Sunday, April 17, 2011

A Point in Space

For Newton the universe lived in an infinite and featureless space.There was no boundary, ad no possibility of conceiving anything outside of it. This was no problem for God, as he was everywhere. For Newton, space was the "sensorium" of God-the medium of his presence in and attachment to the world. The infinity of space was then a necessary reflection of the infinite capacity of God.The Life of the Cosmos By Lee Smolin Oxford University Press; New York, N.Y.: 1997, Page 91-See Also: Configuration Space

Can we be through physicality such a place,  through which  "a point" can be expressed, as the space in which we live?

Three-dimensional space is a geometric model of the physical universe in which we live. The three dimensions are commonly called length, width, and depth (or height), although any three directions can be chosen, provided that they do not lie in the same plane.

In physics and mathematics, a sequence of n numbers can be understood as a location in n-dimensional space. When n = 3, the set of all such locations is called 3-dimensional Euclidean space.

I mean the borders with which perspective is guaranteed is to fill, is to which all life evolves around,  is the perception that is limited to a defined space given through which that point becomes nothing more then the regurgitation of all their own parameters with which the individual builds their own confines? This is what is funneled into their way of thinking, yet out of complexity, such individuality is using the same system with which one can explain universality? How large is your universe?



I presented the idea of Entheorizing as an example of what can be placed over top of Pascal's triangle of possible numbered systems so as to be defined "as a funnel of a parameter spaces" complex and chaotic indeed that can be moved down through a point to a defined position?

Hi Steven,

Yes Pascal has been of quite interest to me as well.

The Galton Box is a interesting correlation in thinking as to outcome? Some might use mountains and pebbles...others still out comes as numbered systems as to the way in which the world expresses itself.

I tried abstractly to show that from symmetry(where is this?) has an asymmetrical relation as to the bean, as if, the energy enters into expression at the peak and arrives somewhere at it's based? Yes pyramidal:)

Space

Space is the boundless, three-dimensional extent in which objects and events occur and have relative position and direction.[1] Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of the boundless four-dimensional continuum known as spacetime. In mathematics one examines 'spaces' with different numbers of dimensions and with different underlying structures. The concept of space is considered to be of fundamental importance to an understanding of the physical universe although disagreement continues between philosophers over whether it is itself an entity, a relationship between entities, or part of a conceptual framework.

Debates concerning the nature, essence and the mode of existence of space date back to antiquity; namely, to treatises like the Timaeus of Plato, in his reflections on what the Greeks called: chora / Khora (i.e. 'space'), or in the Physics of Aristotle (Book IV, Delta) in the definition of topos (i.e. place), or even in the later 'geometrical conception of place' as 'space qua extension' in the Discourse on Place (Qawl fi al-makan) of the 11th century Arab polymath Ibn al-Haytham (Alhazen).[2] Many of these classical philosophical questions were discussed in the Renaissance and then reformulated in the 17th century, particularly during the early development of classical mechanics. In Isaac Newton's view, space was absolute - in the sense that it existed permanently and independently of whether there were any matter in the space.[3]

Other natural philosophers, notably Gottfried Leibniz, thought instead that space was a collection of relations between objects, given by their distance and direction from one another. In the 18th century, the philosopher and theologian George Berkely attempted to refute the 'visibility of spatial depth' in his Essay Towards a New Theory of Vision. Later, the great metaphysician Immanuel Kant described space and time as elements of a systematic framework that humans use to structure their experience; he referred to 'space' in his Critique of Pure Reason as being: a subjective 'pure a priori form of intuition', hence that its existence depends on our human faculties.

In the 19th and 20th centuries mathematicians began to examine non-Euclidean geometries, in which space can be said to be curved, rather than flat. According to Albert Einstein's theory of general relativity, space around gravitational fields deviates from Euclidean space.[4] Experimental tests of general relativity have confirmed that non-Euclidean space provides a better model for the shape of space.

Contents

Philosophy of space

Leibniz and Newton

In the seventeenth century, the philosophy of space and time emerged as a central issue in epistemology and metaphysics. At its heart, Gottfried Leibniz, the German philosopher-mathematician, and Isaac Newton, the English physicist-mathematician, set out two opposing theories of what space is. Rather than being an entity that independently exists over and above other matter, Leibniz held that space is no more than the collection of spatial relations between objects in the world: "space is that which results from places taken together".[5] Unoccupied regions are those that could have objects in them, and thus spatial relations with other places. For Leibniz, then, space was an idealised abstraction from the relations between individual entities or their possible locations and therefore could not be continuous but must be discrete.[6] Space could be thought of in a similar way to the relations between family members. Although people in the family are related to one another, the relations do not exist independently of the people.[7] Leibniz argued that space could not exist independently of objects in the world because that implies a difference between two universes exactly alike except for the location of the material world in each universe. But since there would be no observational way of telling these universes apart then, according to the identity of indiscernibles, there would be no real difference between them. According to the principle of sufficient reason, any theory of space that implied that there could be these two possible universes, must therefore be wrong.[8]


Newton took space to be more than relations between material objects and based his position on observation and experimentation. For a relationist there can be no real difference between inertial motion, in which the object travels with constant velocity, and non-inertial motion, in which the velocity changes with time, since all spatial measurements are relative to other objects and their motions. But Newton argued that since non-inertial motion generates forces, it must be absolute.[9] He used the example of water in a spinning bucket to demonstrate his argument. Water in a bucket is hung from a rope and set to spin, starts with a flat surface. After a while, as the bucket continues to spin, the surface of the water becomes concave. If the bucket's spinning is stopped then the surface of the water remains concave as it continues to spin. The concave surface is therefore apparently not the result of relative motion between the bucket and the water.[10] Instead, Newton argued, it must be a result of non-inertial motion relative to space itself. For several centuries the bucket argument was decisive in showing that space must exist independently of matter.

Kant

In the eighteenth century the German philosopher Immanuel Kant developed a theory of knowledge in which knowledge about space can be both a priori and synthetic.[11] According to Kant, knowledge about space is synthetic, in that statements about space are not simply true by virtue of the meaning of the words in the statement. In his work, Kant rejected the view that space must be either a substance or relation. Instead he came to the conclusion that space and time are not discovered by humans to be objective features of the world, but are part of an unavoidable systematic framework for organizing our experiences.[12]

Non-Euclidean geometry

Spherical geometry is similar to elliptical geometry. On the surface of a sphere there are no parallel lines.
 
Euclid's Elements contained five postulates that form the basis for Euclidean geometry. One of these, the parallel postulate has been the subject of debate among mathematicians for many centuries. It states that on any plane on which there is a straight line L1 and a point P not on L1, there is only one straight line L2 on the plane that passes through the point P and is parallel to the straight line L1. Until the 19th century, few doubted the truth of the postulate; instead debate centered over whether it was necessary as an axiom, or whether it was a theory that could be derived from the other axioms.[13] Around 1830 though, the Hungarian János Bolyai and the Russian Nikolai Ivanovich Lobachevsky separately published treatises on a type of geometry that does not include the parallel postulate, called hyperbolic geometry. In this geometry, an infinite number of parallel lines pass through the point P. Consequently the sum of angles in a triangle is less than 180o and the ratio of a circle's circumference to its diameter is greater than pi. In the 1850s, Bernhard Riemann developed an equivalent theory of elliptical geometry, in which no parallel lines pass through P. In this geometry, triangles have more than 180o and circles have a ratio of circumference-to-diameter that is less than pi.
Type of geometry Number of parallels Sum of angles in a triangle Ratio of circumference to diameter of circle Measure of curvature
Hyperbolic Infinite < 180o > π < 0
Euclidean 1 180o π 0
Elliptical 0 > 180o < π > 0

Gauss and Poincaré

Although there was a prevailing Kantian consensus at the time, once non-Euclidean geometries had been formalised, some began to wonder whether or not physical space is curved. Carl Friedrich Gauss, a German mathematician, was the first to consider an empirical investigation of the geometrical structure of space. He thought of making a test of the sum of the angles of an enormous stellar triangle and there are reports he actually carried out a test, on a small scale, by triangulating mountain tops in Germany.[14]

Henri Poincaré, a French mathematician and physicist of the late 19th century introduced an important insight in which he attempted to demonstrate the futility of any attempt to discover which geometry applies to space by experiment.[15] He considered the predicament that would face scientists if they were confined to the surface of an imaginary large sphere with particular properties, known as a sphere-world. In this world, the temperature is taken to vary in such a way that all objects expand and contract in similar proportions in different places on the sphere. With a suitable falloff in temperature, if the scientists try to use measuring rods to determine the sum of the angles in a triangle, they can be deceived into thinking that they inhabit a plane, rather than a spherical surface.[16] In fact, the scientists cannot in principle determine whether they inhabit a plane or sphere and, Poincaré argued, the same is true for the debate over whether real space is Euclidean or not. For him, which geometry was used to describe space, was a matter of convention.[17] Since Euclidean geometry is simpler than non-Euclidean geometry, he assumed the former would always be used to describe the 'true' geometry of the world.[18]

Einstein

In 1905, Albert Einstein published a paper on a special theory of relativity, in which he proposed that space and time be combined into a single construct known as spacetime. In this theory, the speed of light in a vacuum is the same for all observers—which has the result that two events that appear simultaneous to one particular observer will not be simultaneous to another observer if the observers are moving with respect to one another. Moreover, an observer will measure a moving clock to tick more slowly than one that is stationary with respect to them; and objects are measured to be shortened in the direction that they are moving with respect to the observer.

Over the following ten years Einstein worked on a general theory of relativity, which is a theory of how gravity interacts with spacetime. Instead of viewing gravity as a force field acting in spacetime, Einstein suggested that it modifies the geometric structure of spacetime itself.[19] According to the general theory, time goes more slowly at places with lower gravitational potentials and rays of light bend in the presence of a gravitational field. Scientists have studied the behaviour of binary pulsars, confirming the predictions of Einstein's theories and Non-Euclidean geometry is usually used to describe spacetime.

Mathematics

In modern mathematics spaces are defined as sets with some added structure. They are frequently described as different types of manifolds, which are spaces that locally approximate to Euclidean space, and where the properties are defined largely on local connectedness of points that lie on the manifold. There are however, many diverse mathematical objects that are called spaces. For example, vector spaces such as function spaces may have infinite numbers of independent dimensions and a notion of distance very different to Euclidean space, and topological spaces replace the concept of distance with a more abstract idea of nearness.

Physics

Classical mechanics

Classical mechanics
History of classical mechanics · Timeline of classical mechanics
[hide]Fundamental concepts
Space · Time · Velocity · Speed · Mass · Acceleration · Gravity · Force · Impulse · Torque / Moment / Couple · Momentum · Angular momentum · Inertia · Moment of inertia · Reference frame · Energy · Kinetic energy · Potential energy · Mechanical work · Virtual work · D'Alembert's principle
v · d · e
Space is one of the few fundamental quantities in physics, meaning that it cannot be defined via other quantities because nothing more fundamental is known at the present. On the other hand, it can be related to other fundamental quantities. Thus, similar to other fundamental quantities (like time and mass), space can be explored via measurement and experiment.

Astronomy

Astronomy is the science involved with the observation, explanation and measuring of objects in outer space.

Relativity

Before Einstein's work on relativistic physics, time and space were viewed as independent dimensions. Einstein's discoveries showed that due to relativity of motion our space and time can be mathematically combined into one object — spacetime. It turns out that distances in space or in time separately are not invariant with respect to Lorentz coordinate transformations, but distances in Minkowski space-time along space-time intervals are—which justifies the name.
In addition, time and space dimensions should not be viewed as exactly equivalent in Minkowski space-time. One can freely move in space but not in time. Thus, time and space coordinates are treated differently both in special relativity (where time is sometimes considered an imaginary coordinate) and in general relativity (where different signs are assigned to time and space components of spacetime metric).

Furthermore, in Einstein's general theory of relativity, it is postulated that space-time is geometrically distorted- curved -near to gravitationally significant masses.[20]

Experiments are ongoing to attempt to directly measure gravitational waves. This is essentially solutions to the equations of general relativity, which describe moving ripples of spacetime. Indirect evidence for this has been found in the motions of the Hulse-Taylor binary system.

Cosmology

Relativity theory leads to the cosmological question of what shape the universe is, and where space came from. It appears that space was created in the Big Bang, 13.7 billion years ago and has been expanding ever since. The overall shape of space is not known, but space is known to be expanding very rapidly due to the Cosmic Inflation.

Spatial measurement

The measurement of physical space has long been important. Although earlier societies had developed measuring systems, the International System of Units, (SI), is now the most common system of units used in the measuring of space, and is almost universally used.

Currently, the standard space interval, called a standard meter or simply meter, is defined as the distance traveled by light in a vacuum during a time interval of exactly 1/299,792,458 of a second. This definition coupled with present definition of the second is based on the special theory of relativity in which the speed of light plays the role of a fundamental constant of nature.

Geographical space

Geography is the branch of science concerned with identifying and describing the Earth, utilizing spatial awareness to try and understand why things exist in specific locations. Cartography is the mapping of spaces to allow better navigation, for visualization purposes and to act as a locational device. Geostatistics apply statistical concepts to collected spatial data to create an estimate for unobserved phenomena.

Geographical space is often considered as land, and can have a relation to ownership usage (in which space is seen as property or territory). While some cultures assert the rights of the individual in terms of ownership, other cultures will identify with a communal approach to land ownership, while still other cultures such as Australian Aboriginals, rather than asserting ownership rights to land, invert the relationship and consider that they are in fact owned by the land. Spatial planning is a method of regulating the use of space at land-level, with decisions made at regional, national and international levels. Space can also impact on human and cultural behavior, being an important factor in architecture, where it will impact on the design of buildings and structures, and on farming.

Ownership of space is not restricted to land. Ownership of airspace and of waters is decided internationally. Other forms of ownership have been recently asserted to other spaces — for example to the radio bands of the electromagnetic spectrum or to cyberspace.

Public space is a term used to define areas of land as collectively owned by the community, and managed in their name by delegated bodies; such spaces are open to all. While private property is the land culturally owned by an individual or company, for their own use and pleasure.

Abstract space is a term used in geography to refer to a hypothetical space characterized by complete homogeneity. When modeling activity or behavior, it is a conceptual tool used to limit extraneous variables such as terrain.

In psychology

Psychologists first began to study the way space is perceived in the middle of the 19th century. Those now concerned with such studies regard it as a distinct branch of psychology. Psychologists analyzing the perception of space are concerned with how recognition of an object's physical appearance or its interactions are perceived.

Other, more specialized topics studied include amodal perception and object permanence. The perception of surroundings is important due to its necessary relevance to survival, especially with regards to hunting and self preservation as well as simply one's idea of personal space.

Several space-related phobias have been identified, including agoraphobia (the fear of open spaces), astrophobia (the fear of celestial space) and claustrophobia (the fear of enclosed spaces).

See also

References

  1. ^ Britannica Online Encyclopedia: Space
  2. ^ Refer to Plato's Timaeus in the Loeb Classical Library, Harvard University, and to his reflections on: Chora / Khora. See also Aristotle's Physics, Book IV, Chapter 5, on the definition of topos. Concerning Ibn al-Haytham's 11th century conception of 'geometrical place' as 'spatial extension', which is akin to Descartes' and Leibniz's 17th century notions of extensio and analysis situs, and his own mathematical refutation of Aristotle's definition of topos in natural philosophy, refer to: Nader El-Bizri, 'In Defence of the Sovereignty of Philosophy: al-Baghdadi's Critique of Ibn al-Haytham's Geometrisation of Place', Arabic Sciences and Philosophy: A Historical Journal (Cambridge University Press), Vol.17 (2007), pp. 57-80.
  3. ^ French and Ebison, Classical Mechanics, p. 1
  4. ^ Carnap, R. An introduction to the Philosophy of Science
  5. ^ Leibniz, Fifth letter to Samuel Clarke
  6. ^ Vailati, E, Leibniz & Clarke: A Study of Their Correspondence p. 115
  7. ^ Sklar, L, Philosophy of Physics, p. 20
  8. ^ Sklar, L, Philosophy of Physics, p. 21
  9. ^ Sklar, L, Philosophy of Physics, p. 22
  10. ^ Newton's bucket
  11. ^ Carnap, R, An introduction to the philosophy of science, p. 177-178
  12. ^ Lucas, John Randolph. Space, Time and Causality. p. 149. ISBN 0198750579.
  13. ^ Carnap, R, An introduction to the philosophy of science, p. 126
  14. ^ Carnap, R, An introduction to the philosophy of science, p. 134-136
  15. ^ Jammer, M, Concepts of Space, p. 165
  16. ^ A medium with a variable index of refraction could also be used to bend the path of light and again deceive the scientists if they attempt to use light to map out their geometry
  17. ^ Carnap, R, An introduction to the philosophy of science, p. 148
  18. ^ Sklar, L, Philosophy of Physics, p. 57
  19. ^ Sklar, L, Philsosophy of Physics, p. 43
  20. ^ chapters 8 and 9- John A. Wheeler "A Journey Into Gravity and Spacetime" Scientific American ISBN 0-7167-6034-7

Tuesday, April 12, 2011

Entheorizing

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


I was pretty sure at that time that I was the only one in the world who knew this.

Thoughts cross my mind as it did with Susskind's journey into the understanding of how something like a rubber band could have helped him made sense of anything. Just as with Einstein, and how it finally came to him in the understanding of the geometry Grossmann had presented to him?

It was Grossmann who emphasized the importance of a non-Euclidean geometry called elliptic geometry to Einstein, which was a necessary step in the development of Einstein's general theory of relativity. Abraham Pais's book on Einstein suggests that Grossman mentored Einstein in tensor theory as well.

That intuitive leap is an important one in my view when it has been understood that all the data had been gone through, and ultimately, as if resting in some state of equilibrium( it should be understood that QGP and Lagrangian numbers provide such places in my mind), it was fortunate for an access to potential was realized by working to arrive at such a point.

If you picture probabilistic valuation as a link between such a funnel pointing toward the tip of Pascal's triangle, then what fills that funnel(potential) and what comes out of Pascal's triangle? What s the nature of that numbered system. Choose one?

If you can funnel such potential through a point it is more then the constraint with which others may see this proverbial struggle as to identify it as a koan, but more to realize that such potential is the very essence of accessing such a point and allowing the solution toward materialism, which was logically conducive to combing all that data.

So the idea here is that such a heat death could have happened within any mind that the very essence of such a QGP was to realize that it provide for such "a mean" in which transference of information could take place? So how can any mind ever go there?:)

I mean for sure, not only was I concerned about finding this place inside each of our selves and the truth seeking that goes on, but also toward understanding that this was a cosmological process about which sustenance of the universe could have ever been measured in it's "status quo?"




The shaky game: Einstein, realism, and the quantum theory By Arthur Fine



4 Arthur Fine (1986) characterizes such a move, this not the only instance in Einstein's thinking, as the "entheorizing" of a methodological principle in the form of a physical postulate. Fine, however, argues that determinism is, for Einstein, the entheorized version of realism.
Stanford Encyclopedia of Philosophy Notes to Einstein's Philosophy of Science-Citation Information Don A. Howard

It is most certainly important for myself to maintain some thread of consistency in regard to how we look at reality and how one theorizes about it. So sure... what was Einstein's Realism all about?

So you have to follow that line of thinking?

It still is about truth. About looking to understand it, and being able to know when you have come across it. Does it sound right to you, and does it ring at the very basis of your being when you recognize it?

***


Einstein and the Development of Twentieth-Century

Philosophy of Science
Don Howard
University of Notre Dame

And in a 28 November 1944 letter to Robert Thornton he echoed those words of nearly thirty years earlier:

I fully agree with you about the significance and educational value of methodology as well as history and philosophy of science. So many people today—and even professional scientists—seem to me like somebody who has seen thousands of trees but has never seen a forest. A knowledge of the historic and philosophical background gives that kind of independence from prejudices of his generation from which most scientists are suffering.
This independence created by philosophical insight is—in my opinion—the mark of distinction between a mere artisan or specialist and a real seeker after truth. (Einstein to
Thornton, 7 December 1944, EA 61-574)

Sunday, April 10, 2011

Triangle of Thoughts

Triangle of Thought by Alain Connes, Andre Lichnerowicz, Marcel Paul Schutzenberger

Conversations on Mind, Matter, and Mathematics

 

The original Socratic dialogues were artificially constructed to present a coherent view. The dialogue between Connes and Changeux is quite different. It is the recording of real-life arguments where the speakers are frequently at cross-purposes and operate in different planes. For the reader this can be irritating but it also encourages him to become involved and frame his own answers. . . . -- Sir Michael Atiyah, The Times Higher Education Supplement

See:Conversations on Mind, Matter, and Mathematics Jean-Pierre Changeux (Author), Alain Connes (Author), M. B. DeBevoise (Translator)

***

Do numbers and the other objects of mathematics enjoy a timeless existence independent of human minds, or are they the products of cerebral invention? Do we discover them, as Plato supposed and many others have believed since, or do we construct them? Does mathematics constitute a universal language that in principle would permit human beings to communicate with extraterrestrial civilizations elsewhere in the universe, or is it merely an earthly language that owes its accidental existence to the peculiar evolution of neuronal networks in our brains? Does the physical world actually obey mathematical laws, or does it seem to conform to them simply because physicists have increasingly been able to make mathematical sense of it? Jean-Pierre Changeux, an internationally renowned neurobiologist, and Alain Connes, one of the most eminent living mathematicians, find themselves deeply divided by these questions.

The problematic status of mathematical objects leads Changeux and Connes to the organization and function of the brain, the ways in which its embryonic and post-natal development influences the unfolding of mathematical reasoning and other kinds of thinking, and whether human intelligence can be simulated, modeled,--or actually reproduced-- by mechanical means. The two men go on to pose ethical questions, inquiring into the natural foundations of morality and the possibility that it may have a neural basis underlying its social manifestations. This vivid record of profound disagreement and, at the same time, sincere search for mutual understanding, follows in the tradition of Poincaré, Hadamard, and von Neumann in probing the limits of human experience and intellectual possibility. Why order should exist in the world at all, and why it should be comprehensible to human beings, is the question that lies at the heart of these remarkable dialogues. From Princeton University Press
 ***

See Also: Remarks on Jean-Pierre Changeux & Alain Connes Conversations on Mind, Matter, and Mathematics by Jean Petitot

Friday, April 08, 2011

Invariant Mass Distribution of Jet Pairs

Invariant Mass Distribution of Jet Pairs Produced in Association with a W boson in proton-antiproton Collisions at sqrt(s) = 1.96 TeV
The di-jet invariant mass distribution for candidate events selected in an analysis of W+2 jet events. The black points represent the data. The red line plots the expected Standard Model background shape based on Monte Carlo modeling. The red shading shows the systematic and statistical uncertainty on this background shape. The blue histogram is the Gaussian fit to the unexpected peak centered at 144 GeV/c2. See:

Fermilab’s data peak that causes excitement

Monday, April 04, 2011

It's Lowest Energy State....Matter Formed?

Shape as Memory : A Geometric Theory of Architecture

also

The structure of paintings

 

 
I just wanted to lay out a perspective in relation to how one might describe the engine in relation to the design of the exhaust system as supportive of the whole frame of reference as the engine.

The pipe is a resonant chamber which shapes the exhaust pulse train in a way which uses shock waves to constrain the release of the combustion.Russell Grunloh (boatguy)
I mean it is not wholly certain for me that without perception, once realizing that potential recognizes that like some "source code" we are closer to recognizing the seed of our action, is an expression of the momentum of our being. It is a stepping off of all that we have known, is an innate expression of our being in action.

So as souls, we are immortalized as expressions of,  like a memory that tells a story about our life, our choices and the life we choose to live.

Dr. Mark Haskins
On a wider class of complex manifolds - the so-called Calabi-Yau manifolds - there is also a natural notion of special Lagrangian geometry. Since the late 1980s these Calabi-Yau manifolds have played a prominent role in developments in High Energy Physics and String Theory. In the late 1990s it was realized that calibrated geometries play a fundamental role in the physical theory, and calibrated geometries have become synonymous with "Branes" and "Supersymmetry".

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

This conjecture stimulated much work by mathematicians, but a lot still remains to be done. A central problem is to understand what kinds of singularities can form in families of smooth special Lagrangian submanifolds. A starting point for this is to study the simplest models for singular special Lagrangian varieties, namely cones with an isolated singularity. My research in this area ([2], [4], [6]) has focused on understanding such cones especially in dimension three, which also corresponds to the most physically relevant case.

So it is also about string theory in a way for me as well, and my attempts to understand those expressions in the valley.  Poincare's description of a pebble, rolling down from the hilltop.


It follows then that not all comments will not all be accepted, yet,  I felt it important for one to recognize what Poincare was saying and what I am saying.


HENRI POINCARE Mathematics and Science:Last Essays


Since we are assuming at this juncture the point of view of the mathematician, we must give to this concept all the precision that it requires, even if it becomes necessary to use mathematical language. We should then say that the body of laws is equivalent to a system of differential equations which link the speed of variations of the different elements of the universe to the present values of these elements.

Such a system involves, as we know, an infinite number of solutions, But if we take the initial values of all the elements, that is,their values at the instant t =(which would correspond in ordinary language to the "present"), the solution is completely determined, so that we can calculate the values of all the elements at any period
whatever, whether we suppose />0, which corresponds to the "future," or whether we suppose t<0, which corresponds to the "past." What is important to remember is that the manner of inferring the past from the present does not differ from that of inferring the future from the present.

Contrast the pebble as an issuance of,  from symmetry, and the top of mountain(a sharpened pencil standing straight up) and the decay(asymmetry), as an expression of the solidification of who we are in that valley. as a pebble?? After the example, we are but human form with a soul encased. The present, is our future? Our past, our presence?

Mathematics and Science: Last Essays, by Henri Poincare

8 Last Essays

    "But it is exactly because all things tend toward death that life is
    an exception which it is necessary to explain.

    Let rolling pebbles be left subject to chance on the side of a
    mountain, and they will all end by falling into the valley. If we
    find one of them at the foot, it will be a commonplace effect which
    will teach us nothing about the previous history of the pebble;
    we will not be able to know its original position on the mountain.
    But if, by accident, we find a stone near the summit, we can assert
    that it has always been there, since, if it had been on the slope, it
    would have rolled to the very bottom. And we will make this
    assertion with the greater certainty, the more exceptional the event
    is and the greater the chances were that the situation would not
    have occurred."

Of course I do not believe our lives are just an expression of chance,  but choice as "a memory" we choose. Of course too, how do you set up a life as an expression if you do not continue to learn?



In the pool of symmetry, how did we ever begin? I looked for such expressions as if mathematically deduced from a time where we might be closer to the idea of such a pool. Ramanujan comes to mind.

Then too, if we are to become spiritually immersed back again from where we came from,  then how can we individually be explained "as a spark of measure,"  for each soul as a memory to be chosen from all that has existed before, for such an expression in this life as the task of it's future??

Friday, April 01, 2011

Shifting the Way in Which We See


"Where in this day and age, does one go to ask the questions? Where does one go to find like "minded" people who are also seeking the answers?"What If We Could Ask The Big Questions?
Ask yourself could you have been shifted from the way you have always looked at the world.....is the world different then, or, did you not ever consider looking at the world in new way? Obviously you did. I see the trademarks of one pushing the boundary of one's own perceptions. Your asking others to do the same.

A Path with a Heart
I have told you that to choose a path you must be free from fear and ambition. The desire to learn is not ambition. It is our lot as men to want to know.

The path without a heart will turn against men and destroy them. It does not take much to die, and to seek death is to seek nothing.

We have solidify our places in the reality by our acquiescence to the way we have always looked at it. Some of the older folk might have read Carlos Castaneda as a  past time as much as your Pirsig,  questioned the truth of the experiences.... so let's say such a "tonal shift" could have shocked one out of, as all of your life in localization then what can be gained by using that new perspective?
Often, an increase or decrease in some level in this information is indicated by an increase or decrease in pitch, amplitude or tempo, but could also be indicated by varying other less commonly used components.. Sonification

There has to be a method by which others could see in the same way that another can, that it would allow inspection of the world around us together. It should be as if experimentally procedures,  so as to help us to look at a spectrum of definitions pointing toward another with such  a view of the reality in sameness too? How real is the world around as you look?

BBC article-Click on Image

See Also: LHC sound


This is important, in that what we have always been accustomed too, can be changed in the way the world may be measured in terms of it  being vibrant and harmonic, as if sounding in colourful ways. I mean we would want such a procession to be lawful and intelligently explained that there is no misconceptions as to the basis of such a journey as to seeing the world in that different light.

Solar Dynamics Observatory Pick of the Week

(Click on Image for Larger Veiwing)


Then and Now

A side-by-side comparison of the Sun from precisely two years ago (left, from SOHO) to the present (right, from Solar Dynamics Observatory) dramatically illustrates just how active the Sun has become (Mar. 27-28, 2011). Viewed in two similar wavelengths of extreme ultraviolet light, the Sun now sports numerous active regions that appear as lighter areas that are capable of producing solar storms. Two years ago the Sun was in a very quiet period (solar minimum). The Sun's maximum period of activity is predicted to be around 2013, so we still have quite a ways to go.See: Solar Dynamics Observatory

Tuesday, March 29, 2011

Concentration as a Power of Perceiving

The river Pregel divides the town of Konigsberg into four separate land masses, A, B, C, and D. Seven bridges connect the various parts of town, and some of the town's curious citizens wondered if it were possible to take a journey across all seven bridges without having to cross any bridge more than once. All who tried ended up in failure, including the Swiss mathematician, Leonhard Euler (1707-1783)(pronounced "oiler"), a notable genius of the eighteenth-century.

The lessons of those who are engaged in the mathematics of,  must nurture the powers of intuition to advance the road of uncharted waters so as to be inspired to see nature and what underlies it as if guided by some unseen hand.

How would one tell another of "such a feeling" as they progress on their own journey while having all the tools of their trade in mathematics with them?


Euler was prolific, both in offspring and in intellectual output. He fathered thirteen children, albeit with two wives, and wrote more then eight hundred books and papers in all areas of mathematics. This is all the more astonishing-the part about the papers, that is, not the children-since for a large part of his life he was blind. His power of concentration must have been nothing less then astounding, keeping in mind that he did much of his work without eyesight while screaming kids were scampering around. Late in life he claimed that he had done some of the best work with a baby in his arms and other children playing at his feet.Para 1, Page 54, Poincare's Prize by George G. Szpiro

Outside of themself, one might look to find conducive places sounds, inspirations that would help them on their journey. That journey is usually alone, but if you meet another that has an equal understanding and can help progress you beyond the points on which you are stuck, why would you not collaborate to move forward? To help others move forward?

 The Whole World is a Stage

Euler product formula


Now you must know what sets my mind to think in such abstract spaces. "Probability of seeing a stage in a concert."



A diagram of the Königsberg bridges

Topological ideas are present in almost all areas of today's mathematics. The subject of topology itself consists of several different branches, such as point set topology, algebraic topology and differential topology, which have relatively little in common. We shall trace the rise of topological concepts in a number of different situations.