The book shows how the art of mathematical imagining is not as mysterious as it seems. Drawing on a variety of artistic resources the author reveals how anyone can begin to visualize the enigmatic 'imaginary numbers' that first baffled mathematicians in the 16th century.
Penguin Books Ltd
Publisher and industry reviews
UK Kirkus review
Don't be put off by the subtitle - Particularly the Square Root of Minus Fifteen - because this book isn't just for lovers of mathematical conundrums. It deals with the imagination, or rather the processes of imagining. If we visualise the phrase 'the yellow of the tulip' we can see it effortlessly in our mind's eye, yet we have no experience of the process of imagining it. We take thinking and imagining for granted, the processes are so intimate and automatic for us. The author wants us to experience the imagining process, and to this end he gives this faculty something we are not sure about - 'when some new image or viewpoint is about to reveal itself to us, but it resists emerging, we are forced to angle for it'. Mazur proposes that the inner articulations of the imagining process can be experienced if we attempt to imagine a concept which, even when it was first proposed, seemed devilishly outlandish. This is where the square root of a negative number - a literal impossibility - comes in. With a book dealing in square roots, it is natural that the Latin roots of the word 'imagining' are explored, as are the ideas of poets, thinkers, philosophers and writers. Mazur likens imagination to the sense of smell where the aroma of fresh coffee somehow bypasses the act of smelling: we notice the coffee, not the intricate activity of smell receptors communicating to our brain. All the best mathematical problems are come-ons, the book says - there is a gentle irony behind them. Thus letting our imagination tinker with the concept of the square root of negative numbers should stimulate our imaginations in such a way that we can experience the process of imagining. This is a curious and fascinating book. It's not an easy read by any means because the whole idea is to set the reader a problem, the mental exploration of which will hopefully allow us to experience our mental cognitive processes at work. But it's well written and often humorous, and it shows our conscious and subconscious mental activities in a whole new light. (Kirkus UK)
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