Imagination and the Imagined

In a recent post on math and spin class I touched on the question of “where do ideas (mathematical or otherwise) come from?” or more precisely, “where do my ideas come from?” and mused about connections for me between moving my body and moving my mind. As it turns out, movement is central to what is perhaps the most famous story of a mathematical lightning strike (our version of Newton and the apple): Henri Poincare’s “Bus Story”. As the story goes, Poincare’ (progenitor of chaos theory) has been puzzling over a deep mathematical problem. It leaves his mind for a little while as he makes plans to embark on geological expedition to some local mines. As Poincare’ steps onto the bus, he strikes gold! (sorry!) The solution of the problem is revealed!

“At the moment when I put my foot on the step the idea came to me, without anything in my former thoughts seeming to have paved the way for it…”

Poincare was one of the great science popularizers of his day and believed that as a leading scientist he had something of a responsibility to explicate the world of mathematics and science to the public. He was especially well known for his essays on special relativity and the math of space-time, perhaps so well told and well known that it may have influenced the rise of cubism in the visual arts. Poincare’ takes up in general the topic of mathematical creativity in his essay “Mathematical Creation,” Chapter III of his great expository work Science and Method (1908). His story of the bus is just a part of a thoughtful reflection on the role of the unconscious in the creative process.

My favorite description of mathematical epiphany is —> Read More