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MrMind comments on Does Kolmogorov complexity imply a bound on self-improving AI? - Less Wrong Discussion
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An important remark: a program that is better at a task is not necessearily more complex than a program that is worse. Case in point, AlphaGo: definitely better than almost every human at go, but definitely less complex than a human mind.
Anyway, accepting the premise:
1 is demonstrably false, for any reasonable definition of intelligence (a Turing machine that can solve a problem that another TM cannot solve);
2 is surely true, given that a program can increase in complexity given more memory and a way to do unsupervised learning;
3 is too dependent to the implementation detail to judge, but it may be trivially true for a sufficiently large gap to reach.