Showing posts with label geometries. Show all posts
Showing posts with label geometries. Show all posts

Tuesday, January 22, 2013


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:

Sunday, October 21, 2012

Point Being...It's a Material World?

This provides for a beginning point of discussion about the parameters of our thinking in terms of the resolution to our experiences. Do they run further then the constraints we apply to them? In science your boxed in, and you replay all components in the hopes that you can extend or explain the problem and arrive at a conclusion which provides for a stepping off point for furthering the limitations of those constraints.

Intuition and Logic in Mathematics by Henri Poincaré

On the other hand, look at Professor Klein: he is studying one of the most abstract questions of the theory of functions to determine whether on a given Riemann surface there always exists a function admitting of given singularities. What does the celebrated German geometer do? He replaces his Riemann surface by a metallic surface whose electric conductivity varies according to certain laws. He connects two of its points with the two poles of a battery. The current, says he, must pass, and the distribution of this current on the surface will define a function whose singularities will be precisely those called for by the enunciation.

For me the extension here was to see that billiard balls that collide are somehow extended to believe that the greater opportunity here has been to carry the relevance to the sound that is generated at those moments. This carries in a sense as a geometrical expression defined in in Euclidean beginning about a point and then geometrically "all things follow."  This is a schematically drawing if you like about beginnings, yet it is about the dynamical progression of how the non-euclidean moves even more into projective geometries. All of this is a framework for views about the world in which we live and part of the reality. So you apply this to the cosmos.

So given here a parameter with which one wants to talk about and how we can see in the materialist world,  the constraint is found in the expression of correlation and meaning about the geometry we live with. This was defined by the beginning of a Newtonian experience, and in a sense I am showing the diversity of this explanation about reality as Euclid's determination and postulates which were extended.

Gauss and Riemann gave a freedom that a Euclidean could never appreciate,  had not the quest of others helped Riemann to make the leap.

You have define the issue about spirit as related to  "a Heaven,"  yet we are here talking about the mundane? Moving from the issue of the constraints we have applied to our selves in terms of the archaic forms.  We do not want to induce religion as to define our experience but to talk about what science has to say about the entanglement we have with nature? Would you not agree?

While of course the opening is about Heaven is it defined in terms of the experience portrayed.  I am suggesting that there is a contact with nature that is indeed subtle with regard to consciousness defined "as focus."  So in a sense experience suggests a deep impact and meaning to its person that can be correlated with others of similar experiences?

Thursday, July 19, 2012

Process Fractal vs Geometry Fractals

Let proportion be found not only in numbers, but also in sounds, weights, times and positions, and whatever force there is.Leonardo Da Vinci
The Mandelbrot set, seen here in an image generated by NOVA, epitomizes the fractal. Photo credit: © WGBH Educational Foundation

 "Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line." So writes acclaimed mathematician Benoit Mandelbrot in his path-breaking book The Fractal Geometry of Nature. Instead, such natural forms, and many man-made creations as well, are "rough," he says. To study and learn from such roughness, for which he invented the term fractal, Mandelbrot devised a new kind of visual mathematics based on such irregular shapes. Fractal geometry, as he called this new math, is worlds apart from the Euclidean variety we all learn in school, and it has sparked discoveries in myriad fields, from finance to metallurgy, cosmology to medicine. In this interview, hear from the father of fractals about why he disdains rules, why he considers himself a philosopher, and why he abandons work on any given advance in fractals as soon as it becomes popular. A Radical Mind

As I watch the dialogue between Bruce Lipton and Tom Campbell here, there were many things that helped my perspective understand the virtual world in relation to how the biology subject was presented. It is obvious then why Bruce Lipton likes the analogies Tom Campbell has to offer. The epiphanies Bruce is having along the road to his developing biological work is very important. It is how each time a person makes the leap that one must understand how individuals change, how societies change.

Okay so for one,  the subject of fractals presents itself and the idea of process fractals and Geometry Fractals were presented in relation to each other. Now the talk moved onto the very thought of geometry presented in context sort of raised by ire even though I couldn't distinguish the differences. The virtual world analogy is still very unsettling to me.

So ya I have something to learn here.

I think my problem was with how such iteration may be schematically driven so as toidentify the pattern. Is to see this process reveal itself on a much larger scale. So when I looked at the Euclidean basis as a Newtonian expression the evolution toward relativity had to include the idea of Non Euclidean geometries. This was the natural evolution of the math that lies at the basis of graduating from a Euclidean world. It is the natural expression of understanding how this geometry can move into  a dynamical world.

So yes the developing perspective for me is that even though we are talking abut mathematical structures here we see some correspondence in nature . This has been my thing so as to discover the starting point?

A schematic of a transmembrane receptor

It the truest sense I had already these questions in my mind as  I was going through the talk. The starting point for Bruce is his biology and the cell. For Tom, he has not been explicit here other then to say that it is his studies with Monroe that he developed his thoughts around the virtual world as it relates to the idea of what he found working with Monroe.

So it is an exploration I feel of the work he encountered and has not so far as I seen made a public statement to that effect. It needs to be said and he needs to go back and look over how he had his epiphanies. For me this is about the process of discovery and creativity that I have found in my own life. Can one feel so full as to have found ones wealth in being that you can look everywhere and see the beginnings of many things?

This wealth is not monetary for me although I recognized we had to take care of or families and made sure they were ready to be off on their own. To be productive.

The Blind Men and the Elephant
John Godfrey Saxe (1816-1887)
 So for me the quest for that starting point is to identify the pattern that exists in nature as much as many have tried various perspective in terms of quantum gravity. Yes, we are all sort of like blind men trying to explain the reality of the world in our own way and in the process we may come up with our epiphanies.

These epiphanies help us to the next level of understanding as if we moved outside of our skeletal frame to allow the membrane of the cell to allow receptivity of what exist in the world around as information. We are not limited then to the frame of the skeleton hardened too, that we cannot progress further. The surface area of the membrane then becomes a request to open the channels toward expansion of the limitations we had applied to ourselves maintaining a frame of reference.

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 Péluse-Portrait by Naigeon in the Musée 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 Mémoires des savantes étrangers of the Academy of Paris, the Mémoires of the same Academy, and the Annales de chimie, various mathematical and physical papers. Among these may be noticed the memoir "Sur la théorie des déblais et des remblais" (Mém. 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?

Tuesday, January 30, 2007

Hermetic Ties: Art to Esoteric Form

The father of all perfection in the whole world is here. Its force or power is entire if it be converted into Earth. Separate the Earth from the Fire, the subtle from the gross, sweetly with great industry. It ascends from the Earth to the Heavens and again it descends to the Earth and receives the force of things superior and inferior. By this means you shall have the glory of the whole world and thereby all obscurity shall fly from you. Its force is above all force, for it vanquishes every subtle thing and penetrates every solid thing. So was the world created. From this are and do come admirable adaptations, whereof the process is here in this. Hence am I called Hermes Trismegistus, having the three parts of the philosophy of the whole world. That which I have said of the operation of the Sun is accomplished and ended.Sir Isaac Newton-Translation of the Emerald Tablet
See: Newton on Chymistry

Again I open this blog post with the understanding that what an artist like Raphael may try to do? May include, much of the philosophy of the times, and have these things descriptively enclosing processes indicative of what they had known, but also of what these things could hide within the self.

In center, while Plato - with the philosophy of the ideas and theoretical models, he indicates the sky, Aristotle - considered the father of Science, with the philosophy of the forms and the observation of the nature indicates the Earth. Many historians of the Art in the face correspondence of Plato with Leonardo, Heraclitus with Miguel Angel, and Euclides with Twine agree.

If we watched of distant spot, of century XX aC emphasizes Hermes Trismegisto, - tri three, megisto megas, three times great; perhaps the perception of infinite older than we have and takes by Mercurio name - for Greek and the Toth - for the Egyptians. Considered Father of the Wisdom and Sciences in Greece, in the cult to Osiris it presided over the ceremonies as priest and he was Masterful in Egypt like legislator, philosopher and alchemist during the reign of Ninus in the 2270 aC.

Etimológicamente speaking, of Hermes, the gr. hermenéuiein, “hermetic” - closed, “hermenéutica” - tie art to the reading of old sacred texts talks about so much to the dark as to which it is included/understood in esoteric form. Part of saberes that it accumulated transmitted through the Hermetic Books that only to the chosen ones between the chosen ones could be revealed. As much Pitágoras and Plato as Aristotle and Euclides were initiated in the knowledge of the Hermetic School.

In Man looking into Space, I wanted to show how casual our science has used these images and not realized the context to which the greater meaning had laid hidden, all the while it is used to "describe cosmology" and the science thereof.

A banner has been been written across these times to which scientists hold to all that is true. In this, the reasons to dismiss any implications of history assigned along side, is asking "what validation" can be given to anything that is spoken from our times now.

I went on in that post, "man looking into space," to explain something about the woodcuts. The art form produced, grabbed my thinking in relation to the "alchemical art forms" and grabs my thinking in regards to the "School of Athens picture."

The Yorck Project: 10.000 Meisterwerke der Malerei. DVD-ROM, 2002. ISBN 3936122202. Distributed by DIRECTMEDIA Publishing GmbH.

I just wanted to say that the essence of this blog post is about "the arches," and I am moving toward that description, and what is happening when we take a picture of them. Look at the "design inherent" and "dynamics" as held to gravity in it's construction. Look at what it can signify in it's "internal expression" about our contact with the world around us. The bridging that it can signify.

I would apologize for leaving this post undone, while views pass by the essence of this post. I am indeed busy with life. So I wanted to clarify this push toward the internal dynamics, while speaking to the psychology of this work.

A scientist may side step this look, while quoting the hermetical values of what may be said by the previous first lady Hillary Clinton. In itself, an empty page, only leaves room for what had to be expressed if it was not gotten the first time? Her attempts at humour, are the attempts to break the "rigidity of the personality?"

The Psychology

Myths and metaphors, like dreams, are powerful tools that draw the listener, dreamer, or reader to a character, symbol, or situation, as if in recognition of something deeply known. Myth's bypass the mind's efforts to divorce information. They make an impression, are remembered, and nudge us to find out what they mean, accounting for the avid interest that Ring audiences have in the meaning of the story.1

Who has been so colourful in your journeys across the internet to include a wonderful language that takes you into this world of discovery of self? You had to know something about the "psychology of people" in order to give a story by nature, it's mythic description, and "most artful" to draw attention to what lies underneath.

The Alchemists attempted to perfect the One Thing of Hermes, what they called the First Matter, by using specific physical, psychological, and spiritual techniques that they describe in chemical terms and demonstrated in laboratory experiements. However, while the alchemists spoke in terms of chemcials, furaces , flasks, and beakers, they were really talking about the changes taking place within their own bodies, minds, and souls.2

Thus I have given two examples that I had promised sometime back to illustrate some of the "compelling work" that while ancient indeed, is not without it's efforts in todays world. It is the attempt to cross all boundaries, race, gender, and help one to recognize the diversity of the soul with out it's jacket. Shall we call your soul male or female, black or white?

So I am bypassing this, and that has been my message, while the efforts to climb out of the constraints that we have come to recognize within the boundaries of self. Are the realization of the diversity of "all souls" and their time in expression.

Shall we find the excuse to hold ourselves to the thoughts, that while overcoming, the constraints which still exist "within" had to be continually challenged? We have to break the "chains that bind us."

The Arches

Golden Rectangle
I took the picture at a time of day when the tide was at exactly the right place to create this image: when the surface of the water reflected the underside of the bridge and they combined, together they produced what I named the Golden Rectangle as a nod to Pythagoras (my hero). The sensation I experienced at the time was of balancing consciousness and feeling.

It probably seems that it is taking time to get to the essence of this post. IN order to get to the "psychological effect" that I am getting too it important to think of the images of these arches. It is about "each of us" and how we relate to the world. How, the "teacher and student" can exist within the same person.

I point to the Heaven's in the case of the "school of Athens, while Aristotle points to what is on Earth?" Shall we leave no doubt of the "physical things" while we understand that there are more ephemeral qualities to these matter states? That we move continuously between them?

The Inner/Outer World

The drawn of our focus is the external world, but, if we were to connect the internal world with that "external view" how shall we do that. How shall we describe the whole being in this exercise?

Part of this "exchange with reality," is that we can know by continually moving this information "through us" and creating "the space around us," we add to the total view "beyond what was apparent" with just the brain's condensible qualities in neurological display?

By 'dilating' and 'expanding' the scope of our attention we not only discover that 'form is emptiness' (the donut has a hole), but also that 'emptiness is form' (objects precipitate out of the larger 'space') - to use Buddhist terminology. The emptiness that we arrive at by narrowing our focus on the innermost is identical to the emptiness that we arrive at by expanding our focus to the outermost. The 'infinitely large' is identical to the 'infinitesimally small'.The Structure of Consciousness John Fudjack - September, 1999

While I quote above, the second part of the quote adds directly to the understanding. Not only are we "crossing the wires here," we are identifying "a aspect of consciousness" that is continuous.

In this metaphor, when we are seeing the donut as solid object in space, this is like ordinary everyday consciousness. When we see the donut and the hole at its center, this is like a stage of realization in which 'form' is recognized as 'empty'. When we zoom in extremely closely and inspect the 'emptiness' at the center, or zoom out an extreme distance away from the object and the donut seems to disappear and we have only empty space - this is like certain 'objectless' states of awareness that can occur in meditation. But the final goal is not to achieve the undifferentiated state itself; it is to come to the special perspective that allows us to continue to see all three aspects at once - the donut, the whole in the middle, and the space surrounding it - this is like the 'enlightened' state, in this analogy. 10 The innermost and outermost psychological 'space' (which is here a metaphor for 'concentrated attention' and 'diffused attention') are recognized as indeed the same, continuous.

So given "this relationship" on what we can build within self, then what use all this knowledge if we cannot grow with it? What of Plato's and Aristotle, as figures within the "centre of" Raphael's painting. Their perspective, "as positions in relation too," the "questioning stance" about this "unity of the circle" in our exchange with reality?

So how would you exemplify "this exchange" with reality while "below the surface" all these "probable outcomes" are the manifestation of that which is real? You extend yourself "out there" while you also extend yourself inside? The "infinite regress," is to find oneself, with all that is "past" in front of you, can allow you to stand on what of, "the future" will pass through?

First Principle saids that you acknowledge your place in the scheme of things as you "stretch" the thinking of the mind? Increase the "neurological frontier" in those neurological connections? Increase, the fluttering of the egg's feature, of that condensible brain/body.

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

But, Aristotle thinks that knowledge begins with experience. We get to first principles through induction. But there is no certainty to the generalizations of induction. The "Problem of Induction" is the question How we know when we have examined enough individual cases to make an inductive generalization. Usually we can't know. Thus, to get from the uncertainty of inductive generalizations to the certainty of self-evident first principles, there must be an intuitive "leap," through what Aristotle calls "Mind." This ties the system together. A deductive system from first principles (like Euclidean geometry) is then what Aristotle calls "knowledge" ("epistemê" in Greek or "scientia" in Latin).

From here it would not be to unlikely that such dealings with the "reality of the world" would ask that we experiment and from such experiment, we learn the truth of the reality. While what the past is "in front" of us, to what goes beyond to it's future would be like asking the very nature of expression to manifest as this universe and laws of thermodynamics that the arrow of time only moves one way.

"The future" arises from within then? We'll move forward by what choices we make? About our conclusions, about reality?

1 Ring of Power, Jean Shinoda Bolen, M.D. Page 3

2The Emerald Tablet, Dennis William Hauck, Chapter 10, Page 151

Monday, January 29, 2007

Whose who, in the School of Athens

I was over visiting Clifford's blog called Asymptotia this morning and notice a blog entry called, Heretics of Alexandria. Of course, what first came to mind is the "Library of Alexandria."

Clifford writes and paraphrases:
This full length drama, set in Alexandria Egypt, 415 A.D. features the infamous Philosopher Hypatia, who has come into possession of a document that threatens the very basis of the new religion called Christianity; a document that some would do anything to destroy. Hypatia and a powerful Christian Bishop wage a fierce struggle for the soul of a young priest and for a document which tells a very different version of the life — and death — of Jesus. A true story.
The writing was excellent as was the cast, and Bastian should be extremely proud of himself. (It is a mistake to call it “a true story”, though. It is a story based around historical events, which should absolutely not be confused with being a “true story”. Writers of synopses should not encouarge people to mix up the two.

So I started to do some research on the link offered by Clifford. All of a sudden I could see the many connections bringing "Hypatia of Alexandria" into the fold.

Hypatia of Alexandria (Greek: Υπατία; c. 370–415) was an ancient philosopher, who taught in the fields of mathematics, astronomy and astrology. She lived in Alexandria, in Hellenistic Egypt.
Hypatia was the daughter of Theon, who was also her teacher and the last fellow of the Musaeum of Alexandria. Hypatia did not teach in the Musaeum, but received her pupils in her own home. Hypatia became head of the Platonist school at Alexandria in about 400. There she lectured on mathematics and philosophy, and counted many prominent Christians among her pupils. No images of her exist, but nineteenth century writers and artists envisioned her as an Athene-like beauty.

Many of you who visit here know how much the "School of Athens" picture means to me?

That there was only one woman here named "Hypatia of Alexandria" of course sent me off to have a look. AS well, "more of the meaning" with regards to the Library of Alexandria.

9.Francesco Maria I della Rovere or Hypatia of Alexandria and Parmenides

The frescoe of the "School of Athens" has been a haunting reminder of the many things that Raphael "enclosed in meaning."

School of Athens by Raphael

That I could then give numbers and names to person's within the picture was equally exciting. I started to dissect parts of this picture quite a while back, opening of course with the "very centre of that painting." The labels supplied on this post entry should give links to farther posts about this.

1: Zeno of Citium or Zeno of Elea? – 2: Epicurus – 3: Frederik II of Mantua? – 4: Anicius Manlius Severinus Boethius or Anaximander or Empedocles? – 5: Averroes – 6: Pythagoras – 7: Alcibiades or Alexander the Great? – 8: Antisthenes or Xenophon? – 9: Hypatia or the young Francesco Maria della Rovere? – 10: Aeschines or Xenophon? – 11: Parmenides? – 12: Socrates – 13: Heraclitus (painted as Michelangelo) – 14: Plato holding the Timaeus (painted as Leonardo da Vinci) – 15: Aristotle holding the Ethics – 16: Diogenes of Sinope – 17: Plotinus? – 18: Euclid or Archimedes with students (painted as Bramante)? – 19: Strabo or Zoroaster? – 20: Ptolemy – R: Raphael as Apelles – 21: Il Sodoma as Protogenes

I now realize that with one comment entry gone( maybe both) that I really was not so out of tune. What was Plato's influence on Hypatia of Alexandria?

Letters written to Hypatia by her pupil Synesius give an idea of her intellectual milieu. She was of the Platonic school, although her adherence to the writings of Plotinus, the 3rd century follower of Plato and principal of the neo-Platonic school, is merely assumed.

See also:
  • No Royal Road to Geometry?

  • Euclid belonged to the persuasion of Plato and was at home in this philosophy; and this is why he thought the goal of the Elements as a whole to be the construction of the so-called Platonic figures. (Proclus, ed. Friedlein, p. 68, tr. Morrow)

    Monday, January 08, 2007

    Hubble Maps the Cosmic Web of "Clumpy" Dark Matter in 3-D

    Three-Dimensional Distribution of Dark Matter in the Universe
    This three-dimensional map offers a first look at the web-like large-scale distribution of dark matter, an invisible form of matter that accounts for most of the universe's mass. This milestone takes astronomers from inference to direct observation of dark matter's influence in the universe. Because of the finite speed of light, regions furthest away are also seen as they existed a long time ago. The map stretches halfway back in time to the beginning of the universe.

    The map reveals a loose network of dark matter filaments, gradually collapsing under the relentless pull of gravity, and growing clumpier over time. This confirms theories of how structure formed in our evolving universe, which has transitioned from a comparatively smooth distribution of matter at the time of the big bang. The dark matter filaments began to form first and provided an underlying scaffolding for the subsequent construction of stars and galaxies from ordinary matter. Without dark matter, there would have been insufficient mass in the universe for structures to collapse and galaxies to form.

    Part of this reporting is the way in which one could look at the Cosmos and see the gravitational relationships, as one might see it in relation to "Lagrangian views" in the Sun Earth Relation.

    Diagram of the Lagrange Point gravitational forces associated with the Sun-Earth system.

    Make sure you click on the image for further information. Mouseovers as your cursor is placed over images or worded links are equally important. You learn about satellites and the way they travel through these holes.

    While one can see "dark matter" in terms of it's constraints, what of "dark energy" as it makes it way through those holes? This reveals the expansionary nature in terms of dark energy being repelled, whether you like to think so or not. This explains the dark energy developing free of the dark matter constraints and explains the state of our universe.

    LSST Homepage background image. (Image credit: LSST Corporation, Bryn Feldman) Design of LSST Telescope dome and local facilities, current as of January 2007. Google Inc. has joined with nineteen other organizations to build the Large Synoptic Survey Telescope, scheduled to see first light atop Cerro Pachón in Chile in 2013.
    The Large Synoptic Survey Telescope (LSST) is a proposed ground-based 8.4-meter, 10 square-degree-field telescope that will provide digital imaging of faint astronomical objects across the entire sky, night after night. In a relentless campaign of 15 second exposures, LSST will cover the available sky every three nights, opening a movie-like window on objects that change or move on rapid timescales: exploding supernovae, potentially hazardous near-Earth asteroids, and distant Kuiper Belt Objects. The superb images from the LSST will also be used to trace billions of remote galaxies and measure the distortions in their shapes produced by lumps of Dark Matter, providing multiple tests of the mysterious Dark Energy.

    Two simulations of strong lensing by a massive cluster of galaxies. In the upper image, all the dark matter is clumped around individual cluster galaxies (orange), causing a particular distortion of the background galaxies (white and blue). In the lower image, the same amount of mass is more smoothly distributed over the cluster, causing a very different distortion pattern.

    Here in this post the example of "how one may see" is further expounded upon to show how dark matter and dark energy are in action as a 90% aspect of the cosmos, while the remaining 10% is a discrete measure of what is cosmologically matter orientated. We don't loose sight of these relationships, but are helped to further develope them in terms of this gravitational relationship.

  • Dark Matter in 3D
  • COSMOS Reveals the Cosmos
  • Sunday, January 07, 2007

    PLATO:Mathematician or Mystic ?

    Mathematics, rightly viewed, possesses not only truth, but supreme beauty, a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry.--BERTRAND RUSSELL, Study of Mathematics

    One should not conclude that such a bloggery as this is not without a heartfelt devotion to learning. That I had made no great claims to what science should be. other then what a layman point of view in learning has become excited about. What may be a natural conclusion to one who has spent a long time in science. Do not think me so wanting to knock on your door to enforce the asking of education that may be sent my way was truly as a student waiting for some teacher to appear.

    This did not mean I should not engage the world of science. Not become enamoured with it. Or, that seeing the teachers at their bloggeries, were "as if" that teacher did appear many times. This is what is good about it.

    I did not care how young you were, or that I, "too old" to listen to what scientists knew, or were theoretically endowed with in certain model selections.

    More from the Heart?

    "Let no one destitute of geometry enter my doors."

    You know that by the very namesake of Plato used here, that I am indeed interested how Plato thought and his eventual conclusions about what "ideas" mean. So, of course there is this learning that has to take place with mathematics.

    If I may, and if I were allowed to fast forward any thought in this regard, it would be to say, that the evolution of the human being is much appreciated in what can transfer very quickly "between minds" while a dialogue takes place. Hence the title of this bloggery.

    Science demands clarity, and being deficient in this transference of "pure thought" would be less then ideal speaking amongst those scientists without that mathematics. Yet, I do espouse that such intuitiveness can be gained from the simple experiment, by distilling information, from the "general concepts" which have been mention many times now by scientists.

    So it is of interest to me that the roads to mathematical understanding through it's development would be quick to point out this immediate working in the "world of the abstract imaging" is to know that such methods are deduced by it's numbers and their greater meaning.

    That such meaning can be assign to a "natural objector function" and still unbeknownst to the thinking and learning individual "a numerical pattern that lies underneath it. A "schematics" if you like, of what can become the form in reality.

    No reader of Plato can fail to recognize the important role which mathematics plays in his writing, as would indeed be expected for an author about whom the ancient tradition maintains that he had hung over the entry to his school the words "Let No One Un-versed in Geometry Enter". Presumably it was the level of ability to work with abstract concepts that Plato was interested in primarily, but if the student really had never studied Greek geometric materials there would be many passages in the lectures which would be scarcely intelligible to him. Modern readers, versed in a much higher level of mathematical abstraction which our society can offer, have sometimes felt that Plato's famous "mathematical examples'" were illustrations rather than central to his arguments, and some of Plato's mathematical excursuses have remained obscure to the present time.

    A Musical Interlude

    Plato's Academy-Academy was a suburb of Athens, named after the hero Academos or Ecademos.

    I can't help but say that I am indeed affected by the views of our universe. In a way that encompasses some very intriguing nodal points about our universe in the way that I see it.

    While I may not have shown the distinct lines of the Platonic solids, it is within context of a balloon with dye around it, that it could be so expressive of the Chaldni plate, that I couldn't resist that "harmonics flavour" as to how one might see the patterns underneath reality. How some gaussian coordinates interpretation of the "uv" lines, that were distinctive of an image in abstract spaces.

    Friday, January 05, 2007

    Images or Numbers By Themself

    “Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the mind will never penetrate” (cited by Ivars Peterson in Science News, 5/4/2002).

    I have an idea in mind here that will be slow to show because I am not sure how it is supposed to be laid out. So maybe by showing these numbers by them self? What use, if one did not, or was not able to see in another way?

    Figure 22.10: Double slit diffraction

    I looked at the "straight lines" of Thomas Young's trajectories of photon emission and while quite understandably shown to be of consequence in this post "Interference." I was more interested in how something could start off in one place and do this rotation of sorts, and then come back for examination again in the real world. The Spectrum

    What a novel idea to have the methods used by the predecessors like Maxwell, to have been united from Faraday's principals? To have Maxwell's equation Gaussian in interpretation of Riemann geometry, somehow, united by the geometries of Einstein and defined as gravity?

    But it is also in mind "that the image" has to be put here also before the numbers can show them self. What use these numbers if I do not transcend them to what they can imply in images, to know that the thinking here has to be orientated in such a way that what was simple and straight forward, could have non-euclidean orientations about it?

    Michael Faraday (September 22, 1791 – August 25, 1867) was a British scientist (a physicist and chemist) who contributed significantly to the fields of electromagnetism and electrochemistry.

    So one reads history in a lot of ways to learn of what has manifested into todays thinking. What lead from "Gaussian coordinates in an "non-euclidean way" to know that it had it's relation in today's physics. To have it included in how we see the consequences of GR in the world. It had been brought together for our eyes in what the photon can do in the gravitational field.

    Our Evolution to Images

    The Albrecht Durer's Magic Square

    Ulam's Spiral

    Pascal's Triangle

    Evolve to What?

    Who was to know what Leonard Susskind was thinking when his mathematical mind was engaged in seeing this "rubber band" had some other comparative abstraction, as something of consequence in our world. Yet, people focus on what they like to focus on, other then what "lead the mind" to think the way they do?

    Poincaré Conjecture
    If we stretch a rubber band around the surface of an apple, then we can shrink it down to a point by moving it slowly, without tearing it and without allowing it to leave the surface. On the other hand, if we imagine that the same rubber band has somehow been stretched in the appropriate direction around a doughnut......

    I have to rest now.

    Sunday, December 03, 2006

    Below the Surface is a Pattern

    Stephen Hawking:
    However, by using "matter/antimatter annihilation", velocities just below the speed of light could be reached, making it possible to reach the next star in about six years.

    While I presented the "break through in propulsion system" used for space travel by explaining the ideas behind Susskind's "thought experiment." It is with that thinking, one can go back and re-assess what we had thought about "time travel" and such?

    Some say it is like conscience effort of reflection? That we go back to the "memory reservoir (where is it-a space between the neurons?)" a "QFT realization" and drag it back up from the field to focalized surface awareness imaging, as some feature of this "time travel scenarion" currently being talk about in spacetime geometrics as warpage? As "an analogy" of the "negative aspect" of conscience?

    What is this Inductive/deductive feature then of consciousness?

    What is Toposense? A struggle between "discreteness and continuity?" On "large scale" we get "the jest" I think.

    It's a problem though, when it becomes chaotic and complex. An "entropic" realization. As if "arrow of time" goes forward, then how is it memory can be retrieved? Or that what exists "in" the blackhole can be used to ascertain what is going on inside and adjust for the "gravitational attraction" outside?"

    Perplexities of the theoretical mind

    Is mind, the "brain organ?" Did "mind" evolve "according to" the brain organ? If this is so, then what new "appendage" is currently being developed now? What "attribute of mind" will define it?

    I'm theoretically challenged. :)

    Or, does mind "evolve" the brain matters? If this is so, then "mind" is ahead of the brain matters? What new appendage is formed depends on the mind's development?

    It's as if there was another stage "before" the spacetime fabric? :) That the spacetime fabric is "the result."

    Tuesday, November 28, 2006

    Breakthrough Propulsion Physics?

    Shuttle Main Engine Test Firing-1981-A remote camera captures a close-up view of a Space Shuttle Main Engine during a test firing at the John C. Stennis Space Center in Hancock County, Mississippi.
    Spacecraft propulsion is used to change the velocity of spacecraft and artificial satellites, or in short, to provide delta-v. There are many different methods. Each method has drawbacks and advantages, and spacecraft propulsion is an active area of research. Most spacecraft today are propelled by heating the reaction mass and allowing it to flow out the back of the vehicle. This sort of engine is called a rocket engine.

    While the topic here is about how travel is possible, it is the idea that "new physics" can some how propelled forward the mass in space to do the things of travel necessary.

    In addition, a variety of hypothetical propulsion techniques have been considered that would require entirely new principles of physics to realize. To date, such methods are highly speculative and include

    Within the definitions of the literature it is then possible to deduce what is required? So this saves me the time while speaking to the new physics, of having to explain the rudimentary understandings of how I can leaped forward. No less, the idea of the "thought experiment" that is put in front of us that we create the dialogue necessary, with or without impute, to advance one's thinking.

    Credit: NASA CD-98-76634 by Les Bossinas. Artist's depiction of a hypothetical Wormhole Induction Propelled Spacecraft, based loosely on the 1994 "warp drive" paper of Miguel Alcubierre.


    The term breakthrough propulsion refers to concepts like space drives and faster-than-light travel, the kind of breakthroughs that would make interstellar travel practical.

    For a general explanation of the challenges and approaches of interstellar flight, please visit the companion website: Warp Drive: When? The Warp-When site is written for the general public and uses icons of science fiction to help convey such notions. This website, on the other hand, is intended for scientists and engineers.

    How is a Blackhole Determined?

    PLato:Remember the "closed loop process?"

    From the "blackhole horizon" what value would, "to e or not to e" speak too, if "one" was falling into the blackhole and "one" was out? Are they separated? What is our "state of the universe" then?

    A black hole is an object so massive that even light cannot escape from it. This requires the idea of a gravitational mass for a photon, which then allows the calculation of an escape energy for an object of that mass. When the escape energy is equal to the photon energy, the implication is that the object is a "black hole".

    IN the process of discovering the gravitational variances in space of "gravitational effects" how is it that a spaceship could become sensitive to the variations of that travel and slow down, if it did not have a way in which to calculate these fluctuations?

    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.

    There’s a place from which nothing escapes, not even light? So I have to re-educate some people so that they understand the limtiations that have been applied to current thinking, by what is currently out there in terms of what we know about blackholes. So breaking from of those limitation on perspective is very important with what we know now. How we can determine a blackhole.

    So here to then is a wider perspective about lagrangain perspective of space that is needed in the understanding of travel in space. Implications of ways and means to determine the needed velocities of the space craft to move forward within context of determinations of gravitational influences.

    Special Lagrangian geometry in particular was seen to be related to another String Theory inspired phenomenon, "Mirror Symmetry". Strominger, Yau and Zaslow conjectured that mirror symmetry could be explained by studying moduli spaces arising from special Lagrangian geometry.
    Dr. Mark Haskins

    So while our imagination is being captured by this "gravitational concentration" in the cosmos what use to discern the nature of the "closed loop process" if we did not consider the "thought experiment" of Susskind as I have spoken to it in the last couple of posts?

    Hawking radiation owes its existence to the weirdness of the quantum world, in which pairs of virtual particles pop up out of empty space, annihilate each other and disappear. Around a black hole, virtual particles and anti-particles can be separated by the event horizon. Unable to annihilate, they become real. The properties of each pair are linked, or entangled. What happens to one affects the other, even if one is inside the black hole.

    The first order of business here is that we use methods based on the understanding of the "link of entanglement" around what is inside the blackhole as a measure? What that photon is telling us in relation to the gravitational considerations influencing the space craft? IN this way, "calibration technique" allows for variances in the determination of what we see in the perspective of the cosmos as a vital differential understanding of that pathways through space.

    IN "weak field understanding" we know the loop process is symmetric? Also, if gravity is combined to electromagnetism, what value the photon for determination if we had not understood this relation to gravitation effects in the cosmos? So this process then is understood in terms of developing the means to travel in space that was before not so easily determined(escape velocities for mass in space), but has now been shattered by moving beyond the paradigms of previous thought processes?

    This is the benefit of thinking "thought experiments" to progress any idea. Now what has been written here, is it right or wrong?

    The Propulsion System?

    AIRES Cosmic Ray Showers

    Also no where have I revealed the propulsion system need in order for the space craft to exceed the gravitational variances within the cosmos

    Gamma Ray production in particle creation?

    The Pierre Auger Observatory in Malargue, Argentina, is a multinational collaboration of physicists trying to detect powerful cosmic rays from outer space. The energy of the particles here is above 1019eV, or over a million times more powerful than the most energetic particles in any human-made accelerator. No-one knows where these rays come from.

    Such cosmic rays are very rare, hitting an area the size of a football field once every 10 000 years. This means you need an enormous 'net' to catch these mysterious ultra high energy particles. The Auger project will have, when completed, about 1600 detectors.

    Understanding the collision process within context of our own planet, and what information is received from other events within the cosmos allows us "to rebuild" what happens no less then what "LIGO operations" and it's gathering techniques, allows us from the complexity of the information to a thing of beauty?

    The H.E.S.S. telescope array represent a multi-year construction effort by an international team of more than 100 scientists and engineers

    So how shall we identify such sources if we had not considered the "light house effect?"

    Black Hole-Powered Jet of Electrons and Sub-Atomic Particles Streams From Center of Galaxy M87

    Wednesday, November 22, 2006

    Tunnelling in Faster then Light

    Underneath this speculation of mine is the geometrical inclination of the universe in expression. If it's "dynamical nature is revealed" what allows us to think of why this universe at this time and junction, should be flat(?) according to the time of this universe in expression?

    Omega=the actual density to the critical density

    If we triangulate Omega, the universe in which we are in, Omegam(mass)+ Omega(a vacuum), what position geometrically, would our universe hold from the coordinates given?

    Positive energy density gives spacetime of the universe a positive curvature. A sphere? Negative curvature a region of spacetime that is negative and curved like a saddle? For time travel, and travel into the past, you need a universe that has a negative energy density.

    Thus the initial idea here to follow is that the process had to have a physics relation. This is based on the understanding of anti-particle/particle, and what becomes evident in the cosmos as a closed loop process. Any variation within this context, is the idea of "blackhole anti-particle expression" based on what can be seen at the horizon?

    A anti-particle can be considered as a particle moving back in time? Only massless particle can travel faster then light. Only faster then light massless particles can travel back in time? So of course, I am again thinking of the elephant process of Susskind and the closed loop process of the virtual particle/anti-particle. What comes out of it?

    That's not all. The fact that space-time itself is accelerating - that is, the expansion of the universe is speeding up - also creates a horizon. Just as we could learn that an elephant lurked inside a black hole by decoding the Hawking radiation, perhaps we might learn what's beyond our cosmic horizon by decoding its emissions. How? According to Susskind, the cosmic microwave background that surrounds us might be even more important than we think. Cosmologists study this radiation because its variations tell us about the infant moments of time, but Susskind speculates that it could be a kind of Hawking radiation coming from our universe's edge. If that's the case, it might tell us something about the elephants on the other side of the universe.

    So the anti-particle falls into the blackhole? How is it that I resolve this?? You can consider the anti-particle as traveling back in time. The micro perspective of the blackhole allows time travel backwards.

    Getty Images
    Although a 1916 paper by Ludwig Flamm from the University of Vienna [4] is sometimes cited as giving the first hint of a wormhole, "you definitely need hindsight to detect it," says Matt Visser of Victoria University in Wellington, New Zealand. Einstein and Rosen were the first to take the idea seriously and to try to accomplish some physics with it, he adds. The original goal may have faded, but the Einstein-Rosen bridge still pops up occasionally as a handy solution to the pesky problem of intergalactic travel.

    There are two cases in which the thoughts about faster then light particles are created and this is the part where one tries to get it right so as not to confuse themselves and others.


    So "open doorways" and ideas of "tunneling" are always interesting in terms of how we might look at an area like GR in cosmology? Look for way in which such instances make them self known.

    Are they applicable to the very nature of quantum perceptions that such probabilities could have emerged through them? Held to "time travel scenarios" and grabbed the history of what had already preceded us in past tense, could have been brought again forward for inspection?

    Sure I am quoting myself here, just to show one of the options I am showing by example. The second of course is where I was leading too in previous posts.

    So I was thinking here in context of one example in terms of the containment of the "graviton in a can" is really letting loose of the information in the collision process, as much as we like this "boundary condition" it really is not so.

    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.

    Tunneling 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 "tunneling," although the word in itself explains nothing.

    Chiao's group at Berkeley, Dr. Aephraim M. Steinberg at the University of Toronto and others are investigating the strange properties of tunneling, which was one of the subjects explored last month by scientists attending the Nobel Symposium on quantum physics in Sweden.

    "We find," Chiao said, "that a barrier placed in the path of a tunneling particle does not slow it down. In fact, we detect particles on the other side of the barrier that have made the trip in less time than it would take the particle to traverse an equal distance without a barrier -- in other words, the tunneling speed apparently greatly exceeds the speed of light. Moreover, if you increase the thickness of the barrier the tunneling speed increases, as high as you please.

    "This is another great mystery of quantum mechanics."

    Of course I am looking for processes in physics that would actually demonstrate this principal of energy calculated at the very beginning of the collision process, now explained in the detector, minus the extra energy that had gone where?

    This is the basis for the "Graviton in a can" example of what happens in the one scenario.

    A Bose-Einstein condensate (such as superfluid liquid helium) forms for reasons that only can be explained by quantum mechanics. Bose condensates form at low temperature

    Plasmas and Bose condensates

    So in essence the physics process that I am identifying is shown by understanding that the "graviton production" allows that energy to be transmitted outside the process of the LHC?

    This is the energy that can be calculated and left over from all the energy assumed in the very beginning of this collision process. Secondly, all energy used in this process would be in association with bulk perspective.

    This now takes me to the second process of "time travel" in the LHC process. The more I tried to figure this out the basis of thought here is that Cerenkov radiation in a vacuum still is slower then speed of light, yet within the medium of ice, this is a different story. So yes there are many corrections and insight here to consider again.

    The muon will travel faster than light in the ice (but of course still slower than the speed of light in vacuum), thereby producing a shock wave of light, called Cerenkov radiation. This light is detected by the photomultipliers, and the trace of the neutrinos can be reconstructed with an accuracy of a couple of degrees. Thus the direction of the incoming neutrino and hence the location of the neutrino source can be pinpointed. A simulation of a muon travelling through AMANDA is shown here (1.5 MB).

    So while sleeping last night the question arose in my mind as to the location of where the "higgs field" will be produced in the LHC experiment? Here also the the thoughts about the "cross over point" that would speak to the idea here of what reveals faster then light capabilities arising from the collision process?

    What are the main goals of the LHC?-
    The LHC will also help us to solve the mystery of antimatter. Matter and antimatter must have been produced in the same amounts at the time of the Big Bang. From what we have observed so far, our Universe is made of only matter. Why? The LHC could provide an answer.

    It was once thought that antimatter was a perfect 'reflection' of matter - that if you replaced matter with antimatter and looked at the result in a mirror, you would not be able to tell the difference. We now know that the reflection is imperfect, and this could have led to the matter-antimatter imbalance in our Universe.

    The strongest limits on the amount of antimatter in our Universe come from the analysis of the diffuse cosmic gamma-rays arriving on Earth and the density fluctuations of the cosmic background radiation. If one asumes that after the Big Bang, the Universe separated somehow into different domains where either matter or antimatter was dominant, then at the boundaries there should be annihilations, producing cosmic gamma rays. In both cases the limit proposed by current theories is practically equivalent to saying that there is no antimatter in our Universe.

    So we get the idea here in the collision process and from it the crossover point leaves a energy dissertation on what transpired from this condition and left the idea in my mind about the circumstances of what may have changed the the speed of the cosmos at varying times in the expansion process within our universe. So, this is where I was headed as I laid out the statement below.

    Of course this information is based on 2003 data but the jest of the idea here is that in order to go to a "fast forward" the conditions had to exist previously that did not included "sterile neutrinos" and were a result of this "cross over."

    So what is the jest of my thought here that I would go to great lengths here to speak about the ideas of what happens within the cosmos to change those varying times of expansion? It has to do with the Suns and the process within those suns that give the dark energy some value, in it's anti- gravity nature to align our selves and our thinking to the cosmological constant of Einstein. If we juggle the three ring circus we find that the curvature parameters can and do hold thoughts govern by the cosmological constant?

    It is thus equally important to identify this "physics process" that would allow such changes in the cosmos. So that we can understand the dynamical nature that the cosmos reveals to us can and does allow aspect of its galaxies within context of the universe to increase this expansive process while we question what drives such conditions.