2012 : WHAT IS YOUR FAVORITE DEEP, ELEGANT, OR BEAUTIFUL EXPLANATION?

General Relativity 

General relativity is one example of a beautiful explanation of the way nature works. In fact I would argue that it is a truly extraordinary example because it is beautiful in three distinct ways. However, there's an ugly truth that we also have to consider: the concept of beauty is notoriously subjective.

First, general relativity is beautiful in the mathematical sense. Like a great work of art, it is built on strong, basic, foundations that are free of superfluous adornments. Einstein used a handful of principles to blend two fundamental concepts that had, until he came along, been thought to be independent: space and time, on the one hand, and matter and motion on the other.

The quest for this kind of beauty carries a distant echo of the Aesthetic Movement's battle cry of 'art for art's sake'. Distant, yes, but also distinct and pervasive. Bertrand Russell once said that mathematics had a cold and austere beauty, "like that of sculpture." In his book, A Mathematician's Apology, G. H. Hardy suggests that a beautiful proof possesses "inevitability", "unexpectedness", and "economy". Others talk of universality, simplicity, and elemental power. 

The great Paul Dirac admired general relativity more than any other modern theory (much more than quantum mechanics). He found it as spine-tinglingly inspirational as any great work of music. That is because he valued aesthetic appeal to an extraordinary degree. At a seminar in Moscow in 1956, when asked to summarise his philosophy of physics, Dirac had once scribbled on the blackboard in capital letters, "Physical laws should have mathematical beauty."

But there's another sense in which theories are beautiful. In his award-winning biography of Dirac, The Strangest Man, Graham Farmelo, describes a telling encounter, recorded by the BBC, between Dirac and his friend Werner Heisenberg, when the latter had made the pragmatic, and apparently uncontroversial, remark that beauty is less important than agreement with experimental results.

Dirac countered with the example of another friend, Erwin Schrödinger, whom Dirac greatly admired for his appreciation of mathematical beauty, and whose eponymous equation describes the behaviour of matter in the micro-world of atoms and molecules. He had attempted to formulate versions of the Schrödinger equation that were compatible with special relativity and gave up when he realised this equation (now called the Klein-Gordon equation) gave incorrect results when used to calculate the energy levels of hydrogen.

Dirac pointed out that if Schrödinger had shown more faith in beauty, he would have ended up publishing the first relativistic version of quantum theory. Heisenberg conceded there was indeed a value to being aesthetic (Farmelo remarks: "Dirac's face lit up with the broadest of smiles, revealing two rows of rotting teeth.")

But Heisenberg gave up too easily. There is indeed another, important, sense in which a theory is beautiful, as Heisenberg himself knew only too well. There are plenty of 'beautiful' theories out there that lack relevance: tellingly, Einstein had become obsessed by this ultra-pure form of beauty towards the end of his career, when he was much less creative. He had lost sight of something important. The most elegant theories of all also possess the beauty of utility: in this sense, general relativity has incredible allure. It gives a dazzling account of gravity.

 I would like to argue that there is yet another dimension to the beauty of utility, which goes beyond giving an immaculate account of how nature works. General relativity is also beautiful because it is a fecund theory. It does more than 'give a great account of gravity' – it has yielded new insights in nature, revealing novel vistas that have enabled theorists to keep well ahead of experimenters for decades. Einstein and the likes of Hawking, Penrose, Chandrasekhar and many more used it to shed light on extraordinary phenomena, from the Big Bang 13.7 billion years ago to gravitational waves to the stability of stars to the properties of black holes.

 Beautiful bottom line: the supreme fundamental theories should be elegant at the mathematical level, offer a precise fit with nature and also open up new worlds of intellectual endeavour.

 One ugly fact remains, however: subjectivity. Why is it that mathematics provides the most beautiful depictions of nature that we have? We all assume this is true but we don't know for sure. It seems that the greatest engine of cultural change—the scientific world-view—rests on a foundation that, in some respects, is ultimately religious. Today it has become a cliché to say that, as Dirac put it in a Scientific American article in 1963: "God is a mathematician of a very high order." God's alleged aestheticism is an illusion, however. I put my faith in mathematical physicists. They are on the right path to a profound and objective truth, the beautiful details of which have yet to be revealed in full.