Except the essence of Knuth's up-arrow notation is the recursive nature. This is going one step, and while I agree that it's a first step, it doesn't actually get the recursive nature. So this is a notation for a single thing, not a general thing. It's good, but i's missing the generalisation step that is what makes Knuth's notation particularly special.
Maybe I know too much about the field, maybe I don't know enough, but I've looked over this many times and it doesn't seem to me to be making "the step."
Maybe I'm just expecting too much, but it feels like the heart of Knuth's notation is missing.
<fx: shrug /> I'll leave it at that. Feel free to disagree, perhaps it's an interesting talking point.
Maybe I know too much about the field, maybe I don't know enough, but I've looked over this many times and it doesn't seem to me to be making "the step."
Maybe I'm just expecting too much, but it feels like the heart of Knuth's notation is missing.
<fx: shrug /> I'll leave it at that. Feel free to disagree, perhaps it's an interesting talking point.