Perhaps Quantum Gravity can be Handled by thoroughly reconsidering Quantum Mechanics itself?- Gerard t' Hooft

Albert Einstein used harmonic oscillators to understand specific heats of solids and found that energy levels are quantized. This formed one of the key bridges between classical and quantum mechanics.

Can harmonic oscillators serve as a bridge between quantum mechanics and special relativity?

It is nice Paul that you continue to bring perspective forward here for consideration.

I'll hope you will supply the paragraph one day that made the lights go on for you about what you are percieving, and from what you have understood having read Einstein's words in later life. Many tend to think Einstein was unproductive in his later life?



The basis of the paper you brought forward for inspection, is really quite significant, in my views. I'll tell you what I see and from this discussion, the ideas of what the Riemann's Hypothesis might mean in the expansion of cyclical processes we might have seen in the Ulam spiral perhaps?



You have been developing that perspective for a quite a while, as your numbers attest to this expression. So what are Poincare cycles? This I'll hold off for a bit, becuase I am returning to the earlier discussion wehad about what Zero actually means. Do you remember? Perhaps you could sum it up again from our consversationin the comment section.

You describe returning to the Laughlin and the foundational perspectives, for a better look. Type in "emergence" or "first principle" into the blog search feature, would be quite productive I think.

This is a good indicator to me that the route to describing the process although very difficult in ascertaing value in the "dissapation effect" of the virtual blackhole of Hooft, what value is this insight if it did not have a basis for which it could work?

THE MATHEMATICAL BASIS FOR DETERMINISTIC QUANTUM MECHANICS by Gerard ’t Hooft

One now may turn this observation around. A closed system that can only be in a finite number of different states, making transitions at discrete time intervals, would necessarily evolve back into itself after a certain amount of time, thus exhibiting what is called a Poincar´e cycle. If there were no information loss, these Poincar´e cycles would tend to become very long, with a periodicity that would increase exponentially with the size of the system. If there is information loss, for instance in the form of some dissipation effect, a system may eventually end up in Poincar´e cycles with much shorter periodicities. Indeed, time does not have to be discrete in that case, and the physical variables may form a continuum; there could be a finite set of stable orbits such that, regardless the initial configuration, any orbit is attracted towards one of these stable orbits; they are the limit cycles.

So Hooft is explaining this for us here? Only in a "positive" expression?

Before movng onthen soemthings would have had to been made clear as far as I can tell in regards to the basis of what zero actually means.

An Energy of Empty Space?

Einstein was the first person to realize that empty space is not nothingness. Space has amazing properties, many of which are just beginning to be understood. The first property of space that Einstein discovered is that more space can actually come into existence. Einstein's gravity theory makes a second prediction: "empty space" can have its own energy. This energy would not be diluted as space expands, because it is a property of space itself; as more space came into existence, more of this energy-of-space would come into existence as well. As a result, this form of energy would cause the universe to expand faster and faster as time passes. Unfortunately, no one understands why space should contain the observed amount of energy and not, say, much more or much less.

Once you get to th ebulk space it is extremely hard to explain how I gothere in my visual thinking but it is true that I see dynamcial spaces and all inlcusive views of the science of this original encapsulated in a geometrical process. Whether it's right or not is another question. I know this:)

While D brane analyisis had been given to another for perspective in relation to how we see Belenstein bound and the horizon of value, being describe by CFT, we know well then that the abstraction of D brane thinking has to answer to those microscopial visonistic qualites of a very dynamcial place?

That what has happen inside the blackhole, had something else as well to consider? Anomalies in perception then exist in how we see the quark Gluon plasma in relation to the principals of superfluids.

Why molasses and ice cream production might seem important to some, while others might dismiss the childest antics of the condense matter theorist?

So while these things are happening we should know that the condition elevated to bulk persepctive would have one see graviton production, as constituents of this bulk space. This derivation placed the bulk perspectve within grasp of what the harmonic oscillator means as we move our peceptions to the flat spacetime arrived at in the production of the quark Gluon plasma, that we are so boldly talking about here in views of the langrangian space.

I see in the WMAP perspective held to analogies of the sound in polarization modes as, nodes and anti-nodes and are really interesting when held to that perspective about what we might think of in relation to how we see particle physics having undergone a model change, as well as a perspective one as well.

This is a fifth dimensional view accomplished.

See:

Quantum Harmonic Oscillator

Harmonic Oscillation

Warm Dark Matter

Big Bang Nucleosynthesis

Strangelets Do Not Exist?

I tried to follow the history as best I could, and the resulting worries earlier linked in extra links seen below, attest to the research that I followed. Can we safely say now, that strangelets do not exist?

Quantum character of black holesby Adam D. Helfer

Black holes are extreme manifestations of general relativity, so one might hope that exotic quantum effects would be amplified in their vicinities, perhaps providing clues to quantum gravity. The commonly accepted treatment of quantum corrections to the physics around the holes, however, has provided only limited encouragement of this hope. The predicted corrections have been minor (for macroscopic holes): weak fluxes of low-energy thermal radiation which hardly disturb the classical structures of the holes. Here, I argue that this accepted treatment must be substantially revised. I show that when interactions among fields are taken into account (they were largely neglected in the earlier work) the picture that is drawn is very different. Not only low-energy radiation but also ultra-energetic quanta are produced in the gravitationally collapsing region. The energies of these quanta grow exponentially quickly, so that by the time the hole can be said to have formed, they have passed the Planck scale, at which quantum gravity must become dominant. The vicinities of black holes are windows on quantum gravity.

Having been holding onto the thoughts published by Peter Steinberg," Richard and Me how could I refuse to acknowledge that such strangelets might indeed not exist, having been given experimental verification as to procedures resulting in this Risk assessment consultation.

The relations to cosmic correlations were drawn in my research, as I tried to understand what was going on in a everyday scenario, as we saw the elevation to cosmological colliders making the statements that they do.


Ion-Smashing Yields New Knowledge, But Some Still Question RiskBy Carolyn Weaver

“It’s basically a living embodiment of E=mc squared,” says Brookhaven physicist Peter Steinberg. “Einstein’s theory told us a hundred years ago that you can trade off energy for mass, and vice versa. We’re essentially converting the kinetic energy, the energy from the motion of these nuclei, converting it into lots of particles.”

The four detectors that bestride the collision points are massive machines, with “time projection chambers” that record the collisions and their after-moments. The latest results made big news last year when Brookhaven physicists reported that the quark-gluon plasma was not a gas as expected, but rather a very dense liquid.

So if I had thought for a moment about John Ellis's contributions to furthering the layman understanding, it was quickly understood that the energies involved had to have many events to conclude what may be happening on such a large scale, might be happening in the colliders. Quite simple really?

Would it be so dangerous that such energy considerations required the work of Star to help ease fears with which the layman population could have turned into a frenzy of religious doomsday scenarios?

Strangelet Search at RHICby STAR Collaboration

We report results of the first strangelet search at RHIC. The measurement was done using a triggered data-set that sampled 61 million top 4% most central (head-on) Au+Au collisions at $\sNN= 200 $GeV in the very forward rapidity region at the STAR detector. Upper limits at a level of a few $10^{-6}$ to $10^{-7}$ per central Au+Au collision are set for strangelets with mass ${}^{>}_{\sim}30$ GeV/$c^{2}$.

See:

Blackhole Creations

Strangelets in Cosmic Considerations

Cosmic Ray Collisions and Strangelets Produced

Microstate Blackhole Production

Quark Gluon PLasma II: Strangelets Produced

Accretion Disks

Strangelets Form Gravitonic Concentrations

IN a Viscosity State Production is ?

What Are those Quantum Microstates

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?

EQ and Intuition

A 180 degree stance on how "consciousness," body and emotion, might be directed by mind? So, you might say "mind is emphemeral in quality" in some regards?

All heart you say! "Heart" is the balance between? Involution and evolution

Yet, there is a interplay between, "the body home" and "the abstractual mind" further out, while, they reside "in life," with each other? You had to know that this "schematic" was, and is, deeply implanted within our historical minds in many ways? The strive towards "wholeness" is strong even in the scientist?:)

Harmonical patterns of Jenny's, and the modulation of the brain state? Neural correlates to consiciousness, but of mind working from the other perspective, that inherent patterns will be revealled as the truer source of expression and origination of mind moving and all things following?

If conceived as a series of ever-wider experiential contexts, nested one within the other like a set of Chinese boxes, consciousness can be thought of as wrapping back around on itself in such a way that the outermost 'context' is indistinguishable from the innermost 'content' - a structure for which we coined the term 'liminocentric'.

Things borne in mind, brought to reality, and back again? Liminocentric structures are very important distinction in that toposense, possibly?

When presented with certain ideas it was with the recognition that insight and devlopment might begin from a certain perspective. If you change that perspective arouund a bit, just a bit, and the presumption is a 180 degree position :) how would things look if they had followed from mind directing the neurological flows inside that lump of brain?


Damasio's First Law
The body precedes the mind.

Damasio's Second LawEmotions precede feelings.

Damasio's Third Law
Concepts precede words.

Consciouness emerges when this primordial story-the story of a object causally changing the state of the body-can be told using the universal nonverbal vocabulary of body signals. The aparent self emerges as the feeling of a feeling. When the story is first told, sponataneously, without it ever being requested, and furthermore after that hwhen the story is repeated, knowledge about hwat the organism is living through automatically emerges as the answer to a question never asked. From that moment on, we begin to know.

Pg 31, The Feeling of What Happens, by Antonio Damasio


Having some of these books on related subject of intuition and emotion, other issues on the book shelf, I thought because of the event reported by Clifford and others, I would look directly for any wording that might issue in regards to "intuition." I did not find this word in the index, nor in K.C. Cole 's book, "The Hole in the UNiverse."

It is nice to know that times have changed, in regards to the responsibilty and recognition of how this process plays a role in our developing perspectives.:) I would add Joe Polchinski here, but having moved to such abtract realms, it might be to early for the mind to grapple what "inherent model application" this might play in that developing perspective. Still it is nice that Joe offered his perspective there, and all being respective of the science in knowledge pursuate in that event.

EQ and IQ

It is not to hard, when having done research previously, that we will come across ths idea of the Emotional Quotient(EQ) versus the Intellectual one, (IQ).

There seems to be some recognition now of the importance this role now plays?

Nodes and Anti-nodes

Tool's for measure.

The center of the gyroscope is a jewel-like sphere of fused quartz. These spheres, the size of Ping-Pong balls, are the roundest objects ever made by man. The tiny spheres are enclosed inside a housing chamber to prevent disruption from sound waves, and chilled to almost absolute zero to prevent their molecular structure from creating a disturbance. The accuracy of these gyroscopes is 30 million times greater than any gyroscope ever built.

Making Strings in the lab, made me think of Clifford and the ice cream mix that he was privy too, by joining condense matter [ahem...string:] theorists, on a Friday night? :)Nitrogen, and superconductors seem to go hand in hand? Made me think of GPB and [whoops my mistake-not-nobium sphere], were mention for a reason.:)



Normally I do not like to encourage such a view held to speculations, but the transferance to 3d effective thinking and all that, had me look at WMAP, was a process lead through by valuating sound in such analogies. As a layman, I hope I am forgiven.

Is it the process?

Visitors' shadows manipulate and reshape projected images of "Buckyballs." "Buckyball," or a buckminsterfullerene molecule, is a closed cage-structure molecule with a carbon network. "Buckyball" was named for R. Buckminster "Bucky" Fuller (1895-1983), a scientist, philosopher and inventor, best known for creating the geodesic dome.

Nanomandala:

The purposeful arrangement of individual atoms bears some resemblance to the methods monks use to laboriously create sand images particle by particle, however, Eastern and Western cultures use these bottom-up building practices with very different perceptions and purposes.

Photo and text credit: © 2003 Museum Associates/Los Angeles County Museum of Art


To me it is a interesting way of seeing what is happening in space held by perception. BUcky balls and such, from my early days of reading BuckminsterFuller and his interesting building concepts, had somehow morphed into dynamical triangulation, used in the monte carlo method of quantum gravity perceptions.

Dr. Jenny's cymatic images are truly awe-inspiring, not only for their visual beauty in portraying the inherent res-ponsiveness of matter to sound (vibration) but because they inspire a deep re-cognition that we, too, are part and parcel of this same complex and intricate vibrational matrix -- the music of the spheres! These pages illumine the very principles which inspired the ancient Greek philosophers Heraclitus, Pythagoras and Plato, and cosmologists Giordano Bruno and Johannes Kepler.

Dimensional views of the "quark to quark measure" had me see the dynamics of this distance?

How much more then would such a weak field describe for us the oscillation of the neutrino, from one phase state to another. One distance to another? A revealled in cosmic rays, as "new physics perhaps" that extends beyond the standard model?



Paul Dirac

When one is doing mathematical work, there are essentially two different ways of thinking about the subject: the algebraic way, and the geometric way. With the algebraic way, one is all the time writing down equations and following rules of deduction, and interpreting these equations to get more equations. With the geometric way, one is thinking in terms of pictures; pictures which one imagines in space in some way, and one just tries to get a feeling for the relationships between the quantities occurring in those pictures. Now, a good mathematician has to be a master of both ways of those ways of thinking, but even so, he will have a preference for one or the other; I don't think he can avoid it. In my own case, my own preference is especially for the geometrical way.

If for one moment you continue the thought processes in light of visionary changes sought by and spoken in context of polarization effects in the WMAP, then such views have a profound effect, to what was always interesting data from cosmological apprehensions in discovery.

Mikheyev-Smirnov-Wolfenstein effect92 April 2006 wikipedia)

The Mikheyev-Smirnov-Wolfenstein effect is a particle physics process which acts to enhance neutrino oscillations in matter.

While dynamic functions are being revealled to me of microprocesses( phases states), these dynamics are always interesting from what the geometrical perpecive of what was derived from Dirac.

A "three dimensional view" of what may be happening in the abstraction of space dynamics seen in UV perspective described in analogy to Gauss's coordinates?

Something much more profound and detail in a greater depth of thinking of an abstractual nature perhaps? B Field dynamics, would be a interesting comparison while holding mind in geometrical abstraction?

Antineutrinos From Distant Reactors Simulate the Disappearance of Solar Neutrinos

The potential importance of the Kamland results goes well beyond the solar-neutrino problem. Particle theorists hope that the masses and flavor compositions of the neutrino mass eigenstates will help point the way to an encompassing unification beyond today's manifestly incomplete standard model of fundamental particles and their interactions. Detailed knowledge of the neutrino states might also elucidate a central problem of cosmology: How did matter come to dominate over antimatter in the immediate aftermath of the Big Bang? Does the mixing of neutrino states harbor the symmetry-breaking mechanism that could have done the trick?


Oscillating flavorsThe three neutrino mass eigenstates are presumed to be different coherent superpositions of the three flavor eigenstates (ne, nm, and nt) associated with the three charged leptons: the electron, the muon, and the tau. There is good evidence that only two of the three mass eigenstates contribute significantly to ne. In that approximation, one can write

The question always arises in my mind about the quantum harmonical oscillations, as part of a much larger inherent feature of reality, with which we might view WMAP. Or, events that arise from the sun. Could such analogy, born in the sun's process spit out the nature of the neutrino?

The plates can be made visible by mounting a mirror behind the row of plates, angled so that the top of the plates are visible to the audience (same idea as in Polarization by Scattering). Create the optimum angle for the front rows, as the back rows will be looking down on the plates anyway. Make sure the cello bow is nice and tactile by treating it with rosin before the performance. Sprinkle the sand on the plates so that it forms an even cover. Don't overdo the amount.

Helioseismology

Neutrino oscillation( 31 March 2006 Wikipedia)

Neutrino oscillation is a quantum mechanical phenomenon whereby a neutrino created with a specific lepton flavor (electron, muon, or tau) can later be measured to have a different flavor. More specifically, the probability of measuring a particular flavor for a neutrino varies periodically as it propagates. Neutrino oscillation is of theoretical and experimental interest, as observation of the phenomenon implies nonzero neutrino mass.

If you change the way you look at things sometimes, this change, helps you see in different ways that you might not have before? WMAP?

Sounding the Sun: HelioseismologyP.B. Stark

On the other hand, the Sun is essentially transparent to neutrinos, and to acoustic waves. Using acoustic energy, we can "see into the Sun" in a way that is quite similar to using ultrasound to image the interior of the human body.

Oscillations of stars have been recognized since the late 1700s. The complicated pattern of the Sun's oscillation was first observed in 1960 by Robert Leighton, Robert Noyes, and George Simon.

The explanation of the pattern in terms of trapped acoustic waves came in 1970-71 by Roger Ulrich, John Leibacher, and Robert Stein. This explanation predicted certain detailed features of the spectrum of solar oscillations that were confirmed by observations made in 1975 by Franz Deubner.

The Sun is constantly vibrating in a superposition of acoustic normal modes (like the patterns with which a guitar string vibrates, but for a spherical body rather than a string). The characteristic period of oscillation is about 5 minutes. It takes on the order of a few hours for the energy to travel through the Sun. The velocity amplitude of solar p-modes is about 1 cm/s; the relative brightness variation is about 10-7.

Mode lifetimes range from hours to months. Modes are typically excited many times per lifetime.

Let's look at the origins of the images below. Have I described their origin?

See:

Angels and Demons

The Devil, is in the details of a Mirror World?

While the "true cast" is here? :)

Intuitively Balanced: Induction and Deduction

A VIEW OF MATHEMATICS Alain CONNES

Most mathematicians adopt a pragmatic attitude and see themselves as the explorers of this mathematical world" whose existence they don't have any wish to question, and whose structure they uncover by a mixture of intuition, not so foreign from poetical desire", and of a great deal of rationality requiring intense periods of concentration.

Each generation builds a mental picture" of their own understanding of this world and constructs more and more penetrating mental tools to explore previously hidden aspects of that reality.

Is there truth to the emphemeral qualites of mind. That there is a lighter measure with which we take on to life? How would you weight things of meaning? A pythagorean string perhaps, with a weighted gourd? Meaning on resonance as measure by, that vibrating string?

Behind the image as you click on it is an arche principled of Aristotle.

Would we have found the derivation and essence of what that first principle was. The foundation as it might have been in a intuitive moment released? A place where the freedoms, of smooth travelling satellites would have found the least resistance, in order for mind to travel into the "yellow abstract domains of math" and back?



Sometimes I like to think of a image of a "circle within a circle" as a model of what might be percieved. Yet if we thought, that in the center of this, something like a solid matter existed. Our bodies, our brains. Earth Maybe.

Now an image in mind easily drawn might have been, that matter earth, then color red, then green, and then violet, and we have this range of colors issuing from the center. We are never devoid of the thinking mind, or the emotive feelings we have about things, yet there is some impact in the remembrance of things that are emotively charged?

Of course this is speculation of a kind. a model of a kind, and some way in which I had pecieved the dynamcis of life moving from the center outward and back, and never really stayng in one place to long. We have these circles intertwining. Thought runs the whole length of it. From the center out/in, 5 is 1, or 1 is 5? Thoughts about anyhtng could have been 2, 3, or 4?

Life inside, is outside and all that we think, shown on the collar of our sleeves?

Clifford:

His was the best single sentence summing up the concept, as we were to use it that evening: Intuition is the process of getting to a destination without knowing the route. He also added: Sometimes you did not even know you wanted to get there. I've modified the words a bit, but that's the essence of what he said. It was a definition that was so appreciated, you could hear several audible hhhhmmmmms of recognition from the audience.

You have to wonder about "neural correlates to consciousness?"


Remembrance

We have this brain matter and all kinds of neural firings.

To say the "emotive response" could have been activated from the basis of brain structure, and it's corresponding evolutionary standardization, then to have a reward system( pavlov response), would have been based on early emotive developement on humanization standards, to a evolving society, is puzzling one to say the least?

What "new brain covering" in the formation of the brain matters would correspond to our evolution would say that we are a much more refined society that we would invoke new standards and advancements in our thinking?

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

Fritz London

Fritz London was born in Breslau, Germany, and came to the United States by way of Oxford in 1939. With his younger brother Heinz he began studies of superconductivity in 1935. He was responsible for developing some of our most basic theoretical ideas on the subject, including the London movement, the conjecture that magnetic flux in a superconductor might be quantized, and the realizations that superconductivity must be interpreted as a cooperative phenomenon among large numbers of electrons based on a process known as momentum-ordering.