My intention is not to define intelligence. I choose mathematics just as a test domain for first AGI algorithms.
The reasons: 1. The domain is well understood. 2. The domain has regularities. Therefore a high intelligent algorithm has a chance to outperform less intelligent algorithms 3. The domain can be modeled easily by software. 4. The domain is non-trivial. Current algorithms fail for hard problems in this domain because of the exponential growing complexity. 5. The domain allows a comparison with performance of human intelligence. To decide, whether you have an AGI or not, you also have to evaluate the proofs and not only the fact whether it could prove something or not. For example, the formula 1+2+3+...+n = 0.5*n*(n+1) can be proven by seeing a pattern: 1 + 2 + 3 + ... + n-2 + n-1 + n + n + (n-1) + (n-2) + .. + 3 + 2 + 1 = (n+1) + (n+1) + (n+1) + ... +(n+1) + (n+1) + (n+1) = n*(n+1) AGI will differ from AI by often using such pattern based proofs. An AGI based theorem prover represents expressions by patterns. When it comes to prove a certain formula, patterns of known expressions and rules become active or inactive. -Matthias Matt Mahoney wrote: Goedel and Turing showed that theorem proving is equivalent to solving the halting problem. So a simple measure of intelligence might be to count the number of programs that can be decided. But where does that get us? Either way (as as set of axioms, or a description of a universal Turing machine), the problem is algorithmically simple to describe. Therefore (by AIXI) any solution will be algorithmically simple too. If you defined AGI this way, what would be your approach? -- Matt Mahoney, [EMAIL PROTECTED] ------------------------------------------- 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/?&; Powered by Listbox: http://www.listbox.com ------------------------------------------- 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
