--- Lukasz Stafiniak <[EMAIL PROTECTED]> wrote: > On 4/23/07, Matt Mahoney <[EMAIL PROTECTED]> wrote: > > Ontic looks like an interesting and elegant formalism, but I don't see how > it > > would help an AGI learn mathematics. We are not yet at the point where we > can > > solve word problems like "if I pay for a $4.95 item with a $10 bill, how > much > > change should I get back?" Never mind the harder problem of proving > theorems. > > Give people calculators and they will just unlearn math, not having to > add their fees by themselves. But show them how calculators work, and > who knows, some of them might become mathematicians. > > But you are right in that an AGI could ultimately reprogram itself to > think in Ontic when it wants to.
I think there is nothing wrong with giving a calculator (or a conventional computer) to an AGI to enhance its intelligence, just as computers enhance the intelligence of humans. We need to solve the NLP problem of converting word problems to equations, but then the equations (or programs) can be done more quickly and accurately on a computer. So to predict: I have 3 apples and eat 1. Now I have 2 apples. The first step is to match the first sentence to the learned pattern: I have X (noun)s and (remove) Y. The second step is to plug X - Y into the calculator and get Z. This step could be done by a language model trained by rote memorization, but it would be vastly more inefficient and error prone. That is why people use calculators instead. The brain can execute sequential algorithms, just not very well. The brain is a billion times slower per step, has only about 7 words of short term memory, and has a few percent error rate per step. The third step is to match the pattern "Now I have Z (noun)s". Again, this is a language modeling problem. It is akin to grammar constraints such as number agreement or case agreement, which involve variable substitution spanning sentences that are individually correct. "I had an apple. Then I ate it." (Correct) "I had an apple. Then I ate them." (Number disagreement) "I had an apple. Then I eat it". (Case disagreement) These are chained, context sensitive substitution problems: I had -> I past tense -> I ate, and apple -> singular noun -> it, just like the original problem required a chain of context sensitive substitutions: 3 apples -> X apples, and Z apples -> 2 apples. Current language models are still a few developmental stages away from solving this problem. -- Matt Mahoney, [EMAIL PROTECTED] ----- This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=231415&user_secret=fabd7936
