Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World (39 page)

John Wallis in 1670, at the height of his battle with Hobbes. Engraving by William Faithorne.
(Photograph courtesy of the National Portrait Gallery, London)

We do not need to make any inferences about Hobbes’s political views or the role of mathematics within them, because he wrote it all down in beautiful prose. Wallis, in contrast, wrote extensively on mathematics and authored many religious sermons over the years, but never claimed the mantle of philosopher. To piece together his views on political order, we need to move beyond his personal writing and toward the broader circle in which he moved. In his university days, and in the early days of struggle against the king, this meant the coterie of Presbyterian divines who dominated the Parliamentary party. But beginning in the mid-1640s, Wallis became a leading member of a different and far more diverse group. It met regularly in private homes in London and Oxford throughout the Interregnum and was known by different names at different times. Sometimes it was the “Invisible College”; at other times it was the “Philosophical Society.” In 1662 the returning monarch, Charles II, finally gave it official recognition, a charter, and a name: the Royal Society of London.

SCIENCE FOR A GLOOMY SEASON

Three and a half centuries after its founding, the Royal Society is among the most august scientific institutions the world has ever known. To say that a list of its past fellows includes some of the greatest scientists in history is an understatement. If one counts the foreign fellows, it contains well nigh all of them. Robert Boyle (1627–91), of “Boyle’s Law” fame, was one of the Society’s founders and the most influential among the early fellows. Isaac Newton (1643–1727), often considered the first modern scientist, and whose
Principia mathematica
of 1687 revolutionized physics, astronomy, and even mathematics, was president of the Society from 1703 to his death in 1727. The Frenchman Antoine-Laurent Lavoisier (1743–94), founder of modern chemistry, was a foreign fellow, as was the American founding father Benjamin Franklin (1706–90). In later years there was Charles Babbage (1791–1871), designer of the first programmable computer; and William Thomson, Lord Kelvin, founder of the science of thermodynamics and Society president from 1890 to 1895. Charles Darwin (evolution), Ernest Rutherford (structure of the atom), Albert Einstein (relativity), James Watson (DNA), Francis Crick (also DNA), and Stephen Hawking (black holes) were or still are fellows. This is but a small selection of the most famous names among the fellows, but it is sufficient to get the picture: anybody who was anybody in the history of modern science was a fellow of the Royal Society.

But in 1645, when Wallis began attending informal meetings held by a group of gentlemen interested in natural philosophy, all this lay far in the future. The purpose of the meetings, as the Society’s first historian, Thomas Sprat, wrote some years later, was not to found a scientific academy, and advancing the frontiers of knowledge was a secondary concern. “Their first purpose,” Sprat reports, “was no more than breathing freer air, and of conversing in quiet with one another, without being engaged in the passions and madness of that dismal age.” At a time when Royalists and Parliamentarians, Presbyterians and Independents, Puritans and Enthusiasts, property owners and tenants, were all at each other’s throats, these men were seeking an escape. They found it in the study of nature.

“For such a candid and unpassionate company as that was,” Sprat reflected, “and for such a gloomy season, what could have been a fitter subject to pitch upon than
Natural Philosophy
?” To discuss theological questions or “the distresses of their country” would have been too depressing. But nature could distract them, “draw their minds off past and present misfortunes,” give them a sense of control in a world gone mad, and make them “conquerors over things.” Their meetings were a space in which they could converse quietly, voice opposing views without shouting one another down, and find common ground despite disagreements. Amid the furor, fanaticism, and intolerance of revolutionary England, they were seeking a safe haven of tolerance to pursue a subject they believed would benefit all Englishmen, if not mankind. They called it “natural philosophy,” and we call it science.

Wallis, by his own testimony, had already encountered the New Philosophy in his Cambridge days. Now, with his new companions, he began to pursue it systematically. Meeting weekly at the home of one of their members or at Gresham College, they discussed and experimented on the entire array of new ideas and discoveries that were shaking the foundations of the medieval order of knowledge. Wallis lists them all:

Physick, Anatomy, Geometry, Astronomy, Navigation, Staticks, Magneticks, Chymicks, Mechanicks … the Circulation of the Blood, the Valves in the Veins, the Copernican Hypothesis, the Nature of Comets, and New Stars, the Satellites of Jupiter, the Oval Shape (as it then appeared) of Saturn, the spots in the Sun, and its Turning on its own Axis, the Inequalities and Selenography of the Moon, the several phases of Venus and Mercury, the improvement of Telescopes, and grinding of Glasses for that purpose, the Weight of Air, the Possibility or Impossibility of Vacuities, and Nature’s Abhorrence thereof; the Torricellian Experiment in Quicksilver, the Descent of heavy Bodies, and the degrees of acceleration therein.

There were only two fields, Wallis explains, that were intentionally left out: “Theology and State affairs.”

Wallis took part in the meetings in London for several years, even as he continued his career as a Presbyterian stalwart, protesting the king’s execution and the army’s purge of Parliament. It might be that, as he wrote years later, the apolitical experimentalists provided him with a welcome refuge from the dogmatic intolerance of Interregnum politics. It is just as possible that he was hedging his bets, hoping that his association with the natural philosophers would help him find a measure of security and success if the Presbyterians’ power collapsed. That, in any case, is what happened. Wallis, who had been a mere dabbler in mathematics, started studying more advanced texts, which almost certainly played a part in his surprise appointment to the Savilian chair at Oxford.

The move to Oxford did not end Wallis’s involvement with the group. Several other members ended up in Oxford around the same time, and together with some old Oxonians, they established the Oxford Philosophical Society and met regularly at the home of Robert Boyle. “Those in
London
, Wallis recalled, “continued to meet as before (and we with them, when we had occasion to be there;) and those of us in
Oxford
 … continued such meetings in
Oxford
; and brought those Studies into fashion there.” The two groups interacted closely, and when Charles II chartered the Londoners, the Oxford group was included, its members becoming founding fellows of the Royal Society. Wallis, a moving spirit behind the activities of both groups, became a prominent member of the new organization.

Under the king’s patronage, the Royal Society became a trend-setting scientific organization and, along with the French Royal Academy of Sciences, a model for scientific institutions in Europe and beyond. Its regular meetings in these early years were devoted to public experiments in optics, the structure of matter, the reality of a vacuum, and telescopic observations, among other topics, executed by the Society’s curator of experiments, Robert Hooke. Most famously, Robert Boyle’s experiments with the air pump, in which he investigated the structure and composition of air, were conducted in public laboratories of the Royal Society in front of numerous witnesses. In 1665 the Society’s secretary, Henry Oldenburg, launched
Philosophical Transactions of the Royal Society of London
, one of the first scientific journals, and certainly the longest-running in the world.
Philosophical Transactions
reported not only the investigations of the Society’s fellows but also studies conducted by others, making the Society a world center of scientific research.

Some of the practices of the early Royal Society might seem peculiar to a modern scientist. For example, there was little distinction between what today would be considered amateurs and professionals, and the pages of early
Philosophical Transactions
were filled with reports of unusual weather phenomena and the births of monstrous or malformed livestock. Social rank also mattered a great deal in the Society, and quite a few prominent gentlemen owed their fellowship to their illustrious lineage rather than to any scientific distinction. Also puzzling from our perspective is that the experiments were performed in public, that is, in front of an audience of Society fellows and sometimes other notable guests. All those present would then discuss what they had seen, examining its meaning and significance. To a modern scientist this would seem more like a circus performance than a proper scientific experiment.

Some of the differences between the early Royal Society and modern scientific procedures can be attributed to the fact that science in the seventeenth century was still young, and its practices still very much in flux. The professional career scientist is a creation of the nineteenth, not the seventeenth, century. Other differences are due to the Royal Society’s viewing itself as much more than a scientific institution of the kind we know today. A modern scientific institute or university department is concerned exclusively with scientific research and education, its success measured by the number and quality of its publications and innovations. The Royal Society also emphasized its research and innovation, always insisting on the usefulness of its discoveries. But in addition to this, it took upon itself a mission unlike that of any of its modern counterparts: to provide a model for the operation of the state as a whole.

This mission has its roots in the meetings of the London group, back in the 1640s. Outside their meeting hall the group’s members might be radicals or moderates, Presbyterians or Independents, Parliamentarians or even Royalists, all engaged in a life-and-death struggle for domination. But inside their meetings, none of that mattered: irrespective of their religious and political affiliations, they could all pursue the investigations of nature in peace and civility. “It was
Nature
alone,” wrote Sprat of those early meetings, that “… draws our minds off from past, or present misfortunes … that never separates us into mortal Factions; that gives us room to differ, without animosity; and permits us to raise contrary imaginations upon it, without any danger of
Civil War
.” In pursuing nature, Wallis, Boyle, and their associates created a safe space where even disagreements could be managed in peace and civility. It was a welcome relief from the cutthroat politics of the Interregnum.

But what started as a simple refuge ultimately developed into an ideal: if reasonable men of different backgrounds and convictions could meet to discuss the workings of nature, why could they not do the same in matters that concerned the state? Why could Parliamentarians and Royalists not resolve their differences in peace and civility rather than murdering each other on the battlefields of northern England? Why could Independents, Presbyterians, and Anglicans not come to a reasonable agreement on Church government instead of each trying to impose their own system and suppressing all others? The harmony that prevailed in the natural philosophers’ meetings, even among men who disagreed sharply, seemed to hold an important lesson for the entire English body politic. For as Sprat put it, in those meetings, “we behold an unusual sight to the
English Nation
, that men of disagreeing parties, and ways of life, have forgotten to hate, and have met in the unanimous advancement of the same
Works …
For here they do not only endure each other’s presence without violence and fear; but they
work
and
think
in company, and confer their help to each other’s
Inventions
.”

In the harsh climate of Interregnum politics, Wallis and his fellows reveled in their ability to conduct their business in peace, cooperate despite disagreements, and together advance the cause they all cherished. By the time they emerged from the shadows and were officially chartered by Charles II, they were ready to spread the word, and use their experience to reconstitute the entire body politic. The dogmatism of the preceding decades would be replaced by the moderation and open-mindedness that characterized their meetings and their science. The hubris of the fanatics would be replaced by the modesty of the experimenter, passions by rational debate, and the intolerance of sects by the tolerance of different but reasonable men working together for a shared cause.

Presenting itself as a model for the state, the Royal Society tried to be as inclusive as possible. There was nothing democratic about it, to be sure, and members of the lower classes were unwelcome in its halls just as they were unwelcome in the political class. Wallis, Boyle, and their fellows feared and distrusted the common people, convinced that the only way to achieve peace and order was to restore the authority of the propertied classes. But when it came to gentlemen, the Society sought to set an example of openness, and this meant accepting into their ranks men of even modest accomplishment. For Society fellows to have presented themselves as “professionals,” to the exclusion of “amateurs,” would have smacked too much of the sectarianism of the past, in which one group sets itself up as the judge of all others.

The public experiments of the early days also played a role in the Royal Society’s political mission, serving as an example of how reasonable men of good faith could discuss difficult issues and come to an agreement. The model was to be the private meetings of the Society’s founders during the Interregnum, in which they experimented and debated, offering different interpretations of what they were observing. In the end, though, they would arrive at some interpretation they could agree on—even if it left many questions unanswered. But for such discussions to take place, now that the Society was an official institution, it would not do to conduct the experiments in the privacy of a secluded laboratory. If members were to form an opinion, they would have to observe the proceedings themselves. It was therefore essential that the experiments be conducted before witnesses of unimpeachable character, most often other fellows, who could then discuss what they had seen and come to an agreement on what had occurred. A modern-day laboratory, in contrast, does not carry the ideological burden of the early Royal Society. It relies exclusively on the testimony of experts, safely assuming that laymen would not comprehend the proceedings anyway.