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 Hyper operators in computability theory MphLee Fellow Posts: 95 Threads: 7 Joined: May 2013 02/15/2017, 10:10 AM Some remarks Quote:But aside form these speculations there is a subtle connection going on here between ranks, computation complexity and dimension.(*) I didn't mean that. The paper does not talk about ranks but only about complexity, dimension and entropy. About the analogies... I guess that it's easy to see! There is a subtle and fascinating network of analogies between all these concepts. And if  it is not, start by what is probably the most easy-to-spot analogy. (remember that I'm not making the domains precise, I'm just trying to be suggestive) The ackermann function and all the recursive(but not-primitive) functions that are "beyond" the ${\mathcal E}_n$ hierarchy (finite rank) are a bit like the transcendental functions (or smooth, or analytic) that are beyond the polynomial (finite degree): in both cases we have a procedure going back "through dimensions" (differences and anti-recursion) and  in the other direction a mutivalued procedure (indefinite sum and not based-recursion/iteration) going upstairs... it is like we are generalizing this graded structure of polinomials (well behaved, commutative, familiar objects) to more exotic, non-commuative frameworks (like group of functions, monoids and so on..).  Amazingly this can be made very precise. MathStackExchange account:MphLee « Next Oldest | Next Newest »

 Messages In This Thread Hyper operators in computability theory - by JmsNxn - 02/07/2017, 07:59 AM RE: Hyper operators in computability theory - by tommy1729 - 02/13/2017, 12:09 AM RE: Hyper operators in computability theory - by MphLee - 02/14/2017, 06:53 PM RE: Hyper operators in computability theory - by MphLee - 02/15/2017, 10:10 AM RE: Hyper operators in computability theory - by JmsNxn - 02/15/2017, 04:19 PM RE: Hyper operators in computability theory - by MphLee - 02/15/2017, 10:07 PM

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