The Limits of Understanding

This statement is false. Think about it, and it makes your head hurt. If it’s true, it’s false. If it’s false, it’s true. In 1931, Austrian logician Kurt Gödel shocked the worlds of mathematics and philosophy by establishing that such statements are far more than a quirky turn of language: he showed that there are mathematical truths which simply can’t be proven. In the decades since, thinkers have taken the brilliant Gödel’s result in a variety of directions–linking it to limits of human comprehension and the quest to recreate human thinking on a computer. This program explores Gödel’s discovery and examines the wider implications of his revolutionary finding. Participants include mathematician Gregory Chaitin, author Rebecca Goldstein, astrophysicist Mario Livio and artificial intelligence expert Marvin Minsky.

This program is part of The Big Idea Series, made possible with support from the John Templeton Foundation.

The World Science Festival gathers great minds in science and the arts to produce live and digital content that allows a broad general audience to engage with scientific discoveries. Our mission is to cultivate a general public informed by science, inspired by its wonder, convinced of its value, and prepared to engage with its implications for the future.

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Original Program Date: June 4, 2010
MODERATOR: Paul Nurse
PARTICIPANTS: Gregory Chaitin, Mario Livio, Marvin Minsky, Rebecca Newberger Goldstein

Paul Nurse's Introduction. 00:19

Who is Kurt Godel? 03:36

Participant Introductions. 07:22

What was the intellectual environment Godel was living in? 10:57

Godel's beliefs in Platonism. 19:45

Gregory Chaitin on the incompleteness theorem. 22:30

Platonism vs. Formalism. 27:18

The unreasonable effectiveness of mathematics in the world. 40:53

The world is built out of mathematics... what else would you make it out of? 47:44

Mathematics and consciousness. 53:29

What are the problems of building a machine that has consciousness? 01:01:09

If math isn't a formal system then what is it? 01:07:40

Explaining math with simple computer programs. 01:18:33

Its hard to find good math. 01:25:40

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