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2016-08-12T03:21:21Z n_blownapart: hi I am struggling with ackermann's, after revisiting. I cannot see the code that indicates the base of the exponent is always 2. thanks https://www.refheap.com/122148
2016-08-12T03:21:42Z n_blownapart: *after revisiting the problem in sicp
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2016-08-12T03:26:49Z pierpa: error: question not clear.
2016-08-12T03:28:28Z n_blownapart: pierpa hold on please trying to pose the question
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2016-08-12T03:33:05Z n_blownapart: well yeah when we have (A 0 n), the program calculates 2n, then (A 1 n) calculates 2^n , then (A 2 n) calculates 2^(2^n) I believe. I read that ackermann's was critical in the theory of computation...really I'm just trying to understand it better. pierpa
2016-08-12T03:34:48Z pierpa: good
2016-08-12T03:34:58Z n_blownapart: sicp seems to just rifle through a lot of serious business, though I haven't watched the lecture on this topic yet, if it is covered in the videos at all.
2016-08-12T03:35:28Z pierpa: IIRC, sicp does not explain the significance of this function, right?
2016-08-12T03:35:43Z pierpa: (that would be out of topic fr that book)
2016-08-12T03:37:12Z n_blownapart: IIRC very little is presented in the book, though maybe the video (if it is covered) has something. I don't understand the book's approach. pierpa
2016-08-12T03:38:01Z pierpa: well, SICP is not about theory of computation, so no wonder it doesn't go into this.
2016-08-12T03:38:51Z n_blownapart: the recursion itself is rather complex, maybe it is just showing off : (A (- x 1) (A x (- y 1))) section. that is very cool in and of itself.
2016-08-12T03:39:07Z n_blownapart: to me
2016-08-12T03:40:26Z pierpa: I think you are right. I mean, I don't remember what's the purpose of showing this function in SICP, but probably is just an example of a complex numerical recursive function, with no hommage paid to it's history and significance.
2016-08-12T03:44:02Z n_blownapart: pierpa that is a relief. I'd like to have a better conception of how it is used, perhaps in a practical example? also the question is still, all of the calculations involve 2 : 2n , 2^n , 2^(2^2) etc.
2016-08-12T03:44:31Z n_blownapart: an example for a layman, or some easy to follow classic example
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2016-08-12T03:44:51Z pierpa: there's no practical significance
2016-08-12T03:45:28Z pierpa: it's used in computation theory as an example of total function which is not primitive recursive
2016-08-12T03:45:59Z pierpa: also, it comes up (rarely) in some algorithms analysis
2016-08-12T03:46:30Z pierpa: IF you want to pursue this, you can start from the Wikipedia article
2016-08-12T03:46:44Z n_blownapart: total function ? I read that in wikipedia but couldn't follow that
2016-08-12T03:47:25Z pierpa: yes, understandable. It's not something one can understand in 5 minutes.
2016-08-12T03:49:34Z n_blownapart: thanks pierpa, is it true that 2 is always the base in that algorithm, with the first being an exception (A 0 n) -> 2n  ?
2016-08-12T03:50:48Z pierpa: in the one you pasted, the bae cases either returns 0, or 1, or something multiplied by 2. So no wonder it returns always a power of 2.
2016-08-12T03:51:44Z n_blownapart: right, it is a multiplication. frankly I wasn't looking at it like that. thanks pierpa
2016-08-12T03:52:07Z pierpa: (there are many variants of "the" Ackermann functions, the power of 2 is not a characteristic of all of them)
2016-08-12T03:52:56Z n_blownapart: yeah wow it gets way out of hand when we have (A 2 5)  [ a huge number ]
2016-08-12T03:54:16Z pierpa: that's the point :)
2016-08-12T03:54:26Z n_blownapart: thanks kindly
2016-08-12T03:55:03Z pierpa: :)
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2016-08-12T14:26:36Z jcowan: Strictly speaking, Ackermann's function is only not primitive recursive in a first-order language.
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