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Page 9: 1975, Degree in Mathematics at the University of Amiens

Adjunct Professor of Mathematics in Arras. It was awful. Absolutely Awful.
Fortunately I still had my second passion, Photography.
I decided to go for a change in culture and in language.
Another scattering of odd jobs across Europe. Then…

Topology is a branch of mathematics
In mathematics, topology is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing.

Then the Rolleiflex Single-Lens, 120 format (the negatives measured 6x6cm), of very good quality, but it had some parallax issues due to the 2 lenses and difficult to focus in low light conditions.
Here I am in Grenoble to take photos at my brother Dominique’s wedding.

In France, here is how I, perhaps like you, learned trigonometry: “Take out your notebook, write ‘definition: The tangent of an angle is the relationship between the opposite and adjacent sides’. Learn it by heart for next week”. Fun.
As for myself, I tried to motivate my students by telling them how (in a somewhat simplified version) Eratosthenes calculated the circumference of the Earth in the third century BC. It is an extraordinary tale: Eratosthenes (276-194BC) was a geographer, mathematician, and director of the library of Alexandria.
He had heard travelers say that in Syene, at noon on June 21st, you could see the image of the sun reflected in the bottom of a well. This meant of course that the Sun was precisely vertically above the well.
So on June 21st, at noon in Alexandria, Eratosthenes measured the length of the shadow of one of the city’s obelisks.
The Greeks had already figured out that the world was round, for they were great navigators, often in armadas, and they had remarked that when a boat disappeared over the horizon, it was always the prow that disappeared first, no matter where or in what direction they were traveling. From the Atlantic to the Black Sea, the same thing happened, and only a sphere could explain it. They had also understood that a lunar eclipse happened when the Earth’s shadow was projected onto the moon and that this shadow was circular. They had even understood that the sun’s rays, crossing such a far distance, were parallel.
Which allowed him to draw up the following diagram :

Angles A and B are equal as they are interior angles. So that gives him the angle and the opposite side of an isosceles triangle. Far from being an idiot, Eratosthenes knew that he only needed to calculate the two unknown sides, in this case, the SUN’S RADII! As you well may know, a triangle has only 6 variables: 3 sides and 3 angles. It is evident that once you have 3 of those variables, you can find them all. If you have an angle and two sides, your triangle is well-defined. So there must be calculations that would let you find the other variables. He was right, and so he invented “Trigonometry”.
Eratosthenes was able to find the length of the Earth’s circumference: 39,375km which isn’t too far off. Pretty good job for 300BC.
Bravo, Eratosthenes. Thanks to you, we can learn this so-called Trigonometry. Hurray!
I learned all of these motivating stories by talking to other math students I met while working for the National Trust.

« We have known the radius of Earth since the time of the Greek mathematician and geographer Eratosthenes, about 240 BC. Every year at noon on June 21, the Sun passed directly overhead at Syene, Egypt. Eratosthenes knew this fact. At that same moment, he measured the Sun to be 7.2° off vertical in Alexandria, which is directly north of Syene. Aristotle had argued that Earth, no matter what its orientation, always casts a circular shadow on the Moon during an eclipse of the Moon. The only object that always casts a circular shadow is a sphere; thus, Eratosthenes knew that Earth must be a sphere. He also understood that the 7.2° shift in the altitude of the Sun, as measured from the two cities at the same time, was due to the curvature of Earth’s surface, meaning that the two cities were separated by 7.2° of latitude, or about 1/50 of Earth’s entire 360° circumference. Hire someone to pace off the distance from Alexandria to Syene, multiply by 50, and you have the circumference of Earth—about 25,000 miles. Divide by 2π and you have the radius. It was easy, once someone figured out how to do it! » (de « Welcome to the Universe: An Astrophysical Tour » par Neil deGrasse Tyson, Michael A. Strauss, J. Richard Gott)

My own simplified version of Thales’s theorem.
Legend has it that Thales of Miletus (about 626-547 BC) was invited by King Amasis, warned of his great knowledge. The king declared that he did not know the height of the fantastic pyramids already almost two thousand years old. Thales planted his cane at noon in the sand vertically and said to the king:
"The shadow of my cane is exactly equal to its height, and so must your pyramid." ....

In geometry, Thales's theorem, or intercept theorem, states that on a plane, a line parallel to one of the sides of the triangle cuts it into two similar triangles.
The legend goes that Thales of Milet (around 626-547BC) had been invited by King Amasis who had gotten wind of Thales’s great knowledge. Thales lived up to his reputation when the King declared he did not know the height of the great pyramids, already almost 2000 years old.
At noon Thales planted his cane straight up in the ground and said to the King, “My cane’s shadow is equal to its height, the same must be true for your pyramid.”
The lines AP and BC are parallel so the triangles DBC and DPA are similar and the sides AP, PD, AD are proportional to the sides BC, BD, and CD. As we can measure the lines PD, BC, CB and BD, we can calculate AP. Magic? No, Mathematics. Bravo, Thales.
AP/PD = CB/BD => AP ==> (CDxPD) / BD
Example: If I am 2m tall, my shadow is 5 metres long and I am 10m from the tree, the tree is 2x20/5= 4m tall.

Stand-in Math teacher in Arras, Pas-de-Calais..

I was disgusted by the weight of French administration and the ridiculous pedagogy (or lack thereof). The principal had a fit over my students laughing in Math class. Discipline was taken very seriously, learning not so much…
At that time, to be fair, there was no training at all for teachers. In the French National Education system, it is enough to know your subject, and hup, you’re good to go! You’re a teacher now, thrown into the classroom without a single piece of advice, without any sort of training, theoretical or practical. Good job, you bunch of idiots.
Just because you are good at math, it doesn’t mean you’re able to teach it! Most of my teachers growing up were a good example of this.

Do you think it’s gotten any better today?

I must not laugh
I must not laugh
I must not laugh

When I saw that not only the principal but all my colleagues in mathematics and physics were against all innovations, I understood that a career with these idiots for 40 years would not make me happy.


Other examples of the French national education of that time:

Program of history in 3rd: the French revolution of 1789. Program of history in second: the French revolution of 1789.
The 14-18 war or the Russian revolution: not a word!

The same teacher of English from second to final, Mr. Taquet: for three years, we have never pronounced a single word of English !!!
I learned English with very good teachers: John, Paul, George and Ringo.

My geo history teacher in second (1968), said that the Beatles were aggressive subversive degenerates, so I laughed softly (I understand English): the Beatles sing mostly love songs. Ignorance is a serious fault!

For two years (Math Sup and Math Spé), the word math teacher spoke only with the gifted class, ignoring the other 40 students. The physics teacher said he was against the theory of relativity and did not teach it. I learned everything myself.

My college was named "Lycée Robespierre" after the famous French revolutionary guy. I think this name is inappropriate.

"I will not bow, I will not go away in silence, I will not submit, I will not turn back, I will not conform, I will not shut up.
Courage is to seek the truth and to say it; it is not to suffer the law of triumphant lies." Jean Jaurès.

I don't "believe" in science.
Science works, whether I believe in it or not.

Science teaches us to think rationally

I build a model of the caravel, the Pinta, one of the three Christopher Columbus ships, during his trip to "America".
The other boats were called: Niña and Santa María.
Christopher Columbus' father would have had sufficient financial means to send him to the University of Pavia where he studied, in particular, cosmography, astrology and geometry.
Like me, and I went to America too.
Well, I learn that when other people take a picture of me, I am very often blurry.

Learning maths and physics helps to see the difference between the rational and the irrational.

France loses a good teacher, England gains a great photographer.

I decided to go for a change of culture and language. Again I worked some odd jobs across Europe: volunteer work cleaning up the rubble after an earthquake in Monteaperta di Friuli, near Udine, Italy; photographer for Club Med in Corfou, Greece; photographer/videographer for Butlin’s Holidays Ltd, Bognor Regis Sussex (we had to ask the guests to pay for their photo before taking it! Club Med and cruiseships were easy after that!); salesman/demonstrator for Electrosonic slide projectors in London, I went to Norway to see Ina who I met at Friday Bridge, etc…

Math teacher in France: an endangered profession (2015)

Les performances en mathématiques des élèves en France, aussi bien au primaire que dans le secondaire. Dans les deux cas, le niveau global est en sérieuse baisse.

La situation au primaire est encore plus inquiétante. Dans la dernière étude internationale (TIMSS) qui évaluait le niveau en mathématiques des élèves de CM1, on trouvait la France en dernière position du classement avec un score moyen de 488 points quand la moyenne européenne était de 527 points. Ce résultat est très loin de la perception que l’on peut avoir du niveau en mathématiques de notre pays, il devient donc urgent d’agir pour inverser cette tendance.

Le problème en France n’est pas celui de la « quantité » mais bien celui de la « qualité » d’enseignement. C’est d’ailleurs sur cet aspect qualitatif que la situation devient particulièrement préoccupante. Les difficultés en mathématiques ne se cantonnent pas aux élèves, le mal est plus profond et concerne aussi nos enseignants. Ainsi, les connaissances en mathématiques de ceux qui exercent dans le premier degré (en maternelle et au primaire) sont insuffisantes quand une crise de vocation touche certaines académies du second degré (collège et lycée).

Sur le premier degré, ce constat n’est pas surprenant quand on sait que plus de 80% des étudiants qui se prédestinent à devenir professeur des écoles sont titulaires d’une licence en Lettres, Arts ou Sciences Humaines. Ils ont, pour un grand nombre d’entre eux, en héritage de leur scolarité antérieure, des difficultés, voire une aversion, envers les mathématiques. Ainsi, toujours selon l’étude TIMSS, les enseignants du primaire en France sont moins nombreux à déclarer se sentir à l’aise ou très à l’aise lorsqu’il s’agit d’améliorer la compréhension des mathématiques des élèves en difficulté (61 % contre 79 % en moyenne). Il en est de même lorsqu’il s’agit d’aider les élèves à comprendre l’importance des mathématiques (70 % contre 88 % en moyenne) ou de donner du sens aux mathématiques (72 % contre 85 % en moyenne) (voir la note de la DEPP du ministère de l’éducation pour davantage d’informations).

Les étudiants sont moins nombreux à vouloir devenir prof de math que par le passé. En conséquence, certains postes restent vacants depuis quelques années, notamment pour aller exercer dans les secteurs les plus défavorisés. Cette pénurie d’enseignants nuit aux élèves qui en ont le plus besoin mais ne peut être considérée comme surprenante, tant les salaires en début et en milieu de carrière manquent d’attractivité en France.

Le niveau en mathématiques de nos élèves est en baisse depuis plus d’une décennie. Les solutions sont pourtant nombreuses pour enrayer cette spirale. Il sera important de mettre l’enseignement des mathématiques au cœur d’une réflexion plus globale sur le métier d’enseignant, au risque de voir la chute se poursuivre.

Cette entrée a été publiée dans Education, avec comme mot(s)–clef(s) éducation, enseignants, mathématiques, OCDE, PISA.

Nous vivons dans une société extrêmement dépendante de la science et de la technologie, dans laquelle presque personne ne comprend la science et de la technologie.

"It is better to aim for perfection and miss it than to aim for mediocrity and reach it." Francis Blanche

I’m fully aware that my letters were far lousy in the beginning. I’m a numbers guy, not a words guy! And, well, I wasn’t the best typist on my second-hand Remington. Don’t worry, over time I get much better and I become a decent journalist, combining my pen with my pictures. I am particularly proud of my article on Haiti (page 23), my description of my work on cruise liners (page 19, at the end) and my report on my ruin, written on the verge of suicide (page 41, at the end).

Raphaël Christian Fournier at the residence of M et Mme Courcelle, 22 rue Charles Dubois 80 000 Amiens, February 23 1975.
First, « See you Soon » doesn’t necessarily mean within 20 days. I don’t have a lawyer. I hope you’re doing well… in health, in your studies, emotionally, and all those other things you need to do “well”.
Thank you for your letter, it’s true I haven’t got much free time, I have too much on the go and it’s wearing me down (math, Beaux-Arts, English, Photo club organizer, 10 hours of math tutoring per week to eke out a living, it doesn’t sound like a lot but it is, skating, etc. etc. It all eats up quite a lot of my time. I still manage to somehow mess up my sensitive paper with my photo boxes. I’ve just successfully written my exam for the unit on topology and less successfully the one for algebra.
Why am I in Amiens? For the coffee machine. It is a magnificent machine: SILENCE, precision, efficiency, a part in an erotic slot. A part rings, a button pressed, a soft hum, and it’s ready. It was love at first sight, blinding love at first sight, I signed up without hesitation. You might be thinking that the lid has flipped on this coffee machine, but that’s only because you haven’t got a sentimental coffee machine that doesn’t want to suffer anymore and who knows that it’ll suffer if it gets too attached.
And how are things with you? Where do you live? What are you doing? I am going back to work with the National Trust in the forest for 15 days at Easter in Britain.
I’ve enclosed a photo of my specter seen through a window in Brighton. Your friend, Raphaël Christian Fournier

Here I meet Angelo Falcone, second from the right.

And Christian Parramon.
Who I met again over the years. Here in 2014 in Fontainebleau. In the background, Frédérique Gosky

"Peter Adams: Photography is not about cameras, gadgets and gismos.
Photography is about photographers.
A camera does not make a great picture any more than a typerwriter writes a great novel."

My art work: Leaves in a stream in Peak District, UK.
As ever my photos, more or less abstract. Here, some dead leaves at the bottom of a creek. ART.

At the university in Amiens I met Michère Giry, of whom I haven’t a single photo (yes, it does happen!). She could have been the French Joan Baez, but, contrary to me, she chose to go for her Agrégation (competitive exam allowing you to teach at the secondary and post-secondary level in France) and became a teacher…

I took a shower this morning
And I took my time, too,
As it was Sunday, a rare thing.
What I saw in the mirror plunged me
Into profound reflection.
My wet hair flattened,
My wet bear straightened.
Is there a difference in nature between
These two capillary systems?
A short hair straightens when wet,
A long hair flattens when wet,
Or maybe : Am I just under the weather?
Night is now falling
It was a gloomy Sunday
And the meanderings of my brain have grown tired
After such meandering the whole day.
And I feel quite depressed and worried,
To remain silent
Before this important problem,
This hairy problem,
Bare yet prickly :
Am I under the weather?

Poem (in case it wasn’t obvious) by Christian Fournier. Sad that the main joke doesn’t translate well! “Problème à poil” means “Hair problem” but also “Naked problem”

If you were wondering, the answer to the question is yes.

CAVANNA : "Do the 12 000 people who die on the road every weekend all around the world have exactly the same horoscope?"

If you are born in Israel, you are probably Jewish.
If you are born in Saudi Arabia, you are probably Muslim.
If you are born in India, you are probably Hindu.
If you are born in North America, you are probably Christian.
Your faith is not inspired by a divine truth, it's just geography.

Patriotism is your belief that this country is superior to all others, because you were born there.

In order to understand the universe, you must know the language in which it is written and that language in mathematics.

The imposture of science education in French high schools, by Bertrand Rungaldier
Posted on June 25, 2013

Depuis leur invention il y a environ 2500 ans, les mathématiques passent pour la discipline de déduction par excellence. Si Platon avait inscrit au fronton de l'Académie "Nul n'entre ici s'il n'est géomètre" ce n'était pas parce qu'il exigeait de savoir faire des constructions compliquées à la règle et au compas mais bien parce qu'il demandait à ses élèves de savoir mener un raisonnement et d'avoir un esprit critique envers leurs propres affirmations.

Si 2000 ans plus tard Pascal louait "l'esprit de finesse et de géométrie" c'était pour la même raison : acquérir de la méthode, savoir analyser un problème, savoir le scinder en problèmes plus petits, les résoudre rigoureusement, faire la synthèse du tout. Et ce n'est pas un hasard si à la même époque, Descartes inventait la géométrie analytique dans un essai intitulé "Règles pour la direction de l'esprit" et non un traité de géométrie ou de mathématiques. Partout, en Grèce ou en France, toujours, dans l'antiquité ou à l'époque moderne, les mathématiques ont constitué la discipline de référence en matière de raisonnement.

Il est évident que cette façon de procéder, cette démarche intellectuelle que nous nommons désormais "scientifique" peut s'appliquer à n'importe quelle discipline intellectuelle; l'immense avantage des mathématiques est qu'il est extrêmement facile de savoir si l'on a bien conduit son raisonnement ou si l'on a correctement effectué son calcul tout simplement parce que chaque étape dudit raisonnement est clairement identifiée. Il est infiniment plus simple de savoir si l'on a correctement effectué un calcul ou si l'on a effectivement prouvé tel théorème que de savoir si l'on a correctement traduit un sonnet de Shakespeare, un poème de Goethe ou une page des Frères Karamazov.

Les Mathématiques ont pour fonction de former à l'art du raisonnement et à la méthode scientifique. C'est là leur essence et c'est ce qui les distingue de l'art du calcul pratiqué par les Egyptiens ou les babyloniens.

Il apparaît malheureusement que cette fonction primordiale ait été totalement oubliée par les rédacteurs des récents et actuels programmes d'enseignements des Mathématiques en lycée. On peut même se demander dans quelle mesure ils n'ont pas tout simplement décidé que désormais les Mathématiques ne devaient plus former à la rigueur et au raisonnement tant les programmes de lycée ont été véritablement exterminés au cours de ces dernières années.

"I would rather have questions that can't be answered than answsers that can't be questioned" Richard Feynman

Diana Frances Spencer, née le 1ᵉʳ juillet 1961 à Sandringham et morte le 31 août 1997 à Paris, est une aristocrate anglaise, membre de la famille royale britannique. Elle épouse en 1981 Charles, prince de Galles, avec qui elle a deux enfants : William, en 1982, et Henry, en 1984

Sur mes cahiers d’écolier Sur mon pupitre et les arbres Sur le sable de neige J’écris ton nom
Sur toutes les pages lues Sur toutes les pages blanches Pierre sang papier ou cendre J’écris ton nom
Sur les images dorées Sur les armes des guerriers Sur la couronne des rois J’écris ton nom Sur la jungle et le désert Sur les nids sur les genêts Sur l’écho de mon enfance J’écris ton nom
Sur les merveilles des nuits Sur le pain blanc des journées Sur les saisons fiancées J’écris ton nom
Sur mes refuges détruits ...

Et par le pouvoir d’un mot Je recommence ma vie Je suis né pour te connaître Pour te nommer Liberté

Paul Eluard, Poésies et vérités, 1942


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