What Do You Do With A Super Sore Toe

Fractals, empty and beautiful quantum theories


" Clouds are not spheres, mountains are not cones, and lightning does not travel in straight lines. The complexity of the forms of nature differs essentially from that of the shapes of ordinary geometry , are forms of fractal geometry .
From Introduction to The Fractal Geometry of Nature (B. Mandelbrot)

Years ago I read the book "The fractal objects" by Benoit Mandelbrot, a classic on this new discipline. In the back saying fractals that allow us to meet virtually any discipline in a new way, providing a new perspective and expertise in the same . I drew wide attention from the beginning and started with simple programs to view them. With very few instructions the program I introduced into a new world of incredible wealth. So I spent a while until one day, concentrating on the characteristics essential simplest fractals such as the coasts, I noticed some similarities, at the time of measuring them with the actions we perform the quantum vacuum energy.


simple relationship in the fractal characteristics of its development distances to calculate its fractal dimension. In the figure Koch curve, we note that each side of length 3 is replaced by a broken line of length 4, the next iteration. The fractal dimension of the curve is log 4 / log 3 = 1.26186 ... Based on the ratio of lengths. Similarly, what could be the scale to relate to calculate the fractal dimension the quantum vacuum?. In the vacuum, the scalar determinant of its structure is called virtual power , based on it as the distances decrease its value increases, because their magnitudes are inversely related. That is why we need enormous energy to study the structure of extremely small distances each time particle accelerators have to be huge.

Based on these simple considerations and taking into account the corrections that I detail in the entry " The natural measure of things " I found the value 9 ( 3 dim. + 6 coef. dimensional) for the fractal dimension spatial vacuum quantum fluctuations. This value coincided with the overall dimensions predicted by superstring theories , which in some way mean that the quantum fluctuations of vacuum would be able to cover a space of 9 dimensions of space, or space-time of 10 dimensions.


Based on these results, however, found that these fluctuations distarían much to flush as we know, almost flat and stable, capable of holding the subject and providing a framework of stability to the universe we know. Deepening I noted (it is still theoretical, since later) that a kind of transition happening in matching the number of compact (6 dimensions) with the dimensional ratio (equal to 6) ( see an outline of this idea ). In this transition were masked the 6 extra dimensions and "forged" stable and flat space we know. Without it, our universe would have been uninhabitable and barren. Quantum fluctuations do not depend on the inverse distance and prevent the existence of the stability necessary for foreign matter particles or even stable. The world and the beauty in it would not have been possible. Not exist, neither we nor any beauty that we are able to observe.



That idea was what led me in a moment of "feeling important" to call this possibility theory: "The beautiful theory."



Now that this blog is playing possibly his last I discover the true origin of its name. A hug friends.

Track And Field Cake Ideas

The butterfly effect a strange attractor. Theory of the double outer

The order is associated with a significant degree of prediction, chaos happens otherwise. Linear systems, represent the order, are predictable and comfortable to handle, hence our tendency to generalize. Faced with a myriad of situations we generalize, we plan to present data to try to find a future behavior and almost always goes well. But there are systems that resist: small variations, uncertainties in initial conditions lead to completely uncontrolled and unpredictable end. These are called chaotic systems (Figure , strange attractor "poisson_saturne" done with the program Chaoscope ).


To study these systems requires a different methodology. Their study was done in the so-called phase space, an abstract space in which all variables represent the system dynamics. For example, an ideal simple pendulum would be represented by two variables, speed and the position of the sprung mass. His portrayal may be, therefore, in the plane and would be a circle. Each point on the same two numbers represent the speed and position, at that time.


That figure in the phase space, which approximates the studied phenomenon is called the attractor. In chaotic systems the attractor is not usually a point, a circle, a geometric figure known, but in chaotic systems is shaped "strange", hence receiving the name of "strange attractor" with a fractional or fractal dimension (Figure , attractor Lorenz, 3D with the program Chaoscope ).

The first of these was found , by chance, by the meteorologist Edward Lorenz when he tried to find a mathematical model to predict the behavior of large air masses. Managed to adjust the model to only three variables that indicate how to change the speed and air temperature over time (Lorenz attractor).


After studying the model, re-enter the initial data - this time with fewer decimal places, and the result we got was completely different than before. When reflecting on the results realized the system was extremely sensitive to initial conditions: small perturbations in the initial data have a great influence on the outcome. His equations captured the essence of the real atmosphere. "That first day (Winter 1961) decided that the broad predictions were doomed to extinction." But it was more than chance in their model of time: a fine geometric structure, order disguised as accident.


To explain in a graphical way - and exaggerated - the question occurred to him that the mere flapping of a butterfly, which had not been taken into account in the initial data, a prediction could be modified to make it completely unviable after a certain time.
About

Butterfly Effect have written hundreds of articles, novels, songs and movies have been made. On the topic is very interesting an article Enrique Dans, professor at the Instituto de Empresa, which compares the "Internet ecosystem" with the nonlinear and complex systems like the weather: "The variables involved (in Internet) are not so: if we talk about climate mainly speed and air temperature, the Internet comes to visit, links and related matters. But the potential impact of an infinitesimal change in measurement of background variables can have a brutal impact on the final results ,...". "Criteria for everyone, apparently, taken for good, as the sacred Google PageRank, inbound links account for a website that carries out Technorati or Alexa popularity rankings are measured fully crude, rude, lacking intelligence, which respond only to desire and seek to reduce uncertainty, but they do, in general, pretty bad. "


In this sense we are in the era before the discovery of the butterfly effect, we use linear methods to try analyze complex systems, nonlinear, where the feedback of all kinds, and at all levels, are the very essence of the system. We need to know "the strange attractor of the Internet."

About: "Chaos, Making a New Science" by James Gleik. Seix Barral. Barcelona 1988. A magnificent book. ( Reissue of the post of October 17, 2006.)

Could be the very history of humanity as a very sensitive to initial conditions? :

"There's something amazing that I have always drawn attention to the story. It happened before, happens now and possibly ever will, humanity does not seem to know or can really control, where it goes. The events will happen and when all seems tied up and in place, comes a new incident that disrupts all, wars, revolutions, economic crisis or other catastrophe. In these situations the story, after they occurred, draws conclusions and helps us to prevent their recurrence, but there is always something that escapes us and everything returns to lead a new catastrophe, everything starts over again. "

Continue reading: History , dignity and butterfly effect, my collaboration with Book notes. A hug.

Roger Penrose

How To Get Into The Carrot Factory

physical theories classified into three groups: superb, useful and tentative. The theory of the double outer come, no doubt, in superb theories. It is speculated sandwich and sandwich between the so-called group of theorists: Vicente Martí, Ximo Moll and myself. Among co-workers started calling us and why we came up with theories to explain the reality of an alternative. The relationships between people, between the sexes, at work ... Everything could be seen differently and thus reflect on realities that we take for granted. Feet on the ground (humility) and head in the clouds (imagination and humor).


face of misery and suffering around us and strangers, we decided that each of us must have a double outer in a parallel universe, beyond anything imaginable. When we have a bad day will coincide with the best double sidereal day. If we bounce here on Earth the outer double is hired by the best company to work the best. If we let the bride, the outer two plan to get your life ... Everything good that we can not do, or not leave us, he does it. And so when something goes wrong in how well we will do our twice and laughed for a while because, at the thought, get away, in a way, small or great misery. The "law" that supports this theory is a kind of universal cosmic law of compensation. "

Following the thread, the "theory of the fly" also enter the field of "theoretical" and indicated . It is a sort of "butterfly effect" around the house ("a simple fly is able to change history.") In more serious plan, this theory would dilute the very cause and effect:

"I will make a startling claim that, then try to demonstrate: our life is influenced by people and events that in most cases, we are unknown. These people, if you spend some time with us, are complete strangers but on occasion have changed the course of our existence, purely accidental actions, without any intention, and have gone on without being aware of the facts that have triggered. They, in turn, are less sensitive to the curious web of mutual influence around us, also have their legion of strangers can alter their fate. "Read more .


In memory of my good friend Vicente Martí, the theorist who left us a week ago after painful disease. From where you are, Vicente, you will be laughing a bit with this post. And if heaven awaits us there.

Congratulations to the outer double.

In most transcendent plan: message in a bottle.

Is There Another Name For Trichloracetic

Fractals, natural geometry (*) Triangles

geometry so intuitive that we are taught in school, based on lines, points and surfaces is really a great effort idealized abstraction because these elements do not exist in the everyday world. A real line or surface irregularities are filled overlook to abstract its essence and translate it into simpler concepts as straight and flat.


With fractals, in a way, get rid of this abstraction, and we come a little closer to the real thing. Benoit Mandelbrot uses the simple example of a real object, such as the coastal countries, to approximate fractals. Are broken lines still look like when we change of scale. Precisely these two properties are what define a fractal discontinuity (break, fracture, hence the name) and self-similarity with the change of scale. We measure the degree of fracture and irregularity with a single number called fractal dimension. Reviewing

intuitively the concept of dimension, note that a point has no extent (size zero) to a line we measure in meters or linear feet, which means assigning a dimension (a single measure: length), to a surface must be measured in meters or square centimeters (size two: length and width) and a volume as measured in meters or cubic centimeters (three dimensions: length by width by height). A fractal generally have a dimension (fractal dimension) which is between zero and one, between one and two or between two and three.

Suppose the simplest case, a line represented by a thread fractal crumpled, and imagine that it has fractal dimension 1.25. If another thread has fractal dimension 1.35, the simple comparison of their fractal dimensions implies that the second thread is more wrinkled than the first, presents more irregularities. The whole part of the fractal dimension (in this case 1) is telling us that the object with which we deal is a line, we measured the fractional part of their degree of irregularity.

The fractal dimension also gives the ability for the purpose of occupying the space . The fractal dimension 1.35 thread is able to fill the plane dimension better than 1.25. In fact, if we wrinkles will increase the fractal dimension close to 2 when we managed to fill, almost entirely to surface thread. A classic fractal this type is called the Peano curve.


Fractals are basically simple objects, are easily generated by computer . By programming very few orders, and from a minimum number of data, create real wealth and wonders of extraordinary complexity. The Mandelbrot fractal is an example. As we try to expand, using information technology, any of its parts we find a new landscape similar to the original but with new and surprising details. We can go on as we want and allow us to power our computer, we continue to show a new fantasy world that is never repeated, with each new expansion. A world emerged from almost nothing, a simple expression that binds and new data feeds.

Curiously, the expression is so simple: posterior value = (old) 2 + constant (with a restrictive condition).

The observation of these fractals created by computer, always reminds us of some natural object near unknown but possibly because the economy of means to achieve complexity is a very typical feature of Nature. It is the strategy adopted to achieve better distribution of blood vessels throughout the body, the optimum arrangement of the branches of trees or in the folds of the brain to get the largest area in the smallest space. Real

wonders of fractal art.

(*) In my work with Book of Notes, the monthly column cienciasyletras.