100% of real numbers are normal, so that's pretty strong statistical evidence

What? No they're not, e.g. no rational numbers are normal, and they are real.

The rational numbers make up "zero percent" of the real numbers. It's a little hard to properly explain without assuming a degree in math, since the proper way to treat this requires measure theoretic probability (formally, the rationals have measure zero in the reals for the "standard" measure).

The short version is that the size of the reals is a "bigger infinity" than the size of the rationals, so they effectively have 'zero weight'.

Reference (very technical): https://math.stackexchange.com/questions/508217/showing-that...

But then the original implication, "100% of real numbers are normal, so that's pretty strong statistical evidence", still doesn't make any sense, as it's essentially using "100%" to imply "strong statistical evidence" that the rationals don't exist, which obviously doesn't follow.

I got the impression that the comment was a bit tongue-in-cheek.

The joke lies in the fact that saying "100% of real numbers" isn't *technically* the same thing as saying "all real numbers", because there's not really a good way to define a meaning for "100%" that lets you exclude rational numbers (or any other countable subset of the reals) and get something other than 100%.

> still doesn't make any sense

Right. I'm pretty sure actually that it was a joke...

it was about half a joke. statistical evidence doesn't really exist for the type of problem since polynomialy computable numbers are countably infinite so you can't define a uniform distribution over then