In particular, they explain three principles that they use throughout but that students today may not be familiar with: the

square root of minus one, the exponential series and its connection with the binomial theorem, and Taylor's theorem.

They propose that all the spatial and temporal separations are complex numbers of the form a + bi, where i is the

square root of minus one.

The

square root of minus one, called an imaginary number, is a very real concept that I have used in research articles in mathematics.

To even mention the

square root of minus one invites confusion.

True, juxtaposing complexities gets a decent response in certain sectors of academia--witness Jacques Lacan drawing on the world of high math to assert that the "erectile organ" is "equivalent to the

square root of minus one.

Infallibility is clearly a lie, as the engineer Yevgeny Zamyatin knew; his interest in Nicolai Lobachevsky's non-Euclidean geometry enabled him to translate the abstract thought of mathematics, where the imaginary

square root of minus one is part of the rational number system, into a social theory.

In An Imaginary Tale, Paul Nahin tells the 2,000-year-old history of one of mathematics' most elusive numbers, the

square root of minus one, also know as i, and recreates the baffling mathematical problems that conjured it up and the colorful characters who tried to solve them.

But a philosopher who is caught equating the erectile organ to the

square root of minus one has, for my money, blown his credentials when it comes to things that I don't know anything about.

The

square root of minus one is what is known as an `imaginary number': minus one cannot have a real square root, since when we square a number, the answer is always positive, whether the original number was positive or negative.