Perspective of the Theoretical Scientist

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

There are certain advantages to the theoretical perspective that can best portray the concepts of the world they live in with what appears, however abstract, with the minds value of image solicitor impressionism which helps the minds state of acceptance. So it had to be explained first.

Cubist art revolted against the restrictions that perspective imposed. Picasso's art shows a clear rejection of the perspective, with women's faces viewed simultaneously from several angles. Picasso's paintings show multiple perspectives, as though they were painted by someone from the 4th dimension, able to see all perspectives simultaneously.

Cubist Art: Picasso's painting 'Portrait of Dora Maar'

P. Picasso Portrait of Ambrose Vollard (1910)

 M. Duchamp Nude Descending a Staircase, No. 2 (1912)

J. Metzinger Le Gouter/Teatime (1911)

The appearance of figures in cubist art --- which are often viewed from several direction simultaneously --- has been linked to ideas concerning extra dimensions:

As if, looking at it from a larger perspective. If you stand outside of the image and see that it is capable of illuminating many angles of perspective. This helped us to see that it is derived from a much larger understanding then what is solidified to the everyday we live in.

For the artist it was a bold move to understanding that perspective could help us see Mona Lisa's smile as moving with us as we move around. So that was the challenge then was to appreciate the value of this artistic push into how we see as to understanding the road non- euclidean took was meet by people as well to culminate in a geometrical transitional form


Hyperspace: A Scientific Odyssey

A look at the higher dimensionsBy Michio Kaku

"Why must art be clinically “realistic?” This Cubist “revolt against perspective” seized the fourth dimension because it touched the third dimension from all possible perspectives. Simply put, Cubist art embraced the fourth dimension. Picasso's paintings are a splendid example, showing a clear rejection of three dimensional perspective, with women's faces viewed simultaneously from several angles. Instead of a single point-of-view, Picasso's paintings show multiple perspectives, as if they were painted by a being from the fourth dimension, able to see all perspectives simultaneously. As art historian Linda Henderson has written, “the fourth dimension and non-Euclidean geometry emerge as among the most important themes unifying much of modern art and theory."

Posted by Plato at Thursday, March 24, 2005 

Then, it quickly comes home to mind that maybe what is given,  lets say in context of Lee Smolin's road to Quantum Gravity of the thing will help us quickly see the value of describing "the space of an interior" with what is happening on the screen/label.

Spacetime in String Theory

More then just a Bekenstein imagery to illustrate a conformal approach to describing what are the contends of the tomato soup can from it's label.



Campbell's Soup Can by Andy Warhol Exhibited in New York (USA), Leo Castelli Gallery

It was necessary to see that the geometric used here were helping to shape perspective around not only "time travel" but a means to an end to use mathematical perspective to actually mean something in relation to understanding our world. A way to describe abstract concepts that were correlated with the progression of those mathematics. Klein's ordering of geometries then take on a new meaning as we move deep into the world we all know and love.

In 1919, Kaluza sent Albert Einstein a preprint --- later published in 1921 --- that considered the extension of general relativity to five dimensions. He assumed that the 5-dimensional field equations were simply the higher-dimensional version of the vacuum Einstein equation, and that all the metric components were independent of the fifth coordinate. The later assumption came to be known as the cylinder condition. This resulted in something remarkable: the fifteen higher-dimension field equations naturally broke into a set of ten formulae governing a tensor field representing gravity, four describing a vector field representing electromagnetism, and one wave equation for a scalar field. Furthermore, if the scalar field was constant, the vector field equations were just Maxwell's equations in vacuo, and the tensor field equations were the 4-dimensional Einstein field equations sourced by an EM field. In one fell swoop, Kaluza had written down a single covariant field theory in five dimensions that yielded the four dimensional theories of general relativity and electromagnetism. Naturally, Einstein was very interested in this preprint .

I quickly divert the attention to the world of Thomas Banchoff because it is an extraordinary move from all that we know is safe. It is not lost to some computer animator world that one engages loses the self in the process? It is also to show that what Lee Smolin tried to distance himself from, was in fact seeking to find itself understood in this way. Concurrent agreement that theoretics was trying to arrive at a consensus of different approaches saying the same thing?

Monte Carlo methods are a class of computational algorithms that rely on repeated random sampling to compute their results. Monte Carlo methods are often used in simulating physical and mathematical systems. Because of their reliance on repeated computation of random or pseudo-random numbers, these methods are most suited to calculation by a computer and tend to be used when it is unfeasible or impossible to compute an exact result with a deterministic algorithm.^[1]

Monte Carlo simulation methods are especially useful in studying systems with a large number of coupled degrees of freedom, such as fluids, disordered materials, strongly coupled solids, and cellular structures (see cellular Potts model). More broadly, Monte Carlo methods are useful for modeling phenomena with significant uncertainty in inputs, such as the calculation of riskdefinite integrals, particularly multidimensional integrals with complicated boundary conditions. It is a widely successful method in risk analysis when compared with alternative methods or human intuition. When Monte Carlo simulations have been applied in space exploration and oil exploration, actual observations of failures, cost overruns and schedule overruns are routinely better predicted by the simulations than by human intuition or alternative "soft" methods.^[2]

For me it had to make some sense such transference from that artistic impressionism help to direct the mind to the ways and means of understanding quantum gravity was being inspected in terms of Monte Carlo methods to understanding. These had a surface value in my mind to an accumulate acceptance of the geometry and methods used to model this understanding.




So you understand now how we arrived at an interpretation of the value of lets say Dyson's opinion about how we might view Riemann's Hypothesis?

Dyson, one of the most highly-regarded scientists of his time, poignantly informed the young man that his findings into the distribution of prime numbers corresponded with the spacing and distribution of energy levels of a higher-ordered quantum state. Mathematics Problem That Remains Elusive —And Beautiful By Raymond Petersen

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DNA Computing

DNA computing is a form of computing which uses DNA, biochemistry and molecular biology, instead of the traditional silicon-based computer technologies. DNA computing, or, more generally, molecular computing, is a fast developing interdisciplinary area. Research and development in this area concerns theory, experiments and applications of DNA computing See:DNA computing

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Clifford of Asymptotia is hosting a guest post by Len Adleman: Quantum Mechanics and Mathematical Logic.

Today I’m pleased to announce that we have a guest post from a very distinguished colleague of mine, Len Adleman. Len is best known as the “A” in RSA and the inventor of DNA-computing. He is a Turing Award laureate. However, he considers himself “a rank amateur” (his words!) as a physicist.

Len Adleman-For a long time, physicists have struggled with perplexing “meta-questions” (my phrase): Does God play dice with the universe? Does a theory of everything exist? Do parallel universes exist? As the physics community is acutely aware, these are extremely difficult questions and one may despair of ever finding meaningful answers. The mathematical community has had its own meta-questions that are no less daunting: What is “truth”? Do infinitesimals exist? Is there a single set of axioms from which all of mathematics can be derived? In what many consider to be on the short list of great intellectual achievements, Frege, Russell, Tarski, Turing, Godel, and other logicians were able to clear away the fog and sort these questions out. The framework they created, mathematical logic, has put a foundation under mathematics, provided great insights and profound results. After many years of consideration, I have come to believe that mathematical logic, suitably extended and modified (perhaps to include complexity theoretic ideas), has the potential to provide the same benefits to physics. In the following remarks, I will explore this possibility.

Different Approaches to a 5d world

Smolin: And there are published predictions for observable Planck scale deviations from energy momentum relations[22, 23] that imply predictions for experiments in progress such as AUGER and GLAST. [B]For those whose interest is more towards formal speculations concerning supersymmetry and higher dimensions than experiment, there are also results that show how the methods of loop quantum gravity may be extended to give background independent descriptions of quantum gravity in the higher and super realms[31]-[35][/B]. It thus seems like a good time for an introduction to the whole approach that may help to make the basic ideas, results and methods accessible to a wider range of physicists.

Dealing With a 5d World

I was trying to understand that once you get to see how the equation leads you too a understanding of that 5d world it allowed you to entertain all possibility based on this position.

Extra dimensions sound like science fiction, but they could be part of the real world. And if so, they might help explain mysteries like why the universe is expanding faster than expected, and why gravity is weaker than the other forces of nature.
Three dimensions are all we see -- how could there be any more? Einstein's general theory of relativity tells us that space can expand, contract, and bend. If one direction were to contract down to an extremely tiny size, much smaller than an atom, it would be hidden from our view. If we could see on small enough scales, that hidden dimension might become visible.

Here are some thoughts to consider?:)


Klein's Ordering of Geometries

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

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

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

Nature's Greastest Puzzle

This is a torus (like a doughnut) on which several circles are located. Unlike on a Euclidean plane, on this surface it is impossible to determine which circle is inside of which, since if you go from the black circle to the blue, to the red, and to the grey, you can continuously come back to the initial black, and likewise if you go from the black to the grey, to the red, and to the blue, you can also come back to the black.

Reichenbach then invites us to consider a 3-dimensional case (spheres instead of circles).

Figure 8 [replaced by our Figure 2] is to be conceived three-dimensionally, the circles being cross-sections of spherical shells in the plane of the drawing. A man is climbing about on the huge spherical surface 1; by measurements with rigid rods he recognizes it as a spherical shell, i.e. he finds the geometry of the surface of a sphere. Since the third dimension is at his disposal, he goes to spherical shell 2. Does the second shell lie inside the first one, or does it enclose the first shell? He can answer this question by measuring 2. Assume that he finds 2 to be the smaller surface; he will say that 2 is situated inside of 1. He goes now to 3 and finds that 3 is as large as 1.

How is this possible? Should 3 not be smaller than 2? ...

He goes on to the next shell and finds that 4 is larger than 3, and thus larger than 1. ... 5 he finds to be as large as 3 and 1.

But here he makes a strange observation. He finds that in 5 everything is familiar to him; he even recognizes his own room which was built into shell 1 at a certain point. This correspondence manifests itself in every detail; ... He is quite dumbfounded since he is certain that he is separated from surface 1 by the intervening shells. He must assume that two identical worlds exist, and that every event on surface 1 happens in an identical manner on surface 5. (Reichenbach 1958, 63-64)

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

Today, however, we do have the opportunity not only to observe phenomena in four and higher dimensions, but we can also interact with them. The medium for such interaction is computer graphics. Computer graphic devices produce images on two-dimensional screens. Each point on the screen has two real numbers as coordinates, and the computer stores the locations of points and lists of pairs of points which are to be connected by line segments or more complicated curves. In this way a diagram of great complexity can be developed on the screen and saved for later viewing or further manipulation

Current research said something abut how the brain/mind can assume the reality in terms of randomness or end up realizing some chaotic function?  Well,  if such chaos is measured in the heat of thinking I am surprised we do not end up in some brain/mind heat death?:)

Poincaré Hyperbolic Disk

See also:Poincaré Hyperbolic Disk

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Hyperbolic Geometry


Geometric models of hyperbolic geometry include the Klein-Beltrami model, which consists of an open disk in the Euclidean plane whose open chords correspond to hyperbolic lines. A two-dimensional model is the Poincaré hyperbolic disk.

Weisstein, Eric W. "Hyperbolic Geometry." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/HyperbolicGeometry.html

 

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A computer-generated image showing the pattern of a p-mode solar acoustic oscillation both in the interior and on the surface of the sun. (l=20, m=16 and n=14.) Note that the increase in the speed of sound as waves approach the center of the sun causes a corresponding increase in the acoustic wavelength.

Helioseismology is the study of the propagation of wave oscillations, particularly acoustic pressure waves, in the Sun.

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SOHO Reads the Solar Flares

Measurements of the Sun's oscillations provide a window into the invisible interior of the Sun allowing scientists to infer the structure and composition as well as the rotation and dynamics of the solar interior.

(Extreme ultraviolet Imaging Telescope) images the solar atmosphere at several wavelengths, and therefore, shows solar material at different temperatures. In the images taken at 304 Angstroms the bright material is at 60,000 to 80,000 degrees Kelvin. In those taken at 171, at 1 million degrees. 195 Angstrom images correspond to about 1.5 million Kelvin. 284 Angstrom, to 2 million degrees. The hotter the temperature, the higher you look in the solar atmosphere.


p-Modes

The mysterious source of these oscillations was identified by way of theoretical arguments in 1970 and confirmed by observations in 1975. The oscillations we see on the surface are due to sound waves generated and trapped inside the sun. Sound waves are produced by pressure fluctuations in the turbulent convective motions of the sun's interior. As the waves move outward they reflect off of the sun's surface (the photosphere) where the density and pressure decrease rapidly..

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It's Effect on Earth

The plots on this page show the current extent and position of the auroral oval at each pole, extrapolated from measurements taken during the most recent polar pass of the NOAA POES satellite. "Center time" is the calculated time halfway through the satellite's pass over the pole.

Today's Space Weather

Any threat to communications is always seriously assessed. What we want to see on the other side of the Sun is whether any outburst is coming, that could seriously affect those same communications.

See Also:Backreaction: Reflections on the Sun

So what about the Missing Energy?

"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.

It is unfortunate to have endured the constant flutter of disbelief(cry of pseudoscience) as to what is possible in a given space, that we can say that we do not really have all the facts to it's understanding, yet, to know that in this region, new physics will be produced.

It is also unfortunate to have observed a whole generation of string theorists who have undergone this constant rebuttal and berating over and over again while standing strong to the "educative values" undermined by those who saw no benefit too. You maintained the perseverance of a "thought domain that cover regions within the valleys" to be speaking about a time just after the big bang. How would the normal population of scientists know this?

Thanks to the high collision energy and luminosity of the LHC, the ATLAS detector will be capable of revealing the existence of extra spatial dimensions in some substantial region of parameter space. The talk will summarize recent studies from the collaboration on different possible signals predicted by models where the dimensions are "large", where they are of size ~TeV^-1 or where they are "warped". These signals include direct emission of Kaluza-Klein states of gravitons, virtual effects of graviton exchange and gauge boson excitations. We shall also discuss the possibilities of observing black holes. mini review for search of eXTRA Dimentions

Now this question is an important one to me, because it is based on the amount of energy used in the collision process, and what is to come out of that collision process as tracks, adds up to so much energy. If these two numbers do not equal in parity then where has that extra energy gone?

This has always been a fundamental question to me of where I thought "new physics was to be found" and to have Tammaso Dorigo confirm this is quite a statement indeed of what is leading perspective in terms of what is to be measured and what is going to be measured in the proposed LHC experiments.

Missing Energy Kicks New Physics Models Off The Board

The signature of large missing energy and jets is arguably one of the most important avenues for the study of potential new physics signatures at today's hadron colliders.

The above concept marks an interesting turn of events: the years of the glorification of charged leptons as the single most important tools for the discovery of rare production processes appears behind us. The W and Z discovery in 1983 by UA1 at CERN, or the top quark discovery by CDF and DZERO in 1995 at Fermilab, would have been impossible without the precise and clean detection of electrons and muons. However, with time we have understood that missing energy may be a more powerful tool for new discoveries.

Missing energy arises when a violent collision between the projectiles -protons against antiprotons at the Tevatron collider, or protons against protons at the world's most powerful accelerator, the LHC- produces an asymmetric flow of energetic bodies out of the collision point in the plane orthogonal to the beams: a transverse imbalance. This is a clear signal that something is leaving the detector unseen. And it turns out that there is a host of new physics signals which can do precisely that.

A large amount of missing transverse energy may be the result of the decay of a leptoquarks into jets and neutrinos, when the latter leave undetected; or from the silent escape of a supersymmetric neutral particle -the neutralino- produced in the chain of decays following the production of squarks and gluinos; or it may even be due to the escape of particles in a fourth dimension of space -an alternative dubbed "large extra dimensions". see more in linked title above)

Now this is the thing that has troubled me most about scientists who are working and in the know, had not realized the necessity of pushing perspective back to a time to the first moments of the big bang(not just Steven Weinberg's first three minutes but of the microseconds just after the big bang) in order to understand what we are working on in terms of unification, and of where the products of this missing energy will spring forth from, as we move forward in the experiments to come.

The understanding then has always been in what is in that missing energy, to determine what new physics shall be, that such understanding was already there for the string theorist in their considerations. The contact point has already been defined for them, and reached two extremes. There is a reason why the missing energy escapes.

You had to know already where and what this "contact point meant" and what was to come out of it to know that dynamical qualities could exist in the big bang and where this big bang resides in the cosmos. That such energies can be reached there now. This required us to know that local events in the cosmos could contribute to the very nature of the cosmos and the state of the cosmos in the now. Like some cosmological constant "hidden and growing" in Omega.

To know that the dissipative results from micro collisions decaying fast too, did not mean we would be running short of the elements of this new physics either. It left it's remnants all around us to know that what can come out of such a collision point is not the story of the FLashForward scenario, but of things that travel through the earth to meet Gran Sasso and the likes. It was a whole plethora of particle disseminations that left missing energy around for us to explore in potential as some fictional substrate of the reality of nature that had not been seen before.

Three-body problem and WMAP

"We all are of the citizens of the Sky" Camille Flammarion

In 1858, by the set of its relations, it will allow Camille Flammarion, the 16 years age, to enter as raises astronomer at the Observatory of Paris under the orders of Urbain the Glassmaker, at the office of calculations.

See:The Gravity Landscape and Lagrange Points



Now there is a reason that I am showing "this connection" so that the jokes that go around at the PI institute in regards to Tegmark( not that I am speaking for him and have absolutely no affiliation of any kind) and the "mathematical constructs are recognized" beyond just the jeering section, that while not being a party too, will and can be shown some light.

Three-body problem

For n ≥ 3 very little is known about the n-body problem. The case n = 3 was most studied, for many results can be generalised to larger n. The first attempts to understand the 3-body problem were quantitative, aiming at finding explicit solutions.

* In 1767 Euler found the collinear periodic orbits, in which three bodies of any masses move such that they oscillate along a rotation line.
* In 1772 Lagrange discovered some periodic solutions which lie at the vertices of a rotating equilateral triangle that shrinks and expands periodically. Those solutions led to the study of central configurations , for which \ddot q=kq for some constant k>0 .

The three-body problem is much more complicated; its solution can be chaotic. A major study of the Earth-Moon-Sun system was undertaken by Charles-Eugène Delaunay, who published two volumes on the topic, each of 900 pages in length, in 1860 and 1867. Among many other accomplishments, the work already hints at chaos, and clearly demonstrates the problem of so-called "small denominators" in perturbation theory.
The chaotic movement of 3 interacting particles
The chaotic movement of 3 interacting particles

The restricted three-body problem assumes that the mass of one of the bodies is negligible; the circular restricted three-body problem is the special case in which two of the bodies are in circular orbits (approximated by the Sun-Earth-Moon system and many others). For a discussion of the case where the negligible body is a satellite of the body of lesser mass, see Hill sphere; for binary systems, see Roche lobe; for another stable system, see Lagrangian point.

The restricted problem (both circular and elliptical) was worked on extensively by many famous mathematicians and physicists, notably Lagrange in the 18th century and Poincaré at the end of the 19th century. Poincaré's work on the restricted three-body problem was the foundation of deterministic chaos theory. In the circular problem, there exist five equilibrium points. Three are collinear with the masses (in the rotating frame) and are unstable. The remaining two are located on the third vertex of both equilateral triangles of which the two bodies are the first and second vertices. This may be easier to visualize if one considers the more massive body (e.g., Sun) to be "stationary" in space, and the less massive body (e.g., Jupiter) to orbit around it, with the equilibrium points maintaining the 60 degree-spacing ahead of and behind the less massive body in its orbit (although in reality neither of the bodies is truly stationary; they both orbit the center of mass of the whole system). For sufficiently small mass ratio of the primaries, these triangular equilibrium points are stable, such that (nearly) massless particles will orbit about these points as they orbit around the larger primary (Sun). The five equilibrium points of the circular problem are known as the Lagrange points.

So the thing is, that while one may not of found an anomalousness version of what is written into the pattern of WMAP( some Alien signal perhaps in a dimension of space that results in star manipulation), and what comes out, or how string theory plays this idea that some formulation exists in it's over calculated version of mathematical decor.

String Theory

In either case, gravity acting in the hidden dimensions affects other non-gravitational forces such as electromagnetism. In fact, Kaluza and Klein's early work demonstrated that general relativity with five large dimensions and one small dimension actually predicts the existence of electromagnetism. However, because of the nature of Calabi-Yau manifolds, no new forces appear from the small dimensions, but their shape has a profound effect on how the forces between the strings appear in our four dimensional universe. In principle, therefore, it is possible to deduce the nature of those extra dimensions by requiring consistency with the standard model, but this is not yet a practical possibility. It is also possible to extract information regarding the hidden dimensions by precision tests of gravity, but so far these have only put upper limitations on the size of such hidden dimensions.

Bold was added by me for emphasis. See also:Angels and Demons on a Pinhead

This is/was to be part of the hopes of people in research for a long time. I have seen it before, in terms of orbitals(the analogical version of the event in the cosmos) and how such events could gave been portrayed in those same locations in space. Contribute, to the larger and global distinction of what the universe is actually doing. If it's speeding up, what exactly does this mean, and what should we be looking for from what is being contributed to the "global perspective" of WMAP from these locations??

But lets move on here okay.

If you understand the "three body problem" and being on my own, and seeing things other then what people reveal in the reports that they write, how it is possible for a lone researcher like me to come up with the same ideas about the universe having some kind of geometrical inclination?

You would have to know that "such accidents while in privy to data before us all", and what is written into the calculations by hand would reveal? Well, I never did have that information. What I did know is what Sean Carroll presented of the Lopsided Universe for consideration. This coincided nicely with my work to comprehend Poincaré in a historical sense. The relationship with Klein.

As mentioned before, at the time, I was doing my own reading on Poincaré and of course I had followed the work of Tegmark and John Baez's expose' on what the shape of the universe shall look like. This is recorded throughout my bloggery here for the checking.

What I want to say.

Given the mathematics with which one sees the universe and however this mathematical constructs reveals of nature, nature always existed. What was shown is that the discovery of the mathematics made it possible to understand something beautiful about nature. So in a sense the mathematics was always there, we just did not recognize it.:)

William Thurston

Xianfeng David Gu and Shing-Tung Yau
To a topologist, a rabbit is the same as a sphere. Neither has a hole. Longitude and latitude lines on the rabbit allow mathematicians to map it onto different forms while preserving information.

William Thurston of Cornell, the author of a deeper conjecture that includes Poincaré’s and that is now apparently proved, said, “Math is really about the human mind, about how people can think effectively, and why curiosity is quite a good guide,” explaining that curiosity is tied in some way with intuition.

“You don’t see what you’re seeing until you see it,” Dr. Thurston said, “but when you do see it, it lets you see many other things.”

Elusive Proof, Elusive Prover: A New Mathematical Mystery

Some of us are of course interested in how we can assign the relevance to perceptions the deeper recognition of the processes of nature. How we get there and where we believe they come from. As a layman I am always interested in this process, and of course, life's mysteries can indeed be a motivating factor. Motivating my interest about the nature of things that go unanswered and how we get there.


William Paul Thurston

(born October 30, 1946) is an American mathematician. He is a pioneer in the field of low-dimensional topology. In 1982, he was awarded the Fields medal for the depth and originality of his contributions to mathematics. He is currently a professor of mathematics and computer science at Cornell University (since 2003).

There are reasons with which I present this biography, as I did in relation to Poincaré and Klein. The basis of the question remains a philosophical one for me that I question the basis of proof and intuition while considering the mathematics.

Mathematical Induction

Mathematical Induction at a given statement is true of all natural numbers. It is done by proving that the first statement in the infinite sequence of statements is true, and then proving that if any one statement in the infinite sequence of statements is true, then so is the next one.

The method can be extended to prove statements about more general well-founded structures, such as trees; this generalization, known as structural induction, is used in mathematical logic and computer science.

Mathematical induction should not be misconstrued as a form of inductive reasoning, which is considered non-rigorous in mathematics (see Problem of induction for more information). In fact, mathematical induction is a form of deductive reasoning and is fully rigorous.

Deductive reasoning

Deductive reasoning is reasoning which uses deductive arguments to move from given statements (premises), which are assumed to be true, to conclusions, which must be true if the premises are true.[1]

The classic example of deductive reasoning, given by Aristotle, is

* All men are mortal. (major premise)
* Socrates is a man. (minor premise)
* Socrates is mortal. (conclusion)

For a detailed treatment of deduction as it is understood in philosophy, see Logic. For a technical treatment of deduction as it is understood in mathematics, see mathematical logic.

Deductive reasoning is often contrasted with inductive reasoning, which reasons from a large number of particular examples to a general rule.

Alternative to deductive reasoning is inductive reasoning. The basic difference between the two can be summarized in the deductive dynamic of logically progressing from general evidence to a particular truth or conclusion; whereas with induction the logical dynamic is precisely the reverse. Inductive reasoning starts with a particular observation that is believed to be a demonstrative model for a truth or principle that is assumed to apply generally.

Deductive reasoning applies general principles to reach specific conclusions, whereas inductive reasoning examines specific information, perhaps many pieces of specific information, to impute a general principle. By thinking about phenomena such as how apples fall and how the planets move, Isaac Newton induced his theory of gravity. In the 19th century, Adams and LeVerrier applied Newton's theory (general principle) to deduce the existence, mass, position, and orbit of Neptune (specific conclusions) from perturbations in the observed orbit of Uranus (specific data).

Deduction and Induction

Our attempt to justify our beliefs logically by giving reasons results in the "regress of reasons." Since any reason can be further challenged, the regress of reasons threatens to be an infinite regress. However, since this is impossible, there must be reasons for which there do not need to be further reasons: reasons which do not need to be proven. By definition, these are "first principles." The "Problem of First Principles" arises when we ask Why such reasons would not need to be proven. Aristotle's answer was that first principles do not need to be proven because they are self-evident, i.e. they are known to be true simply by understanding them.

Back to the lumping in of theology alongside of Atlantis. Rebel dreams, it is hard to remove one's colour once they work from a certain premise. Atheistic, or not.

Seeking such clarity would be the attempt for me, with which to approach a point of limitation in our knowledge, as we may try to explain the process of the current state of the universe, and it's shape. Such warnings are indeed appropriate to me about what we are offering for views from a theoretical standpoint.

The basis presented here is from a layman standpoint while in context of Plato's work, brings some perspective to Raphael's painting, "The School of Athens." It is a central theme for me about what the basis of Inductive and deductive processes reveals about the "infinite regress of mathematics to the point of proof."

Such clarity seeking would in my mind contrast a theoretical technician with a philosopher who had such a background. Raises the philosophical question about where such information is derived from. If ,from a Platonic standpoint, then all knowledge already exists. We just have to become aware of this knowledge? How so?

Lawrence Crowell:

The ball on the Mexican hat peak will under the smallest perturbation or fluctuation begin to fall off the peak, roll into the trough and the universe tunnels out of the vacuum or nothing to become a “something.”

Whether I attach a indication of God to this knowledge does not in any way relegate the process to such a contention of theological significance. The question remains a inductive/deductive process?

I would think philosophers should weight in on the point of inductive/deductive processes as it relates to the search for new mathematics?

Allegory of the Cave

For me this was a difficult task with which to cypher the greater contextual meaning of where such mathematics arose from. That I should implore such methods would seem to be, to me, in standing with the problems and ultimates searches for meaning about our place in the universe. Whether I believe in the "God nature of that light" should hold no atheistic interpretation to my quest for the explanations about the talk on the origins of the universe.

See:

The Sound of Billiard Balls

Mathematical Structure of the Universe

Heralded from the 21st Century: String Theory

I know not how, may find their way to the minds of humanity in Some Dimensionality, and may stir up a race of rebels who shall refuse to be confined to limited Dimensionality." from Flatland, by E. A. Abbott

It is sometimes important to know what race of rebels had been raised to realize that such a revolution in the making had started from a place of thinking that many others
began to think about as well?

Cycle of Birth, Life, and Death-Origin, Indentity, and Destiny by Gabriele Veneziano

In one form or another, the issue of the ultimate beginning has engaged philosophers and theologians in nearly every culture. It is entwined with a grand set of concerns, one famously encapsulated in an 1897 painting by Paul Gauguin: D'ou venons-nous? Que sommes-nous? Ou allons-nous? "Where do we come from? What are we? Where are we going?"

See here for more information.

It is important to know where such models began to influence the idea to generate theoretical model for an apprehension of how we view this universe? Given the study at hand here are the following people for consideration.

Whence began this journey and revolution?

LEONARD SUSSKIND:

And I fiddled with it, I monkeyed with it. I sat in my attic, I think for two months on and off. But the first thing I could see in it, it was describing some kind of particles which had internal structure which could vibrate, which could do things, which wasn't just a point particle. And I began to realize that what was being described here was a string, an elastic string, like a rubber band, or like a rubber band cut in half. And this rubber band could not only stretch and contract, but wiggle. And marvel of marvels, it exactly agreed with this formula.
I was pretty sure at that time that I was the only one in the world who knew this.

So we have to take stock of the movements that change democratic societies. To have found such governments will change and fall according to the plight of it's citizens in science. As it goes with "theoretical positions?"

Working to understand the development of the model in consideration was needed in order for one to understand why Lee Smolin methodology to work science from a historical perspective is one I favour as well. It is sometimes necessary to list these developmental phases in order to get to a position to speak with authority. Find that "with certainty" we can make certain comments? Find, we must be confronted again, to say, any progress will go from There.

The Revolution that Didn't Happen by Steven Weinberg

I first read Thomas Kuhn's famous book The Structure of Scientific Revolutions a quarter-century ago, soon after the publication of the second edition. I had known Kuhn only slightly when we had been together on the faculty at Berkeley in the early 1960s, but I came to like and admire him later, when he came to MIT. His book I found exciting.

Evidently others felt the same. Structure has had a wider influence than any other book on the history of science. Soon after Kuhn's death in 1996, the sociologist Clifford Geertz remarked that Kuhn's book had "opened the door to the eruption of the sociology of knowledge" into the study of the sciences. Kuhn's ideas have been invoked again and again in the recent conflict over the relation of science and culture known as the science wars.

So we know where the idea of science wars began do we not? What instigates conflict as a healthy perspective to progress of the sciences. We will see the story unfold within this blog.

For some reason people might of thought my views were just held to Lee Smolin and the work that I had been accumulating with regards to his views of the Universe. While I had shown the cover of his book countless times, I would like to say that I have accumulated "other books," like those of Brian Greene as well.

Does this make me an expert on the subject in question or what ever Lee Smolin has written? Of course not.

But the work I have been doing, has not been limited to what the authors themself have given to the public in their outreach writing books. I have been at this a few years now, so I would like people to think this is not just a jaunt of journalism, that has been given to the public in it's books but has been a labour of love to understand my place in the universe.

The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory

The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory (ISBN 0-375-70811-1) is a book by Brian Greene published in 2000 which introduces string theory and provides a comprehensive though non-technical assessment of the theory and some of its shortcomings.

Beginning with a brief consideration of classical physics, which concentrates on the major conflicts in physics, Greene establishes an historical context for string theory as a necessary means of integrating the probabilistic world of the standard model of particle physics and the deterministic Newtonian physics of the macroscopic world. Greene discusses the essential problem facing modern physics: unification of Einstein's theory of General Relativity and Quantum Mechanics. Greene suggests that string theory is the solution to these two conflicting approaches. Greene uses frequent analogies and mental experiments to provide a means for the layman to come to terms with the theory which has the potential to create a unified theory of physics.

The Elegant Universe was adapted for a three hour program in two parts for television broadcast in late 2003 on the PBS series NOVA.

Thanks Q9 for the link to "Elegant physicist makes string theory sexy." I was going to posted it the day when you gave it to me, but instead seeing that Clifford of Asymptotia had it (same day), I thought I wouldn't. But as fate has it I must.

The Fabric of the Cosmos: Space, Time, and the Texture of Reality (2004) is the second book on theoretical physics, cosmology and string theory written by Brian Greene, professor and co-director of Columbia's Institute for Strings, Cosmology, and Astroparticle Physics (ISCAP).[1]

Greene begins with the key question: What is reality? Or more specifically: What is spacetime? He sets out to describe the features he finds both exciting and essential to forming a full picture of the reality painted by modern science. In almost every chapter, Greene introduces its basic concepts and then slowly builds to a climax, which is usually a scientific breakthrough. Greene then attempts to connect with his reader by posing simple analogies to help explain the meaning of a scientific concept without oversimplifying the theory behind it.

In the preface, Greene acknowledges that some parts of the book are controversial among scientists. Greene discusses the leading viewpoints in the main text, and points of contention in the end notes. Greene has striven for balanced treatment of the controversial topics. In the end notes, the diligent reader will find more complete explanations relevant to points he has simplified in the main text.

Once you get this view of the gravitational connection between everything, the form of graviton, you get this preview of the bulk and what lensing may mean. It is hard not to think of "dimensional perspectives in relation to the energy" describing the particles of science in some way. Witten below in his "Strings Unravel" lets you know what string theory has accomplished.

Warped Passages is a book by Lisa Randall, published in 2005, about particle physics in general and additional dimensions of space (cf. Kaluza-Klein theory) in particular. The book has made it to top 50 at amazon.com, making it the world's first successful book on theoretical physics by a female author. See Where are my keys?

It's alway nice having one's own blog and nice that I can retained my dignity under the name of Plato. It keeps my personal life from being treated with disrespect at the whim of the stroke of a delete key. Of course I am willing to take my lumps understanding such a role as "older student." After being expose to the exchange between people in the tribe, it's thinking can do all kinds of damage to each other? But I would like to think that all sides remain cool to positions they hold in society

A Different Universe: Reinventing Physics from the Bottom Down by Robert B. LaughlinFrom the Publisher:

Why everything we think about fundamental physical laws needs to change, and why the greatest mysteries of physics are not at the ends of the universe but as close as the nearest ice cube or grain of salt.

Not since Richard Feynman has a Nobel Prize-winning physicist written with as much panache as Robert Laughlin does in this revelatory and essential book. Laughlin proposes nothing less than a new way of understanding fundamental laws of science. In this age of superstring theories and Big-Bang cosmology, we're used to thinking of the unknown as being impossibly distant from our everyday lives. The edges of science, we're told, lie in the first nanofraction of a second of the Universe's existence, or else in realms so small that they can't be glimpsed even by the most sophisticated experimental techniques. But we haven't reached the end of science, Laughlin argues-only the end of reductionist thinking. If we consider the world of emergent properties instead, suddenly the deepest mysteries are as close as the nearest ice cube or grain of salt. And he goes farther: the most fundamental laws of physics-such as Newton's laws of motion and quantum mechanics -are in fact emergent. They are properties of large assemblages of matter, and when their exactness is examined too closely, it vanishes into nothing.

See Laughlin, Reductionism, Emergence

Out of all this uncertainty that exists at the level with which we think about in "those dimensions" what value any constructive diagram if it did not lead you to the understanding of the building blocks that a condense matter theorist may describe as manifesting in our reality?

The Year is 2020 and that's our Eyesight

Columbia physicist Brian Greene inhabits a multiple-perspective landscape modeled after M.C. Escher's artwork in a scene from "The Elegant Universe," a public-TV documentary based on Greene's book.

Q: Hawking has said that there could be a “theory of everything” produced in the next 20 years, or by 2020. Do you get that same sense? Or will there ever be a theory of everything?

A: Well, I always find it difficult to make predictions that are tied to a specific time frame, because as we all know, one of the exciting things about science is that you don’t know when the big break is going to happen. It could happen tomorrow, it could happen 10 years from now, it could happen a century from now. So you just keep pressing on, making progress, and hope that you reach these major milestones — ideally in your own lifetime, but who knows? So I don’t know if 2020 is the right number to say. But I would say that string theory has a chance of being that unified theory, and we are learning more and more about it. Every day, every week, every month there are fantastically interesting developments.

Will it all come together by 2020, where we can actually have experimental proof and the theory develops to the point that it really makes definitive statements that can be tested? I don’t know. I hope so. But hope is not the thing that determines what will actually happen. It’s the hard work of scientists around the world.

But anyway onto what I wanted to say and "being censored" I couldn't.

Clifford is defending his position on how Lee Smolin and Peter Woit have assigned a "perspective view" to string theory as a modelled approach. As a theoretical discovery of science, Clifford from my view, had to show that this process is still unfolding and that any quick decision as to giving String theory such a final vote of opinion from Lee Smolin was premature. I have supported Clifford in this view because of where we had been historically in the past years that the formulation of string theory has been given.

D-Branes by Clifford V. Johnson

D-branes represent a key theoretical tool in the understanding of strongly coupled superstring theory and M-theory. They have led to many striking discoveries, including the precise microphysics underlying the thermodynamic behaviour of certain black holes, and remarkable holographic dualities between large-N gauge theories and gravity. This book provides a self-contained introduction to the technology of D-branes, presenting the recent developments and ideas in a pedagogical manner. It is suitable for use as a textbook in graduate courses on modern string theory and theoretical particle physics, and will also be an indispensable reference for seasoned practitioners. The introductory material is developed by first starting with the main features of string theory needed to get rapidly to grips with D-branes, uncovering further aspects while actually working with D-branes. Many advanced applications are covered, with discussions of open problems which could form the basis for new avenues of research.

While Clifford's book I do not have, I understand that the "second revolution" was necessary to help us move to consider where string theory was to take us. It was progressing in the theoretics as a model to help us see science assuming the ways in which such models adjust us to possible new views in science. Clifford may not of liked the implication of a Grokking of a kind that would refer to consuming model approaches and then becoming what you eat?

Clifford:

I’ve found that different people have different takes on what it means to have a “theory of everything”. There is a popular idea (perhaps the most common) that this somehow means that this theory will describe (at least in principle) all known basic physical phenomena (constituents and their interactions, if you like) once and for all. Others mean something less ambitious, a theory that consistently describes the four fundamental forces and the things that interact with them, achieving a unification of all the forces and phenomena that we currently understand. I personally think that the first idea of a theory of everything is rather naive, and my personal hunch (and bias from what I’ve learned about the history of science) is that there is simply no such thing.

So of course entertaining the idea of a "theory of everything" leaves a bad taste in some peoples mouth, and having them to reason that it is the naivity of such a thought, that I immediately felt insulted. Clifford saids,"this theory will describe (at least in principle) all known basic physical phenomena (constituents and their interactions, if you like) once and for all" and may have been the case for those less then spending the time and effort, would have probably been insulted as I was. I of course came to recognize the positive aspect of the second position Clifford assumes.

Bench Marks of theoretical Progress

Anyway there are positions that we can take when we look back and reassess everything that we have been doing in reading the public outreach, like so called "bench marks" to see if such progressions still have have a evolutionary way to go.

Edward Witten-Reflections on the Fate of Spacetime

Unravelling String Theory

But what is string theory? It may well be the only way to reconcile gravity and quantum mechanics, but what is the core idea behind it? Einstein understood the central concepts of general relativity years before he developed the detailed equations. By contrast, string theory has been discovered in bits and pieces — over a period that has stretched for nearly four decades — without anyone really understanding what is behind it. As a result, every bit that is unearthed comes as a surprise. We still don’t know where all these ideas are coming from — or heading to

See more here



So what shall we use to measure what had first seem so abstract in Susskind's mind as a "rubber band," or the start of Veneziano views on such strings at inception? We've come a long way.

Something that I perceived back in 2004 help to "shape my views on the way I speak" "today" allows for us to consider that strings take it's rightful place within the building blocks of matter, that following Robert Laughlins lead, it was that we shifted our times from the first three seconds of Steven Weinberg, to the "First three Microseconds" of strings within the process of the unfolding universe.

The resulting collisions between pairs of these atomic nuclei generate exceedingly hot, dense bursts of matter and energy to simulate what happened during the first few microseconds of the big bang. These brief "mini bangs" give physicists a ringside seat on some of the earliest moments of creation.

See How Particles Came to be?

While Laughlin may have not seen the continued relevance of particle reductionism it was leading to some amazing insights. I now wonder now, if held to the comparisons of this superfluid, how it would have appealed to him? I think Witten in last plate above recognized what had to be done.

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

KK Tower

Like many people who devote their time to understanding the nature of the cosmo and the micro perspective of the world around us, these things have their own motivational packages which move to further rquired comprehensions. In that, one needs to further educateas to what they are talking about.

It's definitiely not easy, but I am trying, and devote a lot of time to this regardless of what schooling is required, it is not my intent to send people down the wrong paths, or, no paths at all, before I have investigated the terrain as best I can.

Mountains can give persepctive where sitting in the valleys circumspect what the greater can be?

KK Tower

What is it?



Kaluza-Klein theory(Wiki 4 Jan 2006)

A splitting of five-dimensional spacetime into the Einstein equations and Maxwell equations in four dimensions was first discovered by Gunnar Nordström in 1914, in the context of his theory of gravity, but subsequently forgotten. In 1926, Oskar Klein proposed that the fourth spatial dimension is curled up in a circle of very small radius, so that a particle moving a short distance along that axis would return to where it began. The distance a particle can travel before reaching its initial position is said to be the size of the dimension. This extra dimension is a compact set, and the phenomenon of having a space-time with compact dimensions is referred to as compactification.

Kaluza-Klein theory is a model which unifies classical gravity and electromagnetism. It was discovered by the mathematician Theodor Kaluza that if general relativity is extended to a five-dimensional spacetime, the equations can be separated out into ordinary four-dimensional gravitation plus an extra set, which is equivalent to Maxwell's equations for the electromagnetic field, plus an extra scalar field known as the "dilaton". Oskar Klein proposed that the fourth spatial dimension is curled up with a very small radius, i.e. that a particle moving a short distance along that axis would return to where it began. The distance a particle can travel before reaching its initial position is said to be the size of the dimension. This, in fact, also gives rise to quantization of charge, as waves directed along a finite axis can only occupy discrete frequencies.

Kaluza-Klein theory can be extended to cover the other fundamental forces - namely, the weak and strong nuclear forces - but a straightforward approach, if done using an odd dimensional manifold runs into difficulties involving chirality. The problem is that all neutrinos appear to be left-handed, meaning that they are spinning in the direction of the fingers of the left hand when they are moving in the direction of the thumb. All anti-neutrinos appear to be right-handed. Somehow particle reactions are asymmetric when it comes to spin and it is not straightforward to build this into a Kaluza-Klein theory since the extra dimensions of physical space are symmetric with respect to left-hand spinning and r-hand spinning particles.

So in order to get to the summation, views of hidden dimenisons had to be mathematically described for us, so a generalization here would suffice in the following diagram.



Now, not having the room to explain, and having linked previous information on extension of KK theory, I wondered about the following. If we understood well, the leading perspective that lead us through to the dynamical realizations, then the road Gauss and Reimann lead us to would help us to understand the visualization materializing by the calorimeter disciptions of each energy placement harmonically describing each particle's value? Even in a empty space, there seems to be something of a harmonical consideration?


If one understood well enough about the direction of discernation of early universe consideration and microstates, then such questions would have been of value in the ideas of topological considerations?

Poincare Conjecture

I am a little bit sad right now?

I accidently deleted a lot of what I would have said about assumption of Sklar's position in relation to discrete and continuous functions. In relation to the value of S-Matrix as a discrete measure and how we might see the gravitational lensing as a continous function using abstract topological understandings.

Moshe:

If string thoery describes the world and it has a compact circle, there are no measurements that will distinguish a small circle from a large one. Since I am only interested in results of measurments there is no reason for me to choose.

Moshe is leaving me hanging on a limb now that he moves into the fighting reality while the poor clod like me is trying to live in the world created by scientists/ theorists.

Now, have to work our way back to reality? :( Now the assunption I have adopted is a fifth dimensional perspective as most know when talking about the horizon and the inner workings of the black hole. Inner workings, really?

Fyodor:

Let me explain. If you look at the history [say 1930] of Kaluza Klein theory, you will find that there were two schools of thought. One said that the 5th dimension was real, the other that it was just a mathematical formalism. Of course, nobody disputed that the KK equations were *exactly equivalent* mathematically to the Einstein-Maxwell system, but nobody assumed that *exact mathematical equivalence* was the same thing as “equally real”. Similarly, string theorists circa 1985 surely knew that a purely formal interpretation of Calabi-Yau compactifications was possible, but evidently nobody felt moved to attach any importance to this observation.

Who would have disputed Smolin's position about responsibility and the S-matrix stance needed to assess this reality? I certainly don't have a probem and the general consensus I am sure would find that all would be in agreement here? A testable and functionable recognizion of dicrete measure?

Now I am left in a state where I cannot distinquish between the inner/outer and of course to think that I am on the surface of a Klein bottle would be very strange to someone who saids it's oks from a distance. I have to say, "holy crap, look what you have done?"

So it is not so easy to think of the Skalr's psotion and the abstract world as ending the conversation as such, pushes me to the wonderment of continuous functions, has me now scratching my head.

Lenny's rubber bands, or sliding rubber bands over apples versus donuts. Now you guys have really done it? Is reality smooth, or discrete? The quandrum of Poincare hold the light of Sklars position in my head, as tohow I should approach the discriptin of that blackhole interior even when the consistancy of the geoemrty expression had come from some real world measure cosmolgically turned inside/out?

Explain to me the jets of the Bose Nova then as anti-matter creations if such a gravitational collapse is not held in view, and the propensity of that action written in a continous mode?

Who would have known that the very idea of the colliders would have taken on abstract proportions, and moved the very thinking to hyperdimensional status. While the few might have restraint themselves to the step by step discrete measure?

Did this move to the abstract say abandon all reason? Or move from the reality of such man made creations and see where the views are taking us into those extra dimensions. Was reason abandon?