He just means the phrasing is kind of poor. A general description of an undefinable number could be something like: given a sequence of Turing Machines, T_1, T_

He just means the phrasing is kind of poor. A general description of an undefinable number could be something like: given a sequence of Turing Machines, T_1, T_2, ..., T_n, where T_1 is the smallest representation of Turing machine over a grammar G, and T_2 is the second smallest representation of a Turing machine over G, and T_3 is the third smallest etc... take the limit of the ratio of said Turing machines that halt to Turing machines that don't halt as n goes to infinite. I mean that's a description of some number, you could even write it out mathematically or write an algorithm to express that number. Of course neither the algorithm or the formula will ever converge and yet it will also always be bounded between 0 and 1 (hence it doesn't diverge to infinity). So is that a description of a number? Well sure in one sense I just described it, there is only one single real number that can satisfy that description, and as I said I could in principle write it out formally and rigorously... and yet in another sense it also doesn't describe anything since no matter how hard you try, there will always be at least two real numbers that could potentially satisfy the definition and no way to eliminate one of them.