As coal mines went deeper, they also became more dangerous, and not merely because of the engineering challenge of supporting tons of overburden; one of the volatile components of raw coal is the hydrocarbon CH4, or methane, which is the main component of the flammable mixture known as "firedamp." Though it is slightly lighter than air, it can still pool in sealed areas of mines, causing a danger of asphyxiation and, far more significant in an age in which the only illumination came from fire in one form or another, explosion.* Savery's "Miner's Friend" was not, as it happens, sold exclusively as a water pump, but also as a means for ventilating such mines.

Anything that improved mining was attractive to the innovators of eighteenth-century England. Three-quarters of the patents for invention granted prior to the Savery engine were, one way or the other, mining innovations; 15 percent of the total were for drainage alone,21 as the shortage of surface coal became more and more acute and prices rose.

Price is the mechanism by which we allocate the things we value, from iPhones to coal, and even an imperfect system sooner or later incorporates the cost of manufacture into the selling price. In 1752, a study was made22 of a 240-foot-deep coal mine in northeast England in which a horse-driven pump lifted just over 67,000 gallons every twenty-four hours at a cost of twenty-four shillings, while Newcomen's engine pumped more than 250,000 gallons using twenty shillings' of coal-a demonstration not only of the value of the engine, but of a newfound enthusiasm for cost accounting. Newcomen's engine, by pumping water out of deeper mines at a lower cost, also lowered the effective price.

The problem was that it didn't lower it enough. The coal-fired atmospheric engines of the type designed by Newcomen and Calley burned so much coal for the amount of water they pumped that the only cost-effective place for their use was at the coal mine itself. This did a lot more for heating British homes than running British factories; as late as the 1840s,23 the smoky fireplaces of British homes still consumed two-thirds of Britain's domestic coal output, and a shocking 40 percent of the world's. An eighteenth-century coal porter in London might carry loads of twice his own weight up rickety stairs and even ladders up to sixty times a day. But no one was using steam engines for much else, because the cost of transporting the coal to a steam engine more than a few hundred yards from the mine itself ate up any savings the engine offered.

For fifty years, lowering the cost of mining coal for heat had been enough to make the Newcomen engine a giant success. It was dominant in Britain, copied all over Europe, and even studied at universities-unsurprisingly, given the experimental methods that had created the engine in the first place. One of the universities interested in producing a superior version of the Newcomen engine was the University of Glasgow, the fourth oldest in the English-speaking world, and home not only to Joseph Black but to James Boswell, Adam Smith, and a dozen other leading lights of what came to be known as the Scottish Enlightenment.

And, of course, to James Watt.

* The modern definition of experimentation-isolation of a single variable, to test and record the effect of changing it-still lay a hundred years in the future. We will meet the creator of this sort of experimental design, John Smeaton, in chapter 6.

* Modern engineers generally measure this as kilojoules/kilogram, but in British Thermal Units (the amount of heat needed to raise the temperature of a pound of water 1F) the numbers are 144 and 965 respectively. Thus, it takes 144 BTUs to turn a pound of ice at 32 into a pound of water at 32, and 965 BTUs to convert a pound of water at 212 into steam.

* Gold died in 2004 after four decades at Cornell University and a lifetime of swimming outside the mainstream of scientific orthodoxy. In the 1950s, along with Fred Hoyle, Gold was the originator of the so-called steady state theory of the universe, which preceded and contradicted the generally accepted big bang theory.

* A back-of-the-envelope calculation, using 33 1012 cubic miles as the rough spherical volume of the planet, concludes that excavating a truly giant mine-2.4 miles down, a mile on a side-gets at no more than 7 10-9 of the earth's volume. Barely a scratch.

* An explosion is essentially a fast-burning fire with nowhere to go. Firedamp, however, can also burn slowly. Very slowly. The mine fire that started in Centralia, Pennsylvania, in May 1962 is, as of this writing, still burning.

CHAPTER FIVE.

SCIENCE IN HIS HANDS.

concerning the unpredictable consequences of sea air on iron telescopes; the power of the cube-square law; the Incorporation of Hammermen; the nature of insight; and the long-term effects of financial bubbles THE FINEST ANCHORAGE IN the Caribbean is found on the southeastern coast of Jamaica, behind an eight-mile-long sandbar that protects the harbor from tropical storms. At the western tip of the sandbar, the original Spanish colonizers built a town they called Santiago, and which the island's English conquerors subsequently renamed Port Royal, retaining it as a base for privateering until it was destroyed by an earthquake in 1692. Kingston, on the mainland side of the harbor, was built as a refuge for survivors of the earthquake. It proved an attractive destination for refugees of another disaster, the Jacobite Rebellions of the early eighteenth century (the fruitless attempts to return the Stuart kings to the throne following the Glorious Revolution of 1688), which resulted in, among other things, the emigration of thousands of Scots to the island.* In 1747, one of them1 (a Scot, not a Jacobite), Alexander Macfarlane, a merchant, a judge, a mathematician, and yet another of those "gentlemen, free and unconfin'd" who could style themselves Fellows of the Royal Society, acquired several dozen state-of-the-art astronomical instruments from another Scot named Colin Campbell. Campbell was not merely a countryman, but a fellow alumnus of Glasgow University, so it was scarcely surprising that when Macfarlane died in 1755, his collection was bequeathed to their alma mater.

The ships that traveled from the Caribbean to Britain had a good deal more experience carrying sugar than they did telescopes and quadrants, whose iron components were not improved by several weeks exposure to salt air. Which is why, when the Macfarlane collection arrived in Glasgow in 1756, the university hired an artificer, just returned from London, "to clean them and to put them in the best order2 for preserving them from being spoilt."

James Watt was then twenty years old, and events had been preparing him for his new job almost since he was born, in Greenock, a borough just to the west of Glasgow on the River Clyde. Or even before. Scotland had formally joined the United Kingdom in 1707, but remained distinct from its southern neighbor in a number of relevant ways: poorer, but more literate, and far less inhibited by the presence of an established church that was turning Oxford and Cambridge into vocational schools for the clergy. The combination of relative poverty, and opportunity in British possessions around the world, explained the particularly Scottish enthusiasm for education: if the nation's most ambitious and smartest sons had to seek their fortunes elsewhere-and they did; during the eighteenth century,3 as many as six thousand trained Scottish doctors left the country in search of employment, and not just in Jamaica-the most valuable property they could take with them was between their ears.

As a result, even members of Scotland's artisan cla.s.ses were better educated than was the case almost anywhere else in Europe-a bit of good fortune for them, but even more so for Britain's ability to maintain its head start on the development of steam power. A 1704 Proposal for the Reformation of Schools and Universities proposed a curriculum in mathematics that would seem daunting to a twenty-first-century honors student: "the first six, with the eleventh and twelfth Books4 of Euclid, the Elements of Algebra, [and] the Plain and Spherical Trigonometry" followed by "The Laws of Motion, Mechanicks, Hydrostaticks, Opticks ... and Experimental Philosophy." Watt, in particular, was taught an impressive amount by a cousin: "John Marr, mathematician," as he appeared in Greenock's census.

Like Marr, Watt's grandfather had been a teacher of mathematics, navigation, and astronomy; his father was a carpenter specializing in shipbuilding who supplemented his income by surveying the land around Greenock, but both were famed for their skill in the repair of delicate instruments. And so, therefore, was James, though whether his combination of mathematical and mechanical apt.i.tude was genetic or the result of early training is as unknowable as it is irrelevant, since all memoirs of Watt's childhood suffer from the sort of retrospective adulation that nations habitually bestow on their heroes' early years. Watt certainly seems to have been a bright and precocious boy, but his childhood history is decorated by a truckload of conveniently postdated reminiscences (see Cherry Tree, George Washington's). In Watt's case, the best one is the story of his aunt's recollection of young James's obsession with the way a teakettle lid was forced upward by steam-suspicious on the face of it, since, as we have seen, the expansive force of steam was not precisely central to the operation of early steam engines. In any event, he certainly benefited from being given the full run of his father's workshop, with its hammers, chisels, adzes, block and tackles, and so on.

When Watt's mother died in 1753, the seventeen-year-old was sent to Glasgow to learn the trade of a "mathematical instrument maker," and though he could find no teacher, he did eventually encounter Robert d.i.c.k, a doctor and the professor of natural philosophy at the University of Glasgow. d.i.c.k was unable to provide training, but he did advise Watt to seek a teacher in London, for which he supplied a letter of introduction. Taking both the advice and the letter, Watt left Scotland on June 7, 1755, arriving in London twelve days later.

The city, then home to more than 600,000 residents, was already the largest outside of Asia, and easily the dirtiest. Though London owes much of its finest architecture to the fire of 1666, which cleared the way for the buildings of Christopher Wren and Robert Hooke, the overwhelming bulk of the city's buildings were constructed to somewhat lower standards than St. Paul's. Moreover, it was still, as of the date of Watt's arrival, using the Thames for both sewage discharge and drinking water, which partly explains why so much of poor London slaked its thirst with gin, a distilled spirit made from fermenting grain that was so bad it couldn't even be used to make beer. The Hogarthian enthusiasm for the cheap liquor was such that Henry Fielding-novelist, do-gooder, and pioneer of London's first police force-wrote, "it is the princ.i.p.al sustenance5 (if it may be so called) of more than a hundred thousand people in this metropolis. Many of these Wretches there are, who swallow Pints of this Poison within the Twenty Four Hours: the Dreadfull Effects of which I have the Misfortune every Day to see, and to smell too." With its large and unwashed populace, its untreated sewage, and the miasma caused by burning nearly two-thirds of the world's output of decidedly dirty coal, the city literally stank.

The smells were part of the cost of supporting the world's most robust commercial and manufacturing economies, but while the former was dominated by newly created speculative ventures, funds, and trading syndicates, the latter had a more medieval flavor. In London, as in most cities of Europe, the making of things had long been the prerogative of guilds, those ancient federations of autonomous workshops whose grip on activities such as weaving cloth, making jewelry, and working metals imposed very substantial costs on the city's economy.

Some of those costs were borne by the guilds' prospective membership in the form of free labor and apprentice fees, paid in return for both training and a de facto license to practice the skills acquired. The training, of course, is what James Watt had traveled to London to acquire, from the city's Worshipful Company of Clockmakers. That particular guild was not a true medieval organization; it had been founded "only" in 1631,6 just in time to define its exclusive franchise as embracing not only clocks but all forms of mathematical instruments. Partly as a result, they were considerably more welcoming of innovation than the more ancient organizations; when Watt arrived in London, their most ill.u.s.trious member, John Harrison, was not only improving on his prizewinning marine chronometer, which he had invented as a solution to the problem of calculating longitude at sea, but also had previously created new versions of both clock escapements and pendulums. Unfortunately for Watt, Harrison's guild was just as jealous of their territorial prerogatives as any thirteenth-century goldsmith; their bylaws prohibited any member from employing-and, especially, training-any "foreigners, alien or English"7 unless they were bound to the member as apprentices.

As a result, the first thing Watt learned in London was that he did not qualify for a "normal" apprenticeship. He was too old, for one thing. And even had he been closer to the usual age of apprentices, he had no interest in spending seven years as one. On the other hand, his willingness to leave London8 once trained was a huge advantage, since the guild rules were explicitly designed to eliminate unauthorized compet.i.tors only within the city. He was also, by training and apt.i.tude, already far more useful to a master clockmaker than a fourteen-year-old still picking hay out of his ears. The combination was evidently appealing enough that John Morgan, a member of the Company in good standing, agreed to take Watt on as a trainee in return for a year of free labor plus twenty guineas. By all accounts, he got a bargain: Since his "apprentice" had neither an interest in frivolity, nor the funds to indulge one, he did nothing but work. Watt was attempting to crowd seven years of training into one, and he succeeded. Most of his training was in fine bra.s.swork, building sectors, dividers, and compa.s.ses; even a Hadley quadrant with a telescope and three mirrors. He boasted to his father that he had mastered an extremely precise "French joint"-a hinge in which one channel folds into another like a fine bound book. By the time he returned to Glasgow in 1756, he was certified "to work as well as most journeymen"9 and was qualified to build and repair the machines representing the eighteenth century's most advanced technology.

Glasgow was then barely a town by London standards, home to around fifteen thousand people, but it was a "large, stately, and well-built city10 ... one of the cleanliest, most beautiful, and best-built cities in Great Britain" in the words of Daniel Defoe,* who visited in 1724 to report on Scotland's integration with England. It was also, in Defoe's words, "a city of business [with] the face of foreign as well as domestick trade" and a textile manufacturing center specializing in "stuff cross-striped with yellow, red, and other mixtures" (i.e. plaid), which meant that it was also home to its own guilds, just as jealous of their prerogatives as their London counterparts. In the case of Watt's newfound skills, the barrier to entry was manned by the rather fearsome-sounding "Incorporation of Hammermen," who, in the time-honored practice of every guild, weren't enthusiastic about recognizing a compet.i.tor who had failed to go through an approved apprenticeship. So when his former patron, Professor d.i.c.k, in need of someone to repair the sea-damaged Macfarlane collection, offered a payment of 5, and more important, permitted him to set up shop as "Mathematical Instrument Maker to the University," it was truly a G.o.dsend.

It is almost irresistibly tempting to see Watt's life as the embodiment of the entire Industrial Revolution. An improbable number of events in his life exemplify the great themes of British technological ascendancy. One, of course, was his early experience with the reactionary nature of a guild economy, whose raison d'etre was the medieval belief that the acquisition of knowledge was a zero-sum game; put another way, the belief that expertise lost value whenever it was shared. Another, as we shall see, was his future as the world's most prominent and articulate defender of the innovator's property rights. But the most seductive of all was Watt's simultaneous residence in the worlds of pure and applied science-of physics and engineering. The word "residence" is not used figuratively: The workshop that the university offered its new Mathematical Instrument Maker was in the university's courtyard, on Glasgow's High Street, a bare stone's throw from the Department of Natural Philosophy.*

He almost immediately started collecting admirers. One of his first friends among the university's "natural philosophers" was the mathematician and physicist John Robison, who was therefore in a privileged position to observe Watt in the years before his great achievements. Nearly forty years later he would recall that "every thing became Science11 in [Watt's] hands ... he learned the German language in order to peruse Leopold's Theatric.u.m Mechanic.u.m [an encyclopedia of mechanical engineering] ... every new thing that came into his hands became a subject of serious and systematical study, and terminated in some branch of Science." He continued: Allow me to give an instance.12 A Mason Lodge in Glasgow wanted an Organ [and] tho' we all knew that he did not know one musical note from another, he was asked if he could build this Organ.... He then began to study the philosophical theory of Music. Fortunately, no book was at hand but the most refined of all, and the only one that can be said to contain any theory at all, Smith's Harmonics. Before Mr. Watt had half-finished this Organ, he and I were completely masters of that most refined and beautiful Theory of the Beats of imperfect Consonances. He found that by these Beats it would be possible for him, totally ignorant of Music, to tune this Organ according to any System of temperament, and he did so, to the delight and astonishment of our best performers.... And in playing with this he made an Observation which, had it then been known, would have terminated a dispute between the first Mathematicians of Europe, Euler and d'Alembert, and which completely establishes the theory of Daniel Bernoulli about the mechanism of the vibration of Musical Chords....

Watt may have been comfortable in the rarefied company of mathematicians like Bernoulli and Leonhard Euler; the business alluded to by Robison is the discovery that any of the overtones of an organ pipe produce frequencies that are exact multiples of the pipe's base pitch. However, like Newcomen (but unlike Boyle, or even Savery), he was as preoccupied by his desire to earn a living as by his pa.s.sion for discovery. Like an ever-growing percentage of his countrymen in the newly United Kingdom, Watt had acquired the tools necessary for scientific invention-the hands of a master craftsman, and a brain schooled in mathematical reasoning-without the independent income that could put those tools to work exclusively for the betterment of mankind. As a result, in 1759, Watt became half of a partnership with John Craig manufacturing optical instruments. In 1763, he became shareholder in the Delftfield Pottery Company. And every year, he spent a portion of the spring and summer working as a surveyor for the roads and ca.n.a.ls just starting to crisscross Britain.

It was upon his return from a surveying trip, in the winter of 1763, that Watt was asked to repair a model of a Newcomen engine in the possession of the university by John Anderson,* who had become Glasgow's professor of natural philosophy with the death of Robert d.i.c.k in 1757. "Repair" is something of a misnomer; the model was not broken, but unlike a full-sized engine, it stopped working after only two or three strokes. Anderson had been importuning the university's new instrument maker for at least four years before Watt "set about repairing it13 as a mere mechanician." Shortly thereafter, he realized that the problem was intrinsic to the size of the model, since "the toy cylinder exposed a greater surface14 to condense the steam in proportion to its content." Watt had intuited the presence of a cube-square problem.

The so-called cube-square law is a recognition of the fact that the surface of any solid object increases in size far more slowly than its volume. Thus, a cube with four-inch sides has a surface area of ninety-six square inches and a volume of sixty-four cubic inches, while an eight-inch cube has a surface of 384 square inches, but a volume of 512 cubic inches. Doubling the cube's edge increases its surface area fourfold, but its volume eight times.

The cube-square law is yet another bequest from the Scientific Revolution to the Industrial; for a change, one with a clear provenance. The phenomenon was first doc.u.mented in the final book of Galileo Galilei, the 1638 Dialogues Concerning the Two New Sciences, in which Galileo's alter ego, the imaginary "Salviato," demonstrates it to the Aristotelian loyalist "Sagredo" and the dim-minded "Simplicio" (Galileo's choice of names was as heavy-handed as d.i.c.kens's). The cube-square law has huge implications for construction, for engineering, and even for biomechanics; it is the reason, for example, that an elephant's legs are so much larger in cross-section than a dog's. More relevantly for the history of steam power, it reveals the most obvious weakness of scale models, which is that a structure's performance can degrade substantially when it is blown up to twenty times its original size. Designs that work when small-a bridge made of toothpicks, for example-can easily fail as the weight to be borne increases disproportionately faster than the strength of the "timbers" bearing it.

But the problem also operates in reverse. The cube-square law can just as easily cause a design to fail when it is miniaturized. This was Watt's initial insight about the model Newcomen engine. Because the scale model, still in the Hunterian Museum at the university, was using far more steam than could be accounted for by any science or experience Watt (or anyone else) had, his first a.s.sumption was that the problem was one of the scale itself, specifically the fact that in a small engine the interior surface was far larger in proportion to the volume; if the heat loss was proportional to surface, then the difference could perhaps be explained.

Explaining it took two years.

Watt's experiments from 1763 to 1765 were an object lesson in the primacy of measurement over intuition, since recognizing the existence of heat loss matters a good deal less than knowing its magnitude; suspecting the nature of the problem wasn't the same as understanding it. Watt needed to calculate exactly how much heat was being lost in the Newcomen design, and that meant converting general theories about steam into precise measurements, which were, to be kind, thin on the ground at the time, even for such elementary benchmarks as the boiling point of water.

Obviously, the story of steam demands constant reference to that benchmark, which even a bright ten-year-old knows is precisely 212F, or 100C, at normal atmospheric pressure. However, as with many such bits of common knowledge, it turns out to be a bit more complicated. Boiling occurs when a liquid's vapor pressure reaches atmospheric pressure, but while vapor pressure is proportional to heat, it isn't the same throughout a volume of liquid. Boiling temperatures change depending on the material containing the liquid, since water adheres better to metal than to gla.s.s and can therefore boil at a somewhat lower temperature in a metal vessel. The temperature can increase or decrease with the shape of the container, the presence of dissolved air, the location of the heat source, and, of course, the amount of air pressure. Thus, the "normal" boiling temperature of water-100C-can climb as high as 200C, as an obsessively compet.i.tive scientist named Georg Krebs demonstrated in 1869. Most textbooks plot a "boiling curve"15 with the boundary between liquid and gas a moving target depending on at least four different variables.

Even in Watt's time, the clear line between liquid and vaporized water was pretty fuzzy. A thermometer dating from the 1750s is marked with two different "boyling" temperatures;16 at 204, water "begins to boyle," and then at 212, "boyles vehemently," a distinction that dates back to Isaac Newton. The measurement problem was acute enough17 that in 1776 the Royal Society appointed a committee, headed by Henry Cavendish (better known as the discoverer of hydrogen) in order to establish the "fixed points" of thermometers.

Watt began his researches on the Newcomen engine fourteen years before the Cavendish committee delivered its conclusions in 1777 and was, in consequence, working with a clunkier set of measurements. He wasn't, however, completely in the dark. Toward the end of his life, Watt himself provided an inventory of the basic knowledge already in circulation before his first great innovation. One small example of it18 was the twenty-year-old discovery, by the physician William Cullen (Joseph Black's teacher, and yet another member of the remarkable faculty of the University of Glasgow), that water boiled at a lower temperature in a vacuum, thus releasing steam that would degrade the cylinder's vacuum. This turned out to be critical, because the fact that the Newcomen engine operated in a vacuum meant that cooling the steam to the point of condensation required cooling it to temperatures even lower than 100C/212F. In order to calculate how much lower, Watt needed to develop an exact scale showing how changes in pressure map to boiling temperatures. Most important, he needed an accurate way of measuring the volume of steam produced by vaporizing a given volume of water, and the water condensed from a measured amount of steam. Watt was a demon for measurement, and he spent months computing the volume of steam as compared to water, the quant.i.ty of steam used by a single stroke of a Newcomen engine, the quant.i.ty of water needed to condense it, and so on. As a case in point, though Samuel Moreland had estimated that boiling a given volume of water would produce steam that would fill a s.p.a.ce 2,000 times greater, J. T. Desaguliers calculated the number as 14,000, and Watt needed to find out for himself. In one of his notebooks,19 he describes an experiment in which he boiled an ounce of water in a "Florence Flask," forced the air and water out, and compared before and after weights, concluding that the accurate relationship between liquid and solid volumes was 1,849 times. Once deriving the critical relationship between the phases of water, as Watt later recalled, I mentioned it to my friend Dr. Black,20 who then explained to me his doctrine of latent heat.... I thus stumbled upon one of the material facts by which that beautiful theory is supported.... Although Dr. Black's theory of latent heat did not suggest my improvements on the steam-engine ... the correct modes of reasoning, and of making experiments of which he set me the example, certainly conduced very much to facilitate the progress of my inventions.

Nothing is more common in the history of science than independent discovery of the same phenomenon, unless it is a fight over priority. To this day, historians debate how much prior awareness of the theory of latent heat was in Watt's possession, but they miss Black's real contribution, which anyone can see by examining the columns of neat script that attest to Watt's careful recording of experimental results. Watt didn't discover the existence of latent heat21 from Black, at least not directly; but he rediscovered it entirely through exposure to the diligent experimental habits of professors such as Black, John Robison, and Robert d.i.c.k.

In the end, it was the habits of recording and comparing results, time after time, that proved truly indispensable for Watt's "rediscovery" of Joseph Black's conjecture of latent heat, one that puzzled not only Watt, but generations of physics students ever since. Boil a quart of water, turning it into steam; it takes up a bit more than 1,800 times the s.p.a.ce it did when liquid. But an atmospheric steam engine doesn't want steam, it wants a vacuum, so it has to condense that steam back into water. Newcomen did so by injecting a stream of water into the sealed cylinder of his engine, but he never measured the amount needed. Watt, diligent experimentalist that he was, did: It took up to six quarts of water at room temperature to condense the steam. A year into the process, Watt had not only rediscovered Black's theory, he was finally able to quantify it. The exhaustive process of experimenting, measuring, and experimenting again had allowed him to calculate how much steam was necessary for each piston stroke, and how much the Newcomen engine was actually generating. He now had quant.i.ties he could measure.

The measurements showed him where the problem was. The engine depended on steam's filling the cylinder before it was ready to produce a vacuum. But every time fresh steam was admitted into the now cooled cylinder, it didn't expand; it just continued to condense, turning back into water until the cylinder heated up to the temperature of the steam itself. Heating the cylinder walls22 wasted up to three-quarters of the steam, or even more: In one test made in 1765, Watt found that an old-style engine was boiling more than three times as much water to heat the cylinder as it was using to create a vacuum.

The problem was exacerbated by the fact of the vacuum itself, which effectively lowered the vaporization temperature of the water, in the same way that water boils at a much lower temperature at high alt.i.tudes: lower pressure, lower boiling temperature. The water, which needed to be heated to 100C/212F to boil at normal pressure, needed only half that to boil in a vacuum. And if water turns to steam at relatively lukewarm temperatures, then condensing it requires either a modest amount of very cold water (obviously impractical without refrigeration) or a huge amount at room temperature, which degraded the engine's efficiency even further.

The Newcomen engine was caught between fundamentally incompatible goals: The engine should use as little water as possible to condense the steam (in order to avoid cooling the cylinder), but as much water as possible to make sure that condensation occurred rather than more vaporization. Put another way: The cylinder needed to be kept at a constant 212F/100C (to avoid condensation that didn't create a vacuum) and it needed to be kept at a constant 100F/45C (to avoid vaporization). Watt, in Usher's terms, had perceived an "unsatisfactory pattern."

Still, after two years of measurement, a.n.a.lysis, and experiment, the unsatisfactory pattern was all he had. Frustrating though that was, he kept at it, to satisfy not merely his curiosity, but also his wallet; in his own words, his mind "ran on making engines cheap23 as well as good." From the beginning, Watt recognized the problem in terms of wasted fuel, which meant wasted money, and therefore an opportunity. An idea that could significantly reduce that waste was clearly going to make someone rich. That someone didn't need to be a skilled artisan. He didn't have to live in a culture that had only recently articulated a property right in ideas and drafted legislation protecting that right. Scientists and philosophers, as we have seen, had been paving the way for centuries before Watt, or even Newcomen. Eighteenth-century Britain wasn't any more hospitable to their brilliant innovations than anywhere else; but it was a lot more hospitable to innovators who couldn't afford to invest years of their lives with no hope of material gain. Watt was brilliant, unusually so. But he was also emblematic of hundreds, soon to be thousands, of men like himself, each of them searching for a "eureka" moment.

ALFRED NORTH WHITEHEAD FAMOUSLY wrote that the most important invention of the Industrial Revolution was invention itself. A number of others compete for second place, but the insight that came to James Watt in the spring of 1765 has a lot of support. By then, he had tried dozens of different ways to find a cylinder that would both heat up and cool down rapidly, even trying different materials for the cylinder itself, experimenting with bra.s.s, cast iron, and even wood "soaked in linseed oil, and baked to dryness," each trial repeated half a dozen times. Nothing had worked, until he had his epiphany,* one he later described as the realization that since steam was an elastic body24 it would rush into a vacuum, and if a communication were made between the cylinder and an exhausted vessel it would rush into it, and might be there condensed without cooling the cylinder. I then saw that I must get rid of the condensed steam and injection-water if I used a jet as in Newcomen's engine. Two ways of doing this occurred to me. First, the water might be run off by a descending pipe, if an outlet could be got at the depth of thirty-five or thirty-six feet, and any air might be extracted by a small pump. The second was to make the pump large enough to extract both water and air....

What he had envisioned was simple enough: a second chamber, connected to the cylinder by a pipe, through which the steam would flow. When it arrived in the new chamber, already surrounded by cool water, the steam would condense, a vacuum would be formed, and atmospheric pressure would pull the piston down-but the cylinder in which the piston traveled could stay hot as a new jet of steam entered it. One chamber would stay cool, the other hot, each time the engine cycled.

The separate condenser would prove not only central to the development of steam power and the entire Industrial Revolution that ran on it, but also an utterly necessary step on the way to the very different sort of engine that powered Rocket. It is also, happily, a rich test case of the mutually reinforcing relationship between abstract theorizing and rule-of-thumb engineering. Literally rule-of-thumb: As with all mechanical inventions, the insight that inspired the separate condenser could be visualized, but it wasn't worth much of anything until it could also be handled-note the linguistic clue. The human eye can see things that don't yet exist, but making them requires the human hand, and it was now time for Watt to return to his university workshop and let his skilled hands turn his insight into a model.

That year training on bra.s.s compa.s.ses and quadrants in London now proved its worth. Within weeks, he had handcrafted all the components for an engine: two cylinders, one piped to a boiler and containing a piston with a valve on the bottom to vent excess water, the other a ten-inch-long bra.s.s syringe with a diameter of 1 containing two ten-inch tin "straws" each about in diameter, and a hand-operated air pump with a diameter.

Fig. 3: The "stovepipe" on the left is Watt's separate condenser. Four years after his brainstorm on Glasgow Green, this was the result: a working cylinder that didn't need to be cooled and reheated for each stroke, thus doubling the utility of Newcomen's design. Science Museum / Science & Society Picture Library The two cylinders were connected by a horizontal pipe, and the syringe immersed in a cistern of cold water. Watt lit his boiler and let the steam flow into the piston cylinder, closed the steam c.o.c.k, and pumped out the air in the syringe, thus pulling in the steam, which immediately condensed around the cold tin straws. The piston in the cylinder immediately lifted a weight of 18 pounds; a cylinder holding barely a pint of water was raising a weight equivalent to more than two gallons. Watt, a perfectionist by temperament, education, and training, had finally (though briefly) satisfied himself. Thirty years later, he would describe the model as being "nearly as perfect25 ... as any which have been made since that time." He was not normally an especially confident man-perfectionists rarely are-but in April 1765 he was optimistic enough to write to his friend James Lind, "I can think of nothing else26 but this Machine. I hope to have the decisive tryal before I see you...."

It is not known when he actually saw Lind, but by the summer of 1765, on the back of 1,000 borrowed from Joseph Black, "the invention was complete27 ... a large model, with an outer cylinder and wooden case, was immediately constructed, and the experiments made with it served to verify the expectations I had formed, and to place the advantage of the invention beyond the reach of doubt."

The time had come for the next step. And the next step was going to cost money-a lot more than he could borrow from colleagues at the university. Watt needed capital. Investment capital, however, wasn't easy to find in 1765 Britain; and it was a lot harder than it had been fifty years earlier. The reason was one of the greatest financial bubbles in history, the collapse of the South Seas Company.

THE SOUTH SEAS COMPANY had been incorporated in 1711, with a charter that granted what was potentially a far more lucrative monopoly than anything Edward c.o.ke had contemplated a century earlier. In return for buying 10 million of government debt, the Company was given exclusive trading rights throughout Central and South America, whose bounty included wool, rum, sugar, and, most profitably, slaves. Promoted like an eighteenth-century Enron, the South Seas Company offered not only the promise of unimaginable wealth, but stock that could be purchased by virtually anyone. This was both a novel and an appealing idea in a time when the world's largest corporation, the British East India Company, had fewer than five hundred investors. Since, however, the Company's only real a.s.set was the British government's promise of access to ports that were entirely controlled by the Spaniards, making money from trading proved difficult. The Company was, even so, brilliant at promoting its own prosperity, placing newspaper stories, hosting parties, and maintaining luxurious offices in the most expensive buildings in London. In January 1720, stock was issued at a par price of 100 a share; by August, at the peak of the bubble, when the average British artisan was earning less than 100 a year, a single share of the Company traded for 1,000. And even worse, it inspired other businesses to issue stock on what might be called speculative ventures, including a company capitalized at 1 million in order to produce a perpetual motion machine. One of the more candid styled itself "A Company for carrying on an undertaking28 of great advantage, but no one to know what it is."

The result, once the bubble burst and the dust cleared, was that Parliament essentially barred the issuing of stock for any business purpose, which limited the potential pool of investors to what would today be called venture capitalists. In the case of Watt's invention, this meant partnering with an entrepreneur with both ready cash and a liking for technology.

John Roebuck was then a forty-seven-year-old serial entrepreneur who had started half a dozen different businesses, each of them intending to exploit a technological innovation, including the first industrial refinery that manufactured sulfuric acid* by combining sulfur dioxide with oxygen and the resulting compound with water, all in a lead-lined chamber. The acid refinery prompted his first patent application, but by no means his last. By the time he met Watt in 1765, he was also master of one of the world's most innovative forges, the legendary Carron Ironworks, and holder of patent number 780-the number of patents granted annually was still, a century after the Statute on Monopolies, measured in dozens-for a new process for making bar iron.

A correspondence between the ambitious young instrument maker and the nearly twenty years older businessman began in the summer of 1765, prompted by Joseph Black, who counted both as friends. In September, Watt wrote to Roebuck inviting an investment in his discovery that producing steam within a vacuum was dramatically more efficient than producing it in air, his excitement such that "I am going on with the Modell29 of the Machine as fast as possible and hope to have it finished in another week."

Rereading the letters, it is impossible to miss the tension present from the beginning. Roebuck fancied himself at least as gifted a scientist as Watt, and insisted on an extreme form of due diligence, demanding to see Watt's drawings, notes, and models. He demanded that Watt try to create a vacuum without a jet of water condensing the steam, and even urged him to discard the separate condenser, which was, after all, the point of the entire exercise. Watt, for his part, was generally courteous, but convinced of both his own talent and of the power of the separate condenser. For months, the two engaged in the sort of epistolary courtship that puts one in mind of the way that porcupines mate. Only when Roebuck, who was nothing if not intelligent enough to recognize Watt's gifts, satisfied himself that the separate condenser promised everything Watt believed, did he agree to a partnership. The terms of the agreement obligated Roebuck to absorb all future expenses related to building a machine that would, in Watt's words, produce the same amount of work for half the amount of fuel. He further agreed to pay off Watt's debt to Black in return for two-thirds of future profits.

Watt's frustrations were just beginning. Vacuum is notoriously unstable, but it needed to be kept intact in order for the engine to do its work. Newcomen's vacuum seal had been nothing more than a leather collar with a layer of water on top, but Watt had to avoid using it on his own engine, since the water would, of necessity, cool the hot cylinder and so eliminate most of the advantage of the separate condenser. But everything else he tried was either too porous-steam escaped and air entered-or created too much friction in the cylinder, costing a huge amount of energy. As a result, he tried dozens of combinations30 of materials for both piston and cylinder: wood, tin, copper, and cast iron, in square and round shapes, sealed with leather, cloth, cork, oak.u.m, asbestos, and numerous alloys of lead, and lubricated with mercury, graphite, tallow, manure, and vegetable oil. "Cotton was proposed31 by my friend Chaillet; I thought of trying it but was deterred first by its price, secondly, by the very thing you have found: that it could not be easily made to cohere without glue or weaving the substances. I have hopes of pasteboard ... mixed with dung; I propose to separate the gall and sand from the dung by washing. I have found by experiment that for making joints steam tight, there is nothing equal to it as it is of no consequence whether the joint be naturally round or not...."

While pasteboard finally worked well enough, it did nothing to solve the central mechanical problem, which was getting the piston to fit into the cylinder as tightly as possible with as little friction as possible-as usual, two objectives fundamentally in conflict with each other. Over the first two years of experimentation, Watt built, again by hand, three models, each with a different cylinder: the original, with a cylinder of 1 bra.s.s, but no steam jacket; a 1 cylinder with steam jacket; and one five or six inches long with a steam jacket made of wood. The tin straws, which worked as a surface condenser, were discarded because of difficulties with consistency and replaced by jet condensers similar to those used by Newcomen.

Not all, or even most, of the revisions-in a nod to Usher's stages of invention, perhaps better to call them "critical revisions"-were the inspirations of a solitary inventor. A friend, Dr. William Small,* advised by letter, "Dear Jim ... Let me suggest a method32 of making your wheel and valves tight: Let the valve frame be made easy for the groove and about half thick; put a ply of pasteboard below the frame ... and place it in the groove in its proper place, then lay a ring of pasteboard all around each side of the groove and over each valve frame, taking care no pasteboard projects over the frames or grooves...."

By 1768, Watt, three years into his deal with Roebuck, acknowledged that "what I knew about the steam engine33 [in 1765] was but a trifle to what I know now." His frustrations were growing p.r.o.nounced. Any slight defect in any component was enough to compromise the design, and therefore the designer's temper. Newcomen's engine had only to be better than a horse-driven pump; Watt's had to be better than Newcomen's, and that meant cheaper. The unforgiving arithmetic of coal obliged him to produce not merely an elegant design, but one that consumed less fuel, and virtually anything less than perfection in the boring of the cylinder or the strength of the solder consumed more.

Watt's perfectionist habits, which had given rigor to his early experiments and made the original separate condensing model work so encouragingly, were no longer much of an advantage. Because while Watt could build a small model to the most exacting specifications, a larger, and therefore practical, version needed a design that could be executed by others; "my princ.i.p.al hindrance34 in erecting engines," he wrote to Roebuck in 1765, "is always the smith-work." Supposedly, the smiths at Roebuck's Carron foundry were the best in England, but even their skills were not up to making a cylinder to tolerances that resulted in one that was (a) perfectly round (so that the piston would fill it) and (b) airtight.

Watt's only "relief amidst [his] vexations"35 was, perversely enough, the need to make a living. Though Roebuck was paying the expenses while Watt was attempting to produce a working engine, and had even set the inventor up in a workshop at Kinneil, near the town of Borrowstounness (more popularly, Bo'ness) in central Scotland, he was not paying Watt a salary. To support his family-in 1764, Watt had married his cousin, Margaret Miller, who would give him five children before her death in 1772-the inventor adopted his father's trade, surveying the ca.n.a.ls of northern England, which, he wrote, "have given me health and spirits36 beyond what I commonly enjoy at this dreary season.... Hire yourself to somebody for a ploughman; it will cure ennui."

At Kinneil, however, the pressure was unrelenting. By the middle of 1768, Watt had built an eighteen-inch cylinder out of tin, but the same malleability that made it an excellent material for sealing in the vacuum also made it something less than robust. Roebuck didn't care. He badly wanted some indication that his investment would be redeemed sometime soon, and he insisted that Watt apply for a patent. And so, in January 1769, Watt, somewhat reluctantly, traveled to London, where, despite the still imperfect design of his engine, he had been granted patent number 913 for "a method of lessening the consumption of steam and fuel in fire-engines." His first meeting after collecting the doc.u.ment from the Great Seal Patent Office was with neither Roebuck-the man who had financed the patent-nor Joseph Black, the friend who had inspired it, but with a Birmingham manufacturer named Matthew Boulton.

BOULTON WAS THEN THIRTY-NINE years old, eight years older than Watt, born into a family that made small metal goods: buckles, b.u.t.tons, graters, household tools-"toys," in the vernacular of the day. When he was still in his teens, he entered the family business, most of whose functions were, typically for the time, jobbed out to others: raw materials were bought from one firm, sales handled by another, transportation by a third. Sometimes the other firms were dependable, sometimes not. But they were always costly, which seemed to Boulton an opportunity. By the time he was twenty-five, he had not only enlarged the business but was in the process of changing it irrevocably. Determined to integrate all possible aspects of manufacturing, Boulton moved the metal stamping operations from one water mill to another, starting construction in 1762 on what would become the world's largest and most famous factory with the relatively modest outlay of 9,000.* Eventually settling two miles from the center of the city of Birmingham, the Soho Manufactory would grow to include workshops, showrooms, stores, offices, worker dormitories, and design studios. It also incorporated a decidedly progressive bent in workforce relations: Boulton used no child labor, and he even offered his laborers, in return for one-sixtieth of their wages, social insurance that paid benefits in the event of illness or injury.

By the time he was thirty, he was already acknowledged as not only a visionary businessman, but also a hugely successful one. Soho's output of jewelry, silverware, and gilt decorative products, as well as the traditional iron and tin "toys," made Boulton, in the words of Josiah Wedgwood (himself a rather remarkable story in the history of ceramics), "the Most compleat Manufacturer37 of Metals in England." And he was more. James Watt is very likely the best known of all the inventors a.s.sociated with the introduction of steam power. Partly this is because his life is such a useful bit of shorthand for the entire world of invention that fueled the perpetual innovation machine we call the Industrial Revolution. But the unique elements that made Britain so hospitable to inventions produced by her artisan cla.s.s, including the legal and cultural incentives articulated in c.o.ke's Statute and Locke's Treatises, were only half of the transaction. Increasing the supply of inventors by permitting them to sell their ideas was useless without a market in which those ideas could be sold. And since ideas don't sell themselves any better than anything does, someone needed to sell them. If James Watt was primus inter pares on the supply side of the steam economy, Matthew Boulton was unquestionably the man best equipped to introduce him to those willing to pay for his supply of ideas.

Watt had already visited the Soho Manufactory once before, in 1767. It is not known whether Watt, whose distaste for dealmaking was one of his most consistent affects-"I would rather face a loaded cannon38 than settle an account or make a bargain"-managed to drop the hint that his partnership might be subject to improvement, but nothing came of it for more than a year, during which Roebuck's fortunes deteriorated dramatically. In one of the most reliable tropes of his life, Roebuck's talent for finding innovative business opportunities was sabotaged by his chronic inability to make them pay off, and his investment in a coal mine was, literally, underwater. He needed cash, and thought he knew the best way to get it.

In December 1768, at the same moment that Watt's patent application was moving through the London bureaucracy, Roebuck sent a letter to Boulton offering to sell him an exclusive franchise for the Watt engine in three English counties: Warwick, Stafford, and Derby; Boulton declined. In January, Watt, in possession of his first patent, stopped in Birmingham on his way back to Scotland; one can only guess what they discussed, but there can be little doubt that both Watt's plans and Roebuck's offer were shared. In the event, on February 7, 1769, Boulton sent James Watt a letter that read in part: I was excited by two motivs39 [sic] to offer you my a.s.sistance which were love of you, and love of a money-getting ingenious project. I presum'd that your engine would require mony [sic], very accurate workmanship, and extensive correspondence, and the best means ... of doing the invention justice would be to keep the executive part out of the hands of the mult.i.tude of empirical Engineers who from ignorance, want of experience ... would be very liable to produce bad and inaccurate workmanship.... My idea was to settle a manufactory near to my own by the side of our Ca.n.a.l [i.e. in Birmingham] where I could erect all the conveniences necessary for the completion of Engines and from which Manufactory We would serve all the World with Engines of all sizes ... it would not be worth my while to make for three Countys only, but I find it very worth while to make for all the World...." (emphasis added) James Watt's new engine was a visionary leap-the separate condenser alone doubled the amount of useful work that the Newcomen engine could extract from a given amount of fuel-but its place in history depended on more than Watt's engineering brilliance, perfectionist temperament, or even the grant of a property right to the idea. Watt (and, for that matter, Roebuck) would have been happy to grow prosperous replacing the Newcomen engines at England's coal mines. Changing the world demanded a far larger ambition, and Matthew Boulton was just the man to supply it. It's no coincidence that Boulton's grandiloquent promise to "make for all the world" (one that he would, in the event, redeem), like Albert Einstein's 1939 letter to Franklin Roosevelt warning about possible German development of the atomic bomb, was written in response to a history-shaking example of what is a very nearly universal human phenomenon: the flash of inventive insight.

The nature of which is the subject of chapter 6.

* Place names like Aberdeen and Culloden testify to the Scottish influence on Jamaican history.

* It wasn't Defoe's first comment on the new world being created in Britain. In his 1697 Essay on Projects, he named his era "the Projecting Age," by which he meant the "projectors" who sought to build commercial empires supported by patents and monopolies (and, to be fair, "projects" like overhyped investments, about which more below).

* And only yards away from the Department of Moral Philosophy, where Adam Smith, whom we will meet in chapter 11, had held a professorship since 1751.

* Anderson, whose nickname among the university's students was "Jolly Jack Phosphorus," is a fascinating character in his own right: A professor of Hebrew and Semitic languages as well as natural philosophy, he is best remembered as an early advocate of higher education for artisans and craftsmen, for whom he held cla.s.ses throughout his forty years at Glasgow. So dedicated was he to this underutilized national resource that his estate was used to found Anderson College, now part of the University of Strathclyde.

* For more about the nature of that flash of insight, see chapter 6.

* An entire book-be undismayed, not this one-could be written on the history of sulfuric acid as a symbol for the evolution of modern civilization. Under the name "oil of vitriol," it was the most important weapon in the a.r.s.enal of medieval alchemists-the original philosopher's stone-and remains critical not only for producing fertilizer and bleaching textiles, but as a precursor chemical for sodium carbonate, which is essential for the manufacture of both paper and gla.s.s. Even now, a number of international economists use its production as a proxy for a nation's level of industrial development.

* Small would have been a key a.s.set in any game of eighteenth-century "Six Degrees of Kevin Bacon" as a correspondent of Watt, a friend of Benjamin Franklin, and, before his return to Scotland from North America, Thomas Jefferson's onetime professor at the College of William & Mary.

* Modest indeed-a fraction of what he would eventually spend on rejiggering Watt's patent.

CHAPTER SIX.

THE WHOLE THING WAS ARRANGED IN MY MIND.

concerning the surprising contents of a Ladies Diary; invention by natural selection; the Flynn Effect; neuronal avalanches; the critical distinction between invention and innovation; and the memory of a stroll on Glasgow Green It was in the Green of Glasgow.1 I had gone to take a walk on a fine Sabbath afternoon. I had entered the Green by the gate at the foot of Charlotte Street-had pa.s.sed the old washing-house. I was thinking upon the engine at the time, and had gone as far as the Herd's-house, when the idea came into my mind, that as steam was an elastic body it would rush into a vacuum, and if a communication was made between the cylinder and an exhausted vessel, it would rush into it, and might be there condensed without cooling the cylinder. I then saw that I must get quit of the condensed steam and injection water, if I used a jet as in Newcomen's engine. Two ways of doing this occurred to me. First, the water might be run off by a descending pipe, if an offlet could be got at the depth of 35 or 36 feet, and any air might be extracted by a small pump; the second was to make the pump large enough to extract both water and air.... I had not walked farther than the Golf-house when the whole thing was arranged in my mind.

THE "WHOLE THING" WAS, of course, James Watt's world-historic invention of the separate condenser. It is one of the best recorded, and most repeated, eureka moments since Archimedes leaped out of his bathtub; but accounts of sudden insights have been a regular feature in virtually every history of scientific progress. The fascination with the eureka moment has endured mostly because it turns out to be largely accurate, in general terms if not in detail (no apple actually hit Sir Isaac's cranium, but one falling from a tree in Newton's garden at Woolsthorpe Manor really did inspire the first speculations on the nature of universal gravitation).

Watt's own flash of insight is worth examining not only for its content, but for what it says about insight itself. Those eureka moments are so central to the process of invention that understanding the revolutionary increase in inventive activity demanded by the steam engine also means exploring what modern cognitive science knows (and, more often, suspects) about the mechanism of insight. Watt's moment is just one instance-an earth-shaking one, to be sure-of a phenomenon that is, among humans, nearly as universal as the acquisition of language: solving problems without conscious effort, after effort has failed.

This is not, of course, to say that effort is irrelevant. The real reason that insights seem effortless is that the effort they demand takes place long before the insight appears. It takes a lot of prospecting to find a diamond (to say nothing of the time it took to make one), which is why-scrambled metaphors aside-"effortless" insights about musical composition don't occur to nonmusicians. And why, of course, insights about separate condensers don't occur to scholars of ancient Greek. Expertise matters.

This seemingly obvious statement was first tested experimentally in the 1980s by a Swedish emigre psychologist, now at the University of Florida, named K. Anders Ericsson, who has spent the intervening decades developing what has come to be known as the "expert performance" model for human achievement. In study after study of experts in fields as diverse as music, compet.i.tive athletics, medicine, and chess, Ericsson and his colleagues were unable to discover any significant inborn difference between the most accomplished performers and the "merely" good. That is, no test for memory, IQ, reaction time, or any other human capacity that might seem to indicate natural talent differentiated the master from the journeyman.

What did separate them was, therefore, not inherited, but created; time, not talent, was the critical measurement. Though Ericsson found that both the violinists and basketball players started playing at roughly the same age, the stars in both pursuits spent more time at it than their less accomplished colleagues. Twice as much time, in fact; against all expectations, an expert musician spent, on average, ten thousand hours practicing, as compared to five thousand spent by the not-quite-expert.

The model turned out to apply to a range of pursuits. Cabinetmakers and cardiologists, golfers and gardeners, all became expert after roughly the same amount of time spent mastering their craft. Of all the legends of James Watt's youth, the one no one doubts is that he spent virtually every waking hour of his "apprenticeship" year with John Morgan mastering the skills of fine bra.s.swork, gearing, and instrument repair. His pride in the fine navigational instrument he built as his graduation project is indistinguishable from that felt by a gymnast doing her first back handspring.

James Watt, however, is remembered not as a master clockmaker, but as one of the greatest inventors of all time. And this is where the expert performance model becomes even more relevant. By the 1990s, Ericsson's research was demonstrating2 that the same phenomenon he had first discovered among concert violinists also applied to the creation of innovations: that the cost of becoming consistently productive at creative inventing is ten thousand hours of practice-five to seven years-just as it is for music, athletics, and chess.

Some of that time is spent acquiring a history of the field: knowledge of what other violinists and inventors have achieved before in order to avoid, in the telling phrase, "reinventing the wheel." The knowledge need not be explicit; the philosopher of science Michael Polanyi* famously thought that leaps of invention were a function of what he called tacit knowing: the idea that, in Polanyi's words, "we know more than we can tell." To Polanyi, the acquisition of such internalized knowledge, via doing, rather than studying, is necessary preparation of the soil for any true insight.

But knowing that inventors acc.u.mulate knowledge of other invention doesn't explain how they acc.u.mulate skills during those ten thousand hours of repet.i.tion. Inventing, after all, isn't a craft like basketball, in which mastery is acquired by training muscle and nerve with constant repet.i.tion.

Nonetheless, in light of Ericsson's discovery that the route to expert performance looks very similar whether the performance in question is a basketball game, or a chess match, or inventing a new kind of steam engine, it seems worth considering whether the brain's neurons behave like the body's muscles. And, it turns out, they seem to do just that: The more a particular connection between nerve cells is exercised, the stronger it gets. Fifty years ago, a Canadian psychologist named Donald Hebb first tried to put some mathematical rigor behind this well-doc.u.mented phenomenon, but "Hebbian" learning-the idea that "neurons that fire together, wire together"-was pretty difficult to observe in any nervous system more complicated than that of a marine invertebrate, and even then it was easier to observe than to explain.

In the 1970s, Eric Kandel, a neuroscientist then working at New York University, embarked on a series of experiments that conclusively proved that cognition could be plotted by following a series of chemical reactions that changed the electrical potential of neurons. Kandel and his colleagues demonstrated that experiences literally change the chemistry of neurons by producing a protein called cyclic Adenosine MonoPhosphate, or cAMP. The cAMP protein, in turn, produces a cascade of chemical changes that either promote or inhibit the synaptic response between neurons; every time the brain calculates the area of a rectangle, or sight-reads a piece of music, or tests an experimental hypothesis, the neurons involved are chemically changed to make it easier to travel the same path again. Kandel's research seems to have identified that repet.i.tion forms the chains that Polanyi called tacit knowing, and that James Watt called "the correct modes of reasoning."

Kandel's discovery of the mechanism by which memory is formed and preserved at the cellular level, for which he received the n.o.bel Prize in Physiology in 2000, was provocative. But because the experiments in question were performed on the fairly simple nervous system of Aplysia californica, a giant marine snail, and doc.u.mented the speed with which the snails could "learn" to eject ink in response to predators, it may be overreaching to say that science knows that the more one practices the violin, or extracts cube roots, the more cAMP is produced. It's even more of a stretch to explain how one learns to sight-read a Chopin etude. Or invent a separate condenser for a steam engine.

Which is why, a decade before