The Philosophical Breakfast Club (13 page)

Mary Herschel wrote to her son that the meeting between Sir William and Mr. Gwatkin to discuss John’s proposal to Miss Gwatkin went “better than I expected.” The two fathers agreed that time should be given to the young couple before a marriage settlement was drawn up. John’s mother expressed herself happy with the intended match, praying that God should bless the union “if it takes place.”
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The parents were leaving a way out for the two, should one or both change his or her mind. Meanwhile, Herschel’s mother asked Babbage to talk to John about the marriage settlement, a task that Babbage performed without much relish.
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Marriages were like mergers in those days, especially where family land and money was involved. For the upper classes, a settlement document—which cost over £100 to draw up—was de rigueur. A daughter received her “portion” of the family’s inheritance when she married; it was her dowry. Actually, the money became her husband’s, but it was typical for wives to receive “pin money,” or a lifetime guaranteed allowance, often equal to one percent of her dowry. If her husband died first, the wife could be provided for by a “jointure,” an income for life from his estate. It was also possible to protect the separate property of the wife, stating that she could not sell it even if she wanted to in order to help her husband, thus keeping it out of reach of his creditors.
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But all of this needed to be put down on paper in legalistic language. As Babbage reminded Herschel, it needed to be done in the proper way, so that the couple could have access to the money in the woman’s portion, which might be in the form of bonds or land. John, a romantic and flighty man, was too “delicate” for such discussions, Babbage complained to Mary Herschel.
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He found such practical matters so distasteful that he refused to discuss them with either Babbage or his intended father-in-law.

Babbage promised to take charge, and he did, apparently raising the issue at a dinner he and his wife gave for the Gwatkins and Herschel. Whether because Babbage was too blunt or for other reasons, the engagement was abruptly called off by the Gwatkin family. Herschel barricaded himself in his dark room for days. Babbage was enlisted by Mary Herschel to take Herschel to Europe to “forget” this youthful love affair and its sour end. Babbage persuaded Jones to join them. The three of them traveled to France in July of 1821.

With the end of the Napoleonic Wars, it was now possible to travel freely to the Continent, and more intercourse was feasible between English men of science and their European counterparts. Before the French Revolution, it had been customary for members of the upper classes in Britain to take the “Grand Tour” to the Continent: from Dover to Calais, then to Paris, Dijon, Geneva, Avignon, Rome, and Naples. During the brief Peace of Amiens in 1802–3, the British desperately flocked back to Paris, and some were trapped in France when war broke out again. They spent the war interned in Verdun, and were freed only in 1814.
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After Napoleon’s defeat at Waterloo, the Grand Tours continued, on a slightly smaller scale, with travelers going from Paris to Italy—Rome, Venice, and Florence, with a trip to Naples to climb Vesuvius, and perhaps even descend into the crater itself!—then returning home through the Tyrol and Munich.
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Herschel and Babbage had already availed themselves of the increased opportunity to travel in January of 1819, visiting France. The following year, Whewell and Richard Sheepshanks met Jones in Paris, and the three friends spent time together there—although, as Whewell complained, there were “no handsome women to be seen!”
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Jones remained behind in Paris while Whewell and Sheepshanks traveled on through Switzerland and Germany.

In the summer of 1821, Herschel, Babbage, and Jones stayed for a time in Paris, where they met with the most important French savants of the day: Arago, Laplace, Biot. Herschel and Biot shared notes on experimental results in optics. The German naturalist Alexander von Humboldt was living in Paris at the time, and the men became acquainted with him at Laplace’s house. Herschel and Babbage then traveled southward through Dijon to French Switzerland, and spent a week in Geneva. Jones again lingered in Paris, enjoying the excellent wines. From Geneva, Babbage and Herschel went south through Chamonix, Aiguebelle, and Modane to Turin, where they visited the astronomer Giovanni Plana. They proceeded to Milan, and returned via Lake Como, Lake Maggiore, and the Simplon Pass.

Along the way they climbed the Breithorn, a 13,000-foot mountain next to Mont Rosa. After five hours of hard walking in knee-deep snow, the high crest of the mountain still remained to be climbed. It was a sharp edge of snow “along which a cat might have walked,” as John wrote to his mother. Three out of their four Swiss guides refused to go any farther,
but Herschel and Babbage persisted, along with one old man who had climbed the mountain before, and reached the summit.
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The two men traveled with a full contingent of scientific instruments in their carriage. Wherever they went, they took barometric readings and temperature measurements, determined angles by a small pocket sextant, and filled entire notebooks with geological and mineralogical observations. When they returned, Babbage published a paper based on the readings they had made from the Staubbach Falls, in the valley of Lauterbrunnen. Each morning they had carried a thermometer and barometer from their inn over a small wooden bridge traversing a torrent, where they took the initial reading. They then followed a path along the bank, rising with a steep descent, to the top of the waterfall, where they took their second reading. This they did over a series of days, to compare the readings at the top and the bottom of the falls, trying to determine whether height could be determined by barometric pressure.
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Their results were inconclusive, but they considered the trip a scientific success nevertheless. They returned home in October 1821, Herschel having recovered from his broken heart. He resumed notations in his experimental notebook in November.

B
Y THIS TIME
, Babbage, Herschel, Jones, and Whewell had each graduated, and had begun to lead their scientific lives. For the next five decades these lives would come together and pull apart, like light rays focused and dispersed in an ongoing series of optical experiments.

O
N THE AFTERNOON OF
D
ECEMBER
20, 1821, B
ABBAGE EXCITEDLY
summoned Herschel. “Can you come to me in the evening as early as you like I want to explain my Arithmetical engine and to open to you sundry vast schemes which promise to reach the third and fourth generation—… Do let me see you for I cannot rest until I have communicated to you a world of new thought.”
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The idea for an “arithmetical engine” had come to Babbage a few weeks earlier, soon after he and Herschel had returned from Europe. One morning the two sat opposite each other in Babbage’s house in Devonshire Street. They were bent over astronomical charts calculated by “computers”—the name given to men and women, usually schoolteachers, clergymen, or surveyors, who picked up extra income on their off-hours by performing routine mathematical calculations by hand, using a fixed procedure over and over again.
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Babbage and Herschel each held a set of data calculated by a different computer using the same formula. If all the figures had been worked out correctly, the two sets of data would match perfectly. Babbage read off one number at a time, waiting for Herschel to check whether it accorded with what was on his sheet, putting a mark in the margin whenever Herschel told him the figures differed. Again and again, the men found discrepancies, indicating error on the part of one or the other (or both) of the computers.

The next year, when he wrote about this moment, Babbage could not recall who had first come up with the idea; but he knew that one of them had sighed in exasperation, “If only a steam-engine could be invented to make these calculations.” Decades later, in his autobiographical
Passages from the Life of a Philosopher
, Babbage told the story differently, taking credit for the notion of a calculating engine.
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Whoever may have initially voiced the idea, it was Babbage who became obsessed with the project of inventing and building such a machine, an enterprise he saw as fulfilling
Francis Bacon’s call for renovating science and improving people’s lives. What Babbage eventually devised would be like nothing that had ever been created before.

A
IDS FOR CALCULATION
went back centuries, of course, to counting pebbles and tokens, tally sticks, the abacus, and the slide rule. But all those methods relied on the human agent to move pebbles or sticks, slide balls across a wire, or manipulate rods, and then read off the results. In the fifteenth century, Leonardo da Vinci dreamed of a completely mechanical calculator, one that would minimize the role of the human operator and thus reduce the possibility of error. By the time of Bacon, in the sixteenth and seventeenth centuries, leading intellects in Europe had seized on this idea. Not only would mechanical calculation increase accuracy, it would free up the mathematician for more lofty operations. Gottfried Leibniz, the philosopher, mathematician, and rival of Newton, remarked that “it is beneath the dignity of excellent men to waste their time in calculation when any peasant could do the work just as accurately with the aid of a machine.”
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At around the same time, workmen were gaining useful experience constructing mechanical devices to amuse the rich and entertain royalty. Mechanical automata—like Babbage’s “admirable dancer” two centuries later—were all the rage. The Smithsonian Institution in Washington has in its collection an automaton friar that may have been constructed as early as 1560. About fifteen inches tall, the friar, driven by a key-wound spring, walks the path of a square, striking his chest with his right arm, while raising and lowering a small wooden cross and rosary in his left hand, nodding his head, rolling his eyes, and mouthing silent prayers. In 1649 an artisan in France created a magnificent automaton for the young Louis XIV: a miniature coach and horses, with a footman, a page, and a seated lady, all exhibiting perfect motion. (The world would have to wait until 1737 for the first digesting automaton—a mechanical duck that seemed to eat and defecate, created by the French engineer Jacques de Vaucanson.) Such mechanical expertise would soon be harnessed to build calculating machines.

The first mechanical calculating device known to have been constructed was designed by Wilhelm Schickard (1592–1635) of Wurttemberg, later part of Germany. Schickard was, impressively, Professor of
Hebrew, Oriental Languages, Mathematics, Astronomy,
and
Geography at the University of Tubingen. Schickard was well acquainted with the famous astronomer Johannes Kepler, discoverer of the elliptical shape of planetary orbits, who had come to Tubingen to help defend his mother when she was accused of being a witch. When Kepler left Tubingen after his mother was freed in 1621, the two men kept up a lively and frequent correspondence. In letters to Kepler, Schickard described a calculating machine he had designed and built in 1623 (though no actual machine has ever been found).

Schickard’s “Calculating Clock,” as it is called, was about the size of an old manual typewriter: twenty-two inches wide, fourteen and a half inches deep, and almost twenty-three inches high.
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It could add and subtract automatically, by the movement of geared wheels at the bottom part of the machine meshed together and linked to a display—much like a car’s odometer today. There were six dials at the bottom of the machine, each connected to a toothed wheel inside the machine. By turning the dials clockwise, the operator could perform addition; subtraction was done by turning the dials counterclockwise.

The machine could automatically carry tens during addition, for example when 1 was added to 9 to make 10. Every time a wheel rotated through a complete turn (passing 9), a single tooth would catch in an intermediate wheel, which would cause the next highest wheel to turn, increasing it by one. However, the force used to execute the carry came from the initial power of the first gear meshing with the next ones, so there was a limit to how many digits could be calculated before the necessary force would damage the initial gear; Shickard’s machine was designed with only six digits.
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Schickard’s machine could not, by itself, perform multiplication and division. The operator of the machine would perform long multiplication and long division using the bottom part of the machine (the adding and subtracting part) in tandem with the top part of the machine, which contained six dials above window openings through which multiplication tables were visible.

Before the letters discussing Schickard’s machine and the drawings of it came to light in 1957, it had been believed for centuries that the first mechanical calculator ever constructed was that of Blaise Pascal (1623–1662). Pascal is known to many college freshmen today for devising “Pascal’s Wager.” Countering atheism, Pascal argued that even though the
existence of God cannot be proved by philosophical argument, it is still the most rational course to act as if (or bet that) God does exist—because if you are right you have everything to gain, and if you are wrong you have little to lose. Pascal turned to philosophy at the end of his life. Before that, he was known as a mathematical prodigy and one of the inventors of probability theory, so it is not surprising that one of his main philosophical tenets was expressed in terms of a gamble.

When he was nineteen, in 1642, Pascal designed and built a mechanical calculator, the “Pascaline.” His father, Étienne, had been appointed tax commissioner in Rouen, and spent hours tediously calculating and recalculating taxes owed. Eager to help his father, the young Pascal devised a machine that could do the calculations for him.