| The author is trying to bridge the gap between the "two cultures" -scientific minded, and the literary minded. He is trying to target the literary camp in particular. He gently tries to introduce the reader to complex numbers by use of examples. We can 'imagine' positive integers, and we can imagine negative ones too. At least, we aren't bothered by not really knowing them; we can find physical analogies for them. Mazur tries to do the same with imaginary numbers. I think he did an okay job. I can imagine adding them now, and multiplying them, and even taking their square roots. He does, however, stop short of raising a number to an imaginary exponent. The imagery is simply transformations on the plane. By reading this book, it is immediately apparent that the author has an encyclopedic knowledge. But, this is the problem however. He's all over the place with analogies. We have drawings of cockroaches, passages about a particular tulip versus an idealized tulip, talks about Allah. None of it has anything to do with imaginary numbers, nor imagining them. Instead, these images are used to describe how ideas come into fruition. He tries to say something like, "hey ideas take time to bubble up into consciousness, we have traces of it in the atmosphere. Later, we can feel it and know it's there. Finally we get a handle on it, and it becomes concrete." Looking briefly through this book right now, I notice these irrelevant imageries don't take much book space, but they are so oddly out of place, they take up a majority of my impression of the book. I can't say this book is a complete waste of time. I enjoyed his explanation of the basics of algebra, and why we can't divide by zero, and why a negative times a negative is a positive. In fact, it's the best explanation I've read so far. Also, the history of the emergence of complex numbers is abbreviated, but informative. However, things are just watered down and lost by these crazy tulip analogies about how ideas become concrete. This book is so-so. I feel that if someone wants to know the history of imaginary numbers and how to think about them, they could probably find a better book. If there is a second edition, I think Barry should expand his bookkeeping example as an introduction to algebraic rules. Then cut to the chase, show us to grasp imaginary numbers, think of them as points on the plane, and operations on them as transformations and vector addition. He can later discuss how this mental model of imaginary numbers came to be, and these tulip images won't stick out so sorely. This would be much like how people view a great painting or a magnificent edifice. Rarely is anyone privileged to see a magnificent work in progress. And those who do rarely grasp or appreciate the beauty that is forming before their eyes. Rather, after appreciating the final work, we then watch a documentary on how such and such a building was built. Barry would do better to follow this formula, instead of immersing us in a work in progress, and more-or-less, confusing his readers. Finally, I hope Barry uses his tremendous intellect to show how imaginary numbers relate in the day to day. And not via electrical engineering! Imaginary numbers are used in electricity, but since electricity is hare to grasp, real world examples using electricity would be confusing. What I'm getting at is this: We can find uses for negative numbers in the day to day: walk 3 north, 4 south, and you'll be 1 south. Perhaps there is something quite simple for complex numbers too. If in succeeding with that last point, then we may not be so bothered by not grasping imaginary numbers, because we have a physical analogy of them, and then we can pretend to know what they are, just as we do the integers. | 
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