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- All page numbers from the trade paperback first edition published by John Wiley & Sons ISBN 0-471-29587-6
- Intriguingly, the mathematics of randomness, chaos, and order also furnishes what may be a vital escape from absolute certainty—an opportunity to exercise free will in a deterministic universe. Indeed, in the interplay of order and disorder that makes life interesting, we appear perpetually poised in a state of enticingly precarious perplexity. The universe is neither so crazy that we can’t understand it at all nor so predictable that there’s nothing left for us to discover.
- Preface, “Infinite Possibility” (p. xiii)
- The theory of probability combines commonsense reasoning with calculation. It domesticates luck, making it subservient to reason.
- Chapter 1, “The Die is Cast” (p. 19)
- Ramsey theory implies that complete disorder is impossible. Somehow, no matter how complicated, chaotic, or random something appears, deep within that morass lurks a smaller entity that has a definite structure. Striking regularities are bound to arise even in a universe that has no rules.
- Chapter 2, “Sea of Life” (p. 25)
- In mathematics, in science, and in life, we constantly face the delicate, tricky task of separating design from happenstance.
- Chapter 2, “Sea of Life” (p. 43)
- Most coincidences are simply chance events that turn out to be far more probable than many people imagine.
- Chapter 10, “Lifetimes of Chance” (p. 188)
- Tversky was fond of describing his work as “debugging human intuition.”...Tversky could establish again and again the existence of mismatches between intuition and probability—between cognitive illusion and reality.
- Chapter 10, “Lifetimes of Chance” (pp. 192-193; ellipsis represents a minor elision of description)
- Indeed, mathematics is full of conjectures—questions waiting for answers—with no assurance that the answers even exist.
- Chapter 10, “Lifetimes of Chance” (p. 199)
- The aim of science is to reduce the scope of chance.
- Chapter 10, “Lifetimes of Chance” (p. 201; quoting Hegel)
- Randomness, chaos, uncertainty, and chance are all a part of our lives. They reside at the ill-defined boundaries between what we know, what we can know, and what is beyond our knowing. They make life interesting.
- Chapter 10, “Lifetimes of Chance” (p. 202)
- All page numbers from the hardcover edition published by Barnes & Noble ISBN 0-7607-2361-3
- Revision of The Mathematical Tourist: Snapshots of Modern Mathematics, originally published in 1988
- More often than not, a piece of mathematics worked out years before—and believed to be totally without practical value—finds a role in the “real” world.
- Chapter 1, “Explorations” (p. 9)
- To an increasing number of practitioners, computer simulations rooted in mathematics represent a third way of doing science, alongside theory and experiment.
- Chapter 1, “Explorations” (p. 10)
- As the mathematician Clifford Taubes noted, “Physics is the study of the world, while mathematics is the study of all possible worlds.” Thus, mathematics unveils the infinite possibilities; physics pinpoints the few that structure our universe and our existence.
- Chapter 4, “Shadows From Higher Dimensions” (p. 114)