Professor Konstantin Novoselov talks about his Nobel Prize winning discovery graphene, and what the future holds for it in the 2012 Kohn Award Lecture SEE: Graphene: materials in the flatland
See Also:
Professor Konstantin Novoselov talks about his Nobel Prize winning discovery graphene, and what the future holds for it in the 2012 Kohn Award Lecture SEE: Graphene: materials in the flatland
Image credit: NASA/CXC/SAO 
One of the most famous objects in the sky  the Cassiopeia A supernova remnant  will be on display like never before, thanks to NASA's Chandra Xray Observatory and a new project from the Smithsonian Institution. A new threedimensional (3D) viewer, being unveiled this week, will allow users to interact with many oneofakind objects from the Smithsonian as part of a largescale effort to digitize many of the Institutions objects and artifacts.See Also:
Scientists have combined data from Chandra, NASA's Spitzer Space Telescope, and groundbased facilities to construct a unique 3D model of the 300year old remains of a stellar explosion that blew a massive star apart, sending the stellar debris rushing into space at millions of miles per hour. The collaboration with this new Smithsonian 3D project will allow the astronomical data collected on Cassiopeia A, or Cas A for short, to be featured and highlighted in an openaccess program  a major innovation in digital technologies with public, education, and researchbased impacts. See: Exploring the Third Dimension of Cassiopeia A
The value of nonEuclidean geometry lies in its ability to liberate us from preconceived ideas in preparation for the time when exploration of physical laws might demand some geometry other than the Euclidean. Bernhard Riemann
The concept of dimension is not restricted to physical objects. Highdimensional spaces occur in mathematics and the sciences for many reasons, frequently as configuration spaces such as in Lagrangian or Hamiltonian mechanics; these are abstract spaces, independent of the physical space we live in. 
"Yet I exist in the hope that these memoirs, in some manner, 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. AbbottFlat Land: A Romance of Many Dimensions
The value of nonEuclidean geometry lies in its ability to liberate us from preconceived ideas in preparation for the time when exploration of physical laws might demand some geometry other than the Euclidean. Bernhard Riemann
Oskar Klein proposed that the fourth spatial dimension is curled up in a circle of 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. (This occurs because electromagnetism is a U(1) symmetry theory and U(1) is simply the group of rotations around a circle).
Similarly, the laws of gravity and light seem totally dissimilar. They obey different physical assumptions and different mathematics. Attempts to splice these two forces have always failed. However, if we add one more dimension, a fifth dimension, to the previous four dimensions of space and time, then equations governing light and gravity appear to merge together like two pieces of a jigsaw puzzle. Light, in fact, can be explained in the fifth dimension. In this way, we see the laws of light and gravity become simpler in five dimensions.Kaku's preface of Hyperspace, page ix para 3
"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 pointofview, 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 nonEuclidean geometry emerge as among the most important themes unifying much of modern art and theory.Hyperspace: A Scientific Odyssey
My most recent research is about extra dimensions of space. Remarkably, we can potentially "see" or "observe" evidence of extra dimensions. But we won't reach out and touch those dimensions with our fingertips or see them with our eyes. The evidence will consist of heavy particles known as KaluzaKlein modes that travel in extradimensional space. If our theories correctly describe the world, there will be a precise enough link between such particles (which will be experimentally observed) and extra dimensions to establish the existence of extra dimensions. Dangling Particles,By LISA RANDALL, Published: September 18, 2005 New York Yimes


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 venonsnous? Que sommesnous? Ou allonsnous? "Where do we come from? What are we? Where are we going?"
Arthur Miller
Einstein and SchrÃ¶dinger never fully accepted the highly abstract nature of Heisenberg's quantum mechanics, says Miller. They agreed with Galileo's assertion that "the book of nature is written in mathematics", but they also realized the power of using visual imagery to represent mathematical symbols.
Paul Dirac
When one is doing mathematical work, there are essentially two different ways of thinking about the subject: the algebraic way, and the geometric way. With the algebraic way, one is all the time writing down equations and following rules of deduction, and interpreting these equations to get more equations. With the geometric way, one is thinking in terms of pictures; pictures which one imagines in space in some way, and one just tries to get a feeling for the relationships between the quantities occurring in those pictures. Now, a good mathematician has to be a master of both ways of those ways of thinking, but even so, he will have a preference for one or the other; I don't think he can avoid it. In my own case, my own preference is especially for the geometrical way.
String theory's mathematical tools were designed to unlock the most profound secrets of the cosmos, but they could have a far less esoteric purpose: to tease out the properties of some of the most complex yet useful types of material here on Earth.What Good are Mathematics in the Real World?Do you know how many mathematical expressions are needed in order to describe the theory?
The language of physics is mathematics. In order to study physics seriously, one needs to learn mathematics that took generations of brilliant people centuries to work out. Algebra, for example, was cuttingedge mathematics when it was being developed in Baghdad in the 9th century. But today it's just the first step along the journey.Guide to math needed to study physics
Betrayal of Images" by Rene Magritte. 1929 painting on which is written "This is not a Pipe" 
Metacognition is defined as "cognition about cognition", or "knowing about knowing."[1] It can take many forms; it includes knowledge about when and how to use particular strategies for learning or for problem solving.[1]
Thus, primary consciousness refers to being mentally aware of things in the world in the present without any sense of past and future; it is composed of mental images bound to a time around the measurable present.[1]
By contrast, secondary consciousness depends on and includes such features as selfreflective awareness, abstract thinking, volition and metacognition.[1][2]
The AIM Model introduces a new hypothesis that primary consciousness is an important building block on which secondary consciousness is constructed.[1]
A quasiperiodic crystal, or, in short, quasicrystal, is a structure that is ordered but not periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks translational symmetry. While crystals, according to the classical crystallographic restriction theorem, can possess only two, three, four, and sixfold rotational symmetries, the Bragg diffraction pattern of quasicrystals shows sharp peaks with other symmetry orders, for instance fivefold.
Aperiodic tilings were discovered by mathematicians in the early 1960s, and, some twenty years later, they were found to apply to the study of quasicrystals. The discovery of these aperiodic forms in nature has produced a paradigm shift in the fields of crystallography. Quasicrystals had been investigated and observed earlier,^{[2]} but, until the 1980s, they were disregarded in favor of the prevailing views about the atomic structure of matter.
Roughly, an ordering is nonperiodic if it lacks translational symmetry, which means that a shifted copy will never match exactly with its original. The more precise mathematical definition is that there is never translational symmetry in more than n – 1 linearly independent directions, where n is the dimension of the space filled; i.e. the threedimensional tiling displayed in a quasicrystal may have translational symmetry in two dimensions. The ability to diffract comes from the existence of an indefinitely large number of elements with a regular spacing, a property loosely described as longrange order. Experimentally, the aperiodicity is revealed in the unusual symmetry of the diffraction pattern, that is, symmetry of orders other than two, three, four, or six. The first experimental observation of what came to be known as quasicrystals was made by Dan Shechtman and coworkers in 1982 and it was reported in print two years later.^{[3]} Shechtman received the Nobel Prize in Chemistry in 2011 for his findings.^{[4]}.
In 2009, following a decade long search, a group of scientists from University of Florence in Italy reported the existence of a natural quasicrystals in mineral samples from the Koryak mountains in Russia's far east, named icosahedrite.^{[5]}^{[6]} It was further claimed by scientists from Princeton University that icosahedrite is extraterrestrial in origin, possibly delivered to Earth by a CV3 carbonaceous chondrite asteroid.^{[7]}
240 E₈ polytope vertices using 5D orthographic_projection to 2D using 5cube (Penteract) Petrie_polygon basis_vectors overlaid on electron diffraction pattern of an Icosahedron ZnMgHo Quasicrystal. 
Special Topic of Supersymmetryby Science Watch 
Since the 1980s, if not earlier, supersymmetry has reigned as the best available candidate for physics beyond the standard model. But experimental searches for supersymmetric particles have so far come up empty, only reconfirming the standard model again and again. This leaves supersymmetry a theory of infinite promise and ever more questionable reality. See Link above.
A diagram showing the first four spatial dimensions. 
The concept of dimension is not restricted to physical objects. Highdimensional spaces occur in mathematics and the sciences for many reasons, frequently as configuration spaces such as in Lagrangian or Hamiltonian mechanics; these are abstract spaces, independent of the physical space we live in.
One of the most confusing things about the Big Bang is that it involves an expanding universe. Any reasonable person, hearing about the Big Bang, will imagine something that he or she has seen expanding: a cloud of smoke exploding outward, or a balloon expanding as it is filled with air. This is very natural. And having imagined this, the reasonable person will ask, “But what is the universe expanding into?”
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.
We cannot directly visualize a hypersphere for the very reason that it is a 4dimensional object and goes beyond our senses. What we can visualize, however, is a hypersphere in the form of 3dimensional slices (as is displayed to the left). A hypersphere is in essence an array of 3 dimensional solid spheres that increase and then decrease in size. This would represent our basic conception of the hypersphere, and is shown in the animated picture here.
Understanding 4 dimensional space
Dimension (n)  Shape  Volume  Surface Area 
2  circle  Ï€ r^{2}  2Ï€r 
3  sphere  (4/3)Ï€ r^{3}  4Ï€r^{2} 
4  4sphere  (1/2)Ï€^{2} r^{4}  2Ï€^{2} r^{3} 
5  5sphere  (8/15)Ï€^{2} r^{5}  (8/3)Ï€^{2} r^{4} 
6  6sphere  (1/6)Ï€^{3} r^{6}  Ï€^{3} r^{5} 
7  7sphere  (16/105)Ï€^{3} r^{7}  (16/15)Ï€^{3} r^{6} 
Where would these other universes be in relation to ours? Is there a way to envision it?
Well, we live in three spatial dimensions: We move back and forth, up and down, left to right. And then there's time, so that's our fourdimensional universe. Another universe might be essentially right next to ours by going in another direction that's not one of those four. We might call it "another kind of sideways." See: Riddles of the Multiverse
SOCRATES: But if he always possessed this knowledge he would always have known; or if he has acquired the knowledge he could not have acquired it in this life, unless he has been taught geometry; for he may be made to do the same with all geometry and every other branch of knowledge. Now, has any one ever taught him all this? You must know about him, if, as you say, he was born and bred in your house.SEE:Meno by Plato
LEE SMOLIN Physicist, Perimeter Institute; Author, The Trouble With Physics
Thinking In Time Versus Thinking Outside Of Time
One very old and pervasive habit of thought is to imagine that the true answer to whatever question we are wondering about lies out there in some eternal domain of "timeless truths." The aim of research is then to "discover" the answer or solution in that already existing timeless domain. For example, physicists often speak as if the final theory of everything already exists in a vast timeless Platonic space of mathematical objects. This is thinking outside of time. See:A "scientific concept" may come from philosophy, logic, economics, jurisprudence, or other analytic enterprises, as long as it is a rigorous conceptual tool that may be summed up succinctly (or "in a phrase") but has broad application to understanding the world.
"There comes a time when the mind takes a higher plane of knowledge but can never prove how it got there. All great discoveries have involved such a leap. The important thing is not to stop questioning." Albert Einstein (1879 1955)
Although it didn't properly describe strong interactions, in studying string theory physicists stumbled upon an amazing mathematical structure. String theory has turned out to be far richer than people originally anticipated. For example, people found that a certain vibrational state of the string has zero mass and spin 2. According to Einstein's theory of gravity, the gravitational force is mediated by a particle with zero mass and spin 2. So string theory is, among many other things, a theory of gravity!See: Why Strings
Guide Review  Hiding in the Mirror by Lawrence KraussSee:Book Review: Hiding in the Mirror
In Hiding in the Mirror, astrophysicist and cosmologist Lawrence M. Krauss addresses the concept of extra dimensions, from its appearance in popular culture such as Alice in Wonderland and The Time Machine to theoretical physics areas such as the theory of relativity and string theory. In fact, I would say that the book splits roughly 50/50 between cultural and scientific topics, which is part of the point of the book (that extra dimensions are tied to both areas), but for those who are specifically interested in the scientific aspects there are other books (such as Lisa Randall's Warped Passages) which address the scientific aspects in far more depth.
According to Krauss, extra dimensions have captured the human imagination well before it entered into exploration by physics in the last century or so. The book covers how the concepts were viewed by those in the past, as well as more recent science fiction, such as Star Trek (one of Krauss' favorite topics, as author of the bestselling The Physics of Star Trek). Much of this material is entertaining, but for those who are wanting to get to the heart of the physics, it can feel like filler.
About 100 pages of the book focuses on the recent work to find a unified theory of quantum gravity, focusing predominantly on string theory (with some mention of predecessors). This has been one of the areas where extra dimensions have become extremely dominant. Though Krauss exhibits some genuine skepticism about the track string theory is on, I think calling the book a criticism of string theory would be going a bit far. Krauss is placing string theory within a larger framework of extra dimensional movements in the past, many of which have proved incredibly enlightening and some of which have not done much. It's left to other books to determine whether string theory has any scientific merit.
Plants soak up some of the 10^{17} joules of solar energy that bathe Earth each second, harvesting as much as 95 percent of it from the light they absorb. The transformation of sunlight into carbohydrates takes place in one million billionths of a second, preventing much of that energy from dissipating as heat. But exactly how plants manage this nearly instantaneous trick has remained elusive. Now biophysicists at the University of California, Berkeley, have shown that plants use the basic principle of quantum computing—the exploration of a multiplicity of different answers at the same time—to achieve nearperfect efficiency.See: When It Comes to Photosynthesis, Plants Perform Quantum Computation
See:Betrayal of Images" by Rene Magritte
Probabilties
(The Fifth Dimension)


Idea of the pipe
/ \
/ \
/ \
Picture of the pipe
/ \
/ \
/ \
The real pipe and form
Where a dictionary proceeds in a circular manner, defining a word by reference to another, the basic concepts of mathematics are infinitely closer to an indecomposable element", a kind of elementary particle" of thought with a minimal amount of ambiguity in their definition. Alain Connes
Can they propose these dimensions as anything more then the copyrighted product of their own imagination and not loose control over the idea?
Here’s an analogy to understand this: imagine that our universe is a twodimensional pool table, which you look down on from the third spatial dimension. When the billiard balls collide on the table, they scatter into new trajectories across the surface. But we also hear the click of sound as they impact: that’s collision energy being radiated into a third dimension above and beyond the surface. In this picture, the billiard balls are like protons and neutrons, and the sound wave behaves like the graviton.
Strings existing in the fivedimensional spacetime can even look pointlike when they are close to the boundary. Polchinski and Strassler1 show that when an energetic fourdimensional particle (such as an electron) is scattered from these strings (describing protons), the main contribution comes from a string that is close to the boundary and it is therefore seen as a pointlike object. So a stringlike interpretation of a proton is not at odds with the observation that there are pointlike objects inside it.
The surface of a marble table is spread out in front of me. I can get from any one point on this table to any other point by passing continuously from one point to a "neighboring" one, and repeating this process a (large) number of times, or, in other words, by going from point to point without executing "jumps." I am sure the reader will appreciate with sufficient clearness what I mean here by "neighbouring" and by "jumps" (if he is not too pedantic). We express this property of the surface by describing the latter as a continuum.Albert Einstein p. 83 of his Relativity: The Special and the General Theory
Much emphasis has been placed during the past fifty years on the reconstruction of the geometric continuum from the natural integers, using the theory of Dedekind cuts or the completion of the field of rational numbers. Under the influence of axiomatic and bookish traditions, man perceived in discontinuity the first mathematical Being: "God created the integers and the rest is the work of man." This maxim spoken by the algebraist Kronecker reveals more about his past as a banker who grew rich through monetary speculation than about his philosophical insight. There is hardly any doubt that, from a psychological and, for the writer, ontological point of view, the geometric continuum is the primordial entity. If one has any consciousness at all, it is consciousness of time and space; geometric continuity is in some way inseparably bound to conscious thought.
We know that that kind of information is encoded in the signal because people in Denmark have created a robotic honey bee that you can plop in the middle of a colony, programmed to dance in a certain way, and the hive members will actually follow the information precisely to that location. Researchers have been able to understand the information processing system to this level, and consequently, can actually transmit it through the robot to other members of the hive.
The workers have a variety of tasks to perform – some collect nectar from flowers, others pollen, some are engaged in constructing new combs, or looking after the developing larvae, some perform the duty of cleaning the cells or feeding the larvae on special secretion that they regurgitate from their mouth parts. In these insects the exact task of any individual depends largely on its age, although there is a certain flexibility, depending on the requirements of the hive.
Consider ants crawling on a tabletop. In their daily experience, they can explore only 2 dimensions, those of the table surface. They may see a bee up flying, or occasionally landing on the table top, but that 3rd dimension is something they can only see or imagine, not experience. Perhaps we are in an analogous situation. Instead of a tabletop, we live in a 3dimensional space called 3brane (a name generalizing 2brane, i.e., membrane). For some reason, we (i.e., atoms, molecules, photons etc.) are stuck in this 3brane, even though there are 6 additional dimensions out there. Gravity, like the bee, can go everywhere. We call this the brane world, a rather natural phenomenon in superstring theory. At the moment, physicists are working hard to understand this scenario better and to find ways to experimentally test this idea.
These free, wild raptures are not the only form abstraction can take, and in his later, sadder years, Kandinsky became much more severely constrained, all trace of his original inspiration lost in magnificent patternings. Accent in Pink (1926; 101 x 81 cm (39 1/2 x 31 3/4 in)) exists solely as an object in its own right: the ``pink'' and the ``accent'' are purely visual. The only meaning to be found lies in what the experience of the pictures provides, and that demands prolonged contemplation. What some find hard about abstract art is the very demanding, timeconsuming labour that is implicitly required. Yet if we do not look long and with an open heart, we shall see nothing but superior wallpaper.I underlined for emphasis.
In the arts and of painting, graphic design, and photography, color theory is a body of practical guidance to color mixing and the visual impact of specific color combinations. Although color theory principles first appear in the writings of Alberti (c.1435) and the notebooks of Leonardo da Vinci (c.1490), a tradition of "colory theory" begins in the 18th century, initially within a partisan controversy around Isaac Newton's theory of color (Opticks, 1704) and the nature of socalled primary colors. From there it developed as an independent artistic tradition with only sporadic or superficial reference to colorimetry and vision science.
Adding a certain mapping function between the color model and a certain reference color space results in a definite "footprint" within the reference color space
CIE L*a*b* (CIELAB) is the most complete color model used conventionally to describe all the colors visible to the human eye. It was developed for this specific purpose by the International Commission on Illumination (Commission Internationale d'Eclairage, hence its CIE initialism). The * after L, a and b are part of the full name, since they represent L*, a* and b*, derived from L, a and b. CIELAB is an Adams Chromatic Value Space.
The three parameters in the model represent the lightness of the color (L*, L*=0 yields black and L*=100 indicates white), its position between magenta and green (a*, negative values indicate green while positive values indicate magenta) and its position between yellow and blue (b*, negative values indicate blue and positive values indicate yellow).
The Lab color model has been created to serve as a device independent model to be used as a reference. Therefore it is crucial to realize that the visual representations of the full gamut of colors in this model are never accurate. They are there just to help in understanding the concept, but they are inherently inaccurate.
Since the Lab model is a three dimensional model, it can only be represented properly in a three dimensional space.
the quantum entanglement would become so spread out through these interactions with the environment that it would become virtually impossible to detect. For all intents and purposes, the original entanglement between photons would have been erased.
Never the less it is truly amazing that these connections do exist, and that carefully arranged laboratory conditions they can be observed over significant distances. They show us, fundamentally, that space is not what we once thought it was. What about time? Page 123, The Fabric of the Cosmo, by Brian Greene
"Yet I exist in the hope that these memoirs, in some manner, 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
So you intuitively believe higher dimensions really exist?
Lisa Randall:I don't see why they shouldn't. In the history of physics, every time we've looked beyond the scales and energies we were familiar with, we've found things that we wouldn't have thought were there. You look inside the atom and eventually you discover quarks. Who would have thought that? It's hubris to think that the way we see things is everything there is.
Second, we must be wary of the "God of the Gaps" phenomena, where miracles are attributed to whatever we don't understand. Contrary to the famous drunk looking for his keys under the lamppost, here we are tempted to conclude that the keys must lie in whatever dark corners we have not searched, rather than face the unpleasant conclusion that the keys may be forever lost.
Two types of the extradimensional effects observable at collides.
So why would it matter to us if the universe has more than 3 spatial dimensions, if we can not feel them? Well, in fact we could “feel” these extra dimensions through their effect on gravity. While the forces that hold our world together (electromagnetic, weak, and strong interactions) are constrained to the 3+1“flat” dimensions, the gravitational interaction always occupies the entire universe, thus allowing it to feel the effects of extra dimensions. Unfortunately, since gravity is a very weak force and since the radius of extra dimensions is tiny, it could be very hard to see any effects, unless there is some kind of mechanism that amplifies the gravitational interaction. Such a mechanism was recently proposed by ArkaniHamed, Dimopoulos, and Dvali, who realized that the extra dimensions can be as large as one millimeter, and still we could have missed them in our quest for the understanding of how the universe works!