A Brief Guide to the Great Equations [Paperback]

As a teenager, you hear music for the first time. The excitement and revelation of new musical inventions is fantastic, a real `high' in life. Then over the years you get used to it all and although some of the music is still enjoyable, you can't `hear it for the first time' anymore. But, very occasionally, you hear something new that brings back some of that original excitement , some of that thrilling bafflement and intrigue.

This book has it in abundance. If you think everything in science is pretty much solved, understood and in fact fairly boring, I would recommend The Great Equations. By following, in some depth, the original journeys, the original struggles and blind alleys, Robert Crease captures the excitement and, in fact, the mystery of all these equations. This is not a straightforward analytical look at the known products, instead it is probably as close as you can get to following the paths of creation through the protagonists' eyes and thoughts. Philosophical issues are here, as they should be (scientists who try to dismiss these aspects are missing something) but the central stories are the personal stories.

At first sight The Great Equations looks like just another popular science book (and there is nothing wrong with that - there are a lot of good ones out there) but I think it is more. It goes deeper than the run of the mill popular science and is so much more rewarding for it. Having said that, it is very well written -I found I was carried along - and apart from chapter headings, equations are largely absent.

I learned a lot from this book, for every equation covered in fact. Some of the equations are quite familiar to me but it is like seeing them for the first time. The fact that they are not given laws of nature in the form written by God, but are contingent on how our minds perceive reality, is really brought home. Of course they have some deep connection with reality, but to me, the fact that there is still a mystery as to what that connection could be, restores the excitement.

Einstein's journey from the first inkling that mass should depend on the motion of the observer to the final famous form of his equation is well covered. It hadn't occurred to me before that the key bit of maths in the derivation of special relativity is the Pythagorean theorem! To mention another chapter where I was learning throughout - Heisenberg's uncertainty principle. I thought I knew the stories but I had little idea of the intense arguments over the approaches to quantum mechanics in Europe in the `20s. Again, this chapter was a bit of a revelation. I felt, after all these years, that I had a fresh insight into quantum mechanics after my struggles with it as an enthusiastic undergrad. It makes me want to have another go at some serious maths (another good book for rekindling excitement is The Art of the Infinite by R & E Kaplan.)

Finally, this book has the best system for looking up chapter notes I have seen. Highly recommended.

Oh, and Cameron Diaz has gone up no end in my estimation! (Robert Crease quotes something from The Biography of an Equation by David Bodanis - another cracking good read).

This is an accessible science book, bringing together a collection of best known (and less well-known) equations and giving just a hint at the beauty of the mathematics that underpins science. Robert Crease opens with Pythagoras' Theorem, a^2 + b^2 = c^2, which most people with school-level mathematics will remember allows you to work out the third side of a right-angle triangle if you already know two sides. He shows some proofs (there are over 500 known proofs of the theorem), and leads on to a wider discussion, including its application to the 4-dimensional geometry of Einstein and spacetime.

Next, Newton's second law (F=ma), which relates applied force to acceleration, and is used as a practical tool by schoolchildren in Physics or Applied Maths. The book reveals that although Newton formulated it, it was not expressed as a formula until Euler came along some years later. The following chapter has the law of universal gravitation, which can be used to describe the motion of a planet around a star, or the gravitational effect of one planet upon another.

Chapter 4 shows the mathematical beauty of Euler's equation, which relates two natural constants, pi and via the so-called imaginary number i (the square root of -1). It goes on to discuss some of the important topics discussed in Euler's work, "Introductio".

Chapter 5 gives us the second law of thermodynamics, which in brief tells us that everything in the universe tends towards increasing entropy (i.e. becomes more disorganised). Chapter 6 brings us to Maxwell's equations. While other scientists (like Faraday) had found and documented interesting aspects of electricity and magnetism, it took Maxwell to express these mathematically. As Crease tells us, Richard Feynman (brilliant scientist and communicator) once said that Maxwell's equations were the most significant event of the 19th century, even including the American Civil War. This is a very interesting chapter, but if I have any criticism of the book, it would be that this chapter is not long enough. I wanted to know more about what the equations mean; what Heaviside's reformulation of the equations brings, and really how they are applied?

Chapter 7 reaches E=mc^2 with some inevitability, and Crease dubs this "the Celebrity equation", because of course nearly everyone knows this formula, even if they have no idea what it signifies. This leads us onto Chapter 8, which covers general relativity (i.e. how spacetime works). This section of the book covers the same material as the Brian Cox book Why Does E=mc2?, but I felt that Crease's version was more readable and less repetitive.

Chapter 9 calls on Schroedinger's equation, and by this point in the book, the equations have ceased to have the simple beauty of Euler, and now are using calculus. However, if you can stand to read on past the mathematics, we start to enter the strange world of quantum physics, where particles and waves can be the same thing, and the certainties of Newton's world are replaced by probabilities. Chapter 10 covers the Heisenberg Uncertainty principle, which means that you can know the position of a particle but only a probability of its momentum (or vice versa). The chapter discusses some of the events and politics among the top physicists of the day; this was an inflection point where the science changed fundamentally, and the personal and professional relationships of some scientists of the day went through incredible turmoil. Crease quotes from Michael Frayn's play Copenhagen [DVD] [2002] [Region 1] [US Import] [NTSC], which covers one aspect of this, i.e. the relationship between Werner Heisenberg and Niels Bohr.

Stephen Hawking said that every equation you include in a book halves the potential audience, and ultimately included only one in his A Brief History Of Time: From Big Bang To Black Holes: From the Big Bang to Black Holes, namely E= mc^2. I hope that Hawking is wrong: not only for the sake of Crease's book, which is an excellent read, but because better familiarity with science would be a benefit to the whole of our society.

This book deals with the interactions between scientists and the struggle not so much to come up with the new concept but to define it concisely. Many advances that are attributed to a particular person are due mainly to that person being able to concisely define (probably by an equation) what was the current thinking at the time. The book is pretty much a biography about the scientists not much about the equations.

I think Lyndal Hughes's review is pretty much spot on. It is certainly not what I was expecting either. It gives no explanations of the equations at all. Basically it just waffles. I got a feeling that the author may have felt it was too hard for a scientist to explain things in a layman's terms (i.e. you needed to be a physicist to understand) so he didn't bother. For this reason I give it one star not five because I wasn't after a soap story but an explanation of the equations and the maths and physics behind them.