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#alanturing #turingmachines #logic #complexity #omega #computerscience #happybirthday
In computer science, we study the behavior of programs. One of the central questions is called the halting problem, as formulated by the famous mathematician Alan Turing. Does any given program halt or not? We explore how far we can take this question, using the Omega number defined by Gregory Chaitin. We also talk about Kolmogorov complexity, gambling, pattern matching, and more.
If you want to learn more, you can use these references:
[WIKI 1] https://en.wikipedia.org/wiki/Kolmogorov_complexity
[WIKI 2] https://en.wikipedia.org/wiki/Halting_problem
[SCIAM 1] Mathematical Games, Martin Gardner, Scientific American November 1979, p22
TOC:
0:00 Introduction
1:34 Random = incompressible
4:14 Most real numbers are random
7:10 Random = unpredictable
9:40 Alan Turing and the halting problem
13:19 The number omega
15:46 How the oracle works
19:57 The oracle is forever out of reach
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( https://creativecommons.org/licenses/by/4.0/ )