People interested on this thread subject might be interested to read a paper we wrote some years ago published by World Scientific:
--- Hector Zenil, Francisco Hernandez-Quiroz, "On the possible Computational Power of the Human Mind", WORLDVIEWS, SCIENCE AND US, edited by Carlos Gershenson, Diederik Aerts and Bruce Edmonds, World Scientific, 2007. available online: http://arxiv.org/abs/cs/0605065 Abstract The aim of this paper is to address the question: Can an artificial neural network (ANN) model be used as a possible characterization of the power of the human mind? We will discuss what might be the relationship between such a model and its natural counterpart. A possible characterization of the different power capabilities of the mind is suggested in terms of the information contained (in its computational complexity) or achievable by it. Such characterization takes advantage of recent results based on natural neural networks (NNN) and the computational power of arbitrary artificial neural networks (ANN). The possible acceptance of neural networks as the model of the human mind's operation makes the aforementioned quite relevant. Presented as a talk at the Complexity, Science and Society Conference, 2005, University of Liverpool, UK. --- On the other hand, Goedelian type arguments (such as http://www.osl.iu.edu/~kyross/pub/new-godelian.pdf) have been widely accepted to be disproved since Hofstadter's Escher, Goedel and Bach in the 70s or before. I consider myself as someone within the busy beaver field since my own research on what we call experimental algorithmic information theory is very related to. I don't see how either Solomonoff's induction or the Busy Beaver problem can be used as evidence or be conceived as an explaination of the human mind as a hypercomputer. I don't see in the development of the two fields anything not Turing computable. There are known values of the busy beaver up to 4 state 2 symbol Turing machines (although it seems they claim to have calculated up to 6 states...). To determine whether a Turing machine halts up to that number of states is a relatively easy task by using very computable tricks, (including the Christmas Tree method). I think their main argument is that (a) once known the value of a busy beaver for n states, one learns how to crack the set of n+1 states and eventually get it. (i) They then use a kind of mathematical induction to proof that any given Turing machine with a fixed number of states will eventually fail, while the human mind can go on. However it seems pretty clear that the method evidently fails for n large enough, and hence disproving their claim. Now suppose their claim is right (a), now let's conceive the following method: (b) that each time we learn how to crack n+1 we build a Turing machine T that computes n+1, using their own argument (i) then Turing machine are hypercomputers! I might be missing something, if so please feel free to point it out. Best regards, -- Hector Zenil http://zenil.mathrix.org ------------------------------------------- agi Archives: http://www.listbox.com/member/archive/303/=now RSS Feed: http://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: http://www.listbox.com/member/?member_id=8660244&id_secret=106510220-47b225 Powered by Listbox: http://www.listbox.com
