But none of those are really random either. The only sensible definition of randomness here is Kolmogorov complexity, and all of those numbers you just mentioned have incredibly low Kolmogorov complexity. I can write a tiny computer program that prints them out to billions of digits.
What the author is probably referring to is "non-computable numbers", which are numbers that cannot be computed to arbitrary precision by ANY Turing machine. But it's incredibly confusing and wrong to use the term "real numbers" to mean "non-computable numbers".
What the author is probably referring to is "non-computable numbers", which are numbers that cannot be computed to arbitrary precision by ANY Turing machine. But it's incredibly confusing and wrong to use the term "real numbers" to mean "non-computable numbers".