Soundings: I and i
Kevin Barraclough · 2001
There is, I think, something ethereal about i—the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in which it did not appear. And yet I always felt that it had, in some way, been slipped in with sleight of hand. It was something from beyond the looking glass. Where did it come from? What exactly was it? Even its name—an imaginary number—heightened the sense of the unreal. Problems that were formulated in the real world, as real equations, always had real solutions. i never came into the problem or into the solution. But to get from the problem to the solution in the world of real mathematics was either difficult or impossible. And yet it seemed that if one moved into the plane of imaginary numbers then the problem and the solution were separated by only a couple of lines of working. In this strange, imaginary world the problem and the solution were almost adjacent. One could effortlessly slip up a dimension, take one step, and drop down with impossibly elegant and simple results. It was like having a secret door into another world from which one could steal treasure and then return. But in this case the treasures were extraordinary and unexpected patterns. For a while I thought that maybe i was just a device that made calculations in the real world easier. I nearly lost my faith. Did it really exist? If the earth and all of mankind were destroyed, would it still exist out there in a silent universe? However, there it was, answering my doubts, deeply embedded in worlds as disparate as quantum spin and special relativity. I showed this piece to my registrar and he looked at me with that sad gaze he normally reserves for train spotters. How can one possibly get excited about something as dull as i ? I suppose the reason for me is that, in a universe that has embedded in its fabric something as impossibly strange as the square root of minus one, almost anything is possible.