Skip to main content

17 Equations that Changed the World [In Pursuit of the Unknown] – Ian Stewart ***

There’s been a trend for a couple of years in popular science to produce ‘n greatest ideas’ type books, the written equivalent of those interminable ’50 best musicals’ or ‘100 favourite comedy moments’ or whatever shows that certain TV companies churn out. Now it has come to popular maths in the form of Ian Stewart’s 17 Equations that Changed the World.
Stewart is a prolific writer – according to the accompanying bumf he has authored more than 80 books, which is quite an oeuvre. That can’t be bad. He is also a professional mathematician – a maths professor – and that potentially is a problem. The trouble is that, much more so than science, mathematicians are not ordinary people. They get excited about things that really don’t get other people thrilled. And it takes an exceptional mathematician to be able to communicate that enthusiasm without boring the pants off you. It’s notable that the most successful maths populariser ever, Martin Gardner, wasn’t a mathematician.
So how does Ian Stewart do here? Middling well, I’d say. The equations he provides us with are wonderful, fundamental ones that even someone with an interest in science alone, who only sees maths as a means to an end, can see are fascinating. In most cases he throws in quite a lot of back story, historical context to get us interested. So the meat of the book is excellent. But all too often there comes a point in trying to explain the actual equation where he either loses the reader because he is simplifying something to the extent that the explanation isn’t an explanation, or because it’s hard to get excited about it, unless you are a mathematician.
The section on the Schrodinger equation, for example, is presented in such a way that it’s almost impossible to understand what he’s on about, throwing around terms like the Hamiltonian and eigenfunctions without ever giving enough information to follow the description of what is happening. (I also always get really irritated with knot theory, as the first thing mathematicians do is say ‘Let’s join the ends up.’ No, that’s not a knot any more, it’s a twisted or tangled loop. A knot has to be in a piece of string (or rope, or whatever) with free ends.)
Inevitably, to give the book real world interest, many of the equations are from science, and Stewart proves, if anything, better at getting across the science than he is the maths (probably because it is easier to grasp the point). The only section I’d argue a little with is the one on entropy, where he repeatedly says that entropy always increases or stays the same, where it’s more accurate to say that statistically it is very, very likely to do so. But there is always a small chance that purely randomly, say a mixture of gas molecules will partly unmix. (He also uses an unnecessarily complex argument to put down the creationist argument that uses entropy to argue for divine intervention, as it’s easiest to explain that you aren’t dealing with a closed system, something he doesn’t cover.)
Overall, then, I am not sure who will benefit from this book. There’s not enough detail to interest people studying maths or physics at university, but it becomes too obscure in a number of places for the general reader. A good attempt, but would have benefited from having a co-author who isn’t a mathematician and who could say ‘Sorry, Ian, I don’t get that. Let’s do it differently.’ Bring back Simplicio. (One for the Galileo fans.)

Paperback:  

Kindle:  
Using these links earns us commission at no cost to you
Review by Brian Clegg
Labels:

Comments

  1. zebedee29 June 2024 at 23:37

    When I bought a second hand copy the first section I read was a formula not an equation. My first thought was that the formula looked wrong and it was - the standard deviation was inside a square root. Re-prints also reprint this error and the publisher didn't acknowledge my e-mail. Perhaps too embarrassed?

    ReplyDelete

Post a Comment

Popular posts from this blog

The Laws of Thought - Tom Griffiths *****

In giving us a history of attempts to explain our thinking abilities, Tom Griffiths demonstrates an excellent ability to pitch information just right for the informed general reader.  We begin with Aristotelian logic and the way Boole and others transformed it into a kind of arithmetic before a first introduction of computing and theories of language. Griffiths covers a surprising amount of ground - we don't just get, for instance, the obvious figures of Turing, von Neumann and Shannon, but the interaction between the computing pioneers and those concerned with trying to understand the way we think - for example in the work of Jerome Bruner, of whom I confess I'd never heard.  This would prove to be the case with a whole host of people who have made interesting contributions to the understanding of human thought processes. Sometimes their theories were contradictory - this isn't an easy field to successfully observe - but always they were interesting. But for me, at least, ...
Post a Comment
Read more

The AI Paradox - Virginia Dignum ****

This is a really important book in the way that Virginia Dignum highlights various ways we can misunderstand AI and its abilities using a series of paradoxes. However, I need to say up front that I'm giving it four stars for the ideas: unfortunately the writing is not great. It reads more like a government report than anything vaguely readable - it really should have co-authored with a professional writer to make it accessible. Even so, I'm recommending it: like some government reports it's significant enough to make it necessary to wade through the bureaucrat speak. Why paradoxes? Dignum identifies two ways we can think about paradoxes (oddly I wrote about paradoxes recently , but with three definitions): a logical paradox such as 'this statement is false', or a paradoxical truth such as 'less is more' - the second of which seems a better to fit to the use here.  We are then presented with eight paradoxes, each of which gives some insights into aspects of t...
Post a Comment
Read more

Einstein's Fridge - Paul Sen ****

In Einstein's Fridge (interesting factoid: this is at least the third popular science book to be named after Einstein's not particularly exciting refrigerator), Paul Sen has taken on a scary challenge. As Jim Al-Khalili made clear in his excellent The World According to Physics , our physical understanding of reality rests on three pillars: relativity, quantum theory and thermodynamics. But there is no doubt that the third of these, the topic of Sen's book, is a hard sell. While it's true that these are the three pillars of physics, from the point of view of making interesting popular science, the first two might be considered pillars of gold and platinum, while the third is a pillar of salt. Relativity and quantum theory are very much of the twentieth century. They are exciting and sometimes downright weird and wonderful. Thermodynamics, by contrast, has a very Victorian feel and, well, is uninspiring. Luckily, though, thermodynamics is important enough, lying behind ...
Post a Comment
Read more