Quora answer: Gödel’s Incompleteness Theorem: Is there a geometric shape that represents Godel’s theorem?

Feb 16 2014

Personally I think that the Godel’s proof is very much like Irrational numbers. These numbers just cannot be handled by fractions. This caused a crisis in Greek Mathematics. Similarly diagonal coding reveals that very simple systems are not closed as we might expect and this produced a very similar crisis of anti-foundationalism in modern times. Hilbert’s program as well as that of Russell and Whitehead crashed. The fact that we cannot expect closure of systems has a big effect on how we view them. But it is precisely the lack of closure that opens things up for change and transformation, so the shape in question is the shape of things to come, i.e. new emergences that are made possible by that openness.

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