Math as a Language in Its Own Right

Alfred Scharff Goldhaber in American Scientist:

Vtemzruvyad9Robyn Arianrhod’s theme in Einstein’s Heroes: Imagining the World Through the Language of Mathematics is that mathematics is a language, with its own grammar and (implicitly) a number of dialects. Her view implies that mathematics, like more familiar languages, is something characteristically human, an idea appealing to anyone fond of math. The notion of mathematics as a language is not new, but what distinguishes her take on it is that she focuses on a particular, critical event in the use of mathematics, where we can see mathematical language growing in front of our eyes until it reveals a brand-new piece of physics.

She starts her account with a riff on Remembering Babylon, David Malouf’s novel in which a young English boy has been marooned in an aboriginal community in Australia and suffused with its language and culture. On rejoining British society he feels strange—and seems strange to those around him—having been virtually transformed into an aboriginal thinker by being steeped in that language. With this prelude Arianrhod makes a point of the power of language, which she proceeds to bring home with her mathematical exploration.

Who are the heroes of the title? The first is Isaac Newton, who created the earliest grand vista of mathematically encapsulated physics through his universal theory of gravitation. Then comes Michael Faraday, who replaced Newton’s notion of forces acting instantly between separated objects with a new concept, a field generated by an object in one place, flowing from there throughout space to influence the motion of anything that encounters it. Finally, James Clerk Maxwell reformulated the field concept, which Faraday had conceded was not properly mathematical, by using a new language—(differential) vector calculus. This led to a spectacular deduction, the existence of electromagnetic waves traveling at the speed of light. Maxwell’s reformulation invited scientists to identify light as an electromagnetic wave and also to try generating in the laboratory new waves of much lower frequency. Heinrich Hertz later achieved this feat, and today these waves are that commonplace of daily life, radio.

More here.  [Maxwell’s electromagnetic equations shown on upper right.]