--- On Tue, 10/21/08, Dr. Matthias Heger <[EMAIL PROTECTED]> wrote: > Sorry, but this was no proof that a natural language > understanding system is > necessarily able to solve the equation x*3 = y for > arbitrary y. > > 1) You have not shown that a language understanding system > must necessarily(!) have made statistical experiences on the > equation x*3 =y.
A language model is a probability distribution P over text of human origin. If you can compute P(x) for given text string x, then you can pass the Turing test because for any question Q and answer A you can compute P(A|Q) = P(QA)/P(Q) using the same distribution that a human would use to answer the question. This includes any math questions that the average human could answer. > 2) you give only a few examples. For a proof of the claim, > you have to prove it for every(!) y. You originally allowed *any* y. To quote your earlier email: > > For instance, I doubt that anyone can prove that > > any system which understands natural language is > > necessarily able to solve > > the simple equation x *3 = y for a given y. Anyway I did the experiment for y = 12. You can try the experiment for other values of y if you wish. Let me know what happens. > 3) you apply rules such as 5 * 7 = 35 -> 35 / 7 = 5 but > you have not shown that > 3a) that a language understanding system necessarily(!) has > this rules > 3b) that a language understanding system necessarily(!) can > apply such rules It must have the rules and apply them to pass the Turing test. -- 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/?member_id=8660244&id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
