Showing posts with label Dimension. Show all posts
Showing posts with label Dimension. Show all posts

Thursday, August 28, 2014

The Extra Dimensions



The weakness of gravity compared to the other subatomic forces is a real mystery. While nobody knows the answer, one credible solution is that gravity has access to more spatial dimensions than the other three known forces. In this video, Fermilab's Dr. Don Lincoln describes this idea, with the help of some very urbane characters. See: Big Mysteries: The Extra Dimensions

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The extra dimensions of string theory which were originally viewed as a source of embarrassment for the theory, have proven to be instrumental in resolving a number of puzzles associated with 3+1 dimensional physics. I discuss examples of this in the context of black holes, gauge theory and particle phenomenology. See: Strings and the Magic of Extra Dimensions - Cumrun Vafa

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Savas Dimopoulos
(link now dead)Here’s an analogy to understand this: imagine that our universe is a two-dimensional 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.

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Sunday, November 17, 2013

The Third Dimension of Cassiopeia A

There are certain advancements when one sees in a geometrical sense as to understand the Supernova in all it's glory. So there are many materialistic things with which we can identify as to the course and direction with regard to it's evolution.

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 X-ray Observatory and a new project from the Smithsonian Institution. A new three-dimensional (3D) viewer, being unveiled this week, will allow users to interact with many one-of-a-kind objects from the Smithsonian as part of a large-scale effort to digitize many of the Institutions objects and artifacts.

Scientists have combined data from Chandra, NASA's Spitzer Space Telescope, and ground-based facilities to construct a unique 3D model of the 300-year 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 open-access program -- a major innovation in digital technologies with public, education, and research-based impacts. See: Exploring the Third Dimension of Cassiopeia A
See Also:

Cassiopeia A: Exploring the Third Dimension of Cassiopeia A



The value of non-Euclidean 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. High-dimensional 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.


Sunday, July 07, 2013

Dimensionality


See:
Cumrun Vafa: Strings and the magic of extra dimensions


 "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
Flat Land: A Romance of Many Dimensions

Again given a framework that is schematically written, how can we lay over top of it, analogies that fit? IN a sense, there is a certain amount of liberation and freedom granted when such schematics are revealed.

The value of non-Euclidean 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


While being revealed as a dimensional foundation, this shows that while being abstract, there is a possible connection to the real world, and that is the work that must take place. Possible connection, may even be written and explain dimensionally?
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 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.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 Kaluza-Klein modes that travel in extra-dimensional 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

Monday, July 16, 2012

Where is Our Starting Point?



"The end he (the artist) strives for is something else than a perfectly executed print. His aim is to depict dreams, ideas, or problems in such a way that other people can observe and consider them." - M.C. Escher


Can you trace the patterns in nature toward matter manifestations?


To them, I said,
the truth would be literally nothing
but the shadows of the images.
-Plato, The Republic (Book VII)

The idea here is about how one's observation and model perceptions arises from some ordered perspective. Some use a starting point as an assumption of position. Do recognize "the starting point" in the previous examples?

 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?"


The effective realization that particle constructs are somehow smaller windows of a much larger perspective fails to take in account this idea that I am expressing as a foundational approach to that starting point.




If you do not go all the way toward defining of that "point of equilibrium" how are you to understand how information is easily transferred to the individual from a much larger reality of existence? One would assume information is all around us? That there are multitudes of pathways that allow us to arrive at some some probability density configuration as some measure of an Pascalian ideal.

Of course there are problems with this in terms of our defining a heat death in individuals?

That's not possible so one is missing the understanding here about equilibrium. I might have said we are positional in terms of the past and the future with regard to memory and the anticipated future? How is that heat death correlated? It can't.

So you have to look for examples in relation to how one may arrive at that beginning point. Your theory may not be sufficiently dealing with the information as it is expressed in terms of your approach to the small window?

There are mathematical inspections here that have yet to be associated with more then discrete functions of reality as expressive building blocks of interpretation. The basic assumption of discrete function still exists in contrast to continuity of expression. This is the defining realization in assuming the model that MBT provides. I have meet the same logic in the differences of scientific approach toward the definition of what is becoming?

On the one hand, a configuration space as demonstrated by Tom that is vastly used in science. On the other, a recognition of how thick in measure viscosity is realized and what the physics is in this association. Not just the physical manifestation of, but of what happens when equilibrium is reached. Hot or very cold. Temperature, is not a problem then?

See my problem is that I can show you levitation of objects using superconductors but I cannot produce this in real life without that science. Yet, in face of that science I know that something can happen irregardless of what all the science said, so I am looking as well to combining the meta with the physical to realize that such a conditions may arise in how we as a total culture have accepted the parameters of our thinking.

So by dealing with those parameters I too hoped to see a cultural shift(paradigm and Kuhn) by adoption of the realization as we are with regard to the way in which we function in this reality. So if your thinking abut gravity how is this possible within the "frame work" to have it encroach upon our very own psychological makeup too?

Monday, May 14, 2012

Questions on the History of Mathematics



Arthur Miller
Einstein and Schrödinger 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.


For most people I am sure it is of little interest that such an abstract language could have ever amounted to anything,since we might have been circumscribed to the natural living that is required that we could do without it. But really,  can we?

 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.

So of course one appreciates those who start the conversation to help raise the questions in ones own mind. Might it be a shared response to something existing deeper in our society that it would warrant descriptions that we might be lacking in. Ways in which to describe something about nature. There is something definitely to be said about the geometer that can visualize the spaces within which they are working. It has to make sense. It has to describe something? Why then not just plain English(whatever language you choose)


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 cutting-edge 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


Conversations on Mind, Matter, and Mathematics

How mathematics arose from cognitive realizations. Ex. Newton and Calculus. The branches of mathematics. Who are it's developers and what did they develop and why?

 It may be as important as the history in relation to how one may perceive the history and development of mathematics. These were important insights into the way one might of asked how did emergence exist if such things could have been imagined in the mind of the beholder. To attempt to describe nature in the way that one might do by invention? So are these mathematical things discovered or are they invented? Why the history is important?

 This is the basis of the question of what already exists in terms of information has always existed and we are only getting a preview of a much more complicated system. It does not have to be a question of what a MBT exemplifies in itself, but raises the questions about what already exists, exists as part of what always existed. Where do ideas and mathematics come from?

This is a foundation stance that is taken right throughout science? If it exists in the universe, it exists in you? How does one connect?


See Also:

WHAT IS YOUR FAVORITE DEEP, ELEGANT, OR BEAUTIFUL EXPLANATION? 

See Also: Some Educational links to look at then.




Sunday, April 15, 2012

Exploring Subtle Levels of Consciouness

 In 2004 I struggled to define the mapping...while speaking in terms of Kaluza/Klein and fifth dimension. Today I am fully aware of the mathematically representation in terms of the use of dimensions.  At the time this was related to spirit.  I was searching for how to describe where ideas came from?

This also forms the basis of my thoughts about geometry.

Betrayal of Images" by Rene Magritte. 1929 painting on which is written "This is not a Pipe"
 
 Betrayal of Images" by Rene Magritte

While a theoretical train of thinking is demonstrated below....subjectively dream information study and my own exploration help to form my thoughts.
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 self-reflective 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]
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Partial map of the Internet based on the January 15, 2005 data found on opte.org. Each line is drawn between two nodes, representing two IP addresses. The length of the lines are indicative of the delay between those two nodes. This graph represents less than 30% of the Class C networks reachable by the data collection program in early 2005. Lines are color-coded according to their corresponding RFC 1918 allocation as follows


Part of the exploration was to understand that we can build models for apprehension and this was my intent since lacking a teacher. I had to think about how knowledge could be held to being truthful within self. So I looked at my tendency with which to class information in an architectural way so as to house that information. As well to understand the meaning of mandalas and how these are housed in our makeup so as to reveal our previous attempts at soul full unification.

Was this tendency within my own self evident in others? Well ultimately recognizing indeed we each are different how is it you have concluded such a sate of mind as to the reason for believing what you do? So this is a conclusive statement for you and a connection to the way in which you will engage the world? Never mind that you will inherently try and describe what is intuitive to you so as to list the attempt at philosophically showing such "a location" as to being inductive/deductive so as to form what is self evident to you? The synapse?

Consider then you are an individual in your own court of justice? Judge and jury about the way in which you conduct yourself? Teacher and student as to the way in which you will acquire knowledge in life? Who will you look for so as to find these truths, but not to recognize as a soul that you will acquire these truths as a progress of your desire to be truthful? To evolve? How will you weight these things?

Historically then, I built a pyramid. The geometric proportions were to show how we can internalize and house information about ourselves. Early lessons were to understand that ancient minds were locked toward thinking about "lines of light and shadows" so as to direct this line to point toward other things?


Philosophically to me, "line of shadow and light" were in itself demonstrative of this idea of a geometrical explanation to how we might explain our first attempts at "components of that reality?" The sun had to be a source of inspiration?

Is the sun a centralize thing in our own being so as to say that our expressive lives are now the objects of reality? Is this en tropically pleasing to you? So how do you touch that source? How do you align yourself internally?

In that exploration, this was the ultimate realization. Some may describe it as an epilepsy while sensing/feeling this electricity that runs through you? How powerful a motivator so as to describe that in each of us such an alignment can take place?

Wednesday, January 04, 2012

Quasicrystal: Prof. Dan Shechtman



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 six-fold rotational symmetries, the Bragg diffraction pattern of quasicrystals shows sharp peaks with other symmetry orders, for instance five-fold.

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 non-periodic 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 three-dimensional 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 long-range 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 extra-terrestrial in origin, possibly delivered to Earth by a CV3 carbonaceous chondrite asteroid.[7]

240 E₈ polytope vertices using 5D orthographic_projection to 2D using 5-cube (Penteract) Petrie_polygon basis_vectors overlaid on electron diffraction pattern of an Icosahedron Zn-Mg-Ho Quasicrystal.

Monday, November 28, 2011

History of Supersymmetry to Today

Special Topic of Supersymmetry

by 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.

Also: What's Inside ScienceWatch.com This Month - ScienceWatch.com - Thomson Reuters



 Update-

See Also :

Monday, November 14, 2011

Two Dimensions

A diagram showing the first four spatial dimensions.

 The concept of dimension is not restricted to physical objects. High-dimensional 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.
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Big Bang, Classic Confusions-

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 4-dimensional object and goes beyond our senses. What we can visualize, however, is a hypersphere in the form of 3-dimensional 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
π r2
2πr
3
sphere
(4/3)π r3
4πr2
4
4-sphere
(1/2)π2 r4
2 r3
5
5-sphere
(8/15)π2 r5
(8/3)π2 r4
6
6-sphere
(1/6)π3 r6
π3 r5
7
7-sphere
(16/105)π3 r7
(16/15)π3 r6


See: Spacetime 101

Tuesday, August 16, 2011

Another Kind of Sideways

 I wanted to expand on where the title,"Another Kind of Sideways." This blog posting  came from an interview with Clifford of Asymptotia by PBS. He had a posting of his own entitled Multiverse Musings about a Nova series on PBS in the Fall related to Brian Greene's book, The Fabric of the Cosmos.

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 four-dimensional 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

The whole context of the idea of the Multiverse could have in my layman view be classified as speaking about and argued as the basis of "existing outside of time." I just wanted to say that mathematically this definition of the Multiverse can actually exist in that framework, yet had to be extrapolated to the real universe we live in and how other universes may apply.


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


I am always interested in the way a correlation is struck, from a scientist's mind when looking at the world and the comparisons they may find in the real world. I mean, to stand on top of a mountain as I did, you get this sense of the terrain, and how the landscape appears. How from an idealist position, a mathematical position is described and how the universe can be described?

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 re-search 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.

I find it hard sometimes to try and explain something that is "not outside of time."  That such description of reality while confounding to those like me less able to understand the mathematical world of such truths that contrary to Lee Smolin's opinion such schematics can be found to exist "within each of us." How we build our world from the inside, and how we contain it.

Is the mathematical description of  polytopes any less real as a mathematical basis?

If one is to believe that a mountain top represents some "perfect symmetry" then what said all those places in the valleys can exist and would not represent some genus figure? What are we saying about the possible universes, locations within the universe,  and the creation of?

That a pencil standing on point, could fall one way or another, or a description of a false vacuum to a true could represent something leading away from such symmetry? Why the problem with such mathematical and schematize attributes? Would you as a scientist turn your back on such mathematical interpretations of the world?

Tuesday, February 17, 2009

Nature is the Architect

.....and we are it's builders?



So beyond indeed, is the static realization of the structure of things. This is a more definable recognition of something that is very fluid and expressive. It is by our own humanistic natures that we like to compartmentalize?

"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)


While this quote of Einstein is somewhat revealing of what can flash across the mind, it is by intense work that such a time allows for things to gather, and in this work, it will inevitable makes sense. Such cultivation allows for new things to be born and in such nurture and contemplation, something will eventually emerge.

A picture of flux lines in QED (left) and QCD (right).
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

This points to a reductionistic view about the nature of reality. That we are part and parcel creating the constituents of the reality that we see, has a glue that binds, and keeps it together. For each this glue is a process that has meaning for each of us. While one would wonder where such motivation would allow each to perceive it as so one might ask what value is assign each stage of expression to see that such a scale has been reduce to a quality of a kind? It's music?


Cover of Hiding in the Mirror: The Mysterious Allure of Extra Dimensions, from Plato to String Theory and Beyond by Lawrence M. Krauss
Viking Press



Guide Review - Hiding in the Mirror by Lawrence Krauss
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.
See:Book Review: Hiding in the Mirror

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See Also:

  • Where are my keys?
  • So string theory is, among many other things, a theory of gravity!
  • EOT-WASH GROUP(4)
  • Friday, January 23, 2009

    It's Reason for Being

    See:Central Theme is the Sun

    When looking at the entropic valuation of the way the universe one can just plainly accept the insight that heat when cooled can manifest the objects of that reality. Just simply accept this without thinking about it's finer dispositions?

    Infinite regress is limited by the very logic presented, and any intention that such probability will play an important part in the outcome. You have to have a lot of information to be able to do this. Pattern recognition then accepts some foundational need for interpretation other then, what one assumes is the basis of the argument, which also is constraint by that limitation.

    Plants soak up some of the 1017 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 near-perfect efficiency.
    See: When It Comes to Photosynthesis, Plants Perform Quantum Computation

    While the life cycle is readily apparent, it does not explain the potential nor the expression of how this "motivation came into being." That one can say that there is the subtle and then the gross, and think this is the nature of the world. That by rubbing one's hands and creating friction and heat, they have somehow supplanted the idea as a question about the world and wonder where information fits in. Somehow having the idea of starting a fire "with a cylinder shape," somehow deeper defines the meaning of that question about the information then just hands rubbing. That cylinder, is a measure of the strings value.



    So the hand rubbing becomes a thing of the world in its scientific notation as the basis of interpretation. One wonders then, how indeed such a thought came to them and thusly, to have express itself as a model of acceptance. We have thusly define the idea in this context of information as something that rests in the probabilistic expression, and that the ideal is something that manifests from such a field of probabilities. The nature here then, is that "any idea has a much finer disposition" then what the ideal represents in reality.


    Probabilties
    (The Fifth Dimension)
    |
    |
    Idea of the pipe
    / \
    / \
    / \
    Picture of the pipe
    / \
    / \
    / \
    The real pipe and form
    See:Betrayal of Images" by Rene Magritte

    ***


    See:
  • Time Travel in the Quantum Harmonic Oscillator
  • Fear and Ignorance
  • Central Theme is the Sun
  • Saturday, November 17, 2007

    Self Evident Dimensional Perspective

    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


    John Merryman in comment section:
    Can they propose these dimensions as anything more then the copyrighted product of their own imagination and not loose control over the idea?


    Okay I have a problem with the term "static."

    I'll just give you an example of what I am thinking in relation to how we may perceive dimension and then of course, there is a mathematical interpretation of topological spaces that others are better qualified to speak on. How could there be such a geometrical interpretation at such quantum levels.

    Is there such thing as "a breakdown of time" within the context of measure? It is my ignorance that separates me from the more educated here, yet it is not without wanting to understand, that I am pushing this point further.

    Think about the following concept for a moment.

    Savas Dimopoulos:

    Here’s an analogy to understand this: imagine that our universe is a two-dimensional 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.


    Here we are given a new look into another dimension? A shift from what is euclidean, to what is now non-euclidean. It is really quite simple to understand "what Einstein did" when we now talk about gravity.




    Juan Maldacena:

    Strings existing in the five-dimensional space-time can even look point-like when they are close to the boundary. Polchinski and Strassler1 show that when an energetic four-dimensional 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 point-like object. So a string-like interpretation of a proton is not at odds with the observation that there are point-like objects inside it.


    While it is abstract, the move to thinking in the new way is important while we are looking at the whole picture.

    Albert Einstein

    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


    There are deeper philosophical questions here about being a realist and an anti-realist.?

    René Thom

    See:René Thom:René Thom (September 2, 1923 – October 25, 2002) was a French mathematician. He made his reputation as a topologist, moving on to aspects of what would be called singularity theory; he became celebrated for one aspect of this latter interest, his work as founder of catastrophe theory (later developed by Christopher Zeeman). He received the Fields Medal in 1958.



    Photograph by Paul Halmos

    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.

    Tuesday, April 03, 2007

    The Elixir of the Bee Community

    You should know that that the names of the Bee people have their names protected, to protect the community at large. Some larger human species, like to use the benefits of this society, without recognizing the constructive efforts that goes into this elixir Production.

    Marc D. Hauser:

    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.


    See Bumblebee Wing Rotations and Dancing

    Many times people have used Ant world to illustrate their ideas, but the time has come, that the relationship to perspective dynamics at that level should think about the vast literature of Bee people.

    The second of five Lagrangian equilbrium points, approximately 1.5 million kilometers beyond Earth, where the gravitational forces of Earth and Sun balance to keep a satellite at a nearly fixed position relative to Earth.

    See Second of Five Lagrangian Equilibrium Points

    One should not think these people have been disassociated from reality, and that it has only been our ignorance of the economics and flight patterns, that we failed to see the dynamical community that bee propagation goes through, in order to continue it's rich development. The elixir production is coming out of that community.

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

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


    See Solidification of Geometrical Presence

    Flower pollination is a interesting thing having considered the world that the Bee people live in. After all, the dynamics and travel used, one could not help being enamoured with the naturalness with which one may try to reproduce in human mechanistic movement, that the Bee people live and breathe.

    Humanistic intelligences is a larger format, to what they do in that Bee community?

    Cell construction provides for the further propagation of the community, but no where do the Bee people give the particulates of the cell construction? Humanistic intelligences only see the community with regards to the Bee movements :)The Bee people have a greater depth to what is seen.

    Observing the community at large, the Bee people have much more to present then thinking just in the way they work. Who is Navier Stokes of the humanistic intelligences to think only he could reveal anomalistic perception in the nature of viscosity, not to think there is relativistic conditions that the Bee people bring to reductionism views in physics?

    Worker bees perform a host of tasks from cleaning the hive cells to looking after the larvae
    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.


    So I've taken a different tack here. If it is so hard for the community at large to comprehend that extra dimensional thinking then there has to be some way in which we as lay people can envision the acrobatics of a busy bee and their flight plans? What the community is all about. Who is doing what?

    How many dimensions are there?

    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 3-dimensional space called 3-brane (a name generalizing 2-brane, i.e., membrane). For some reason, we (i.e., atoms, molecules, photons etc.) are stuck in this 3-brane, 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.


    The Bee people had graduated from the world of the ant people, jsut by their evolutionary timeline. They were "much more visionary" then the ant people. Because they could leave their three dimensional world of the table top, and pop into ant world's frame of reference. Ant people were never the wiser. Just that, Bee people existed.

    Providing a rigorous theoretical framework that incorporates both recent developments such as Aubrey-Mather theory and established fundamentals like Kolmogorov-Arnold-Moser theory, this book represents an indispensable resource for graduate students and researchers in the disciplines concerned as well as practitioners in fields such as aerospace engineering.

    See Wolf-Rayet star

    Brane theory development needed a boost from the Bee people. Not only now do we understand the "dynamical thinking that goes with the Bee's flight patterns," we are now thinking, hey, "can these things apply" to the current solutions the humanistic intelligences persevere to unfold in their space travels?

    Not just "our waist lines" as some might think in regards to "lensing" and the circles we apply in "computerize efforts." The range of territory of the Bee's community is well considered?

    Sunday, February 25, 2007

    The Colour of Gravity

    I am not sure how this post is to unfold, yet in my mind different exercises were unfolding as to how I should explain it. Can I come from an artist's perspective I wondered? Say "by chance" anything that seems relevant here in writing, and any relation to science "is" metaphorical by nature?

    Yellow, Red, Blue
    1925; Oil on canvas, 127x200cm; Centre Georges Pompidou, Paris


    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, time-consuming 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.

    Does one want to gleam only what is coming across in geometrical form as a painting without understanding the depth of the artist in expression? Some may say, why any association at all, and just leave science to what it knows best without implicating any theoretical positions with the thought pertaining to gravity here.

    Yes that's why I selected the title of this post as thus, and why I am going to give perspective to what I may, "as artist in writing" see with these words, and then you decide whether it is useful to you.

    The Field as the Plane

    An ancient thought penetrated my thinking as I thought of "the field" that a society can work in agriculture, and yet, by definition it was the plane, "length and width" that was also appealing here. I did not want to loose it's "origination" while I moved any thinking to the "abstract of brane" and the like, without firmly attaching it to the ground.

    But who was to know that this plane could be moved to any "fifth dimensional understanding" without having studied the relationship to dimensional thinking and the like. The physics elevated.

    I allow this one time escapism to "other thinking" to demonstrate what use the colour of gravity implies while at the same time "theoretical positions" talk about it's place in the universe. If one did not accept the moves in science and the way it expressed itself to allow geometrical inclination, then how the heck could non-euclidean thinking ever make it's way into how we will discuss "the fields" about us?

    It meant that a perspective "on height" be adopted? As an observer I was watching from a position. While in that sleeping/dosing state, I wondered how else to express myself as these concepts were amalgamating themselves into a "conceptual frame of reference?"

    The picture of the field(I am referring to the ancient interpretation) continued in my mind, and "by abstract" I thought to introduce a line extend from the centre of this field upward. So here I am looking at this field before me. Now I had wondered off previous by bring "the brane" in here, yet is not without that sight I thought how the heck could any idealization so ancient make sense to what the colour of gravity to mean.

    Title page of Opticks .... by Sir Isaac Newton, 1642-1727. Fourth edition corrected by the author's own hand, and left before his death with the bookseller. Published in 1730. Library call number QC353 .N48 1730.

    So "an idea" came to mind.

    While correlating Newton's work here and the "extra dimensional thinking," I also wanted to include the work of the "Alchemist Newton". "To expand" the current thinking of our "emotive states" as a "vital expression of the biological being."

    Draw into any further discussion of the "philosophical or other wise," these views of mine which are a necessary part of what was only held to a "religious and uneducated evolutionary aspect of the human being."

    A cosmologist may still say that such thoughts of Einstein used in this vain is wrong, but I could never tear myself away from the views of "durations of time."

    Colour Space and Colour Theory

    The CIE 1931 colour space chromaticity diagram with wavelengths in nanometers. Note that the colors depicted depend on the color space of the device on which you are viewing the image.

    So by having defined the "frame of reference," and by introducing "Colour of gravity" I thought it important and consistent with the science to reveal how dynamical any point within that reference can become expressive. The history in association also important.

    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 so-called primary colors. From there it developed as an independent artistic tradition with only sporadic or superficial reference to colorimetry and vision science.


    So you tend to draw on your reserves for such comparatives while thinking about this. I knew to apply "chemical relations" to this idea, and the consequential evidenced, by the resulting shadings by adding. I wanted to show "this point" moving within this colour space and all the time it's shading was describing the "nature of the gravity."

    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


    By adding that vertical line in the field, the perimeter of my field of vision had to some how be drawn to an apex, while all kinds of thoughts about symmetry and perfection arose in my pyramidal mind.

    All these colours, infinite in their ability to express the human emotive state, as a consequence of philosophical and expressed as function of the emotive being?

    CIE 1976 L*, a*, b* Color Space (CIELAB)

    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.


    Entanglement

    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


    So many factors to include here, yet it is with the "idea of science" that I am compelled to see how things can get all mixed up, while I say emotive state, or Colours of gravity?

    It gets a little complicated for me here, yet the "Fuzzy logic" introduced or "John Venn's logic" is not without some association here. Or, the psychology I had adopted as I learnt to read of models and methods in psychology that could reveal the thinking we have developed, and what it included.

    Least I forget the "real entanglement" issues here, I have painted one more aspect with the "Colour of Gravity" to be included in this dimensional perspective, as we look to the models in science as well?

    Working from basic principles and the history of spooky has made this subject tenable in today's world. A scientist may not like all the comparisons I have made based on it, I could never see how the emotive and mental statements of the expressive human being could not have been included in the making of the reality.

    That I may of thought the "perfection of the human being" as some quality of the God in us all, would have granted sanction to some developing view of "religious virtuosity," against the goals of the scientist. So as ancient the views painted, there was something that may have been missed of the "Sensorium," and goes toward the basis of the philosophy shared currently by Lee Smolin.

    This entanglement to me is a vital addition to our exploration of the universe. Our place and observation within it? It did not mean to discount our inclusion within it, within a larger "oscillatory perspective."

    Friday, February 23, 2007

    Where are my keys?

    "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




    The Extra-Dimensions?


    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.


    And what is it that we don't see? I thought of a comment somewhere that spoke about what first started to make it's appearance in how we communicate?

    Time is the Unseen fourth Dimension

    They were able to create what we recognize today as the "elliptical" and "hyperbolic" non-Euclidean geometries. Most of Saccheri's first 32 theorems can be found in today's non-Euclidean textbooks. Saccheri's theorems are prefaced by "Sac."

    One of my greatest "aha moments" came when I realized Non-euclidean geometries. I had to travel the history first with Giovanni Girolamo Saccheri, Bolya and Lobachevsky, for this to make an impression, and I can safely say, that learning of Gauss and Riemann, I was truly impressed.

    Einstein had to include that "extra dimension of time." Greater then, or less then, 180 degrees and we know "this triangle" can take on some funny shapes when you apply them "to surfaces" that are doing funny things.?:)



    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.


    Let me just say that "it is not the fact that any drinking could have held the mind" of the person, but when they absentmindedly threw their car keys. The "point is" that if the light shines only so far, what conclusion should we live with?

    Moving to the Fifth

    So of course whatever real estate you are buying, make sure the light is shining on what your willing to purchase? Is this not a good lesson to learn?

    Moving any idea to a fifth dimension I thought was important in relation to seeing what Einstein had done. See further: Concepts of the Fifth Dimension. I illustrate more ways in which we may see that has not been seen for most could have helped the mind see how this is accomplished in current day geometric methods.

    Why was this thought "wrong" when one may of thought to include "gravity and light" together, after the conclusion of spacetime's 3+1? Gravity. What Had Maxwell done? What Had Riemann done?

    You knew "the perfect symmetry" had to be reduced to General Relativity?

    Greg Landsberg:
    Two types of the extra-dimensional effects observable at collides.



    A graviton leaves our world for a short moment of time, just to come back and decay into a pair of photons (the DØ physicists looked for that particular effect).

    A graviton escapes from our 3-dimensional world in extra dimensions (Megaverse), resulting in an apparent energy non-conservation in our three-dimensional world.
    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 Arkani-Hamed, 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!


    Of course these ideas are experimentally being challenged, like any good scientist would want of his theory. See EOT-WASH GROUP(4)