Episode 85 Dr. John Allen Paulos NOV 18, 2012

Neil deGrasse Tyson
 

Paulos Episode 85 Dr. John Allen Paulos NOV 18, 2012Dr. Paulos received his PhD in mathematics from the University of Wisconsin and is now a professor of that same subject at Temple University. Mathematical logic and probability has been the focus of of his academic work and the subject of many scholarly papers. The recipient in 2003 of the American Association for the Advancement of Science’s Award for Promoting the Public Understanding of Science and Technology, Dr. Paulos has been a long time contributor to print, radio, and television media, including the New York Times, the London Review of Books, the Wall Street Journal, the BBC, ABC’s 20/20, CNN’s Larry King Live, and more. He is the author of several popular level books, among which are Innumeracy: Mathematical Illiteracy and Its Consequences (a New York Times Best Seller), A Mathematician Reads the Newspaper, and Irreligion: A Mathematician Explains Why the Arguments for God Just Don’t Add Up. We asked Dr. Paulos to join us to get the thoughts of a mathematician on critical thinking and the arguments for God. Join us!

2 Responses to Episode 85 Dr. John Allen Paulos NOV 18, 2012

  1. Eric

    That bit about being asked to choose between two envelopes, one containing one amount of dollars and the other twice as much, and then being asked if you wanted to switch – well, that didn’t fool me a bit.

    The faulty reasoning went like this:

    “If I change, then half the time I’ll get twice as much money as I have or 2x dollars, and half the time I’ll get half as much money or x/2 dollars. So averaging both options leaves me with (2x+x/2)/2 = 5x/4. Therefore, I should switch.”

    But wait! The proper way to reason this out is as follows:

    If I pick the envelope having x dollars, then I’ll get 2x dollars if I switch.

    If I pick the envelope with 2x dollars, then I’ll get x dollars if I switch.

    The average of x dollars and 2x dollars is 3x/2 dollars. Which is more than 5x/4 dollars …

    Which gives me even more reason to switch … and then switch back … and then switch again …

    Wait a minute … I’m confused …

    I know, I’ll undo my last two switches, which means I go with just one switch … Hmmm

  2. Eric

    Imagine there are three envelopes, #1, #2, and #3. One contains x dollars, another 2x dollars, and the third 3x dollars.

    Monty asks you to pick one. You pick #1.

    Then Monty opens #2 and it contains the 2x dollars.

    Do you switch?

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