Sir William Rowan Hamilton 
by Thomas Hankins.
Johns Hopkins, 474 pp., £19.50, July 1981, 0 8018 2203 3
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Gentlemen of Science: Early Years of the British Association for the Advancement of Science 
by Jack Morrell and Arnold Thackray.
Oxford, 592 pp., £30, August 1981, 0 19 858163 7
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The Parliament of Science: The British Association for the Advancement of Science 1831-1981 
edited by Roy MacLeod and Peter Collins.
Science Reviews, 308 pp., £12.25, September 1982, 0 905927 66 4
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In the London Review of Books, John Maynard Smith said about scientists: ‘however interested they may be in politics or history or philosophy, their first love is science itself.’ If only I could follow this bent, and tell something of Hamilton as a mathematician. As it happens, he also wrote a good deal of poetry, but his poems lack the magic of his equations, which seem more beautiful and moving now than when they were imagined 150 years ago. His abstract and ‘useless reformulation of Newton’s equations of motion was taken up a century later by Heisenberg and Schrödinger and fashioned into the central formalism of quantum theory, where H – ‘Hamilton’s function’ – now stands for the Hamiltonian operator which drives every physical system through time. The theory of quaternions, Hamilton’s four-dimensional generalisation of complex numbers, was the first really abstract algebraic system, but turned out to be too complicated for practical use in theoretical physics – until proved to be equivalent to the spinor calculus that links quantum mechanics with relativity. You see, a complex number is really an ordered couple of real numbers, so that ... No, I’m sorry, I will have to write about politics, history and philosophy, after all.

Hamilton himself was very interested in philosophy. He was a friend of Coleridge, and was one of the first people in Britain to read Kant. Kant had written about pure space as a realisation of geometry: it was Hamilton’s attempt to construct a corresponding algebra of pure time that led him eventually to quaternions. Professor Hankins apparently accepts Hamilton’s own assertion that his philosophical argument necessitates his mathematical theory – but philosophically-minded scientists are often stimulated into marvellous discoveries which they then see as a justification of their philosophical views. In the case of Hamilton, it seems more likely that his philosophising (like his poetry) was just another manifestation of the intellectual and spiritual idealism that shines most clearly through his mathematics.

In childhood, he was sheltered under the wing of a good kind uncle, in the slightly threadbare clerical gentility of the Protestant Ascendancy in early 19th-century Ireland. He was an infant prodigy, and carried all before him, in Classics as well as mathematics, at Trinity College, Dublin. His creative mathematical genius received prompt recognition. He was appointed professor of mathematics and Astronomer Royal of Ireland at the age of 22, and was knighted at 30. He had four adoring and talented sisters, and innumerable sympathetic friends, including Maria Edgeworth and William Wordsworth. His scientific star never publicly waned: just before his death, in 1865, he was being honoured as one of the world’s greatest scientists. In the Encyclopaedia Britannica he merits a longer column than either of those two other Sir William Hamiltons with whom he is often confused – Nelson’s Emma’s, of course, and the Scottish metaphysician. A highly achieving career, one might say, graced with public acclaim.

And yet, there was pathos, if not downright tragedy, in the core of his being. His idealism extended, naturally enough, to women, and fastened upon the sister of some college friends, Catherine Disney. She loved him too – but before the mutual affinity became evident to them both, she allowed herself to be married to another man to whom she had already given her promise. He was only 20, but he never quite got over it. He worshipped the image of his Catherine for the rest of his life. Her marriage was unhappy, but it was too late, and they were too conventionally bound, to do anything about it when they met again, a few years before she died. He himself had by then married a sickly, shy girl, who proved an unsympathetic and ineffectual wife. The precise circumstances are discreetly veiled, but there are those who say that he drank himself into an early grave.

What does it matter how he suffered in private? There is little difference between a precociously creative mathematician like William Rowan Hamilton and a precociously creative musician like Wolfgang Amadeus Mozart: they produce all that sparkling beauty because it is in their nature, regardless of personal circumstances. That is why I would really like to talk about those number quadruples, represented as vectors on an anticommuting basis set ...

Religion and politics then – and history. Naturally, given his idealism, he took his religion very seriously. ‘Starting as an Evangelical, he had been drawn to Coleridge’s vision of the church universal. The Oxford Movement then drew him towards high-church practice and belief, until the shock of the first conversions to Roman Catholicism’ – this was an Irish Anglican – ‘turned his path back towards the Broad Church.’ Hankins carefully charts these private movements of the spirit, which are really much more interesting than Hamilton’s professional involvement in the controversy over the wave nature of light. The political turmoil of Ireland touched him less. Call him a reactionary, if you will, for he had a profound reverence for royalty and never wavered from support for the Union. But he was not a political animal at all. His observatory was isolated from the mob violence of Dublin, and his secure salary was quite enough to support him above any discomforts of the 1845 famine – although never enough to keep him out of debt. Describe him more kindly as a ‘liberal Tory’ and pass on.

Describe him, above all, as a gentleman. He applied his idealism to his own actions. He knew how to behave well to other people, to say gracefully what needed to be said in public, and to be charming and conciliatory in private. High-mindedness gave him both high moral standards and the strength to live up to them. He did not shirk the administrative and intellectual responsibilities of professional leadership. That is to say, he was a characteristic member of a certain class, and influential in a certain circle that played a significant part in the cultural transformation from Regency to Victorian Britain. This very thoughtful and scrupulous biography conveys an authentic sense of history in its cooler, deeper tides.

If there was a surface wave to that tide, then it began to crest in 1831, with the first meeting of the British Association for the Advancement of Science. A latent scientific clerisy found itself, in that week at York, and reared astonishingly into public visibility. Next year at Oxford, the following year at Cambridge, and so on, from city to city (Hamilton’s knighthood was conferred at the Dublin meeting of 1835), the annual meeting toured the kingdom, drawing together enormous crowds of peripatetic savants and local gentility. Three or four thousand people would attend, many from distant parts of the country, not only to be entertained and uplifted by public addresses on the latest scientific marvels, but also to visit local industrial works, watch the launching of a battleship, tramp or ride out on geological expeditions, listen to courteous controversies on esoteric topics such as the wave theory of light, and especially to eat and drink together most convivially. It had become ‘a vehicle of social intercourse, rational amusement, intellectual improvement, personal advertisement and civic pride’. It was also remarkably practical. It was a major source of grants for research, it was an effective lobby for government support for scientific projects, it commissioned unique reports on the state of various branches of science, and provided a much livelier forum for genuine scientific debate than most of the formal learned societies. For a generation or so, it was more central to the British scientific community than any other institution, including the Royal Society.

Morrell and Thackray go into the first decade or so of the BAAS in fine detail. There are plenty of light touches. For the York meeting Lord Milton is told that ‘philosophers are very fond of venison. Can you contribute to the culinary part of science by sending from Wentworth some venison and game?’ At Bristol, in 1836, some women used ‘most extraordinary muscular exertions’ to gain admission to evening meetings: by 1838, they could not even be kept out of the zoological section, where Richard Owen ‘modified the reproductive part’ of an address on marsupials ‘as delicately as possible’. By dissecting the chronicle of events thematically, the authors tease out the various sinews which they weave into a coherent interpretation of a historical phenomenon.

The occasional cause of the foundation of the BAAS was a letter from David Brewster, in Edinburgh, to Charles Babbage, in London, suggesting this new initiative in their campaign to halt the ‘decline of science’ in Britain. The efficient cause of success was the Reverend William Venables Vernon Harcourt, founder of the York Philosophical Society, who became the first General Secretary of the new organisation and turned it away from controversial topics such as ‘declinism’ to more positive consensual policies. He skilfully yoked together an unlikely combination of political and social forces: provincial independence of London, middle-class cultural aspirations, deference to the aristocracy, yearnings for symbols of national unity transcending class conflict and religious sectarianism, technological innovation, industrial achievement and commercial expansion. How shrewd it was to avoid the obvious trap of holding an annual meeting in the metropolis itself, so that newfound cities like Liverpool and Manchester might compete fairly for the honour. How natural to confine membership to respectable people who could afford to pay for at least the appearance of comprehension. How invaluable the patronage of a local magnate. How reassuring to celebrate together the advancement of knowledge when riot and dissension were threatening the civilised order. Indeed, who could fail to join hands on behalf of the pursuit of truth, whence came the brightest hope of prosperity and concord through technical progress?

Harcourt’s most inspired creation was the constitution of the Association, which had the effect of giving the form of power to the members and their local societies, whilst the substance was retained by a small select group. In any case, those members who were just interested in science could scarcely expect to have much influence compared with those who were entitled to contribute to it by presenting a paper. The real trick was to make sure that the affairs of this lumbering, wandering, eclectic organisation were managed firmly by, and on behalf of, an energetic and competent élite within the much larger community of practising scientists.

William Rowan Hamilton was, indeed, a very typical member of this coterie. They were predominantly cultured Anglicans, of the Broad Church party, many in holy orders. ‘The core members had a definite meliorist, centrist, reforming political attitude within the confused and turbulent party politics of the 1830s and 1840s. Temperamentally they were conservative, piecemeal reformers, opposed to the political claims of both die-hard Tories and fierce democrats.’ They were already, of course, or soon became, influential in the universities and some of the learned societies, but were not yet dominant in the Royal Society. The 23 Gentlemen of Science whom Morrell and Thackray choose to identify specifically were only one group within the scientific clerisy; and yet they ruled supreme over the most powerful organisation speaking for science in that era.

Not surprisingly, in spite of their high moral principles, they did fairly well out of the BAAS. Their personal careers benefited from research grants, professional patronage, government lobbies, public appearances and mutually congratulatory addresses, but they served themselves much more effectively as a group than as individuals. The real fascination of this minutely detailed study of the early years of the ‘British Ass’ – the ‘Mudfog Association for the Advancement of Everything’, as Dickens sarcastically called it – is that it shows how a powerful ideology of science was shaped by the interests of this small but relatively homogeneous social group.

We like to believe that the notion of truth is unique and transcendental. We would like to believe that it is simply our duty to pursue it to the utmost. But scientific truth is evidently a social construct. For the Gentlemen of Science, the constraints were quite clear: ‘Only if science were separated from politics and theology could members of opposing social and religious groups unite for its advancement. Only if science were linked to progress and cut off from the controversial inquiries of statisticians and phrenologists, would its appeal be authoritative and clear. Only if science were rendered attractive to various constituencies would it serve as an instrument of social expression and social integration.’ Their structure has stood for a century and a half: ‘The ideological categories into which natural knowledge was then cast remain familiar today: science as value-free and objective knowledge; science as the key to economic and technological progress; science as the firm fruit of proper method; science as an available, visible and desirable resource.’

Is this ideology obsolete, along with the Association which embodied it? This is the fundamental question posed by The Parliament of Science. These essays, specially written for the York Meeting of 1981, are more sober and less self-congratulatory than one would expect in a volume celebrating the 150th birthday of a venerable institution. Once again, the specific subject of the book is of less general interest than the light it throws on its historical context – the state of British science, from Victoria I to Elizabeth II.

The external form is astonishingly permanent. The annual meeting leaps across the map, from city to city, occasioning civic and academic ceremonial, presidential pontifications and gee-whiz popularisations, visits to industry, restrained junketing and a few column inches in the national press. Attendance at these meetings is certainly not very buoyant at present, but this indicator has had its ups and downs. History teaches that it is not safe to predict the imminent decease of the BAAS on such evidence alone.

But what is it all for? Science is ‘visible’ enough nowadays, in and out of the media. Nobody supposes that a mediocre ‘popular’ lecture to an audience of a hundred is somehow more efficacious than a television or radio programme crafted for the millions. Boosts for the provinces are more welcome in government cash than in coy carnivals of progress. The BAAS did its bit long ago in encouraging state support of science: now it has no funds of its own even for the most modest research projects. It used to meet occasionally in Canada, South Africa or Australia to symbolise the bonds of Empire: on that aspect of history, enough said. Its more general proclamation of transnationalism in science is put into practice on a vast scale in conferences, exchange programmes, co-operative research projects and international organisations. Would anyone in Whitehall or Westminster listen to a deputation of BAAS worthies (don’t smirk. Sir Humphrey) in competition with far more powerful internal lobbies of scientific mandarins? Even on such general issues as the style and quality of science education, the BAAS no longer speaks with evident authority or concern.

Although the past influence of the BAAS may have been exaggerated, it is clear from these admirable essays that it was once a factor to be reckoned with in all these traditional functions. Indeed, each essay could be the base camp for a major expedition exploring one or another of these particular aspects of science in the last 150 years. But I do not think that any of them would persuade me to rescue the BAAS as a whole from the dustbin of history. And yet, like all traditional social institutions, it retains an evocative, elusive presence far beyond its immediate power. For the British scientific community it ought to stand for the ‘General Meeting of Science’. But it is poorly representative of the rank and file. As already bemoaned in the 1890s, the younger generation of scientists tend to display ‘an attitude of clear indifference to the Association’s meetings’, although they will usually agree to come for the day to contribute to a specialised session. It is much more effective as a medium of scholarly recognition. Indeed, the BAAS is so integrated into the honorific scientific Establishment that its policy organs are continually choked by the flux of notables on the way through, year by year. Nobel laureates may have replaced Harcourt’s aristocrats as figureheads, but the key office of General Secretary no longer gets a diplomatic manager, nor an advisory committee of relatively permanent supporters.

In any case, the founders of the BAAS saw clearly that it would lose its public support if it were seen to serve too closely the interests of the scientists. The natural tendency to become too esoteric and specialised has always had to give way to more generalised, popularised and transdisciplinary themes. It is precisely in such discourse, from scientists to the lay public, about the place of science in the scheme of things, that the BAAS has had its most pervasive influence. As we have seen, from the beginning it propagated a very particular ideology. Science itself has grown, and changed shape, and exerted enormous powers and been subject to immense influences, and generally transformed itself out of recognition: within the BAAS this ideology is still much as it always was. One should note, for example, ‘the Association’s continuing role in supporting the “amateur” tradition so central to British scientific life until at least 1939, and possibly still characteristic of its operational “style”.’ There is still the emphasis on science as a ‘method’, an attitude of the spirit, a mental discipline, which favours the basic sciences above intellectually messy, morally questionable technologies. Above all, there are all those subjective, value-laden issues of social responsibility and relevance, which had been tossed out with a pitchfork in the 1830s and still keep crowding in at the windows, especially at times of social and political crisis, in the 1930s and again now.

Scientistic detachment is now obsolete. It blinds people to the harsh realities of our day. Surely science is no longer curiosity and doubt and discovery: it is a social institution, at the power centre of the ‘military-industrial complex’. This is no longer a world in which a William Hamilton may neglect his astronomical observations, and ignore the starving Irish peasants, whilst imagining a beautiful mathematical dream: it is not even a world where he need drink himself to death for unattainable love. It is not a world where illiterate engineers can be trusted to know their betters and ladies to have delicate susceptibilities. It is not a world where pure science can be worshipped either as a manifestation of, or a secular alternative to, revealed religion. And yet the sheer innocence of science retains its charm. ‘Lectures on black holes or the chemistry of fireworks can attract audiences of hundreds: a discussion on dissident scientists may be lucky to attract two dozen,’ writes David Morley. If only experience had not torn the veil. If only one might take that secret path, away from politics or history or philosophy, back to one’s first love – science itself.

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