During autumn in the UK, if you look to the skies shortly before dusk you may see a spectacular natural phenomenon as thousands of starlings fly together in a huge aerial formation known as a murmuration. This can be an incredibly dramatic sight as hundreds or even thousands of birds swoop through the air in perfect synchronicity, an immensely complex display of formation flying that looks like a carefully choreographed dance through the evening air.
But ask yourself this - if you had only ever seen one single starling, could you have predicted this dramatic display? It’s pretty unlikely that you’d be able to guess the rules governing this flocking behaviour based on a single bird, no matter how carefully you analysed it.
This is an example of a deeper phenomenon known as ‘emergence’. To put it simply, it is the idea that a complex system can be more than the sum of its parts - that by adding many individual constituents together, new behaviour may arise that cannot be predicted from the individual pieces alone. This new behaviour is every bit as fundamental as the rules that make up the building blocks of our world, but rather than by dissecting reality on ever smaller and smaller scales, emergent behaviour can only be observed by putting things together.
Different Points of View
Often when people think of science, they think of it as a process by which we carefully unpick reality on smaller and smaller length scales, perhaps going from biology to chemistry, on to quantum physics and particle physics. As physics is my particular area of interest, and the only one I can voice anything close to an informed opinion on, this is the aspect we’ll concentrate on to discuss the difference between reductionism and emergence. These days I don’t think it’s controversial to say that both philosophies have their place, and that (at least in science) both are valid, useful and necessary, but this wasn’t always the case. Famously, in 1972, physicist Phil W. Anderson penned a piece titled ‘More is Different’ in which he argued that contemporary science (and in particular, physics) had become too focused on reductionism. Arguing that ‘The ability to reduce everything to simple fundamental laws does not imply the ability to start from those laws and reconstruct the universe,', this article was sufficiently influential that even in 2012 it was recommended reading in my undergraduate courses on condensed matter physics.
But what’s the different between reductionism and emergence? Take one of the greatest physical discoveries in recent memory, made by one of the most famous experimental facilities on the planet: the discovery of the Higgs boson. This is one of the grandest examples of reductionism in all of science, as one of the biggest machines ever made accelerated some of the smallest known particles to some of the highest possible velocities and then smashed them together to see what bits flew off, and from there work backwards to understand the subatomic structure of our universe.
From a certain intuitive point of view, this idea makes a lot of sense. For example, as a child I was forever taking things apart to see how they worked1. It always seemed to make sense to me that this was the way to figure stuff out, from computers to telephones, and when I took these things apart and found only circuit boards and wires, I figured that the only way to make sense of those was to keep going deeper and understand circuitry.
But now consider the starlings we talked about at the start of this post - if you tried to collide two starlings together at high velocity, the first thing you would have one your hands are two non-working starlings2. Sure, you’d then be able to dissect them and in so doing learn a lot about the inner workings of a starling - but you would never be able to predict from this the astonishing formation flying that groups of starlings effortlessly engage in when their numbers are large enough. This is the key difference between reductionism (i.e. reducing an object to its constituent parts, trying to understand each of them and then from this understanding, figure out how the object as a whole functioned) and emergence (i.e. putting large numbers of ojbects together and seeing what they do).
Examples of Emergence
You don’t have to look far to see examples of emergence in every day life. From starlings whirling through the skies to weather systems, emergent behaviour is all around us. Even something as common as temperature is an emergent phenomenon, as this is a collective property of a large number of particles. Temperature is related to the average velocity of a large number of particles: by itself, a particle can’t have a temperature. In fact, this is just a specific example of a more general case: the entirety of the field of statistical mechanics is essentially an emergent property of underlying microscopic rules that govern the motion of particles.
This is not to say that emergent behaviour can only occur on large scales. We see emergence even in quantum mechanical systems on tiny length scales, so long as there are sufficiently many particles. How many is ‘many’? That depends, but usually as soon as we hit anywhere from a few hundred to a few thousand particles, we start being able to see signs of emergent behaviour. One particularly dramatic example is Bose-Einstein condensation, where large numbers of (bosonic) atoms at sufficiently low temperatures can enter a cooperative phase of matter where they behave in essence like a single giant particle, all obeying the same wavefunction. This is closely related to (but distinct from) the equally impressive collective behaviour of superfluidity, where atoms enter a collective liquid state that flows with zero viscosity.
There are many other examples of emergent physics in quantum systems, including local integrals of motion (LIOMs) in many-body localized matter, something I’ve spent a lot of my career working on, as well as intriguing properties such as emergent symmetries which can occur in systems which have no explicit symmetries in their mathematical description, but nonetheless find it energetically favourable to adopt particle-hole symmetry. This is true at specific points in the Bose-Hubbard model, for example. The same holds true in other fields too, with examples including protein folding, the swarming behaviour of a variety of animals and insects, and perhaps even the emergence of life and consciousness from inanimate matter.
The key thing to take away from this list of examples is that emergent behaviour is all around us, at all length scales from planetary to atomic – and that it can be every bit as interesting and fundamental as any other aspect of science – but it is only by putting things together, rather than taking them apart, that we stand any chance of ever seeing or understanding any of it.
So there you have it - science isn’t just an endless race to the bottom, and in fact we can learn as much from our world by putting things together as we can from taking them apart. Are there any great examples of emergence that I’ve missed or should have included? Am I wrong in suggesting that emergent phenomena are every bit as fundamental as small-scale physical laws? Drop me a message on Twitter and let me know!
This post was written as part of public engagement component of the Ergodicity Breaking in Quantum Matter project (EBQM). This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No.101031489. The featured image for this article is from Wikimedia Commons, taken by Walter Baxter and licensed under the Creative Commons Attribution-ShareAlike 2.0 Generic license.