A surprise new “theory of everything” involves symmetry

Is our world ruled by order or by disorder? It is not just a big question. It is an old question that has engaged philosophers and scientists for thousands of years. We can trace it back to ancient Greek philosophers, to Egypt’s pharaoh dynasties, to ancient Chinese Taoists, and to Buddhism’s origins in India. And it is also a question that is very relevant to life in the West today. 

Towards the end of 2019, before the coronavirus pandemic hit the world, I was visited in my laboratory by the writer and philosopher Benedict Rattigan, who invited me to join a fascinating project he was launching. He presented an idea that we have fundamentally misunderstood symmetry, and that its reach is far more extensive than has previously been recognised. 

Rattigan’s theory intrigued me, and we worked together to invite other leading Oxford professors specialising in multiple disciplines to explain in lay terms the role of symmetry in their fields of mathematics, music, logic, philosophy, physics, chemistry, astronomy, and biology. Their lectures were delivered at a public event at the British Museum in January 2022.

What is the common theme running through the various “languages” of symmetry? There may not be just one common theme, of course. The concept of symmetry is used in significantly different ways, for example, in physics, where symmetry-breaking plays a central role in explaining the evolution of the universe, and in its use in art, where good proportions are key. But there is one sense of symmetry that stands out from the variety of forms: a fundamental symmetry is that between order and disorder. 

It may seem paradoxical to suggest that Nature’s ordering principle encompasses a symmetry between order and… well precisely disorder. Virtually all 19th-century scientists, and most 20th-century scientists, would have recoiled in horror at such an idea. But what we found as the talks were drafted was that each form of the language of symmetry revealed a new aspect of the order–disorder principle. 

In my own field of genetics, for example, I have been able to demonstrate that rather than disorder being passively experienced by living organisms, they harness that randomness and use it as a tool with which they can generate many possible solutions to environmental challenges. I presented a paper on this subject at The Royal Society in 2016, but at the time I didn’t see it as a symmetry issue. More recently, however, I have come to understand why this process happens: it places the harnessing of disorder as part of a deeper symmetry process by which order and disorder interrelate. 

Empirical evidence for the symmetry between order and disorder is hiding in plain sight all around us. In 1999, the Danish physicist Per Bak suggested to a group of neuroscientists that the brain works on the same fundamental principles as a sand-pile. Imagine an hourglass. Grain after grain, sand falls from the top of the hourglass to the bottom. The pile of sand at the bottom of the hourglass becomes increasingly unstable, and at any moment a single grain of sand might cause a small avalanche. When this happens, the base of the sand-pile widens, which increases its overall stability, after which the process repeats itself. Bak observed that the sand-pile maintains order by means of these random and unpredictable avalanches, which is an example of disorder being “harnessed” by the sand-pile as a means of maintaining order. In other words, there is a fundamental interdependence between them. It has been demonstrated that this model can be applied to a wide variety of different phenomena, from financial markets and traffic flows to earthquakes, black holes, and the distribution of galaxies in the universe. 

Another example of order and disorder forming a symmetry can be found in that most random of phenomena, crowd behaviour. Rattigan writes: 

Watching a group of people negotiating a bottleneck at the doors as they filed into a lecture theatre, I observed what I, as a layman, would describe as chaos. But any social scientist will tell us that the behaviour of a cluster of people conforms to broadly predictable patterns, patterns that are determined by factors such as geometric boundary conditions or time gap distributions. It’s these factors which are calibrated in order to improve design elements in lecture halls or theatres. So what I perceive as chaos is, in fact, randomness existing within a framework of order… Life seems to exist at this border between order and randomness.

As the team at Oxford explored symmetry in their different disciplines, we realised just how multifaceted it is. One is aware of it in musical composition as assonance and dissonance, or you might catch sight of it in biology as a transformation that leaves an object unchanged. Frequently it is elegantly simple, whilst occasionally it can be so contradictory as to be almost incomprehensible. It is both orderly and disorderly, logical and illogical, transparent and opaque. But why is symmetry so symmetrical? The conclusion we reached is this: because it conditions its own structure. Whereas all the laws of Nature are built upon certain symmetries, symmetry alone is subject to itself. 

In Nature’s laws, complexity never develops beyond necessity. The best designs are simple, and the best designer is Nature itself. Finding that there is a fundamental symmetry between order and disorder that can run through all our explanations is like discovering a clarification that was always waiting there to be revealed. Whereas this seems at first to be illogical, if symmetry were life’s ordering principle then it would necessarily have infinite reach and encompass everything, including itself. This would create a paradoxical universe of symmetry and asymmetry, of cosmos and chaos. Our universe, in other words — a place of infinite symmetries in which the co-existence of order and disorder is not only in evidence, it is inevitable. If symmetry has no deeper cause than itself, then the cosmos has been structured in the only way possible.