Complexity, emergence and networks

By Shaun Hendy 11/07/2013

What do magnets, stock markets, and Facebook all have in common? With Get Off the Grass off to the printers, I now have some time to ponder such important questions. So tonight at 8.40pm, I’ll be back talking to Bryan Crump on Radio NZ Nights about what it is that these things share: namely, complexity. (You can listen the interview here.)

It’s complicated
We are surrounded by complicated things. It seems obvious that both the behaviour of the stock market, which is a result of many individual investment decisions made by thousands of investors, and the behaviour of a magnet, which is the aggregate of the magnetic properties of a very, very large number of individual atoms, are complicated.

What is much less obvious is that the stock market and a magnet should behave anything like each other. Yet this is what scientists have found: in certain circumstances, complicated systems that consist of many entities that interact with each other often exhibit similar patterns of collective behaviour.

What are these similarities? It turns out that statistically, the ups and downs of the stock market are similar to the microscopic fluctuations of the strength of a magnet like iron. Because individual atoms will occasionally flip the orientation of their own magnetic field, the net magnetic field of a collection of magnetic atoms will fluctuate. These fluctuations tend to be small, because if an individual atom flips, it will then experience a magnetic force from the other atoms that will eventually make it flip back again to line up with all the others.

If you heat the magnet up though, each atom in the magnet will jiggle more and is more likely to flip. The hotter the magnet becomes, the more the strength of its magnetic field will fluctuate. But if the magnet becomes too hot, it can actually lose its magnetic field altogether, because the flipping becomes so random that the tiny magnetic fields of each of the atoms cancel each other out.

Sell-offs, seagulls and sand
What has this got to do with the stock market? It turns out that investors can behave a little bit like atoms. Most of the time, investors tend to invest independently of each other. They make their own decisions to buy and sell stocks based on the prospects and performance of individual companies, without worrying too much about what everyone else is doing.

Just prior to a stock market crash, this behaviour changes. If you buy a stock at the point where everyone else is selling, then you will soon see the price of that stock drop below what you have just paid for it. This can look like a strong incentive to sell your stock before its price drops any further. If this starts happening across too many stocks, then investors will see the value of their stock portfolios falling and this can trigger an even larger sell-off. The value of the market plummets.

When the stock market behaves normally, investors act independently, just like atoms in a piece of iron that is too hot to have a magnetic field. When it crashes, investors all start doing the same thing – selling –  just like the atoms in a magnet that have all aligned their magnetic fields. You can also make mathematical analogies with flocks of birds, when they all fly together in the same direction. Even the avalanches that occur on the slopes of sand dunes have things in common with the movement of stock prices during a crash.

Systems that are normally so complicated that we might think of them as nearly random can, on occasion, start to act collectively. Stock markets can plummet in minutes, birds of a feather flock together, while atoms can align to produce powerful magnets. When systems start to behave coherently, scientists see complexity, not just complication. In other words, complexity is what results when the components of a complicated system start to behave in a collective, self-organised fashion. And remarkably, these complicated systems exhibit very similar behaviour when they self-organise.

Breaking symmetry
Despite examples like these, complexity remains a tricky concept to nail down. You know it when you see it, but it’s hard to come up with a single definition that encompasses all aspects of complexity that we see in nature and human society. Nonetheless, complexity has become an increasingly important concept in science over the last few decades.

One of the seminal articles in the field was written by theoretical physicist Philip W Anderson in 1972. Anderson noted that surprising behaviour can arise in systems that contain many interacting components, like the atoms in a magnet or investors in the market.  He pointed out that we can’t always understand such complex systems by focussing on their individual components.

When New Zealanders travel to Europe or North America, they often find themselves bumping into other people when they walk down a busy footpath. Kiwis tend to pass people on the left, while people overseas often pass on the right. At least for the first few days, this means we are constantly walking into people. It probably has something to do with the side of the road that we drive on, but this is not universal. In my experience, when the British are on foot, they seem to want to pass each other on the right despite the fact they drive on the left.

This is an example of what physicists call spontaneous symmetry breaking. It’s really only possible to walk down a busy street if we all agree on the way in which we’ll pass each other. Kiwis have made one choice, while people in other countries have made others, yet there is nothing in particular about any of us individually that says it has to be the left or the right – we just have to agree with those we walk past on a daily basis.

Something very similar happens in biology. Bio-molecules that are mirror images of each other are said to be left- or right-handed, by analogy with the way your left hand becomes your right when you look at yourself in the mirror. The chemistry of left or right-handed molecules is identical, at least when those molecules are in isolation or interact with chemicals that don’t have a handedness. However, in much the same way as you would find it hard to shake someone’s left hand with your right, left-handed molecules are not always able to react with right-handed molecules.

So biology has to make a choice. If life is going to work properly, it needs to stick to either left- or right-handed molecules, neither of which is preferred by the chemistry of the individual molecule. On Earth at least, life chose to be left-handed. So despite the fact that the building blocks of biology are chemicals, biology is not just applied biochemistry.

Complex societies
In other words, complex systems cannot be completely understood by studying their components in isolation. Understanding how one investor or molecule behaves in isolation won’t necessarily tell you why stock markets crash or how life works. The properties of complex systems, like the biosphere or the stock market, only emerge when the components of the system have to interact with each other.

Networks have become very important these days in our increasingly connected world. If you have read this far, it won’t surprise you that the networks that underpin both society and the economy also show complex, emergent behaviour. In recent times, studies of social networks like Facebook have led to some of the biggest advances in understanding complexity, but as with other complex systems, it is impossible to understand a network by considering just a single person in that network.

We have a lot more to learn about our society and the economy, but the lessons we should take from the study of complex systems is that we are not just a collection of individuals. Society is more than just the sum of its parts.