Carnivals of Progress

John Ziman

  • Sir William Rowan Hamilton by Thomas Hankins
    Johns Hopkins, 474 pp, £19.50, July 1981, ISBN 0 8018 2203 3
  • Gentlemen of Science: Early Years of the British Association for the Advancement of Science by Jack Morrell and Arnold Thackray
    Oxford, 592 pp, £30.00, August 1981, ISBN 0 19 858163 7
  • 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, ISBN 0 905927 66 4

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 ...

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