This site is not maintained. Click here for the new website of Richard Dawkins.

The Mathematics of Changing Your Mind

THE THEORY THAT WOULD NOT DIE
How Bayes’ Rule Cracked the Enigma Code, Hunted Down Russian Submarines and Emerged Triumphant From Two Centuries of Controversy

Sharon Bertsch McGrayne introduces Bayes’s theorem in her new book with a remark by John Maynard Keynes: “When the facts change, I change my opinion. What do you do, sir?”

ayes’s theorem, named after the 18th-century Presbyterian minister Thomas Bayes, addresses this selfsame essential task: How should we modify our beliefs in the light of additional information? Do we cling to old assumptions long after they’ve become untenable, or abandon them too readily at the first whisper of doubt? Bayesian reasoning promises to bring our views gradually into line with reality and so has become an invaluable tool for scientists of all sorts and, indeed, for anyone who wants, putting it grandiloquently, to sync up with the universe. If you are not thinking like a Bayesian, perhaps you should be.

At its core, Bayes’s theorem depends upon an ingenious turnabout: If you want to assess the strength of your hypothesis given the evidence, you must also assess the strength of the evidence given your hypothesis. In the face of uncertainty, a Bayesian asks three questions: How confident am I in the truth of my initial belief? On the assumption that my original belief is true, how confident am I that the new evidence is accurate? And whether or not my original belief is true, how confident am I that the new evidence is accurate? One proto-Bayesian, David Hume, underlined the importance of considering evidentiary probability properly when he questioned the authority of religious hearsay: one shouldn’t trust the supposed evidence for a miracle, he argued, unless it would be even more miraculous if the report were untrue.
Read more

TAGGED: BOOKS, MATH, PSYCHOLOGY, REVIEWS


RELATED CONTENT

Pierre de Fermat's Last Theorem...

Nathan Green - guardian.co.uk 19 Comments

The Mind-Reading Salmon: The True...

Charles Seife - Scientific American 13 Comments

The Unreasonable Beauty of Mathematics...

George Musser - Scientific American 15 Comments

Science, Culture And The Google Ngram...

Ajita Kamal - Nirmukta 15 Comments

Numberplay: Rare Coincidences Are Very...

PRADEEP MUTALIK - The New York Times 28 Comments

Richard Dawkins at the 'Genius of...

May 26 2010 at the Science Museum in... 13 Comments

MORE

MORE BY JOHN ALLEN PAULOS

MORE

Comments

Comment RSS Feed

Please sign in or register to comment