Leibniz, Complexity and Incompleteness
published: Oct. 15, 2008, recorded: September 2008, views: 3851
Report a problem or upload filesIf you have found a problem with this lecture or would like to send us extra material, articles, exercises, etc., please use our ticket system to describe your request and upload the data.
Enter your e-mail into the 'Cc' field, and we will keep you updated with your request's status.
I will discuss Leibniz's ideas on complexity (Discours de metaphysique, 1686), leading to modern work on program-size complexity, the halting probability and incompleteness. Leibniz's principle of sufficient reason asserts that if anything is true it is true for a reason. But the bits of the numerical value of the halting probability are mathematical truths that are true for no reason. More precisely, as I will explain, they are irreducible mathematical truths, that is, true for no reason simpler than themselves.
Link this pageWould you like to put a link to this lecture on your homepage?
Go ahead! Copy the HTML snippet !