whether mathematics is an invention (a creation of the human mind) or a discovery (something that exists independently of us). The author suggests it is both.
It is, of course, a philosophical issue that goes back to Plato (and modern philosophers who assert the natural existence of mathematical ideas are called platonists). It’s also one that’s of cinematic and, more generally, artistic import. Art is the conjuring of ideas and emotions, and the touchstone for their reality is far more elusive than for scientific propositions—but these ideas and emotions are nonetheless as real as the objects that are photographed or represented or described in order to evoke them.
Everyone knows about the connection between math and science; I’m also fascinated by the mathematical implications of art, which came up a few weeks ago during a long subway ride with my younger daughter, Louise. She’s fourteen and has long had a nostalgia thing going for the material effluvia of bygone days—typewriters, LPs, rotary phones—and, though she’s got a good digital point-and-shoot camera, she’s intrigued by my 35-mm. SLRs (which, sadly, fell into disrepair not long ago). As the train lurched downtown, she caught notice of a tourist’s camera (actually a digital SLR) and asked me to explain to her how my film cameras worked.
I described the elements—the choice of film and of lens, the decisions regarding shutter speed, aperture, and focus, the concept of exposure—and told her that there were some odd particulars to master, such as the idea that the smaller the aperture, the larger the number, and relations of those numbers. I told her that it would be great if she wants to learn photography, and that it would also entail mastery of the mathematical elements of photography. She plays the clarinet, and we compared the mathematical side of photography to that of music—and suddenly it struck me why so many movie-lovers are also mad about music, and why we speak of images as compositions, and why images seems both metaphysical and deeply structured. Few filmmakers have made the explicit connection, but I think it’s an ongoing pathology of filmmaking, and of criticism, to bind the art of the cinema closer to theatre and to literature, which are its faux amis—false friends, deceptive cognates.
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