by Bill Bryson
CONCLUSION
At all times in The Divine Comedy Dante knew where he was. He was embedded in a cosmos that gave him a position physically, spiritually and psychologically. One of the many strengths of the Comedy is that it gives a concrete landscape to both soul and psyche. While the book must be read as the journey of a Christian soul through Hell and Purgation towards Paradise, it can also be read as a journey of psychological self-examination and healing. The descent into Hell is a literal depiction of human psychic suffering; the trip up Mount Purgatory is the therapeutic path. We can gauge Dante’s progress by the state of his surroundings – we feel the anguish as we slog with him through the ditches of the Malebolge, we rejoice with relief as he trots up the marble ramps of the mountain. Dante may be a sinner, but he is never lost – his cosmos tells him in the very texture of his surroundings where he stands as a material body, as a Christian soul and as a human self.
Several years ago I gave a lecture at a small university in the American South. After the lecture I was taken aside by a professor at the school, an anthropologist who had done field work in Namibia with the Himba tribe. One day, he told me, he was approached by a Himba man who asked him a question: ‘Do you Westerners really see the space between you as empty?’ ‘Yes,’ my American interlocutor replied, ‘that is the way our science tells us to see the world.’ The Himba man went on to explain that, in his culture, people saw the world in a different way. According to their worldview, each person is surrounded by a kind of self-space which extends out around the individual. Going about their daily business, he and his fellow villagers found their self-spaces continually intersecting. They rarely found themselves ‘alone’ – their ‘selves’ being continually in touch with others. Having explained this way of seeing, the Namibian man asked the American professor a second question: ‘If you people really see yourselves as isolated points alone in empty space, how do you bear it?’
It seems to me that as a society we are not bearing it. Unlike Dante, we are lost in space.
4 NEAL STEPHENSON
ATOMS OF COGNITION: METAPHYSICS IN THE ROYAL SOCIETY, 1715–2010
Neal Stephenson is the author of the three-volume historical epic The Baroque Cycle (Quicksilver, The Confusion and The System of the World) and the novels Cryptonomicon, The Diamond Age, Snow Crash and Zodiac. He lives in Seattle, Washington. His latest novel is the alternate reality epic Anathem.
THE LOOSENING OF THE MOORINGS OF THOUGHT WHICH CAN BE SENSED IN THESE EARLY DAYS OF THE SOCIETY HELPED SUSTAIN SOME VAST INTELLECTUAL DISPUTES. AS NEAL STEPHENSON EXPLAINS, ONE OF THE SHARPEST, BETWEEN THE TWO GIANTS NEWTON AND LEIBNIZ, INVOLVED SOME VERY STRANGE METAPHYSICS – NEARLY AS STRANGE, IT TURNS OUT, AS TWENTY-FIRST-CENTURY PHYSICS.
This philosophy is a gift of God to this old world, to serve as the only plank, as it were, which pious and prudent people may use to escape the shipwreck of atheism which now threatens us.
– Leibniz, in a 1669 letter to Thomasius
Isaac Newton was slow to join the Royal Society – in the Charter Book that lives in the Society’s vault, his signature does not appear until the ninth page – but by the second decade of the eighteenth century he had become its President. His unquestioned status as the greatest mind of his generation, combined with his political connections as Master of the Mint and his ruthlessness toward those he perceived as rivals, had given him an unusual degree of power. This he brought to bear against the only living person who could even hope to challenge his intellectual supremacy: Gottfried Wilhelm Leibniz, who despite being a foreigner (he was Hanoverian) had been made a Fellow of the Royal Society in 1673, largely in recognition for his invention of the Stepped Reckoner, a mechanical computer.
The contrasts between Newton and Leibniz were lavish. Newton seems to have had an entirely accurate sense of just how he compared to his contemporaries, and acted accordingly without concern for dusty precedents or the personal feelings of those who clung to them. When confronted with anything less than uncritical acceptance of his work, he lashed out and then secluded himself. He published rarely but ex cathedra, handing down nearly flawless treatises over which he had toiled for years or decades, perfectly organised into definitions, axioms, lemmas and laws, framing a mathematical physics that could be used to explain past observations and to make verifiable predictions.
Leibniz was an accomplished courtier who maintained long friendships with the Electress of Hanover, the first Queen of Prussia, the sister-in-law of Louis XIV, and the future Queen Consort of England, while moonlighting, late in his career, for Peter the Great. He corresponded so heavily that scholars are still sorting through his unpublished papers. In his philosophy he practised an ecumenicism that in a lesser mind would strike us as suspicious or even craven. Leibniz seems never to have met a philosopher or a theologian he didn’t like, and his metaphysics developed out of an effort to harmonise the ancient thinking of (both) Plato and Aristotle with tenets of Christian and Jewish theology and with the ‘mechanical philosophy’ the Royal Society had been created to champion. It is impossible to know precisely what he was thinking without perusing his vast legacy of papers. In effect, Leibniz’s philosophy ceased to exist at the moment he died. Since then, anyone who has wanted to know it has first had to reconstruct it, which is only possible for forensically inclined scholars, fluent in Latin, French and German, and well versed in the history of Western philosophy, Christian theology and Enlightenment science.
Given Leibniz’s stature as one of the great thinkers of Western history, one might expect that, as of the 350th anniversary of the founding of the Royal Society, all of his writings would long since have been published, and that everything would be known about his philosophy. But the question of ‘what did Leibniz believe, and when did he believe it?’ is unsettled and is the topic of current research and debate.
A squalid row over the origins of the calculus, which these two men had independently invented decades earlier, became the public face of the conflict, which is regrettable since it is not very interesting and since it reflects dreadfully on the combatants. Much more significant in the long run was a debate on topics that reach so deeply into the foundations of science that they are still discussed in our times. This broke the surface in the last year of Leibniz’s life, in an exchange of letters that has come to be known as the Leibniz–Clarke correspondence.
The year was 1715, and because of two royal deaths (in England, Queen Anne; in Hanover, Electress Sophie), Princess Caroline of Brandenburg-Ansbach had just become the Princess of Wales. To the modern reader, Caroline seems less like a real historical personage than a plucky, clever, independent-minded heroine from some post-feminist historical novel. A noble but poor orphan, raised as a ward of the Prussian court, she was conversant with scientific topics of the day, largely because she had been tutored in them by Leibniz. She had married into the Hanoverian dynasty and had moved with it to London, where her father-in-law had been crowned King George I. The sixty-nine-year-old Leibniz, who had become unfashionable and, because of the dispute over the calculus, something of a political problem, had been left behind in Germany. He wrote a short letter to Caroline, warning her that religion was declining in England; that John Locke did not believe in the immortality of the soul; and that Sir Isaac Newton held to some strange views about the relationship between God and the physical universe.
Anyone who has blithely forwarded a private email to a corporate mailing list, with incalculable consequences, will recognise what happened next: Caroline made Leibniz’s letter known, and one Samuel Clarke stepped forward to rebut Leibniz’s charges. The result was a series of letters (five each by Leibniz and Clarke) over the course of a year, at which point Leibniz died. Clarke, though he had serious credentials in his own right both as theologian and scientist, was acting as a spokesman for Newton, and so the correspondence can fairly be read as a debate between Leibniz and Newton.
In the opening round, the combatants practically trip over each other in their eage
rness to remind the Princess that atheism is bad and that true natural philosophy in no way conflicts with religion. There is no reason to think that either of them is being disingenuous. The scientific revolution had created doubts about the existence of God, or at least the veracity of religious dogma, in the minds of many; but not Newton or Leibniz.
These concerns are dispensed with in a few paragraphs. The bulk of the correspondence, which runs to about eighty pages, resembles an email exchange that devolves, as it goes on, into several distinct threads, each concerning a specific sub-topic. The correspondents begin to number their paragraphs (Leibniz’s fifth letter contains 130 of them), the better to keep track of all the rebuttals and counter-rebuttals. The over-arching theme is the relationship of God to the universe, and more specifically the universe as perceived, measured and understood by scientists. Leibniz, in the universal manner of authors promoting their latest work, finds frequent occasion to mention his books Theodicy and Monadology. Even when he isn’t mentioning them by name, he is presenting arguments, and using terminology, derived from them.
My theme is the legacy of Leibniz’s metaphysics from the time of his death down to the present day, and so a direct summary of that system, based on the scholarship of latter-day researchers, will do better service than any attempt to untangle the points and counter-points in the correspondence. The account presented below is patterned after the work of Christia Mercer of Columbia University. Her book Leibniz’s Metaphysics: Its Origins and Development, published in 2001 by Cambridge University Press, is a formidable work of forensic scholarship that can in no way be improved by my attempts to summarise it.
In 1661, at the age of fourteen, Leibniz had formed a resolution to embrace the new mechanical philosophy. For most natural philosophers of the era, this meant rejecting the Aristotelian worldview of the medieval schoolmen. As mentioned, though, Leibniz was an ecumenicist and a conciliator, and so for him it meant, rather, the beginning of a lifelong quest to reconcile certain select, precisely defined tenets of Aristotelian and Platonic thought with modern science.
In his metaphysical reasoning, Leibniz is at least as meticulous as is Newton in his mathematical physics. Bertrand Russell called Leibniz’s system ‘profound, coherent, largely Spinozistic, and amazingly logical’. Newton, however, can verify his results by comparing them to observations, while Leibniz is beholden to no one except Leibniz. By pure thinking, Leibniz fabricated a metaphysical system that could hardly be more at odds with that of Newton, or indeed any other person who attempts to think in a commonsensical way about how the world might work.
Where Newton’s work is grounded in Euclidean geometry, Leibniz begins with certain precepts that he takes to be axiomatic, such as the Principle of Sufficient Reason (nothing exists without a reason; there is no effect without a cause) and the Identity of Indiscernibles (two individual things cannot differ in number alone; it must be possible to explain why they are distinct based on some intrinsic difference). Newton developed calculus because it enabled him to solve problems in his theory of gravitation; Leibniz developed it as an outgrowth of his fascination with the problem of the Continuum, which asks how a line can be made up out of points, a span of time from instants, or a thought from the minute perceptions and endeavours of a mind. Just as Newton would not bother developing a physics that could not explain the fact that planets move in elliptical orbits, Leibniz had no time for any metaphysics that was incompatible with the transubstantiation of the Eucharist (both the Protestant and the Catholic versions!) and the incarnation of God in Christ. Much of the pick-and-shovel work of his Monadology came from a 1671 tract about the Incarnation of God.*
The modern reader, following the development of Leibniz’s ideas over the years between 1661 and his death in 1716, veers between finding it all quite reasonable and feeling as though it must have come from an alien planet. Just when one is about to judge Leibniz as having the strangest mind of anyone who ever lived, one remembers Newton and his lifelong obsession with alchemy and his strenuous efforts to predict the exact date of the End Times by ransacking the Book of Revelation for encrypted clues.
It takes an entire book such as Mercer’s to explain Leibniz’s full chain of reasoning, so there is not room here to attempt any such thing. The end point – Leibniz’s mature system, as described in Monadology – may be summarised as follows:
Matter, assumed by most to be the primary stuff of the universe, extended in space and time, is, in fact, unreal. Atomism in its conventional form – the idea that physical objects can be divided and subdivided up to a certain point, but (for some, usually unspecified, reason) no further, and that the result is a collection of tiny indivisible matter-bits moving around in empty space and banging into one another – is all wrong. The true atoms – the fundamental, indivisible units that make up the universe – are not spatiotemporal and so are not bound by spatial and temporal constraints; rather, space and time are epiphenomena of their activities, which are mental (today we might say computational) rather than physical. Leibniz calls these mind-atoms by the name of monads.
Use of ‘mind’ and ‘mental’ is apt to give modern readers the wrong idea. Many translators of Leibniz (including Russell) choose the word ‘soul’ instead of ‘mind’, which is even more confusing. A word about those words is, therefore, in order. Extension (occupying physical space) and duration (persisting through time) are obvious properties of matter that had long been of interest to natural philosophers. Beginning around 1671, Leibniz added a third element, namely cognitio, which can be translated as ‘thought’ or ‘knowledge’. In his metaphysics, cognitio is a property that things can possess and that makes them different from inert matter. Early in his career, it is as fundamental as extension. Later, it becomes more so. Previously, he had admitted God and the human mind as the only two incorporeal principles in his system; the key move he now made was to admit the possibility of cogitating entities (‘minds’ or ‘souls’) that were neither divine nor human, and to make them and ‘endeavour’ – the smallest possible unit of cogitation, which is to cognitio as a point is to a line or an instant is to time – as fundamental as space and time. Later, he goes on to deny the primary reality of space and time altogether and to assert that the created world consists entirely of these unextended monads and that the universe is created from moment to moment as a result of their cognition. In this he breaks from the metaphysics assumed by Newton (and almost anyone else who has thought in a commonsensical way about space, time and atoms) in which space and time have an absolute reality, and form a sort of lattice on which the laws of physics are enacted, and, indeed, without which they cannot even be written down.
Because the monads do not exist in space and time, they are free to take on certain powers and properties that would otherwise be implausible: (1) each monad perceives the state of every other monad in the universe, and (2) each exists in a certain state, and is capable of changing that state. This process of continual internal state-change is the cogitation that is the raison d’être of the monad and the fundamental process of the universe.
Internal and intrinsic to each monad is a rule (dubbed by Mercer the Production Rule) that governs how it changes its state in response to its current state and the perceived state of all of the other monads. And just as the constraints of space and time are inapplicable to monads, so cause and effect work differently, for each monad is causally independent of all other monads. It makes its own decisions by its own lights, obeying its intrinsic rule.
This raises the obvious objection that if the states of the other monads serve as inputs to the production rule, then there would seem to be a cause-and-effect relationship at work, but Leibniz doggedly maintains that no such relationship exists and that coordination among monads comes about, not through causal linkages, but as the result of a divinely ordained pre-established harmony that brings all of the monads into a kind of synchronisation without encroaching on their independence. For minds and cogitation are, to Leibniz, t
he ultimate reality, and unless the minds have free will, they are not minds at all but physical mechanisms numbly obeying deterministic rules.
This is the one feature of the Monadology that might (I speculate) have aroused some competitive anxiety in Newton’s mind. The Leibniz–Clarke correspondence probably would not have drawn the attention of so many important people were it not that traditional (spatiotemporal) atomism, combined with the then-new science of mathematical physics, seems to lead ineluctably to what was later called Laplacian determinism. If the behaviour of all objects can be explained in terms of spatiotemporal atoms, and if the atoms’ behaviour, in turn, is subject to Newton’s deterministic mathematical laws, then there is no room for free will. Humans are robots and religion is a fraud.
