> > I am not sure about your statements 1 and 2. Generally responding, > I'll point out that uncomputable models may compress the data better > than computable ones. (A practical example would be fractal > compression of images. Decompression is not exactly a computation > because it never halts, we just cut it off at a point at which the > approximation to the fractal is good.)
Fractal image compression is computable. > But more specifically, I am not > sure your statements are true... can you explain how they would apply > to Wei Dai's example of a black box that outputs solutions to the > halting problem? Are you assuming a universe that ends in finite time, > so that the box always has only a finite number of queries? Otherwise, > it is consistent to assume that for any program P, the box is > eventually queried about its halting. Then, the universal statement > "The box is always right" couldn't hold in any computable version of > U. Based on a finite set of finite-precision observations, there is no way to distinguish Wei Dai's black box from a black box with a Turing machine inside. -- Ben G ------------------------------------------- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?member_id=8660244&id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
