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Showing posts with label Projective Geometry. Show all posts
Showing posts with label Projective Geometry. Show all posts
Monday, December 12, 2016
Step Inside the Perimeter
Saturday, February 08, 2014
Tuesday, January 22, 2013
Materialism/Physicalism
In philosophy, the theory of materialism holds that the only thing that exists is matter or energy; that all things are composed of material and all phenomena (including consciousness) are the result of material interactions. In other words, matter is the only substance, and reality is identical with the actually occurring states of energy and matter.
To many philosophers, 'materialism' is synonymous with 'physicalism'. However, materialists have historically held that everything is made of matter, but physics has shown that gravity, for example, is not made of matter in the traditional sense of "'an inert, senseless substance, in which extension, figure, and motion do actually subsist'… So it is tempting to use 'physicalism' to distance oneself from what seems a historically important but no longer scientifically relevant thesis of materialism, and related to this, to emphasize a connection to physics and the physical sciences."^{[1]} Therefore much of the generally philosophical discussion below on materialism may be relevant to physicalism.
Also related to materialism are the ideas of methodological naturalism (i.e. "let's at least do science as though physicalism is true") and metaphysical naturalism (i.e. "the physical world is all that exists").
Contrasting philosophies include idealism, other forms of monism, dualism, and pluralism.
Defining matter
The nature and definition of matter - like other key concepts in science and philosophy - have occasioned much debate.^{[12]} Is there a single kind of matter (hyle) which everything is made of, or multiple kinds? Is matter a continuous substance capable of expressing multiple forms (hylomorphism),^{[13]} or a number of discrete, unchanging constituents (atomism)?^{[14]} Does it have intrinsic properties (substance theory),^{[15]}^{[16]} or is it lacking them (prima materia)?
One challenge to the traditional concept of matter as tangible "stuff" came with the rise of field physics in the 19th century. Relativity shows that matter and energy (including the spatially distributed energy of fields) are interchangeable. This enables the ontological view that energy is prima materia and matter is one of its forms. On the other hand, the Standard Model of Particle physics uses quantum field theory to describe all interactions. On this view it could be said that fields are prima materia and the energy is a property of the field.
See Also:
Tuesday, January 08, 2013
Visible Earth
http://visibleearth.nasa.gov/ (Click on Image for Larger Viewing) |
See Also:
- Blue Marble Navigator
- Spaceship Earth: Who Is In Control?
- http://www.overviewinstitute.org/
- http://www.overviewthemovie.com/
Saturday, September 15, 2012
Noncommutative standard model
In theoretical particle physics, the non-commutative Standard Model, mainly due to the French mathematician Alain Connes, uses his noncommutative geometry to devise an extension of the Standard Model to include a modified form of general relativity. This unification implies a few constraints on the parameters of the Standard Model. Under an additional assumption, known as the "big desert" hypothesis, one of these constraints determines the mass of the Higgs boson to be around 170 GeV, comfortably within the range of the Large Hadron Collider. Recent Tevatron experiments exclude a Higgs mass of 158 to 175 GeV at the 95% confidence level.^{[1]} However, the previously computed Higgs mass was found to have an error, and more recent calculations are in line with the measured Higgs mass. ^{[2]}
Contents |
Background
Current physical theory features four elementary forces: the gravitational force, the electromagnetic force, the weak force, and the strong force. Gravity has an elegant and experimentally precise theory: Einstein's general relativity. It is based on Riemannian geometry and interprets the gravitational force as curvature of space-time. Its Lagrangian formulation requires only two empirical parameters, the gravitational constant and the cosmological constant.
The other three forces also have a Lagrangian theory, called the Standard Model. Its underlying idea is that they are mediated by the exchange of spin-1 particles, the so-called gauge bosons. The one responsible for electromagnetism is the photon. The weak force is mediated by the W and Z bosons; the strong force, by gluons. The gauge Lagrangian is much more complicated than the gravitational one: at present, it involves some 30 real parameters, a number that could increase. What is more, the gauge Lagrangian must also contain a spin 0 particle, the Higgs boson, to give mass to the spin 1/2 and spin 1 particles. This particle has yet to be observed, and if it is not detected at the Large Hadron Collider in Geneva, the consistency of the Standard Model is in doubt.
Alain Connes has generalized Bernhard Riemann's geometry to noncommutative geometry. It describes spaces with curvature and uncertainty. Historically, the first example of such a geometry is quantum mechanics, which introduced Heisenberg's uncertainty relation by turning the classical observables of position and momentum into noncommuting operators. Noncommutative geometry is still sufficiently similar to Riemannian geometry that Connes was able to rederive general relativity. In doing so, he obtained the gauge Lagrangian as a companion of the gravitational one, a truly geometric unification of all four fundamental interactions. Connes has thus devised a fully geometric formulation of the Standard Model, where all the parameters are geometric invariants of a noncommutative space. A result is that parameters like the electron mass are now analogous to purely mathematical constants like pi. In 1929 Weyl wrote Einstein that any unified theory would need to include the metric tensor, a gauge field, and a matter field. Einstein considered the Einstein-Maxwell-Dirac system by 1930. He probably didn't develop it because he was unable to geometricize it. It can now be geometricized as a non-commutative geometry.
See also
- Noncommutative geometry
- Noncommutative quantum field theory
- Timeline of atomic and subatomic physics
Notes
References
- Alain Connes (1994) Noncommutative geometry. Academic Press. ISBN 0-12-185860-X.
- -------- (1995) "Noncommutative geometry and reality," J. Math. Phys. 36: 6194.
- -------- (1996) "Gravity coupled with matter and the foundation of noncommutative geometry," Comm. Math. Phys. 155: 109.
- -------- (2006) "Noncommutative geometry and physics,"
- -------- and M. Marcolli, Noncommutative Geometry: Quantum Fields and Motives. American Mathematical Society (2007).
- Chamseddine, A., A. Connes (1996) "The spectral action principle," Comm. Math. Phys. 182: 155.
- Chamseddine, A., A. Connes, M. Marcolli (2007) "Gravity and the Standard Model with neutrino mixing," Adv. Theor. Math. Phys. 11: 991.
- Jureit, Jan-H., Thomas Krajewski, Thomas SchÃ¼cker, and Christoph A. Stephan (2007) "On the noncommutative standard model," Acta Phys. Polon. B38: 3181-3202.
- SchÃ¼cker, Thomas (2005) Forces from Connes's geometry. Lecture Notes in Physics 659, Springer.
External links
Update:
Monday, January 09, 2012
Loci: A Gallery of Ray Tracing for Geometers
The crystalline state is the simplest known example of a quantum , a stable state of matter whose generic low-energy properties are determined by a higher organizing principle and nothing else. Robert Laughlin
Figure 10 with linked animation: Five-fold rotational symmetry of the dodecahedron |
Modern expositors of mathematics, with computers and open source ray tracing software at their disposal, have the tools necessary to create vivid and effective geometric constructions in 3-space. With a little additional effort, animations can be generated, adding the fourth dimension of time. The web provides a viable medium for enhancing mathematical presentations with photo-realistic graphics and video. A Gallery of Ray Tracing for GeometersSee Also: Creating Photo-realistic Images and Animations
Tuesday, November 22, 2011
The Body Canvas
Let no one destitute of geometry enter my doors." |
Who would have known about the distinction I had thought only myself could bare the artistic rendition of a thought processes that had unfurled in my own expressive way many others had expressed. Yes I had seen students of science with qualitative formulas tattooed over their body....but it becomes personal when you hold the idea of the Body Canvas to iterate something you believe in. So, for the rest of your life?
See Also: Science Tattoo Emporium
In 2007, Carl Zimmer posed a question on his blog: are scientists hiding tattoos of their science? It turned out that many of them were, and they were willing to share their ink with him and the world. Zimmer has posted hundreds of these images in the years since. In Science Ink, he assembles his favorite images from his blog, along with previously unpublished ones, and writes about the science behind the pictures, and the scientists behind the science. From archaeology to astronomy, from neuroscience to chemistry, Science Ink is a guide to the universe, illustrated on the bodies of scientists. See: Carl Zimmer on Science Ink
So for me it didn't matter anymore, but then I thought how can one remain in anonymity if one helps to identify it's owner(have I really released previous convictions)? So tattooing for me was more about the way in which your tattoo is depicted, then on how beautiful designs can be relabeled, or new ones drawn and located on. The story for me is truly fascinating and I found it so for those not knowing.
Carl Zimmer
Contents |
Career
Besides his popular science writing, Zimmer also gives frequent lectures, and has been on many radio shows, including National Public Radio's Fresh Air and This American Life. His most recent award was a 2007 prize for science communication^{[1]} from the United States National Academy of Sciences, for his wide-ranging and fascinating coverage of biology and evolution in newspapers, magazines and his internet blog "The Loom". Since 11 November 2009 (episode 35) he is host of the periodic audio podcast Meet the Scientist of the American Society for Microbiology (replacing Merry Buckley).Zimmer received his B.A. in English from Yale University in 1987, and began freelance writing for Natural History magazine. In 1989, Zimmer started at Discover magazine, first as a copy editor and fact checker, eventually becoming a contributing editor.^{[2]}
Tuesday, December 04, 2007
Descriptive geometry
At this point in the development, although geometry provided a common framework for all the forces, there was still no way to complete the unification by combining quantum theory and general relativity. Since quantum theory deals with the very small and general relativity with the very large, many physicists feel that, for all practical purposes, there is no need to attempt such an ultimate unification. Others however disagree, arguing that physicists should never give up on this ultimate search, and for these the hunt for this final unification is the ‘holy grail’. Michael Atiyah
The search for this "cup that overflow" is at the heart of all who venture for the lifeblood of the mystery of life. While Atiyah speaks to a unification of Quantum theory and Relativity, it is not without a understanding on Einstein's part that having gained from Marcel Grossmann, that such a descriptive geometry could be leading Einstein to discover the very basis of General relativity?
Marcel Grossmann was a mathematician, and a friend and classmate of Albert Einstein. He became a Professor of Mathematics at the Federal Polytechnic Institute in Zurich, today the ETH Zurich, specialising in descriptive geometry.
So what use "this history" in face of the unification of the very large with the very small? How far back should one go to know that the steps previous were helping to shape perspective for the future. Allow for perspective to be changed, so that new avenues of research could spring forth
Gaspard Monge, Comte de PÃ©luse-Portrait by Naigeon in the MusÃ©e de Beaune Born: 9 May 1746 in Beaune, Bourgogne, France
Died: 28 July 1818 in Paris, France-was a French mathematician and inventor of descriptive geometry.
Monge contributed (1770–1790) to the Memoirs of the Academy of Turin, the MÃ©moires des savantes Ã©trangers of the Academy of Paris, the MÃ©moires of the same Academy, and the Annales de chimie, various mathematical and physical papers. Among these may be noticed the memoir "Sur la thÃ©orie des dÃ©blais et des remblais" (MÃ©m. de l’acad. de Paris, 1781), which, while giving a remarkably elegant investigation in regard to the problem of earth-work referred to in the title, establishes in connection with it his capital discovery of the curves of curvature of a surface. Leonhard Euler, in his paper on curvature in the Berlin Memoirs for 1760, had considered, not the normals of the surface, but the normals of the plane sections through a particular normal, so that the question of the intersection of successive normals of the surface had never presented itself to him. Monge's memoir just referred to gives the ordinary differential equation of the curves of curvature, and establishes the general theory in a very satisfactory manner; but the application to the interesting particular case of the ellipsoid was first made by him in a later paper in 1795. (Monge's 1781 memoir is also the earliest known anticipation of Linear Programming type of problems, in particular of the transportation problem. Related to that, the Monge soil-transport problem leads to a weak-topology definition of a distance between distributions rediscovered many times since by such as L. V. Kantorovich, P. Levy, L. N. Wasserstein, and a number of others; and bearing their names in various combinations in various contexts.) A memoir in the volume for 1783 relates to the production of water by the combustion of hydrogen; but Monge's results had been anticipated by Henry Cavendish.
Descriptive geometry
Example of four different 2D representations of the same 3D object
Descriptive geometry is the branch of geometry which allows the representation of three-dimensional objects in two dimensions, by using a specific set of procedures. The resulting techniques are important for engineering, architecture, design and in art. [1] The theoretical basis for descriptive geometry is provided by planar geometric projections. Gaspard Monge is usually considered the "father of descriptive geometry". He first developed his techniques to solve geometric problems in 1765 while working as a draftsman for military fortifications, and later published his findings. [2]
Monge's protocols allow an imaginary object to be drawn in such a way that it may be 3-D modeled. All geometric aspects of the imaginary object are accounted for in true size/to-scale and shape, and can be imaged as seen from any position in space. All images are represented on a two-dimensional drawing surface.
Descriptive geometry uses the image-creating technique of imaginary, parallel projectors emanating from an imaginary object and intersecting an imaginary plane of projection at right angles. The cumulative points of intersections create the desired image.
So given the tools, we learnt to see how objects within a referenced space, given to such coordinates, have been defined in that same space. Where is this point with in that reference frame?
What is born within that point, that through it is emergent product. Becomes a thing of expression from nothing? It's design and all, manifested as a entropic valuation of the cooling period? Crystalline shapes born by design, and by element from whence it's motivation come? An arrow of time?
Sunday, December 02, 2007
Projective 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.
It is always important to see the progression geometries follow. So you have to know "the origins of geometry" before you can begin to expand into the abstract spaces that space will allow and accomadate.
Eventually it was discovered that the parallel postulate is logically independent of the other postulates, and you get a perfectly consistent system even if you assume that parallel postulate is false. This means that it is possible to assign meanings to the terms "point" and "line" in such a way that they satisfy the first four postulates but not the parallel postulate. These are called non-Euclidean geometries. Projective geometry is not really a typical non-Euclidean geometry, but it can still be treated as such.
In this axiomatic approach, projective geometry means any collection of things called "points" and things called "lines" that obey the same first four basic properties that points and lines in a familiar flat plane do, but which, instead of the parallel postulate, satisfy the following opposite property instead:
The projective axiom: Any two lines intersect (in exactly one point).
Monday, November 26, 2007
Gino Fano
Gino Fano (5 January 1871 - 8 November 1952) was an Italian mathematician. He was born in Mantua, Italy and died in Verona, Italy.
Fano worked on projective and algebraic geometry; the Fano plane and Fano varieties are named for him.
Ugo Fano and Robert Fano were his sons.
There are reasons with which I wanted to share information about this gentlemen. What has been written in context of "finite geometry." You must know I am never the expert, but one who aspires to learn what is needed to learn and understand what is happening with regards to model presented by Garrett Lisi.
You must know that my mind thinks in abstract spaces and is involved in a wide range of variables expressed in terms of the dimensional attributes of actions within that space.
Diagram of the Fano plane
In finite geometry, the Fano plane (after Gino Fano) is the projective plane with the least number of points and lines: 7 each.
See: Elements of Finite Geometry
Fano worked on projective and algebraic geometry; the Fano plane and Fano varieties are named for him.
Ugo Fano and Robert Fano were his sons.
There are reasons with which I wanted to share information about this gentlemen. What has been written in context of "finite geometry." You must know I am never the expert, but one who aspires to learn what is needed to learn and understand what is happening with regards to model presented by Garrett Lisi.
You must know that my mind thinks in abstract spaces and is involved in a wide range of variables expressed in terms of the dimensional attributes of actions within that space.
Diagram of the Fano plane
In finite geometry, the Fano plane (after Gino Fano) is the projective plane with the least number of points and lines: 7 each.
See: Elements of Finite Geometry
Saturday, March 31, 2007
Great Pyramid was built inside out, Frenchman says
Man ponders shadow, or shadow ponders itself?
Great Pyramid of Giza was the world's tallest building from c. 2570 BC to c. 1300 AD.†
For me, this has always been somewhat of an interest of mine. I'll tell a little bit of why this is so as well. Give you some ideas about what the pyramid represents to me and then of course you can add your own theories like anyone one else does, who has a similar interest.
Great Pyramid of Giza. From a 19th century stereopticon card photo
Given the "artifact of the structure," we like to inject our own ideas about things. Stand amazed, as if "on the site" we are some how transported back in time to the history that must be recorded some place?
I would just as soon turn on the television of the event linked in some "physics way" then on the psychometry subjectively induced perceptions that can be held. We would have to remove "our bias" in place of "the connection" not understood.
Will We Travel Back (Or Forward) in Time? by RICHARD GOTT III
Einstein proved we can travel forward by moving near light speed. Backward requires a wormhole, cosmic string and a lot of luck
Do the laws of physics permit time travel, even in principle? They may in the subatomic world. A positron (the antiparticle associated with the electron) can be considered to be an electron going backward in time. Thus, if we create an electron-positron pair and the positron later annihilates in a collision with another, different electron, we could view this as a single electron executing a zigzag, N-shaped path through time: forward in time as an electron, then backward in time as a positron, then forward in time again as an electron.
When I think of Ronald Mallet and the time travel issue, I like to think of what history can show in it's most intimate moments. That it could place a spell upon us as "a window" to that past. You must know of my attempts at the cosmology used to discern gamma ray detection and the depth perception "enhanced" using that method.
The Window to our past becomes much clearer as time in science also progresses.
Signal Travels Farther and Faster Than Light By MALCOLM W. BROWNE
Another deep quantum mystery for which physicists have no answer has to do with "tunneling" -- the bizarre ability of particles to sometimes penetrate impenetrable barriers. This effect is not only well demonstrated; it is the basis of tunnel diodes and similar devices vital to modern electronic systems.
Tunnelling is based on the fact that quantum theory is statistical in nature and deals with probabilities rather than specific predictions; there is no way to know in advance when a single radioactive atom will decay, for example.
The probabilistic nature of quantum events means that if a stream of particles encounters an obstacle, most of the particles will be stopped in their tracks but a few, conveyed by probability alone, will magically appear on the other side of the barrier. The process is called "tunnelling," although the word in itself explains nothing.
So anyway, many theories arise as to how it was constructed. That is not my concern at this time, although, I show the latest in the news. It is more about the geometry that exists, and what I think this model is used for?
Great Pyramid was built inside out, Frenchman saysBy Tim Hepher, Reuters Fri Mar 30, 2007 12:20PM EDT
PARIS (Reuters) - A French architect said on Friday he had cracked a 4,500-year-old mystery surrounding Egypt's Great Pyramid, saying it was built from the inside out.
Previous theories have suggested Pharaoh Khufu's tomb, the last surviving example of the seven great wonders of antiquity, was built using either a vast frontal ramp or a ramp in a corkscrew shape around the exterior to haul up the stonework.
But flouting previous wisdom, Jean-Pierre Houdin said advanced 3D technology had shown the main ramp which was used to haul the massive stones to the apex was contained 10-15 meters beneath the outer skin, tracing a pyramid within a pyramid.
Map of the Giza Pyramid complex
So of course in order to get close to what I want to show it is important that I show a map of the Giza Pyramid complex so you understand what it is that I propose.
It was important that I show dominate features of the history of the thinking. That it helps to display what the purpose was and how the Giza Plateau was marked according to a Calendar.
Yes a calender, You heard it here for the first time and going back to my early research I will show what I drew then and what this calendar is of. As well, how it was used to demonstrates key locations on that Giza Complex.
Map of Giza pyramid complex.
Models built for thought progression were important features in understanding what any theory does for us as we want to progress our views of the world we live in. No matter how abstract the idea, if it can lead one to new perceptions and bring new perspective to the way in which we see the world then it is not the illusions with which we wish to further perpetuate, but the understanding of our place in the world.
Plato- Book VII of The Republic-The Allegory of the Cave
And now, I said, let me show in a figure how far our nature is enlightened or unenlightened: --Behold! human beings living in a underground den, which has a mouth open towards the light and reaching all along the den; here they have been from their childhood, and have their legs and necks chained so that they cannot move, and can only see before them, being prevented by the chains from turning round their heads. Above and behind them a fire is blazing at a distance, and between the fire and the prisoners there is a raised way; and you will see, if you look, a low wall built along the way, like the screen which marionette players have in front of them, over which they show the puppets.See here as well.
So to get to the points I make it is important to understand some of Plato's writings in order for you to get the jest of the influences of that Egyptian culture. As well, I was lead to believe, this is the beginning of the work for those in science who begin their education.
I go back to this because of what is needed to be place in mind. What I gather from that culture, and what I perceive is influencing science deep within it's consciousness, as humanity, struggles to become clear about it's place in the universe.
The Landscape and Quantum Tunnelling
Quantum tunnelling (or tunneling) is the quantum-mechanical effect of transitioning through a classically-forbidden energy state. It can be generalized to other types of classically-forbidden transitions as well.
Consider rolling a ball up a hill. If the ball is not given enough velocity, then it will not roll over the hill. This scenario makes sense from the standpoint of classical mechanics, but is an inapplicable restriction in quantum mechanics simply because quantum mechanical objects do not behave like classical objects such as balls. On a quantum scale, objects exhibit wavelike behavior. For a quantum particle moving against a potential energy "hill", the wave function describing the particle can extend to the other side of the hill. This wave represents the probability of finding the particle in a certain location, meaning that the particle has the possibility of being detected on the other side of the hill. This behavior is called tunnelling; it is as if the particle has 'dug' through the potential hill.
The landscape presents the idea of tunnelling which I had been thinking about. I showed the link again in a the previous post discussing the "elephant and the horizon" to demonstrate that the "question of time" by Smolin. That it may undergo some features, while talking about the issues of quantum gravity? How were we to measure this knowing Planck Time? So you need ways in which to measure this. At Planck length how are you to do this?
Substituting this mass back into one of the length expressions gives the Planck length
and the light travel time across this length is called the Planck time:
Keep in mind that this is a characteristic time, so its order of magnitude is what should be noted. Sometimes it is defined with the wavelength above divided by 2Ï€, so don't worry about the number of significant digits.
I draw attention to the plasmatic events demonstrated by the Quark Gluonic perception. How is this perceived and measured at this level? So you are sending measure to reductionistic views. Lee Smolin accepts this I think? While we understand the comparative view of all particles associated to a energy valuation, I wanted immediate results in the colour of our thinking for it to incur some understanding of the nature of gravity at the energies involved.
It had to be immediate, and the discrimination of the photon in it's colour was a necessary feature of knowing the particle energies as well in the nature of the gravity. You had to move to a "fifth dimensional perspective" electromagnetism plus gravity, in order to follow what I am saying.
Quantum Effect, however allow a manifold to change state abruptly at some point-to tunnel through the intervening ridge to a nearby lower valley.
Beyond the 3+1 of Spacetime
So we have moved to the holographic principle and the understanding about the shadows? Again, I return to the context of the pyramid here in this post. I am also revealing an aspect of this geometrical feature that sits at the basis of my thinking when it come to geometrical interpretation.
While the "pyramid is a solid," there is a Sun that shines, and shadows cast from that pyramid we become aware of the "rays of that Sun." The Sun is a very important feature of Plato's Cave, as well as seeing it's use in the Giza Complex.
So I gave you a map above.
I would like you all to know that "carbon dating" is a science in itself.
Carbon dating was developed by a team led by Willard Libby. Originally a carbon-14 half-life of 5568±30 years was used, which is now known as the Libby half-life. Later a more accurate figure of 5730±40 years was determined, which is known as the Cambridge half-life. However laboratories continue to use the Libby figure to avoid inconsistencies when comparing raw dates and when using calibration curves to obtain calendrical dates.
But in this model, I am assuming that the "time clock" assigned to the archaeology of the Pyramid is much different then the one we currently see in current literature. Just from this point alone you could depart. But please, stay around a little bit, so I can show how the model of the pyramid was used as a Sun Dial. How the structures were following "the times" in progression? An interesting story nonetheless?
I have the issues of the meme's in people's experiences to draw upon. How mankind's development in it's observation were gained from what the sun could do to the objects of our world. Given in our youth, a compass of Einstein or a License plate revealing symmetry, or a lamp shade that sends it's line, as a shadow across one's living room. Dust particles that announce themselves once the "ray of light" is invoked?
Hi Q9
Plato:
If you "step back from the article" I am placing a lot of things for consideration.
I am trying to give one "the flavour" of the past, which we know is very difficult at best to describe, as any taste incurred from consuming and digesting foods.
Current issues on the landscape? Tunnelling? Time travel? Tunnelling in faster then light?
I include this response in this post article so that I could answer you immediately. It seems Haloscan is not working?
Hi Q9
Great Pyramid was built inside out, Frenchman says-PostThe term "landscape" comes from evolutionary biology (see Fitness landscape) and was first applied to cosmology by Lee Smolin in his book.[11] It was first used in the context of string theory by Susskind.[12] There are several popular books about the anthropic principle in cosmology.[13] Two popular physics blogs are opposed to this use of the anthropic principle.[14]
See String theory landscape
Dumbo is a 1941 animated feature film produced by Walt Disney and first released on October 23, 1941 by RKO Radio Pictures. The fourth film in the Disney animated features canon, Dumbo is based upon a children's book of the same name by Helen Aberson and illustrated by Harold Perl based on true events. The main character is Jumbo Jr., a semi-anthropomorphic elephant who is cruelly nicknamed Dumbo. He is ridiculed for his big ears, but it turns out that he is capable of flying by using them as wings. His only friend is the mouse Timothy, parodying the stereotypical animosity between mice and elephants. Dumbo was a deliberate exercise in simplicity and economy for the Disney studio, and is today considered one of its finest films.
See "Pink Elephant"A reference to pink elephants occurs in the 1941 Disney animated classic Dumbo. Dumbo, having taken a drink of water from a bucket spiked with moonshine, begins to hallucinate singing and dancing "Pink Elephants on Parade."
One should not assume that heighten perception refers to "some state of being" other then what is normal? :)
Some see non euclidean geometries at work, does not make you special?
Although such an attribute discovered to me was exceptional. It has it's history though, that cannot be overlooked.
Yet, it is relevant to "projective geometries" and how these arose. So Hilbert saids a list of 23 problems and one of them is "continuity?" What kind of geometry is that? :)
Yet too, should we move so far from what is "solidified in our world," to have said, there cannot exist the designs of geometry that describe this object? Some model? Reveals, aspect of the sociological side of our interactions, that we could have excelled to become better human beings?
Imagine some people draw mountains when in class and are bored with the lecture, or others, dream of some far off places in thought. Why not that such a gravity be included in all peoples thought to have them colour their lives accordingly?
The hard example supplied is Susskind's elephant and entanglement in relation too, what is in the blackhole and what is outside, by describing the horizon. It's colour.
Surely the colour of the gravity can be revealed by such entanglement? You may think a "blackhole in technology" while I am thinking, that by it's very nature, the history of that time allowed us to view it? How so?
Rocket Science
I am having problems trying to respond in Haloscan Q9. So what's that saying, "It's not Rocket Science?"
Now look here:) We now know that Susskind's elephant is "not Pink" and it is not "Dumbo." :) The elephant we are talking about, while still held to "blind men" holding parts of the reality, there is a serious question here about what quantum gravity is. So I have given perspective to what we shall see in terms of colour and the blackhole. All the while I was still speaking about Quantum Gravity.
There’s a place from which nothing escapes, not even light, where time and space literally come to end. It’s at this point, inside this fantastic riddle, that black holes exert their sway over the cosmos … and our imaginations. See Breakthrough Propulsion Physics?
There are different processes out there to which Quantum gravity is being model according to other perspectives. What comes of those persepctives if they have been consumed by their modelled approaches, that they say, "I have the tail" or, "I have the ear." We are still all blind as hell. But it's fun to create the language, new models, new perspectives to help understand our place in the world. Not to continue to perpetuate illusions we all like to create, but ways in which to speak to what is most troubling.
The Blind Men and the Elephant-John Godfrey Saxe (1816-1887)
So this brings me back to the Pyramid.
So what is the calendar in this particular place and I would like to think that I could immerse myself in this windowed view of reality as to what once was. Say, that this television, is based on the nature of the Colour of gravity and that while we watch it. We had to take into consideration the quantum dynamical world that is trying to be spoken to in General Relativity, not just at the classical level, but at the quantum one as well.
Lest I had taken you now to Banchoff and his wonderful 5d explanations of a 2d screen?
Knowing the Giza Complex and the requirement of the Sun, it is now apparent that I will make a subtle exposure to the valuation of how the pyramid was orientated to the sociological aspects of Egyptian thinking.
The Egyptians believed that a person's essence or soul was composed of several elements that at the point of death would become separate entities:
The "ka"
Should we be so foolish to think that the subtle aspect of our humanity could not operate on levels, other then the physical? I give you colour as a consequence of what transpires in life, and holds any person to the realm of their thinking. If they did not know that the gravity associated to every thought manifests as some colour in the disposition of the human body what becomes of the disposition of the soul?
See the Name and Shadow
Monday, March 19, 2007
Pasquale Del Pezzo and E8 Origination?
"I’m a Platonist — a follower of Plato — who believes that one didn’t invent these sorts of things, that one discovers them. In a sense, all these mathematical facts are right there waiting to be discovered."Donald (H. S. M.) Coxeter
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.
Clifford of Asymptotia drew our attention to this for examination and gives further information and links with which to follow.
He goes on to write,"Let’s not get carried away though. Having more data does not mean that you worked harder to get it. Mapping the human genome project involves a much harder task, but the analogy is still a good one, if not taken too far."
Of course since the particular comment of mine was deleted there, and of course I am okay with that. It did not mean I could not carry on here. It did not mean that I was not speaking directly to the way these values in dimensional perspective were not being considered.
Projective 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.
There had to be a route to follow that would lead one to think in such abstract spaces. Of course, one does not want to be divorced from reality. So one should not think that because the geometry of GR is understood, that you think nothing can come from the microseconds after the universe came into expression.
At this point in the development, although geometry provided a common framework for all the forces, there was still no way to complete the unification by combining quantum theory and general relativity. Since quantum theory deals with the very small and general relativity with the very large, many physicists feel that, for all practical purposes, there is no need to attempt such an ultimate unification. Others however disagree, arguing that physicists should never give up on this ultimate search, and for these the hunt for this final unification is the ‘holy grail’. Michael Atiyah
The Holy Grail sure comes up lots doesn't it:) Without invoking the pseudoscience that Peter Woit spoke of. I thought, if they could use Babar, and Alice then I could use the Holy Grail?
See more info on Coxeter here.
Like Peter I will have to address the "gut feelings" and the way Clifford expressed it. I do not want to practise pseudoscience as Peter is about the landscape.:)
When ones sees the constituent properties of that Gossett polytope 4_{21} in all it's colours, the complexity of that situation is quite revealing. Might we not think in the time of supergravity, gravity will become weak, in the matter constitutions that form.
As in Neutrino mixing I am asking you to think of the particles as sound as well as think them in relation to the Colour of Gravity. If you were just to see grvaity in it's colourful design and what value that gravity in face of the photon moving within this gravitational field?
We detect the resulting "wah-wah-wah" in properties of the neutrino that appear and disappear. For example, when neutrinos interact with matter they produce specific kinds of other particles.
For example, when neutrinos interact with matter they produce specific kinds of other particles. Catch the neutrino at one moment, and it will interact to produce an electron. A moment later, it might interact to produce a different particle. "Neutrino mixing" describes the original mixture of waves that produces this oscillation effect.
The "geometry of curvature" had to be implied in the outcome, from that quantum world? Yet at it's centre, what is realized? You had to be lead there in terms of particle research to know that you are arriving at the "crossover point." The superfluid does this for examination.
5. Regular polytope: If you keep pulling the hypercube into higher and higher dimensions you get a polytope. Coxeter is famous for his work on regular polytopes. When they involve coordinates made of complex numbers they are called complex polytopes.
Pasquale Del Pezzo, Duke of Cajanello, (1859–1936), was "the most Neapolitan of Neapolitan Mathematicians".
He was born in Berlin (where his father was a representative of the Neapolitan king) on 2 May 1859. He died in Naples on 20 June 1936. His first wife was the Swedish writer Anne Charlotte Leffler, sister of the great mathematician GÃ¶sta Mittag-Leffler (1846-1927).
At the University of Naples, he received first a law degree in 1880 and then in 1882 a math degree. He became a pre-eminent professor at that university, teaching Projective Geometry, and remained at that University, as rector, faculty president, etc.
He was mayor of Naples starting in 1919, and he became a senator in the Kingdom of Naples.
His scientific achievements were few, but they reveal a keen ingenuity. He is remembered particularly for first describing what became known as a Del Pezzo surface. He might have become one of the strongest mathematicians of that time, but he was distracted by politics and other interests.
So what chance do we have, if we did not think this geometry was attached to processes that would unfold into the bucky ball or the fullerene of science. To say that the outcome had a point of view that is not popular. I do not count myself as attached to any intelligent design agenda, so I hope people will think I do not care about that.
NATHAN MYHRVOLD
I found the email debate between Smolin and Susskind to be quite interesting. Unfortunately, it mixes several issues. The Anthropic Principle (AP) gets mixed up with their other agendas. Smolin advocates his CNS, and less explicitly loop quantum gravity. Susskind is an advocate of eternal inflation and string theory. These biases are completely natural, but in the process the purported question of the value of the AP gets somewhat lost in the shuffle. I would have liked more discussion of the AP directly
See here for more information
So all the while you see the complexity of that circle and how long it took a computer to map it, it has gravity in it's design, whether we like to think about it or not?
But of course we are talking about the symmetry and any thing less then this would have been assign a matter state, as if symmetrical breaking would have said, this is the direction you are going is what we have of earth?
Isostatic Adjustment is Why Planets are Round?
While one thinks of "rotational values" then indeed one would have to say not any planets is formed in the way the sun does. Yet, in the "time variable understanding" of the earth, we understand why it's shape is not exactly round.
Do you think the earth and moon look round if your were considering Grace?
On the moon what gives us perspective when a crater is formed to see it's geological structure? It's just not a concern of the mining industry, as to what is mined on other orbs, but what the time variable reveals of the orbs structure as well.
Clementine color ratio composite image of Aristarchus Crater on the Moon. This 42 km diameter crater is located on the corner of the Aristarchus plateau, at 24 N, 47 W. Ejecta from the plateau is visible as the blue material at the upper left (northwest), while material excavated from the Oceanus Procellarum area is the reddish color to the lower right (southeast). The colors in this image can be used to ascertain compositional properties of the materials making up the deep strata of these two regions. (Clementine, USGS slide 11)
See more here
Posted by
PlatoHagel
at
10:42:00 PM
Tuesday, September 12, 2006
Coxeter and Plato's Cave
IN Beyond the Dance of the Sun I give an image of Plato's Cave for consideration, about dimensinal perspectve.
This is not only held in my mind in terms of what free people are chained in their perspectives, but I also feel, that the leading characteristics were kindly put forward not only by my own position, but by those who I have listed throughout this blog.
Bolya, Heisenberg and Hooft?
There are "no wares" here to market(no advertising) other then what perception has granted me by "learning" and assuming the inherent nature of the leading perspectves in geometries and their relation to the real world.
Visitors' shadows manipulate and reshape projected images of "Buckyballs." "Buckyball," or a buckminsterfullerene molecule, is a closed cage-structure molecule with a carbon network. "Buckyball" was named for R. Buckminster "Bucky" Fuller (1895-1983), a scientist, philosopher and inventor, best known for creating the geodesic dome.
Imagine then, that such nanotechnology sites have taken us down to microperspectives and there are such things in the "geometry of being" that would dictate the technolgies that we use?
Was it so distant from the real world that such "projective geometries" exposed the correlation of knowledge from a man like Coxeter, that you would say "I would rather demomnstrate the technological aspect because this is real?"
You know you had to be more suttle then this. You knew you had to think of the sun's ray and "think" beyond in the Sun/Earth Relation in a lagrangian perspective. But you refuse?
It is better then, that the cynics remain chained. And allow themselves to spread their venom about the callousness of "good people who had ventured forth" and asked about dimensional perspective. Who is it, that remains in the box?
Focus then, on the science and what has been accomplished. You need no further explanation. No "back reaction" to what constituted this science.
HOUSTON, Texas, Oct. 31 -- Nobel laureate Richard Smalley, co-discoverer of the buckyball and widely considered to be one of the fathers of nanotechnology, died Friday at the age of 62 after a long battle with cancer.
Rice University professor Smalley shared the 1996 Nobel Prize in chemistry with fellow Rice chemist Robert Curl and British chemist Sir Harold Kroto for the 1985 discovery of a new form of carbon nicknamed buckyballs. Shaped like soccerballs and no wider than a strand of DNA, buckyballs each contain 60 carbon atoms arranged in a hollow sphere resembling two conjoined geodesic domes. Smalley coined the name "buckminsterfullerene" for the discovery in honor of architect and geodesic dome inventor Buckminster Fuller.
Fullerenes -- the family of compounds that includes buckyballs and carbon nanotubes -- remained the central focus of Smalley's research until his death. According to colleagues, Smalley's belief that nanotubes were a wonder material that could solve some of humanity's problems -- such as clean energy, clean water and economical space travel -- led him to crusade for more public support for science and to help found a business, Carbon Nanotechnologies Inc., in 2000 to make sure his discoveries made it to the marketplace where they could benefit society. Smalley was convinced that nanotubes could only be used to solve society's problems if they were manufactured in bulk and processed economically.
The socialogical foundation of thinking about our world here then is a far cry from the very foundationof the geometries and how human being may envision. How they may descend into mind. Thre posisbilties are endless,a nd I would just point to the images of flowers and the kalidescope they cause, as they reveal strange nodes and anti-nodes brought forth in mandalic pattern interpretations.
What symmetry is this, that we can create such patterns and see how beautiful they are? Some like Clifford like th easymmetry of certain flowers?
Again such liminocentric structure are a inhernet part of our consciousness developement and following this process, into reality is a very important step. Some will only like the pictures and some will venture deeper. That's always be the way of it.
How would I know this?:)
Posted by
PlatoHagel
at
1:20:00 PM
Tuesday, April 04, 2006
Krauss Speaks, People React? :)
We understand that Alice is just part of the developing perspective we have about interactions? THis is consistant with Glast, as well as any calormetrical understanding, from an interaction?
That we had not explain the extra energy should still be held respective positions in mind if incoming and outcoming energy calculatins do not match? That left room in mirror world for other possibilities and had not explain all "sum over paths?"
Lubos:
My understanding is that the very main point of his latest book, Hiding in the mirror, is to present the idea of extra dimensions as an essentially religious idea in order to diminish the credibility of the research of modern high-energy physics - because he knows that most of the readers are anti-religious.
Everyone who has ever worked in phenomenology or string theory knows very well that this research has nothing to do with religion. The link is an invention of Krauss' - one that is intended to politicize things and to encourage his readers to think about completely irrational relations between different ideas.
Foot, R., and S.N. Gninenko. 2000. Can the mirror world explain the ortho-positronium lifetime puzzle?
(belongs to another article words that follow within link)
Welcome to the mirror world, in which every particle in the known universe could have a counterpart. This cosmos would hold mirror planets, mirror stars, and even mirror life.
While Alice in Wonderland may be a fictional story and pervasive in terms of many paths taken, the consequence of the photon in this enviroment and under gravitational influences, is well understood I think?
Lubos's first paragraph quoted is a questionable one to me, "on character," as I have understood Krauss to be.
Startreking explanatory on the understanding of reality, to make sure we understand what is going on, as well as, explaining the idea's of scientists who write for the public, in the movie production scenario's?
Kip Thorne and Brian Greene?
Would the normal public understand the evolution of Abbott and flatland, or the develomment of non-euclidean geometries?
You have taken the word geocentrism in vain Lubos:)
As a "liminocentric structure" wholeness is important to me, not just as some circle, a sphere, or how a genus figure is move from one form to another, but that other things are happening as well, when this happens? If it happens many times microscopically will this have satisfied our viewing of Coleman de Luccia Instanton?
It's just another way of "toposeeing" is all" ( many microprocesses make for many new physics to emerge?), and as far I understand it, it is necessary back ground with which to develope a consistant picture of what is going on with our universe, macroscopically, as well as microscopically, continously? Wmap polarization is topolgical driven by perpective sound valuations, blendings so that sucha 2d pciture measured is much more dynamcially seen?
Yes I know, no one knows what geometry this is in the blackhole or what new physics will emerge, so we needed to look for this consistancy beyond the standard model?
How could one not attempt to join this with quantum and cosmological views?
This just may mean that "uncertainty" is encapsulated?
I am glad to have "information" that would maintain my current hold on reality, as I expand the brain's coverings.
As we project our "evolutionary mind in projective geometries" further into the strange world of high energy, as well as reducing to a weak field measure, some hope of a consistant picture.
Okay, I have not forgotten what string theory has already done in regards to bulk pespective:)
So the bulk perspective is "nothing," or does it act as a catelysct?
Posted by
PlatoHagel
at
6:53:00 AM
Sunday, March 26, 2006
On Gauss's Mountain
You must understand that any corrections necessary are appreciated. The geometrical process spoken too here must be understood in it's historical development to undertand, how one can see differently.
These tidbits, would have been evidence as projects predceding as "towers across valleys" amd "between mountain measures," to become what they are today. Allows us to se in ways that we are not used too, had we not learnt of this progression and design that lead from one to another.
8.6 On Gauss's Mountains
One had to recognize the process that historically proceeded in our overviews "to non-euclidean perspectives," "geometrically enhanced" through to our present day headings, expeirmentallly.
Michelson interferometer(27 Mar 2006 wikipedia)
A quick summation below leads one onto the idea of what experimental validation has done for us. Very simply, the graduation of interferometer design had been taken to astronomical proportions?
Today the Count expands on this for us by showing other information on expeirmental proposals. How fitting that this historical drama has been shown here, in a quick snapshot. As well the need for understanding the "principal inherent" in the project below.
See:
Apollo Moon Measure
Euclidean geometry, elementary geometry of two and three dimensions (plane and solid geometry), is based largely on the Elements of the Greek mathematician Euclid (fl. c.300 B.C.). In 1637, RenÃ© Descartes showed how numbers can be used to describe points in a plane or in space and to express geometric relations in algebraic form, thus founding analytic geometry, of which algebraic geometry is a further development (see Cartesian coordinates). The problem of representing three-dimensional objects on a two-dimensional surface was solved by Gaspard Monge, who invented descriptive geometry for this purpose in the late 18th cent. differential geometry, in which the concepts of the calculus are applied to curves, surfaces, and other geometrical objects, was founded by Monge and C. F. Gauss in the late 18th and early 19th cent. The modern period in geometry begins with the formulations of projective geometry by J. V. Poncelet (1822) and of non-Euclidean geometry by N. I. Lobachevsky (1826) and JÃ¡nos Bolyai (1832). Another type of non-Euclidean geometry was discovered by Bernhard Riemann (1854), who also showed how the various geometries could be generalized to any number of dimensions.
These tidbits, would have been evidence as projects predceding as "towers across valleys" amd "between mountain measures," to become what they are today. Allows us to se in ways that we are not used too, had we not learnt of this progression and design that lead from one to another.
8.6 On Gauss's Mountains
One of the most famous stories about Gauss depicts him measuring the angles of the great triangle formed by the mountain peaks of Hohenhagen, Inselberg, and Brocken for evidence that the geometry of space is non-Euclidean. It's certainly true that Gauss acquired geodetic survey data during his ten-year involvement in mapping the Kingdom of Hanover during the years from 1818 to 1832, and this data included some large "test triangles", notably the one connecting the those three mountain peaks, which could be used to check for accumulated errors in the smaller triangles. It's also true that Gauss understood how the intrinsic curvature of the Earth's surface would theoretically result in slight discrepancies when fitting the smaller triangles inside the larger triangles, although in practice this effect is negligible, because the Earth's curvature is so slight relative to even the largest triangles that can be visually measured on the surface. Still, Gauss computed the magnitude of this effect for the large test triangles because, as he wrote to Olbers, "the honor of science demands that one understand the nature of this inequality clearly". (The government officials who commissioned Gauss to perform the survey might have recalled Napoleon's remark that Laplace as head of the Department of the Interior had "brought the theory of the infinitely small to administration".) It is sometimes said that the "inequality" which Gauss had in mind was the possible curvature of space itself, but taken in context it seems he was referring to the curvature of the Earth's surface.
One had to recognize the process that historically proceeded in our overviews "to non-euclidean perspectives," "geometrically enhanced" through to our present day headings, expeirmentallly.
Michelson interferometer(27 Mar 2006 wikipedia)
Michelson interferometer is the classic setup for optical interferometry and was invented by Albert Abraham Michelson. Michelson, along with Edward Morley, used this interferometer for the famous Michelson-Morley experiment in which this interferometer was used to prove the non-existence of the luminiferous aether. See there for a detailed discussion of its principle.
But Michelson had already used it for other purposes of interferometry, and it still has many other applications, e.g. for the detection of gravitational waves, as a tunable narrow band filter, and as the core of Fourier transform spectroscopy. There are also some interesting applications as a "nulling" instrument that is used for detecting planets around nearby stars. But for most purposes, the geometry of the Mach-Zehnder interferometer is more useful.
A quick summation below leads one onto the idea of what experimental validation has done for us. Very simply, the graduation of interferometer design had been taken to astronomical proportions?
Today the Count expands on this for us by showing other information on expeirmental proposals. How fitting that this historical drama has been shown here, in a quick snapshot. As well the need for understanding the "principal inherent" in the project below.
VLBI is a geometric technique: it measures the time difference between the arrival at two Earth-based antennas of a radio wavefront emitted by a distant quasar. Using large numbers of time difference measurements from many quasars observed with a global network of antennas, VLBI determines the inertial reference frame defined by the quasars and simultaneously the precise positions of the antennas. Because the time difference measurements are precise to a few picoseconds, VLBI determines the relative positions of the antennas to a few millimeters and the quasar positions to fractions of a milliarcsecond. Since the antennas are fixed to the Earth, their locations track the instantaneous orientation of the Earth in the inertial reference frame. Relative changes in the antenna locations from a series of measurements indicate tectonic plate motion, regional deformation, and local uplift or subsidence.
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