The Philosophical Breakfast Club (6 page)

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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.”
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What began as a joke became a serious, and ultimately successful, endeavor.

T
HE 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.
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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.’ ”
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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.”
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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.
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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!”
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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.”
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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.”
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Babbage and Herschel were struck by a
“mania analytica,”
which did not rest even when the academic year ended.
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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.…”
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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.
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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.”
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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.
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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.”
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A
T 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.”
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