Ball’s Critical Mass

Philip Ball Critical Mass: how one thing leads to another Arrow Books 2004

Being an enquiry into the interplay of chance and necessity in the way that human culture, customs, institutions, cooperation and conflict arise.


This book was written as ‘popular science’. It had a mixed reception, but was commercially successful. It was one of many similar works that I looked at it briefly in the run-up to the financial crisis of 2008 in the hope that it might prove useful, but found nothing in it for me. I recently noticed that it was enjoying a resurgence in popularity, and have re-read it following the crash. What are people seeing in it?

The title is misleading. In classical physics mass is often very important. For example increasing mass can lead to a ‘tipping point’ and qualitative change. But actually the book is about criticality more generally: what factors (not just mass) are critical? What are the implications for such criticality?

Taken as a whole, I see the book as:

  1. Casting doubt (at the least) on the view (then prevalent in economics, for example) that classical physics provided appropriate metaphors for social interaction.
  2. Promoting the view that contemporary physics can provide some ‘better’ metaphors, and that these can have significant implications (e.g., for economics).
  3. Acknowledging that there are still some anomalies for which physics has no reasonable explanation, and so one needs to regard any metaphor with a critical eye.

On this last point, I differ from the Guardian’s 2004 review:

Ball’s argument is that this time, it’s different, guv. In other words, mathematical and statistical physics has attained such a sophistication that its insights into the behaviour of particles of matter can be transferred to the mass behaviour of human beings, whether investing in the stock market or racing for the exits after a fire at a football ground.

In addition, and sotto voce, Ball tells us that society in mass has now become so mechanical that human beings really do resemble atoms of physical matter interacting with one another through forces of attraction and repulsion.

Perhaps, then I should go along with a 2010 review:

Ball’s survey raises more questions than it answers, but one fascinating constant emerges: “Regardless of what we believe about the motivations for individual behavior, once we become part of a group we cannot be sure what to expect.”

The Crash

In 2004 I saw ‘critical mass’ as providing a reasonable summary of the grounds for doubting that there was genuinely ‘an end to boom and bust’ and that there might be a bust in the making. The book provides a good account of the distinction between genuine stability and what it calls ‘meta-stability’ and other strange states and  ‘phase transitions’, with many good examples, including traffic flow. However others were talking about the same problems in terms of ‘bubbles’, making the distinction between soundly-based growth (perhaps due to technological innovation) and bubbles (perhaps due to band-wagon speculation). If the book had led to all players having a common base with which to uncover and discuss the issues of the day it might have been useful. But it didn’t.

Insights from Physics

With the benefit of hindsight, the Guardian’s review suggest to me an important issue: If the ‘insights’ of mathematical and statistical physics had been ‘transferred’ to ‘the mass behaviour of human beings … investing in the stock market’, as the Guardian says that Ball is suggesting, and if it had sufficiently affected such investments,  then the particular follies contributing to the financial crash would have been avoided, and possibly the bubble might have been deflated before it burst. So not only do I think the Guardian wrong, I think the truth is the opposite of what they espoused then. I wonder if they have changed their mind?

After the crash Lord Turner was notoriously critical of the role of ‘sophisticated mathematics’ in contributing to the crash. This mathematics is that of the same ‘mathematical and statistical physics’ that the Guardian is critical of. So it seems as if events proved the Guardian right and me wrong.

At this point I wish to make a distinction between insights and methods. We can all agree that using off-the shelf methods (no matter how ‘mathematical’ outside their proper domain can go horribly wrong. So is it safe to apply the methods of physics to social systems (including economies)? Lord Turner says that it was a mistake. I agree.

So what are the ‘insights’ from physics? Some people seem to think what the Guardian accuses Ball of thinking: that social systems are ‘nothing but’ physical systems. If this were so then one might be forgiven for thinking that it would be rational (or at least pragmatic) to apply the methods of physics to social systems. But this would be to apply a pre-existing world-view, not an insight from physics. The insight that Ball seems to me to have got from physics is that one cannot rely on pre-existing world-views or ‘common sense’, and that in going beyond classical physics one has to go beyond classical concepts such as ‘critical mass’, and be critical of existing views.

(Of course, Ball may not make any of these distinctions and may only be caveating his words ‘for forms sake’ while actually having the kind of fundamentalist views that the Guardian seems to think. But I prefer to give people the benefit of the doubt.)

Causality and Enquiry

Critical mass’s sub-title is: how one thing leads to another. From this one might expect it to be about ‘causality’. Its conclusions have implications for causality which often conflict with common sense. But it rather skirts around the topic. The book also describes itself as ‘an enquiry into the interplay of chance and necessity ‘. It clearly has implications for the nature of enquiry and of chance and necessity, but doesn’t bring these out. It may be that unless common misunderstandings on these topics are overturned, misunderstandings like the Guardian’s and of mainstream economists prior to 2008 will prevail. But then the book would have to have been considerably larger, may not have been finished prior to 2008, and may not have been so accessible. Such is life.


Ball is advocating a judicous use of insights from mathematical and statistical physics, which seems to have its origins in the 1980s with a focus in the rightly famed Santa Fe Institute. The book – like many others – makes no recognition of the relevant mathematics of Whitehead, Russell, Keynes and Turing, excluding from its enquiry critical insights on the nature of chance and necessity, and on their interplay. It seems to me that this mathematics was very influential on our developing world-views, and I don’t see how we can expect to address contemporary isues (such as those that Ball raises) without their insights. Hence my blog.

My Conclusion

If anyone has a clear view on this book, I think it might well provide an exceptionally good strating point for a continuing enquiry into the issues that it seeks to address. But unfortunately, it seems to have left many of its readers muddled. If anyone can recommend a better book, that would inform reasonable debate, I would be glad to hear of it.

Dave Marsay

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