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Leibniz, Complexity and Incompleteness

This video was recorded at 4th European Phd Complexity School. 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.

Keywords:: videolectures, ocwc, oec

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Social Sciences

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Material Type:: Open (Access) Textbook
Date Added to MERLOT:: February 8, 2015
Date Modified in MERLOT:: February 8, 2015
Author:: Gregory Chaitin, University of Auckland
Submitter:: The Open Education Consortium
Primary Audience:: College General Ed, College Lower Division, College Upper Division
Technical Format:: Video

Mobile Compatibility:: Not specified at this time
Language:: English
Cost Involved:: No
Source Code Available:: No
Creative Commons:: This work is licensed under a Attribution-NonCommercial-NoDerivs 3.0 United States