Leibniz, Complexity and Incompleteness
author: Gregory Chaitin,
University of Auckland
published: Oct. 15, 2008, recorded: September 2008, views: 25460
published: Oct. 15, 2008, recorded: September 2008, views: 25460
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Description
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.
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Reviews and comments:
Really brilliant lecture! This fellow is SHARP!!! Let's hear it for empirical mathematics!!
Thanks a lot for putting this online. Great and interesting lecture. Shame it has so few views!
For my latest views on incompleteness,
please see my 2012 book
Proving Darwin: Making Biology Mathematical.
--- Gregory Chaitin
Can these results be used compute these results?
Time to calculate.
If I determine if my own consciousness is a halting problem and the answer is yes my own consciousness has halted.
If the answer is no then my consciousness is not a halting problem and my consciousness is not a halting problem.
Is this like asking what is the difference between an infinitely straight pure line and an infinitely curved pure line in two dimensions?
Any work in using something like this to increase code optimization?
Can you write a code that is simple but powerful enough to optimize code from other languages?
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