User blog comment:Mh314159/A new approach/@comment-39585023-20190703020905/@comment-39585023-20190703185943

Yes, thanks Ubersketch, I will keep that idea in mind. I think I've been trying to do it but haven't been very good at finding said limit, not being fluent in ordinals, and then I have a tendency to change recursion types, thinking linearly as I noted. It came to me yesterday that I need to think dimensionally. I'll post my first few expressions soon. The idea is that I have a strongly recursive "f" function based on successorship, and have linked it to a bracket function. [a] recurses f in a linear fashion, if you use a down arrow to represent subscripts. Then [a,1] represents a plane, where the string specified by [a] is recursed by layers of [a] functions. [a,b] recurses [a,b-1] (or maybe something more recursive, but not sure how much more it would add in terms of FGH), ending in [a,1]. Then [a,b,1] generates a cube, which I had a hard time visualizing at first. So imagine [a,b] as a plane where the number of terms and rows are specified by another plane, etc, many planes terminating in a number that is the size of the cube "edge". And then [a,b,c] recurses [a,b,c-1] down to [a,b,1]. I think I can extend this process to n dimensions [n,n,...n] and then I don't know what would come next, but I would guess the next step would be to make the number of dimensions itself a dimensional number, so something like [n/1] (or other notation, haven't gotten there yet) would be a number where the number of dimensions is [n,n,...n]. Feedback, anyone?? Better than what I have been trying? Possible a good first YIP of the PUPPY?