Circularity : a common secret to paradoxes, scientific revolutions, and humor

"The book is divided into 8-10 chapters that are each only 2 or 3 pages long . . . this feels like a nice feature of the book, since you can dip in and just read a short bite before moving on. The author clearly has some interesting ideas and at times I found his writing to be quite engaging." Maa Review "I did enjoy reading (and re-reading) this book very much. Reading it deserves a warm recommendation not only for mathematicians but for anybody . . . this book makes you think about how and what you think you are thinking." European Mathematical Society "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. Another aspect of circularity, its ability to entertain, leads to a surprising insight on the time old question "What is humor". The book presents the ubiquity of circularity in many fields, and its power to confuse and to instruct. '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. Another aspect of circularity, its ability to entertain, leads to a surprising insight on the time old question'What is humor'.Contents:The Dark Side -- Paradoxes:MagicFree WillThe Mind--Body ProblemThe Illuminated Side -- Scientific Breakthroughs:Large Infinities and Still Larger OnesGödel's Incompleteness TheoremTuring Invents the ComputerFor the Experienced Hikers Readership: Researchers in mathematics, philosophy and general public.Key Features:It represents the Godel theory in a clear yet rigorous wayIt studies paradoxes in a unified way -- unifying the so-called'logical paradoxes'and the philosophical paradoxesIt is a popular introduction to set theory '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. Another aspect of circularity, its ability to entertain, leads to a surprising insight on the time old question 'What is humor'. The book presents the ubiquity of circularity in many fields, and its power to confuse and to instruct.See Press Release: Vicious circles -- confusing, instructive, amusing? ""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. Another aspect of circularity, its ability to entertain, leads to a surprising insight on the time old question "What is humor."--Provided by publisher "Circularity" is he story of a Janus-face conceptual structure, that on the one handled to deep scientific discoveries, and on the other hand is used to trick the mind into believing the impossible. Alongside mathematical revolutions that enventually led to the invention of the computer, the book describes ancient paradoxes that arise from circular thinkig. Another aspect of Circularity, its ability to entertain, leads to a surprising insight on the time old question " What is humor."