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Vicious circles — confusing, instructive, amusing?


Ron Aharoni's little daughter returned one day from a visit to the dentist, and asked him, "Do you know how to make the anesthetic shot painless? You['ve] give[n] an anesthetic shot before". Of course, to make the anesthetic shot painless, another shot is needed.

Amusing? Indeed. But strangely, this mode of thought also has a serious side called 'circularity', or 'self-reference', and it is the protagonist of our story.

'Circularity' is the story of a Janus-faced conceptual structure that, on the one hand led to deep scientific discoveries, and on the other hand is used to trick the mind into believing the impossible. Alongside mathematical revolutions that eventually led to the invention of the computer, the book describes ancient paradoxes that arise from circular thinking.

What is the affinity between jokes and the celebrated theorem of Gödel, stating that not everything true about numbers can be proved from a simple set of axioms? And how do these two connect to the problem of moral responsibility–how can a person be held responsible for his or her actions if his or her choice is governed by physical rules? And what is the connection of all these to the invention of the computer?

Aharoni's fascinating book, Circularity: A Common Secret to Paradoxes, Scientific Revolutions and Humor, discusses all these and binds together mathematics, philosophy and the secrets of humor.

This book retails at US$28 / £18 (paperback) and US$58 / £38 (hardback) at major bookstores. More information on Circularity can be found at


About the Author

Ron Aharoni is a professor of mathematics at the Technion, Israel Institute of Technology. A previous book of his, Arithmetic for Parents, on his experience of teaching in elementary school, was a bestseller in several languages. His book Mathematics, Poetry and Beauty won the CHOICE Outstanding Academic Title 2015 award.

About World Scientific Publishing Co.

World Scientific Publishing is a leading independent publisher of books and journals for the scholarly, research, professional and educational communities. The company publishes about 600 books annually and about 130 journals in various fields. World Scientific collaborates with prestigious organizations like the Nobel Foundation, US National Academies Press, as well as its subsidiary, the Imperial College Press, amongst others, to bring high quality academic and professional content to researchers and academics worldwide. To find out more about World Scientific, please visit For more information, contact Amanda Yun at [email protected]

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