Thursday, May 27, 2021

"This Is Math's Fatal Flaw": complete? consistent? decidable?

 

used books, 2021/5

Veritasium presents “This Is Math’s Fatal Flaw” (33 min, animated).

That sounds like “Ephram’s Fatal Flaw” on “Everwood”.

Complete?  Consistent?  Decidable?

Is there an infinite number of successive primes?  We don't know. 

There are things that are true but not provable.  Is this why we need faith?

The speaker analyzes the Turning Machine, and then states the tragic and absurd way Turning’s life ended.  He had practically won WWII.  But he was gay, and the British government made him take chemical castration as an alternative to prison.  He died of cyanide poisoning in 1954.  This absurd end to his life is also incredibly ironic.

But the film also gives us a history of set theory, and of all the contradictions could lead us to.

He talks a lot about self-reference in set theory.

The mathematicians discussed here include Cantor, Goedel and Hilbert as well as Turing.

The “hole” in mathematics explains why consciousness is necessary, to have the agency to make choices.   The “hole” would also seem to explain entropy. 

In some ways, some of the demonstration games in this video resemble ideas from John Fish's posts, especially a recent one on simulating natural selection. 

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