The Toposense of Spacetime

Topo-Greek, from topos, place.

Basic Examples

In the early 1960s Grothendieck chose the Greek word topos (which means “place”) to denote a mathematical object that would provide a general framework for his theory of étale cohomology and other variants related to his philosophy of descent. Even
if you do not know what a topos is, you have surely come across some of them. Here are two examples:

See: What is a Topos? by Luc Illusie

Of course I am looking and trying to describe "Topo" in a different way. I do not want to diminish the significance of the mathematical intents. Just the realization of what we are doing with our perceptions, as we send them to extraordinary depth of of creation.



In 1952, in his book Relativity, in discussing Minkowski's Space World interpretation of his theory of relativity, Einstein writes:

Since there exist in this four dimensional structure [space-time] no longer any sections which represent "now" objectively, the concepts of happening and becoming are indeed not completely suspended, but yet complicated. It appears therefore more natural to think of physical reality as a four dimensional existence, instead of, as hitherto, the evolution of a three dimensional existence. Albert Einstein

Of course it was necessary to understand the evolution of Euclidean geometries to the non-euclidean, and the history associated with this. The word "Toposense" is one that becomes endearing when you realize that if your were to take to the meaning of "slide of light to heart" you would see the implications of what gravity could mean in the presence of the photon and it's explanatory revolutionary ideas about how it can encourage "Gravities Rainbow" here within context of this blog.

"On the Effects of External Sensory Input on Time Dilation." A. Einstein, Institute for Advanced Study, Princeton, N.J.

Conclusion: The state of mind of the observer plays a crucial role in the perception of time.

Unfortunately the link to the article below( now shows as Intuitively Excellent) has been removed from Scientific America's data base or has changed, or, I may of copied it wrong in my search. Nevertheless, I do not have the link, but would like to conclude the remark above, in terms of those pointed out for further repercussions of that conclusiveness.

Einstein scholars disagree, but the pretty girl/hot stove experiment also may have led to another of his pithy remarks, namely: "If we knew what it was we were doing, it would not be called research, would it?" Then again, Einstein was a bit of a wag. Consider his explanation of wireless communication: "The wireless telegraph is not difficult to understand. The ordinary telegraph is like a very long cat. You pull the tail in New York, and it meows in Los Angeles. The wireless is the same, only without the cat." This quote reportedly kept Schrödinger awake well past his bedtime.

Summing over Histories?

So how does all this come together into a physical theory? It turns out that the proper procedure is to construct every possible diagram allowed by the theory (for a given state of input and output particles and how they're moving) and add up the corresponding complex numbers. The result is essentially the "wave function" for that specific input-output state combination, and by squaring that number you can determine the probability that the given input will result in the given output. Doing that is how theorists at particle accelerators earn their keep.

See: An Introduction to String Theory by Steuard Jensen

So you look at the basis of interactions that Feynman produced in his Toy models and having some insight to the elemental consideration of those same interactions, what comes out, if we were to see the world in such a way, that continuity of expression is "the Wave that was generated in the very beginning," could have been reduce to some refractive expression of all life. The Spectrum, Hydrogen, or other wise.

Do we then know the nature of the source, that we are all derivatives of some coherent plan that manifests toward the "cyclical nature of being?" Some Shakespearean version of, "to E or not to E?"

Every known particle has an antiparticle; if they encounter one another, they will annihilate with the production of two gamma-rays. The quantum energies of the gamma rays is equal to the sum of the mass energies of the two particles (including their kinetic energies). It is also possible for a photon to give up its quantum energy to the formation of a particle-antiparticle pair in its interaction with matter.

No longer Reducible and Working from the Horizon?



How far can our perceptions be pushed? Can consciousness still remain as part of this "ability of creation," that we are still "part and parcel" of it to consider it's full scope?

So no geometrical idealizations in sight, other then to consider the significance of a place that is far removed from our looking to the cosmos, and while thinking about it, how far it has been reduce to a fuller picture of it's reality?

See: Colour of Gravity

Determinism/Indeterminism

Determinism

Determinism (also called antiserendipity) is the philosophical proposition that every event, including human cognition and behavior, decision and action, is causally determined by an unbroken chain of prior occurrences.[1] With numerous historical debates, many varieties and philosophical positions on the subject of determinism exist from traditions throughout the world.

Determinism, quantum mechanics and classical physics

Some people have argued that in addition to the conditions humans can observe and the rules they can deduce there are hidden factors or hidden variables that determine absolutely in which order electrons reach the screen. They argue that the course of the universe is absolutely determined, but that humans are screened from knowledge of the determinative factors. So, they say, it only appears that things proceed in a merely probabilistically determinative way. Actually, they proceed in an absolutely determinative way. Although matters are still subject to some measure of dispute, quantum mechanics makes statistical predictions that would be violated if some local hidden variables existed. There have been a number of experiments to verify those predictions, and so far they do not appear to be violated although many physicists believe better experiments are needed to conclusively settle the question. (See Bell test experiments.) It is, however, possible to augment quantum mechanics with non-local hidden variables to achieve a deterministic theory that is in agreement with experiment. An example is the Bohm interpretation of quantum mechanics.

So quantum mechanics is deterministic, provided that one accepts the wave function itself as reality (rather than as probability of classical coordinates). Since we have no practical way of knowing the exact magnitudes, and especially the phases, in a full quantum mechanical description of the causes of an observable event, this turns out to be philosophically similar to the "hidden variable" doctrine.

Libertarianism (metaphysics)

Libertarianism is a philosophical position in metaphysics with respect to free will and determinism. It entails the belief that human beings possess free will, that free will is incompatible with determinism, and that determinism is false.

Although not held by the majority of contemporary philosophers, libertarianism is still widely discussed and avidly defended by several leading philosophers in the field, such as Peter van Inwagen, Robert Kane, Timothy O'Connor and Laura Ekstrom.

Natural libertarianism

Naturalistic libertarians believe that the universe contains an indeterminstic element, for instance as demonstrated by quantum mechanics, and that human beings exploit this to achieve freedom of choice. There is no separate, dualistic self in this theory: the self is the total activity of the brain as a system.

-----------------------------------------------------------

Indeterminism

At one time, it was assumed in the physical sciences that if the behavior observed in a system cannot be predicted, the problem is due to lack of fine-grained information, so that a sufficiently detailed investigation would eventually result in a deterministic theory ("If you knew exactly all the forces acting on the dice, you would be able to predict which number comes up"). However, the advent of quantum mechanics removed the underpinning from that approach, with the claim that (at least according to the Copenhagen interpretation) the most basic constituents of matter behave indeterministically, in accordance with such properties as the uncertainty principle. Quantum indeterminism was controversial on its introduction, with Einstein among the opposition, but gradually gained ground. Experiments confirmed the correctness of quantum mechanics, with a test of the Bell's theorem by Alain Aspect being particularly important because it showed that determinism and locality cannot both be true. Bohmian quantum mechanics remains the main attempt to preserve determinism (albeit at the expense of locality).

Bohm interpretation

The Bohm interpretation of quantum mechanics, sometimes called Bohmian mechanics, the ontological interpretation, or the causal interpretation, is an interpretation postulated by David Bohm in 1952 as an extension of Louis de Broglie's pilot-wave theory of 1927 . Consequently it is sometimes called the de Broglie-Bohm theory. Bohm's interpretation is an example of a hidden variables theory. It is hoped that the hidden variables would provide a local deterministic objective description that would resolve or eliminate many of the paradoxes of quantum mechanics, such as Schrödinger's cat, the measurement problem, the collapse of the wavefunction, and similar concerns. However, Bell's inequality complicates this hope, as it demonstrates that there is no local hidden variable theory that is compatible with quantum mechanics. Thus, one is left with choosing between the lesser of two evils: discarding locality, or discarding realism. The Bohmian interpretation opts for keeping realism and accepting nonlocality.

Nonlocality

Others see the consequences of EPR and Bell's theorem in a different way. They regard the correct conclusion to be related not so much to quantum theory itself, but only to deterministic interpretations of the same (i.e., to hidden-variable theories such as Bohm's interpretation). According to the people who think this way, what has been shown is that all deterministic theories must be nonlocal. For example, Niels Bohr was a member of this group. This group would claim that retaining orthodox quantum mechanics — with its nondeterministic character — permits one to retain locality, or at least to avoid the EPR type of nonlocality, at the expense of having no way to picture particles as objective elements of reality that occupy definite regions of space at all times. Armed with such a viewpoint, these physicists tend to be less receptive to Bohm's interpretation.

Seen as isomorphic to many worlds

Explicitly non-local. Bohm accepts that all the branches of the universal wavefunction exist. Like Everett, Bohm held that the wavefunction is real complex-valued field which never collapses. In addition Bohm postulated that there were particles that move under the influence of a non-local "quantum- potential" derived from the wavefunction (in addition to the classical potentials which are already incorporated into the structure of the wavefunction). The action of the quantum- potential is such that the particles are affected by only one of the branches of the wavefunction. (Bohm derives what is essentially a decoherence argument to show this, see section 7,#I [B]).

The implicit, unstated assumption made by Bohm is that only the single branch of wavefunction associated with particles can contain self-aware observers, whereas Everett makes no such assumption. Most of Bohm's adherents do not seem to understand (or even be aware of) Everett's criticism, section VI [1], that the hidden- variable particles are not observable since the wavefunction alone is sufficient to account for all observations and hence a model of reality. The hidden variable particles can be discarded, along with the guiding quantum-potential, yielding a theory isomorphic to many-worlds, without affecting any experimental results.
—Michael Clive Price

See Also: 

• The Free Will Function

Richard Feynman

"The adventure of our science of physics is a perpetual attempt to recognize that the different aspects of nature are really different aspects of the same thing" -- Richard Feynman

Source:Amazon.com Richard Feynman: Cover of The Feynman Lectures on Physics See also: The Feynman Lectures on Physics

Incompatible Arrows

Commerce is of trivial import; love, faith, truth of character, the aspiration of man, these are sacred.Ralph Waldo Emerson

I just happen to visit Cosmic Variance yesterday after not visiting for some time. The timing seemed appropriate to my questions about our histories, not only from a detailed research perspective, but from a personal one as well in terms of our memories. I do not care who is an atheist or not. Why should I apply a stereotype to another person and dictate the way the conversation can go?:)

Sean Carroll has a interesting set of four entires about the backwardness of the arrow of time and how it would appear. This is an interesting exercise for me on how perception about the current direction of the universe could have represented "the Egg before the chicken" scenarios.

Incompatible Arrows, I: Martin Amis
Incompatible Arrows, II: Kurt Vonnegut
Incompatible Arrows, III: Lewis Carroll
Incompatible Arrows, IV: F. Scott Fitzgerald

Chicken or Egg

Illustration from Tacuina sanitatis, Fourteenth century

Reverse chronology — narrating a story, or parts of one, backwards in time — is a venerable technique in literature, going back at least as far as Virgil’s Aeneid. Much more interesting is a story with incompatible arrows of time: some characters live “backwards” while others experience life normally.

There are reasons why I find this fascinating and why the topic of Kurt Godel was introduced in that comment section. It is something that caught my eye while researching Kurt Godel. I will try and find this point and put it here for consideration. While considering the version I saw of his authored biographical comment, it made me think of the views people "can have" about the nonsensical. The feelings they can have about the "incompleteness of this life" and the succession of our views on this life as a "metamathematical position." Where is that? Some "OverSoul" perhaps?:)

It reminded me about the perspective we can have "from the here and now."

Mind Body problem

Proud atheists

Steve Paulson:I know neither of you believes in paranormal experiences like telepathy or clairvoyant dreams or contact with the dead. But hypothetically, suppose even one of these experiences were proven beyond a doubt to be real. Would the materialist position on the mind-brain question collapse in a single stroke?

PINKER: Yeah.

GOLDSTEIN: Yeah, if there was no other explanation. We'd need to have such clear evidence. I have to tell you, I've had some uncanny experiences. Once, in fact, I had a very strange experience where I seemed to be getting information from a dead person. I racked my brain trying to figure out how this could be happening. I did come up with an explanation for how I could reason this away. But it was a very powerful experience. If it could truly be demonstrated that there was more to a human being than the physical body, this would have tremendous implications.

While I had read your link Phil on Goldstein, I am not an atheist(I try and refrain from groupings) in any form, and, like the topics of "Intelligent design" or the Anthropic principle, this has no bearing on how I want to move and think in the world. I am convinced, as Goldstein was, on what is consider "proof of the afterlife" that I do not need to be reminded of what is evidenced to the contrary, until it is proofed conclusively.

"Death, so called, is but older matter dressed
In some new form. And in a varied vest,
From tenement to tenement though tossed,
The soul is still the same, the figure only lost."Poem on Pythagoras, Dryden's Ovid.

I may share a trait of Plato eh?:)Emerson? Benjamin Franklin?

From A Defense of an Essay of Dramatic Poesy (1668) by John Dryden

Imagination in a man, or reasonable creature, is supposed to participate of reason, and when that governs, as it does in the belief of fiction, reason is not destroyed, but misled, or blinded: that can prescribe tot he reason, during the time of the representation, somewhat like a weak belief of what it sees and hears; and reason suffers itself to be so hoodwinked, that it may better enjoy the pleasures of the fiction: but it is never so wholly made a captive as to be drawn headlong into a persuasion of those things which are most remote from probability: 'tis in that case a free-born subject, not a slave; it will contribute willingly its assent, as far as it sees convenient, but will not be forced....Fancy and reason go hand in hand; the first cannot leave the last behind; and though fancy, when it sees the wide gulf, would venture over, as the nimbler; yet it is withheld by reason, which will refuse to take the leap, when the distance over it appears too large

See:

The Universal Library

Kurt Godel

He turned the lens of mathematics on itself and hit upon his famous "incompleteness theorem" — driving a stake through the heart of formalism By DOUGLAS HOFSTADTER

Source:ALFRED EISENSTAEDT/TIME LIFE PICTURES-Kurt Godel at the Institute of Advanced Study See: The Time 100-Scientists and Thinkers

Kurt Gödel (IPA: [kuɹtˈgøːdl]) (April 28, 1906 Brno (Brünn), Austria-Hungary (now Czech Republic) – January 14, 1978 Princeton, New Jersey) was an Austrian American mathematician and philosopher.

The Time 100-Scientists and Thinkers

The upshot of all this is that the cherished goal of formalization is revealed as chimerical. All formal systems — at least ones that are powerful enough to be of interest — turn out to be incomplete because they are able to express statements that say of themselves that they are unprovable. And that, in a nutshell, is what is meant when it is said that Gödel in 1931 demonstrated the "incompleteness of mathematics." It's not really math itself that is incomplete, but any formal system that attempts to capture all the truths of mathematics in its finite set of axioms and rules. To you that may not come as a shock, but to mathematicians in the 1930s, it upended their entire world view, and math has never been the same since.

Gödel's 1931 article did something else: it invented the theory of recursive functions, which today is the basis of a powerful theory of computing. Indeed, at the heart of Gödel's article lies what can be seen as an elaborate computer program for producing M.P. numbers, and this "program" is written in a formalism that strongly resembles the programming language Lisp, which wasn't invented until nearly 30 years later.

Princeton

In the late 1940s, Gödel demonstrated the existence of paradoxical solutions to Albert Einstein's field equations in general relativity. These "rotating universes" would allow time travel and caused Einstein to have doubts about his own theory. His solutions are known as the Gödel metric.

Closed timelike curves

Because of the homogeneity of the spacetime and the mutual twisting of our family of timelike geodesics, it is more or less inevitable that the Gödel spacetime should have closed timelike curves (CTC's). Indeed, there are CTCs through every event in the Gödel spacetime. This causal anomaly seems to have been secretly regarded as the whole point of the model by Gödel himself, who allegedly spent the last two decades of his life searching for a proof that death could be cheated, and apparently felt that this solution provided the desired proof. This strange conviction came to light decades after his death, when his personal papers were examined by a startled astronomer.[citation needed].

A more rational interpretation of Gödel's motives is that he was striving to (and arguably succeeded in) proving that Einstein's equations of spacetime are not consistent with what we intuitively understand time to be (i.e. that it passes and the past no longer exists), much as he, conversely, succeeded with his Incompleteness Theorems in showing that intuitive mathematical concepts could not be completely described by formal mathematical systems of proof. See the book A World Without Time (ISBN 0465092942).

General Relativity

CTCs have an unnerving habit of appearing in locally unobjectionable exact solutions to the Einstein field equation of general relativity, including some of the most important solutions. These include:

* the Kerr vacuum (which models a rotating uncharged black hole)
* the van Stockum dust (which models a cylindrically symmetric configuration of dust),
* the Gödel lambdadust (which models a dust with a carefully chosen cosmological constant term).
* J. Richard Gott has proposed a mechanism for creating CTCs using cosmic strings.

Some of these examples are, like the Tipler cylinder, rather artificial, but the exterior part of the Kerr solution is thought to be in some sense generic, so it is rather unnerving to learn that its interior contains CTCs. Most physicists feel that CTCs in such solutions are artifacts.

Timelike topological feature

No closed timelike curve (CTC) on a Lorentzian manifold can be continuously deformed as a CTC to a point, because Lorentzian manifolds are locally causally well-behaved. Every CTC must pass through some topological feature which prevents it from being deformed to a point. A test particle free falling along a closed timelike geodesic transits this feature; in the test particle's frame, the feature propagates toward the test particle. This features resembles a glider in Conway's Game of Life, but in a continuous spatial automaton rather than a (discrete) cellular automaton.

Continuous spatial automaton

It is an important open question whether pseudo-photons can be created in an Einstein vacuum space-time, in the same way that a glider gun in Conway's Game of Life fires off a series of gliders. If so, it is argued that pseudo-photons can be created and destroyed only in multiples of two, as a result of energy-momentum conservation.

Time is Like a River

How can a speck of a universe be physically identical to the great expanse we view in the heavens above? (Greene, The Elegant Universe, pages 248-249)

As Alice learned, it's not always clear what's a looking glass, and what's a window to another world. Mirrors and windows are often interchangeable: we look out into the world, and see ourselves reflected back. We look at a reflection, and believe it's showing us a world beyond. We internalize the mirror image and project the one inside. Objects, actions and ideas can become so confused with their reflections that it's impossible to untangle them. What's phantom and what's real? Is there even a relevant difference?

It is necessary that one see the very action of "reflection and memory" on our behalf as a continuance of the interplay between our environment and ourselves. Where "attention and awareness constantly brings us back to the waking reality around us."

I needed some geometrical(topological) way for this continuance of motion, while giving examples of what happens in our universe, as it it expressed itself in that moment of creation. That we may say that while so macroscopically large there exists within us in the nature of the microscopic, the very blueprints of this same creation.

Now, please spare me the nonsense of Intelligent design and the creation principle that all have argued time and time again. I do not take to those aspects of the debate, whilst I fumble amongst my own illusions, to make sense of what can happen in my own experience.

Yes, Skeptically this is of no value to you as you read this, as it is a measure against the back drops of science. But there is something that must be said about what we are all are capable of.

"The worst disease afflicting human kind is hardening of the categories." - Artist Bob Miller.

They had to be some overriding principle that has evaded our attention when it comes to what is possible and what is not. That I shall choose "time is like a river" does not discount that the river shall have it's eddies and pools for consideration that while in the flow of the process of this unfolding of our own "psychological natures" there is a history to each of us that is beyond the measure of this life?


The Super Hero Versions

Miracles StudiosThrone Plates

To activate Thorne plates, the distance between each plate must be less than the width of an atom. The resulting wormhole will be equally small, so getting in and out might be difficult. To widen the portal, some scientists suggest using a laser to inject immense amounts of negative energy. In addition, Thorne believes that radiation effects created by gravitons, or particles of gravity, might fry you as you enter the wormhole. According to string theory, however, this probably won't happen, so it's scant reason to cancel your trip.

Miracles StudiosGott Loop

To take you back one year, the string must weigh about half as much as the Milky Way galaxy. You'll need a mighty big spaceship to make that rectangle.

Many scientists believe the big bang that created the universe left behind cosmic strings - thin, infinitely long filaments of compressed matter. In 1991, Princeton physicist J. Richard Gott discovered that two of these structures, arranged in parallel and moving in opposite directions, would warp space-time to allow travel to the past. He later reworked the idea to involve a single cosmic-string loop. A Gott loop can take you back in time but not forward. The guide to building your own:

Miracles StudiosGott Shell

This is a relatively slow method of time travel, and life inside the shell could become tedious.

In essence, a Gott shell is a huge concentration of mass. The shell's sheer density creates a gravitational field that slows down the clock for anyone enclosed within it. Outside, time rolls along at its familiar pace, but inside, it creeps. Thus the Gott shell is useful for travel into the future only. If you're planning a jaunt to the past using a Gott loop, you might want to bring along a Gott shell for the return trip. What to do, step by step:

Miracles StudiosVan Stokum Cylinder

The cylinder must be infinitely long, which could add slightly to its cost.

Mass and energy act on space-time like a rock thrown into a pond: the bigger the rock, the bigger the ripples. Physicist W. J. van Stockum realized in 1937 that an immense cylinder spinning at near-light speed will stir space-time as though it were molasses, pulling it along as the cylinder turns. Although Van Stockum himself didn't recognize it, anyone orbiting such a cylinder in the direction of the spin will be caught in the current and, from the perspective of a distant observer, exceed the speed of light. The result: Time flows backward. Circle the cylinder in the other direction with just the right trajectory, and this machine can take you into the future as well. How it works:

Kerr Ring

The Kerr ring is a one-way ticket. The black hole's gravity is so great that, once you step through it, you won't be able to return.

When Karl Schwarzschild solved Einstein's equations in 1917, he found that stars can collapse into infinitesimally small points in space - what we now call black holes. Four decades later, physicist Roy Kerr discovered that some stars are saved from total collapse and become rotating rings. Kerr didn't regard these rings as time machines. However, because their intense gravity distorts space-time, and because they permit large objects to enter on one side and exit on the other in one piece, Kerr-type black holes can serve as portals to the past or the future. If finding one with the proper dimensions is too much trouble, you can always build one yourself:

See:A User's Guide to Time Travel-Superpower Issue

Just Plain Ole Us

I have always been fascinated by the Time Travel Scenarios.

There is a reason for me to go beyond what we know with regards to the avenues of science in terms of Time Travel. That one could have created a version of a superhero's ability to make this journey, and somehow, come out on the other side? Wonderful:)

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.

No I do not believe that we can measure what consciousness is able to do in terms of this time travel( unless some artifact could have found it's place amongst the value of carbon dating to have said, hey, "lets take this television and turn it on.") So that we may look into the objects very past. I have some ideas about this that I will try and lay out here that has become part of my belief system. People can make of it what they like.

The Complexity of Belief

Crucifixion (Corpus Hypercubus) (1954)-

Salvador Domingo Felipe Jacinto Dalí i Domènech, 1st Marquis of Púbol (May 11, 1904 – January 23, 1989), was a Spanish surrealist painter born in Figueres, Catalonia, Spain.

Some try and internalize the basis of reality as having some "point of expression" while they give empathetic meaning to the nature of geometrical forms. That one may of thought of the crystalline nature as an expression of "some other plan", is of interest to me( not that God created this, but that is part of the genetics of our discovery of self), whether we just talk about the "social aspect of our interactions" or some expression of an geometrical construct being the basis of the universe. I like this phrase of Stephen Hawkings as he enters the Wormhole. He writes,"In the future it is proved that the dynamical evolution of generic initial conditions can never produce a naked singularity."

Image Source: The Universe in a Nutshell, by Stephen Hawking, page 198

It is important to keep perspective on where the fire is. Some may understand this if I was to infer the cave for examination. yet having moved the idea here then to a 2D map of a 5D reality would be part of the plan as I write the Mind map and process of merging two historical points over top of one another.

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

It would be as if "one looked at the cube just the right way," what they saw of the cube could be turned into the hypercube, and from this, this inference of the multiplicity of probabilities. This again points to what I see of the Pyramid and what enters from "such a location as the pebble" could have housed all possibilities, and yet, any soul would have found itself following an "arrow of time," and if able too, and done in just that same way, bring into the line the ability of continuity to be induced as a flow.

See:

Alice and the Cosmic Ballet, Now Meet Higgins
Abraham Maslow and Peak Experience

Images of Super-Kamiokande events from tscan

The Navier-Stokes equations are also of great interest in a purely mathematical sense. Somewhat surprisingly, given their wide range of practical uses, mathematicians have yet to prove that in three dimensions solutions always exist (existence), or that if they do exist they do not contain any infinities, singularities or discontinuities (smoothness). These are called the Navier-Stokes existence and smoothness problems. The Clay Mathematics Institute has called this one of the seven most important open problems in mathematics, and offered a $1,000,000 prize for a solution or a counter-example.

SETH LLOYD — HOW FAST, HOW SMALL, AND HOW POWERFUL?: MOORE'S LAW AND THE ULTIMATE LAPTOP

His stunning conclusion?

"The amount of information that can be stored by the ultimate laptop, 10 to the 31st bits, is much higher than the 10 to the 10th bits stored on current laptops. This is because conventional laptops use many degrees of freedom to store a bit whereas the ultimate laptop uses just one. There are considerable advantages to using many degrees of freedom to store information, stability and controllability being perhaps the most important. Indeed, as the above calculation indicates, to take full advantage of the memory space available, the ultimate laptop must turn all its matter into energy. A typical state of the ultimate laptop's memory looks like a plasma at a billion degrees Kelvin — like a thermonuclear explosion or a little piece of the Big Bang! Clearly, packaging issues alone make it unlikely that this limit can be obtained, even setting aside the difficulties of stability and control."

Ask Lloyd why he is interested in building quantum computers and you will get a two part answer. The first, and obvious one, he says, is "because we can, and because it's a cool thing to do." The second concerns some interesting scientific implications. "First," he says, "there are implications in pure mathematics, which are really quite surprising, that is that you can use quantum mechanics to solve problems in pure math that are simply intractable on ordinary computers." The second scientific implication is a use for quantum computers was first suggested by Richard Feynman in 1982, that one quantum system could simulate another quantum system. Lloyd points out that "if you've ever tried to calculate Feynman diagrams and do quantum dynamics, simulating quantum systems is hard. It's hard for a good reason, which is that classical computers aren't good at simulating quantum systems."

Bold emphasis added by me.

The issue of computer language would have been to reveal the deeper implications of the cosmos, while we entertain the "phase changes the universe will go through." While we may think of the blackhole used as a weapon on April fools day, what use the Ipod in Mission Impossible III if it were to melt into a superfluid and bring forth all the ills of the past? It 's in the supefluid state that all of the information of the past makes it's way again into this universe, and supplies the dark energy for the current state of the Universe?

Plato said:

Hey I got one for you. You remember mission impossible. Well in this case, your only able to use the ipod once, then it turns into a super liquid.

While we consider newer technologies what use to "see the sun in a different way" now that we understand the range of "the window of the universe" now incorporates gamma ray detection, it forces upon us the end result of Tscan compiled data?

The Tip of the Pyramid and Quantum Gravity

Michio Kaku:

I like to compare it to wandering in the desert, and stumbling over a tiny pebble. When we push away the sand, we find that this "pebble" is actually the tip of a gargantuan pyramid. After years of excavation, we find wondrous hieroglyphics, strange tunnels and secret passageways. Every time we think we are at the bottom stage, we find a stage below it. Finally, we think we are at the very bottom, and can see the doorway.

One day, some bright, enterprising physicist, perhaps inspired by this article, will complete the theory, open the doorway, and use the power of pure thought to determine if string theory is a theory of everything, anything, or nothing.

Only time will tell if Einstein was correct when he said, "But the creative principle resides in mathematics. In a certain sense, therefore, I hold it true that pure thought can grasp reality, as the ancients dreamed."

Tscan

Tscan ("Trivial Scanner") is an event display, traditionally called a scanner, which I developed. It is a program that shows events graphically on the computer screen.

It was designed to be simple ("trivial") internally, and to have a simple user interface. A lot of importance was given to giving the user a large choice of options to display events in many different ways.

Tscan proved to be a very useful tool for the development of fitters. A particularly useful feature is the ability to show custom data for every photpmultiplier tube (PMT). Instead of the usual time and charge, it can show expected charge, scattered light, likelihood, chi-squared difference, patches, and any other data that can be prepared in a text format.

See:Trivial Scanner

Credit: Super-Kamiokande/Tomasz Barszczak Three (or more?) Cerenkov rings

Multiple rings of Cerenkov light brighten up this display of an event found in the Super-Kamiokande - neutrino detector in Japan. The pattern of rings - produced when electrically charged particles travel faster through the water in the detector than light does - is similar to the result if a proton had decayed into a positron and a neutral pion. The pion would decay immediately to two gamma-ray photons that would produce fuzzy rings, while the positron would shoot off in the opposite direction to produce a clearer ring. Such kinds of decay have been predicted by "grand unified theories" that link three of nature's fundamental forces - the strong, weak and electromagnetic forces. However, there is so far no evidence for such decays; this event, for example, did not stand up to closer scrutiny.

See:Picture of the Week

What is AMS?

General objectives:To collect precision cosmic ray data at high energies, including 10^10 protons; to discover or rule out certain particles as explanations for dark matter; to study cosmic ray propagation in the galaxy; to search for exotic particles or spectral features among cosmic rays

See:AMS experiment mission overview

The Alpha Magnetic Spectrometer Experiment

AMS is a particle detector for the International Space Station. A group of high-energy physicists are taking their experimental expertise - acquired in thirty years of experience at particle accelerators - into orbit. Space is full of high-energy particles of many types (collectively called "cosmic rays"), many of them originating in supernova explosions in distant galaxies. AMS detects them using a huge superconducting magnet and six highly specialized, ultra-precise detectors. It will sit on the ISS main truss - far above the obscuring atmosphere, and making full use of the ISS's irreplaceable support systems - and gather data for three years.

Long-Awaited Cosmic-Ray Detector May Be ShelvedBy DENNIS OVERBYE Published: April 3, 2007 The New York Times- Spacer and Cosmos

Beyond the experiment itself, the standoff represents a clash between two of the more strong-willed and brilliant leaders of Big Science in America: Dr. Ting of the Massachusetts Institute of Technology, who is known for his autocratic management style and obsession with detail, and Michael D. Griffin, the NASA administrator, who has shown himself willing to make tough calls in reshaping the space program away from the shuttle and toward the Moon and Mars.

Photographs by The AMS Collaboration

NASA agreed in 1995 to carry the Alpha Magnetic Spectrometer to the space station. But now the agency says its remaining shuttle flights are booked.

I have a thought to be considered here, that might spark some ideas about what happened to AMS. The question to my mind was whether this was more then political or money issue?

Think of Dennis Overbye's article of 2007, in face of the current article presented of his.

I thought along the way that this issue was resolved in regards to strangelets, and would had been "the issue" that solved allowed this to languish. But maybe there is more?

Numerical Relativity and the Human Experience?

"I’m a Platonist — a follower of Plato — who believes that one didn’t invent these sorts of things, that one discovers them. In a sense, all these mathematical facts are right there waiting to be discovered."Donald (H. S. M.) Coxeter

I contrast the nature of Numerical Relativity to the computer and the way we would think human consciousness could have been linked in it's various ways. Who hasn't thought that the ingenuity of the thinking mind could not have been considered the Synapse and the Portal to the thinking Mind?:)

Also think about what can be thought here as Gerardus t" Hooft asked as to think about in the limitations of what can be thought in relation to computerizations.

There is something to be said here about what conscious is not limited too. It is by it's very nature "leading perspective" that we would like to have all these variables included in or assertions of what we can see while providing experimental data to the mind set of those same computerization techniques?

Numerical Relativity Mind Map

So we of course like to see the mind's ingenuity( computerized or otherwise) when it comes to how it shall interpret what is the road to understanding that gravity is seen in Relativities explanation.

Source:Numerical Relativity Code and Machine Timeline


It is a process by which the world of blackholes come into viewing in it's most "technical means providing the amount of speed and memory" that would allow us to interpret events in the way we have.

The information has to be mapped to computational methodology in order for us to know what scientific value scan be enshrined in the descriptions of the Blackhole. Imagine that with current technologies we can never go any further then what we can currently for see given the circumstances of this technology?


Source:Expo/Information Center/Directory-Spacetime Wrinkles Map

So on the one hand there is an "realistic version" being mapped according to how we develop the means to visualize of what nature has bestowed upon us in the according to understanding Blackhole's and their Singularities.

Numerical Relativity and Math Transferance

Part of the advantage of looking at computer animations is knowing that the basis of this vision that is being created, is based on computerized methods and codes, devised, to help us see what Einstein's equations imply.

Now that's part of the effort isn't it, when we see the structure of math, may have also embued a Dirac, to see in ways that ony a good imagination may have that is tied to the abstractions of the math, and allows us to enter into "their portal" of the mind.

NASA scientists have reached a breakthrough in computer modeling that allows them to simulate what gravitational waves from merging black holes look like. The three-dimensional simulations, the largest astrophysical calculations ever performed on a NASA supercomputer, provide the foundation to explore the universe in an entirely new way.

Scientists are watching two supermassive black holes spiral towards each other near the center of a galaxy cluster named Abell 400. Shown in this X-ray/radio composite image are the multi-million degree radio jets emanating from the black holes. Click on image to view large resolution. Credit: X-ray: NASA/CXC/AIfA/D.Hudson & T.Reiprich et al.; Radio: NRAO/VLA/NRL

According to Einstein's math, when two massive black holes merge, all of space jiggles like a bowl of Jell-O as gravitational waves race out from the collision at light speed.

Previous simulations had been plagued by computer crashes. The necessary equations, based on Einstein's theory of general relativity, were far too complex. But scientists at NASA's Goddard Space Flight Center in Greenbelt, Md., have found a method to translate Einstein's math in a way that computers can understand.

Quantum Gravity

Now their is a strange set of circumstance here that would leave me to believe, that the area of quantum gravity has lead Numerical Relativity to it's conclusion? Has the technology made itself feasible enough to explore new experimental data that would allow us to further interpret nature in the way it shows itself? What about at the source of the singularity?

See: Dealing with a 5D World

I would not be fully honest if I did not give you part of the nature of abstract knowledge being imparted to us, if I did not include the "areas of abstractness" to include people who help us draw the dimensional significance to experience in these mathematical ways. It is always good to listen to what they have to say so that we can further developed the understanding of what becomes a deeper recognition of the way nature unfolds of itself.

There are two reasons that having mapped E8 is so important. The practical one is that E8 has major applications: mathematical analysis of the most recent versions of string theory and supergravity theories all keep revealing structure based on E8. E8 seems to be part of the structure of our universe.

The other reason is just that the complete mapping of E8 is the largest mathematical structure ever mapped out in full detail by human beings. It takes 60 gigabytes to store the map of E8. If you were to write it out on paper in 6-point print (that's really small print), you'd need a piece of paper bigger than the island of Manhattan. This thing is huge. Emphasis and underlined, my addition.

Computer Language and Math Joined from Artistic Impressionism?

Most people think of "seeing" and "observing" directly with their senses. But for physicists, these words refer to much more indirect measurements involving a train of theoretical logic by which we can interpret what is "seen."- Lisa Randall

THOMAS BANCHOFF has been a professor of mathematics at Brown University in Providence, Rhode Island, since 1967. He has written two books and fifty articles on geometric topics, frequently incorporating interactive computer graphics techniques in the study of phenomena in the fourth and higher dimensions

The marriage between computer and math language(Banchoff) I would say would be important from the prospective of displaying imaging, seen in the development of abstract language as used in numerical relativity? Accummalated data gained from LIGO operations. Time variable measures?

See:Computer Graphics In Mathematical Research

Cosmic censorship hypothesis

The New Bet

Whereas Stephen W. Hawking (having lost a previous bet on this subject by not demanding genericity) still firmly believes that naked singularities are an anathema and should be prohibited by the laws of classical physics,

And whereas John Preskill and Kip Thorne (having won the previous bet) still regard naked singularities as quantum gravitational objects that might exist, unclothed by horizons, for all the Universe to see,

Therefore Hawking offers, and Preskill/Thorne accept, a wager that

When any form of classical matter or field that is incapable of becoming singular in flat spacetime is coupled to general relativity via the classical Einstein equations, then

A dynamical evolution from generic initial conditions (i.e., from an open
set of initial data) can never produce a naked singularity
(a past-incomplete null geodesic from scri-plus).

The loser will reward the winner with clothing to cover the winner's nakedness. The clothing is to be embroidered with a suitable, truly concessionary message.

Stephen W. Hawking, John P. Preskill, Kip S. Thorne
Pasadena, California, 5 February 1997

In general relativity, the cosmic censorship hypothesis (CCH) is a conjecture about the nature of singularities in spacetime.

Singularities that arise in the solutions of Einstein's equations are typically hidden within event horizons, and therefore cannot be seen from the rest of spacetime. Singularities which are not so hidden are called naked. The weak cosmic censorship hypothesis conjectures that no naked singularities other than the Big Bang singularity exist in the universe. The hypothesis was conceived by Roger Penrose in 1969.