"It now appears that the way the universe began can indeed be determined, using imaginary time," Stephen said. We discussed this a bit. Stephen had been using a mathematical device in which time is replaced, as a notational convenience, by something called imaginary time. This changes the nature of the equations, so he could use some ideas from the tiny quantum world. In the new equations, a kind of tunneling occurs in which the universe, before the Big Bang, has many different ways to pass through the singularity. With imaginary time, one can calculate the chances for a given tunneling path into our early universe after the beginning of time as we know it.

"Sure, the equations can be interpreted that way," I argued, "but it's really a trick, isn't it?"

Stephen said, "Yes, but perhaps an insightful trick."