[throwawaymath]

> Chapernowne's constant, 0.123456789101112... isn't "random" at all and contains very little information, yet it is known to be normal in base 10.

Why is Chapernowne's constant not random?

> The number would still have "infinite information" in the sense of the author of this paper. It would still be "just as random", it would still have "no pattern". But it would not be a normal number anymore.

That's not true. It would not be just as random. If the set you're sampling from includes a 7 (i.e. the set of digits which can be represented in any single place in the sequence), and you never see a 7 for an extremely long time, this is exceptionally good heuristic evidence that the number is not random. And if we know 7 never shows up, we also know that the number is not random, because we know it's not uniformly sampling from the set of base 10 digits.