Proof
The Art and Science of Certainty
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- ¥3,000
発行者による作品情報
An award-winning mathematician shows how we prove what’s true, and what to do when we can’t
“Engaging and uncondescending” – Financial Times
How do we establish what we believe? And how can we be certain that what we believe is true? And how do we convince other people that it is true? For thousands of years, from the ancient Greeks to the Arabic golden age to the modern world, science has used different methods—logical, empirical, intuitive, and more—to separate fact from fiction. But it all had the same goal: find perfect evidence and be rewarded with universal truth.
As mathematician Adam Kucharski shows, however, there is far more to proof than axioms, theories, and laws: when demonstrating that a new medical treatment works, persuading a jury of someone’s guilt, or deciding whether you trust a self-driving car, the weighing up of evidence is far from simple. To discover proof, we must reach into a thicket of errors and biases and embrace uncertainty—and never more so than when existing methods fail.
Spanning mathematics, science, politics, philosophy, and economics, this book offers the ultimate exploration of how we can find our way to proof—and, just as importantly, of how to go forward when supposed facts falter.
PUBLISHERS WEEKLY
"Even mathematical notions of proof not always as robust... as they might seem," according to this thought-provoking analysis. Kucharski (The Rules of Contagion), an epidemiology professor at the London School of Hygiene and Tropical Medicine, uses historical examples to explore the challenges of establishing objective truths through math and science. For instance, he discusses how Abraham Lincoln's efforts to use Euclidian logic to prove that slavery was at odds with America's founding principles failed because such reasoning requires both parties to agree on certain foundational axioms, which Lincoln's pro-slavery opponents didn't subscribe to. Modern science determines what counts as a statistically significant result based on an "arbitrary" cutoff, Kucharski contends, describing how in the 1920s statistician Ronald Fisher first proposed disregarding findings if "the probability of obtaining a result that extreme by chance" is more than 5% because that figure was just large enough to validate his recent research. Lamenting how scientists have exploited this threshold, Kucharski notes that for every 10 experiments, "there's a 40 percent chance that one will cross the traditional... cutoff purely by chance," leading some researchers to repeat experiments until they get the desired result and omit mention of the unsuccessful iterations in publication. The straightforward prose renders the quirks of research methodology approachable for lay readers. This edifies.
