Five Equations That Changed The World - Michael Guillen
Five Equations That Changed The World
Abacus Science Greats
ISBN: 0349110646 (Amazon link)
I've always felt that it was a pity that the general readership for popular science isn't exposed to more of the interesting detail ; I realise that there is a danger in scaring off the casual reader, but there is no particular reason why an equation or chemical formula can't be as easily explained as the sometimes forced analogies we're familiar with. I like the conceit of this book - that there are certain equations of physics which are so important, and so elegant, that no educated person should be unfamiliar with them. This appeals to me anyway as I've never really held with Snow's view of two cultures; in my experience it's much rarer to find a scientist with no appreciation for the liberal arts than vice versa.
Guillen decides to present five equations which allow him to cover scientific history, by which he usually means physics, from the C17th to the present day, as well providing an opportunity to profile some of the more colourful personalities behind the science. (General rule of thumb, the better a mathematician a physicist is, the madder they're likely to be.)
Each essay comprises a historical overview of the science of the day, and a biography of the scientists or mathematicians who derived each equation. Somewhat more clumsily, each section also has an afterword which describes how that equation has shaped our modern technology - these jarred structurally with the rest of each essay and, to me anyway, somewhat belaboured the point in most cases. However, Guillen does an admirable job of deriving each equation in a non-technical manner, with the minimum of calculus, without losing the elegance of each solution.
For his five most important equations, Guillen chooses conservatively but well - Newton's Universal Law of Gravity, Bernoulli's Law of Hydrodynamic Pressure, Faraday's Law of Electromagnetic Induction, Clasusius' Second Law of Thermodynamics, and, of cource, Einstein's energy/mass relation. It's interesting to note that it's major hassle for me to actually write these equations in HTML , evidently it's assumed that the general internet using population doesn't use equations  - which I suppose says something about we need more books like this one! Evidently it's not that easy for Guillen to get the equations typeset in their familiar form either, each is expressed in a clumsy, 'longhand' version instead of the compact forms familiar to me from my Physics days. I found that decision odd as one of his themes is the poetry implicit in mathematical descriptions of the world, that an equation can be appreciated properly only in its proper notation. Still, that's a minor quibble - a bigger quibble is his penchant for truly awful puns - electromagnetic induction is 'shocking', the naming of Bernoullis's equation remains 'up in the air' etc. The biggest quibble of all however would be with his implying that we once had perpetual energy machines by using dynamos!
Overall, a neat and enjoyable little set of essays pairing biographies of equations with biographies of those who derived them. Recommended if you haven't already been exposed to biographies of many of the great physicists.
 Disclaimer: I've a PhD in physics so my standards of 'interesting detail' might be atypical, but (pathetically) I still find electromagnetism difficult to think about, so I appreciate a good explanation when I see one! As for what I do for a living now, well, it explains why I count from zero. 
 The best way to show equations on the web is still to write LaTeX documents, install and compile a LaTeX to HTML translator, then generate GIFs of the equations to include in your pages. How very disappointing...
 Don't say MathML is the solution, at least not until my browser cheerfully displays it with no fuss, plugins or external readers.
 Programmer humour. Physics humour pretty much is restricted to comedy footnotes and "assume the [whatever] is a sphere" punchlines.
Posted: Mon - November 17, 2003 at 01:49 AM