Very few things in science have such iconic status as E=mc2 has… Why?
When the 14-year-old Richard Feynman first encountered eiπ + 1 = 0, the future physics Nobel laureate wrote in big, bold letters in his diary that it was "the most remarkable formula in math". Stanford University mathematics professor Keith Devlin claims that "like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler’s equation reaches down into the very depths of existence". Meanwhile Paul Nahin – a retired US electrical engineer – says in his recent book, Dr Euler’s Fabulous Formula, that the expression sets "the gold standard for mathematical beauty".
For some people this expression, named after the 18th-century Swiss mathematician Leonhard Euler, even seems to have become an icon, having special significance apart from its mathematical context. It once even served as a piece of evidence in a criminal trial. In August 2003 an eco-terrorist assault on several car dealerships in the Los Angeles area resulted in millions of dollars worth of damage when a building was set alight and over 100 vehicles were destroyed or defaced. The vandalism included graffiti on the cars that read "gas guzzler" and "killer" – and, on one Mitsubishi Montero, eiπ + 1 = 0. Using this as a clue and later as evidence, the FBI arrested William Cottrell, a graduate student in theoretical physics at the California Institute of Technology, who was later tried and convicted. Cottrell testified at his trial that "Everyone should know Euler’s theorem".
Icons, legitimate and illegitimate
The only equation that most people actually do know is another icon, E = mc2. Einstein’s famous equation has appeared in countless movies, pop songs and cartoons. Those of a certain age, for instance, may remember the hit single Einstein A Go-Go by 1980s electronic pop band Landscape, the lyrics of which went "You’d better watch out, you’d better beware, coz Albert says that E equals mc squared". More recently, during last year’s World Cup, the six large outdoor sculptures that were erected in Berlin to illustrate Germany’s status as the "land of ideas" included a car, a pair of football boots and a gigantic representation of E = mc2.
Icons can have a dark side, when they call more attention to their image than to what they stand for. The spell cast by equations can tempt us to think that all knowledge can and ought to be couched in the form of equations, with neat packages, balanced amounts and simple units. Equations have, for example, been composed for making perfect sandwiches, workable relationships and successful sitcoms. These are, however, illegitimate attempts to create algorithms for things that cannot be quantified.
The spell of equations that I want to discuss is something different, that of genuine equations that enthral authentic scientists. In addition to the two I mentioned already, other equations that I think are legitimate icons include Maxwell’s equations – "Was it a God who wrote these signs?" Boltzmann wrote about them, quoting Goethe’s Faust – and Einstein’s equations of general relativity.
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