Can You Build A Tolerance To Allergies

Wonders of the analogy - the remix

On the advice of Alexander , I just finished "Wonders of the analogy and Vertigo," by Jacques Bouveresse and I was a little disappointed. I expected to see it described the fascination of thought for a well chosen analogy, still more convincing argument that rigorous, sometimes to the detriment of basic common sense. Bad luck, Bouveresse polarizes the famous controversy sparked by Sokal and his essay is only an information (convincing the rest) of verbiage philosophical basis of scientific concepts as poorly digested Theorem Gödel's incompleteness or the Heisenberg uncertainty principle. While he sometimes refers to our unreasonable penchant for beautiful images when he writes about such a nice formula Regis Debray (which he persists long): "It's obviously much too simple to be true, but it is so well told that it becomes one. " (P99). But it does not analyze the reasons that make these formulas also pretty compelling for the spirit that light to the moth *.
had neither the talent nor the erudition Bouveresse, I propose in this post xochipillesque synthesis of what I liked see in his essay. In essence, the analogy is central to our mental toolbox . Its fascination for the mind is precisely because it is THE method of learning and memory par excellence. I venture to think that through this cognitive ability altogether that we constitute our primary benchmark mental representation of our world, our beliefs, values etc.. You tell me what you think of this Bouveresse remixed.

Abstract thinking comes from the analogy
I already told in this post the power of learning by unconscious association. The analogy is a sophisticated form of mental association is equally impressive. To convince you, try to unravel what lies behind a word abstract (one furniture, a city ...). The philosopher Wittgenstein showed that a term like "games" covers so many different activities that you can not find them the least common denominator: some games are fun but not all, they are sometimes several times alone, there are often winners and losers, but not always, sometimes and sometimes not so rules. He must give up to define a game by a set of prerequisites. "The result of this review, here it is: a complex network of similarities overlapping and crisscrossing: sometimes overall similarities, sometimes similarities of detail. I see no better expression to characterize these similarities than resemblance Family as the various resemblances between members of a family: the conformation traits, eye color, gait, temperament, etc.., overlap and intersect in the same way. And I say: the 'games' form a family. " An activity is a game if it is sufficiently similar to one or another well-known game. In other words, an abstraction is built on analogies rather than on logical rules.

Analogy: a very basic cognitive ability mental
This comparison is probably a very basic cognitive ability as it can look very easily even if you have no idea of the comparison criteria. Take the example of musical genres. If you're not a seasoned musician, you're probably unable to specify a style of music (jazz, rock, country, salsa, etc..) In terms of rhythms, melodies, harmonics, tempo etc. . (Me, I always wondered about that makes the difference between the "rock" and "pop" if you have an idea that interests me) And yet you'll have no trouble labeling the style of a song you hear for the first time just because you mentally closer style of another song you know.

Knowledge is recognized
Let us one step further reasoning. When you meet a friend in the street by chance, you recognize instantly as you automatically associate her with the mental image as you do. Ditto when you recognize a smell or a noise you make a natural correspondence between a real perception and mental representation, disregarding any differences. Borges describes in his novel, the story of Funes, a man with a memory so prodigious that he could not forget. Funes felt all the pains of the world to recognize things because he could not forget the differences between the dog he had seen the day before and the same dog today, seen from another angle and in a different light.
And if the knowledge was within the same type of bridging mental thrown this time not from a particular perception and category (the trick is to coat all drooling a dog) but between several different classes and a super-category that encompasses (dogs and cats, the family of mammals )? Borges is the idea of when he wrote about the unfortunate Funès: "I suspect however that it was not very capable of thinking. To think is to forget differences, generalizing, abstracting. In overloaded world of Funes there were only details, almost immediate. "The analogy would be the pillar of our minds since thinking = conceptualize, design = recognition, and recognize = An analogy.

Logic is nothing without the analogy
course, there are other mental processes that shape our thinking, logic, for example ("All men are mortal, Socrates is a man therefore Socrates is mortal "). But all that is rigorous, no reasoning is rooted in our minds that if he manages to associate itself with concrete illustrations that stores easily. That whole concept of mnemonic techniques (source). If the formula E = mc ² is so famous is that it makes sense , that is to say that we can associate an interpretation (the idea that matter is a form of energy as another), an application (the civilian or military applications of nuclear power), images (the formula itself, or very simple pictures of Einstein) and so on. Our memory and our more general representations of the world find their place in our mind that with the hierarchical network of associations, analogies that have sedimented in our brain.

I found in my favorite podcast ( Radiolab in English unfortunately) an illustration of the contrary idea. Eureqa (downloadable for free here ) is a great program to infer the equations of any system to be studied (mechanical, electronic, biological, etc.) from just the observed data over time. Faced with a mechanical movement, he finds himself all Newton's laws, the laws of energy conservation of momentum etc.. Crazy right? A biologist has sought to capitalize on this revolutionary program to understand the law of evolution of a particularly complex biological system that had some very strange recurrences. Eureqa he quickly spat a very simple equation that not only was fully account the comments, but predicted that in addition to other hidden reasons we have been able to check afterwards. Except that the meaning of the equation is far remained completely opaque to researchers: the exact formula but it seems unable to interpret its meaning and the mystery has only thickened. Unable to link it with other known laws, discovered the formula does not fit into our body of knowledge, it is literally indigestible by our mind.

Do not confuse Eureqa and Eureka!
Eureqa The program provides equations but can not trigger in the user clicks the famous brand that understanding, this delicious moment where things suddenly take effect by associating with each other. The image of the light that lights up above the head of him who has understanding (Source: iStockphoto / Kutay Tanir) seems particularly well chosen: this time apparently translates a sharp transition in the functioning of our neurons that synchronize their sudden shocks. It is almost Lacanian: we think in resonant in his head. I found nothing in the literature regarding the discharge of pleasure that accompanies this moment, but I am convinced that there is not much difference between this kind of pleasure "intellectual" and other carnal pleasures. And it must be true for some animals, because we have discovered several wild dolphins spontaneously practicing to "walk on their tails" just for the pleasure of overcoming this challenge, after hanging around one of their fellows drawn to do and then released.


A shortcut to the intelligibility of the world
back to our sheep. We have, I think he all elements of explanation to understand the attraction of well-chosen analogies. The analogy is even more tempting when the image is familiar and used its natural association with the object in question. If in addition, it provides a simple explanation for a phenomenon difficult to understand, it becomes irresistible. It became almost impossible to talk about the economy other than sports or war metaphors, like "France wins / loses the battle for jobs"; "The G20 down growth"; "MEDEF is resisting "etc.. The problems begin when the analogy is both natural and biased.
- We saw in the series of notes on globalization , the famous image of an economic war between nations is dangerous because, unlike war,
international competition is certainly not a game zero sum.
- Equally misleading picture of the economic pie that we share (speaking of jobs, wealth etc.), since often the size of the pie in question depends largely on how one chooses to cut it!
- In medicine, the image of the burning fever patient has long led the fight when it is the best defense of the organism against disease.
- In polique, the personification of the electorate is the source of the most outlandish comments ("the electorate wanted to give a measured warning to the government" or "voters showed cautious support to such candidate") as if the average vote reflected the opinion of the majority of voters.
- In biology, comparing the brain to a super-powerful computer has thick skin, then it ignores the role of emotions in its operation.
- Finally, there are unfortunate pseudo-Darwinian analogies used to justify the survival of the fittest ("survival of the fittest"). Obviously

Proverbs are all built on questionable analogies ("it does not make an omelette without breaking eggs" or "a bird in hand is worth two in the bush"), and I'm not going to get into everything limits. But as public health, I still leave this post open in order to record false analogies evident as they fall under my nose ...

* To illustrate my thesis xochipillesque all, I put images or analogies green in this post.

Sources:
Jacques Bouveresse: Dizziness and Wonders of analogy

Related posts:
Praise the rule of thumb how the solution comes to the dreamer
International Trade: an example of equality! on analogies too obvious in the economic field
Magic Pavlov: about the wonders of the mental association

Christmas Movie Raisins

Libertee associative and expressions

We can not but be surprised by the behavior of representatives still in place elected by the tenants on the board of Habitat Kremlin and defend their interests, opposed to those tenants the development of their friendly independent.
This behavior is shameful and derogatory and does not reflect what we expect Delusion tenants this one is Partisi, sectarian. I would note that the function of elected director is a responsibility to serve all residents without discrimination and not the arm of an organization to destabilize another.
The value and interest that we raised in our people is measured in concrete proposals suggested to them to serve their interests and not the ability to harm those they are supposed to protect their rights.
Again this childishness is conducted in the miscellaneous section of the crushed and dogs do not make the headlines.

ARB FALC

How To Use An Immobilizer

REPORT ANTENNA RELAY

Meeting with Kremlinois on the subject of antennas in the Kremlin Bicetre

http://risques-gsm.ifrance.com/gsm-194.htm
http://arazi.fr/wp2/2010 / 11/kremlin-bicetre-antenne-relais-ondes-et-sante /

The question is asked to elect a guarantor of public health.
How much is our health in collective housing, 10 €, 20 €, 30 € per year or more, it is negotiable and how many residents we are we willing to sell it, if indeed we are. What is the benefit for those who are most concerned.
The federation shall establish a health surveillance on the subject of electromagnetic radio waves and wants to relay the concern we put residents directly located under the antennae.

Dog Old Age Skin Tags

Capa or self-realization

Robert Capa he really existed?
Did you know that the story of Robert Capa was born of an incredible hoax? It all began in 1934 when Endre Friedmann, a young Hungarian photographer arrives in Paris. His girlfriend Gerda Pohorylle , a German Jewish refugee, pat the legends of his photos and he serves as an agent with Parisian newsrooms. Their medium business market until it had a brilliant idea: they are invented out of whole cloth a character whose agents they are, a famous American photographer, supposed to be rich, smart and who live a hectic life, between worldliness and stories around the world, therefore unreachable. The two young men now offer pictures of Endre as those of this fabulous Robert Capa Gerda whose claims agent. To be credible, it triples the price of shots and it works! It must be said that at that time nobody could googling to check. The maneuver ends up being more or less stale but it did not prevent the editors of Seen and Regards Endre post and Gerda cover the English Civil War. Their photographs (his own and those of Gerda) go around the world. Endre Friedman gradually disappears behind the legendary Robert Capa which he finally adopted the name. Legend Forged all p ièces in 1934 is gradually becoming reality: has near death of Gerda, accidentally killed during the English war in 1937, Endre, Robert Capa covers all fields battle with extraordinary success. In 1939, he emigrated to the United States and became naturalized American. After the war, he led the life of gambler he had imagined for her character, drinking shots with Hemingway, Steinbeck traveling and playing poker with John Huston. He flits from one mistress to another, living in luxury hotels and squandering the money of the prestigious Magnum agency he founded after the war with Cartier-Bresson. And of course all he surveyed the battlefield from which it takes pictures legendary. His end is worthy of his legend: he died in reporting, won by a landmine in Indochina.

The mysteries of the prophecies self-fulfilling Robert Capa he really existed? Yes, of course if it is seen simply as the nickname of Endre Friedmann. No, it is recognized that the initial lie about it was probably what he has set foot in the stirrup. Side undecidable this lie that is not really a tickle our logic. As Baron Munchausen (the source of the image is here), who manages to get out of the marsh where it became stuck, he and his horse, pulling hard on her hair, lying on eradicates the ability of his condition and converted as magic indeed. This process of "bootstrapping" (which literally means "to rise by pulling on his shoes") is the characteristic of self-fulfilling prophecies that come true only because their statement upsets the difference. Speech, yet very human, creates reality as if it was divine and it's probably not a coincidence that the oracles of the Pythia were operating on this principle, to the great misfortune of Oedipus. Less class but closer to home, Michael Vendetta is a nobody become ultra-famous just because he claimed he was going to be everywhere: the method Coue or the wishfull thinking, it works ... sometimes! In all cases, they are a good illustration of these cascade reactions that fascinate me so much.

Cascades collective
The runaway group from a vague statement or rumor can have dramatic effects. In 1973 the rumor in the United States that the oil shock would cause a shortage of toilet paper . People rushed to replenish their stocks as a precaution. This group has actually led to rush an early shortage that created panic, validating the rumor afterwards. Financial bubbles or obey stock crash the same principle, without any need to blame traders or hedge funds: already in 1637 the price of tulip bulb reached twenty times the annual salary of a craftsman, creating the first bubble history . How is such madness possible? Very simply: it is enough that each reasons not based on what he thinks is a fair price, but based on what he believes to be the opinion of the market on this price (even if he is even convinced that the market is wrong). optimism of some other cause for optimism that in turn reinforces the general optimism. And the opposite in case of a crash.

The price curve at the Tulipomania in 1637 (source: Wikipedia )

Even in normal times self-fulfilling prophecies are common on the stock markets. They work much like the reasoning by induction math: if the market is influenced by the number of sunspots, just a recognized expert shows that such influence was indeed observed in the past and predict that of such influence will endure. Even if everyone thinks it's crazy, everyone's interest to take into account the possibility others will follow this prediction. Therefore speculate as if each thought himself the prediction, which validates it for sure. You laugh but for the Dow Jones, the correlation is quite spectacular, but we understand exactly why:

Comparative evolution of the average Dow Jones (DJIA averaged over 11 years) and the number of sunspots ( Source: pdf)

polls may have the same effect, when each voter adjusts its own electoral strategy based on polls, as if it were a reality indifferent his own choice. Polls can and credible a particular application. In 2002 they had the opposite effect (self-defeating prophecy) because voters left scattered their votes gained by believing instead of Jospin in the second round .
loops inter-individual
If prejudices die hard, partly because they often have this gift of self-realization. Our expectations conscious (or unconscious as we saw in this post ) influence our behavior in order to confirm them. This loop behavior known to Pygmalion effect was dramatically demonstrated in laboratory rats. Researchers have been led to believe that a student group of rats (actually chosen at random) were gifted to exit a maze, in contrast to another group of rats had no particular aptitude. Students have they been more friendly or friendlier with the first group? The fact is that both groups of rats are generally performed according to the label they had been assigned (arbitrarily remember). Many experiments similar, with students we had to be particularly gifted examiners have confirmed this strange phenomenon.

Basically, most of the conflicts arises from this kind of self-reinforcing loop when one of mistrust that fuels the other. For such pathological behavior: the morbid jealousy for example, or feeding the paranoia of all the efforts that the entourage is to avoid provoking a new crisis. This is no joke: it gets really paranoid when everyone conspires against you!

Auto-suggestion: the ability to lie to yourself? When
works without anyone except himself, the self-fulfilling prophecy takes on a mystery. The placebo effect, for example, which works because I believe in the prediction that treatment will heal me. Its twin, the nocebo effect that works in reverse, is equally spectacular.
More prosaically, self-suggestion is a powerful engine: it succeeds all the better what we are undertaking convinced (wrongly or rightly) that we will succeed. And like Robert Capa, one reaches heights rarely without a small dose of megalomania. Is this evidence that psychological explain that we have found the best 1991que Athletes are those who are most successful at fooling themselves , that is to say those which occur most easily be satisfied simultaneously a thing and its opposite? Even as Spain has won the World Cup, simply because the octopus had predicted? This strange result would in any case consistent with everything we have just seen: we have more chance of winning if we are convinced we can beat his opponents. But such a belief necessarily requires that we ignore all of its weaknesses. In other words, to be a fighter should learn to lie a little to himself when the time comes. Well, well ...

Sources
The biography of Robert Capa, the site of the BNF who recently had an exhibition.
Wikipedia, as usual

Related posts
Consciousness in flagrante delirium, our good-bad faith
Discrimination in cascades, on the way born and rooted prejudices

Wording Candyland Birthday Invitaitons

BREAKER / 2010 / Matthew Crimersmois

Sculpture sound installation, interactive.

Material: Records 250 Oil, metal, motion sensor. 60x170 cm

"BREAKER" is a sculpture / sound installation presented at the exhibition

MOTHERSHIP UNION Michael Sellam, in October 2010. It is located within the School of Architecture of Nantes, in the context of HEART OR THE ART IN THE HEART OF THE TERRITORY, organized by ELIA (European League og Institute of Art).

"... the interference of Matthew Crimersmois returns to a more disturbing and

animal. The Spider, exiled and isolated on the second floor, is as at odds with the surrounding architecture

transparent, contrasting it with its dark and materiality dissenting

inspired Afro-futurist like sculpture of Mr. Sellam. ;

It consists of vinyl records

thermoformed, soft as the body of the spider whose heart beats are suggested, even that of

the position of passive self-defense. A built-in webcam (the eye of the beast?) Introduces a form of interactivity

since perceives the movement of visitors, according to which it deploys

sounds.

Enlarged, as a thought to the human scale, she returns the image of a

part of ourselves that we have forgotten and which we fear (as in "The

Metamorphosis" by Kafka, or "The Fly" by D. Cronenberg ... ). It causes a return of the repressed

revealing its pristine nature, inaccessible to civilization. Disgusting, but fascinating

, fantastic, it is beyond the scope smooth often associated with new technologies. "

Martine Bubb

This piece is futuristic and has imagination. It is steeped in the atmosphere of science fiction in which the presence of insect or spider "alien" is often pervasive. The LPs are thermo-formed to represent the globe, between the shell of an "alien" and a flying saucer. Its name recalls a dance HIP HOP. As Mothership is the title of a disc Afro-futurist (Parliamenti), which will give life to this culture. (Movement from guettos black Americans).

The legs are hinged and designed to be read heads which are also the claws of the beast. The arachnid apparently in self-defense passive (techique that spiders use to simulate the death against their predator).

Acknowledgment:

Especially Jérémie Laurent, Michael Sellam, ESBANM, Jean-Claude Martin and Celine.

Graphics Designers Best Printer 2010

an enriching experience

WITH THE PARTICIPATION OF SENATOR JOHN
Desessard ECOLOGY GROUP EUROPE THE GREEN
MADAM PRESIDENT THE NATIONAL Priartem JANINE CALVEZ
NEGOTIATOR COMOP MARC Araz
NATIONAL REPRESENTATIVE OF THE EXPERT AND MARC CRIEREM FILTERMAN
ANIME BY BERNARD CHAPELLIER MEMBER OF THE EXECUTIVE EUROPE ECOLOGY

GREENS DU VAL DE MARNE

AND ACTIVE AND HUNGRY AUDIENCE INFORMATION OF A FIFTY PEOPLE WHOSE VERY REPRESENTATIVE OF SEVERAL ASSOCIATIONS KREMLINOISES
THEY HAVE TO BE VERY MUCH ALIVE Contributed THIS MEETING.

THANKS AGAIN TO OUR GUESTS FOR RESIDENTS their interest KREMLINOIS

minutes of the meeting

http://risques-gsm.ifrance.com/gsm-194.htm

Red Brown Violet Hair

The principle of least action, a gem of physics.

Well, now I knew that one day or another I did not cut off and it happened this weekend. I was preparing to question a long time, collecting educational explanations, demonstrations more or less comprehensible and historical exegesis on the subject. This weekend, my numberOne asked me the killer question: "where it leaves the law with sinuses on the refraction of light?". I am therefore the answer today and took the opportunity to present the "principle of least action", a little known law of physics also fascinating that explains both the laws of optics that of classical mechanics, relativistic or quantum, no less! Ticket X-rated course, but if you're allergic to math you can still follow this post (hopefully) simply by skipping paragraphs reserved furious. Go!

A little reflection to begin.
been known or almost always (since Heron of Alexandria at least) one ray of light is reflected from a surface by an angle of reflection (i2 in the figure) equal to its angle of incidence (i1 ), just like a billiard ball bounces off a surface perpendicular to it.

The rule seems obvious, but how to explain it? A clue: the trajectory is obtained by chance in the shortest possible, once it has become the starting point and ending point. The proof of this property is not too complicated (Xochipillette died laughing):

The radius he always chooses the shortest path connecting two points? You have to see, but it could explain why it moves in a straight line between two obstacles. There would be a universal law?

How does the lifeguard is not a light?

When a stick is dipped in water it look like broken image (source here) In the seventeenth century, Scientists struggled to find a rigorous explanation of this phenomenon of refraction. We suspected that the speed of light was different in the air and water and Pierre de Fermat made up his mind to demonstrate this by itself on the assumption that light always follows the trajectory faster. To understand the problem, it usually takes the following image: imagine a lifeguard on the beach, which sees a person in the water drowning. What path should it take to rescue her as soon as possible, knowing that it is faster when running on the beach only swim in the sea?

If it chooses the path in a straight line, it will waste time by swimming too long. Better to let him run a little farther to have less to swim. Not too much, otherwise it will lose too much time to run! Not a trivial question, but it's cake for a genius like Pierre de Fermat. "A little geometry we can pull through" as he says (I quote here the solution proposed comment ticket Alexandre Moatti on the subject):

(For furious only) In triangles and OFH OFK, was HF = OF sin i and sin r = OF OK deduced that HF / OK = sin i / sin r = V air / V water If there XY} {travel time from X to Y was so {HF} = {} OK Moreover AL> AO and LF> HF ( ALO as triangles and rectangles are HLF) therefore AF> AO + HF we can rewrite in terms of journey times {AF}> {AO} + {HF} Similarly {FB}> {KB} Adding these two inequalities we obtain {AF} {FB} +> {AO} + {HF}} + {KB But we have seen that {HF} = {OK} {this inequality is then written AF} {FB} +> {AO} +} + {{OK} KB therefore {AF} {FB} +> {AO} + {OB} which is what we wanted to show ...

The reasoning is exactly the same if you replace the lifeguard by passing a light beam in two different media (water and glass for example) along the fastest route. This is called the index of a medium (denoted n) is an amount inversely proportional to the speed of light in that medium. If the light is as intelligent as the lifeguard, it adopts the fastest route, and will therefore increase by the same point O defined by the rule n1 sin (i) = n2 sin (r). It is the law of Snell-Descartes!

When Fermat succeeded in demonstrating this result in 1661 from the single principle of "least time" of the light he is fascinated: "The fruit of my work has been most extraordinary, most unexpected and that was the happiest ever. " He feels that there is a law of physics very general he calls "principle of natural economy ", that" nature always acts by the shortest ways "*. The story would prove him right beyond anything he could imagine ...

From the perspective in mechanics: the principle of least action
Fermat's approach is obviously disturbing to the rational mind: how light she know that this path is the shortest and not another? Its principle also appears to violate principle of causality: how the department knows it the way to go from its final destination? minds thinking of the time saw in this principle very simple and a little magical expression of a certain perfection God who ruled all laws of physics. As Leibniz wrote eg

"For given that the bill is the whole world that is more perfect and has been run by the creator wiser, it does absolutely nothing in the world, which manifests itself in a certain method of maximum or minimum, so there can be no doubt that all effects of the world can be easily deduced as final causes, through the method of maximum and minima, as efficient causes themselves "(quoted by Jacques Bouveresse here).

other words, Leibniz defended a teleological argument, that is to say that could explain natural phenomena rather than from their causes (forces suffered etc..) But from their purpose. The principle is that the result must be the "best" possible, ie a maximum or minimum. This explanation
upside Voltaire brought out of its hinges and it inspired the famous tirade Pangloss in Candide (image source: here ):

"Pangloss taught metaphysical -theologo-cosmolonigologie. He proved admirably that there is no effect without cause, and that in this best of possible worlds, the castle of the Baron was the most beautiful castles and Madam best possible baronesses. "There is evidence, he said, that things can not be otherwise: for all being created for a purpose, everything is necessarily for the best end. Note that noses were made to wear spectacles, as did our glasses. The legs are visibly designed for stockings, and we have stockings. " (Candide chap1)

Good, but there was more to stop our scientists in their quest for a metaphysical principle. After all billiard balls behave like light rays when they roll in a straight line or they bounce against the walls; generalized Maupertuis therefore Fermat's approach to the mechanics and postulated in 1744 what he called a "principle of least action"
"Now here this principle, so wise, so worthy of the supreme being: when a change occurs in nature, the amount of action used to change is always the smallest it is possible. "
Rather than explain Newton as the movement of a body describing every moment its variations of speed and position with the laws of such acceleration = force / mass, Maupertuis conjectured that one can directly find its global trajectory once one knows the points of departure and arrival. His approach is bold: among all conceivable paths between these two points, one that chooses the nature is one that maximizes (or minimizes) the famous "action". A small scheme is better than a long explanation:

Optimize yes ... but what exactly?
What was this "action" that nature strives to extremal? For Maupertuis was accumulating momentum of the particle along its trajectory. Its side Euler, Maupertuis who helped to formalize the theory itself, rather bent on the accumulation of potential energy (that which gives the altitude for instance), all bodies seeking to voluntarily put themselves in the state of the lowest potential energy. It was Lagrange which put everyone agreed in 1788 with a general formulation still in force today. In the particular case of a body subjected to a potential (gravity, electromagnetic forces, for example), the amount and the actual path minimizes time interval, is the average the difference between kinetic energy (T) and potential energy (U).

For furious action Lagrange written: S = action between points a (at time t a) and b (in time t b ) £ = Lagrangian system, depending on the position, velocity and time T = kinetic energy (½ mv ²) U = potential energy (dependent on position) For Maupertuis action rather spelled: If the total energy is constant and can be written as E = T + U, the two approaches coincide. One can indeed write that TU-2T = E = E + E = TU-2U Since E is a constant, it is the same look for the extremum of UT (like the Lagrangian), 2T (as Maupertuis) or U (as Euler)! can also demonstrate the principle of Fermat, starting from the action of Lagrange, but it is much more complicated!

Not only does it work, but he showed more perfect equivalence between the principle of least action and reformulated all laws (causal) of Newton. (See demo here example). Fortiche this Lagrange. But then, I do not know about you, but me the story of minimizing the "difference between kinetic and potential energy" does not speak to me at all. As much as I can see what is the sum of these energies, the total energy (E)-which keeps both the physical sense of their difference (TU) escapes me. Besides, I do not have to be alone, because this principle of least action is often seen as a kind of mathematical trick more or less abstruse. By dint of searching, I finally found one yet interpretation physics at each of the three expressions of this principle of least action as expressed by Lagrange, Euler and Maupertuis. You choose the one that speaks to you most!

A reluctance to change gears
expression Maupertuis based momentum finally seems easiest to understand: to change the momentum of a body should be a strength, it seems logical that the trajectory "chooses" to be one that avoids the most to suffer the action of these forces. I sees a similar path of least resistance, resistance to change etc.. I request advance the reader's indulgence if I say a donkey, but I also see why the golf ball has the unfortunate tendency to bypass the hole rather than to go and come out eventually.

According to the Maupertuis principle of the ball follows the path of accumulating the least average kinetic energy in a given time (the calculation is in the box above). Now the kinetic energy varies with the square of speed, so from the point of departure and arrival, his average is still above the square of the distance (AB on the diagram) divided by the square of the time limit (t ). More speed will vary, the greater the average kinetic energy will grande.D after the principle of Maupertuis, the ball "repugnant" to borrow so paths where the speed varies in all directions. If it must go through the hole and come out, its speed will increase suddenly when she plunges lower then when it comes out. Not good in terms of action that! Better it nicely circumvents the hole without accoups in its speed and too bad for the player ...

Why difference between kinetic and potential energy?
Leave a ball vertically and let it fall into your hand. It rises very quickly, slows, stops, then falls accelerating. If we measure the evolution of its altitude and time, we obtain a parabolic curve that looks like this:

The ball spends little time at low altitudes (U is low) when its speed is large (so T also). As the takeoff and landing are short, they contribute little to the average of TU on the total duration of the trajectory. That's good because at that time TU is great. Conversely, the ball goes much longer at high altitudes (when U is large), and low speed (when T small). Not stupid ball, because of the low blow TU contributes significantly to the average. In short, the ball flight seems well optimized. You can try all other forms of convoluted curves, since departure, arrival and duration are fixed, the dish actually described by the ball is the curve that minimizes the average over TU.

course these considerations do not have much interest if we remain in case as simple. But in real life, we often deal with forms of fields (including electromagnetic) horribly complicated that we can possibly know the approximate value in every point in space but certainly not the whole equation. Therefore impossible to apply Newton's laws if we do not know the field equation! For cons, the previous approach of seeking optimal trajectory is super simple: just simulate computationally different trajectories for fixed and calculate the total amount for each UT. accumulated. The actual path will be that which minimizes the quantity: easy!

geodesics in space?
Returning for a moment on the approach of Fermat. Light minimizes the travel time in the medium, ie it follows a geodesic : a straight line when the index of the medium is constant, a curve when it changes. As the travel time is proportional to the index, the path actually traveled by light is that which minimizes the average of the index along the trajectory. For light, a high index has exactly the same effect as a greater distance, ie the index variations indicate a deformation of the metric space for the beam.

In the case of a body subjected to forces derived from a potential (gravity, electric field or magnetic ...), we saw that the principle of least action can be expressed as the minimization of average potential energy along the real trajectory (this is the approach of Euler). So there is a formal analogy between the index of the medium for light and potential energy U to the body in motion. We can consider the trajectories of the coup as physical geodesic space deformed by a potential energy field. In other words, according to the principle of least action sauce Euler, there is equivalence between the motion of a particle subject to a potential independent of time in a Euclidean space and the trajectory of a free particle in a curved space. According Basdevant, Einstein would have had this idea in mind in 1908 when he built his theory of general relativity, a theory which rightly concludes that gravity bends the light path in the same way that a change in refractive index.

However, Jacques Leon with whom I had the pleasure to discuss this issue told me the limits of this analogy in the case of physical bodies. The intensity of the potential energy for an object depends not only on its position but also its mass. So the faux "gravitational refractive index 'is not an intrinsic property of space as it depends on the mass of moving bodies. That problem does not arise with the light because photons are massless: the trajectories of light are real geodesic space-time so that the trajectories of massive bodies are not really.

A unifying principle fascinating
Since Hamilton Jacobi and gave it its modern formulation, the principle of least action has found applications in all areas. The Lagrangian formalism is very convenient as it applies any coordinate system (spherical, cylindrical or composite). And when the motion is constrained by barriers or links between elements of a system is a breeze to integrate these constraints in the Lagrange equations (as multipliers Lagrange for those interested).

to my knowledge there is no area of physics whose evolution can be described as a maximization or minimization of something: the shape of soap bubbles, the cells of honeycomb , spirals of nature etc.. can always be explained by the maximization of some function of the system. The principle of least action is the only theory which has so far never been found wanting. Better still, it can find almost all the laws of physics! Thanks to him, Emmy Noether showed that behind every symmetry of the laws of nature lies a conservation law of a certain physical magnitude. David Hilbert found the equations of general relativity using this principle. Finally, this strange principle proved perfectly compatible with the quirks of quantum physics. At that point Richard Feynman has done with his concept of "path integral", the basis of its quantum electrodynamics, a theory which he says allows "to describe all the phenomena of the physical world, excluding gravitational effects.

short, 300 years since the principle of least action has ceased to inspire all the history of physics and I'm fascinated by the amount and strength of its applications from a simple statement, even simplistic. Is it because its power of unification continues to scare us a bit that is not taught at school or in preparation? At a time when we deplore the lack of interest young people in science, we would lose nothing by showing them this little jewel of the laws of nature.

* To be exact, the light always follows a path whose length is extremal: minimum but most often it happens that the route will be maximized. To simplify this post is already well quite complicated like that, whenever I talk about "minimum" or "maximum" should read "extremal" ...

Sources:
R Feynman: The Principle of least action, special reading (pdf )
The Wikipedia article on the subject
An excellent summary (ppt format ) on the subject
Florence Robine conference in 2007 (pdf )

Related posts:
Noether's theorem: Swiss Army knife of physics
classified Ticket (power) X why we always find the Fibonacci sequence in heart of sunflowers, pine cones etc. ...

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