For scientists, the subject of complexity really begins with computing. This actually is not that different from what people normally think about when they refer to complexity because computers are used by scientists to explore difficult, messy, problems that cannot be represented by neat easily solvable equations or easily described theories.

 

Before computers, theories of nature had to be understood and represented by human minds alone. Even if that meant understanding mathematics like calculus, geometry, or statistics, it didn’t require computers for us to make progress.
 

It turned out that lots of nature can be represented by pretty short, simple equations or relatively easy to understand and explain theories. This meant that scientists made lots of progress before scientific computing. Newton certainly didn’t need computers, neither did Darwin or Einstein, or the physicists and mathematicians who developed quantum theory.
 

However, when computing began in the 1950s some people began to realise that we could use computing to try to explore problems that previously were impossible for human beings to even begin to make all the necessary calculations to be able to understand and broadly predict the aspect of nature they were studying.
 

The first use of scientific computing was to predict weather systems. Before computers, weather people could only look at the current weather information and find previous charts or records of weather that looked similar, then they used to discuss with each other which historical chart looked most like the current picture. They predicted the weather that way. This was despite the fact that most of the physics of weather was well understood. The problem was that the physics equations just took far too long for a group of human beings to solve.
 

Nowadays, complexity is a subject in its own right and refers to the study of systems in nature that are best modelled by simple or complex computer programs and algorithms. Computers can be used to make calculations about these systems that human beings alone do not have the time to solve. So what are these systems? They are systems at the edge of chaos and order or 'messy' problems for scientists to deal with. They usually involve concepts like 'emergence', and 'path dependence'.
 

What kinds of systems might display these exotic properties?  Well, they include the brain, economic systems, many biological systems, and presumably the primordial soup at the beginning of life on earth. They are not easy to describe or calculate using conventional mathematics but we could try to use computers to help us to get at these difficult subjects.
 

So how did the complexity researchers get on since computers were invented? It turned out that these 'messy' problems are much harder than we thought. Complexity researchers have had some success, however. For instance, simple rules can be used to describe amazing behaviour like the flocking patterns of birds. No one bird is in control, each one just follows its nearest neighbours. Despite this, the whole flock appears to behave intelligently and complex patterns of flocking emerge from the simple rules each bird follows, which together can be modelled by a simple computer program.

 

The future could be that 'small is beautiful'. This is because some complexity research shows that very small computer programs could describe apparently complex aspects of nature.

 

Do we need complexity? Well, we need to improve our world and deal with the challenges we face, and complexity science can help. For instance, economics is famous for ignoring historical processes and preferring to model everything with numerical equations. Consequently, they generally don’t teach economics students about past financial crises. In the future, complexity science could be the answer to blending the messiness of history with economics methodology. One day, potential economic crises may be modelled with computers much as we now model the weather, with reliable predictions of brewing storms.