Whewell reveled in his recognition that he was surrounded by the “best and the brightest.” The professors of the university included E. D. Clarke, the wildly popular professor of mineralogy, whose lecture hall was crammed with hundreds of eager students; Isaac Milner, the Lucasian Professor of Mathematics who, although he never lectured in the subject, was still renowned for his result in the Tripos exams years before: the examiners had thrillingly described his performances as “Incomparibilis”; and Francis Wollaston, Jacksonian Professor of Natural Philosophy, who publicly demonstrated more than three hundred experiments a year. The Chemistry professor was Smithson Tennant, discoverer of the element osmium, later used in the manufacture of fountain-pen tips and phonograph needles.
Even more than the faculty, the students and fellows were men of growing reputation who would soon remake the scientific, political, and literary worlds. Whewell befriended George Peacock, the reforming mathematician who would later be appointed dean of Ely Cathedral, and Julius Charles Hare, the theologian and scholar of German literature and history, who would bring the study of German language and scholarly methods into vogue in England. Whewell became close friends with the future astronomer Richard Sheepshanks and with Richard Gwatkin, a young mathematician who would later be reckoned the finest private tutor at Cambridge. Whewell met and befriended Adam Sedgwick, then a fellow of Trinity, soon to be considered one of the founders of modern geology. But the most important of his new acquaintances were those men he later called “friends of a lifetime”: John Herschel, Charles Babbage, and Richard Jones.
In February of 1813 Whewell reported excitedly to his father that he had “been several times in company” with John Herschel, “son of Dr. Herschel, the celebrated Astronomer Royal.” Herschel was three years ahead of Whewell, a student of St. John’s College, the fierce rival and next-door neighbor of Trinity. Trinity men called the Johnians “pigs” or “hogs,” meaning “gluttons,” after Horace’s self-deprecating comment that he was “epicuri de grege porcum,” a pig from the herd of Epicurus; the men from the two colleges regularly fought with clubs and fists. But once Whewell and Herschel met in late 1812 through Herschel’s close friend John Whittaker, they recognized each other as intellectual soul mates. Herschel presented him to Charles Babbage, whose wit and hearty, ringing laugh appealed to the younger man. Around the same time, Whewell was introduced to Richard Jones by Charles Bromhead at Caius College, elder brother to Edward Bromhead, a Trinity man in Whewell’s year.
Herschel and Babbage had become acquainted in 1810, soon after Babbage came up to Cambridge; Herschel was a second-year man by then. They quickly became fast friends; within two years Herschel was signing summer letters to Babbage with “yours till death / shall stop my breath.” Both were from well-off families. Herschel had the additional accoutrement of a famous father, the astronomer Frederick William Herschel (known as William), discoverer of the planet Uranus.
The elder Herschel was the son of an army musician in Hanover, Germany, who adopted the same profession as his father when he was fourteen. In 1758 William Herschel came to England, a penniless refugee of the Seven Years’ War. He eked out a small living as a musical copyist and instructor to a small military band in the north of England. In 1766 William Herschel was appointed to the post of organist at Bath Spa.
The springs at Bath Spa had been considered medicinal for hundreds of years. In the sixteenth and seventeenth centuries, the ill or depressed would come to sit, wearing coarse smocks, in the iron-rich water. In the eighteenth century this cure was modified to the more socially appealing one of drinking a glass or two of the water each day. Now the wealthy would come to socialize, attend balls and dinners, and “take the waters” during a social season that extended from September to May. Bath had the largest entertainment market outside London, with a lively concert schedule.18 William Herschel eventually had so many wealthy private pupils among the visitors and residents that more than twenty recitals a year were needed just to display their talents.
Busy as he was, Herschel began to read works on astronomy, and longed to have a telescope of his own. He resolved to make one, painstakingly grinding his own eyepieces. Finally he had a seven-foot reflecting or Newtonian telescope, that is, one with a curved optical mirror to reflect the image from the heavens. He began to examine the skies late at night, after his concerts had ended. On March 13, 1781, he observed an object not on any celestial chart. Assuming it was a new comet, he wrote a short notice for the Transactions of the Royal Society of London, a publication read by men of science all over the world. The famous French astronomer Pierre-Simon Laplace realized that Herschel had, in fact, found a new planet, which would become known as Uranus. This was amazing. Since antiquity it had been assumed that the planets that could be seen with the naked eye (Mercury, Venus, Mars, Jupiter, and Saturn)—plus Earth, once Copernicus realized it was a planet as well—were the only ones orbiting our sun. Herschel was the first discoverer of a new planet.
This striking accomplishment gained Herschel an appointment as the king’s personal astronomer at Windsor Castle. He and his sister, Caroline, who had been helping him with his observations, moved to Slough, then a small village near Windsor. Herschel was given an income of £200, and Caroline, notably, her own income of £50, by King George III. They undertook the construction of a huge telescope with a focal length of forty feet and a main mirror forty-eight inches in diameter, weighing over 2,000 pounds. Until dismantled by John Herschel in 1839, this would be the largest reflecting telescope in the world, the first to extend observations beyond our solar system.
While the ironworks for the motions of the telescope were being fitted, it became a fashion for visitors to use the huge empty tube, then lying on the ground, as a promenade. One day George III and the Archbishop of Canterbury were walking inside; when the archbishop became disconcerted due to the darkness, the king, who was in front, turned back and said, “Come, my lord bishop, I will show you the way to heaven.”19
When the works were completed, the telescope became one of the scientific wonders of the age. Even Franz Joseph Haydn visited Herschel while in England and spent an evening looking through the telescope and discussing music; Haydn had already shown an interest in astronomy some years earlier when he wrote the opera Il Mondo della Luna, in which Ecclitico poses as an astronomer in order to win the hand of the beautiful Clarice—in the process fooling people into believing that he has used a telescope so strong that he could see men on the moon!20 When Haydn returned to Europe, he publicized Herschel’s symphonies, which the musician/astronomer had composed between 1759 and 1770.21
Ladders fifty feet in length led up to a movable podium, where the observer sat. The whole mechanism stood on a revolving platform. Two workmen would move the platform slowly to follow the diurnal course of the heavens. This remarkable telescope had a magnifying power of one thousand times. But in England’s climate it could only be used about one hundred hours a year; its large mirror was prone to be dewed up in damp weather or frozen in cold weather.22 William Herschel used it to describe accurately, for the first time, the Milky Way, and to find two new satellites of Saturn.
In 1788 Herschel married Mary Pitt, née Baldwin, the widow of a wealthy London merchant. William was then fifty, and Mary thirty-eight. After four years, John was born, on March 7, 1792. He would have no siblings, and was doted on by both parents. He was also quite close to his aunt Caroline, who had moved out of William’s house when he married, to a small cottage nearby. John inherited his father’s and aunt’s musical skills, and music was an important part of his entire life. It would later be said that “the Herschels were a musical family; music was their vocation, science was their recreation.”23 But John found his “recreation” early: Caroline later wrote that “many a half or whole holiday [John] was allowed to spend with me was dedicated to making experiments in chemistry, where generally all boxes, tops of tea-canisters, pepper-boxes, teacups, etc., served for the necessary vessels and the san
d tub furnished the matter to be analysed. I only had to take care to exclude water, which would have produced havoc on my carpet.”24 Although John would later say that “light was my first love,” it seems more the case that his heart was lost first to chemistry.
Just before he was eight, his parents sent John to Eton, only a mile away from Slough on the highway to Windsor. But one day, while visiting, Mary saw John knocked down by an older boy, and she withdrew him from the school straightaway. He entered instead a school run by his father’s friend Dr. Gretton at Hitcham, a village in the neighborhood of Slough, where his mother could keep a watchful eye on him. There he mostly studied classics—ancient Greek and Roman history and literature. John’s parents engaged a private tutor, a Scottish mathematician named Rogers, to teach him science, modern languages, literature, music, and mathematics.25 By the time he went up to Cambridge, John could speak German, French, and Italian, and knew Latin and Greek.
His formal education was supplemented by watching his father and aunt in their astronomical labors, and by travel; before he reached the university, John had already taken carriage trips with his family throughout England, Wales, and Scotland, and had even gone across the Channel to Paris, where the famous astronomer and his family were entertained by Napoleon Bonaparte.
He went up to St. John’s in 1809, uncertain of his future plans. Soon after, a friend of the family told John that he would one day rival Isaac Newton in greatness.26 He initially fought against the idea of following Newton and his father into astronomy, but in the end he found himself doing just that. The immense forty-foot telescope, which loomed above his childhood, would soon point the way to his own fame.
HERSCHEL WOULD OFTEN confide his doubts about the future to Charles Babbage. Like John, Charles came from a privileged background. Charles was born on December 26, 1791, in Walworth, Surrey, a hamlet within walking distance across London Bridge from the City, where his father was a partner in the banking firm Praed, Mackworth and Babbage. Both his father, Benjamin, and his mother, Elizabeth (Betty) Plumleigh Teape, were from old Devonshire families, in the countryside surrounding Totnes and Teignmouth on the southern coast of England. When Charles was fifteen, his father retired and bought a house in Teignmouth; Charles lived there until he left for Cambridge.27
Charles had two brothers, both of whom died young, and a sister, Mary Ann, with whom he remained close all his life. Babbage was sickly in his youth, and as a result his schooling was intermittent at best. For a short time, when he was older and stronger, he was sent to the academy of the Reverend Stephen Freeman, in Enfield, Middlesex, where he studied mathematics and ignored classical studies, which were not of interest to him. As he later boasted, the young Babbage mostly taught himself.
Babbage was always fascinated by mechanical things. As a child, he would take apart his toys to find out what was inside them, and how they worked. One day his mother took him to an exhibit of mechanical wonders in Hanover Square put on by a man named Merlin. Such exhibits were common at the time. The novelist Fanny Burney—mother of Babbage’s Cambridge friend Alexander D’Arblay—described the protagonists of her Evelina visiting an exhibition much like this one, seeing a metal peacock that spread its tail every hour, a swan that “swam” across a mirrored pond, and a pineapple that opened to reveal a nest of singing birds.28 Reading this novel after meeting Alexander would have struck a chord with Babbage, as he vividly remembered his visit to Merlin’s exhibition for the rest of his life. He recalled that Merlin, noticing the boy’s evident precociousness, took him up to his workshop. There Babbage and his mother were shown two silver figurines, each about one foot high. One of these appeared to walk or glide back and forth over a surface about four feet in diameter, raising an eyeglass to her face and bowing frequently. Babbage remembered her as being “graceful” in her motions. But he was most struck by the second figure. He called her an “admirable danseuse” who “attitudinized in a most fascinating manner. Her eyes,” Babbage rhapsodized years later, “were full of imagination, and irresistible.”29
Babbage never forgot this admirable dancer. Somewhat improbably, thirty years later, he purchased that same figure at an auction held by Merlin’s heirs. He sewed special clothing for her, and made a tiny wig woven from strands of his daughter’s auburn hair. She held pride of place in Babbage’s drawing room, attracting more attention from guests than the demonstration model of his calculating machine displayed nearby.
When Babbage came up to Cambridge in 1810, he was already advanced in mathematics through his self-led study of the great Continental mathematicians, especially the French mathematician Sylvestre François Lacroix. Through his studies, Babbage had been exposed to the elegant methods of the calculus of Gottfried Wilhelm Leibniz. He was surprised to find Cambridge still ruled by the older, more convoluted methods of Newton. Newton and Leibniz had simultaneously and independently invented the calculus—a heated debate about who deserved priority for the discovery followed—but each developed his own system of notation. Newton used a “dot” to indicate differentials, while Leibniz used the dy/dx notation. Both mean the same thing, but since the Leibnizian notion contains explicitly the concept of a quotient, it is more effective for certain equations. The Leibnizian form had been used already on the Continent for a hundred years, making Cambridge in some ways a century behind the times.30
Questions to his tutor—Hudson, who would soon be tutoring Whewell—about the Continental mathematics were met with the response, “It will not be asked in the Senate House [during the Tripos examinations] and is of no sort of consequence.” Babbage left Trinity in disgust at such an attitude, knowing that at the college of Newton he would never succeed. He migrated to Peterhouse from Trinity in 1812, just as Whewell was entering. At that smaller college, which had only three senior wranglers in the first sixty years of the century, Babbage was more appreciated; he quickly became their “crack man,” the one expected to carry away top honors and bring glory to the college.31 Unfortunately for Peterhouse, as we shall see, that ambition was thwarted by Babbage’s own obstinacy.
Babbage believed that the d notation of Leibniz was much more convenient and less liable to error than Newton’s fluxion dot notation.32 It was more precise, and more readily impressed on the memory. Further, if English students mastered Leibniz’s notation they would be better able to follow the progress of science on the Continent, where those methods were applied.33 The French mathematician Pierre-Simon Laplace had used the Leibnizian methods in his Traité de Mécanique Céleste to solve problems left unanswered in Newton’s Principia. Reading Laplace, and following his mathematics, was crucial for serious students of Newtonian mechanics.34 A fellow of Caius, Robert Woodhouse, had made similar points in his Principles of Analytic Calculation, published in 1803, but his call for the adaption of the differential notation was not heeded.35
Cambridge students suffered for the way they were taught as well; Babbage wanted students taught the abstract principles of analysis prior to its application, rather than, as was done in his time, teaching technique only through the repetition of physical problems with limited scope.36 He felt students were being trained to be mere mathematical calculators rather than great mathematical discoverers. His disdain for rote calculation would eventually lead Babbage to his greatest invention, the calculating machines that prefigured modern computers. But for now he began to plot a way to reform the study of mathematics at Cambridge. The inspiration for the instrument of reform came from a most unlikely source.
At that time, Cambridge was beset with controversy over attempts by some students to establish a branch of the British and Foreign Bible Society. This society had been formed in 1804 with the purpose of attempting to encourage a wider circulation of the Holy Scriptures. It was open to all Christians, not only Anglicans (its origin was the lack of Bibles in the vernacular, rather than Latin, in predominantly Presbyterian Wales). The society was seen as potentially heretical because it was open to Dissenters—non-Anglican Christians�
��and also because it aimed to distribute Bibles only, without any commentary on Scripture; the members of the society viewed such commentary as profane attempts to mend that which was perfect. An opposing society, the Society for the Promotion of Christian Knowledge, which was open only to Anglicans and sought to spread the Anglican faith, distributed Bibles with notes to make them intelligible to the common people.37 The battle between these opposing groups was fierce, as religious controversies often are.
Although life could be difficult for Dissenters in Britain at that time, Protestant Nonconformists still had it easy compared to the Catholics. Catholics could not vote, were excluded from state offices and both houses of Parliament, were barred from degrees at the universities, had no right to own property, were subjected to punitive taxation, and were forbidden to bear arms. This changed only with the Catholic Emancipation Act of 1829, which ameliorated the situation.38 Slowly, after that, Catholics and other non-Protestants (such as the Jews) gained equal civil rights.
In the context of debates about the merits of the two opposing Bible societies, Babbage had the clever idea for a society for promoting the Continental knowledge in mathematics. Babbage recalled later that “the walls of the town were placarded with broadsides, and posters were sent from house to house. One of the latter forms of advertisement was lying upon my table.… I thought it, from its exaggerated tone, a good subject for a parody. I then drew up the sketch of a society to be instituted for translating the small work of Lacroix on the Differential and Integral [Calculus]. It proposed that we should have periodical meetings for the propagation of D’s; and consigned to perdition all who supported the heresy of dots. It maintained that the work of Lacroix was so perfect that any comment was unnecessary.”39 What began as a joke became a serious, and ultimately successful, endeavor.
THE FIRST MEETING of the new Analytical Society was held in 1812, attended by Babbage, Herschel, Michael Slegg, Edward Bromhead, George Peacock, Alexander D’Arblay, Edward Ryan, Frederick Maule, and several others. They hired a meeting room, which was opened daily to members for reading, discussing, and gossiping. They held weekly meetings at which mathematical papers were presented and critiqued.40 They recruited new members, such as the much-talked-about mathematical prodigy William Whewell, who by this time was already reputed to have gone through the entire Encyclopaedia Britannica, “so as to have the whole of it at his ‘fingers’ ends.’ ”41 The Society published a Memoir, written entirely by Herschel and Babbage, which set out the aims of the group: “Discovered by Fermat, concinnated [elegantly adapted] and rendered analytical by Newton, and enriched by Leibniz with a powerful and comprehensive notation,” is how they described calculus (Fermat is called the initial “discoverer” because he had first found a general procedure for how to find the minimum and maximum values of a function, though his solution was geometric rather than algebraic). But because it was “as if the soil of this country [was] unfavourable to its cultivation, [the calculus] soon drooped and almost faded into neglect; and we now have to re-import the exotic, with nearly a century of foreign improvement, and to render it once more indigenous among us.”42
The Philosophical Breakfast Club Page 4