Strings and No_Sense?

Well for me, if theorists have mathematically created a vision of things, how is it possible not to have generalized their views on what they had learnt about the theories they talk about?

"Shut up and Calculate" would definitely appeal to a lot math minded there at the forefront of Cosmic Variance. But really, how are you going to distance yourself from such generalizations? It seeps out of your pores :)

So, no_sense could capture it? Now, Now, if this were the case then such analogies would not have been shared by the more briiliant. Non? Thank you, Michio Kaku.

As to "first principle," what are these building blocks called that make up the reality we so cherish. Robert Laughlin has something to say about this, and I am sure condense matter physicists would also say, it don't matter, if you use bricks or sergeant majors.

You arrive at some "point of view" where all agree that the Physicist's walking across the room, will have in tow, their students? Okay a bad comparison, but all branches form a wonderful view of the insurgency theorists attack, using a method to recognition of that "emergent property" will speak too, and so kindly of.

So we are to the point of the model? Bring it on, Clifford. Do you really want me to sumarize this point?

I can but it would take time and I would have to explain why high energy valutions had run into limitations. Now if it had been a experiemental setup that one could incorporate in space, and we do, don't get me wrong here. John Ellis helped to make this clear in our recognition of the Pierre Auger experiments and Steinberg's recognition of microstate blackholes that would quickly dissipate.

But in a tighter control recognition of particle reductionism, a " extra enormous energy valution" is inherently needed? NOn? They progressively/reductionistically move to this point, through the trial and errors, of their ways.

Ah heck! Clifford, I got ahead of myself here. So I'll think I'll stop, so you can fill us in from a more expert opinion.

Improve Classic Clock Tests

I think one had to understand what increasing complexity means in our universe? What relation to time would have been of value here while pointing to the quantum levels??

While there must be some pervasive view overlooking all of our ideals about gravity considerations and bulk perspective, the consistancy of the return too, and resulting complexities in expression, would be very hard to define, if such probabilistic manifestation of matter distinctions were to arise from some "specific rotational values?" We have a image of the developement of our cosmo, so what pray tell would enlist these rotational values to become some other universe and not this one? This "information" had to exist, as it's collapse and consequencal negativity expression manifested?



At the time such "anti-situations" are raised towards the very idea of findng a means to see such insight into a value issuing from this collapse. What would intiate such "jets" to emerge from a cosmological event or a quantum one??

This relationship between matter particles and force carriers is called supersymmetry.

If such a view was consistent within the framework of the "collapsing event" then how would supersymmetrical valuation ever be held to the creation of these "negative values"? It's beginning? So where would the information rest in the bulk. It's condensive features in graviton gatherings indicate such a value would have been triggerred in this collapse.




Of course we deal with historical perspectives first so we get a good sense here.

The two clocks depicted in the official logo for the CPT '04 meeting are related by the parity transformation (P). The inversion of black and white represents charge conservation (C), while time reversal (T) is represented by the movement of the hands of the clock in opposite directions.

Of course this starts out as a philosphical journey but it gets more detailed as time moves on, and we look for such issues in subject Sean writes above? From whence all things come and at whch point would a pendulum point of swing detail the very nature of such oscillating features? So if ones understand flat euclidean plane where no gravity exists, then what value would arise to a dynamcial view of the nature GR sets our minds too?

The same picture can be generalized to quantum field theory (QFT), the ground state becoming the vacuum state, and the role of the little man being played by ourselves. This means that there may exist symmetries of the laws of nature which are not manifest to us because the physical world in which we live is built on a vacuum state which is not invariant under them. In other words, the physical world of our experience can appear to us very asymmetric, but this does not necessarily mean that this asymmetry belongs to the fundamental laws of nature. SSB offers a key for understanding (and utilizing) this physical possiblity.

Hidden Symmetries

I think this is one of my greatest struggles to comprehend how such a beginning could have been discerned as a supersymmetrical state, and then have symmetry breaking actions form from from it.

So how do you reconcile the "vacuum state" with the idea of this "elasticity" spread throughout all space, and then have these kinds of actions conceptually form from it?



While we may look at events within this space, "as individual" as some orbital might be seen, it does not pass some my attention that such cosmological events look vaguely familiar?



While I am being quite vague in my discriptions, it is not without some comparisons that one would ask how this universe came into to being. That we would not wonder abut some overall consensus realization from birth to death, and a recyclical nature, as necessay in the forming of these universes?

While I may see these same similarities, I am not sayng this is the way of it, just that there are two perspectives here in relation to the cosmological pallete and the quantum one, that sees some relation? Is there any, I do not know, but I know that this issue needs some more clarification.

Dirac hypothesized that what we think of as the "vacuum" is actually the state in which all the negative-energy states are filled, and none of the positive-energy states. Therefore, if we want to introduce a single electron we would have to put it in a positive-energy state, as all the negative-energy states are occupied. Furthermore, even if the electron loses energy by emitting photons it would be forbidden from dropping below zero energy.

Thus it comes from my mind that a supersymmetrical state of existance, would have found the possibilites and probabilites as a place from which all could express itself. Would we not consider such abilties of vacuum states to have produced a beginning in the form of bubble states, and from the understanding of "Dirac's sea" what possibiltes exists that such virtual particle would show itself and then quickly dissappear? All of this had to come from some where.

So quickly again, the "condense matter physics" comes to mind on how the building blocks of matter, have found some "predesigned abstract schematics"{this is a math reference} speaking to how such symmetry breaking shall make itself known in the forming constituent particles. That as we look deeper, we wonder indeed about this professor crossing the room. The marble drop or dalton board is a wonderful way in which Pascals triangles serves to initiate this idea of a pre-condition for such math expression in the world of abstract math. So what math shall lead this way?

So it held in my mind that zero pont exemplified the condition in the universe that space is really never "empty." That it needed "some thing" in which to arise from.

What geoemtrical and all incluisve could take hold of this action and reveal the wonderful events in our cosmos? So I looked at blackholes in relation to what could dissipate quite quickly(mircrostate balckholes) to what what was happening on a comsological scale in regards to to those same blackholes.

Think Math

Nature's patterns

So who is right? Well, there is much that is attractive in the Platonist point of view. It's tempting to see our everyday world as a pale shadow of a more perfect, ordered, mathematically exact one. For one thing, mathematical patterns permeate all areas of science. Moreover, they have a universal feel to them, rather as though God thumbed His way through some kind of mathematical wallpaper catalogue when He was trying to work out how to decorate His Universe. Not only that: the deity's pattern catalogue is remarkably versatile, with the same patterns being used in many different guises. For example, the ripples on the surface of sand dunes are pretty much identical to the wave patterns in liquid crystals. Raindrops and planets are both spherical. Rainbows and ripples on a pond are circular. Honeycomb patterns are used by bees to store honey (and to pigeonhole grubs for safekeeping), and they can also be found in the geographical distribution of territorial fish, the frozen magma of the Giant's Causeway, and rock piles created by convection currents in shallow lakes. Spirals can be seen in water running out of a bath and in the Andromeda Galaxy. Frothy bubbles occur in a washing-up bowl and the arrangement of galaxies.

Well the following article came to my recognition by the "picture above". When reference was made to what some might think, as what underlying reality exists as a mathematical pattern, could ever been associated to some divine will? Who or what would decide this, as representing the very idea of resonant possibilties of expression in symmetry breaking?

But crystals exhibit clear mathematical patterns of their own, such as a regular geometric form, and while nobody can deduce this in full logical rigour from the quantum mechanics of their atoms, there is a chain of reasoning that makes it plausible that the laws of quantum mechanics do indeed lead to the regularities of crystal structure.

How would one define a crystal, as having preconcieved viabilties in the quantum world? This would be very hard and uncertain thing to deal with. What rational would allow such previews of a reality before it can become something else?



See. Some might of recognized that picture above to the issue of Science and Mind by Sir Roger Penrose?

Strings: The First Three Seconds

I didn't want to invoke God here, but in any "flash" is there not some pattern that mathematically needed to describe the way everything began? A word, or sound?

An equation means nothing to me unless it expresses a thought of God.Srinivasa Ramanujan

Before the Beginning
Interview with Sir Martin Rees, Part 2

Helen Matsos (HM):

Last year the big "science event" was measuring the cosmic microwave background and dating the big bang to 13.8 billion years ago, within an 8 to 10 percent margin of error. Can you give us some idea of the boundaries of the big bang -- what was it like in the first seconds, and how far will the universe expand in the future?

So indeed the universe become entrophically considered, as the evidence starts to make itself known in all it's forms, yet there is a space. Now by itself, such expression of the universe would have one event, but imagine down on earth our moments, can cause such repercussions ahead in time?

AM:

You played yourself--twice--in the movie, "Frequency". The movie is about a father communicating from 1969 with his son in the present on a ham radio, due to an unusual atmospheric aurora that bounces radio signals across time, not just space. You played Brian Greene being interviewed by Dick Cavett as both a younger and older man. Any reflections on either the interesting premise of the movie, or the adventures of being on the big screen?

So how we categorize such encounters with the child in our hopes of encouraging it's future, or our very presence and example lead. As a sign post, of what any society could become in the eye of good moral men and women? So one can move quietly no doubt and remain unseen, while the work can be a gentle reminder, of how we can affect "each" in time. Words like "etc" that could take on greater meaning, to have the hand slight a deletion. Remember how sensitive we can be to music? In Plato's academy I had made this point clear. I make clear what dissonance can do:)It can definitiely ruffle the field. Straight up and straight forward, a comment should do for those that would like to learn.

Brian Greene

Time is far more subtle than our everyday experience would lead us to believe. In many ways, time may simply be a psychological construct for organizing the world. It is a device we scientists have found useful, but it may in fact be a dim approximation of something far more complex."

WEll here is a better view on the relation to the The Powers of Ten

I talked briefly on the "chance encounter" of a child with a scientist, and the alluring role of powers of ten takes on. As if, it can "reverberate" in the probabilities of a future time.

Who is responsible for this creative surge?:)Creative endeavors, are always fueled by another?

IN such a cultural context, how is it that we could not see underlying reality is a musical inclination taken form in what any future could become. So, by the very value of the resonance contained, a feature of any moment?

Resonance: Brownian Motion

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

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

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

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



Brownian Motion Problem: Random Walk and
Beyond ,

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

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

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



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

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

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

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

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

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


Gaussian Coordinates

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

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

Plato:

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

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

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

Tall Tales and Sailing Ships

I am a photon, and my name is "Christopher Columbus." Like Plato, I have taken a great adventure into the "world of possibilties" that not only encompassed the scope of man's thinking in terms of horizons, but I enlist these same minds to venture into the inclinations of a "ship that follows a global perspective."



In the looking glast I poke fun at what some think is "fictional story" that although mathematically embued and hidden from view, has a basis in our scientific pursuates. That some indeed, would like to curtail to "fiction?"



To have seen such a path followed by Young's experimental "fashionable photon," I like to take "trips" and having recognized the personality with which I as photon assume. I can take this tremendous journey across the great seas, like Columbus did.

But there is more to this story as the "link on the sailing ship" indicates. It is about the pursuate of technologies where such advancements in early universe detection methods arise. They brought me into view, where before, I was some mathematican's play thing. A Toy model, that was representative of my current ability to shine light. Now many see me in this day and age as a "flashlight and torpedo" piercing the veil of "illusions."

That's what I do. I like physics of the moment, and of course theoretical places that I would like to think that I can go. I would like to be present at the beginning of the universe, but I don't think I know how this trigger was initiated or how I came into being. Ah, it would be so easy, if I was just a sailing ship and soliton wave carrier, that could intermingle, and place points of consideration as ports of possible places and home I would like to rest in?

How scare they were these Greek man. Who thought safe harbour was the hope that falling off the world of, would enlisted cubism to discrete things and safety. While greater men looked beyond, and sailed honestly and with integrity to the horizon. Where they were no longer afraid to realize, that gravity had some influence indeed.

Reimann whispers in my ear, "Little photon, you have to follow the course I set."

A Perspective on Powers of Ten?

What do chance encounters bring to the quality of life?


Tabula rasa >(Latin: "scraped tablet", though often translated "blank slate") is the notion that individual human beings are born "blank" (with no built-in mental content), and that their identity is defined entirely by events after birth.

Sometimes we see ingenuity display itself and having a whiteboard and blank slate in front of us, as we see where the expression of ideas can manifest. Low and behold, the flower can become the inherent expression of balance and love in the world, and how quickly such changes to the child can easily be thought of as powers of ten. Did the child know? What did the flower reveal of the child's soul? Quickly aside then, the "truth of science," must shine through?

As a parent, the idealization of ingenuity is always a strong lure for observation in those we hold with pride. A proud mother or father who see years of advancement beyond the normal facets of our everyday life now, in the simplicity of a child.

Many physical quantities span vast ranges of magnitude. Figures 0.1 and 0.2 use images to indicate the range of lengths and times that are of importance in physics.

News From the Front I
Clifford:

Below is a snapshot of a computation I was working on earlier this summer.(There's no wrong answer here. )

So when you see a cartoon like the one to follow, what does it make you think of? In one instance, Cliffords questions as to what topological form expressed, was immediately raised in my mind, but now on a more practical level, do we understand exactly what Clifford was doing? Do we understand what a child can bring from the innocence of perspective, and initiate the idea of powers of ten?

Plato:

While later life provides ample time to have a look at what mathematicains are doing, it is equally nice to understand these relations with the normal world? Is there “theoretically” such a thing?:)

I think so and such relevance in relation to the toy models of feynman diagrams, are these not readily available for introspection among such a blackboard as this?

These are not distractions from trying to understand physics, but are the tools needed to make that understanding possible. It is only through using mathematics that a secure understanding can be achieved. When you see an equation, welcome its concision and clarity and try to ‘read’ the equation just as you would the large number of words it replaces. Learn to get beneath the squiggles and the equals sign and to understand the quantitative assertion that is being made.

So we learn as parents, to supply the little sparks, that could inflate the world of wonder. Draw a child to the mystery of the color of a rainbow, as it shines through one's front door of cut glass.

How much greater the responsibility then of "powers of ten" that any one child could become the spark that ripples throughout the world. All waves, setting probabilities beyond the reverberations of this one chance encounter, could multiply?:)

So do we really think that a child's mind is empty, or that to be born would reveal the deeper implications of abilites that lie dormant for a future time. That only chance encounters would bring perspective later on, that such a design indeed, would have been this encounter, and all reverberations there after, seen in the responsibility of the moment.

So lets think about this, devoid of all implication of racism or sexism. That the truth is much deeper, and the longing for understanding of this empty space( blank slate), can hold so many potential things?

Neurological developments of a spark that can set many trails beyond the image segments of each others brain, that set the mind beyond the limits of probabilities.

Yet, it could be such a simple idea, that "space," is not really empty?:) That "space" is not really empty beyond the stars.

What are those Quantum Microstates

Now two points occupy my mind that hold questions as to what and how such counting can be done in terms of geometric propensity, that would allow these geometries into topological states. First point is:

Lubos Motl said:

We need to get closer to the "theory of everything", regardless of the question whether the destination is a finite or infinite distance away. (And yes, the path should not be infinitely long because there is no physics "below" the Planck length.)

And the second:

Black holes and branes in string theory

But it has been discovered through string duality relations that spacetime geometry is not a fundamental concept in string theory, and at small distance scales or when the forces are very strong, there is an alternate description of the same physical system that appears to be very different.

So what then would say that non linear approaches would now have taken form in our talks, that what was once geoemtrically feasible, had been taken down to the length where no new geometry is involved. So lets see then how shall we verbalize what happens at the horizon, in terms of radiation, that such states never existed to make this possible?

Now there are always reasons that one moves into the historical to gain perspective. By doing this, you gain insight and advance thinking to reveal theoretical developement, and where it has taken us. So by using thse linked paragraph statements, we are revealling something about Blackholes that had been culminative, to have discussions in todays world. Like BPS blackhole dynamics.

Andrew Strominger is an American theoretical physicist who works on string theory. He is currently a professor at Harvard University and a senior fellow at the Society of Fellows. His contributions to physics include:

Now one thing that troubles me about Lubo's statement, is the idea that supersymmetry valuation could ever be entertained, had we not consideedr this avenue of some importance. Not just in terms of symmetry breaking, but of the illustrous states of existance, that would exemply this idea where the superfluid could rest itself, and provide for the base of operation for these new universes?

To the second point, by providing for the idea of a geometry to emerge from this vast ocean of vast probabilites. Again for me, to see this I recognized that "space is not empty", and that such a congregation of gravitonic perception would have to be culminative, in some form for such a superfluid to exist?

So one had to get there geometrically from this ten dimensional perspective to have some basis to fuel developement into other stages of existance. Some geometric form, that would reduce, such valuations to supersymmetrical thinking and allow such a developemental process to cyclical natures. of that same universe.

Strominger: That was the problem we had to solve. In order to count microstates, you need a microscopic theory. Boltzmann had one–the theory of molecules. We needed a microscopic theory for black holes that had to have three characteristics: One, it had to include quantum mechanics. Two, it obviously had to include gravity, because black holes are the quintessential gravitational objects. And three, it had to be a theory in which we would be able to do the hard computations of strong interactions. I say strong interactions because the forces inside a black hole are large, and whenever you have a system in which forces are large it becomes hard to do a calculation.

The old version of string theory, pre-1995, had these first two features. It includes quantum mechanics and gravity, but the kinds of things we could calculate were pretty limited. All of a sudden in 1995, we learned how to calculate things when the interactions are strong. Suddenly we understood a lot about the theory. And so figuring out how to compute the entropy of black holes became a really obvious challenge. I, for one, felt it was incumbent upon the theory to give us a solution to the problem of computing the entropy, or it wasn't the right theory. Of course we were all gratified that it did.

So indeed then three conditions had been satisfied, that issues about the physics involved had something to say about quantum mechanics, gravity and computation of entrophy of blackholes respectively.

The animation shows schematically the behavior of the gas molecules in the presence of a gravitational field. We can see in this figure that the concentration of molecules at the bottom of the vessel is higher than the one at the top of the vessel, and that the molecules being pushed upwards fall again under the action of the gravitational field.

What is black hole entropy?

Suppose we have a box filled with gas of some type of molecule called M. The temperature of that gas in that box tells us the average kinetic energy of those vibrating molecules of gas. Each molecule as a quantum particle has quantized energy states, and if we understand the quantum theory of those molecules, theorists can count up the available quantum microstates of those molecules and get some number. The entropy is the logarithm of that number.
When it was discovered that black holes can decay by quantum processes, it was also discovered that black holes seem to have the thermodynamic properties of temperature and entropy. The temperature of the black hole is inversely proportional to its mass, so the black hole gets hotter and hotter as it decays.

Microstate Blackhole Production

Peter Steinberg

Unfortunately, all of this is overstated. At RHIC we don't make a "real" black hole, in the sense envisioned by Einstein's General Theory of Relativity. Rather, Nastase's point of view is that RHIC collisions can be described by a "dual" black hole. But what does "dual" mean in this context? It's not "two-ness" in any sense, but rather indicates that one can write down a theory which describes the collision as a black hole, but in a completely different world than that we see around us. To make his model work, he (and many other researchers who are exploring this direction) make a calculation of a black hole in 10 dimensions in order to describe difficult (but gravitationally benign) aspects of the strong interaction in 4 dimensions.

Lagrange points

As always, the pictures serve as links, as well as highlighted paragraphs in blue, and having once visited, purple. Pictures and paragraphs that are highlighted in gold are in conjunction and are direct links to sites, as well as fawcetts, within this blog. The neurolgical funcxtion of imagery was designed this way and I would encurgae wikipedia to use this idea in the images that they use. I suspect server updates reduce links back to them, which is retarded since all apragraph staements can be assigned to them quite easily.

This is the advancement in imagery use that mental powers had to keep pace with in computer developement. We know streaming video is quite useful, so why not the neurological fucntioning of "the image" that your minds can produce, that connect as these highlighted paragraphs can do?



These ideas make sense when you understand the effects of gravitational variances, and can see, what the effect of a fifth dimensional perspective can do. I think the writer understood what I was saying in article that follows?

Figure 2 shows a map of the gravity field of the Sun-Earth restricted three body problem. The contours show that the steepest gradients surround the Earth and Sun, with the five Earth Lagrange Points located in equilibrium regions with relatively gentle gradient. L1-L3 are unstable saddle points, and spacecraft positioned here will always drift away from the equilibrium. L4 and L5 are stable equilibria, and objects can orbit here indefinitely. The blue arrows show that L4 and L5 are actually atop a potential hill - it is the additional effect of the "Coriolis force" that makes them stable.
-----------------------------------------------

This newly found Interplanetary Superhighway is a perfect example of the overlap between classic analysis and modern numerical techniques. The genius minds of Euler and Lagrange used the new technique of calculus to solve the restricted three body problem and show the existence of these intriguing equilibrium points in space. Now, 200 years later, we are employing our own ground-breaking methods using dynamical systems theory and supercomputers, and taking our first steps along the invisible tunnels stretching through the solar system

If one didn't understand this application from a fifth dimensional perspective how would "this viewer" made any sense?



Such develoepments and perspective allow other views to develope in relation to how we see this planet, beyond the bubble enclosures one might have developed and culminates in this Thalean view.:)

This all leads to the developement of the Thalean view It is mathematically orientated although I have much to learn, I made use of a developing perspective that few would have realized, had they not put these things together. That's what I try to do, anyway.