One sentence explanations of mathematical concepts and proofs:

**Triangle inequality**: Stopping by Starbucks on your way to class cannot be a shortcut.
**Yoneda lemma**: If you know the directions for all the paths from your house to everywhere else, you know where your house is.
**Pigeonhole Principle**: Among any three gloves, there must be two for the same hand.
**Intermediate Value Theorem**: If you were there a while ago, and now you are here, then there must have been some time that you were exactly halfway.
**Gödel’s Incompleteness Theorems**: If the axioms are the rules, and mathematics is the game, Gödel showed that no set of rules could get to every space without being able to go off the board.
**Halting Problem**: In a world like the one in the movie Matrix, the Oracle cannot predict the future of all programs correctly because For all such Oracles there exists a program Neo which uses the same method the Oracle uses to see the future and simply avoids Oracle’s prediction from becoming true. e.g. If Oracle predicts Neo will sit, Neo will stand.

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But what if Neo both stands and sits?

Well then he wouldn’t have avoided oracle’s prediction

I like the “There is no original thought” description for this problem more. That associates the problem of free will as well.

But yes in a limited system the responses are limited and all participants play on the same field.

Even an infinite system is limited by infinity the question then becomes if the players can attain that level or not (which answer is yes because they have all the time necessary to do so), and what happens when there’s more then one player attaining that level of response repertoare.

So here comes the dilemma of God. The one to first reach the limit of an infinite system.

Once more then one reaches a point, the point reached loses its uniqueness, and the infinite system begins to fragment into infinite systems for infinity.

I should start taking LSD….

Another thing that came to mind is the matter of perception. Yes Oracle cannot predict all futures correctly, but from a linear first person view of the the process she can fool herself into thinking that she is an oracle. But this is long way from the actual theorem so…

@uzsibox You should read about the idea of the Intentional Stance by Daniel Dennett. He extends the ability to predict intentions exhibited by the Oracle, into the sense of self we all possess. His argument is that self is the brain predicting its own intentions.

BTW David Wolpert disproved the existence of Laplace Demons using a version of this Oracle vs Neo argument that Turing used which is called Cantor’s diagonalization in mathematical circles.

Thanks It’s nice to finally find thoughts that I can use to finally finish my thesis. The framework of academic progression can be a hassle at times.