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One of my favorite insights is that the existence of undecidable problems is the same thing as the uncountability of real numbers.

Too bad the author didn't get into it.

I had exactly the same reaction, which prompted me to write this comment: https://news.ycombinator.com/item?id=44122045

...which is the same thing as Rice's theorem, and many other mind-bending results. It's all diagonalization under the hood =)