How the Natural World has Been Painted

While some are intrigued by EM waves, I have a fascination for GW and the way we can portrait the natural world, we do not see.



The sounds of gravitional waves are probably too low for us to actually hear. However, the signals that scientists hope to measure with LISA and other gravitational wave detectors are best described as "sounds." If we could hear them, here are some of the possible sounds of a gravitational wave generated by the movement of a small body inspiralling into a black hole.

There is a lesson in this, when you learn to hear what billiard balls sound like, and what the resulting "click" could represent.

Savas Dimopoulos

Here’s an analogy to understand this: imagine that our universe is a two-dimensional pool table, which you look down on from the third spatial dimension. When the billiard balls collide on the table, they scatter into new trajectories across the surface. But we also hear the click of sound as they impact: that’s collision energy being radiated into a third dimension above and beyond the surface. In this picture, the billiard balls are like protons and neutrons, and the sound wave behaves like the graviton.

It helps you to see the world as a very much different place then the one we are accustomed too.

Can these be applied to such romantic reasoning, that we are encouraged to poetry and other things, where such idealizations, are battling for whose interpretation is right? What portraits are these that there is no romm for them to hang for observation? A glimpse of Mona Lisa's smile, that if taken from various perspective it would seem to be always looking at you? How could you distance yourself, if you are what you think?

Quantum Gravity

The jump from conventional field theories of point-like objects to a theory of one-dimensional objects has striking implications. The vibration spectrum of the string contains a massless spin-2 particle: the graviton. Its long wavelength interactions are described by Einstein's theory of General Relativity. Thus General Relativity may be viewed as a prediction of string theory!

Imagine the very canvas is string theories very fabric of the cosmos:)


J. Metzinger Le Gouter/Teatime (1911)

"Dynamical triangulations" and such, that such a painting will explore the greater potential of perception, from varying perspectives?

Art Mirrors Physics Mirrors Art

The French mathematician Henri Poincaré provided inspiration for both Einstein and Picasso. Einstein read Poincaré's Science and Hypothesis (French edition 1902, German translation 1904) and discussed it with his friends in Bern. He might also have read Poincaré's 1898 article on the measurement of time, in which the synchronization of clocks was discussed--a topic of professional interest to Einstein as a patent examiner. Picasso learned about Science and Hypothesis indirectly through Maurice Princet, an insurance actuary who explained the new geometry to Picasso and his friends in Paris. At that time there was considerable popular fascination with the idea of a fourth spatial dimension, thought by some to be the home of spirits, conceived by others as an "astral plane" where one can see all sides of an object at once. The British novelist H. G. Wells caused a sensation with his book The Time Machine (1895, French translation in a popular magazine 1898-99), where the fourth dimension was time, not space.

Three Sphere

There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world.

— Nikolai Lobachevsky

Bernhard Riemann once claimed: "The value of non-Euclidean geometry lies in its ability to liberate us from preconceived ideas in preparation for the time when exploration of physical laws might demand some geometry other than the Euclidean." His prophesy was realized later with Einstein's general theory of relativity. It is futile to expect one "correct geometry" as is evident in the dispute as to whether elliptical, Euclidean or hyperbolic geometry is the "best" model for our universe. Henri Poincaré, in Science and Hypothesis (New York: Dover, 1952, pp. 49-50) expressed it this way.

A sphere is, roughly speaking, a ball-shaped object. In mathematics, a sphere comprises only the surface of the ball, and is therefore hollow. In non-mathematical usage a sphere is often considered to be solid (which mathematicians call ball).

More precisely, a sphere is the set of points in 3-dimensional Euclidean space which are at distance r from a fixed point of that space, where r is a positive real number called the radius of the sphere. The fixed point is called the center or centre, and is not part of the sphere itself. The special case of r = 1 is called a unit sphere.

Spheres can be generalized to higher dimensions. For any natural number n, an n-sphere is the set of points in (n+1)-dimensional Euclidean space which are at distance r from a fixed point of that space, where r is, as before, a positive real number. Here, the choice of number reflects the dimension of the sphere as a manifold.

a 0-sphere is a pair of points

a 1-sphere is a circle

a 2-sphere is an ordinary sphere

a 3-sphere is a sphere in 4-dimensional Euclidean space


Spheres for n ¡Ý 3 are sometimes called hyperspheres. The n-sphere of unit radius centred at the origin is denoted Sn and is often referred to as "the" n-sphere. The notation Sn is also often used to denote any set with a given structure (topological space, topological manifold, smooth manifold, etc.) identical (homeomorphic, diffeomorphic, etc.) to the structure of Sn above.

An n-sphere is an example of a compact n-manifold.

In mathematics, a 3-sphere is a higher-dimensional analogue of a sphere. A regular sphere, or 2-sphere, consists of all points equidistant from a single point in ordinary 3-dimensional Euclidean space, R3. A 3-sphere consists of all points equidistant from a single point in R4. Whereas a 2-sphere is a smooth 2-dimensional surface, a 3-sphere is an object with three dimensions, also known as 3-manifold.

In an entirely analogous manner one can define higher-dimensional spheres called hyperspheres or n-spheres. Such objects are n-dimensional manifolds.

Some people refer to a 3-sphere as a glome from the Latin word glomus meaning ball.

Poincare 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, then there is no way of shrinking it to a point without breaking either the rubber band or the doughnut. We say the surface of the apple is "simply connected," but that the surface of the doughnut is not...

In mathematics, the Poincaré conjecture is a conjecture about the characterisation of the three-dimensional sphere amongst 3-manifolds. It is widely considered to be the most important unsolved problem in topology.

The Poincaré conjecture is one of the seven Millennium Prize Problems for which the Clay Mathematics Institute is offering a $1,000,000 prize for a correct solution. As of 2004 it is becoming accepted that a proof offered by Grigori Perelman in 2002 may have disposed of this question, after nearly a century. Perelman's work is still under review.

Artists such as M. C. Escher have become fascinated with the Poincaré model of hyperbolic geometry and he composed a series of "Circle Limit" illustrations of a hyperbolic universe. In Figure 17.a he uses the backbones of the flying fish as "straight lines", being segments of circles orthogonal to his fundamental circle. In Figure 17.b he does the same with angels and devils. Besides artists and astronomers, many scholars have been shaken by non-Euclidean geometry. Euclidean geometry had been so universally accepted as an eternal and absolute truth that scholars believed they could also find absolute standards in human behavior, in law, ethics, government and economics. The discovery of non-Euclidean geometry shocked them into understanding their error in expecting to determine the "perfect state" by reasoning alone.

Deterministic Chaos Theory and the Cosmos

This gallery was inspired by a lecture of Dr. Julien Sprott and his work.To learn how these are created, check out my Strange Attractor Tutorial. Click on the images to enlarge them.

It was important for me to reveal how I am seeing the cosmo. How the superhighway has been spoken too, in regards to the Langrange points.These points are lead to and from unstable orbits. Points, where gravity balances out between bodies, like the earth and the moon. These are not to be considered stable equilibrium points.

Here we speak of the interactions of the Sun-Earth Lagrange point dynamics with the Earth-Moon Lagrange point dynamics. We motivate the discussion using Jupiter comet orbits as examples. By studying the natural dynamics of the Solar System, we enhance current and future space mission design."

So what would these winding paths around this point look like? You had to be able to see this work on a cosmological scale and in seeing this used in practise we have now gained in deterministc systems where previously we did not recognize the multiplicty of rotations within regions afffected, between gravitational points called L1 and L2.

The Roots of Chaos Theory

The roots of chaos theory date back to about 1900, in the studies of Henri Poincaré on the problem of the motion of three objects in mutual gravitational attraction, the so-called three-body problem. Poincaré found that there can be orbits which are nonperiodic, and yet not forever increasing nor approaching a fixed point. Later studies, also on the topic of nonlinear differential equations, were carried out by G.D. Birkhoff, A.N. Kolmogorov, M.L. Cartwright, J.E. Littlewood, and Stephen Smale. Except for Smale, who was perhaps the first pure mathematician to study nonlinear dynamics, these studies were all directly inspired by physics: the three-body problem in the case of Birkhoff, turbulence and astronomical problems in the case of Kolmogorov, and radio engineering in the case of Cartwright and Littlewood. Although chaotic planetary motion had not been observed, experimentalists had encountered turbulence in fluid motion and nonperiodic oscillation in radio circuits without the benefit of a theory to explain what they were seeing.

13:30 Lecture
Edward Norton Lorenz
Laureate in Basic Sciences
“How Good Can Weather Forecasting Become ? – The Star of a Theory”

Now I came to the image below in a most unusual way. Now when one sees the image as a butterfly, it is not hard to see how it might have some deterministic quality to it, that Edward might thought it significant for presenting to the masses on issues of climate change?

Edward Norton Lorenz is an American mathematician and meteorologist, and a contributor to the chaos theory and inventor of the strange attractor notion. He coined the term butterfly effect.

Now as I awoke after looking at this superhighway that is used inthe Genesis project I could not have helped identifying the strange attractor, somehwere in this interactive phase spoken about in the points of unequilibrium, and as possible changes in the patwern from one orbit to another. Not only did I see this in Lorenz's image, but in another one as well. so I'll place this one later at the end.

Edward Lorenz, an American meteorologist, discovered in the early 1960s, that a simplified computer model of the weather demonstrated extreme sensitivity to the initial measured state of the weather. He demonstrated visually that there was structure in his chaotic weather model, and, when plotted in three dimensions, fell onto a butterfly-shaped set of points. This is the trajectory of a system in chaotic motion, otherwise known as the "Butterfly Effect". A system in chaotic motion is completely unpredictable. Given the configuration of the system at any one point in time, it is impossible to predict with certainty how it will end up at a later point in time. However, the motion of the chaotic system is not completely random, as evidenced by the general pattern of the trajectory in this image.
Picture courtesy of: Scott Camazine / Photo Researchers, Inc.

It all starts to come togehter when it is undertsoo dthat visionistic qualites could have entered a new phase in human understanding where once this feature was unexpainable in a non deterministic way. Such a cosmlogical interactive system exist all through this cosmos now that we have undertsood the places where such capabilties are to exist? Thank you ISCAP for the "mantra of images" that have been displayed.



Time, seems to have brought them together for me, and what a strange way it has materialized. If Thales of Miletus was to have wondered about the basis of of the primary principal it would have been in Edward Lorenz's views that we had seen a system come together that was not fully understood before.

In the Time Variable Gravity measures of Grace it seems that the measure of the planet would have this basis to consider? While the mass features zeroed and changes according to the hills and valleys, would see this primary principal of some use?

Using Thales of Miletus primary principal, as a basis in the time variable measures of climate perspective, are we given a preview of what is not only happening in the cosmo, but is also happening in our deterministic approaches to weather predictions?

The theory of relativity predicts that, as it orbits the Sun, Mercury does not exactly retrace the same path each time, but rather swings around over time. We say therefore that the perihelion -- the point on its orbit when Mercury is closest to the Sun -- advances.

Given a appropriate response to the Daisey, Taylor was very helpful in explaining Mercuries orbital patterns, but now, this proces having moved to higher dimensional understanding recognizing the value of such images that the strange attractor brings to us? In a way, we have brought quantum mechanical processses together with relativity?

A Model for Thought?

Bernhard Riemann once claimed: "The value of non-Euclidean geometry lies in its ability to liberate us from preconceived ideas in preparation for the time when exploration of physical laws might demand some geometry other than the Euclidean." His prophesy was realized later with Einstein's general theory of relativity. It is futile to expect one "correct geometry" as is evident in the dispute as to whether elliptical, Euclidean or hyperbolic geometry is the "best" model for our universe. Henri Poincaré, in Science and Hypothesis (New York: Dover, 1952, pp. 49-50) expressed it this way.

See:

Science and Hypothesis

Rasmus said:

If you accept mathematical platonism, which is by far the prevalent philosophy of mathematics, at least among mathematicians, then you accept that to say that "x exists" is not necessarily to posit a single way of "existing": this very much depends on the x that is being spoken of.

This is a difficult one. The basis of existance arrived from nothing? What is nothing, and as soon as you do this, you have no frame work?

So one percieves that there is always something and from it? So we postulate X ?

In this platonist are discretism people, while the people who believe there is always something, an expression of the continuity of something called X? The true vacuum? The Quantum harmonic oscillator?

This all might be "abtraction to some" but it goes to the heart of any logic. In my case, I have to assume something always existed. So how do you deal with that logically?

Now you might be better educated then me, yet to me, numbers reveal a strange world of things we can't see yet we know exist. We have ways to measure it, and numbers in which to express it.

Now it would be very hard to assume that the average person, that scienitific progress can ever have any basis in what I just say above, but they are articluated from real issues that pervade thinking.

Now real things discrete as they are reveal matter constitutions, and the basis of this dealing with the likes of a Robert Mclauglin, or the likes of those who wish to expound on the continuity of expression. Leading into the understanding of Genus figures, this becomes a interesting analogy to way such continuity can be expressed?

Let me just say here that topologically this wold have arisen from a euclidean based perspective and move dynamically into revelations of curvature and such. So we know that above euclidean perspective and coordinated frames of reference this is discretism's way?

Dynamically the non-euclidean world condensing into a box? Some of us like things this way, but there are higher realms of thinking, that are transcendance to a platonist like me. :)

This is not a "superiority wording," but the true recognition of higher forms of mathematical derivation that the lay person would not understand. This intellectual was moved too, as I developed away from material things? :)

Here I am respective of the lineage of geometries, and anyone could interject in this consistancy. Some will be better equiped to move past the abstraction, while others perfectly comfortable with what I just said.

Is it transcendance? IN a way it is. In that we had moved intellectual academia into and away from emotive causations that might have ruled our thinking?

Is this feature absent from our intellectual developement, or is it more well defined? "Better perspective," as we move away from articulated matter constitutions and speak about "the finer things" above those same material things?

As one knows, one can become very abstract to the lay individual. While any who deal intellectually and emotively from the lay people, are not removed from and have perfected the emotive causes of memory inducement:?) Your history. Although we know of prospective change, as viable opportunites in the future. Continuity of expression.

Rasmus

But many are those who say that this is NOT what they mean when they say they believe in God. If atheists wish to argue against THESE religionists, then first they must reckon with what they are arguing against
No doubt.

How far can science go here? So they look for this beginning.

It's not easy if you assume nothing in the beginning and it is always much easier to change the models of perception. Adjust the view point, to see that a new model can change the way we always viewed things. That what model assumption does when you grokked it.

So like I said in the beginning, and where if such a continous nature is implied, can we deal with the idealization in science?

So if you took a look at calorimentric views and encapsulte this action you would find the point to which this beginning spoke? So a blackhole, is just not some sinkhole, but a transformation of a kind that we hope we can measure finding some means.

Energy in energy out if unbalanced leaves some room for questions? This dimensional perspective is very relevant in math, yet soe do not like to infer this and deem it unrealistic.

Early universe and glast determination have detailed discretism in interactions, as a viable means to measure. Yet we understand well the photon is massless, yet it can be indicative too. Thanks LIGO for engrandizement of the interferometer.

Artists such as M. C. Escher have become fascinated with the Poincaré model of hyperbolic geometry and he composed a series of "Circle Limit" illustrations of a hyperbolic universe. In Figure 17.a he uses the backbones of the flying fish as "straight lines", being segments of circles orthogonal to his fundamental circle. In Figure 17.b he does the same with angels and devils. Besides artists and astronomers, many scholars have been shaken by non-Euclidean geometry. Euclidean geometry had been so universally accepted as an eternal and absolute truth that scholars believed they could also find absolute standards in human behavior, in law, ethics, government and economics. The discovery of non-Euclidean geometry shocked them into understanding their error in expecting to determine the "perfect state" by reasoning alone.

Discretized 2D quantum gravity

Ancient Comparisons for thought

Now in itself, and of itself, the triangle when hit produces sound. IN this we understand the vibrational field that is generated. Hold your finger to a spot and where will the resonances slow down and come to a stop?

The chaldni plate is a easy experiment in using sound, "as an analogy of this higher quality." Some like the magnetic field, and its demonstration. Gaussian arc?
Imagine that the "earth based square," as the basis of mass considerations. Call it iron if you like.

Now in light of the triangle, or "trinity," what ever, lets say that the vibrational nature can be associated to this triangle.

That low notes that are slow in vibrations, also can reveal the mass considerations at the base , with greater vibration intensity at the peak? You now have a scale and iron as the core/base? We know there are certain energy values to elemental consideration?

How would you apply this to the chaldni plate? How would this apply to the world at large. How would you apply this in yourself?

Visualization: Changing Perspective

I give some perspective on "image use and artistic expression." But such journeys are not limited to the "ideas of a book" or "a painting" in some form of geometric code.

Some will remember Salvador Dali picture I posted. I thought it okay, to see beyond with words, or how one might see a painting and it's contribution to thoughts. Thoughts about a higher dimensional world that is being explained in ways, that we do not generally think about.

So while it is not mysterious, there is some thought given to the ideas of moving within non-euclidean realms. In the one hand, "discrete forms" have us look at how such a model in terms of quantum gravity is built, and these images and paintings, accordingly?


Arthur Miller
Miller has since moved away from conventional history of science, having become interested in visual imagery through reading the German-language papers of Einstein, Heisenberg and Schrödinger - "people who were concerned with visualization and visualizability". Philosophy was an integral part of the German school system in the early 1900s, Miller explains, and German school pupils were thoroughly trained in the philosophy of Immanuel Kant.


Click on image for a larger view

On page 65 of Hyperspace by Michio Kaku, he writes, "Picasso's paintings are a splendid example, showing a clear rejection of the perspective, with woman's faces viewed from several angles. Instead of a single point of view, Picasso's paintings show multiple perspectives, as though they were painted by someone from the fourth dimension, able to see all perspectives simultaneous

Talk of the Nation, August 20, 2004 · How did Leonardo da Vinci use math to influence the way we see the Mona Lisa? And how does our visual system affect our perception of that, and other, works of art? A look at math, biology and the science of viewing art.

This idea of dimension seemed an appropriate response to what I see in the Monte Carlo effect. I mean here we are trying to dewscibe what dimenison might mean in terms of a gravity issue. Is there any relevance?

What are Surfaces and Membranes?

Surfaces are everywhere: the computer screen in front of you has a smooth surface; we walk on the surface of the earth; and people have even walked on the surface of the moon.

By surface we mean something 2 dimensional (*). Clearly objects like a coffee cup or a pencil are 3 dimensional but their edges - their surfaces - are 2 dimensional. We can put this another way by seeing that the surface has no thickness - it is just the places where the coffee cup ends and the air or coffee begins.

Surfaces can be flat, like a table top, or curved like the surface of a football, a balloon or a soap bubble. The surface of water can be either flat without ripples, or curved when it has ripples or waves on it.

We use the word membrane to mean a sheet-like 2 dimensional object, an object with area but very little or no thickness. Good examples are sheets of paper or a piece of plastic food wrap. Just like surfaces, membranes can be flat or curved; rough or smooth.

Quantum Gravity Simulation

P. Picasso
Portrait of Ambrose Vollard (1910)
M. Duchamp
Nude Descending a Staircase, No. 2 (1912)
J. Metzinger
Le Gouter/Teatime (1911)

The appearance of figures in cubist art --- which are often viewed from several direction simultaneously --- has been linked to ideas concerning extra dimensions:

Dimensionality


Cubist Art: Picasso's painting 'Portrait of Dora Maar'

Cubist art revolted against the restrictions that perspective imposed. Picasso's art shows a clear rejection of the perspective, with women's faces viewed simultaneously from several angles. Picasso's paintings show multiple perspectives, as though they were painted by someone from the 4th dimension, able to see all perspectives simultaneously.

Art Mirrors Physics Mirrors Art, by Stephen G. Brush

The French mathematician Henri Poincaré provided inspiration for both Einstein and Picasso. Einstein read Poincaré's Science and Hypothesis (French edition 1902, German translation 1904) and discussed it with his friends in Bern. He might also have read Poincaré's 1898 article on the measurement of time, in which the synchronization of clocks was discussed--a topic of professional interest to Einstein as a patent examiner. Picasso learned about Science and Hypothesis indirectly through Maurice Princet, an insurance actuary who explained the new geometry to Picasso and his friends in Paris. At that time there was considerable popular fascination with the idea of a fourth spatial dimension, thought by some to be the home of spirits, conceived by others as an "astral plane" where one can see all sides of an object at once. The British novelist H. G. Wells caused a sensation with his book The Time Machine (1895, French translation in a popular magazine 1898-99), where the fourth dimension was time, not space.

Piece Depicts the Cycle of Birth, Life, and Death-Origin, Indentity, and Destiny by Gabriele Veneziano

The Myth of the Beginning of Time

The new willingness to consider what might have happened before the big bang is the latest swing of an intellectual pendulum that has rocked back and forth for millenia. In one form or another, the issue of the ultimate beginning has engaged philosophers and theologians in nearly every culture. It is entwined with a grand set of concerns, one famously encapsulated in a 1897 painting by Paul Gauguin: D'ou venons? Que sommes-nous? Ou allons-nous? Scientific America, The Time before Time, May 2004




Sister Wendy's American Masterpieces":

"This is Gauguin's ultimate masterpiece - if all the Gauguins in the world, except one, were to be evaporated (perish the thought!), this would be the one to preserve. He claimed that he did not think of the long title until the work was finished, but he is known to have been creative with the truth. The picture is so superbly organized into three "scoops" - a circle to right and to left, and a great oval in the center - that I cannot but believe he had his questions in mind from the start. I am often tempted to forget that these are questions, and to think that he is suggesting answers, but there are no answers here; there are three fundamental questions, posed visually.

"On the right (Where do we come from?), we see the baby, and three young women - those who are closest to that eternal mystery. In the center, Gauguin meditates on what we are. Here are two women, talking about destiny (or so he described them), a man looking puzzled and half-aggressive, and in the middle, a youth plucking the fruit of experience. This has nothing to do, I feel sure, with the Garden of Eden; it is humanity's innocent and natural desire to live and to search for more life. A child eats the fruit, overlooked by the remote presence of an idol - emblem of our need for the spiritual. There are women (one mysteriously curled up into a shell), and there are animals with whom we share the world: a goat, a cat, and kittens. In the final section (Where are we going?), a beautiful young woman broods, and an old woman prepares to die. Her pallor and gray hair tell us so, but the message is underscored by the presence of a strange white bird. I once described it as "a mutated puffin," and I do not think I can do better. It is Gauguin's symbol of the afterlife, of the unknown (just as the dog, on the far right, is his symbol of himself).

"All this is set in a paradise of tropical beauty: the Tahiti of sunlight, freedom, and color that Gauguin left everything to find. A little river runs through the woods, and behind it is a great slash of brilliant blue sea, with the misty mountains of another island rising beyond Gauguin wanted to make it absolutely clear that this picture was his testament. He seems to have concocted a story that, being ill and unappreciated (that part was true enough), he determined on suicide - the great refusal. He wrote to a friend, describing his journey into the mountains with arsenic. Then he found himself still alive, and returned to paint more masterworks. It is sad that so great an artist felt he needed to manufacture a ploy to get people to appreciate his work. I wish he could see us now, looking with awe at this supreme painting.

"