Showing posts with label france. Show all posts
Showing posts with label france. Show all posts

Thursday, March 02, 2023

Prof. Gilles Saint-Paul (Ecole Normale): the Yellow Vests, French Politics, and Hypergamy (Manifold #31)

 

Audio (podcast only)


Gilles Saint-Paul is Professeur à l'Ecole Normale Supérieure. He is a graduate of Ecole Polytechnique in Engineering and received his PhD from MIT in Economics. Gilles and Steve discuss the French elite education system, the Yellow Vest movement, French politics and populism, and Saint-Paul's paper on marriage markets and hypergamy. 

0:00 Introduction 
1:43 Gilles Saint-Paul's background and education 
6:31 French and American elite education - Les Grandes Ecoles 
14:44 The Yellow Vests 
41:46 Mating and Hypergamy 

Links: 

On the Yellow Vest Insurrection 

Genes, Legitimacy and Hypergamy: Another Look at the Economics of Marriage https://ideas.repec.org/p/ide/wpaper/9118.html

Tuesday, September 15, 2020

Schrodinger's Cat and the Normaliens


Yesterday I had cause to look something up related to macroscopic superposition states ("Schrodinger cat states") in Serge Haroche's book Exploring the Quantum. Curiosity led me to Haroche's 2012 Nobel Lecture and autobiography, which I found fascinating. 

One wonders how long an elitist, highly meritocratic and undeniably productive system like the French Grandes Ecoles can continue to function in the current political climate. Quel dommage.
... I was fascinated by astronomy and by calculus, the notion of derivatives and simple differential equations which describe so directly and so well the laws of dynamics obeyed by moving bodies. This was the time of the first artificial satellites, the sputniks which orbited the earth and launched the American-Soviet race to the moon. 
I marveled at the fact that I was able, with the elementary calculus I knew, to compute the escape velocity of rockets, the periods of satellites on their orbits and the gravitational field at the surface of all the planets … I understood then that nature obeys mathematical laws, a fact that did not cease to astonish me. I knew, from that time on, that I wanted to be a scientist. For that, I embarked in the strenuous and demanding “classes préparatoires” of the famed Lycée Louis-Le-Grand, one of the preparatory schools which train the best French students for the contest examinations leading to the “Grandes Ecoles.” They are the engineering and academic schools, which since the French Revolution, have formed the scientific elite of France. These were two years of intensive study where I learned a lot of math and of classical physics. I eventually was admitted in 1963 to the Ecole Polytechnique (ranking first in the national examination, to the great pride of my parents) and at the Ecole Normale Supérieure (ENS). I chose to enter the latter because, at that time, it offered a much better opportunity to embark in a scientist career. 
The years as a student at ENS (1963–1967) have left me wonderful memories, contrasting sharply with the strenuous training of the preparatory school. Here, in the middle of the Latin Quarter, I was free to organize my time as I wished, to meet and discuss with students working in all kinds of fields in science or humanities and to enjoy all the distractions and cultural activities Paris has to offer. And I was paid for that, since the “Normaliens” as the ENS students are called, are considered civil servants and receive a generous stipend! These were my formative years as a scientist. Coming so to speak from the physics of the 19th century which was taught in the classes préparatoires, I was immediately thrown into modern physics and the quantum world by the classes of exceptional teachers. Alfred Kastler gave us a lyrical description of the dance of atomic kinetic moments, and gave atoms and photons a near poetic existence. Jean Brossel brought us back to Earth by describing the great experiments thanks to which quantum concepts were established, instilling in us the austere passion for precision. And Claude Cohen-Tannoudji revealed the theory’s formalism to us with extraordinary depth and clarity. I still remember three books I read avidly at the time: Quantum Mechanics by Albert Messiah, where I truly understood the depth and beauty of the quantum theory; Principlesof Nuclear Magnetism by Anatole Abragam, who introduced me to the subtle world of atomic magnetic moments; and Feynman’s Lectures on Physics, which was a revelation.
See also 

Saturday, July 27, 2019

Brainpower Matters: The French H-Bomb


Michel Carayol, father of the French H-Bomb.

The article below illuminates several mysteries concerning the French development of thermonuclear weapons. Why did it take so long? Did the French really need help from the British? Who had the crucial idea of radiation compression?

The original inventors were Ulam and Teller. In the USSR it was Sakharov. The PRC inventor was Yu Min (see Note Added at bottom).

Without men such as these, how long would it have taken to develop breakthrough technologies that defined the modern age?

See also Les Grandes Ecoles, One hundred thousand brains, and Quantum GDP.

THE REAL STORY BEHIND THE MAKING OF THE FRENCH HYDROGEN BOMB

Nonproliferation Review 15:2 353, DOI 10.1080/10736700802117361

Based on the first-person account of coauthor Pierre Billaud, a prominent French participant, this article describes for the first time in such detail the history of the development of the French hydrogen bomb in the 1960s and the organization of military nuclear research in France. ...
On November 1, 1952, the United States conducted its first thermonuclear test, ‘‘Ivy Mike,’’ seven years and three and a half months after its Trinity test. It took the Soviet Union four years (August 29, 1949 -- August 12, 1953) and the United Kingdom four years and seven months (October 3, 1952 -- May 15, 1957) to achieve thermonuclear capacity. And in the following decade, China did it, with its sixth test, in fewer than three years (October 16, 1964 -- June 17, 1967). Yet after Gerboise Bleue it took France eight and a half years to reach the same landmark, detonating its first thermonuclear device on August 24, 1968. Why such a long delay, especially since the French were pioneers in nuclear research?

1965: What We Knew About the Technical Aspects

From 1955 to 1960, as we prepared for the first French atomic test, we were also pondering thermonuclear weapons. But the prospect of hydrogen weapons seemed so far into the future that we did not work seriously on it. ... Li6D was commonly considered the best fuel for thermonuclear weapons, but we did not have any idea about how to burn it. All the problems with the thermonuclear bomb can be summarized by this question: how to discover the process that will allow the Li6D to undergo a fusion reaction?

... Compared to our American colleagues in 1948, French scientists had many advantages: we knew that hydrogen bombs existed and worked and that they used Li6D, and we understood the reactions at work. We also had powerful computers, of U.S. origin, which were not available in the late 1940s. And we knew, more or less, the dimensions and weights of the nuclear weapons deployed at NATO bases in Europe and their yields. ...

De Gaulle: It’s taking forever! ... I want the first experiment to take place before I leave! Do you hear me? It’s of capital importance. Of the five nuclear powers, are we going to be the only one which hasn’t made it to the thermonuclear level? Are we going to let the Chinese get ahead of us? If we do not succeed while I am still here, we shall never make it! My successors, from whatever side, will not dare to go against the protests of the Anglo-Saxons, the communists, the old spinsters and the Church. And we shall not open the gate. But if a first explosion happens, my successors will not dare to stop halfway into the development of these weapons.


... In January 1967, I published a voluminous report wherein I presented and developed my idea from late 1965, left idle since, explaining why the current studies were going in the wrong direction and producing a ridiculously low thermonuclear efficiency. I proposed a scheme with two consecutive steps: a cold Li6D compression increasing the density, from the normal value of 0.8 g/cm3, by a factor of at least 20, followed by a sufficient temperature increase (the ignition). In this report, I also gave orders of magnitude of the energies involved in each step... [[ One can make the (flawed) analogy of Billaud to Ulam (multi-stage insight, but no mechanism for compression), and Carayol to Teller (proposed the right mechanism for compression, although in Teller's case he may have learned of it from von Neumann and Fuchs!!!). ]] 
In early April 1967, Carayol had the idea that the x-rays emitted from the fission explosion could transport the fission energy to the thermonuclear fuel chamber to induce the necessary compression. He published a brief paper wherein he presented, and justified mathematically, his architectural idea. This was the key to the solution for an efficient thermonuclear explosive device, consistent with the current data about U.S. hydrogen weapons. Carayol had rediscovered the radiative coupling concept first introduced by Americans Stanislaw Ulam and Edward Teller in January 1951.

Michel Carayol, the Genuine Father of the French H-Bomb

Michel Carayol was born in 1934 and died in 2003. His father was an industrialist and his mother a teacher. He entered Ecole Polytechnique in 1954, graduated in 1956, and joined the Armament. In 1962, he was part of the DEFA assigned to CEA-DAM at Limeil. In 1967, Carayol was part of the advanced studies branch.

... Soon after, in April 1967, Carayol wrote a brief report describing his proposal for a cylindrico-spherical case in dense metal, containing a fission device on one side and a thermonuclear sphere on the other. The report showed that the photons radiated by the primary *still very hot* in the X-ray frequency range, swept into the chamber rapidly enough to surround completely the thermonuclear sphere before the metal case would be vaporized. Carayol had discovered independently a scheme equivalent to the concept developed by Ulam and Teller in the 50s.
But Carayol's insight was ignored! It was British assistance that alerted project leadership to the value of Carayol's ideas. It is not enough for some isolated genius to make a breakthrough -- the people in charge have to understand its value.
... During the first months of 1967, Viard had told me, ‘‘A British physicist is showing some interest in what we do.’’ At several embassy parties, a first-rate British atomic scientist, Sir William Cook, former director during the 1950s of thermonuclear research at Aldermaston, the British center for atomic military applications, had approached the military attache´ at the French Embassy in London, Andre´ Thoulouze, an Air Force colonel, and had hinted to our nuclear research program. Thoulouze had previously been in charge of an air force base and knew Rene´ David, who would later work at the DAM. For this reason, instead of contacting the French main intelligence services, Thoulouze directly contacted our information bureau at CEA, the BRIS, where David was working at the time. In analyzing the fallout from the French tests, the Americans, the British, and the Soviets knew that we had not made any real progress on the thermonuclear path. In 1966 and 1967 we had tested some combination of fission with light elements. Cook told Thoulouze that we had to look for something simpler.

Two weeks after the Valduc seminar, on September 19, and while the work resulting from the Valduc decisions had not yet concretely gotten under way, Thoulouze came from London bearing information from this qualified source. Jacques Robert immediately convened a meeting, in the DAM’s headquarters in Paris, to debrief this information. Only three other people attended the meeting: Viard, Bonnet (DAM’s deputy), and Henri Coleau (head of the BRIS). The information, very brief and of a purely technical nature, did not consist of outlines or precise calculations. Nevertheless, it allowed Bonnet to declare immediately that the Carayol design, proposed unsuccessfully as early as April 1967, could be labeled as correct.23 Had this outline not already been in existence, we would have had a difficult time understanding the information and might have suspected an attempt to mislead us. In fact, this was a reciprocal validation: Carayol’s sketch authenticated the seriousness of the source, while the latter confirmed the value of Carayol’s ideas. Without realizing it, as very few were aware of Carayol’s discovery (and surely not Cook), he had given us a big tip and unexpected assistance, as this information also freed us from the ministerial harassment to which we had been constantly subjected. From that moment, things moved briskly.
Encyclopedia Britannica:
Physicist Michel Carayol laid out what would be the fundamental idea of radiation implosion in an April 1967 paper, but neither he nor his colleagues were immediately convinced that it was the solution, and the search continued.

In late September 1967, Carayol’s ideas were validated by an unlikely source, William Cook, who had overseen the British thermonuclear program in the mid-1950s. Cook, no doubt at his government’s behest, verbally passed on the crucial information to the French embassy’s military attaché in London. Presumably, the British provided this information for political reasons. British Prime Minister Harold Wilson was lobbying for the entry of the United Kingdom into the Common Market (European Economic Community), which was being blocked by de Gaulle.

Sakharov sketch:


Note Added: Perhaps someone can translate part of this paper, which gives some details about the Chinese thermonuclear step, credit to Yu Min. Did they invent a mechanism different from Ulam-Teller? I can't tell from this paper, but I suspect the initial Chinese design used U-T. There are claims that Yu Min later developed, in the pursuit of miniaturization and improved safety, a qualitatively different design.

Yu Min was a student of Peng Huanwu (also a key figure in the bomb effort), who was a student of Max Born. Yu Min only recently passed, in early 2019!


Saturday, September 22, 2018

The French Way: Alain Connes interview


I came across this interview with Fields Medalist Alain Connes (excerpt below) via an essay by Dominic Cummings (see his blog here).

Dom's essay is also highly recommended. He has spent considerable effort to understand the history of highly effective scientific / research organizations. There is a good chance that his insights will someday be put to use in service of the UK. Dom helped create a UK variant of Kolmogorov's School for Physics and Mathematics.

On the referendum and on Expertise: the ARPA/PARC ‘Dream Machine’, science funding, high performance, and UK national strategy


Topics discussed by Connes: CNRS as a model for nurturing talent, materialism and hedonic treadmill as the enemy to intellectual development, string theory (pro and con!), US, French, and Soviet systems for science / mathematics, his entry into Ecole Normale and the '68 Paris convulsions.

France and Ecole Normale produce great mathematicians far in excess of their population size.
Connes: I believe that the most successful systems so far were these big institutes in the Soviet union, like the Landau institute, the Steklov institute, etc. Money did not play any role there, the job was just to talk about science. It is a dream to gather many young people in an institute and make sure that their basic activity is to talk about science without getting corrupted by thinking about buying a car, getting more money, having a plan for career etc. ... Of course in the former Soviet Union there were no such things as cars to buy etc. so the problem did not arise. In fact CNRS comes quite close to that dream too, provided one avoids all interference from our society which nowadays unfortunately tends to become more and more money oriented.


Q: You were criticizing the US way of doing research and approach to science but they have been very successful too, right? You have to work hard to get tenure, and research grants. Their system is very unified in the sense they have very few institutes like Institute for Advanced Studies but otherwise the system is modeled after universities. So you become first an assistant professor and so on. You are always worried about your raise but in spite of all these hazards the system is working.


Connes: I don’t really agree. The system does not function as a closed system. The US are successful mostly because they import very bright scientists from abroad. For instance they have imported all of the Russian mathematicians at some point.


Q: But the system is big enough to accommodate all these people this is also a good point.


Connes: If the Soviet Union had not collapsed there would still be a great school of mathematics there with no pressure for money, no grants and they would be more successful than the US. In some sense once they migrated in the US they survived and did very well but I believed they would have bloomed better if not transplanted. By doing well they give the appearance that the US system is very successful but it is not on its own by any means. The constant pressure for producing reduces the “time unit” of most young people there. Beginners have little choice but to find an adviser that is sociologically well implanted (so that at a later stage he or she will be able to write the relevant recommendation letters and get a position for the student) and then write a technical thesis showing that they have good muscles, and all this in a limited amount of time which prevents them from learning stuff that requires several years of hard work. We badly need good technicians, of course, but it is only a fraction of what generates progress in research. It reminds me of an anecdote about Andre Weil who at some point had some problems with elliptic operators so he invited a great expert in the field and he gave him the problem. The expert sat at the kitchen table and solved the problem after several hours. To thank him, Andre Weil said “when I have a problem with electricity I call an electrician, when I have a problem with ellipticity I use an elliptician”.

From my point of view the actual system in the US really discourages people who are truly original thinkers, which often goes with a slow maturation at the technical level. Also the way the young people get their position on the market creates “feudalities” namely a few fields well implanted in key universities which reproduce themselves leaving no room for new fields.

....

Q: So you were in Paris [ Ecole Normale ] in the best place and in the best time.

Connes: Yes it was a good time. I think it was ideal that we were a small group of people and our only motivation was pure thought and no talking about careers. We couldn’t care the less and our main occupation was just discussing mathematics and challenging each other with problems. I don’t mean ”puzzles” but problems which required a lot of thought, time or speed was not a factor, we just had all the time we needed. If you could give that to gifted young people it would be perfect.
See also Defining Merit:
... As a parting shot, Wilson could not resist accusing Ford of anti-intellectualism; citing Ford's desire to change Harvard's image, Wilson asked bluntly: "What's wrong with Harvard being regarded as an egghead college? Isn't it right that a country the size of the United States should be able to afford one university in which intellectual achievement is the most important consideration?"

E. Bright Wilson was Harvard professor of chemistry and member of the National Academy of Sciences, later a recipient of the National Medal of Science. The last quote from Wilson could easily have come from anyone who went to Caltech! Indeed, both E. Bright Wilson and his son, Nobel Laureate Ken Wilson (theoretical physics), earned their doctorates at Caltech (the father under Linus Pauling, the son under Murray Gell-Mann).
Where Nobel winners get their start (Nature):
Top Nobel-producing undergraduate institutions

Rank School                Country               Nobelists per capita (UG alumni)
1 École Normale Supérieure France       0.00135
2 Caltech                               US             0.00067
3 Harvard University            US             0.00032
4 Swarthmore College          US             0.00027
5 Cambridge University       UK             0.00025
6 École Polytechnique          France       0.00025
7 MIT                                   US              0.00025
8 Columbia University         US              0.00021
9 Amherst College               US              0.00019
10 University of Chicago     US              0.00017

Friday, October 12, 2012

The Normaliens


In an earlier post I mentioned that Serge Harouche (2012 Nobel Prize in physics) is a normalien: a graduate of France's Ecole Normale Superieure. Admission to ENS is strictly meritocratic, based on a competitive exam. The result: 12 Nobel Prize laureates and 10 Fields Medalists from a school with fewer than a thousand undergraduates. (The school is similar in size to Caltech; smaller than most high schools.)

See Defining Merit for the story of Harvard's internal debates of the 1950's, during which a realistic and shrewd admissions dean faced down idealistic faculty committees that wanted to make Harvard more meritocratic.
"Do we want an Ecole Normale Superieure, a 'cerebral school' ... ?"

"What's wrong with Harvard being regarded as an egghead college? Isn't it right that a country the size of the United States should be able to afford one university in which intellectual achievement is the most important consideration?"

Tuesday, October 12, 2010

Les Grandes Ecoles Chinoises

Note Added (2022): Wikipedia has a long entry on this topic.

The American intellectual elite are endlessly fascinated by the French Grandes Ecoles, which employ a rigorous examination system for admissions. See example below from today's NY Times.

In the past I'd read that the British and French based their civil service and educational examination systems on the much older Chinese model, but was not sure to what extent it is true. See here for an interesting discussion.
... Brunetiere believed that French education was really based on the Chinese system of competitive literary examinations, and that the idea of a civil service recruited by competitive examinations undoubtedly owed its origins to the Chinese system which was popularized in France by the philosophers, especially Voltaire. This definite conclusion that the French civil service examination system came from China is adopted by several authors ...
Summary of the case of Britain and colonial India can be found here. Amusingly, 19th century British writers opposed to the new system of exams referred to it as "... an adopted Chinese culture" (p. 304-305).

NYTimes: ... Born out of the French Enlightenment, the grandes écoles have long been the cradle of the governing class. “Normaliens” (graduates from École Normal Supérieure, whose 12 Nobel laureates include Henri Bergson and Jean-Paul Sartre), “Gadzarts” (from École Nationale Supérieure d’Arts et Métiers, like Jean-Lou Chameau, president of the California Institute of Technology), “X-iens” (from École Polytechnique, including the physicist Sadi Carnot, the philosopher Auguste Comte and the mathematician Benoît B. Mandelbrot), and “Enarques” (from École National d’Administration, including almost all recent prime ministers) occupy a place in French national life similar to Oxbridge graduates in England or the Ivy League in the United States.

Internationally, however, these institutions have far less clout than their Anglo-American counterparts.

... The grandes écoles run along very different lines. Admission is selective, with candidates generally required to complete a grueling two-year preparatory course. This “prépa” includes intensive study in mathematics, economics, philosophy and literature, plus at least two foreign languages. Of 1,079 candidates who took the entrance exam for the business school HEC in 2009, only 50 were offered places, and most of those already held master’s degrees from other institutions. The competition for science places is even tougher.

... Yet he, too, alluded to the new reality of global competition: “When I was a student we spoke of ‘le défi américain’ — the American challenge. Now we speak of ‘le défi asiatique’ — the challenge from Asia.”

How will France face this challenge? Dr. Tapie pointed out that while France “has only 1 percent of the world’s population, we make up 33 percent of Fields medalists,” the mathematics equivalent of Nobel laureates.

It was Cédric Villani, a 37-year-old professor at Lyon who won the 2010 Fields Medal, who gave the most spirited reply to France’s critics. Calling himself “a pure product of the French system,” Mr. Villani, a Normalien who has often taught in the United States, said that while American academic salaries were higher “and it’s easier to make big projects,” France also has particular strengths: “Our tradition, our quality of life, our social cohesion. My big problem in Princeton was finding a place to buy a decent cheese.”

Saturday, October 02, 2010

The hard truth about the French Foreign Legion

NY Review of Books: The world contains more misfits, sadists, masochists, and people who enjoy fighting than we sometimes like to suppose. How else can one explain the fact that the French Foreign Legion is heavily overrecruited? In an age when most of the world’s armies strive to make military service a less bestial and more enlightened experience than it used to be, the Legion still drives its trainees to scrub floors manically, fold kit and uniforms with obsessive precision, and march, march, march. ...

The Legion did much service to France in its colonial wars—by 1925 twelve battalions were deployed in Morocco alone. Windrow compares its experience to that of the US Army in America’s earlier frontier wars. Its soldiers were seldom required to display much initiative or imagination. They were merely expected to march, suffer, fight, and die for five centimes a day, with a minimum of reflection, much less complaint. One unit in Morocco in 1900 marched 1,134 miles in seventy-two days, losing only six of four thousand men to sickness. Most of the remainder reached barracks with their broken boots held together with wire and string. ...

It is safe to assume that only a tiny minority of the readers of this book have ever known lives of real Third World hardship, hunger, superstition, and arbitrary violence without appeal. For the nineteenth-century European underclasses such experiences might be the norm…. When men born into such conditions were offered [in the Legion] regular meals, a comprehensible system of reward and punishment, clearly-defined tasks and a sense of collective self-esteem, they could be shaped into a weapon, but it would remain a rather indiscriminate one….

Before [World War I]…people simply did not question the need for wars nor the moral status of those who fought them, and the things that might happen on campaign were no business of civilians; after all, the adversaries that they were fighting never took prisoners themselves, except with the very worst of intentions.


Both sides displayed absolute ruthlessness in the Legion’s long, inconclusive struggle with the North African tribes. All the combatants were men of their time, and what passes for civilization was far away. These two books go far to explain the enduring fascination of the Legion for armchair warriors and historians. But only the foolish seek to romanticize this bleak, cruel fighting machine, loyal only to its own.

Wednesday, May 21, 2008

Vive la France!

En route to Paris today. Hope the May 22 general strike doesn't strand me somewhere along the way!

Summer 2008 Conference fun.

Sunday, February 17, 2008

Les Grandes Ecoles

This Times article on the elite world of French business has some interesting facts about Ecole Polytechnique and Ecole Nationale d'Administration (ENA). In physics, we typically encounter graduates of Ecole Normale Superieure ("normaliens"), which boasts 9 Fields Medalists and at least 8 Nobel Laureates in physics. 15 years ago a normalien friend complained to me that the ENArques were getting the upper hand, but it appears from the article the polytechniciens are hanging tough! The greatest polytechnicien of all time might be Poincare, but then again there are also Cauchy and Ampere and Poisson and Navier...

An earlier post on Les Grandes Ecoles. I must say, these schools, with their strictly meritocratic admissions policies, sound a lot more like Caltech than like Harvard.

NYTimes: ...AT least half of France’s 40 largest companies are run by graduates of just two schools, the École Polytechnique, which trains the country’s top engineers, and ENA, the national school of administration. That’s especially remarkable given that the two schools together produce only about 600 graduates a year, compared with a graduating class of 1,700 at Harvard.

...Rather than a rigid class system, it was Mr. Fourtou’s and Mr. Bébéar’s admission into the École Polytechnique that assured their place in the elite. And that is one of the great ironies of the French establishment: while it enjoys the privileges associated with the elites of the United States, entry is, if anything, much more rigorously meritocratic, based on exams and ever-narrowing selection from an early age.

Indeed, getting into Harvard, which accepted 9 percent of its applicants last year, is a breeze compared with getting into the École Polytechnique.

Out of 130,000 students who focus on math and science in French high schools each year, roughly 15 percent do well enough on their exams to qualify for the two- to three-year preparation course required by the elite universities. Of those who make it through that, 5,000 apply to École Polytechnique, which is commonly called simply “X,” and just 400 are admitted from France.

Admission is based strictly on exam grades; there isn’t even an essay requirement or interview. And there are no legacy admissions, sports scholarships or other American-style shortcuts for getting into X.

“You can be the president’s nephew and it won’t help you get in,” says Bernard Oppetit, a 1978 graduate of X who later worked for BNP Paribas before starting Centaurus Capital, a London investment fund with $4 billion under management.

The École Polytechnique was founded in 1794, during the French Revolution, to train the country’s military engineers, and it officially remains under the umbrella of the French ministry of defense. Not only is the school free, but students also receive a stipend from the government to cover their expenses.

“We call it l’élitisme démocratique,” says Pierre Tapie, dean of Essec, a leading French business school. “These are places where you meet extraordinary people who are there because they worked hard and are among the most brilliant of a generation.”

Although the school teaches high-end fare like physics, engineering, and computer sciences, its broader goal is to create a leadership cadre that shares an ordered, prioritized view of the world, says Xavier Michel, the president of the École Polytechnique and an active-duty general in the French armed forces.

In France, this is known as the Cartesian system, after the mathematician and philosopher René Descartes, and Mr. Michel says the school encourages its students “to modelize” the world. And when they eventually become chief executives, he says, “they understand what are the capabilities of their companies. They understand what they can do and what they can’t do.”

Until, of course, models run off the rails — as they so often do in the business and financial worlds, regardless of what country devises them.

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