Edited by Graham Farmelo

Many popular science books shun equations, partly due to overzealous editors who fear that the appearance of anything that looks like mathematics will frighten off potential readers. In contrast, here is a book that relishes equations, which celebrates their power and beauty, and which still manages to explain rather than baffle.

Graham Farmelo of the Science Museum has brought together an eminent team of writers, including a lord, a knight and a Nobel laureate, who have each written a chapter about one of the great equations of the twentieth century. The title, “It Must be Beautiful”, alludes to the belief common among many scientists that those successful equations invariably seem to be beautiful. Albert Einstein even went as far as declaring that, “the only physical theories that we are willing to accept are the beautiful ones.’

Scientists seeking objective truths are often guided by aesthetics, but it is difficult to explain why one hypothetical equation is more beautiful than another. Sometimes the beauty in an equation is based on its intricacy, but at other times it emerges from simplicity. Often the beauty is a result of surprise. Nothing is more beautiful that the shocking realisation that quantities that appear contrary (e.g., energy and mass) are intimately related to each other (E = mc2). And, of course, all valid equations must accurately describe the universe, and there is an inevitable beauty in truth.

Farmelo’s selection of beautiful equations is biased towards physics, and in particular three of the eleven chapters are devoted to the equations of the greedy genius Einstein. However, the book does include a few equations relating to chemistry, evolution and chaos, so there is a nod towards the other sciences.

Indeed, it was gratifying to see a chapter on Claude Shannon’s equations, which gave birth to information theory, which in turn laid the foundations for the Information Age. It was cheering to see an attempt to popularise the work of Shannon. He is one the great heroes of the last century, whose work has transformed our lives, yet in the fame game he probably ranks below the first person to get evicted from the Dutch version of the Big Brother household.

The book ends with a chapter by Aisling Irwin entitled “An Environmental Fairytale”, a brilliant account of the Molina-Rowland chemical equations that eventually revealed the effects of chlorofluorocarbons (CFCs) on the ozone layer. As with most of the other chapters, Irwin not only unpicks the equation, but also tells the story of the scientists who discovered and understood it.

Ozone is the name of the molecule containing 3 oxygen atoms, whereas normal oxygen contains only 2 atoms. Ozone is a pungent, pale blue gas that lurks in the upper atmosphere, where it absorbs harmful ultraviolet light known as UVB and UVC. Without ozone, ultraviolet rays would reach the ground, causing cancer, cataracts and damaging our immune system, which is why it was never a good idea to pump ozone-destroying CFCs into the air.

CFCs were invented in 1930 by Thomas Midgely, whose other great claim to fame was putting lead in petrol to reduce ‘knocking’. If anybody deserves a Nobel prize for damaging the environment, it is Midgely. To be fair, both ideas seemed good at the time. In particular, CFCs are incredibly stable molecules, which is why they were used so widely in domestic appliances. Why should a stable CFC molecule destroy a molecule like ozone, which is 50 Km above us?

CFCs were considered such a cuddly chemical that James Lovelock, whose green credentials include the Gaia model for the Earth, suggested releasing CFCs into the atmosphere in order to track air currents. In fact, it was this idea that got the American Sherry Rowland and his Mexican graduate student Mario Molina interested in CFCs and ozone.

They were the first to realise that although CFCs are stable at sea level, they could be broken up by high energy ultraviolet rays if they went high enough. The first of the equations shown earlier describes how a chlorine (Cl) atom can be chipped away from the CFC molecule. The second equation shows how the rampant Cl atom tears an oxygen atom away from the ozone to make normal oxygen and ClO. Finally, The ClO picks up a stray oxygen atom on its travels, making more normal oxygen and recreating a stray chlorine atom. Once again the lone chlorine atom is free to destroy another ozone molecule, and the cycle repeats over and over again.

In the mid-70s nobody had measured a drop in ozone, so there was no solid experimental evidence as such. Nevertheless, the theoretical evidence from the equations was enough to raise concerns, and by 1978 several countries took action against CFCs, making this one of the first implementations of the precautionary principle. It was only in 1985 that scientists working for the British Antarctic Survey announced the discovery of the ozone hole.

The bad news is that ozone hole is still growing, but this is due to CFCs released back in the 1950s and 1960s. The good news is that the hole should be replenished by 2075, assuming that China does not break the ban on CFCs.

Today we debate global warming. The equations are much more complex, probably less accurate than the CFC equations turned out to be, and are therefore much uglier. However, they are the best equations we have so far, and the scientific consensus represents the best understanding we have of the problem. There is no guarantee that the scientists are 100% right, but they should be listened to and the necessary measures implemented.

Unfortunately, it will be much harder than it was for CFCs for scientists to win this argument, as we have already seen in America. As Irwin points out, banning CFCs was relatively painless, because CFCs were associated with luxury goods, such as hairsprays and fridges, whereas carbon fuels are integral to our lives. There is every reason for governments and corporations with short-term ambitions to focus on the gaps in the science and to claim innocent until proved guilty. The rest of the world should point to the equations and demand that the precautionary principle be brought to bear once again.

I must admit that I still have a few chapters to read, including the alluringly entitled “Erotica, Aesthetics and Schrödinger’s Wave Equation”. Nevertheless, I am already hoping that there will be a second volume, which could be dedicated to the great equations of previous centuries. Maxwell’s equations, Newton’s equation of gravity, and the equations that describe Archimedes’ principle would all make ideal chapters. It is important to remember that old equations can also be beautiful, especially if they continue to encapsulate the truth.