The link between the cosmos and earthly aesthetic beauty

Are we living under a work of art? A new book argues that the connection between the aesthetic and universal is more than sensory, supporting an age-old theory that the universe is indeed a masterpiece, Robert Matthews writes.

Sheikh Zayed Grand Mosque in Abu Dhabi has been built to a design that is rich in patterns and symmetry. Lee Hoagland / The National

To visit Sheikh Zayed Grand Mosque is to experience the ineffable. Its sheer size and spaciousness suffuse it with a cosmic sense of serenity. But that feeling of being at the centre of immensities is enhanced by something more subtle: the absence of figurative imagery.

While places of worship of many other religions are adorned with familiar icons and images, the grand mosque follows the Islamic tradition of abstract decoration. From floor to ceiling, and even the building itself, it is rich in patterns and symmetry. And for the two million-plus visitors of the mosque each year, it adds to that wondrous sense of transcendence.

Now, a new book by a Nobel Prize-winning scientist argues that this connection between the aesthetic and the universal is more than sensory.

According to Professor Frank Wilczek of the Massachusetts Institute of Technology, its bears witness to a cosmic truth: that the universe as a whole is a work of art.

The idea that nature’s symmetries are of more than aesthetic appeal dates back at least 2,500 years.

In his famous work Timaeus, Plato describes the universe emerging from chaos to produce earthly things from the four basic elements of fire, earth, air and water, with the heavens being made from a fifth element, quintessence.

Plato linked each of these with five geometrical shapes: the tetrahedron, the cube, octahedron, icosahedron and the 12-sided dodecahedron.

These were not picked at random, however; Greek mathematicians had proved they were the only regular closed solids that can exist in three dimensions. But they also had the alluring property of symmetry. Rotate any of the five shapes about their axes and they look the same on each of their sides.

Their symmetry allowed them to be unchanged in the face of change, so to speak.

The notion of a link between symmetry and cosmic order blossomed under Islamic scholars, artists and architects about the 10th century. Avoiding icons, they chose instead patterns of often breathtaking complexity and symmetry.

By the 14th century, the Alhambra Palace, near Granada, southern Spain, was adorned by tiles in no fewer than 17 types of symmetry – a number whose significance was only recognised centuries later, with the discovery that it represents all the symmetries capable of covering flat surfaces.

Only in the last century has western science finally caught on to the cosmic significance of symmetries. But as Prof Wilczek argues in A Beautiful Question, the results have been astounding – and have led to an affirmative answer to the question at the core of his book: does the universe embody beauty?

Given the notoriously subjective nature of beauty, this hardly sounds like a scientific question. Yet according to Prof Wilczek, about a century ago a deep connection was found between the coldly objective laws of physics and beauty as embodied by symmetry.

It took the form of Noether’s theorem (pronounced “Ner-ter”), named after the German mathematician who published it in 1918.

Put simply, it showed that the celebrated laws of conservation of momentum and energy are actually manifestations of symmetries.

For example, if – as seems reasonable - the laws of physics are unchanged by changes in where they’re applied (giving them “spatial symmetry”), the theorem shows that must be a law of conservation of momentum.

Similarly, if the laws of physics are unchanged by changes to when they’re applied – and thus possess “temporal symmetry” – there must be a law of conservation of energy.

According to Prof Wilczek, this link between symmetry and the laws of physics has proved invaluable in resolving cosmic mysteries: “Through it, we relate the theoretical aesthetics of possible symmetry and the question ‘Are my equations beautiful?’, to the hard reality of physical measurements, and the question ‘Are my equations true?’”

And he should know: in 2004 he won the physics Nobel prize for revealing bizarre truths about the nature of the forces that hold together atomic nuclei.

But we can all get a glimpse of the power of Noether’s theorem – even while sitting in an office chair.

If the laws of physics aren’t affected by changes in when or where applied, it seems plausible they should also be unchanged by rotation.

Plug that symmetry into Noether’s theorem and out pops another law of physics: the law of conservation of angular momentum.

And to confirm its existence, all we need do is start spinning on an office chair. If we draw our legs in, the law compensates for our smaller effective size by making us spin faster – just like a spinning figure skater on ice.

Of course, the symmetries pondered by Prof Wilczek and his colleagues are far more esoteric. But among them is one causing growing unease among physicists, as it may prove a symmetry too far.

Known as supersymmetry, it plays a crucial role in attempts to succeed where Einstein himself failed, and create a single, unified account of all the particles and forces in the cosmos.

Such a Theory of Everything must show some underlying unity between the familiar particles of matter, such as electrons and protons, and those that transmit forces between them, such as photons.

In other words, there must be a symmetry between them, allowing them to be swapped over without changing anything.

First mooted by theorists over 40 years ago, the existence of supersymmetry has never been confirmed by experiment.

Now the biggest and best attempt ever made is under way at the Large Hadron Collider in Switzerland. And concern is mounting that so far, they’ve seen no sign of it.

Prof Wilczek is among those who are keeping faith with the theory, still convinced by the power of symmetry to hint at cosmic truths. And in that at least, his belief will be shared by the many visitors to the Sheikh Zayed Grand Mosque.

Robert Matthews is visiting professor of Science at Aston University, Birmingham