03/09/2021, 02:31 PM
(03/09/2021, 10:29 AM)MphLee Wrote: Hi Daniel,
That was unexpected.
I've skimmed many times thru your site in the last 5 years or so but I was never able to see your work on iteration explicitly applied to the hyperoperations (with that I mean non integer ranks).
However I was puzzled by this post All Maps Have Flows & All Hyperoperators Operate on Matrices but I never had time to ask you to expand on it. Is it related? Can you expand on this?
About the project, is the syllabus, or a sketch of it, already available?
Hello MphLee,
After writing my first paper on tetration in 1990, I began to reflect on what I could generalize as per my conversation with Wolfram. I soon realized my technique was in no way dependent on tetration, but applied to iterated functions in general. When I refer to the hyperoperators I mean tetration, pentation and so on and not the operators in between.
Quote:Wolfram:
Having recently been working on https://writings.stephenwolfram.com/2021/03/after-100-years-can-we-finally-crack-posts-problem-of-tag-a-story-of-computational-irreducibility-and-more/ (see particularly the later sections) I am increasingly curious about rapidly growing iterations and their relationships to axiom systems (cf https://www.wolframscience.com/nks/notes-12-9--examples-of-unprovable-statements/ )
All this is preliminary. I've kept Wolfram in the loop of what I was researching as both of us are tracking similar issues. I will let folks know how this develops.
Daniel