The Natural Philosophy of James Clerk Maxwell 
by P.M. Harman.
Cambridge, 232 pp., £35, April 1998, 0 521 56102 7
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Late 20th-century sciences are publicised through hands-on exhibitions, press conferences, chat shows and interactive CD-Roms. The Victorians had a different system and, as usual, painstakingly classified it. There was the conversazione and the soirée; the grand lecture and the subscription dinner; the amateur society and the private club; above all, there were periodicals and public museums. Whether at the Crystal Palace, the Athenaeum or the local working men’s college, disseminating science was as much a moral as a material issue, since understanding the Creation might yield principles of ethics as well as mastery of nature.

Invited in 1873 to join a new society for metropolitan physicists, the Cambridge professor James Clerk Maxwell set out in his witty way the practical philosophy of this public science. He thought soirées were like clouds of gas particles: they allowed buttonholing only during the brief if violent collisions of their participants. Lecture-rooms were crystalline, everyone fixed in their place, bathed in the diffuse light of scientific oratory. The dinner table resembled a badly-designed electrical circuit, ‘with flowers in the middle to prevent cross-currents’. The ideal, the ‘intermediate plastic condition’, was the genteel clubroom, in which ‘confused talk’ let each member know which of his companions might be interested or interesting. This colloidal world was where Maxwell and his like developed much of their philosophy. Politely portentous reflections on destiny and free will, materialism and evolution, causality and probability, provided topics for metaphysics laced with madeira. The leather-bound world of these natural philosophers can seem, and often was, deliberately insulated from the highly-charged milieux of the Age of Steam, Soap and Steel. Peter Harman’s new book tries to demonstrate how much metaphysics mattered in the everyday labours of Victorian Britain’s greatest mathematical physicist.

Comparisons are odious, but league-tables are another feature of the public life of contemporary science. A couple of years ago, I was asked by a BBC producer to nominate candidates for inclusion in a radio series, On Giants’ Shoulders, the plan being to juxtapose comments by current scientists and by historians on great scientific figures of the past, from Archimedes to Crick and Watson. I at once suggested Maxwell, not only the acknowledged progenitor of electromagnetic field theory and statistical thermodynamics, but a man of self-mocking humour, whose obiter dicta would well fill thirty minutes’ chat. In vain: a physicist and eminent populariser of science told the producer that whereas a genius such as Michael Faraday would have been awarded three different Nobel Prizes had they then existed, Maxwell would only have won one. No room for him on Auntie’s Olympus. I have no idea which of Maxwell’s achievements might have gained this anachronistic reward: his projection of the first three-colour photograph in 1861; his invention of a new kind of vector algebra; his brilliant use of reciprocal diagrams to analyse stresses in bridges or his innovative work in topology; his papers on the way governors maintain stability in rotating systems or his application of probability calculus to the motion of gases, including his amazing proof that the viscosity of a gas is independent of its pressure; even, perhaps, his argument that light must be a kind of transverse vibration in a universally distributed electromagnetic ether, an inspiration for the work of Heinrich Hertz and other physicists of the radio epoch.

Maxwell worried about his public. He combined a Christian Socialist commitment to teaching science to workers with the gentlemanly administration of Cambridge’s first experimental physics laboratory and the production of major textbooks in electromagnetism, mechanics and heat theory. The insightful Austrian physicist Ludwig Boltzmann once compared Maxwell’s style to that of a Wagnerian: ‘as if by a magic wand hopeless confusion is reduced to order. Obediently, his formulae deliver result after result, until we reach the final surprise effect.’ More prosaically, Maxwell’s lifelong friend Lewis Campbell saw him as ‘a country gentleman, or rather, to be more accurate, a North Country laird’. Maxwell lived in a rather less divided culture than that of C.P. Snow’s absurd caricature. In 1873, he suggested a joke question for the Cambridge mathematics examination, inviting candidates to interpret every vector ‘in literary geometrical terms’, and in the same year humoured his classicist friend Campbell with the thought that Middlemarch was just a solar myth, Rosamond standing for the Dawn and ‘Lyd Gate, being compounded of two nouns, both of which signify something which opens, as the eye-lids of the morn and the gates of day’. There were comic verses on submarine telegraphy and moving sonnets on his religious enthusiasms; brief postcards in mirror-writing or playful Greek lettering embodying radical new models of space alongside sketches of clever experiments on colour vision and thorough drafts of treatises on heat and electromagnetism.

Harman is an authority on this extraordinary Nachlass. In 1990, he published the first of three large volumes of Maxwell’s scientific papers and letters, and he now uses this experience to reflect on some of the major themes, or, as Boltzmann might have put it, Leitmotiven, of Maxwell’s natural philosophy. Once upon a time, the eight centuries before 1850 to be precise, natural philosophy meant the rational study of God’s creation. Newton wrote down its ‘mathematical principles’ in 1687. Other fields, such as biology or geology, were hived off, leaving natural philosophy of the mid-19th century roughly co-extensive with our notion of physics. The term is still used this way in the titles of chairs in Scottish universities, as Maxwell would have been delighted to learn. Today the official story is that the 19th century was populated by ‘classical’ physicists, tidying up the numbers in Newton’s wake or else waiting stolidly for Einstein. Harman’s book helps demolish this silly picture. Natural philosophy was a protean enterprise of impressive creativity, not least in its extraordinarily rich metaphysics. ‘The articulation of scientific theories rests on metaphysical as well as empirical constraints,’ Harman once argued and this is his focus here.

When Maxwell thought about the nature of fate, the reality of atoms, the existence of a continuous ether subject to dynamical principles, or the status of the various models and analogies he invented to describe light, electricity and magnetism, he of necessity engaged in metaphysics. In 1856, in his inaugural lecture as professor of natural philosophy at Aberdeen, the 25-year-old Maxwell told his audience that ‘Scotchmen are born with an instinctive tendency towards metaphysics and when they run short of practical arguments, they take refuge in a higher and more impregnable region,’ in a philosophical Caledonia wrapped in the ‘mists of rhetoric’ and ‘the thunders of declamation’. Physics was good for the Scots, the Edinburgh-trained Maxwell reckoned, because they would be forced to work ‘till these metaphysical principles are at peace with those incontrovertible facts’. Perhaps this is why it’s been hard to see where a ‘classical’ figure like Maxwell fits into the pantheon: he was so explicit about the role of philosophy that he cannot be used to sustain an image of the classical sciences as a simple mixture of facts and sums.

The key term in Maxwell’s natural philosophy was ‘dynamics’, a resonant theme of Victorian scientific culture. Good theories, such as those already worked out by Newton and his successors in astronomy or optics, described individual particles moving through space under the influence of law-like forces whose behaviour could be analysed by the principles of rational mechanics. Harman identifies three related puzzles which dominated Maxwell’s dynamical philosophy: how to get a complete picture of the electromagnetic ether; how to distinguish between dynamical and merely probable laws of nature; and how to leave a space for free will. The first of these puzzles emerged in the 1850s, when Maxwell, fresh from his triumphs in the prestigious Cambridge mathematics course, set out to reinterpret Faraday’s experiments on batteries, wires and magnets performed during the three decades from 1820 in the basement of the Royal Institution.

Maxwell reckoned Faraday had destroyed fashionable French and German models which described electromagnetism as the result of instant actions across empty spaces along straight lines between the centres of isolated particles. He saw it as dependent on some kind of space-filling, fluid ether whose tension and stress stored energy and transmitted action at finite speeds. When he got the physics chair at King’s College, London in 1860, Maxwell published a famous diagram of this ether as a vast array of spinning gears separated by long strings of ball-bearings, a bit like Charles Babbage’s newfangled calculating engine on show in the College museum next door. He showed that the equations of such a complex array, suitably adjusted, were exactly the same as those of electromagnetism, and even managed to prove that the speed of energy transmission in the mechanical ether was the same as that of light. British natural philosophers, led by the prodigious Glasgow professor William Thomson, liked this kind of model, because they reckoned dynamical machinery was uniquely comprehensible and informative. Trained to think in terms of the physics of gyroscopes, pulleys, pumps, calf’s-foot jelly or rubber bands, they extended this behaviour to Creation. Their critics, like the waspish French scientist Pierre Duhem, thought this mechanical obsession was a typically British weakness: ‘we thought we were entering the tranquil and neatly ordered abode of reason,’ Duhem complained on opening a textbook by one of Maxwell’s disciples, ‘but we find ourselves in a factory.’

Maxwell combined these interests in mundane mechanisms with an unusually clear grasp of the vivid mathematics of spatial relationships. As Harman shows at length, his development of vector algebras and topology proved decisive when, during the 1860s, he abandoned his model of gearwheels and ball bearings and instead described the field exclusively through its abstract dynamical principles. Thomson, for one, never really forgave Maxwell his apostasy from the creed of intelligible machinery. Harman points out that Maxwell reckoned his first ether model was ‘awkward, inconceivable and misty’, that it was rather like an orrery, which gave an appealing, simplified but inaccurate image of the real motions of the planets. Hence arose the first great philosophical puzzle, which Maxwell never quite solved before his tragically early death in 1879, of linking the mathematical behaviour of the dynamical ether with its real structure. In the final decades of the century physicists worked hard on this problem. They believed, in the words of the great American physicist Robert Millikan, that Maxwell ‘created our modern electrical world’, and this modernity is worth remembering.

The second metaphysical puzzle he faced was also a problem of knowing the underlying realities of physical systems. Natural philosophers of the steam revolution got used to thinking of hot gases as systems of moving particles, the temperature corresponding to how fast they moved. In 1859, Maxwell came across a German article which suggested that such particles must constantly collide, so it was impossible to follow each of their paths, and no dynamical account of an individual body was possible. Maxwell compared Saturn’s rings, which he claimed were composed of such an array of particles, with the air round Sebastopol during a ferocious bombardment. He also read Henry Buckle’s History of Civilisation in England, ‘a bumptious book, but not mere brainspinning’, which offered a neat model of the application of statistical methods to history. Maxwell decided to ‘abstain from asking the molecules where they last started from, avoiding all personal enquiries which would only get me into trouble’. But maybe it was possible to get useful results by deriving the most probable behaviour of aggregate populations of molecules. Sociology could help the physicist. ‘A general law of distribution prevails like that of wealth in a nation.’ It might be impossible (or at least impolite) to know everyone’s earnings, but ‘the proportion having so much above or below the average is calculable.’

The approach paid rich dividends in the science of heat, gas viscosity and pressure. It also generated a big puzzle. Thomson had shown that warm bodies could not immediately gain heat from colder ones: the celebrated second law of thermodynamics. Maxwell now realised that this ‘law’ had the same ‘degree of truth as the statement that if you throw a tumblerful of water into the sea, you cannot get the same tumblerful of water out again’. In 1867, he proposed a famous thought-experiment. Imagine a ‘very intelligent and neat-fingered being’ stationed at a door between two compartments containing equal numbers of gas particles. If this being let quicker particles into one compartment, and an equal number of slower ones into the other, the two zones would end up at different temperatures without any work being done. The second law would have been violated. Thomson called Maxwell’s being a ‘demon’: Maxwell himself thought of it as a humble railway pointsman. The law was merely statistical. Harman quotes what he calls the ‘jocular barbs’ which Maxwell directed at German physicists such as Boltzmann, who tried in vain to turn this statistical thermodynamical principle into a determinate dynamical theorem. According to Maxwell, Boltzmann was an Icarus ‘flapping his waxen wings in cloud cuckoo land’.

The problems of dynamics and reversibility took Maxwell, with his talent for expressing his ideas in images, into the stormy world of Victorian journalism, where public scientists such as T.H. Huxley and John Tyndall preached materialism, evolutionism and other views Maxwell (among many others) found loathsome. In 1868, the Saturday Review, edited by the erudite and chilly Oxford don Mark Pattison, biographer of the original Casaubon, summarised recent dangerous French claims that modern physics implied an uncreated and eternal universe. Maxwell protested to Pattison that the arrow of time was real. If the only natural laws were indeed dynamical, then the world could run backwards, ‘all living things would regrede from the grave to the cradle and we should have a memory of the future, but not of the past’. But of course things were not like this. There were truly irreversible processes, those described by the second law of thermodynamics, and this, in turn, showed that not all of nature was governed solely by dynamics.

Maxwell concluded that the best modern science destroyed radical determinism and instead showed that the world must have an end, a beginning and thus, with the right kind of metaphysics, a Creator. During the 1870s, established at Cambridge and more frequently appearing on the platforms of the British Association for the Advancement of Science and in the pages of the Encyclopedia Britannica, he went further, pointing out that the world was full of causal but incalculable events, already obvious in his statistical thermodynamics, evident, too, in such events as sparks which set forests on fire, or the puzzling inheritance which ‘makes us philosophers or idiots’. These ‘singular points’, as Maxwell called them, set severe limits to the perfect predictability of the universe and left a space for free will in a world of physical law. It is with this puzzle of determinism that Harman concludes his account of Maxwell’s complex, clever and graphic metaphysics.

When Cambridge students asked Maxwell about his success at solving scientific problems, he replied: ‘I dream about them.’ The wealth of detail supplied by Harman can overwhelm rather than clarify the scope, direction and purpose of these reveries, but he has a point when he attacks those philosophers of science who have hijacked restricted selections from Maxwell’s oeuvre to illustrate some favoured theory of knowledge. Harman understandably emphasises his subject’s broad traditionalism: his devotion to natural philosophy’s metaphysical inheritance, insistence that scientific understanding is always limited and partial, rejection of views such as those of Tyndall and Huxley, who touted their utilitarian ambitions, unchallengeable professional expertise and secularist morality. Maxwell’s Victorian values were not those now propagated in the name of the public understanding of science, and there’s a kind of pleasurable nostalgia and an educative excitement in revisiting his moral universe.

This survey leaves some major problems still untouched, however, as Harman acknowledges. When Duhem saw the Maxwellian tradition as entranced by the factory, he was not a simple-minded victim of Gallic prejudice against British machination. At least two kinds of Victorian workshop provided Maxwell and his colleagues with the matter and spirit of their natural philosophy. One was located in the sternly disciplined studies of the Cambridge mathematics coaches, that remarkable group of academic taskmasters under whose rigid tutelage generations learnt the difficult techniques of analysis and dynamics. One of Maxwell’s friends recalled the ‘cram’ system which the coaches cultivated: he preferred the kind of benevolently chaotic ‘social entropy’ of the new physics labs, such as the one Maxwell started in the 1870s. Harman gives a good example of the way the Cambridge system of drilling worked: when in 1855 a group of university astronomers and mathematicians encountered a major new research puzzle in the structure of Saturn’s rings, they set the puzzle as a prize question for their best students, hoping that one would solve their difficulty for them – and in 1857 Maxwell did just that, using all the techniques he’d learnt from his coach, so launching his remarkable interest in the behaviour of gaseous particle systems. Up in Aberdeen he also got a local instrument-maker expert in building spinning tops to illustrate his Saturn model ‘for the edification of sensible image worshippers’.

Such technicians populated the other kind of workshop which Maxwell reckoned important, set up by ambitious engineers and hard-nosed entrepreneurs to furnish hardware and trained personnel for telegraphy, railways, high-class instruments trades and new teaching laboratories. Though never quite the Victorian version of the Internet which some would like to find there, the electric telegraph system tied the British Empire together and posed the urgent, hard, practical and theoretical problems which Maxwell and his allies had to solve in their labs and studies: the propagation of signals in electromagnetic networks, the reliability of measuring instruments, the analysis of charge, force and current. Spectroscopes in the hands of a new kind of astronomer, keen to investigate the chemistry of stars and cosmic evolution, also provided material for Maxwell’s speculations on the ether, the uniformity of creation, and the fate of the universe. Harman records that he even told one astronomer in 1868 about the visionary possibility of a field theory of gravity, a direct counter to Newton’s classical version of celestial mechanics.

By stressing the deep traditionalism of Maxwell’s enterprise, Harman makes him a participant in a philosophical conversation about matter, motion and mind, well-established by the time of Newton and continuing into this century. One aim of this book is to suggest, correctly, that the continuity of this kind of metaphysics does not mean it lacked the power dramatically to innovate the sciences. Duhem’s jibe that English physicists never thought about metaphysics is obviously false. But this picture of profound philosophy and innovative physics flourishing in Victorian Britain also makes it harder to see what happened in the decades immediately after Maxwell as a great revolution which brought the atavistic complacencies of classical Newtonian mechanics crashing down. The image of that great Fin-de-Siècle transformation distorts most popular accounts of physical science. To correct the image, and so gain a better sense of physics’ modernity, we need more compelling historical stories of the workshops, classrooms, laboratories and lecture-theatres where the Victorians crystallised and diffused their philosophical and physical visions.

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