It was a natural impulse to form a club. By the eighteenth century, clubs had come to be seen as part of civilized Britain. There were reading clubs, coffee-drinking clubs, cardplaying clubs, dining clubs, social clubs. It has been estimated that by the mid-eighteenth century as many as twenty thousand men were meeting every night in London in some kind of organized group, and many more in the provinces. Johnson was inspired to coin the term clubbability, as an important characteristic for a gentleman to have. The Goncourt brothers—Parisian novelists and diarists—mocked the British by quipping that if two Englishmen were washed up on a desert island, their first act would be to start a club.43
But while it was a natural impulse, forming the Analytical Society was also a political act. By the nineteenth century, clubs were strictly monitored in Cambridge. No societies at the time were allowed to discuss politics; any student group suspected of harboring such discussions was shut down at once. Indeed, even the Foreign Bible Society was barred as an undergraduate initiative, and a chapter had to be started under the auspices of a group of dons.
Britain was then in the midst of a war with France, and anything with the whiff of sedition—which meant anything remotely political—was suspect. Worse was showing support for something French, even French mathematics. England had been almost constantly at war with the French for over a hundred years: battles between the nations had raged in 1689–97, 1702–13, 1743–48, 1756–63, 1778–83, 1793–1802, and, most recently, from 1803 until the present time—the “Napoleonic Wars,” which would not end definitively until Napoleon was defeated at Waterloo in the summer of 1815. Even during periods of ostensible peace, the two nations spied upon and plotted against each other. Animus against the French had become so ingrained that it was said of the English that “before they learn there is a God to be worshipped they learn there are Frenchmen to be despised!”44 Britons saw France—with its larger population and landmass, its more powerful army, and, no less, its Catholic aristocracy—as a threat to their safety and freedom until the end of the century. Aligning with the French in any way was a dangerous stance for Babbage and his friends to take. Babbage later remembered, with barely suppressed pride, that “it was darkly hinted [by the dons] that we were young infidels, and that no good would come of us.”45
The meetings of the society were boisterous and fun. Frederick Maule later wrote Babbage that he was reminiscing about the gatherings with pleasure, and “transported myself in thought to the scene of action & heard the damns, the nonsense, the arguments, the objections, etc. with greater personal safety if not with the same clear perception.”46
Babbage and Herschel were struck by a “mania analytica,” which did not rest even when the academic year ended.47 In the summer of 1812, letters shot back and forth between Herschel, who had remained at St. John’s, and Babbage, vacationing with his family in Teignmouth. Pages and pages went to and fro over the south of England, filled with proofs, theorems, and analytical equations, letters the length and complexity of mathematical papers. Herschel admitted to Babbage that “I rejoice to find that you are still labouring in the cause of reason and truth. To speak in the language of mortals I am glad to see that you are reading analytics in the retirement of a vacation. I too have been dour. Newton was my companion.” Babbage, in return, told Herschel, “I have received yours and you see in return what an attack I have commenced on your patience.” And, Herschel responded, “Your comprehensive letter was so direct a challenge that I am resolved to shew you that I am no recreant knight, nor willing to be outdone in the combats of analysis—prepare yourself for an overwhelming torrent.…”48 Once they were both back in Cambridge, the meetings of the Analytical Society resumed.
Later, in 1816, Babbage, Herschel, and Peacock translated Lacroix’s Traité élémentaire de calcul différentiel et de calcul intégral, which was eventually adopted as a university textbook at Cambridge. Herschel and Babbage supplemented this with two volumes containing examples of the calculations, published in 1820. By 1817, questions based on the new Continental methods had begun to appear on the Tripos examinations.49 It helped that Peacock was one of the moderators of the exam, and that the moderators were allowed to set any questions they wished, in any form they liked. Peacock’s questions used the differential notation of Leibniz. He was moderator again in 1819. By 1820, Whewell was a moderator, and all the questions used the Leibnizian d’s exclusively; after that, the dots never appeared again. So Babbage and Herschel’s “Principle of D-ism” won, “in opposition to the Dot-age of the University.”50 By the mid-1820s a candidate for the Tripos was required not only to use the Continental notation, but also to have a strong grounding in the most advanced analytical techniques.51 As Jones told Whewell around this time, “I hear the old mathematics have died and faded away with scarcely an audible groan before the bright flood of analytical love.”52
AT THE MEETINGS of the Analytical Society, Whewell was especially captivated by Herschel, whose charm and brilliance appealed to the younger man. He also liked Babbage, a convivial chap. Both Babbage and Herschel had large allowances from their fathers, and both were generous with their money; they were happy to invite Whewell out for wine parties and dinners. Whewell introduced Herschel and Babbage to Richard Jones, who, unlike the other three, had no deep interest in mathematics and was not planning to take an honors degree. But he was a bon vivant who thoroughly enjoyed a good meal, and who purchased crates of excellent wine, which he was pleased to share with the others. Over emptied platters of food and many bottles of claret, Jones would tell the others risqué jokes and the juiciest gossip. The famous wit Sidney Smith would later quip that Jones carried “a vintage in his countenance” and “his last week’s bill of fare on his waistcoat.”53
Jones was the eldest of the group, having been born August 12, 1790, at Frant, Sussex, and baptized in September in nearby Tunbridge Wells, a town in western Kent (now called Royal Tunbridge Wells, located not far east of Gatwick Airport). At that time Tunbridge Wells had a population of 1,500; dating back to Roman times, it was the oldest watering place in Britain after Bath. His parents were Sophia Gilbert and Richard Jones, an eminent solicitor from Welsh stock. Whewell, ever sensitive to his own Lancashire inflection, would sometimes remark on Jones’s Welsh accent.
As a young man Jones was sent to Chelsea to attend Durham House, a school noted for its fine education in Classical studies. The forty to fifty students at the school were mainly sons of nobility or professional men. For two years Richard studied with a Mr. Ouisseau, known for his skill in languages. The plan was that, after school, Jones would enter the law profession. When he was twenty years old he left the Durham House and was admitted to the Inner Temple, London, to study for the bar.
Illness intervened, however. Like Babbage, Herschel, and Whewell, Jones had been a sickly child; unlike the others, he grew up into a sickly adult (one may speculate that his diet and drinking habits contributed somewhat to this result). His father, a strong-willed man, took his son’s future in his hands and decided Richard was too delicate for the law. He insisted his son enter Cambridge with the goal of studying for the ministry; a nice, easy position as a parish priest seemed just the thing for a man of uncertain health. Richard found himself powerless to resist his father, although he liked the law and had no interest in becoming a country curate. And so, in 1812, at the age of twenty-two, Richard matriculated at Caius College. He thus entered Cambridge at the same time as Whewell, though he was four years older.
Babbage, Herschel, Jones, and Whewell soon realized that they shared a common interest, and a common bond. They began to meet on Sunday mornings, after the compulsory chapel services held at their respective colleges (Babbage often dodged the services at Peterhouse, which drew upon him many a fine and warnings about “rustication,” or being sent home for a term or two). The meetings of the Philosophical Breakfast Club took place probably from the end of 1812 until the spring of 1813, when Herschel left Cambridge after receiving his degree. Breakfast
parties were widespread in the day, and continued to be so for some time. The dons considered these parties a bad influence on the young men, causing them to fritter away the day in discussions, drinking, and smoking, instead of reading and studying. Whewell must have chuckled when, forty years later, a junior dean wrote to Whewell as Master of Trinity that he hoped to “put a stop to breakfast parties on Sunday morning (which are at present common and very mischievous).”54
After the chapel service ended at around 9:00 a.m., the men made their way to Herschel’s rooms in St. John’s College. Herschel had a bedroom and sitting room on the right-hand side of staircase K, in the southwest corner of the second of the three successive courts. On the ground floor, the rooms looked out onto the courtyard. The occasional noise of the passing students and fellows was sometimes distracting to Herschel as he tried to read in his rooms, but this defect was compensated for by the ease of the return home after having too much to drink at a dinner party in the town (no stairs to climb!) and the ability of passing revelers to knock at Herschel’s window, inviting him to join them. Herschel’s former residence is today the Junior Combination Room, where undergraduates gather to play pool, gossip, and drink, which seems a fitting tribute to its history.
When the men arrived, they were relieved to find a roaring fire that had been prepared by Herschel’s “gyp,” or college servant. The mornings during term time were typically cool and damp, and in the winter it was still dark. As they took off their robes and warmed themselves, Herschel would motion for his gyp to go to the kitchen of the college and retrieve the bountiful breakfast he had ordered: tea, coffee, and “audit ale,” so called because it was the best beer, by tradition reserved for the feast or “audit” days; tongue, cold beef, ham, chicken, anchovies, and eggs; toast, muffins, crumpets; honey, marmalade, and butter (which was shaped into rolls an inch in diameter and sold in town by inches, “measured out by compasses, in a truly mathematical manner,” as the novelist Maria Edgeworth put it after a visit to Cambridge around this time).55
The men set to eating, gossiping, laughing (more ale than coffee was drunk). When this prodigious breakfast was finished, the gyp cleared the remains, and the four, sometimes joined by others, including Thomas Forster, who wrote the letter reminding Whewell of the meetings, and their friend George Peacock, gathered around the fire. Whewell and Jones sat right in front of the hearth, with their feet up on the fireplace fender; the others arrayed themselves nearby. In later years Whewell would fondly recall that these meetings of the Philosophical Breakfast Club were among the happiest moments of his life.56
Herschel, the host, would bring up the topic of the week. Generally it was a passage from the writings of Francis Bacon, the statesman, lawyer, essayist, and scientific reformer, who lived from 1561 to 1626. In his famous, uncompleted magnum opus, the Great Instauration, or the Great Renewal, Bacon had called for a revolution of thought and action. His most radical idea was that knowledge should bear fruit—that science should help transform the condition of life. This was a sea change from earlier ancient and medieval philosophers, who did not expect the drastic improvement in men’s lives that Bacon insisted upon, and certainly did not think that the study of the natural world could bring about such a change. As Bacon colorfully put it, “Knowledge may not be as a courtesan, for pleasure and vanity only, or as a bond woman to acquire and gain to her master’s use, but as a spouse, for generation, fruit, and comfort.” To his uncle Bacon explained that he preferred the title “philanthropist” to “philosopher,” so important was his view of the profitable inventions and discoveries that should come from science. He pointed to the printing press, gunpowder, and the compass as the great inventions of the past that had changed lives and societies, and hoped that with a new method even more novel discoveries and inventions would emerge.57
“Knowledge is power,” Bacon proclaimed provocatively, meaning that by understanding nature, man would have the power to take control of the natural world in order to bring about improvements necessary for society. Gaining knowledge of nature required a complete renovation of the human mind. “It is idle to expect any great advancement in science from the super-inducing and grafting of new things upon old,” Bacon observed. “We must begin anew from the very foundations, unless we would revolve forever in a circle with mean and contemptible progress.” He compared himself to Christopher Columbus, changing the old world by finding the new one. Bacon wanted to find a new way of thinking; and this new way of thought, a “logic,” was to be applicable to all realms, to the natural world and the social world, to the study of nature and the study of men. He accordingly called for a “logic that embraces everything.” It was heady stuff to a group of young, highly educated men, eager to make their mark on the intellectual world.
The starting point for Bacon was the clearing of certain “idols” or misconceptions standing in the way of the new knowledge; the mind must be “purged and swept and leveled.” One of those idols was the philosophy of Aristotle, which had dominated thought for centuries, especially since medieval times. Bacon had studied Aristotle at Cambridge, and understood his logic better than most. He saw that Aristotle’s medieval readers, such as Thomas Aquinas, had perverted it by focusing on only one part of logic, deductive reasoning. This is the kind of thought that starts from assumed universal statements (such as “all triangles have 180 degrees”) and then infers more-specific statements from these (“right triangles have 180 degrees,” “isosceles triangles have 180 degrees,” “scalene triangles have 180 degrees”). The particular statements follow necessarily and immediately from the general; if the general assumption is true, the conclusions must be true as well. No information about the particular triangles, or about the world, is required to draw these conclusions. Neither is any new knowledge created: once you know that all triangles have 180 degrees, you already know implicitly that a right triangle has 180 degrees, even if you have not yet expressed this knowledge explicitly.
Aristotle never intended such reasoning to be the main engine of scientific discovery. But medieval scholars—whose views became so dominant in Europe because of their connection with the Church—distorted his system and argued that deduction was the logic of science. Bacon believed this view to be responsible for the “Dark Ages” into which science had been plunged for centuries.
Once the mind was cleared of this “idol,” it could be receptive to Bacon’s logic, which was a kind of inductive reasoning in which individual instances are used to infer a general conclusion. Those individual instances are gained by observation of the world. Thus, for example, from the observation of one black crow, another black crow, and another, we can conclude that “all crows are black.” But Bacon’s inductive method was much more sophisticated than this example suggests. His method of “the interpretation of nature” cautions us that we should not reach generalizations without very careful consideration of the particulars. So, for instance, it is not just a matter of concluding after seeing one or two or even ten black crows that “all crows are black,” but rather making sure you observe many crows of different sexes and ages, in different countries, at different times of the year.58 And the end result of Bacon’s method was not just a universal statement, or law, but also a new concept, in this case the concept of what it is to be a crow.
Bacon proposed methods of observation and recording of data, in what he called “Natural Histories,” to help ensure that the inductive conclusion was true. In his own example of his method, his “investigation into heat,” Bacon listed all instances he could find of objects or beings that were hot; he then listed all cases of objects or beings similar in many respects to those that were hot, but lacking the property of heat. For example, rays of the sun are hot. But rays of the moon, though similar in some respects to rays of the sun (in emanating from a celestial body, and being light-conducting), are not hot. This indicated to Bacon that heat did not need to be associated with light, or with celestial bodies. By this kind of reasoning Bacon eventually conc
luded—rather impressively in the days before molecules had been discovered—that heat was a kind of motion of imperceptible particles. He then pointed out that by knowing what heat was, we could create heat—by producing that type of motion.
In a famous aphorism, Bacon proposed that the man of science must be like the bee, not the spider or the ant. The spider “spins webs out of his own substance,” creating theories based only on what he already knows or believes; nothing comes from outside his mind. A younger thinker during Bacon’s lifetime, the philosopher and mathematician René Descartes (1596–1650), would have struck Bacon as a paradigmatic philosophical spider. Descartes desired to construct a coherent and absolutely certain system of knowledge, in which metaphysics provided the required grounding of all other subjects, including physics. Accordingly, when Descartes turned to physics (in work published only after Bacon’s death), he began not with experiments, but with various assumptions about God: God exists; He is constant or unchanging; and He is the source of all motion in the inanimate world. From these assumptions, Descartes deductively reasoned to laws of motion, including a general conservation law, stating that the same quantity of motion is always preserved in the world. These laws are grounded in God’s nature, specifically in his immutability, or unchangeability. “God himself,” Descartes explained, “who created motion and rest in the beginning … now, through his ordinary concourse alone preserves as much motion and rest in the whole as he placed there then.”59 Descartes did not reach his laws of motion through any particular observations or experiments, though he did describe some experiments to illustrate the truth of the laws. From those laws he “spun out” explanations of everything, from celestial motions to volcanic eruptions to the fluorescence of dead fish.60 Descartes’s work in physics was influential on the Continent, but mainly ignored in Britain, especially after Newton’s cutting rebuttals of his method and conclusions.
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