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Search - Euclid in the Rainforest : Discovering Universal Truth in Logic and Math

Euclid in the Rainforest Discovering Universal Truth in Logic and Math
Author: Joseph Mazur

How do we know that something is true? How do we know that things really are what they seem? Many people think math and science are the ultimate authorities on reality. Math defines abstract, universal truths; scientific truths are established by experiments in the real world-but underlying both kinds of knowledge is logic. In 'Euclid in the Rai... more »nforest', Joseph Mazur examines the three types of logic that are the basis of our knowledge about the world we live in: the classical logic of the Ancient Greeks, the weird logic of infinity, and the everyday logic of plausible reasoning that guides all science today.

Through tales of great moments in the history of math and science, stories of students making discoveries in the classroom, and his own quirky adventures in the Greek Islands, New York, and the jungles of South America, Mazur illuminates how we uncover truth in the tangled web of our experiences-and convince ourselves that we are right.

Euclid took the incipient logic of his time to new heights with his magnificent geometry, the whole edifice of which is built on just five assumptions. That logic rigorously defined proof, cleverly avoiding problems with infinity that were introduced when the Pythagoreans discovered that the diagonal of a square could not be measured and Zeno of Elea used infinity to argue that motion is logically impossible. It would be almost two millenia, though, before a good understanding of the logic of infinity emerged and made all kinds of technology possible. Plausible reasoning-which is based on the math of probability-lets us assess the general conclusions we derive from specific cases in scientific studies. It gives us the confidence to believe that a conclusion reached today will be true tomorrow, ultimately driving scientific, and human, progress.

In lucid, ebullient language, Mazur, a professor of mathematics for over thirty years, makes the fundamentals of the three fundamental types of logic widely accessible for the first time. Deeper questions at the heart of the process of discovery are laid bare: What does it mean to believe a proof? Where does the finite end and the infinite begin? How can we be sure that the statements we make about the material world are accurate? Exposing the surprising roles of intuition, belief and persuasion in logic and math, Mazur tells a real-life detective story that has been going on for millenia: the pursuit of ultimate truth about our world, our universe, and ourselves.

ISBN-13: 9780131479944
ISBN-10: 0131479946
Publication Date: 10/4/2004
Pages: 352
Rating:

Currently 5/5 Stars.

5 stars, based on 1 rating

Publisher: Pi Press
Book Type: Hardcover
Other Versions: Paperback
Members Wishing: 0
Reviews: Amazon | Write a Review

Genres:

Science & Math >> Mathematics >> General
Science & Math >> Mathematics >> Pure Mathematics >> Logic
Engineering & Transportation >> Professional Science >> Mathematics >> Pure Mathematics >> Logic

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