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.