Special thanks to Ian Stewart for answering 6 questions about his recently featured book – Seventeen Equations that Changed the World
Ian Stewart is a professor of mathematics at the University of Warwick, England, and a widely known popular-science and science-fiction writer. – Adapted from Ian’s Wiki Entry.
#1 – What was the impetus for 17 Equations that Changed the World?
My current publisher was at a book fair, talking to a Dutch publisher who translates popular science books, and they asked him whether he knew of a book about mathematical equations that would show readers whey they are important and what they have done for us. He asked me, and my view was that although there are several excellent books on topics like the beauty of equations, I didn’t know one that dealt with their historical role and importance in everyday life.
The more we discussed the idea, the more attractive it seemed. So we decided to fill what we thought was a gap and produce such a book. My publisher originally suggested the title (without the ‘17’) as an offhand description of what the book should be about, and then we decided to use it for the real thing. (In the USA it’s a subtitle — for marketing reasons, which I left to the publisher’s discretion.)
#2 – You give us a view of history through these 17 equations. How did you limit to 17? Could it have been 50? Did you have a set of criteria?
In principle it could have been 50 — it wouldn’t be hard to list that many highly influential equations — but there were practical issues. The equations were the main characters in the story, so to speak, so I needed one chapter per equation. A typical ‘mainstream’ popular science book runs to about 100,000 words, which meant that 20 or so chapters was the upper limit if I wanted to do a thorough job on each equation.
I started with a ‘long list’ of everything that sprung to mind, which ran to about 30. Then I had to whittle it down. One criterion was to provide as much variety as I could, and breadth of coverage. Of course that could easily lead to a larger number, so I had to compromise. It did suggest that if several equations were basically all part of the same big topic, then I ought to combine them under one heading. So the main equation of a chapter would open up the area, and represent it, but might not be the sole topic covered. So Einstein’s relativity, with at least five major equations, was represented by E = mc2, and introduced other equations along the way. And Newton’s Law of Gravity and Laws of Motion ended up in a single chapter.
Another criterion was that it should be possible to present a historical case for the equation having genuinely changed the world. The impact had to be big. A good example is Maxwell’s equations for electromagnetism, which led fairly directly to the discovery of radio waves, leading to radio, TV, radar, and modern communications including the internet.
Next, it had to be possible to tell the story of the equation in an interesting way. That was easier for some than for others. For example, the wave equation began from a question related to music, and ended up telling us about everything from sound to earthquakes. Everyone knows what a wave is. So that one didn’t get the chop.
That cut my list down to about 20, but I felt it was still a bit too long. I discarded a few more, on various grounds — too similar to something else on the list, too esoteric — and tried arranging them in a sensible order. Although each chapter stands alone, and covers a long historical period which usually overlaps a lot of other chapters, the whole book had to flow in a logical fashion. Which is why I started with Pythagoras rather than Einstein.
When I got to 17, it occurred to me that this is one of those mysterious-sounding numbers that would make a much more intriguing title than ’20 equations’. At the very least, people would ask ‘why 17?’. So I froze the decision there and went ahead with the writing.
Of course there are other equally important equations that I left out. Hooke’s law for springs, which underpins materials science. Google’s equation for ranking websites. The equations used in weather forecasting. But the book doesn’t claim that only 17 equations changed the world.
#3 – Equations such as the famous E=mc2 are notoriously simple on paper. How did you unpack the intricacies and implications of these equations?
The easy parts were the cultural and historical aspects. What was the world like before the equation was introduced, and how did it change as a result? It’s important to realise that just writing down an equation has no effect on history whatsoever: it’s what gets done with it that counts, and that involves all sorts of other things. The Navier-Stokes equation was a key step towards the invention of aircraft, but that also needed engineers, businessmen, pilots, and so on. The key thing is that the equation made a vital contribution.
I started each chapter with a large image of the equation, with each symbol labeled to say what role it played. Also a brief summary of what it says, why that’s important, and what it led to. The main idea here was to overcome a common fear of symbolic mathematics by tackling it head on. ‘If you’ve got a wooden leg, wave it,’ as they say in show business.
Within that framework, you’ve got a certain amount to build on when it comes to explaining the more technical aspects. In some ways E=mc2 is an easy one. E = energy, m = mass, c = speed of light — anyone can understand that. Since light travels very fast, c is big, so c2 is very big. Conclusion: a small amount of mass ‘contains’ an awful lot of energy.
Now you have to do your history honestly. It’s often said that Einstein’s equation led to the atomic bomb. Lots of energy = big explosion, OK? But actually, it didn’t, not in any vital way. Physicists already suspected that matter contained a lot of energy, and the problem was how to liberate it. Einstein’s equation helped check some of the back-of-the-envelope sums, but it didn’t lead to the atom bomb.
In fact the main application of Einstein’s’ theories of relativity in everyday life is the Global Positioning System. Your car’s satnav wouldn’t work without relativistic corrections to the timing signals.
#4 – Do you write the books on your own? Or do you have a group of readers to ensure that the book is pitched at the right level of understanding?
On the whole I don’t send books out for people to read in draft. This is probably a bit arrogant, but I generally know what I want a book to look like, and can recognise when it’s done. Or, more accurately, I think I can do that. I do sometimes ask people with special expertise to check a chapter or two, to make sure I’m working along sensible lines. So I mostly sit at a desk with a computer, and write.
I generally start out with a clear plan of the book, and write whichever bit seems most appealing at a given moment. I don’t start at the front and work my way systematically to the back. Usually the introduction is the last thing I write. This may sound chaotic, but (a) it’s more fun that way, and (b) the plan never survives contact with the enemy (as the military say) anyway. Books — well, my books, definitely — seem to develop minds of their own as they evolve. Entire chapters can be discarded, new ones inserted. They get split, combined, and rearranged. It kind of grows organically. I find out what works by trying it, and chucking it away if it doesn’t. I usually write about 20% more material than I need, and then dump the bits that don’t seem to fit or feel clumsy or whatever.
I should add that I also write books in collaboration with other people, and the technique there is a bit different. It depends on the book and the people. The most extreme (and successful) examples are the four Science of Discworld books with Terry Pratchett and Jack Cohen. Terry is of course a world-famous bestselling author; Jack is a biologist friend and I’m a mathematician. Interesting combination… Anyway, we found an effective way to work together, and all four got to number 1 or 2 on the non-fiction bestseller lists. (I do suspect Terry’s involvement helped a little with that… but the Discworld fans kept asking us ‘when’s the next one?’ whenever we said we were going to stop the series, so they must have approved.)
#5 – What has the reaction from your readers been?
This particular book went to number 6 on amazon in the UK (a math book at number 6! Amazing…) and it continues to sell very steadily. The reviews were generally good, and it was shortlisted for a history of mathematics prize (coming second). I get quite a few e-mails about the book, mostly positive; a few suggest alternative equations, which is fair enough and could be useful if I ever do a sequel. A bunch of Warwick University students started a thread about the book on Twitter, discussing that kind of issue. Generally, a lot of readers seem delighted that someone has dared to tackle those dreaded equations!
#6 – Are you working on any new projects/books you can tell us about?
Oh, yes. Am I ever. Professor Stewart’s Casebook of Mathematical Mysteries (third in a series of math miscellanies, but this time featuring the lesser-known detective Hemlock Soames and his sidekick Dr Watsup) has just appeared, and is already reprinting in the UK. A big project for the last two years was in iPad app Incredible Numbers, now available and getting very good reviews. It’s great fun and easy to use. A companion book, Professor Stewart’s Incredible Numbers, is in production for Easter 2015. Two more popular math books are under contract, one for 2016 and one for 2017, but I’m not supposed to tell anyone what they’re about. Also in the pipeline are revised editions of two undergraduate textbooks. And there’s a science fiction novel written with Tim Poston, an old friend of mine. We almost finished it in 1983, but he moved away and we lost momentum. It sat on the back burner for 30 years, but now we’ve updated everything and finished to story. A publisher is currently looking at the manuscript; fingers crossed. Oh, and there’s a research-level book on dynamics of networks under discussion with Marty Golubitsky, my main research collaborator. And possibly a small book about… but enough said.