Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World (40 page)

Not all forms of natural philosophy were equally suited for the Society’s goals of promoting peace, tolerance, and public order. Particularly suspect were grand philosophical systems that claimed to arrive at indisputable truths through the power of pure reason. One such system, which was very much on the minds of the Society’s founders, was Cartesian philosophy (named after its originator, René Descartes), which was sweeping the Continent at that very time. In his writings, Descartes purported to dismantle all unsubstantiated presuppositions, reducing all knowledge to a single unshakeable truth: “I think, therefore I am.” From this rock of certainty he then recreated the world through rigorous step-by-step reasoning, accepting the validity of only clear and distinct ideas. And since his reasoning was flawless, Descartes (and his followers) argued, his conclusions must inevitably be true.

Boyle, Wallis, Oldenburg, and the other leaders of the early Society were deeply impressed by Descartes, but also very critical of his approach and conclusions. They were even more concerned with another system anchored in pure reasoning that was lurking in their own backyard, and that of course was Hobbes’s philosophy. Hobbes and Descartes differed radically on many critical issues, but this much they had in common: both believed that their system was structured like Euclidean geometry, founded on self-evident assumptions and proceeding through rigorous reasoning to truths. And it was precisely this unquestioning confidence in the validity of their systematic reasoning and the absolute truth of their conclusions that the founders of the Royal Society found particularly dangerous.

The problem with dogmatic philosophy, Sprat explained in his
History of the Royal Society
, “is that it commonly inclines such men, who think themselves already resolv’d, and immovable in their opinions, to be more imperious, and impatient of contradiction.” Such an attitude is detrimental to science because “it makes them prone to undervalue other men’s labours, and to neglect the real advantage that may be gotten by their assistance. Least they should seem to darken their own glory.” It “is a Temper of mind, of all others the most pernicious,” Sprat continued, and one to which he attributes the “slowness of the increase of knowledge amongst men.” Even worse, this kind of arrogance easily leads to the subversion of the state: “The
reason
of men’s contemning all
Jurisdiction
and
Power
proceeds from their idolizing of their own
Wit
 … they suppose themselves
infallible
.” This leads inevitably to sedition, because “the most fruitful parent of
Sedition
is
Pride
, and a lofty conceit of men’s own
wisdom
; whereby they presently imagine themselves sufficient to direct and censure all the
Actions
of their
Governors
.”

Sprat was only twenty-eight when he was elected fellow in 1663, a young and not particularly distinguished man who was probably recruited for the express purpose of writing the Royal Society’s history. But if Sprat was a relative nonentity at the time, the men who commissioned him to write were the Society’s greatest men. These included the Society’s president, Lord Brouncker; its secretary, Henry Oldenburg; and its leading scientist, Robert Boyle, all of whom reviewed and corrected Sprat’s text to make sure it accurately presented their views. As a result,
History of the Royal Society
is not just a summary of Sprat’s private reflections, but a public statement of the goals and purpose of the Royal Society as understood by its leaders at the time. And when it came to their views on dogmatic philosophies, their verdict was clear: dogmatism leads to sedition and subversion of the state, and was
not
the kind of approach that would be practiced in the Royal Society.

The alternative to the dogmatic rationalism of Descartes and Hobbes, the founders of the Royal Society believed, was experimental philosophy. Instead of pride, experimentalism bred humility, and whereas the rationalist philosophies led to pettiness and envy of rival philosophers, experimentalism fostered cooperation and mutual trust. Most important, instead of sedition and subversion, “the influence of experiments is
Obedience to the Civil Government
.” Unlike the rationalist philosopher, the experimentalist never claims he has discovered the only true system or that his results are absolutely and irrefutably true. Instead, making no assumptions about what he will find, he humbly proceeds from experiment to experiment, trying to make sense of what he finds. His conclusions are always the best that he can supply at the moment, but can always be overturned by the next experiment. Not for him are Hobbes’s bold pronouncements about matter, human nature, and the only viable commonwealth. To the contrary, he proceeds slowly, conducting many different experiments many times over, and only then will he venture, carefully and somewhat reluctantly, to provide a provisional interpretation of the results.

Experimentalism is a humbling pursuit, very different from the brilliance and dash of systematic philosophers such as Descartes and Hobbes. It is, wrote Sprat, “a laborious philosophy … that teaches men
humility
and acquaints them with their own
errors
.” And that is precisely what the founders of the Royal Society liked about it. Experimentalism, as Sprat noted, “removes all haughtiness of mind and swelling imaginations,” teaching men to work hard, to acknowledge their own failures, and to recognize the contributions of others. This is precisely the attitude the founders of the Royal Society hoped to engender in the body politic as a whole. In place of the intolerant fanaticism of the parties and sects that had thrown the commonwealth into violence and chaos, experimentalism would breed moderation, cooperation, respect for differing opinions, and ultimately civic peace.

When members of the Royal Society celebrated the glories of the experimental method, they also celebrated the man whom they considered the founder of it all, the “one great man who had the true imagination of the whole extent of this Enterprize.” He was Francis Bacon, Lord Chancellor to James I, who in his retirement had authored some of the most influential works ever on proper scientific method. In contrast to his younger contemporary Descartes, who had argued that true knowledge must be based on clear and rigorous reasoning, Bacon had insisted that true knowledge of nature could be acquired only by observation, experimentation, and the careful gathering of facts. To the Royal Society, Bacon was the prophet of the experimental method, and the spiritual father of the Society itself, though he died many years before its founding. In fact, the Society considered itself the true incarnation of Bacon’s “Salomon’s House,” a state institution for the study of nature that he proposed in his utopian work
New Atlantis
.

There is irony here, because Bacon’s secretary in his final years was none other than Thomas Hobbes. As an avowed rationalist, Hobbes had derided the value of experiments in his dispute with Robert Boyle, and his thinking was not much influenced by his distinguished employer (except perhaps in his abiding interest in the natural sciences). But there was no getting around the fact that for all their idolization of Bacon, none of the Society grandees had actually known the Lord Chancellor, whereas their enemy Hobbes had been his intimate companion.

The brilliance of Bacon’s reputation has hardly diminished, even to this day. Though not a creative scientist himself, he is nevertheless considered one of the crucial figures in the scientific revolution, whose writings made possible the growth and expansion of science. Bacon provided a brilliant defense of the experimental method, which had been viewed as suspect during the centuries in which Scholastic dispute and reliance on ancient authority were considered the proper path to true knowledge. He provided a road map for the development of experimental science, advocating for the systematic collection of data by a multitude of field-workers, and its concentration in a centralized institution for systematic evaluation. More than anything, perhaps, he made the experimental method respectable.

Long before Bacon’s time, there were always those who tried to extract the secrets of nature through the rough method of trial and error. Sometimes they succeeded brilliantly, as in the inventions of gunpowder and the compass, other times less so, as in the case of the alchemists, who built sophisticated laboratories equipped with chemicals and furnaces in their search for the elusive philosopher’s stone. But any knowledge gained by these methods, even when it proved useful, was not considered appropriate for teaching in institutions of higher learning. It was “rude” and “mechanic,” associated with the lower classes, who dirtied their hands and worked for a living. No self-respecting gentleman would ever stoop to engage in such work, for fear of being tainted by its plebeian association. True knowledge, worthy of academic study, was to be found in the writings of the great masters of the past, or derived from them through exacting logical reasoning. Experimental results were not considered knowledge at all, since they relied on the notoriously unreliable senses and did not therefore rise to the required level of certainty. Bacon, almost single-handedly, demolished this perception. Here was no less a personage than the Lord Chancellor of England promoting experimentalism as the proper path to true knowledge. At a stroke, the uncouth practices of “rude mechanics” became a worthy pursuit for the intellectually curious gentleman.

There is one aspect of Bacon’s methodology, however, that has often been criticized: his belittlement of mathematics as a tool of science. It is not that he ignored mathematics completely, since he did acknowledge that objects in the world had quantity, and mathematics was the science of quantity. But Bacon thought that mathematical knowledge was far too general to be of serious use. “It is the nature of the human mind,” he wrote, “to delight in the open plains (as it were) of generalities, rather than the woods and inclosures of particulars,” and mathematics was the best field to “satisfy that appetite.” Such an approach, however, is “to the extreme prejudice of knowledge,” because all knowledge worth pursuing lies in the particulars of the tangled woods, not in the generalities of the open plains. Mathematics can be useful, Bacon concedes, but only as the handmaiden of the experimental fields, not as a science unto itself. Nothing could be worse for the growth of knowledge than “the daintiness and pride of mathematicians, who will need have this science almost domineer over Physic.”

Bacon’s suspicion of mathematics as a tool for comprehending the world is not hard to understand. For mathematics to describe nature correctly, nature must be mathematical—that is, structured according to strict mathematical principles. If that is the case, then all one needs in order to gain insight into the workings of nature is to follow the rules of rigorous mathematics, and all observations and experiments are superfluous. But Bacon made no such assumption. There is no way of knowing how the world is structured, he believed, until one engages in careful and systematic observations. The idea that one can deduce the workings of nature by mere mathematical reasoning is a dangerous illusion based on unwarranted pride, and is bound to lead any scientist astray.

Bacon’s warning against the “daintiness and pride” of mathematicians was not lost on his followers, the founders of the Royal Society. Although the Society was officially described as a “Colledge for the Promoting of Physico-Mathematicall Experimentall Learning,” in practice the “mathematicall” studies were strictly subordinated to the “experimentall” ones. For the Society leaders shared Bacon’s concern that mathematics breeds pride and makes it easy to assume that God created the world according to rigid mathematical strictures. Like Bacon, they were worried that mathematical reasoning would lure scientists away from the laborious work of experimentation.

But the Royal Society founders had other concerns, concerns that went beyond Bacon’s warning half a century before. Mathematics, they believed, was the ally and the tool of the dogmatic philosopher. It was the model for the elaborate systems of the rationalists, and the pride of the mathematicians was the foundation of the pride of Descartes and Hobbes. And just as the dogmatism of those rationalists would lead to intolerance, confrontation, and even civil war, so it was with mathematics. Mathematical results, after all, left no room for competing opinions, discussions, or compromise of the kind cherished by the Royal Society. Mathematical results were produced in private, not in a public demonstration, by a tiny priesthood of professionals who spoke their own language, used their own methods, and accepted no input from laymen. Once introduced, mathematical results imposed themselves with tyrannical power, demanding perfect assent and no opposition. This, of course, was precisely what Hobbes so admired about mathematics, but it was also what Boyle and his fellows feared: mathematics, by its very nature, they believed, leads to claims of absolute truth, dogmatism, threats of tyranny, and, all too easily, civil war.

Yet, despite the ideological and political dangers, mathematics could not be simply dispensed with. Some of the greatest accomplishments of the New Philosophy were heavily mathematical. Advancements in medicine, such as Harvey’s discovery of the circulation of the blood, were certainly experimental, as were the barometric measurements of atmospheric pressure known as the Torricellian experiment, and William Gilbert’s investigations into the nature of magnetism. But the greatest scientific triumphs of the age were indeed in astronomy, and these were deeply indebted to mathematics.

What, then, could the Royal Society leaders do? They could not simply ignore the brilliant contributions that mathematics had already made to science, or the strong indications that the former would continue to play a central role in the latter’s advancement. But how could the Society embrace the important contributions of mathematical science and yet avoid its dangerous methodological, philosophical, and political implications? It was a conundrum that left the Society with an ambivalence toward mathematics that characterized its science for many years. And no one felt this conflict more keenly than John Wallis.