I read through most of the paper we are all nominally talking about. He doesn't use normal numbers as you say. He is talking about computable numbers as you say. My apologies.
But a normal number has "random" digits in the sense that all finite sequences of digits (in a given base) occurs uniformly in the expansion. What other notion of random can one meaningfully give for an expansion of a number's digits? Without getting into too much philosophy.
From [1]: We call a real number b-normal if, qualitatively speaking, its base-b digits are “truly
random.
My expertise is in commutative algebra so I'm outside of my comfort zone.
But a normal number has "random" digits in the sense that all finite sequences of digits (in a given base) occurs uniformly in the expansion. What other notion of random can one meaningfully give for an expansion of a number's digits? Without getting into too much philosophy.
From [1]: We call a real number b-normal if, qualitatively speaking, its base-b digits are “truly random.
My expertise is in commutative algebra so I'm outside of my comfort zone.
[1]: https://www.davidhbailey.com/dhbpapers/bcnormal.pdf