‘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 ShapesandFlow). 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.