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... can not find a more aesthetic notion that the recent
Catastrophe Theory of René Thom, which applies
the navel parabolic geometry as the continental drift.
Theory of René Thom has charmed all my atoms since the
met. ...
Dalí, 1985.


topological theory of singularities and bifurcations, called Catastrophe Theory (CT) was introduced by French philosopher and mathematician René Thom to study breaks or changes that occur in dynamic systems. Studied from the mathematical point of view what is commonly known as the "straw that broke the camel's back, the slightest hint that causes water to spill and moving from an unstable state to another stable.


Intuitively, and simplified form (topology "superelemental"), the interior points of a continuum would be regular points and the points that form the border points would be catastrophic. The regular points are surrounded by points having the same qualitative appearance in which no "nothing happens", as usual (continuity). In border points or catastrophic always "something happens" happens to be a continuity of the system to meet changing radical.__ This distinction between regular points and is preliminary catastrophic not only for the theory of catastrophes but for any discipline set alerts on any theoretically __. René Thom showed that for systems in which one or two variables involved and influencing the four parameters (time, temperature gradients or breaks ...), there are seven elementary catastrophes (morphologies or shapes), which Names have been very plastic and intuitive: folds, cusps, dovetails, butterflies and navels elliptical, hyperbolic and parabolic.


In his words: "The TC seeks to describe the discontinuities that might arise in the evolution of the system .. Intuitively, it is recognized that the global evolution of a system is presented as a continuous succession of developments, separated by sharp jumps of qualitatively different nature. For any continuous evolution remains within the classical differential type, but the jumps are to be passed to a differential system to another. Skips of a continuous evolution described by a system of differential equations to other continuous evolution described by another system and can not be excluded that a finite number of systems is not sufficient to describe the situation completely. " really clarifies that only a theory is a methodology , or perhaps a kind of language, which allows you to organize data experience in the most diverse.


René Thom has managed to bring math to the "morphology" and has studied the emergence topology tools, stability and the disappearance of forms, has found the meaning of things, as long as they are forms or morphologies, from certain invariants that are broken or singularities. This has been possible to classify the ways to proceed against such failures, the famous "catastrophe" elementary "in dynamical systems as varied as can be physical, linguistic, biological or social.



Despite the failure, according to the canons of TC-positivism of the scientific theory applied mathematics Thom opened the forms or morphologies of the world, to understand, to find its meaning, and not just driven by the interest in predicting events, classic exercise of the nineteenth century science. And it has begun to show their power to do so by permitting come across many of its fundamental concepts, structural stability, bifurcations, attractors ...- to understanding natural phenomena as complex and as common as "the form of a cloud a falling leaf, the foam of a beer glass. "



-> Paper : "Parables and disasters", by René Thom. A long interview in which he manages to clarify the deeper meaning of analogies ("parables") that explain some of the most enigmatic and fascinating phenomena discontinuous (or "catastrophe"). René Thom, in the seventies, challenged on his own ground for physicists and biologists, economists and linguists, proposing his theory of catastrophes, a new way of looking at all the changes that occur so sudden, unexpected, dramatic.


-> Web: morphological mathematics and science. Homage to Rene Thom.

reissue of an old post from 2007. I add a little humorous reflection on the subject. Happy summer friends, family calls me.

Stupidity and catastrophe theory

Normally, what we live at a particular time can be predicted with a reasonable margin, resulting in a certain awareness of continuity (normal). This continuity is often broken by unexpected events, many times by our own ignorance, we usually get in a sac called random. A percentage of these often have their origin in human stupidity.

Life consists of a rational, continuous and, therefore, expected and dashed Moreover, in many cases the rich. Stupidity can be very destructive (a priori almost always is), but the breakdown can be introduced by enriching and positive effects. In this respect their contribution can be understood as an "engine" but as a modulator of events. I think the engine always will.

rupture of continuity is studied by the so-called catastrophe theory (catastrophe understood that the single break of continuity). In that sense stupidity as opposed to capacity ratio, and the continuity it represents, could be regarded as catastrophic.

Disasters aside, the best book ever written on human stupidity is, without doubt, the book of Italian professor Carlo M. Cipolla: "Allegro ma non troppo." Includes two essays, "The role of pepper in the economic development of the Middle Ages" and "The fundamental laws of human stupidity," whose first fundamental law states: "Always and inevitably each one of us underestimate the number of individuals stupid move around the world. " It is a 85-page booklet published by Mondadori (1999), ISBN: 8439703058.

Why Is My Broken Leg Not Healing

Parables and Miss Leavitt, the depth of the universe and forgetting

The universe was a flat photograph. We only knew the distance of nearby stars using geometric methods, but the distant nebulae and star clusters were only bright spots in the cosmic panel with no depth. This was the situation at the beginning of the twentieth century, until a woman of fragile health, he found a tool to discover the true grandeur of the universe.


One of the objectives of International Year of Astronomy past was to claim the role of women in research astronomical. Generally, only the left part is, nothing more marginal issues, well into the twentieth century. This was the case Henrietta Swan Leavitt, who was among a group of women calculators Harvard Observatory.

With a limited budget, the director of the center wanted to save and hired women, with a minimum wage, were attentive, polite and patient, the right people to analyze thousands of photographic plates boring star fields. But Miss Leavitt, who was graduated from Radcliffe with a curriculum such that if it had been a man, would have provided a degree in humanities at Harvard, he accepted the tedious job of measuring the brightness of the stars in the Small Plates Magellan Nebula. And it was there that made the discovery of sixteen stars that have good properties curious: its brightness varies periodically and brightest have long-period variation. Since the distance that separates us from them is basically the same, the effect, now called period-luminosity relation of Cepheids, is really intrinsic and is an ideal tool to measure distances in our galaxy or beyond.


In a few years when I was alive the debate over whether the Milky Way was the only galaxy and therefore the whole universe, or if there were many galaxies and ours was one of many, Leavitt's contribution was essential to discern. Shapley was the first to use Miss Leavitt's stars to measure the Milky Way, but was Hubble who sensed the true dimensions of the universe, when cefeides first discovered in the Andromeda galaxy and then when he showed that galaxies are moving away from them suggesting a universe in motion and expansion.

Without the contribution of Miss Leavitt this spectacular progress in extragalactic astronomy the twenties of last century would not have been possible . She, meanwhile, never failed any academic recognition or labor. His employment status was not an assistant, despite the contribution to science he had done. Only at the end of his life he dared to the profession of an astronomer assigned to answer the question of an official census of Boston. Translation

beautiful overview of Enric Marco i Soler (Univ. Dept. Astronomy and Astrophysics Vcia) the book: "Before Hubble, misss Leavitt." George Johnson. Antoni Bosch Ed. Barcelona.2009. Number 66 of the Review Method of the University of Valencia.

Another review:
nearly a century ago, in a crowded office of the Centre Harvard, a brilliant woman, now almost forgotten, discovered the secret of the vastness of the universe.
Her name is Henrietta Swan Leavitt, and in the days when women were forbidden to have careers in science, was what was known as a "calculator"-a human calculator of numbers, that, struggling against a very weak health, discovered a new law that transformed cosmology.


Leavitt Using the law of the legendary astronomer Edwin Hubble showed that there were stars-and-whole galaxies beyond the Milky Way and the universe as we now know, is immeasurably large.
With the grace and skill that have made him one of the most distinguished science writers today, George Johnson astutely contrasts the magnitude of the discovery of Leavitt with the quiet darkness of his short life. Before Hubble, Miss Leavitt is both a brilliant story of how we measure the universe as the emotional story of a forgotten genius.

Comments from other astronomers today:
"Starting with the discovery of Henrietta Leavitt, who was instrumental in restoring the cosmological distances, the author describes the history of research an issue that even today is fascinating: how tall the universe. "
Cristina Manuel - Research Scientist, Space Science Institute, Spain

"This book weaves a wonderful way history, astronomy and the struggle of a young woman to make their mark in science."
Yolanda Gomez - Investigating Radio Astronomy Centre, Mexico

"Henrietta Swan Leavitt, and other astronomers at Harvard, worked almost anonymously in a world dominated by men, leaving an impressive legacy at that time were not recognized as they deserved, because their role was merely assistants, called "calculators" Harvard. "
Margarida Hernanz - Research professor, Institute of Space Sciences, Spain