Many people have had ideas on how to build a better society - this book starts by telling us about Thomas Hobbes and his plans in the Leviathan. However it is difficult to know whether these ideas would have the desired effects if put into practice - maybe they just reflect the biases of the originator. Contrast this with physical science which is driven by the requirement of being able to predict the outcome of an action. This book shows work which has been done to put social science on a similar footing.

Phase changes in physics are central to the book. We are introduced to first order phase transitions such as melting and evaporation, and to higher order phase transitions such as demagnetisation. Phase changes are dealt with by thermodynamics, which is built on the random behaviour of molecules leading to definite macroscopic properties such as temperature. Hence it is possible that the seemingly random behaviour of individual people might lead to definite predictions on a large scale, and so looking at thermodynamic behaviour of physical systems might give inspiration for predicting the behaviour of social systems. Interestingly, Ball points out that the ideas of randomness first travelled in the other direction. In the middle of the 19th century the gathering of social statistics greatly increased, highlighting the occurrence of the normal distribution and its relation to probability, and so leading to the acceptance of such thinking in physics.

I felt that the question of the order of a phase change wasn't dealt with as well as it could have been. Sometimes it is suggested that a social system has a higher order phase change (like demagnetisation), but then it is compared to melting (1st order), and I was left wondering whether this was stretching the analogy or whether I was missing something.

Naturally many people would like to be able to predict the stock market, so as to be able to make a fortune. This book seems to suggest that current models are inadequate, especially those based on a simple random walk. Hence there seems to be the possibility of making money from a better model of the ups and downs of the market. However it looks like this is probably a path to ruin.

There is a chapter on modelling the size of businesses, trying to show the effects of mergers, bankruptcies and the like. I found it interesting that one of the most realistic models assumed that businesses will grow in size due to economies of scale, but then lose out as they attract 'freeloader' employees, with the more industrious employees leaving to form their own businesses. Of course you need to be careful, just because a model matches the data doesn't mean that it's details are correct. One of the points made by this book is that it is often some general property of a model which is important, rather than the details of how it works, just as different physical systems may undergo similar phase changes.

Several chapters deal with the properties of networks, and in particular the World Wide Web. It is shown that connectivity often obeys a power law, that is if we look at nodes with a given number N of connections, then the number of such nodes will be proportional to a power of N. This is also known as a scale-free system. Such networks lead to 'small world' effects, where the path length to connect any two nodes is shorter than might be expected. However, this was one area where I felt the book wasn't as useful as it could have been - I was left with the general impression that scale-free networks differ from the original small-world networks, but this difference isn't really explained properly.

People have a natural tendency to group together. From early man forming groups to hunt a large animal, up to the present multinational collaborations, cooperation means that tasks can be carried out which would be impossible for an individual. But there is always the question of whether everyone is pulling their weight. In this book Ball has several chapters on the prisoner's dilemma, and looks at when it is favourable to stick to agreements. He also examines the tendency of nations to divide into two separate alliances.

The decision making of large populations is another form of grouping together. Ball looks at how elections are likely to be decided, and at how a new fashion might sweep through a society.

This book contains lots of interesting material, and is easy to read. However it is rather long at nearly 600 pages. Ball doesn't go in for conciseness, and I felt that sometimes there was too much historical material. There are nearly 200 pages of history and physics before the book gets on to what I feel is its proper subject which is the application of ideas from physics to the social sciences. On the other hand, I did feel I wanted to find out more about the ideas mentioned, which is one of my criteria for a good science book. So if you have the time then it is well worth reading.