Earlier quoted context omitted.
For me it was when he said that the cardinality of integers is the same as real numbers. Then I saw his twitter and all the politics and crazy stuff about QM.
Some light, coffee reading "Cardinality of the continuum" [1]: in short, the cardinality of real numbers (ℝ) is often called the cardinality of the continuum, and denoted by 𝔠 or 2^ℵ_0 or ℶ_1 (beth-one [2); whereas, interestingly [3], the cardinality of the integers (ℤ) is the same as the cardinality of the natural numbers (ℕ) and is ℵ_0 (aleph-null) [perhaps what was meant initially?]. Related: the Schröder–Bernste…
As for the set of real numbers, we have the subset of irrational numbers which are uncountably infinite (see cantors diagonalization argument) thus making the whole set of real numbers, a set whose cardinality is ℵ_1.
The annotated turing book goes into this pretty well in the first couple pages.