Thanks so much! This is fun. I think, with your explanation, there's still a big handicap for the halting machine code. To illustrate.. If I were to say to yo

Thanks so much! This is fun. I think, with your explanation, there's still a big handicap for the halting machine code. To illustrate.. If I were to say to you: Is the correct answer yes or no, considering that later I will reverse my answer, and enforcing that you can't later change your answer? It's like, okay, of course, with that model, you can never win. I don't think it reveals any limitation of your understanding, you just got pulled into a game that you can't win. The limitation that is put on the code and in your example too is, although the machine can take in extra input along the way, at a certain point the mathematician gets the last word. If you have G(H,M) which at each point gives you [0|1]:H', a more interesting question is if what happens if you define M = "if H(M)[0]: print H(M)[1] and then loop". Then, does the printed out H(M)[1](M) produce any contradiction? Hopefully I'm making sense here! Thanks again for engaging.