I wouldn't argue that any software system capable of learning human language, would necessarily be able to learn mathematics
However, I strongly suspect that any software system **with a vaguely human-mind-like architecture** that is capable of learning human language, would also be able to learn basic mathematics ben On Tue, Oct 21, 2008 at 2:30 AM, 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. > > 2) you give only a few examples. For a proof of the claim, you have to > prove > it for every(!) y. > > 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 > > In my opinion a natural language understanding system must have a lot of > linguistic knowledge. > Furthermore a system which can learn natural languages must be able to gain > linguistic knowledge. > > But both systems do not have necessarily(!) the ability to *work* with this > knowledge as it is essential for AGI. > > And for this reason natural language understanding is not AGI complete at > all. > > -Matthias > > > > -----Ursprüngliche Nachricht----- > Von: Matt Mahoney [mailto:[EMAIL PROTECTED] > Gesendet: Dienstag, 21. Oktober 2008 05:05 > An: [email protected] > Betreff: [agi] Language learning (was Re: Defining AGI) > > > --- On Mon, 10/20/08, Dr. Matthias Heger <[EMAIL PROTECTED]> wrote: > > > 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. > > It can be solved with statistics. Take y = 12 and count Google hits: > > string count > ------ ----- > 1x3=12 760 > 2x3=12 2030 > 3x3=12 9190 > 4x3=12 16200 > 5x3=12 1540 > 6x3=12 1010 > > More generally, people learn algebra and higher mathematics by induction, > by > generalizing from lots of examples. > > 5 * 7 = 35 -> 35 / 7 = 5 > 4 * 6 = 24 -> 24 / 6 = 4 > etc... > a * b = c -> c = b / a > > It is the same way we learn grammatical rules, for example converting > active > to passive voice and applying it to novel sentences: > > Bob kissed Alice -> Alice was kissed by Bob. > I ate dinner -> Dinner was eaten by me. > etc... > SUBJ VERB OBJ -> OBJ was VERB by SUBJ. > > In a similar manner, we can learn to solve problems using logical > deduction: > > All frogs are green. Kermit is a frog. Therefore Kermit is green. > All fish live in water. A shark is a fish. Therefore sharks live in water. > etc... > > I understand the objection to learning math and logic in a language model > instead of coding the rules directly. It is horribly inefficient. I > estimate > that a neural language model with 10^9 connections would need up to 10^18 > operations to learn simple arithmetic like 2+2=4 well enough to get it > right > 90% of the time. But I don't know of a better way to learn how to convert > natural language word problems to a formal language suitable for entering > into a calculator at the level of an average human adult. > > -- 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/?&; > Powered by Listbox: http://www.listbox.com > -- Ben Goertzel, PhD CEO, Novamente LLC and Biomind LLC Director of Research, SIAI [EMAIL PROTECTED] "Nothing will ever be attempted if all possible objections must be first overcome " - Dr Samuel Johnson ------------------------------------------- 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
