> At least with busy beaver numbers there isn’t some stupid paradox, we just can’t practically solve them. No! In computability theory we work with Turing Mach

> At least with busy beaver numbers there isn’t some stupid paradox, we just can’t practically solve them. No! In computability theory we work with Turing Machines that have unlimited memory. Since they have unlimited memory, the sizes of individual busy beaver numbers are not the problem. Individual busy beaver numbers are in fact all computable because every integer is computable. What is uncomputable is the busy beaver function. The busy beaver function is uncomputable because of the halting problem -- I suggest finding or reading a proof. Therefore the BB function provides zero additional insight into undecidability. I'm also amazed that there are people on this technology website - like you - who see all of this progress happening in AI with programs that are close to human intelligence, and still think that human beings can do things like determine arbitrarily large busy beaver numbers. We have concrete evidence that human beings are themselves limited by computability. People cannot just write arbitrarily good programs (to determine the first n busy beaver number, let's say) because people are programs.