User blog comment:Wythagoras/All my stuff/@comment-7484840-20130715121715/@comment-7484840-20130716084342

If a higher order iota function refers to the future, and so diagonalises over the entire universes timeline, including the future, which leads to numbers that are impossible to even guess at. A function that does this is equivalent to the limit iota function. I suppose that you could improve it a tiny bit by diagonalising over the input of this final function, but really this is hardly an improvement at all. Without referring to the future, any higher iota function that moves through time will only be able to refer to past versions of any other order iota functions, and so even future versions of the base function will be able to refer to past higher order functions.

As for the googleplex character thing, rayos number manages to use a googolplex characters, and even if we do not know what they are, it still works as a function. The ¥ function tries to diagonalise over, in /a sense, itself, and even though it cannot refer to precisely itself, this does not stop it diagonalising over very similar functions, inevitably leading to a kind of self referral, and infinity. Likewise with rayo's function. If you can define rayo's function in rayo's function it breaks the whole thing, and although this may be difficult in FOST, with the whole of language to use, I think it is just impossible to keep it finite. (Or at least away from the 'largest finite number' idea)