It Must Be Beautiful: Great equations of modern science

My current reading is rather fascinating. It’s actually a reread. I picked it up, along with Deborah Cameron’s The Myth of Mars and Venus, in a bookshop in Naas. I was in Naas for a job interview (I’ve forgotten what the job was for, but this must have been a chemistry job before I got into writing code, so a couple of years ago now). I’d not heard of either book before, and both called out to me as books I absolutely had to buy. I’ve read both more than once, so the instinct was a good one.

The concept of “beauty” in a scientific equation is perhaps a tricky one, and not all the equations in this book actually are beautiful. The Drake equation stands out as an odd choice. (For a start, despite its name, it’s a formula, not an equation. Also, it is not, by any reasonable definition, beautiful. It’s an interesting subject, yes, and the article on it is very well written, but the formula is emphatically not beautiful: it’s an ugly kludge.) There’s a different author for each equation, and some talk quite a lot about mathematical beauty, while others seem uncomfortable with the concept the editor has chosen and skip over it quickly, with an embarrassed cough.

The essays on Dirac and Einstein (there are three essays on Einstein) all make a great deal about mathematical beauty, but then so did both of those physicists, particularly Dirac.

I quite liked David’s review on Good Reads and shuttledude’s review on Amazon.com. I agree with both that the writing is uneven, and the style of the essays is very varied, with some focusing directly on the equations themselves and others being more biographical sketches. I also agree with both that Robert May’s article on the logistic map and how chaos theory is applied to evolution, “The Best Possible Time to be Alive”, is absolutely top class: science writing at its best.

I do have a background in chemistry, and perhaps it is for this reason that I disagree with the assertions by David and Helen Joyce that chemical equations don’t count. I think the essay on the ozone layer and the effects of CFCs is perfectly at home in this book, and well written to boot. (There is, of course, real maths in chemistry too, but that’s not what’s covered in this chapter. It is mentioned that the rates of certain reactions seemed inconsistent, which lead to further research, but the mathematics of reaction kinetics (which is calculus) was not explored.)

From reading the reviews, it looks like the chapters are ordered differently in different editions. A few state conclusively that the book opens with the famous E=mc2. My edition, however, begins with an essay arguing that E=hf was actually Einstein’s most important work, even if it was Planck who came up with the equation itself.

The review by William G. Faris of the American Mathematical Society is rather in-depth, and is actually more an expansion on some of the mathematical concepts treated in the book than a typical review.

The authors of the chapters in this volume do a remarkable job of showing how each of the great equations is situated in a broad cultural context. The equation itself is at the center. But the geometry is something like that of a black hole; the actual equation remains nearly invisible to the general reader. One of the privileges of being a mathematician is that one is allowed a glimpse inside.

Is it a strength or a weakness of the book that in many of the essays the equation itself is “nearly invisible to the general reader”? (The Dirac equation is relegated to the notes at the end of the book.) Probably a weakness. The strongest essays in the book tackle their equations head-on. Once again I’ll mention the logistic map, and add Igor Aleksander on the Shannon equations. Next to those two I’d place the other biological entry, John Maynard Smith talking about evolution and game theory. And then I’d put the essay that other reviewers felt was out of place, Aisling Irwin on the Molina-Rowland chemical equations and the hole in the ozone layer.

A review by American Scientist, quoted in the book itself, praises specifically Christine Sutton’s essay on the Yang-Mills Equation (an essay which managed to cover interesting historical and biographical detail, and also tackle particle physics in great detail) and Roger Penrose’s article on the Einstein equation of general relativity.

TRiG.

2 thoughts on “It Must Be Beautiful: Great equations of modern science

  1. Late to comment because I’ve been doing intensive oral exams. I agree that chemical equations should count, and I think you could argue that metabolic pathways do, too: the Kreb’s cycle has a lot of beauty to it, although less when you have to memorize it. I thought about Michaelis-Menton when I started reading the post.

    It sounds like a book worth checking out from the library, at the least.

  2. Ah, I’d either forgotten, or possibly never heard about, Michaelis-Menton. But then, biochemistry was the subject I struggled with the hardest in chemistry. I think I never got enough of a grasp of it to see the grand scale, so it was just lots and lots of learning without much sense or pattern. I know there are patterns there, and that many of them are indeed beautiful, but I never really got far enough in the subject to grasp them.

    Organic chemistry, on the other hand, I loved. Specially anything to do with benzene rings.

    TRiG.

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