Émilie du Châtelet and the Foundations of Physics

Émilie du Châtelet linocut, 11" x 14", by Ele Willoughby, 2019

This is a hand-printed portrait of Gabrielle Émilie Le Tonnelier de Breteuil, Marquise du Châtelet (1706-1749), a natural philosopher, mathematician and physicist, inspired by contemporary portraits, and shows her along with her diagrams. Each 11" x14" (27.9 cm x 35.6 cm) linocut print is printed on lovely, delicate, Japanese paper. The diagrams are from Principes Mathématiques de la Philosophie Naturelle, a two-volume translation and commentary of Newton’s Principia, published in 1759 in French in Paris.

While historically she was merely remembered as Voltaire's lover, she in fact was not only responsible for all his ideas about physics but was the first to postulate the conservation of total energy (which includes kinetic and other forms of energy combined). Further, she found the relationship between kinetic energy, mass and velocity of an object. Before translating Newton, she published her magnum opus Institutions de Physique (or Foundations of Physics) in 1740 and within a mere two years it had been translated into many languages and republished. Debate raged at the time about how the measure the force of an object and how to formulate conservation principles. She was an active participant in this dispute known as the vis viva debate. There was a schism between the Newtonians in England and the continental philosophers who followed Leibniz, particularly in German-speaking regions; she wanted the best of both while contemporaries viewed Newton and Leibniz' work as fundamentally opposed interpretations of the world. Institutions de Physique covered philosophy, space, time, matter, laws of nature and gravity including Galileo's results and Newton's more general work. In Principes Mathématiques de la Philosophie Naturelle, she combined Newton's text with Leibniz' more elegant formulation of calculus, pushing physics forward. She was recognized during her lifetime by the greatest thinkers of the day including renowned mathematicians such as Johann II Bernoulli and Leonhard Euler, her works were translated into other languages and discussed in scholarly journals and represented in (or even plagerized by) the Encyclopédie of Denis Diderot and Jean le Rond D'Alembert. She made a large impact on contemporary physics and philosophy.

Fronstispiece from Algorotti's
Il Newtonianismo Per Le Dame, 1737 Venice

After much goading and many years, Newton finally published the bulk of his understanding of mechanics and his famous three laws in Philosophiæ Naturalis Principia Mathematica, known simply as the Principia, in 1687 with two further corrected editions in in 1713 and 1726. As the title implies, the text is written in Latin. Though he had to derive the concepts of calculus to complete the work, it's largely absent from the text in favour of the geometrical approaches to infinitessimal calculus. So Émilie du Châtelet's work does not simply represent a translation - she reorganized the work using Leibniz' calculus, wrote commentaries and explanations and most importantly, added her own discoveries about kinetic energy. To this day, du Châtelet's version is the standard French translation of the Principia and modern translators still rely on Émilie's translation.

She taught herself mathematics, and then was tutored in algebra and calculus by Moreau de Maupertuis, a member of the Academy of Sciences (who had been trained by mathematician Johann Bernoulli, who also taught Leonhard Euler).  Then she turned to his protégé mathematician Alexis Clairaut, author of Clairaut's equation and Clairaut's theorem, who became a life-long friend, and other top French mathematicians. On one occassion she was ejected from Café Gradot, where men held intellectual discussions, for being a woman. So, she had some men's clothing made and boldly returned. She became a world authority on Newtonian mechanics, at a time when few imagined a woman capable or even interested in such a thing. Émilie's impact on continental physics, and bringing Newton's Principia to Europe (and to those in England more able to read French than Latin) cannot be overstated.

She was aristocrat who not only dedicated herself to knowledge, writing about physics and experimentation, she enjoyed clothing and could be extravagant. She loved fashion, gambling and jewellery.  She used her mathematics ability to devise successful gambling techniques, when she needed money for books as a teen. Voltaire was known to call her Madame Newton-Pompom-du Châtelet for the pompoms she wore. His own writings on physics were written in collaboration with her and often quoted her word for word. It wasn't long before her skills and interest far exceeded his own. She had some insight into the relationship between light, colour and heat, long before a modern understanding of energy. At the time, scholars debated whether kinetic energy or momentum was the pertinent thing - we now know that both are important, yet distinct. She leaned towards Leibniz' ideas on the subject, which shows how she was at the cutting edge of contemporary physics knowledge and debate.

She translated Mandeville's The Fable of the Bees into French and used the preface to denounce the prejudice that prevented women from access to a proper education. Nonetheless, a product of her time, she focused more on her daughter's marriage prospects and her son's education. She had to fight to be taken seriously and deal with sexism from even the well-meaning; she and contemporary part-time Bolognese physics professor Laura Bassi were not impressed when their friend Algarotti wrote a rather patronizing popularization of Newton's physics called (I wish I were kiding) Newtonianism for the Ladies. Worse, the frontispiece of his book shows a man speaking to a lady who suspiciously ressembles du Châtelet, implying he had explained Newtonianism to her. Her short-term mathematics tutor Samuel König, a student fo Mauterpuis, also tried to undermine her by claiming responsibility for Institutions de Physique. This lead to her estrangement from Mauterpuis. Ironically König later fell out with Euler and accused Mauterpuis of having plagerized him.


The story of her long-lasting relationship with Voltaire is quite fascinating, a relationship she pursued with the knowledge and blessing of her husband, Marquis Florent-Claude du Chastellet-Lomont (Châtelet is the modernized spelling of Chastellet). She first met Voltaire as a child at one of her father's salons. They became close when she re-entered society after the birth of her children. She invited Voltaire to live at their country house, a refuge for him when he was in disfavour, and there they worked together on their publications and set up a lab. They both submitted essays to the 1738 Paris Academy prize contest on the nature of fire; neither won (they lost to Euler) but they both earned honourable mention and their essays were published by the Academy. Hence, du Châtelet because the first woman to have a scientific paper published by the Academy. Eventually their relationship became a comfortable, platonic collaboration. At age 42, she began a new affair with the poet Jean François de Saint-Lambert. She feared she could not survive her subsequent unplanned pregnancy. Six days after the birth of a daughter, on 10 September 1749, at Lunéville, she suffered a fatal pulmonary embolism. Voltaire, her husband and final lover Saint-Lambert were all at her bedside with she died.

References
Project Vox, Duke University, accessed August, 2019
Émilie du Châtelet, Wikipedia, accessed August, 2019
Philosophiæ Naturalis Principia Mathematica, Wikipedia, accessed August, 2019
Robyn Arianrhod, Seduced by Logic: Émilie du Châtelet, Mary Sommerville and the Newtonian Revolution, Oxford University Press, 2012

Émilie du Châtelet, Principes mathématiques del la philosophie naturelle, vol. 1.,  Paris, Desaint & Saillant etc., 1759

Cynthia J. Huffman, Mathematical Treasure: Émilie du Châtelet’s Principes Mathématiques, Convergence (January 2017)

Imaginary Friends of Science: Descartes' Demon

The 2nd in my 'Imaginary Friends of Science' series - after Maxwell's Demon* - is Descartes' Demon. Despite (or because) of his rationalism, René Descartes hypothesised the existence of an evil** daemon, a personification who is "as clever and deceitful as he is powerful, who has directed his entire effort to misleading me." The evil d(a)emon presents a complete illusion of an external world, including other people, or even his own body, when perhaps they didn't in fact exist. This is a sort of thought experiment to test the very idea of empiricism.

The modern version of this is the "brain in vat" (i.e. how do we know we aren't just brains in vats of biochemicals being stimulated to simulate what we sense). Descartes' Demon moves with the times, except perhaps when it comes to fashion. In fact, he bares an uncanny ressemblance to René Descartes himself, except for the horns, and the brain in a vat, of course.

Prior to taking the methodological skepticism (or, in the lovelier original, doute hyperbolique) to its extreme, in the Demon, Descartes used the dream argument as a thought experiment. Do we know this reality we each observe and experience exists or is it nothing but a dream? He uses this to show that in fact we can distinguish dream from reality. In this argument he was preceeded by two millenia by Zhuangzi (庄子;), 4th century BCE Chinese philosopher, who wrote, amongst other things "Zhuangzi dreamed he was a butterfly", which I came across in Jorge Luis Borges' famous essay "A New Refutation of Time".

Once Zhuangzi dreamt he was a butterfly, a butterfly flitting and fluttering around, happy with himself and doing as he pleased. He didn't know he was Zhuangzi. Suddenly he woke up and there he was, solid and unmistakable Zhuangzi. But he didn't know if he was Zhuangzi who had dreamt he was a butterfly, or a butterfly dreaming he was Zhuangzi. Between Zhuangzi and a butterfly there must be some distinction! This is called the Transformation of Things. (2, tr. Burton Watson 1968:49)

This philosopher was influential to Zen.

It's little wonder that in more recent and contemporary culture, we are still fascinated by these ideas. Consider Tweedledee and Tweedledum's warning to Alice in Through the Looking-Glass that the Red King asleep in the grass is dreaming about her, and that if he were to wake up she would "go out—bang!—just like a candle." Or The Matrix, which directly alludes to Alice. Likewise "Abre Los Ojos" (Open Your Eyes) (or its American remake, Vanilla Sky). Also the brain in a vat specifically makes appearances everywhere from Star Trek to Donovan's Brain.



Descartes himself was quite the character, alarming to contemporaries, even the scientists and philosophers. He liked to stay in bed until noon. It seems the enthuasism of his last great patron, Queen Christiana of Sweden, who demanded early morning tutorial, may have killed him. The moral of the story kids: no good come from studying before noon. Also, it's fun to try and tie all one's favorite things together.

*Remember him? Maxwell's Demon fights entropy, rather than empiricism. I love these far-out gedenkenexperiments (or thought-experiments, but if you are trained in physics you take language cues from Einstein) of such solid rationalists. Maxwell's Demon is more benign... after all, he might yet save the Universe from heat death.

**Personally, I would translate malin in le malin génie as wicked, rather than evil. I associate the word with mischievious, clever elves in fairytales... a trickster rather than something you'd see on Supernatural.