** Albert Einstein: If only our bankers had his capacity for profound thought**

In 1976 the composer Philip Glass wrote a surrealistic "opera" called *Einstein on the Beach*, recently revived at the Barbican. This curious museum piece lasts more than five hours without a break, the audience being welcome to wander in and out at will, which I did. It deals with courtrooms and lawyers, but has little to do with the beach or with Einstein, apart from a reference in one of the poems forming the text: "...green Christmas Trees. So Santa Claus has about/red. And now the Einstine [sic] trail is like in Einstein on the Beach. So this will."

At this late point in the opera the staging shows a vision of the nuclear explosion that destroyed Hiroshima. It's hard to remember now, but back in the 1960s and early '70s there was huge guilt — and worry — about the nuclear bomb. Looking back at the Queen's Silver Jubilee in 1977 one newspaper recently recalled a man saying, "We're due a celebration . . . we've made it to 1977 without a nuclear war." Do you recall CND, and those Aldermaston marches? All gone, and as for regarding Einstein as the father of the nuclear bomb, no one thinks of him this way any more. But what exactly did Einstein do?

Just after seeing the opera I received a mathematics book to review: *The Universe in Zero Words* by Dana Mackenzie (Princeton, £19.95). It presented, among other things, Einstein's famous equation *E*=*mc*^{2}, linking mass *m* with energy *E*. The large number* c*^{2} shows that a small amount of mass is equivalent to a huge amount of energy, leading to nuclear power and nuclear bombs. Einstein derived the equation in 1905. That was when he produced his first theory of relativity, showing that a moving body, particularly one travelling close to the speed of light, would appear distorted: lengths shortened, time going more slowly, and mass increased. A thought experiment about a body emitting two photons in opposite directions then led him to see that an apparent increase in mass would be matched by an apparent increase in the energy of the photons as their wavelengths were foreshortened. This led him to his famous equation.

Yet Einstein did much more than this. Before explaining what, let's consider some other equations taken from Mackenzie's book. One is Newton's famous equation giving the gravitational attraction between two bodies, depending on the mass of each and the distance between them. Using his invention of the calculus, Newton then derived the equation of motion for planets orbiting the Sun, hence confirming and explaining empirical laws governing these orbits, discovered by Kepler. This stupendous achievement was the beginning of what became known as Newtonian mechanics, which reigned supreme until the late 19th century. Then came various discoveries leading to relativity theory and quantum mechanics. However, for sizeable bodies at reasonably low speeds all was well, and equations of motion could in principle be written down. Or so it seemed.

Indeed in 1954, in the early days of electronic computers, John von Neumann suggested computers would one day be able to predict the weather 30-60 days in advance. It hasn't happened, though computer power has grown to measures unimaginable to von Neumann. One problem is that Newtonian mechanics contained surprises. The problem of two bodies was solved immediately but the three-body problem resisted all attempts.

Now you would think that given enough mathematical ingenuity equations would be found governing the motion of a mere three bodies such as Earth, Sun and Moon, affected only by gravitational forces between them. However, in the 20th century it turned out that a tiny alteration in position or velocity could lead to grotesque differences in the resulting motion. Move by a hair's breadth and a stable motion of the three could turn unstable, with the Moon heading off to infinity. Tiny changes could lead to huge effects, and as is often said, the flutter of a butterfly's wings in Siberia could alter the weather in London.