This is another of Philip Ball’s quirky, scholarly, illuminating studies of the patterns of nature, the second in a trilogy. The others deal with shapes and branches; this one deals with flow of all kinds, from convection in the sun to avalanches in a pile of rice.

Ball has struck popular science gold with this trilogy, because he has a subject matter that is at the same time scientifically intriguing, visually engaging, and easy for the layperson to grasp. Fluid flow – the paradigm of flow in this book – is a typical case. Eddies and turbulence are interesting for scientists because they are horribly complicated. But because they are horribly complicated, the only hope of understanding many features of fluid flow is through a kind of simple qualitative modelling, the kind that is easy to explain to a popular audience. The Kelvin-Helmholtz instability, for example, is a mechanism by which flowing water forms wavy currents. It is a simple mechanism, communicable in a picture, and it creates delicate plumed patterns in water that make great images. And like most of the patterns in this book, it crosses mediums easily – it is present in clouds as well as rivers.

It turns out, as Ball reveals in the last chapter of the book, that real turbulence is not susceptible to any simple models like the Kelvin-Helmholtz model. But this is a rare exception. And even with turbulence Ball finds a pretty way of illustrating the science: he concludes as he began the book, with a work of art. This artistic theme – the first chapter is about representations of fluid flow in Western and Eastern art, with a focus on Leonardo da Vinci – is typical of Ball’s playfulness in this trilogy, his fondness for interesting diversions. These are indeed diverting, but they can also be disorientating. In the case of this volume, I finished the first chapter without having much idea of what the book would be about.

This book is certainly about something, though, even if it that something is hard to pin it down. It’s about fluid motions, of course: aside from the relatively conventional topics of water flow and convection, we have intriguing chapters on the collective behaviour of grains (in dunes, piles, and sheets) and on the movement of flocks of animals, crowds of people, and lines of traffic. But it’s also about deeper themes, which Ball mentions now and then but never instructs us about systematically. It’s about trying to describe and understand a wide class of phenomena through a single parameter – whether it is Rayleigh’s number for describing the tendency of fluids to give convection patterns, or Reynold’s number for describing the eddy-forming habits of a liquid stream. In a vague way it is about self-organisation, the capacity of macroscopic entities to form complex patterns with no outside help except a steady influx of energy. And in a fleeting way it is also about self-organising criticality, the quality that some phenomena have of spontaneously entering highly unstable states – a quality that the now-legendary sand-pile is supposed to have.

Readers who are not interested in these themes, perhaps because they would rather see them treated front-on rather than in the occasional sidenote, will still find plenty to enjoy in this book. The simplest pleasure it offers is to witness similar patterns in disparate phenomena: lane-forming on human footpaths and in the trails of army ants; convection not just in boiling water but inside the earth, in clouds, in cereal packets, and in the regularly-spaced circular craters that shape some landscapes in Norway and Alaska. Another of the book’s pleasures is its narration of the process of science, the sequence of attacks by different scientists, using different methods, on the same problem. In Flow, Ball’s account of successive attempts to explain sand dunes is typical of his blow-by-blow coverage of the process of discovery.

The breadth and detail of Ball’s interests in this book means there are many other pleasures besides, from the historical (Faraday’s prescient thoughts on convection in grains) to the domestic (an explanation of why shaking a cereal packet drives the chunky bits to the top). The downsides are that the scientific detail is sometimes heavy-going, and that the underlying themes of the book (aside from the general idea of fluid motion) are nebulous. On a more specific note, Ball’s discussion of self-organising criticality did not ease much of my confusion about that topic. On the whole, however, Flow deserves its place in Ball’s trilogy – and that is high praise.

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Review by Michael  Bycroft

‘They are formed from chaos, from the random swirling of water vapour that condenses molecule by molecule, with no template to guide them. Whence this branchingness? Wherefore this sixness?’

This is Philip Ball, in his grand and mildly pompous style, describing how a snowflake forms. Branches (like this review) starts with concrete details rather than a general introduction. And the book (but not this review) starts as it means to go on: it has lots of examples and plenty of themes, but no thesis. But don’t let it put you off this rich, thoroughly-researched exploration of trees, rivers, bacteria, cracks, cities, and other kinds of branching growth.

The reason Branches lacks an introduction is probably that it is one third of a trilogy that Ball published as one volume back in 1999, and Branches has not quite disentangled itself from the other two books (see also Shapes). Ball often ‘reminds’ the reader of what they ‘learned’ in Book I or Book II. And the conclusion of Branches looks like it has been lifted straight from the 1999 volume, since it describes many ideas that do not appear in Branches. The promotional material on the back cover is also confused about the book’s identity. According to the blurb, Branches depicts nature as an ‘ever-changing, kaleidoscopic array of forms’; on the other hand, it is about the ‘deep elegance, simplicity, and unity of nature.’

So what is it, kaleidoscopic or simple and unified? The point is that it (nature) is both. And so is this book. On the one hand it deals with an impressive range of phenomena, from the natural (leaves, rocks, lightening) to the human (social networks, urban development); from the wondrous (snowflakes, lightening) to the mundane (opening an envelope, rain on a window, cracks on a mug); from the big (cities and rivers) to the small (bacteria and electric charges) and many things in between (trees, lungs, minerals in rocks). It does not deal with the very big (galaxies, black holes) or the very small (quarks, curled-up dimensions), but this is part of its charm: it finds pattern and excitement where we would not expect it, in the everyday world of middle-sized objects.

On the other hand Branches shows that each of these phenomena have something in common. As the book’s many illustrations tell us, they all look a bit like the branches of a tree, with a medium splitting repeatedly into two. And they also show (in Ball’s words) ‘a delicate balance of chance and determinism’: rain falling randomly on a randomly rough surface gives rise to patterned river networks; weaknesses spread randomly through a piece of glass give rise to a predictable crack pattern. Many of them are also examples of fractals: each branch splits into two branches, which split again, and so on down the magnitudes. The shapes of many of the phenomena in the book can also be explained by a ‘minimization principle’: a branching river network minimises the rate at which the water loses energy; the branch network on a tree minimises (according to some scientists) the length of each branch.

But these general ideas can only go so far. Ball is wary of becoming a fractal bore, someone who goes round collecting examples of fractals and putting them on display. The interesting phenomena are those that share a particular degree or kind of fractalling, and the remarkable thing is that the same degree or kind appears in completely different contexts: two different cities that show a different ‘fractal dimension’ are less alike than a city and a bacterial colony that have the same fractal dimension. As with fractals, so with the other general ideas in the book. The maximisation principle in animal veinous systems is different from that in the branches of a tree; chance and determinism have different roles in the formation of a glass fracture than in the formation of the Giant’s Causeway in Ireland. Branches is kaleidoscopic not just in its variety but also its intricate patterning.

Another unstated theme of the book is models. The main technical problem for the scientists in Branches is not detection and measurement but abstraction and simulation. A tree or crack scientist, unlike a quark or star scientist, does not have much problem getting in touch with their phenomena: trees and cracks are right here, and easily observed. The problem is that trees and cracks are devilishly complicated and disorderly phenomena, and the scientist wants to find two or three basic principles that explain how all the different kinds of trees and cracks form. Ball describes how scientists look for these principles using concrete models that slow down or scale down phenomena, like an artificial snow-flake that crystallises on a thread of rabbit hair, miniature mountains formed in the lab, and slow-motion cracks made by gradually lowering a plate of hot glass into hot water. But most of the models exist on computer programs or in equations, and these models are the real heroes of the book.

By giving us the essence of each model without writing down any programs or equations, Ball shows his own talent for abstraction. At one point (to take an example at random) he describes how models borrowed from physics can mimic the growth of cities. First he describes the model input, the basic picture a team of modellers used for a growing city: new developments appearing around a central hub, favouring areas have empty space nearby. Ball then gives the model outputs – pictures of cities generated by the model – and compares these outputs to present-day Cardiff. He describes how a new modelling team adds complexity to the model inputs, to account for the fact that new developments feed off existing, successful developments. The new model generates new outputs, which Ball again compares to a real-life example, Berlin this time. In this way Ball describes how a particular model works, and how model-based science works, without describing a single program or equation.

Ball’s prose is lively but sober, constrained by the gritty details of the science he writes about. But the phenomena are often vivid, and Ball has a sense of their poetry. Here he is describing how a sawtooth-shaped tear develops in a soft material like paper when a hard object is run through it:

‘So each crest of the cycloid, where the rip changes direction, corresponds to the switch from bending to stretching the strip. The crack swings constantly from side to side, at the same time surging ahead and then slowing down like the juddering stick-and-slip of a heavy object being pushed across a floor.’

Branches is at the serious end of popular science writing. You don’t need a physics degree to enjoy it, but you do need concentration. Ball (a physics PhD) has a practitioner’s interest in the details of science, and each chapter introduces a new crowd of scientists, models, and physical phenomena. Readers may find themselves flipping back to earlier chapters to understand ideas in the current chapter. They also may find themselves reading some chapters twice to retrace Ball’s zigzagging exploration of an idea, and the lack of clearly stated themes (or a working introduction or conclusion) makes it easy to get lost in the details. But if you are interested in science, nature, and how the former can explain the latter, this book is a superb study.

Hardback:  

Review by Michael Bycroft

This is a bit of an oddity, in that Philip Ball has taken an earlier book (The Self-Made Tapestry), split it into three, of which this is one part, and updated it – but going on what’s in this book it was a good move, as there’s plenty to be going on with.

A lot of the content is driven by an early twentieth century work, On Growth and Form by the Scottish zoologist D’Arcy Thompson. Thompson’s thesis was that the new-fangled Darwinian thinking was all very well, and not incorrect, but it wasn’t the right explanation for many of the natural forms of things, which were more driven by the physics and chemistry of the processes that made them than any evolutionary adaptation. Ball doesn’t always agree with Thompson, but primarily demonstrates this again and again from the shape of beehive cells to the patterns on animals’ fur.

There’s a lot to like here. This whole aspect of why, for instance, a snail’s shell is a particular shape, with a certain pattern on it is not something many of us think of, but it needs explaining once you it occurs to you. I particularly liked the strange way that some cicadas seem to benefit from a very strange pattern, finding survival benefit from having a life cycle that is a prime number of years. We also see quite a lot on the strange oscillating chemical reactions that change colour or produce shifting patterns time and again.

Unfortunately, though the subject is excellent, Ball’s prose, which starts off very approachable, gets a bit bogged down and stuffy in later parts of the book. There’s too much technical detail on some of the processes and the whole thing gets a trifle dull and textbook like. This is a shame after an excellent opening. It will, however, make an excellent introduction for any one hoping to study more on the subject.

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Review by Peter Spitz

Even though this would be a hard book to pin down to a specific category, the “overview” categorization we’ve given it is no cop-out as it pulls together everything from sociology and political economy to physics, biology and maths.

It’s fascinating to learn early on in the book that those who in the 20th century worried about the application of a mathematical technique like statistics to the human populace had got things entirely back-to-front. Statistics originated as a collection of information on people, a crude form of census and developed into a mathematical discipline, rather than the other way round.

It’s a big book and it’s necessary to bear with Philip Ball through the rather (aptly?) ponderous chapter on Hobbes’ Leviathan up front, but once he gets into statistical physics he takes off.

There’s a lot on economics, on political power, globalization and even the Internet. Again and again the book comes back to the way that mass human action has some resemblances to the physics of large quantities of interacting objects. In physics this has produced a lot of theory based on statistics that does very well at predicting what will actually happen. When it comes to the human world, not entirely surprisingly, things are more complicated. Not only are most human masses not closed systems – so you have to take into account the impact of external forces – but a single individual can have a huge impact. When you are looking at gas molecules you aren’t going to have a Jesus or a Hitler – we, on the other hand, can expect that.

Because of this disparity, there are always problems with using the methods of statistical physics to make predictions. Ball spends ages describing how different models can be built, but often then has to come to the conclusion that while they can explain a lot that has happened, they aren’t much use at predicting the future – which is what we really want them to do. (One scientist Ball quotes did dare to make a prediction based on his model, that the UK housing price bubble would burst by the end of 2003 – while it will inevitably come, we’ve reached June 2004 without it happening.)

This gives us one of the two big problems with this book, and the reason it doesn’t score more than three stars. It is a great idea for a book, but everything’s really a work in progress. There are few conclusions it just goes on. And there’s the other problem. It goes on, and on, and on. There seems to be a bit of a Harry Potter phenomenon occurring with popular science books (it’s probably following a good statistical pattern) – the incidence of over-long books is on the rise. At around 640 pages, this book was twice the length the content deserved and in the end it was hard not to start skimming the material.

There is also one striking omission. Ball several times refers to fiction and speculative writing in considering the application of maths to mass human behaviour, but strangely never mentions Isaac Asimov’s remarkable 1950s Foundation trilogy, which features “psychohistory” a concept relying on a vast mathematical model of human space. While Asimov’s idea is not practically possible, neither are many of the others that Ball mentions, and nothing else has quite the magnificent sweep of Asimov’s confection.

Despite all this, it’s a fascinating subject and often Ball makes his points well, it’s just a shame he’s made it such a slog. If you’d like an easier time of it, try the overlapping and much better Sync.

Paperback:  

Review by Brian Clegg