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Small World – Mark Buchanan ***

It’s entirely possible for something to be both fascinating and intensely unsatisfying – and that is how I felt about Small World and the topic it covers.
The subject at the book’s heart is ‘small world networks’. This is the idea behind the famous (or infamous) concept of six degrees of separation. Based on an experiment by Stanley Milgram in 1970, the idea is that everyone in the world is connected to everyone else by no more than six links. The original experiment has been criticized for being limited to the US (hardly the whole world) and not taking in enough barriers of language, class and ethnicity – yet even when these are taken into account, there is a surprisingly small number of jumps required to get from most of us to most others.
What’s even more fascinating is that this type of network occurs widely in self-organizing systems, whether it’s the structure of the internet or biological food chains. What tends to crop up are networks where there are local clusters with a few long distance links, which drastically increase the chances of wide ranging connectivity. There isn’t a single style of these small world networks – some, for instance, have vast hubs with many spokes, while others are more democratic. (Interestingly, the internet, which was supposed to be democratic to avoid losing connectivity, as it was originally a military network that had to survive attack, has gone entirely the other way with huge hubs.)
What strikes me is the vagueness of it all. There seems to be an imprecision that’s most unusual for a mathematical discipline. This could be down to the way Buchanan is presenting things of course – his style is very readable but this does sometimes (not always!) bring a degree of smoothing over. Just as an example, we are told about Erdös in 1959 solving the puzzle of how many roads are required, placed randomly, to join 50 towns. Buchanan tells us ‘It turns out, the random placement of about 98 roads is adequate to ensure that the great majority of towns are linked.’ I’m sorry? What does about 98 mean? How about ensuring the vast majority are linked? That’s small consolation if you live in one of the towns that is isolated.
The other vagueness, in the ‘six degrees of separation’ model is what we really count as an acquaintance. It’s such a fuzzy concept, it’s hard to see just how it can be made to operate with the precision required by mathematics. I have nearly 1,000 people in my email address book. Are they all acquaintances? How about those lovely people on the Nature Network with whom I often exchange comments about blog entries, but none of whom have I ever met or spoken to, and only two have I ever emailed? For that matter, what about my ‘harvest’ emails? Is somebody an acquaintance because I’ve seen their email address? Probably not. How about when someone sends me an email and copies in lots of other people. Are those email addresses part of my contact circle? I don’t know – and I doubt if the people who play around with this interesting, but in some senses rather futile feeling, research do either.
Both these examples relate to why there’s an underlying lack of satisfaction. Like chaos theory, this is a concept where initially you feel ‘wow, this should give amazing insights’ because it’s so fascinating, but then it doesn’t. I’m reminded of Rutherford’s famous remark ‘All science is either physics or stamp collecting.’ Dare I say it – this feels a bit like stamp collecting.

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Review by Brian Clegg
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