5

ALMOST A PRODIGY

The view from the top of Maurits’s tower in the Binnenhof reveals the Huygenses’ world. At the foot of the tower lies the Hofvijver lake with the stadholder’s court stretching along its bank to the right. Beyond it, van Campen’s grand houses, the Mauritshuis on the far corner of the lake, and just to its right, Huygens’s on the Plein. A little way to the north, the saplings of the Voorhout, where Constantijn Huygens spent his youth, wave their leaves above the rooftops. To the west rises the hexagonal brick tower of the city’s great church, Sint-Jacobskerk. You hardly need take up Lipperhey’s telescope to see the rest: three miles to the south-east, the little town of Voorburg and the Vliet canal with Constantijn’s retreat, Hofwijck, on its bank; to the north, a great band of dunes, with the spire of Scheveningen church beyond, and behind that only the sea.

Imagine the house on the Plein not as a mausoleum or a museum – though it was almost two-thirds the size of the next-door Mauritshuis, the picture gallery which now holds some of the most important paintings of the Huygens family – but with four small boys tearing through the hallways and up and down the stairs, and the infant Susanna adding her gurgles to the din. When he was at home, Constantijn Huygens ran the house along modern, bourgeois lines rather than in emulation of the stilted manners that he saw in operation at court. The family took their meals together even when the children were still very young. The father showed an attentive concern for their development, observing their different characters and finding for each of them activities suited to their individual temperaments, as well as moulding them in the way he thought best. Punishments were fines taken out of pocket money rather than beatings.

But often, he was absent, either serving in the field with the stadholder, or called away on diplomatic errands. Then, there were only his serious portraits looking down from the walls of the great house to remind the children of their only parent’s existence. At these times, the youngest had the household staff to turn to, while the older boys must have developed a strong degree of self-reliance and found their own ways to keep themselves amused.

Constantijn’s commitment to family life shines out from a portrait by Adriaen Hanneman, completed in 1640, nearly three years after Sterre’s death. It shows the five children, the boys’ ages ranging from eleven to six and Susanna not yet three years old, in medallions closely encircling their father. A possible early sketch by the artist showing a central married couple with only four medallions spaced around them for the children suggests that the painting may have been planned before the arrival of their last child. If so, then the fact that Huygens went ahead with the commission after Susanna’s death reveals a stoical acceptance of the disaster that has befallen him.

In the finished painting, the boys appear remarkably alike, despite their range of ages, each with similar tumbling auburn hair and pretty face. Young Constantijn looks out of the canvas with a watchful expression and the barest trace of amusement on his lips, as if he is taking in everything the painter is doing with his big brown eyes. Christiaan’s rounder cheeks, retroussé nose and pursed lips make him look the most girlish. He was, his father noted, ‘the image of his mother’, and before the boys were breeched he was indeed sometimes mistaken for a girl. Unlike his older brother, he is not inspecting the artist, but looking past him into some greater distance. Lodewijk, aged eight, looks hardly younger than Christiaan, and was in fact sometimes taken to be his twin; he is obviously more comfortable with the idea of sitting for the artist. Six-year-old Philips is wearing a plumed cap and a gold-embroidered cloak that makes him look older than he is, closing the gap with his brothers. Perhaps conscious of his extravagant attire, he appears to be suppressing a smirk into the serious expression that the artist requires. The toddler Susanna, in the topmost medallion, has fairer hair than her brothers and is wearing a white lace bonnet with a floral attachment and clutching an apple tightly in both hands.

A few weeks after his wife’s death, Huygens arranged for a cousin, Catharina Zuerius (or Sweerts), to join the household. By all accounts, she was unable to fulfil many of the maternal functions – an impossible thing to expect. Huygens soon came to dislike her, and in time so too did his sons, although she remained in the family’s service for thirty years. Years later, writing letters that criss-crossed Europe, the brothers would still bring each other up to date on her latest antics, and treat her as a yardstick against which other women could only be favourably compared. When she died in October 1680, twelve years after her retirement from her thankless labours, Huygens wrote a brutal memorial verse:

Here lies Auntie Catharine: what more can there be writ?

Because, dare it be said,

In eighty years and three what deeds did she befit,

Than that she haggled and nagged and domineered and died.

Although the boys were indeed close enough in appearance to be mistaken for one another, Christiaan was less physically robust than his elder brother and would always remain in respectful awe of him. But he soon showed himself to be his equal in other respects, and Tien and Tiaen, as they were affectionately abbreviated, spent a lot of their time together. They were not sent to school as their father judged that this would be a waste of their time and the syllabus would be too restricted. The far broader and more ambitious education that they received at home had the consequence of making the two still more alike. The teaching was modelled on their father’s upbringing, and included classical and modern languages, mathematics, theology, logic and philosophy, as well as classes in horsemanship, fencing, dancing, music and drawing and painting. Christiaan early on showed himself to be the better musician, able to sing and play several instruments, while Constantijn was the superior draughtsman.

Young Constantijn was the quieter and more serious of the two boys, and perhaps felt the paternal burden of expectation more keenly. Christiaan, on the other hand, generally bubbled with enthusiasm, cheerfully chattering and singing, and following his father ‘dog-like’ around the house to pester him with questions. It is possible that his true intellectual potential was not identified as early as it might have been because he was the younger.

Lodewijk was always the most difficult son, less bright and less well behaved than Tien and Tiaen, always seeking attention by playing the fool. His predominant childhood passions were horses and fencing, and Huygens feared that he would become a soldier. Philips was also less academic than the older boys, and his father followed his progress with less interest. Susanna, on the other hand, was clearly intelligent. Nearly four years younger than the youngest of the boys, she was schooled separately. She learned sewing and embroidery like any girl of her social status. She also learned French – the language of the court – but not Latin or Greek. In addition, she proved to be highly musical, which greatly pleased her father, who taught her at the keyboard. As she grew up, Huygens recognized her potential to become like the intellectual women he knew in the Muiden Circle, but he did not want this life for his daughter.

Huygens was proud of all his children. It is an indication of his closeness to them, as well as of his familiar relationship with the Prince of Orange, that sometimes when he was at army camp, he would show him the letters they had sent him. Another time, in The Hague, Huygens took little Susanna along when he had a meeting with him. Once back home, Susanna declared that she had seen no prince, but only ‘a worn old man’. Huygens repeated this afterwards to Frederik Hendrik, who roared with laughter.

The file heading has been amended in Christiaan’s own hand: Juvenilia pleraque, it reads. He has crossed out the word Puerilia: ‘Mainly juvenilia’, not ‘Mainly boyhood’. He does not wish to be thought of as a child genius. A scrap of paper among the loose sheaf in the file illustrates his youthful range. On one side is a sketch of a tree and some bushes, rapidly executed in charcoal and red chalk, with expressively upward-reaching branches and grass in the foreground suggested by confident flicks; on the other is a scattering of diagrams, one showing a device for drawing perfect ellipses, another of a circular board cut with perpendicular slots, probably for lens-grinding, together with some geometric doodles in the margins – tangents and parabolas and a catenary curve.

Their father was able to offer instruction in arithmetic and music, but soon the older Huygens boys began to see a procession of tutors to their new home. The first to arrive, in July 1637, was Abraham Mirkinius, who taught them Latin. A year later came Hendrik Bruno, only eighteen years old himself, who had studied theology at Leiden University and was an aspiring poet in neo-Latin. Unfortunately, his first gift to the boys was scabies, and he had trouble keeping them under control. But he must have soon established a good working relationship for he stayed on for nine years.

Teaching both boys together over such a long period, Bruno naturally began to notice their particular aptitudes. Christiaan had such ability that ‘he might almost be called a prodigy’, he wrote in one report to the father – if only he wouldn’t spend so much time on ‘devices of his own invention, constructions and machines, which, though they might be ingenious, are but distractions that will always break down’. These elaborate toys – little contraptions with wheels and gears resembling model mills and lathes – concerned Christiaan’s father, too, who discouraged such unscholarly activity. He had regarded the third and fourth years of his boys’ lives as dull because they were concerned entirely with play of a kind in which he had no contribution to make. Now that they were a little older, everything had to be directed towards learning, and the rare games at home always had a moral lesson. As Christiaan grew older, such manual recreations raised an unthinkable new fear in his father’s mind that his son might be content merely to pursue a handicraft trade.

Other tutors came. Jan Stampioen, who had studied with the mathematician Frans van Schooten, moved in during the spring of 1644 to give the fifteen-year-old Christiaan a more solid grounding in the subjects for which it was now clear that he showed the greatest flair: logic, philosophy, physics, astronomy, optics and geometry. His reading list for Christiaan included Descartes on lens-grinding, Stevin on perspective, Lansbergen on astronomy, Al-Hazen’s astrology and Scamozzi’s books of architecture.

Stampioen had been the professor of mathematics at the illustrious college in Rotterdam and then a tutor to Frederik Hendrik’s son, the future William II of Orange. A specialist in geometry and trigonometry, he had earned a degree of notoriety for engaging in public exchanges of mathematical problems and solutions, even going so far as to announce anonymously solutions to problems he himself had set in order to publicize his talents. One challenge nearly went too far. When Stampioen set Descartes a problem whose solution required the use of an unstated quartic equation, Descartes responded by giving the equation, but failed to use it to solve the problem. Stampioen judged that the answer was therefore incomplete, which provoked Descartes to an angry response. With a wager of 600 guilders at stake, this soon led to a duel being arranged between the disputants. As one who knew both men, it was the Huygens boys’ father who reluctantly agreed to step in and defuse the row.

This makes the appointment of Stampioen as his son’s tutor seem somewhat surprising. Stampioen’s track record with the royal family, as well as Huygens’s awareness of Descartes’s short fuse, ultimately may have counted in his favour. Or, he may have simply matured by the time of this appointment. Hendrik Bruno observed his startling impact on Christiaan in mathematics, and gave a critical description of his methods, noting that he required ‘first a good intelligence, secondly constant application, and finally a perfect desire to achieve; if all these conditions are met, this understanding can be acquired not all at once, but little by little, each piece in its turn, by prolonged study’.

On 11 May 1646 the two brothers matriculated at Leiden University, with their father’s detailed academic and moral instructions for how they were to conduct themselves in their pockets. They were encouraged to write home frequently and always to employ proper forms of address. Constantijn adapted better to this regime than Christiaan, who was inclined to write only as necessary, for example when, two months after arriving at university, he found he had run out of money. Both were quiet, diligent students who tended to avoid the more boisterous side of student life. On one occasion Constantijn was shocked to find that he had incurred the wrath of the violent landlord with whom they were lodging, and wrote home about the incident. His father felt it necessary to intervene in his son’s interests, influential as always.

From its beginning, the Dutch Revolt had seen a great flowering in education. Leiden was chosen in 1575 as the location of the first university in the Netherlands, with the object of preparing the young men who would run the new country and its Reformed church. By the 1640s, with more than 500 students, half of them drawn from abroad, it was the largest university in the Protestant world. Although natural philosophy did not feature explicitly on the curriculum, the foundation boasted one of the first botanic gardens and the first anatomy theatre in northern Europe. In 1633, Leiden became the first university anywhere to have its own astronomical observatory.

Encouraged by their father, who thought good things might come of it if their rivalry were constructively harnessed, Constantijn and Christiaan took several classes together, including law with Arnold Vinnius and mathematics with Frans van Schooten. Constantijn perhaps gained more from the former, a celebrated jurist, but for Christiaan, it was undoubtedly van Schooten who most greatly inspired him among his professors at Leiden.

Frans van Schooten (the younger) was a notable Protestant, a freethinker and – of greatest significance for Christiaan’s education – a convinced Cartesian. A fine mathematician specializing in analytical geometry, he had known Descartes personally for ten years, and defended his work at Leiden, where his philosophical ideas could be discussed only with the greatest circumspection, and would soon be banned altogether because they could be taken as sympathetic to atheism. Other talented students taught by van Schooten would also go on to notable achievements in mathematics and in other fields. Chief among them, a year above Christiaan, was Johan de Witt, the Holland councillor whose spell as the de facto national leader during the long period from 1650 to 1672 when the Dutch provinces were without an overall stadholder did not stop him also publishing his own treatise on geometry. The two did not overlap directly, however, and it seems that Christiaan perhaps did not find many like-minded souls with whom to forge the sort of lifelong friendships that university often provides.

Van Schooten had a rare ability to take the geometries found in the practical world and distil their pure essence. Like his father, he had been schooled in Stevin’s mathematics of military engineering. This training left him with a ‘kinematic’ feel for geometric curves; he was able to sense, as it were, the meaning behind their shape. For example, he showed that the ‘gardener’s ellipse’ – a method of generating ellipses empirically by using a board with two pegs and a rope in order to set out plant beds – was the same as the pure ellipse in the family of conic sections. This sense of a deep connection between abstract geometry and the physical world was something that he transmitted to Christiaan Huygens, who began to tackle the problem of the catenary – the ‘natural’ curve followed by a chain freely hanging between two points, which had resisted all attempts to reveal its mathematical secret – during his year with van Schooten. As well as enjoying close relations with Descartes, van Schooten had travelled to Paris a few years earlier, and had made the acquaintance of the leading mathematicians there. Many of these men would later welcome Christiaan Huygens into their midst.

Christiaan’s father was also busy building connections. On 12 September 1646 he wrote to the French mathematician and theologian Marin Mersenne, with whom he corresponded regularly on musical matters and scientific curiosities such as the magnet, drawing attention to his teenage sons’ mathematical prowess. They were, he improbably claimed, ‘most eager about your quadrature of the hyperbola and your centre of percussion’. The boys’ own enclosed letters demonstrated that this was indeed the case. Mersenne was so impressed that he sent back a new mathematical puzzle to test the boys. Christiaan returned something promising on catenaries, Mersenne responded by setting another problem about pendulums, and so the correspondence blossomed. After a few months of such exchanges, Mersenne wrote to Christiaan’s father: ‘I don’t doubt that if he continues he will one day surpass Archimedes.’ Thereafter, both men habitually spoke of Christiaan as their ‘little Archimedes’ or the ‘Dutch Archimedes’. Mindful perhaps that such a badge could weigh heavily on the young student, Mersenne gave Christiaan an old man’s advice: ‘do not worry too much, for you have so many years remaining, that if you were to make one demonstration each year, as beautiful as that of this chord [i.e. the catenary], you would have enough to rank at the top end of all the nobility’. Mersenne soon spread word of Christiaan’s unique facility to other French mathematicians such as Blaise Pascal, who also began to share their problems with him. But Christiaan’s correspondence came to an abrupt end with Mersenne’s death in 1648, and the eruption of civil war in France in that year put paid to plans for an excursion to Paris.

What was the power of curves? Why did these shapes engage such able minds at this time? Some were surely drawn by the promise that greater understanding would help them to address practical challenges in construction or ballistics. But for others it must have been the sheer abstraction that appealed. With the discovery of perspective, the artists of the Renaissance had tamed the straight line. It was a line that pointed to where it was headed and went directly there. Its intention, if it could be said to have one, was clear. But curved lines were another matter. Some, such as the circumference of a circle, clearly followed a simple rule. But others, like the line taken by a quill producing an extravagant signature, could clearly go anywhere. What lay in between? Some curves, such as the conic sections, those exposed by slicing at angles through a cone – the ellipse, parabola and hyperbola, seemed almost as fundamental as the circle. Could these be represented mathematically like the circle? And what of other curves found in nature, in the growth of plants or the waves on the sea?

Then there was the question of quadrature. Quadrature, or squaring, a precursor of integral calculus, was the general method of calculating areas bounded by lines, using pure algebra rather than direct measurement. But curved lines resisted squaring, the circle famously so. Indeed, Christiaan, who busied himself with these matters after his year with van Schooten, was to become caught up in a ten-year dispute with French and Flemish rivals over their methods of performing this particular calculation.

The catenary seemed to be another fundamental curve. Like the parabolic path followed by a rising and falling cannonball, it is found in the real world: Huygens uses the Latin word catenaria, derived from catena, meaning ‘chain’ in his notes and correspondence, because a catenary is the curve made by a rope or chain of uniform heaviness hanging under gravity. But efforts to generate and manipulate this curve using geometrical methods had failed. Huygens approached the problem in a physical way, drawing upon his investigation of the centre of gravity of beams hung with weights. This was the problem of ‘centres of percussion’ set by Mersenne, the centre of percussion being the point along a beam suspended by its end where it should be struck in order to make it swing like a pendulum without producing a reaction at the pivot. From there, Huygens began to explore where the centre of gravity of a suspended flexible cord would lie when weights were hung at various points along its length. The first weight forces the cord to adopt a path of two straight lines angled at the point where the weight is hanging. Then, by adding more weights along the length of the cord, Huygens was able to approach the condition of a uniformly heavy chain. In this way, he was able to prove that the catenary was not the same as the parabola, which it closely resembles, and as Stevin and Galileo had thought, but a new kind of curve not found among the conic sections.

Early on in their correspondence in 1646, Mersenne drew the young Huygens’s attention to another special curve that had thwarted efforts to understand it. This was the cycloid, the path traced by a point on the circumference of a wheel as it rolls along a flat surface. Such a curve might almost have been designed to demonstrate the link that would become so important for Huygens between pure mathematics and the mechanical world. Although Huygens did not get to grips with the problem at this time, it was not to be many years before the cycloid returned to occupy a central place in his life.

Constantijn left Leiden after only a few months in order to join his father in secretarial service to the stadholder. Christiaan left in March 1647 to move on to the House of Orange college at Breda, established following the Dutch recapture of the city in 1637 as a training academy for the diplomatic service. Although his father was one of the governors, the school had struggled, with only around sixty students by the time Christiaan arrived there, and moral scandals among the staff. Christiaan wrote to Constantijn about the girls and the music he found in Breda, but he attended only a few lectures of the unpopular mathematics professor. The classes in law were little better, but he was able to defend his thesis in the subject. Christiaan’s more boisterous brother Lodewijk was clearly better suited to the place and had already been there for two years when Christiaan joined him. When Lodewijk became involved in a duel, however, their father finally realized it was not right for either young man and pulled them out.

It was a new kind of world into which the Huygens brothers were now stepping. For the whole of their father’s life, and for the whole adult life of his father, the country had been at war. Now, five years of negotiations between overextended Spanish forces and the tired and sick stadholder were drawing to a close. Frederik Hendrik died in March 1647 and was succeeded by his son William. The Peace of Münster, ending the Eighty Years War and finally confirming the independent sovereignty of the Dutch Republic, was signed in April 1648. Feasts and celebrations were held in many Dutch cities. From The Hague, Constantijn wrote to Christiaan, who was still in Breda: ‘Today we burn the Victory and the artillery that has been brought to the Denneweg will be discharged nine times.’ Perhaps as a personal gesture of rapprochement, their father wrote his first piece of verse in Spanish, later to be followed by translations of Spanish proverbs no doubt gleaned from his negotiating sessions during the long years of the war.

Did Christiaan remember the man with the strange accent who surely must have called on his father at the old house when he was small? Although many accounts suggest that the boy must have met Descartes, it seems unlikely, or at least that, if he did, he did not recall it as a special occasion in a household accustomed to seeing many illustrious visitors. Constantijn’s close involvement with Descartes ended in 1637, when Christiaan was just eight years old, although the two men maintained a lively correspondence for another ten years. Circumstantial evidence leans the other way. Christiaan offered no anecdote of an encounter when he wrote in later years about the deep impression Descartes made on him as a young man. And in the autumn of 1649, after leaving the college at Breda, Christiaan set off on a diplomatic mission to Holstein and Denmark, with hopes of travelling on to see Descartes at the court of the Queen Christina in Sweden – a quest that might have lacked urgency if he had met him properly during his student years.

What is certain is that Christiaan did absorb Descartes’s ideas at a young age, thanks to his father’s assistance with publication of his works, as well as to Stampioen’s and van Schooten’s teaching. Before long, he too was a Cartesian. He read Principia Philosophiae, in which Descartes outlined his scientific theories in detail, on its publication in 1644, when he was no more than sixteen years old. It is clear that he found the logic of Descartes’s arguments highly persuasive. The Cartesian pattern of thought, which was logical and unpedantic, stayed with him all his life, and his own descriptions of physical phenomena in optics and mechanics and other fields, though informed by more thorough observation and experiment, always followed Descartes’s lucid example.

Descartes’s philosophy was exciting in its radicalism and in its ambition to construct an entirely new understanding of nature. The Frenchman believed that all matter extended through space and time in a manner that could be quantified. Geometry, and in particular Descartes’s introduction of algebra into geometry, was an important tool for revealing this universal framework. His best-known innovation, of what are now called Cartesian coordinates, broke down dimensional space in such a way that it might be manipulated in terms of algebra, which provided a powerful new weapon for analysing spatial events such as the motion of bodies.

In mechanics, Descartes accepted that moving bodies tend to continue moving in a straight line (later known as Newton’s first law of motion), but he did not believe in the existence of atoms, the vacuum, or action produced at a distance. Gravitational attraction he interpreted, like all physical interactions, as the result of impacts between bodies. Where bodies did not make actual physical contact, as in the case of the sun holding the planets of the solar system within its orbit, the action was explained by the presence of ‘vortices’ around each body. Light, for example, was transmitted as a form of luminous pressure acting from vortex to vortex through the transparent medium between the light source and the receiver.

Despite his conviction that everything could be understood in terms of numbers, Descartes himself did not have the facility to make much practical headway. Huygens was struck by the fact that his work on optics, La dioptrique, for example, contained no mathematical proofs. Spying an opportunity, Huygens set about trying to understand the geometry of all curves in terms of spherical curves only. His underlying practical hope was that it might become easier to grind telescope lenses with the complex shapes required to bring an image to a perfect focus if they could be ground in a sequence of operations using moulds shaped to different spherical radii. He did not achieve this goal, but the work did enable him to produce a general theory of the properties of spherical lenses that took spherical aberration into account, and yielded a set of rules for calculating the focal distance of such lenses.

That Huygens came to be known as a leading Cartesian now reads as something of a slur. This has little to do with Huygens, and much more to do with the changing reputation of Descartes during the latter half of the seventeenth century and after. The term ‘Cartesian’ quickly gained a pejorative edge owing to the philosopher’s dogmatic insistence on the separation of body and soul, his disagreeable assertion that animals are unfeeling machines, and the fear that ‘Cartesian doubt’ might be a cover for atheism – none of which conceptions was central to Huygens’s concerns. While Descartes’s reputation as a philosopher has prospered since these troubled beginnings, his standing as a scientist has sharply declined. This is in part a relative decline that must be set against the rising standard of scientific investigation during this period, which ushered in a clearer understanding of experimental method and emerging protocols for the reporting of results – developments to which, ironically perhaps, Huygens was a principal contributor. In fact, Huygens was never an irrational defender of Descartes, and when his observations or calculations had the unintended effect of challenging the philosopher’s beliefs, it was his own results that he tended to trust more. Nevertheless, Huygens remained faithful all his life to Descartes’s broad philosophy of nature, and very much shared his serious ambition to know.

Once Newton’s physics had exposed the errors in Descartes, it would become easy to criticize Huygens for being a Cartesian. But in 1650, it would have been astonishing if he had been anything else.