Christiaan Huygens
gigatos | June 23, 2022
Summary
Christian Huygens (in Latin Christianus Hugenius), born on April 14, 1629 in The Hague (in the United Provinces) and died on July 8, 1695 in the same city, was a Dutch mathematician, astronomer and physicist.
He is considered an alter ego of Galileo, especially for his discovery of Titan, which he describes in The Saturn System (1659), where he makes the first exhaustive description of the Solar System with six planets and six moons, with an unprecedented accuracy. For the first time, it is possible to have an idea of the size of the system, the distance of the stars and the exact position of the Earth within it, as well as its exact size, clearly larger than Mars or Mercury, slightly larger than Venus, but clearly smaller than Jupiter and Saturn. He also built the first pendulum clock, which improved the accuracy of existing clocks from 15 minutes to 15 seconds per day (1656). Huygens is generally credited for his fundamental role in the development of modern calculus, in particular for developing the summation and integration techniques necessary for the discovery of cycloid isochronism. In the physical sciences, he is noted for the formulation of the wave theory of light and the calculation of the centrifugal force.
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Youth
In 17th century Europe, more precisely in the republic of the United Provinces, the name Huygens evokes a family in the service of a young state. Christian”s father was given the name Constantijn, as a tribute to the constancy of the inhabitants of Breda during the five sieges of the city.
Christian Huygens is the son of Constantijn Huygens – a poet and diplomat – and Suzanna van Baerle, a highly educated woman. He was born in The Hague on April 14, 1629 and grew up surrounded by the rumbling of battles against the Spaniards. He and his brother Constantijn were the eldest of four boys and a girl. Far away from his children because of his duties, Constantijn father nevertheless takes care of and supervises their study program – assumed by their Latin teacher, Hentk Bruno. He keeps a diary in which he records his children”s progress. Christian stutters, has trouble memorizing, nods his head and likes to talk to himself, but by the age of eight his progress is meteoric. His mother died of an infection two months after her last delivery and he refused to give up mourning for a long time. At the age of fourteen, he refused to learn Virgil”s poems by heart and wanted to do arithmetic. His first tutors were theology students and poets; the child caused little trouble when left alone, but offered diamond-like resistance when forced to waste his intelligence on things that did not interest him. When Christian was fifteen, his father gave up and hired a private teacher, the mathematician Jan Stampioen, who established a vast reading program for the teenager that included the works of Ptolemy, Copernicus, Stevin, Brahe, Kepler and even Descartes, all of whom were the renovators of astronomical knowledge. He kept his student up to date with the most current scientific fields, but advised him to try, as far as possible, to draw his own conclusions instead of assimilating those of others. Constantijn respects his son”s scientific curiosity, but never gives up on his wish to make him a perfect court man. Before entering university, Christian knows rhetoric and fencing, plays the lute, viola da gamba and harpsichord, rides a horse, hunts, sings, dances, ice skates and paints. In addition to his native language, Dutch, he is fluent in Greek, Latin, Italian and French. Even better, he is skilled in the art of conversation and knows how to conduct himself like a perfect aristocrat.
At the age of sixteen, Christian enrolled at the University of Leiden, where he took two classes in jurisprudence and one in mathematics, taught by Frans Van Schooten, a talented teacher. After two years, Christian was sent to the less scientifically successful Orange College in Breda to study law. In a letter of introduction, his father introduced Christian to Count Henry of Nassau-Siegen who, in October 1649, hired him on a mission to the embassy in Denmark. The early death of William II of Orange-Nassau marked a halt to Christian”s diplomatic career: the Huygens” loyalty to the House of Orange forbade them access to official posts. Christian finally had free time to devote himself to science.
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Private and family life
Illustrious men were not the only ones to hold his attention. In 1663, there was also a French woman, Marianne Petit, the daughter of an engineer. But Marianne”s vocation was to retire to a convent, in which case a Protestant heretic was not suited to dissuade her. He courted her in vain, and this disappointment in love plagued him for months. In his correspondence, we can see several sentimental relationships and even some intention to get married, but, like most of his works, this project never comes to fruition. In the private sphere, there is no lack of reasons for him to sink into melancholy. As the years passed, the originality of his scientific mind rubbed off on his domestic life. His brothers and sisters married one after the other: Susanne in 1660, Constantijn in 1668 and Lodewijk in 1674. He writes to the latter “You are the father of a beautiful son and I of an invention, which is beautiful in its own way”. In January 1670, he feels physically indisposed, but it is his psychological health which is also at stake. Convinced that he was on the verge of death, he wrote down all the important discoveries that he had not taken the time to publish. The uncertainty about the outcome of his illness continued for weeks. Finally recovered, he left Paris and took refuge in his old house in The Hague where he found the family atmosphere and the affection of his relatives. Towards the end of 1670, he was able to resume his everyday life. At the end of his life, Huygens dragged his solitude like a ball and chain.
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Relations with colleagues
Huygens was close to Spinoza, they talked about optics and astronomy. He has a lot of esteem for Spinoza”s manual skill, but he is not tempted by his philosophy. Maxime Rovère underlines their social differences and especially their different conceptions of rationality, Huygens refusing to see it as the source of all certainty, contrary to Spinoza. For his part, Spinoza admired the science of his colleague, but was not convinced by his polishing technique.
In July 1655, Huygens was invited by his father to go to Angers and took the opportunity to visit Paris, where he stayed for four months. At the intercession of his father, he was introduced to the circles of the mathematician Claude Mylon and the scholar Habert de Montmor, who were at the origin of very well organized and equipped scientific institutions, such as the French Academy of Sciences and the “Academy” of Marin Mersenne. At the Royal Library, he had the opportunity to meet the poet Jean Chapelain, the astronomers Adrien Auzout and Ismaël Boulliau, the mathematician Gilles Personne de Roberval, and a constellation of curious minds interested in mathematics. It was there that Jean Chapelain encouraged him to publish – in 1656 – his observations and the discovery of Titan, which he would regret throughout his scientific career.
In 1666, Colbert created the Royal Academy of Sciences of which Huygens was appointed as the first scientific director. In 1667, the construction of the Paris Observatory began (completed in 1672) with a memorable founding act: the mathematicians of the Academy under the direction of Huygens traced the meridian of Paris on the summer solstice, June 21. In the autumn of 1672, a 26 year old man arrived in Paris and knocked on the door of the Royal Library. Gottfried Wilhelm Leibniz had set out to learn mathematics, Huygens agreed to teach him and the two men quickly became friends. Gradually, the roles of master and apprentice were reversed due to Leibniz”s rapid mathematical progress. Huygens remained in Paris for fifteen years, until 1681, when, ill and depressed, he returned to The Hague. He tried to return to Paris in 1685, but his project was destroyed by the Revocation of the Edict of Nantes.
He was mocked by Robert Hooke – as prolific as he was suspicious – when Hooke claimed that Huygens wanted to appropriate his discovery of the spring clock. Huygens is a man of science motivated by the quest for knowledge and living on the emotion of discovery. He was lazy as soon as he had to think about publishing, and he hated the conflicts that his research activity brought about.
Isaac Newton and Huygens did not always agree in the scientific field, but they respected each other. They even met on June 12, 1689 during his third visit to England. Newton praised Huygens” physical geometry and his approach to problems. He saw in Newton”s work a magnificent mathematical demonstration, to which he did not really find any physical significance.
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The astronomer
At the end of October 1652, Huygens confessed to Frans Van Schooten: “Dioptricity absorbs me entirely. He wants to realize the telescope of which Descartes dreamed, but with glasses that the craftsmen know how to make. He was the first to apply Snell”s law to calculate the focal length with accuracy, as well as the magnification of any spherical lens, and he knew how to determine the size, position and orientation of images. He realized Johannes Kepler”s ambition to reduce dioptric to a mathematical problem. In two years, he completed the first draft of a treatise in which he presented his mathematical interpretation of dioptric in a hundred pages and in a series of linked propositions. In 1654, with the help of his brother Constantijn, he began to cut his own objectives and eyepieces. In March 1655, the Huygens brothers completed the assembly of their first telescope. Christian first observed the Moon and then scanned the vicinity of Mars and Venus, looking for new satellites. The first of his sketches of Saturn dates from March 25, 1655; this night, he distinguishes a bright point near the planet and follows its evolution the following nights. After sixteen days, the point returned to its initial position. He had observed what would later be named Titan, the first and largest observed satellite of Saturn. Luck was on his side, indeed, he observed it at the time when the ring was about to hide.
He also examined the rings of Saturn and established that it is indeed a ring surrounding the planet. In a letter dated February 8, 1656, he boasted of having found the cause of what was taken for “ears” of Saturn by Galileo. In March 1656, he published De Saturni luna observatio nova (New observations of a moon of Saturn), a two-page pamphlet predicting that the “ears” would reappear in April of that year, and inviting scientists to come up with an explanation that could compete with his. He published his explanation only in the summer of 1659, in his treatise Systemia Saturnium where he wrote about Saturn: “It is surrounded by a flat and thin ring, which does not touch it at any point and which is inclined with respect to the ecliptic”.
Despite what the title of the treatise suggests, it is not only about Saturn. Huygens was the first to observe features on the surface of Mars, and by following the displacement of the Syrtis Major spot – a vast region of volcanic rock – he noticed that the planet rotates around an axis and was even able to establish the duration of the Martian day. He also made new observations on Jupiter and on the Orion nebula, discovered by Peiresc in 1610, where he saw three of the stars that form the trapezium cluster in its center. He equipped his telescope with a sophisticated wire micrometer – invented in 1640 by the amateur astronomer William Gascoigne – which allowed him to measure precisely the angular diameter of celestial objects and to appreciate their diameter in relation to the earth”s diameter, which was known with a good approximation at that time. On a fragile basis, he obtained that the diameter of the Sun is 111 times larger than that of the Earth (the correct figure is 109).
After the publication of the Systema Saturnium, Huygens was still determined to develop the perfect telescope. From 1665, he invested a lot of energy to eliminate the spherical aberration, his efforts succeeded on February 1st 1669. Instead of acting on the eyepiece, he preferred to double the lenses of the objective. The system formed by a biconcave lens and another plano-convex lens behaves like a hyperbolic objective without spherical aberration. The model bears his stamp: it is a successful marriage of physics and geometry, where the material corrects its defects by following mathematical instructions. He was soon disillusioned: he read the article published by Newton in the Philosophical Transactions of the Royal Society where the author questioned the future of the refracting telescope, which did not (yet) correct chromatic aberration. With a heavy heart, he replaces the word Eureka written on February 1, 1669 by “This invention is useless because of the Newtonian aberration that produces colors”. This half-failure will lead him to research on the nature of light. He also discovered some nebulae and some double stars.
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The mathematician
It was in the field of geometry that Huygens made his first discoveries, in a branch like quadratures. At the age of 22, he detected an error in the results obtained by the Flemish Jesuit Gregory de Saint-Vincent and perfected one of the latter”s methods for creating quadratures, and applied it to conic sections (ellipses, hyperbolas and parabolas). From a quadrature of the circle made by approximation, he improves Archimedes” method of calculating the decimals of π.
After hearing about the correspondence between Blaise Pascal and Pierre de Fermat on the subject of the party problem during his first trip to Paris in 1655, Huygens, encouraged by Frans Van Schooten, published the first book on the calculation of probabilities in games of chance in 1657. He introduced as a fundamental notion the “expectation value” of a situation of uncertainty. This book, which he translated into Dutch in 1660, played a decisive role in the diffusion of this new mathematics; it was taken up in English (anonymously) by John Arbuthnot in 1692, in Latin by Juan Caramuel y Lobkowitz in 1670, and decisively by Jacques Bernoulli in the first part of his Ars conjectandi published in 1715.
He opposed Leibniz, at the end of his life, insofar as it seemed to him that the infinitesimal calculus was basically only a matter of language, geometry alone having to intervene in the mathematical shaping of phenomena. After having assimilated it, he did not see the point of it, because he was able, with his magnificent geometrical developments, to solve any problem that Leibniz submitted to him to demonstrate the superiority of his calculus. In his reply to a letter from the Marquis de l”Hospital, who was debating the same question, he comments “I do not see how Mr. Leibniz”s method of calculation would be necessary in this field, nor do I believe that it is as useful as he seems to assert. The development of the infinitesimal calculus at the end of his life will show him all the same, as his correspondence with Leibniz and the Marquis reveals, the power of this tool.
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The physicist
Huygens” hyperactive curiosity pushes him to work on several fronts at the same time. He moves from one to the other according to his desires or the pressures of his entourage. His researches can advance or stagnate, progress frontally or delay each other. Two contradictory impulses end up paralyzing him: his reluctance to consider a project and his propensity to constantly engage in new research.
The first works of the young Huygens concerned the elucidation of the rules of shock. As early as 1652, he began to examine the rules set out by Descartes in the Principles of Philosophy, which he thought were incorrect. Using the Cartesian conservation of momentum mv, he cleverly used the principle of relativity to change the reference frame and succeeded in determining the correct laws of elastic shock. On this occasion, he highlighted the conservation of the sums of quantities mv 2, without giving it any particular physical meaning. He published these rules only with delay, in 1669, during a competition launched by the Royal Society, where John Wallis and Christopher Wren also gave satisfactory rules, although less general.
In 1659, Christian Huygens made the first projection instrument.
Between 1658 and 1659, Huygens worked on the theory of the oscillating pendulum. He had the idea of regulating clocks by means of a pendulum, in order to make the measurement of time more precise. He discovered the formula of rigorous isochronism in December 1659: when the end of the pendulum travels through a cycloid arc, the period of oscillation is constant regardless of the amplitude. Contrary to what Galileo had thought he was demonstrating in his 1638 Discourses Concerning Two New Sciences, the circular oscillation of the pendulum is not perfectly isochronous if it exceeds an amplitude of 5 degrees from the lowest point.
To apply this discovery to clocks, two cycloidal “cheeks” must be placed near the suspension point of the pendulum, which force the semi-rigid rod to run in a cycloid. Obviously, the work entitled Horologium that Huygens published in 1658 did not yet bear the fruits of this theoretical discovery and was content to describe a model that was innovative in its regulation and escapement system, but which still lacked a theoretical mastery that would only be published in the Horologium Oscillatorium of 1673. Huygens determines the period of the simple pendulum, which is expressed algebraically in the following form (l being the length of the pendulum, g the gravity and T the period) :
In 1659, Huygens discovered the formula for the centrifugal force, but did not publish the theorems he had discovered until 1673. In 1666, he began to conceive that the centrifugal force due to the rotation of the Earth could have an influence on a difference in gravity between the poles and the equator. He was interested in the results given by several expeditions in the following decades aiming at detecting such a difference. Around 1690, at the same time as Newton, he thought that this difference in gravity was incompatible with a purely spherical shape of the Earth and gave an estimate of its flatness.
In 1665, following experiments aimed at putting clocks on ships, Huygens discovered that two clocks suspended from the same beam placed on two chairs could be synchronized, which he called clock sympathy
In 1661, Huygens attended the coronation of Charles II in London, with the diplomatic delegation of which he was a member. In 1662, he enthusiastically attended the vacuum experiments of Robert Boyle and Robert Hooke, inspired by the pioneering work of Otto von Guericke. Back in The Hague during the summer, he decided to build his air pump and by the end of the year, he boasted that he had improved on Boyle”s model. He concealed the details of his model for fear of being plagiarized. It is only in June 1663 that he presents it in London, ready to prove its superiority. Robert Hooke explained to Robert Boyle – who was not present at the presentation – that the Dutchman”s invention was not much better than his own.
Huygens is also known for his arguments that light is composed of waves (see: wave-particle duality).
After reading the article published in February 1672 by Newton in the Philosophical Transactions of the Royal Society, in which the author questioned the future of the refracting telescope, which did not correct chromatic aberration, his first reaction was circumspection. He suspects that the Englishman”s devastating criticism is part of a strategy to highlight his proposal for a reflecting telescope
In response to Isaac Newton, he embarked on the study of the nature of light, following scientists such as Ignace-Gaston Pardies and Rasmus Bartholin. On August 6, 1677, he noted in his notebook a new “Eureka”: he discovered, thanks to the properties of the crystals and their geometrical cut, in particular thanks to the Icelandic spar, that the laws of reflection and refraction of Snell-Descartes are preserved if one supposes a propagation of the light in the form of waves. The double refraction of Icelandic spar can be explained with the wave theory, which is not the case with a corpuscular theory. In October 1677, he wrote to Jean-Baptiste Colbert to announce that he had solved the puzzle, and in the middle of 1679, he made an orderly presentation of his theory to the Royal Academy of Sciences.
The wave theory, published in 1690 in his Traité de la Lumière, in a form that was still very underdeveloped and quickly eclipsed by Newtonian successes, brought back to light the work of an author such as the Jesuit Father Pardies. Augustin Fresnel took up Huygens” work in 1815 as the starting point for his research on the diffraction of light.
In 1673, Huygens and his young assistant Denis Papin, demonstrated in Paris the principle of internal combustion engines, which would lead to the invention of the automobile in the 19th century. They succeeded in moving a piston driving a 70 kg load over 30 cm, by heating a metal cylinder emptied of air, filled with gunpowder. Huygens is thus considered as the precursor of the internal combustion engine.
We also owe him a theorem (Huygens” theorem) concerning inertia matrices in solid mechanics.
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Academic recognition
Huygens was elected a fellow of the Royal Society in 1663. In 1666, he became the first scientific director of the Royal Academy of Sciences founded by Colbert in Paris. He proposed several research projects to the young Academy, including the creation of a catalog listing and describing all known plants. In 1676, Denis Dodart published his Mémoires pour servir à l”histoire des plantes.
Participating in the realization of the Paris Observatory, completed in 1672, he made other astronomical observations.
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Speculations and meditations
He is also led to meditate on the relations between science and belief in general. It is at this moment that he wonders about the way to confirm the Copernican hypothesis. In his posthumous book Cosmotheoros, sive De terris cœlestibus, earumque ornatu, conjecturæ (The Hague, 1698) he illustrates in two parts the consequences of the Copernican thesis he supports: “who shares with Copernicus the opinion that our Earth is a planet attracted and illuminated by the Sun, as are exactly all the others, cannot avoid forming an idea about the possibility that the other planets too have inhabitants endowed with their own culture and arts” (incipit). In this, he is in the tradition opened by Pierre Borel, Cyrano de Bergerac, Galileo or Gassendi. On the one hand, he speculates about the possibility of other forms of life in a universe where each sun is another world. This reflection leads him to justify the existence of planets as a consequence of the divine grace that must necessarily extend to the whole universe and not be limited to our Earth. The Cosmotheoros was immediately translated into English in 1698, then into Dutch in 1699, into French in 1702, into German in 1703 and into Russian in 1717, at the request of Peter the Great, although the director of the typography of St. Petersburg considered it as a book “of a satanic perfidy”. Piergiorgio Odifreddi provided the first Italian translation in 2017; in his essay that also includes Plutarch and Kepler, and entitled Dalla Terra alle Lune (From the Earth to the Moons), Odifreddi praises this work by Huygens (Rizzoli, September 2017).
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End of life
After fifteen years in Paris, Huygens returned to The Hague in 1681 after a serious illness, and prolonged his convalescence there. The death in 1683 of his main protector Colbert and the revocation of the Edict of Nantes in 1685 did not allow him to escape the hostility towards the Dutch and the counter-Reformation currents that were stirring up France. His father Constantijn offered him his position in the service of William III, but he was tired of the constraints of the court and refused. Afflicted by the death of his father in 1687, he retired to the family summer residence of Hofwijck, where he felt like an exile. He softened the rigors of solitude by reading Isaac Newton”s Philosophiae naturalis principia mathematica – Mathematical Principles of Natural Philosophy – which Edmond Halley had sent him. In mid-June 1689, he was in London where he met Robert Boyle and Newton. At Gresham College, a conference was organized, the irony and originality of which will not be forgotten in the history of science. Huygens explains gravity and Newton, the double refraction of Icelandic spar. The details of their conversations during the summer are unknown. The stay in London, in the company of the most brilliant scientific society, made the austerity of Hofwijck unbearable for him and, at the end of 1689, he rented an apartment in Noordeinde Street in The Hague. From then on, he spent half the year in the country and the other half in the city. In February 1690, he resumed his correspondence with Leibniz and sent him his Treatise on Light. Leibniz sent him a course on infinitesimal calculus, the future importance of which he did not understand. It was at this time that he wrote several manuscripts on the need to synthesize his work, which was finally published in its entirety. In March 1695, he called a notary to draw up his will. He died in The Hague on July 8, 1695.
The Cassini spacecraft that landed on Titan was named after Huygens. The asteroid (2801) Huygens was also named in his honor.
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Bibliography
: document used as a source for the writing of this article.
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External links
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