Carnivals of Progress
John Ziman, 17 February 1983
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.