Emilie du Chatelet

Early life

Emilie du Chatelet was born on 17 December 1706 in Paris, the only girl amongst six children. Three brothers lived to adulthood: Rene-Alexandre (b. 1698), Charles-Auguste (b. 1701), and Elisabeth-Theodore (b. 1710). Her eldest brother, Rene-Alexandre, died in 1720, and the next brother, Charles-Auguste, died in 1731. However, her younger brother, Elisabeth-Theodore, lived to a successful old age, becoming an abbe and eventually a bishop. Two other brothers died very young. Du Chatelet also had an illegitimate half-sister, Michelle, who was born of her father and Anne Bellinzani, an intelligent woman who was interested in astronomy and married to an important Parisian official.

Her father was Louis Nicolas le Tonnelier de Breteuil, a member of the lesser nobility. At the time of du Chatelet's birth, her father held the position of the Principal Secretary and Introducer of Ambassadors to King Louis XIV. He held a weekly salon on Thursdays, to which well-respected writers and scientists were invited.

Early education

Du Chatelet's education has been the subject of much speculation, but nothing is known with certainty.

Among their acquaintances was Fontenelle, the perpetual secretary of the French Academie des Sciences. Emilie's father Louis-Nicolas, recognizing her early brilliance, arranged for Fontenelle to visit and talk about astronomy with her when she was 10 years old. Emilie's mother, Gabrielle-Anne de Froulay, was brought up in a convent, at the time the predominant educational institution available to French girls and women. While some sources believe her mother did not approve of her intelligent daughter, or of her husband's encouragement of Emilie's intellectual curiosity, there are also other indications that her mother not only approved of du Chatelet's early education, but actually encouraged her to vigorously question stated fact.

In either case, such encouragement would have been seen as unusual for parents of their time and status. When she was small, her father arranged training for her in physical activities such as fencing and riding, and as she grew older, he brought tutors to the house for her. As a result, by the age of twelve she was fluent in Latin, Italian, Greek and German; she was later to publish translations into French of Greek and Latin plays and philosophy. She received education in mathematics, literature, and science. Her mother Gabrielle-Anne was horrified at her progress and fought Louis-Nicolas at every step, once attempting to have Emilie sent to a convent.

Emilie also liked to dance, was a passable performer on the harpsichord, sang opera, and was an amateur actress. As a teenager, short of money for books, she used her mathematical skills to devise highly successful strategies for gambling.

Marriage

On 12 June 1725, she married the Marquis Florent-Claude du Chastellet-Lomont. Her marriage conferred the title of Marquise du Chastellet. Like many marriages among the nobility, theirs was arranged. As a wedding gift, the husband was made governor of Semur-en-Auxois in Burgundy by his father; the recently married couple moved there at the end of September 1725. Du Chatelet was eighteen at the time, her husband thirty-four.

Children

The Marquis Florent-Claude du Chastellet and Emilie du Chatelet had three children: Francoise Gabriel Pauline (born 30 June 1726), Louis Marie Florent (born 20 November 1727), and Victor-Esprit (born 11 April 1733). Victor-Esprit died as a toddler in late summer 1734, likely the last Sunday in August. In 1749 Emilie du Chatelet gave birth to Stanislas-Adelaide du Chatelet (daughter of Jean Francois de Saint-Lambert). She was born on 4 September 1749. The infant died in Luneville on 6 May 1751.

Resumption of studies

In 1733, at the age of 26, du Chatelet resumed her mathematical studies. Initially, she was tutored in algebra and calculus by Moreau de Maupertuis, a member of the Academy of Sciences. Although mathematics was not his forte, Maupertuis had received a solid education from Johann Bernoulli, who also taught Leonhard Euler. By 1735, however, du Chatelet had turned for her mathematical training to Alexis Clairaut, a mathematical prodigy known best for Clairaut's equation and Clairaut's theorem.

Relationship with Voltaire

Du Chatelet and Voltaire may have met in her childhood at one of her father's salons; Voltaire himself dates their meeting to 1729, when he returned from his exile in London. However, their friendship began in earnest in May 1733, upon her re-entering society after the birth of her third child.

Du Chatelet invited Voltaire to live in her country house at Cirey-sur-Blaise in Haute-Marne, northeastern France, and he became her long-time companion (under the eyes of her tolerant husband). There she studied physics and mathematics and published scientific articles and translations. To judge from Voltaire's letters to friends and their commentaries on each other's work, they lived together with great mutual liking and respect. As a literary rather than scientific person, Voltaire implicitly acknowledged her contributions to his 1738 Elements of the Philosophy of Newton, where the chapters on optics show strong similarities with her own Essai sur l'optique. But she was able to contribute further to the campaign by a laudatory review in the Journal des savants.

While sharing a passion for science, they had scientific collaborations. They set up a laboratory in du Chatelet's home. In a healthy competition, they both entered the 1738 Paris Academy prize contest on the nature of fire, since Emilie disagreed with Voltaire's essay. Although neither of them won, both essays received honourable mention and were published. She thus became the first woman to have a scientific paper published by the Academy.

Final pregnancy and death

In May 1748, du Chatelet began an affair with the poet Jean Francois de Saint-Lambert and became pregnant. In a letter to a friend, she confided her fears that she would not survive her pregnancy. On the night of 3 September 1749, she gave birth to a daughter, Stanislas-Adelaide, but died a week later, at Luneville, from a pulmonary embolism, at the age of 42. Her daughter died twenty months later.

Criticizing Locke and the debate on thinking matter

In her writings, Emilie du Chatelet criticizes John Locke’s philosophy. She emphasizes the necessity of the verification of knowledge through experience: Locke’s idea of the possibility of thinking matter is […] abstruse. Her critique on Locke originates in her Bernard de Mandeville commentary [on the Fable of the Bees]. She confronts us with her resolute statement in favor of universal principles which precondition human knowledge and action, and maintains that this kind of law is innate. […] Du Chatelet claims the necessity of a universal presupposition, because if there is no such beginning, all our knowledge is relative. In that way, Du Chatelet rejects John Locke’s aversion of innate ideas and a priori principles. She also reverses Locke’s negation of the principle of contradiction, which would constitute the basis of her methodic reflections in the Institutions. On the contrary, she affirms her arguments in favor of the necessity of a priori and universal principles. “two and two could then make as well 4 as 6” if a priori principles did not exist.

Pierre Louis Moreau de Maupertuis’ and Julien Offray de La Mettrie’s reference to Du Chatelet's deliberations on motion and free will, on thinking matter and numbers and on the way to do metaphysics indicate the importance of her reflections. She rebuts the claim to finding truth by using mathematical laws, […] and argues against Maupertuis.

Heat and light

In 1737, Chatelet published a paper entitled Dissertation sur la nature et la propagation du feu, based upon her research into the science of fire, that predicted what is today known as infrared radiation and the nature of light.

Institutions de Physique

Her book Institutions de Physique (“Lessons in Physics”) appeared in 1740; it was presented as a review of new ideas in science and philosophy to be studied by her thirteen-year-old son, but it incorporated and sought to reconcile complex ideas from the leading thinkers of the time.

Forces Vives

In 1741, du Chatelet published a small book entitled Reponse de Madame la Marquise du Chastelet, a la lettre que M. de Mairan. Dortous de Mairan, secretary of the Academy of Sciences, had published a set of arguments addressed to her regarding the appropriate mathematical expression for forces vives. Du Chatelet presented a spirited point by point rebuttal of de Mairan's arguments, which caused him to withdraw from the controversy.

Immanuel Kant’s first publication in 1747 'Gedanken zur wahren Schatzung der lebendigen Krafte' focuses on Du Chatelet's pamphlet against the secretary of the French Academy of Sciences, Mairan. Beyond this, it is also an interesting fact that Kant’s opponent, Johann Augustus Eberhard, is accusing Kant of having taken ideas from Du Chatelet.

Advocacy of kinetic energy

Although in the early 18th century the concepts of force and momentum had been long understood, the idea of energy, as a transferable currency between different systems, was still in its infancy and would not be fully resolved until well into the 19th Century. It is now accepted that the total mechanical momentum of a system is conserved and none is lost to friction. Simply put, there is no 'momentum friction' and momentum can not transfer between different forms, and particularly there is no potential momentum. Emmy Noether proved this to be true for all problems where the initial state is symmetric in generalized coordinates. Mechanical energy, kinetic and potential, may be lost to another form, but the total is conserved in time. The Chatelet contribution was the hypothesis of the conservation of total energy, as distinct from momentum. Inspired by the theories of Gottfried Leibniz, she repeated and publicized an experiment originally devised by Willem 's Gravesande in which balls were dropped from different heights into a sheet of soft clay. Each ball's kinetic energy - as indicated by the quantity of material displaced - was shown to be proportional to the square of the velocity. The deformation of the clay was found to be directly proportional to the height the balls were dropped from, equal to the initial potential energy. Earlier workers, such as Newton and Voltaire, had all believed that "energy" (so far as they understood the concept at all) was indistinct from momentum and therefore proportional to velocity. In classical physics the correct formula is , where is the kinetic energy of an object, its mass and its speed.) Energy must always have the same dimensions in any form, which is necessary to be able to relate it in different forms (kinetic, potential, heat…). Newton's work assumed the exact conservation of only mechanical momentum. A broad range of mechanical problems are soluble only if energy conservation is included. The collision and scattering of two point masses is one of them. Leonhard Euler and Joseph-Louis Lagrange established a more formal framework for mechanics using the results of du Chatelet.

Translation and commentary on Newton's Principia

In 1749, the year of her death, she completed the work regarded as her outstanding achievement: her translation into French, with her commentary, of Newton’s Principia Mathematica, including her derivation of the notion of conservation of energy from its principles of mechanics. Published ten years after her death, today du Chatelet's translation of Principia Mathematica is still the standard translation of the work into French.

Development of financial derivatives

Much later in life, she once lost the huge sum of 84,000 francs—some of it borrowed—in one evening at the table at the court of Fontainebleau, to card cheats. To quickly raise the money to pay back her debts, she devised an ingenious financing arrangement similar to modern derivatives, whereby she paid tax collectors a fairly low sum for the right to their future earnings (they were allowed to keep a portion of the taxes they collected for the King), and promised to pay the court gamblers part of these future earnings.

Biblical scholarship

Du Chatelet wrote a critical analysis of the entire Bible. A synthesis of her remarks on the book of Genesis was published in English in 1967 by Ira O. Wade of Princeton in his book "Voltaire and Madame du Chatelet: An Essay on Intellectual Activity at Cirey" and a book of her complete notes was published in 2011, in the original French, edited and annotated by Bertram Eugene Schwarzbach.

Discourse on happiness

Du Chatelet also wrote a monograph, Discours sur le bonheur, on the nature of happiness, both in general and specialized to women.

Translation of the Fable of the Bees, and other works

Du Chatelet translated The Fable of the Bees in a free adaptation. She also wrote works on optics, rational linguistics, and the nature of free will.

Support of women's education

In her first independent work, the preface to her translation of the Fable of the Bees, du Chatelet argues strongly for women's education, particularly a strong secondary education as was available for young men in the French colleges. By denying women a good education, she argues, society prevents women from becoming eminent in the arts and sciences.

Legacy

Du Chatelet made a crucial scientific contribution in making Newton's historic work more accessible in a timely, accurate and insightful French translation, augmented by her own original concept of energy conservation. Her scientific role deserves more exposure in educational curricula.

A main-belt minor planet and a crater on Venus have been named in her honor, and she is the subject of three plays: Legacy of Light by Karen Zacarias; Emilie: La Marquise Du Chatelet Defends Her Life Tonight by Lauren Gunderson and Urania: the Life of Emilie du Chatelet by Jyl Bonaguro. The opera Emilie of Kaija Saariaho is about the last moments of her life.

Du Chatelet is often represented in portraits with mathematical iconography, such as holding a pair of dividers or a page of geometrical calculations. In the early nineteenth century, a French pamphlet of celebrated women (Femmes celebres) introduced a possibly apocryphal story of du Chatelet's childhood. According to this story, a servant fashioned a doll for her by dressing up wooden dividers as a doll; however, du Chatelet undressed the dividers and intuiting their purpose, made a circle with them.

Works