I was in Montreal at the time, to give a lecture, and it was miserably cold. I tried to see the city, but I could stand being outdoors for only a few minutes before I had to dash back inside again to warm up with a hot drink. So I was kind of forced to stay in my hotel room--and calculate. Ingrid Daubechies was recalling her momentous discovery, in February 1987, of a particular type of mathematical construct called wavelets, which subsequently sent ripples of excitement through the arcane community of applied mathematicians. It was a period of incredibly intense concentration. I was engaged to be married, and at the same time totally wrapped up in my ideas, even when I was sightseeing, or washing my hair, or cooking. But then everything sort of fell into place pretty quickly. By the end of March it was all finished. I felt drained and elated. And then we got married.
Picturing her struggling through the snowdrifts of Montreal, clutching her freezing ears while images of wavelets careered through her brain, was a bit difficult when she told me about it last June, with the mercury hovering around 90. We were sitting over iced tea in her native city of Brussels, at a table resplendent with roses, strawberries, and sliced watermelon, while through the open French windows we could hear her two toddlers tumbling about on the lawn. But the excitement of her intellectual adventure sparkled in her blue eyes, and her discourse became increasingly urgent as she searched for ways to cast her mathematical thought processes into ordinary words.
The subject on which Daubechies (pronounced DOhB-shee) quickly became one of the world’s leading authorities is signal processing--a branch of applied mathematics that is concerned with analyzing, transmitting, manipulating, storing, and reconstructing signals. A signal is simply a wiggly line, like a graph of the daily temperature throughout the year or a tracing of the trembling electrical output of a human brain. The multitude of applications of signal processing to physics, astronomy, computer science, engineering, and medicine is boundless. Daubechies visibly delights in the interdisciplinary nature of her work: she loves to talk to people in other fields and to help them adapt her insights and results to their own particular problems.
Signal processing isn’t something that only scientists do. We all do it, all the time, without thinking. Consider the unmatched ability of our eyes and brains to lift hidden images out of seemingly meaningless backgrounds. In the internationally best-selling book Magic Eye and its sequels, random-looking jumbles of colored dots and streaks--jumbles that look like pointillist abstract paintings but that are in fact patterns produced by powerful computer programs--turn out to be hypnotic picture puzzles. With sufficient relaxation of the eye muscles and a little patience, the viewer soon discovers three-dimensional images of weird creatures like winged lions displayed as if on a stage behind the page. The wondrous moment when the image begins to coalesce out of the chaotic foreground justifies the title of the book and bears witness to the power of the human mind--a power that is far ahead of technology. No robot yet built can come close to duplicating a feat of pattern recognition that any bright preschooler can master in a few minutes.
