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Wittgenstein gave some lectures on mathematics and logic, where Alan Turing was present and they had discussions about mathematics (a book is available with the lectures on mathematics). That was 3 years after on Turing's paper on computable numbers.
I am reading "Enigma" the book, that the recent Turing movie was made from. I am exactly at the point where Alan is taking classes with Witgenstein. Hehehe :-)
Yeah, and Wittgenstein owns him if I remember correctly. Reading their conversations is like watching Frazier and Ali, absolute brilliance. I particularly remember one exchange where Turing argues that a solution to a chess problem could not be considered a mathematical proof, and W takes him down.
Lectures on the Foundations of Mathematics is the published title. There are some pretty amusing exchanges between W. and Turing in that book.
The episode with the poker-assisted demonstration of the "simplicity of matter" could probably be interpreted as an expression of Wittgenstein's belief that metaphysics (which presumably a discussion of the nature of matter would constitute) could not be meaningfully discussed in words. When it comes to metaphysics (and other "nonsense": poetry, ethics), "show, don't tell."

This is how, for example, Janik and Toulmin's book Wittgenstein's Vienna, explain his obsession with Westerns (the film genre, not the people): they show what cannot be said about morality in their depiction of good, evil, loyalty, etc. Talk of "the simplicity of matter" would be nonsense, but we can definitely get something across by vigorously swinging a poker around. (There is general agreement, I believe, that Wittgenstein significantly revised his stance on what can be meaningfully said/done in language between the Tractatus and Philosophical Investigations in the 50s.)

On the other hand, maybe he was just angry (he "threatened" Karl Popper with a poker during a philosophical disagreement).

Take all of this with a grain of salt, I am not a Wittgenstein expert.

A philosopher who is not taking part in discussions is like a boxer who never goes into the ring. - Wittgenstein