Icons of Ideas

(A Brief Guide to) The Great Equations: The hunt for cosmic beauty in numbers

by Robert P Crease (2008/2009, Constable & Robinson

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• A + B = C
• Newton + Apple = Myth
• Art + Science = Education
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  • Elsewhere on the bookshelf
  • Elsewhere on the blog

A + B = C

The Great Equations is a well constructed little book [300 pp – not so little!] with a selection of 10 more or less well-known equations, mostly from physics. These are presented chronologically with each chapter telling the story of the people and ideas that led up to one of the equations. And what are they? Each may be seen as an icon of understanding, each a pithy encapsulation of a leap forward in humankind’s understanding of how the Universe works.

But how does this book differentiate itself from the hundreds that make the noble attempt to popularise the history of science? And of all the millions of equations and ideas that there have been, why choose these ten, and the episodes which lead up to their appearance? Some equations could not be overlooked (Pythagoras’ Theorem and Einstein’s E = mc²) and others put in an appearance in the public imagination and wider culture (the 2nd Law of Thermodynamics and perhaps the astonishing Euler’s equation). Is it referred to in The Simpsons? Then it’s probably in!

e^i*pi + 1 = 0

e the base of natural logarithms (an irrational number), raised to the power of pi (another irrational number), multiplied by i, the square root of minus 1 (an imaginary number), plus 1 equals zero [discovered by Leonard Euler]

Also on the team sheet are Maxwell’s equations which underpin all electricity and magnetism. which provide understanding of virtually ALL of the tools of our modern world. Here is Einstein’s general theory of relativity, together with Schr­ödinger’s wave equation and Heisenberg’s Uncertainty Principle which represent the foundations of modern physics and cosmology. It’s a selection that well represents some of the high points in scientific thought. But of course we know that, as the publishers of A Brief History of Time warned Stephen Hawking, for every equation in a book you can halve the expected sales! So who is this book for? And does it work?

Newton + Apple = Myth

It takes a certain commitment and curiosity to embark on a book which not only presents some daunting equations, but in places seems to assume quite a bit of scientific or mathematical understanding. For example the chapter on Schr­ödinger’s wave equation and the stories behind the development of quantum mechanics is an truly entertaining one, full of eccentric characters from the 1920s. The account is one that I have been familiar with since my teens. Yet a working knowledge of the wave equation is something that I only briefly attained in an advanced physics degree course. I recall that in my finals exam one nailed on question was the derivation of Maxwell’s equations and demonstration that light is an electro-magnetic wave. But in places Robert Crease almost assumes that a reader would have these kind of experiences to draw on, while elsewhere he writes in an accessible, popular science style.

His accounts of the human histories behind these iconic equations is the main substance of the book, and these are very readable and lively. And these stories reveal one of the themes of Crease’s writing: these great scientific achievements are hardly ever the outcome of a lonely, scorned genius but are inevitably the result of many minds, many rejected hypotheses, many debates, a relay race in which the baton is often handed across generations or disputed between rivals. Almost always international collaborative teamwork. Even when extraordinary minds such as Isaac Newton or James Clerk Maxwell or Albert Einstein appear, they are depending on others’ observations, painstaking experiments or more comprehensive mathematical expertise, “standing on the shoulders of giants”.

Newton’s fabled falling apple is a myth of his own making and that was burnished by the same canny PR that airbrushed his obsession with alchemy and biblical end-times prophesy out of history. Einstein’s Special Law of Relativity was an idea in the air for decades, most of it having been described and demonstrated piecemeal before he neatly put it together into something coherent. (His General Theory of Relativity, however, which later revolutionised our understanding of gravity, matter, space and time was an outstanding and singular work of genius, albeit with a lot of heavy maths lifting done by others.)

Art + Science = Education

But in my view the real value of The Great Equations, which gives it a distinctive voice and which, for me, will last longest in my memory lies in the several short essays sandwiched between the main chapters. These are digressions into topics of scientific philosophy and comment on the intersections of science with popular culture and consciousness. He discusses “Equations as Icons”, in which he looks at how non-scientists package ideas in the form of equations to lend them some often inappropriate weight.

He also addresses the misleading idea that because “celebrity” equations (like E = mc²) appear simple, that the ideas they represent are anything less than profound. Elsewhere he speaks to the myths that either Science is a monolithic body of knowledge that is given from on high (instead of an ever-revised process of best understanding), or that Science is just a matter of opinion and that in a “post-truth” world it carries equal weight to whatever alternative facts some group of ignorant or malevolent conspiracy quacks come up with this week. These are well argued and elegant little pieces.

I suppose my overall concern with what I think is a very fine book, rests with my doubt that it can really reach anyone who doesn’t already buy into an appreciation for the beauty and simplicity of scientific discovery. Would it appeal to someone who may not already trust or understand the complexities of the gestation of these great ideas. I would like to think it is a game attempt to bridge over those “Two Cultures” of the sciences and humanities which C P Snow railed against (over 60 years ago!). But although science is now better represented in the media and has some first class communicators, there are still so many people who see the effort to understand perhaps one or two of The Great Equations, as somehow beneath them. I maintain, along with Snow and Crease, that not caring about understanding the Second Law of Thermodynamics is equivalent to someone boasting that they have never read anything by Shakespeare.

What do you think?

Elsewhere on the bookshelf

• The Two Cultures and the Scientific Revolution by C P Snow (1959, OUP) – we’re still trying to respond to his ideas.
• Newton – The Making of a Genius by Patricia Fara (2002, Picador) This tells the story of how Newton’s reputation has waxed and waned. It is about how an image and reputation is made, often far detached from the facts of a man’s life. Well written by an eminent academic.
• A Brief History of Time: from the Big Bang to Black Holes by Stephen W Hawking (1988, Bantam Dell) – one of the most popular – yet legendarily unread – books of popular science.
• Books do Furnish a Life: Reading and Writing Science by Richard Dawkins (2021, Penguin Random House) – this is a terrific compilation, which looks hard at how best to communicate science to a wider audience.

And elsewhere on the blog

Fred amongst the Stars – Welcome (grandpops-bookshelf.co.uk) – a young astronomer getting the message across on the wireless in 1950.

At the Cutting Edge – Welcome (grandpops-bookshelf.co.uk) – another way to tell a history of science, through the story of one idea: Occam’s Razor.

So what do you know? – Welcome (grandpops-bookshelf.co.uk) – it’s not what you know, but how you know!

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