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

Hyperspace

Science is that human activity in which we aim to show towards nature that respect that in a democracy we endeavor to show towards each other."

There is no doubt my views are biased. For all the wrong reasons I have cited the questions about how I see, has been strongly encouraged. There is no leader for me in this question( driven in my own research), with something that lead me through the mathematics and divergences from Euclidean perspectve.

It was joined on a level with the geometrical implications of GR conclusions and assignments to Rienmann's positive views. Held in context of his teacher, I have given respect to the Gausssian approach of thinking, and definitions, assigned Hyperspace. If I see Gaussian coordinates as viable, then how shall I refrain myself from seeing in such spaces?

So of course this is troubling to me, that if I was to proclaim my true belief in the religiousity of stringevangelism, then how could I ever give someone the clear and concise picture of this graduation?

So shall I put aside my views of the translation given to hyperspatial views, in context of all the "colorings" I have given the "dynamical relation" of what is not seen, and is hidden, I want to understand this better, from the layman point of view.

So a strong debate needs to be fuelled in regards to the validation process of what hyperspace actually means. Has it been a means to an effort to geoemtrically assign right thinking through the stages of what we have been given to perspective. That the beginning of this universe, had circumstances given to micro perspective views, had lost touch with the validation process, that this geometry, could have ever given credence in mathematical basis. There are no physics at that level, yet my view had been reduced to the superfluid.

While "the debate" is not mine, by layman status, I do follow the logic.

Deflating Hyperspace" by: David Pacchioli (Research/Penn State, Vol. 16, no. 4 (December, 1995))

For Chernosky, a Ph.D. candidate in English literature, this isn't exactly the same thing as asking what hyperspace means. Hyperspace seems to mean a lot of things, and then again not to mean much at all; its meaning shifts with the user, if not with the wind. It is, Charnesky writes, "an almost empty signifier capable of almost limitless application."

"This fuzziness," he adds in person, "is its power." It is also a quality that puts hyperspace in rather crowded company. Our language is loaded with terms appropriated from science for use in popular discourse. Along the way, the borrowed word's highly technical, narrowly precise -- not to say arcane -- meaning is typically transformed. What emerges is a fluttering, eye-catching, all-purpose concept that can be used interchangeably for explaining the weather or selling toothpaste.

So conduct becoming, and of what I asked of others I am working to see this transition through. How I still believe in "my God, my religiousneess, and faith in humanities struggle for perfection" and still offer, perspective here, while biased?

No one speaks here so I have to lead myself through intuitive journies, if there is not the willingness at other points in the blogopshere for this debate to take place. Of course, in my silent way I will try and be fair. I like to thank Peter for the toning down that has taken place.

What views have been put out there then that we could answer and put aside comparative functions to "alien cultures" and all the sort, to speak a truth that would move perception accordingly.

Are mathematcians divided in this case?

Hyperspace(23 Jan 2006)

Hyperspace theories are concerned with theoretical systems that have more than the familiar three spatial dimensions. Hyperspace theories are largely a mathematical theory but their developers often attempt to make them of use to physicists. Hyperspace theorists generally believe that the laws of nature are simpler in higher dimensions

What are Degrees of Freedom


If we travel to Peter Woit's site, can we point to the article introduced and go from there? If I quote the next source above, then this would have given reason to wonder if the trailing thoughts of those who wished to deal with this(above Wiki article and references), might create recognition of some of the things Peter Woit is describing.

So lets open it here then.

Einstein Has Left the Building
By JOHN HORGAN
Published: January 1, 2006 NYTimes

Today, government spending on physics research has stagnated, and the number of Americans pursuing doctorates has plunged to its lowest level since the early 1960's. Especially as represented by best sellers like "A Brief History of Time," by Stephen Hawking, and "The Elegant Universe," by Brian Greene, physics has also become increasingly esoteric, if not downright escapist. Many of physics' best and brightest are obsessed with fulfilling a task that occupied Einstein's latter years: finding a "unified theory" that fuses quantum physics and general relativity, which are as incompatible, conceptually and mathematically, as plaid and polka dots. But pursuers of this "theory of everything" have wandered into fantasy realms of higher dimensions with little or no empirical connection to our reality. In his new book "Hiding in the Mirror: The Mysterious Allure of Extra Dimensions, from Plato to String Theory and Beyond," the physicist Lawrence Krauss frets that his colleagues' belief in hyperspace theories in spite of the lack of evidence will encourage the insidious notion that science "is merely another kind of religion."

Krauss and Susskind versus Horgan

Peter Woit:

I don’t see Horgan here criticizing the attempt to quantize gravity as “frivolous”. His criticism of physicists as having “wandered into fantasy realms of higher dimensions with little or no empirical connection to our reality”, is a justifiable one that deserves to be seriously addressed. Krauss and Susskind’s comment that Horgan would be surprised that both of them think that new degrees of freedom will be needed to characterize elementary particle physics doesn’t seem to have any basis in fact. Horgan isn’t making broad claims that physicists shouldn’t look for new degrees of freedom, he is very specifically referring to the use of extra space-time dimensions.

Earth Bound Solutions to All Possible Pathways

Will I might have been guilty of taking Physics down a road so similar in conceptualization bastardizing, that I would have driven a nail in the very deaths of what could have emerged from the outcome of all possibilties? That we were indeed attached to the consequences of our ever actional decisive forays into human contact. Decision making, action orientated, outcomes, of the original simplectic intiated ideas?

It had to arise from something?

Would it be so easy to lay out the pathway required, that each of us woud have recognized our time in existance, would have indeed been the measure of all things that we choose to endorse in our ever perfecting evolution as cyclcical choices of perfecting our thinking.

This is a interesting thought held in my mind when you think of about what is held in context thinking, if we hold the photons in context of earthbound recognitions of those time orientated distances.

Many will know instantly what this means while others, scoff at the notion that we could have seen such influences telling us anything useful about the space of these interactions.

All the while the initial plectic recognition of Gellman's arose to complexities. We lost sight of the simple ideas about what might happen to the spin rotations over those vast distances? That the connectiveness, would have ever acknowledged equative relations that these two photons under the squared earthbound views, would include all probabilites being still held to view. While we still look at all possible actions? So what about time indeed.

Einstein's prettty girl scenario and hot stove, served to help me see conceptual framesworks about speed attributions of the nature of fast and slow moving world in terms of our earthbound considerations. This action was decisive, and held in context of that experience. He helped me to see that experience is indeed fleeting, depending on our circumstances, where such nature would have embedded the very nature of the spacetime fabric itself to include, how we will measure that distance of mind.

Is there another story here that we might be convinced of a rational behind?

Here is something that Brian Greene mentions to reinforce where I had come to in looking at the completion of that chapter.

the quantum entanglement would become so spread out through these interactions with the environment that it would become virutually impossible to detect. For all intents and purposes, the original entanglement between photons would have been erased.

Never the less it is truly amazing that these connections do exist, and that craefully arranged labratory conditions they can be observed over significant distances. They show us, fundamantally, that space is not what we once thought it was. What about time?

Page 123, The Fabric of the Cosmo, by Brian Greene

Does gravity vary over time?

If you did not have this in mind, what value would you attribute gravity in any scenario, as you mull over all the geometrical implications if a positive geometric solutions to Riemann's spherical solutions. The persective that GR holds for us, in our considerations?

Theory, experiment and fine structure

Were it not for relativity, the three states with different J would all have the same energy, and the light emitted in the transition would have a single frequency of about 277 000 GHz. However, relativistic effects mean that the states have slightly different energies, and when this light is analysed carefully, splittings of the order of 10 GHz are seen.

If ever driven to micro-perspectives how would time been of value if held to the quantum perspective as a strong enviriomental influence. One which spreads out all interactive phases that we could no longer discern, a viable solution to what is presented to us, unless in "symmetry breaking" realizations. So what was that beginning. Again Kravstov computer simulations help to drive that concept home.

Another laser beam is used to make the atoms fluoresce, and the amount of fluorescence is measured as a function of the microwave frequency to plot a "resonance curve". An ultra-precise measurement of time can be made by measuring the frequency of the peak in this resonance curve (see "Atomic clocks" by Pierre Lemonde in Physics World January 2001 pp39-44).

So simplicity for me asks what image in mind would hep one to discern entropic valuation to what this universe had become from temperature orientated view of that early universe, to have said, "that the probabilites that are evident now, have become like this?"

Two things formed in my mind as to the consequence of numbered systems, and pascal triangle, as to the source of all probabilitistic valuations and the marble drop held in context of BINOMIAL DISTRIBUTION.

So having defined the early universe and quantum valution arising from temerature, it helps to think about the outcome emerging from what had never been understood or have in "measured stick," to what would become our universe today? It still is the earthboud experience that we have, has emerge from astate that was equal in it's determinations. Ideas are like that.

So you had to see simplicity settling into our minds in such a way that If Plato indeed points up, then you would understand immediately, what he is pointing too. If you hold that image in mind of the triangle, then how would you ever assess Riemann's hyptohesis, as to the spirlaic outcome of Ulam's spiral indications? While the spiral opens up to the vast potential of outcome originating from ideas, it still settles into minds in it's concrete form.

So you have to define this relationship very carefully, and if I had said Liminocentrically topologically organized, what the heck would I have been saying?


Heaven's ephemeral Qualities?

It seems it would have far reaching enlightening features of what the buddhist mind might have to offer? What subtle arrangement the conceptual framework might have said about our everyday interactions with each other? Then you might have said what color indeed are the emphemeral qualities to our [mathematical]decisive minds that we would choose such abstract colors as yellow in our mental appreciations of what nature hides in the color of flowers around us? :)

Drawing a Venn diagram: Entanglement Issues

Plectics, by Murray Gellman

It is appropriate that plectics refers to entanglement or the lack thereof, since entanglement is a key feature of the way complexity arises out of simplicity, making our subject worth studying.

The person above was kind enough to send information held in context of picture link for consideration, to help out with comprehension. I mean certain things hold us to consequences, that while I might have been thinking of Einsteins example of a pretty girl and a hot stove, this thinking did not pass my attention when one held the photon to certain enviromental influences as we gave these things thought processes. I context of "gravity as the square," is appropriate I think, about what combinations are realistic.



At the very heading of this post there is a link directly attached for consideration in context of all these possibilties. Some things come to mind in terms of Feynman's toy models, as strict interactive phase that we would like to keep track of. So what one might have done to say, hey, if we are given a possibility of scenarios about Entanglement issues, how shall we solve these interactive phases, as we try to build a multiphase integrative model held in context that perfect human being.

Entanglement applies to two or more particles even if one of them is used as input to the two slit experiment, it is not applicable to single particle experiments.

YOu know it is not that simple, but there are always grand designs on what we think something is nifty in society, as we progress our models of the future. As to how we will create the perfect models for apprehension about our universe, and how we interact with it.

Pictorial represenations can be very useful in presenting information or assisting reasoning. Venn diagram is an example. Venn diagrams are used to represent classes of objects, and they can also assist us in reasoning about the relations between these classes. They are named after the English mathematician John Venn (1834 - 1923), who was a fellow at Cambridge University.

While it is true that I am being fascinated by mathematical processes, and how they are used in our visionary quest for understanding, one would have to be a computer to remember all the interactive phases that could have manifested from a situation held in context of a "societal problem." One we might have encountered in our lifetimes.

It's statistical outcome that held to such micromanagement processes, would have been lost on all our minds, if we did not think some science process could have been touted with all these combinations.



Each time I am presented with this thinking, the elementals of the model for apprehension, it always seemed easier to me to just have a look and see what "buddhist principles" are telling us about how we have a hold of our world in all it's realisms. The choices we make, and how we are to conduct ourselves "becoming." Einstein used that term well I think.

So why such association and "combinations", that we have move the thinking here to what was gained in our emotive and abstract thinkings, as productive human beings? To see what a new foundational logic is being developed around our lives. Did we did not readily see the significance of the technologies involved. One had to dig a little deeper I think.

So here is a preview of what entanglement issue has been shown to help orientate views on this issue. Some diagram perhaps, to show the developing scenarios around such entanglement issues?



Quite early these indications about the possibilties of entangled states, raised all kinds of questions in my mind. Thinking of Hooft and others, about the issues of classical quantum processes, over top of these wide and incomprehensible statistical possibilties, seems held under the auspice of our reality model. That "square", given earthbound recognizitons, happily according to the basic pricniples, have so far held our views in gravitational model assumptions. IN essence, we have boxed the views on entanglement. As we have boxed Andrey Kravstov computerized model of the orignations of this universe in a supersymmetrical view of origination. What could have arisen from such situations. Probable outcomes?

Whether such a "quantum computer" can realistically be built with a value of L that is large enough to be of practical use is a topic of much debate. However, the mere possibility has led to an explosive renaissance of interest in the host of curious and classically counterintuitive properties associated with entangled states. Other phenomena that rely on nonlocal entanglement, such as quantum teleportation and various forms of quantum cryptography, have also been demonstrated in the laboratory

Venn Logic and TA

I always lke to inject a piece of my young child's perspective, becuase it helps explain things a bit about "the neighborshood." As we move through them. He asked me about the neighborhood that we were moving too, as if, that was the world. That was his question. "Is this the World," Dad? He was about 4 years old at the time. He's gone now, married, and leadng a very productive life.



The purpose of this picture above comes later down the length of this post. We are all not perfect, are we?

As a youth my first reading of this topic was from a book called, I'm Okay Your Okay, by M.D. Thomas A. Harris.

It helped in defining aspects of myself in context of what was happening in my environment, while being introspective. Is this always a good thing that we take stock of what is going on inside ourselves to wonder indeed what is all these parts of ourselves. How do we look at them in context of the way the "I" is being used.

These lessons were also derived from other places, so it becomes culminative in how one might look at society, and from it, a biased view forms no dfferent then one who has been transplanted from historical context of experience, moving from the lands of the Carribean to the UK society, held in context and views of the community in which they had lived, and live now. There were comparative features drawn from expeirence to consider here?

So as you move, you grow in perspective, all the while the pictures of mountains and similarities strike poises in our mind of of wnating recognition. Who was this person at the time of youth, who, like myself saw farms of a early history, to know that today this historical past is all but forgotten in the real world struggle of lives held in context of these farms? The picture today, contains the picture of our youth.

Parent ego state

This is a set of feelings, thinking and behaviour that we have copied from our parents and significant others.

As we grow up we take in ideas, beliefs, feelings and behaviours from our parents and caretakers. If we live in an extended family then there are more people to learn and take in from. When we do this, it is called introjecting and it is just as if we take in the whole of the care giver. For example, we may notice that we are saying things just as our father, mother, grandmother may have done, even though, consciously, we don't want to. We do this as we have lived with this person so long that we automatically reproduce certain things that were said to us, or treat others as we might have been treated.

As we grow up we take in ideas, beliefs, feelings and behaviours from our parents and caretakers. If we live in an extended family then there are more people to learn and take in from. When we do this, it is called introjecting and it is just as if we take in the whole of the care giver. For example, we may notice that we are saying things just as our father, mother, grandmother may have done, even though, consciously, we don't want to. We do this as we have lived with this person so long that we automatically reproduce certain things that were said to us, or treat others as we might have been treated.

Adult ego state

The Adult ego state is about direct responses to the here and now. We deal with things that are going on today in ways that are not unhealthily influenced by our past.

The Adult ego state is about being spontaneous and aware with the capacity for intimacy. When in our Adult we are able to see people as they are, rather than what we project onto them. We ask for information rather than stay scared and rather than make assumptions. Taking the best from the past and using it appropriately in the present is an integration of the positive aspects of both our Parent and Child ego states. So this can be called the Integrating Adult. Integrating means that we are constantly updating ourselves through our every day experiences and using this to inform us.

In this structural model, the Integrating Adult ego state circle is placed in the middle to show how it needs to orchestrate between the Parent and the Child ego states. For example, the internal Parent ego state may beat up on the internal Child, saying "You are no good, look at what you did wrong again, you are useless". The Child may then respond with "I am no good, look how useless I am, I never get anything right". Many people hardly hear this kind of internal dialogue as it goes on so much they might just believe life is this way. An effective Integrating Adult ego state can intervene between the Parent and Child ego states. This might be done by stating that this kind of parenting is not helpful and asking if it is prepared to learn another way. Alternatively, the Integrating Adult ego state can just stop any negative dialogue and decide to develop another positive Parent ego state perhaps taken in from other people they have met over the years.

Child ego state

The Child ego state is a set of behaviours, thoughts and feelings which are replayed from our own childhood.

Perhaps the boss calls us into his or her office, we may immediately get a churning in our stomach and wonder what we have done wrong. If this were explored we might remember the time the head teacher called us in to tell us off. Of course, not everything in the Child ego state is negative. We might go into someone's house and smell a lovely smell and remember our grandmother's house when we were little, and all the same warm feelings we had at six year's of age may come flooding back.

Both the Parent and Child ego states are constantly being updated. For example, we may meet someone who gives us the permission we needed as a child, and did not get, to be fun and joyous. We may well use that person in our imagination when we are stressed to counteract our old ways of thinking that we must work longer and longer hours to keep up with everything. We might ask ourselves "I wonder what X would say now". Then on hearing the new permissions to relax and take some time out, do just that and then return to the work renewed and ready for the challenge. Subsequently, rather than beating up on ourselves for what we did or did not do, what tends to happen is we automatically start to give ourselves new permissions and take care of ourselves.

Alternatively, we might have had a traumatic experience yesterday which goes into the Child ego state as an archaic memory that hampers our growth. Positive experiences will also go into the Child ego state as archaic memories. The positive experiences can then be drawn on to remind us that positive things do happen.

The process of analysing personality in terms of ego states is called structural analysis. It is important to remember that ego states do not have an existence of their own, they are concepts to enable understanding. Therefore it is important to say "I want some fun" rather than "My Child wants some fun". We may be in our Child ego state when we say this, but saying "I" reminds us to take responsibility for our actions.

Go ahead and Click on John Venn's picture

A painting of John Venn by Charles E. Brock. Photograph by Christopher Hurst, Hamilton-Kerr Institute, University of Cambridge

IN a strange world where such things are to become part of our analysis of subjective experience will we have created the perfect human being? Such models becme the logic structure of new computerized systems of thinking that will somehow recognize these factors in the human beings that we are, to have it done better in a traditional methods of logic, formed around and in computerized thinking.

Science and TA by Chris Boyd

Do we selectively ignore other models from artificial intelligence such as Zadeh's Fuzzy Logic? This is a logic used to model perception and used in newly designed "smart" cameras. Where standard logic must give a true or false value to every proposition, fuzzy logic assigns a certainty value between zero and one to each of the propositions, so that we say a statement is .7 true and .3 false. Is this theory selectively ignored to support our theories?

I had engaged this kind of exercise on my own, as I moved through different research avenues trying to piece together in my own mind, a process held in context of these neighborhoods, and such. How such interactive phases might have been thought about in science procedures. Looking at the basis of this logic, I was looking to find comparsions for this thinking in which the foundational perspectives might make sense.

Science and TA by Chris Boyd

If deduction is another way of knowing in TA, where and when is it applicable? Berne did use Venn diagrams, circles either distinct or overlapping, which were borrowed directly from symbolic logic to visually describe transactions. Perhaps TA in part can be considered a theory that analyzes ones own deductions based on childhood primitive assumptions. Perhaps it focuses on how people become irrational in decision making. In this case, TA provides critical thinking skills for human relations and can be considered a basis for analyzing the accuracy of our reality testing. Much as mathematics provides the language for science, TA may provide the logic for human relations and can be at least in part a deductive language.

Now as usual I did not have many to direct my thinking as I was developing thought processes, that the statements I highlighted were recognized as features I myself found along the journey to make sense of characteristic features we have of our thinking minds.

As you see clicking on John Venn's picture I would like to draw science into how I am seeing to support this "model of thinking." For clear and consise methods incorporating that clear mind.

Do we have to be robots with parts of ourselves missing from the supposed framework of that perfect being? This is what makes us unique in our perspectives as we move forward and share our point of views. We would have had to have been you to become who you are today. So it is never easy to see and be all that you want everyone to be.

Review of Ethics for a New Millenium Status

Jack Shoemaker

Like any good teacher, he understands that ethical matters are individual matters, that an ethical society is only the sum of its ethical citizens.

The Washington Post
September 12, 1999

ETHICS FOR THE NEW MILLENNIUM
By the Dalai Lama

Riverhead. 320 pp. $24.95

Reviewed by Jack Shoemaker
Now we've arrived at the end of the century, where crime, moral chaos, and politics driven by the often hollow sophistications of sociology and psychology all alert us to the breakdown of too many previous assumptions, particularly the coming apart of what might be called our ethical agreements with one another. Late capitalism, in apparent triumph, seems to encourage self-interest over any lingering sense of a commonwealth.

A New Way of Seeing?

Sorry couldn't resist. How many before us in our speculations and way of seeing? :)

When looking at Gaussian coordinates, the very idea that our views of "length of lines" had to have another way in which to interpret how we would see such divergences in the UV considerations. Now I might use UV differently then most, but it is always in context of gaussian coordinates that I always do this.

If I had created a triangle in much the same context(empheral qualties) we might have seen in 2D idealizations then, in how would you transfer such thinkng to three dimensional view held in context of the spiral, and the ever widening primes? These views would have to be locked in Gaussian interpretations, whether they came from Riemann or not. But such trancendance to 5d worlds had to have interpetation that would make you see this in other ways?

Saccherri introdces us to the 5th postulate and we move accordingly into the views of Riemann and others, in ways that are different.

Observations on the Regularity of Prime Number Distribution Peter Marteinson

Stanislaw Ulam’s (1964: 516) most general observation on his famous spiral, that a “property of the visual brain” allows patterns relating to the characteristics of primes to be discovered, may indeed stimulate the mathematical imagination, and inspire further creative attempts at visual pattern recognition in this area, but his spiral (fig.1), like its derivatives, has yet to be successfully interpreted in terms of possible arithmetic principles that can explain the genesis of the known distribution of prime numbers. Of his spiral he says only that it “appears to exhibit a strongly nonrandom appearance” (Stein et al. 1964). A corollary of this somewhat disappointing observation is that Euler’s pessimistic prognosis has yet to be disproved: “Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the mind will never penetrate” (cited by Ivars Peterson in Science News, 5/4/2002).

While it is never easy to take it all in it seems certain phrases and sentence structure stand out as important. While they may seem familiar I refrain from specify what this is, while I continue the search.

Topological Primes

The combinatorial concept of cartesian product allows decomposition of topological structure. Thus, a cylinder is the cartesian product of the circle and the line segment.

This provides for what might be called "topological primes" -- comparable to prime numbers in arithmetic wich form composite numbers. Thus, every mathematical structure may be considered as formed of the basic components:

vertex;
edge;
face;
hole;
cross-cap.

See Also:

Riemann's Hypothesis: A Pure Love of Math

The Mathematical Problems of David Hilbert

What are some of the characteristics of superfluids, and if one looked to the collider for results in RHIC, what information is leaked through the wall? How does the superfluid coat the wall? Where is that extra energy going?

SUPERFLUID 3He WEAK LINK PHYSICS

Although Josephson's first theoretical results for weak links were verified in superconductors shortly after his discovery, they have lain dormant waiting for verification by another type of phase coherent system. There were two candidates that could most likely fulfill this prophecy, superfluid 3He and 4He. Superfluids are phase coherent systems that can be described by a "macroscopic" quantum wave function (fulfilling the first requirement of the theory). However, is it possible to create a weak link separating the superfluid? And secondly, how does one measure such small mass currents through the weak link?

In order to weakly couple two volumes of superfluid it is necessary to separate them by a strong thin wall containing a small hole. In addition, the dimensions of the thin wall and the hole must be on the order of the healing length for the superfluid. The superfluid healing length is the length over which the order parameter or wave function can vary while still minimizing the free energy (similar to the coherence length for superconductors).

Can all Quantum probabilites pass a "open doorway" somehow? If one held to thinking about some level of these quantum probabilities as having a place in which to reside, then one might ask, what pattern would establish itself, in the entropic gathering from superfluid states?

Hilbert's address of 1900 to the International Congress of Mathematicians in Paris is perhaps the most influential speech ever given to mathematicians, given by a mathematician, or given about mathematics. In it, Hilbert outlined 23 major mathematical problems to be studied in the coming century. Some are broad, such as the axiomatization of physics (problem 6) and might never be considered completed. Others, such as problem 3, were much more specific and solved quickly. Some were resolved contrary to Hilbert's expectations, as the continuum hypothesis (problem 1).

So the question might also be asked about the algorithm that would allow all probabilities to have implemented their "pattern organization recognition" that would be unique to every fawcett of our human experience, and where might these probabilities exist?

I have always wondered how perception could have been changed, if our world was colored in some way, as to the emotive and intellectual challenges? Held to mass configurations, as a comparative view of what the body is thinking. Of what many people were thinking. But this might have been considered as crackpotism. :)

Wormholes?

So "open doorways" and ideas of "tunnelling" are always interesting in terms of how we might look at an area like GR in cosmology? Look for way in which such instances make themself known.

Are they applicable to the very nature of quantum perceptions that such probabilites could have emerged through them? Held to "time travel scenarios" and grabbbed the history of what had already preceded us in past tense, could have been brought again forward for inspection?

Some may blame Josephson for what had not occurred, yet, this quest for understanding is quite strong as to how such processes work, not only, in a computer manufactured processes, but in a human capacity as well. That change from technology to human desire for understanding about our natures would have sent some over the edge, but they are indeed caring individuals who would like to push back the boudaries of our understanding, not just in the physics sense. This again, held to crackpotism is unfortunate.

Maybe we can change our stripes to LQG and reap the rewards of another venue held to QG in the blogosphere, that would make you feel better? The issues are still troubling what ever you call the validation process.

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?

Wolfram's Ring Tone

What makes this a little bit, well more then a bit interesting is the evaluation you might try to assign reality of the unseen. IN Mendeelev's table, I like to think in a different way, and if one held the Riemann hypothesis up for grabs, what said that any elemental consideration would have been derived from some Probabilistic evaluated state, not to have formed into views with which all nature might have embued itself?

Lubos Motl:

If you're interested in the more precise isomorphisms between the cellular automata and the anthropic principle, there is a cute analogy invented by Nima that looks as follows: the negative cosmological constant is mapped to the automata that die out (big crunch) while the large positive cosmological constant is mapped to the trivial (solvable) automata - and the nontrivial automata that don't die out represent the anthropically allowed window for the cosmological constant. :-)

You need a background for this, about how such perceptions could have arisen from the very nature that all things, will continue to vibrate even in a empty space.The quantum harmonic oscillator would have something to say to this, and if held to the very nature of flat spacetime, where would this be stopped?

Wolfram's Theory of Everything


So such expansions to the entropically large valuation of all that is in materiality, had to come from some kind of "soup of thnking" that rests itself from all the myriad forms that could have been emitted? So our thnking is "colored" then from musical interludes analogistically based. But indeed, how did you get there and you have this strict regimentation to follow in the probabilitic valution that the Pascal triangle would have surmounted, when thinking of Wolfram's work.

Plato:

How do such things make there way into reality and these prime numbers as signatures of the atoms and ways in which they would relate themself to this elemental table for viewing, and something then shifts in my perception. I don't know why? :)

How can you not help but think in new ways, once your given perspective about the ways we have always done things. A Serpinski fractoriallization about the nature of the world in a myriad of ways, and the probabilistic valuation about events in the unseen. How could they ever be captured?