AW: [agi] Language learning (was Re: Defining AGI)
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: agi@v2.listbox.com 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/?member_id=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
Re: [agi] Language learning (was Re: Defining AGI)
2008/10/21 Matt Mahoney [EMAIL PROTECTED]: 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 Not only this though. If I remember correctly from school the way that this was taught was at least partly geometric, so that you can see the numbers moving to different places in a particular pattern rather like doing a chess move or some other stereotypical physical action. --- 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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
AW: [agi] Language learning (was Re: Defining AGI)
There is another point which indicates that the ability to understand language or to learn language does not imply *general* intelligence. You can often observe in school that linguistic talents are poor in mathematics and vice versa. - Matthias --- 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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
Re: [agi] Language learning (was Re: Defining AGI)
2008/10/21 Dr. Matthias Heger [EMAIL PROTECTED]: There is another point which indicates that the ability to understand language or to learn language does not imply *general* intelligence. You can often observe in school that linguistic talents are poor in mathematics and vice versa. The usual explanation given for this is that understanding mathematics may require thinking about spatial organisation/imagery/mental rotation, which according to popular mythology are located in the opposite hemisphere from speech understanding and production. How true or not this is I don't know. Have any fMRI studies been done specifically on learning of maths concepts? --- 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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
Re: AW: AW: [agi] Re: Defining AGI
If MW would be scientific then he would not have asked Ben to prove that MWs hypothesis is wrong. Science is done by comparing hypotheses to data. Frequently, the fastest way to handle a hypothesis is to find a counter-example so that it can be discarded (or extended appropriately to handle the new case). How is asking for a counter-example unscientific? The person who has to prove something is the person who creates the hypothesis. Ah. Like the theory of evolution is conclusively proved? The scientific method is about predictive power not proof. Try reading the reference that I gave Ben. (And if you've got something to prove, maybe the scientific method isn't so good for you. :-) And MW has given not a tiny argument for his hypothesis that a natural language understanding system can easily be a scientist. First, I'd appreciate it if you'd drop the strawman. You are the only one who keeps insisting that anything is easy. Second, my hypothesis is more correctly stated that the pre-requisites for a natural language understanding system are necessary and sufficient for a scientist because both are AGI-complete. Again, I would appreciate it if you could correctly represent it in the future. Third, while I haven't given a tiny argument, I have given a reasonably short logical chain which I'll attempt to rephrase yet again. Science is all about modeling the world and predicting future data. The scientific method simply boils down to making a theory (of how to change or enhance your world model) and seeing if it is supported (not proved!) or disproved by future data. Ben's and my disagreement initially came down to whether a scientist was an Einstein (his view) or merely capable of competently reviewing data to see if it supports, disproves, or isn't relevant to the predictive power of a theory (my view). Later, he argued that most humans aren't even competent to review data and can't be made competent. I agreed with his assessment that many scientists don't competently review data (inappropriate over-reliance on the heuristic p 0.5 without understanding what it truly means) but disagreed as to whether the average human could be *taught* Ben's argument was that the scientific method couldn't be codified well enough to be taught. My argument was that the method was codified sufficiently but that the application of the method was clearly context dependent and could be unboundedly complex. But this is actually a distraction from some more important arguments . . . . The $1,000,000 question is If a human can't be taught something, is that human a general intelligence? The $5,000,000 question is If a human can't competently follow a recipe in a cookbook, do they have natural language understanding? Fundamentally, this either comes down to a disagreement about what a general intelligence is and/or what understanding and meaning are. Currently, I'm using the definition that a general intelligence is one that can achieve competence in any domain in a reasonable length of time. To achieve competence in a domain, you have to understand that domain My definition of understanding is that you have a mental model of that domain that has predictive power in that domain and which you can update as you learn about that domain. (You could argue with this definition if you like) Or, in other words, you have to be a competent scientist in that domain -- or else, you don't truly understand that domain So, for simplicity, why don't we just say scientist = understanding Now, for a counter-example to my initial hypothesis, why don't you explain how you can have natural language understanding without understanding (which equals scientist ;-). - Original Message - From: Dr. Matthias Heger [EMAIL PROTECTED] To: agi@v2.listbox.com Sent: Monday, October 20, 2008 5:00 PM Subject: AW: AW: AW: [agi] Re: Defining AGI If MW would be scientific then he would not have asked Ben to prove that MWs hypothesis is wrong. The person who has to prove something is the person who creates the hypothesis. And MW has given not a tiny argument for his hypothesis that a natural language understanding system can easily be a scientist. -Matthias -Ursprüngliche Nachricht- Von: Eric Burton [mailto:[EMAIL PROTECTED] Gesendet: Montag, 20. Oktober 2008 22:48 An: agi@v2.listbox.com Betreff: Re: AW: AW: [agi] Re: Defining AGI You and MW are clearly as philosophically ignorant, as I am in AI. But MW and I have not agreed on anything. Hence the wiki entry on scientific method: Scientific method is not a recipe: it requires intelligence, imagination, and creativity http://en.wikipedia.org/wiki/Scientific_method This is basic stuff. And this is fundamentally what I was trying to say. I don't think of myself as philosophically ignorant. I believe you've reversed the intention of my post. It's probably my fault for choosing my words poorly. I could have conveyed
Re: [agi] Language learning (was Re: Defining AGI)
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: agi@v2.listbox.com 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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
Re: AW: AW: [agi] Re: Defining AGI
My apologies if I've misconstrued you. Regardless of any fault, the basic point was/is important. Even if a considerable percentage of science's conclusions are v. hard, there is no definitive scientific method for reaching them . I think I understand. --- 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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
Re: AW: AW: [agi] Re: Defining AGI
Oh, and I *have* to laugh . . . . Hence the wiki entry on scientific method: Scientific method is not a recipe: it requires intelligence, imagination, and creativity http://en.wikipedia.org/wiki/Scientific_method This is basic stuff. In the cited wikipedia entry, the phrase Scientific method is not a recipe: it requires intelligence, imagination, and creativity is immediately followed by just such a recipe for the scientific method A linearized, pragmatic scheme of the four points above is sometimes offered as a guideline for proceeding:[25] 1.. Define the question 2.. Gather information and resources (observe) 3.. Form hypothesis 4.. Perform experiment and collect data 5.. Analyze data 6.. Interpret data and draw conclusions that serve as a starting point for new hypothesis 7.. Publish results 8.. Retest (frequently done by other scientists) - Original Message - From: Dr. Matthias Heger [EMAIL PROTECTED] To: agi@v2.listbox.com Sent: Monday, October 20, 2008 5:00 PM Subject: AW: AW: AW: [agi] Re: Defining AGI If MW would be scientific then he would not have asked Ben to prove that MWs hypothesis is wrong. The person who has to prove something is the person who creates the hypothesis. And MW has given not a tiny argument for his hypothesis that a natural language understanding system can easily be a scientist. -Matthias -Ursprüngliche Nachricht- Von: Eric Burton [mailto:[EMAIL PROTECTED] Gesendet: Montag, 20. Oktober 2008 22:48 An: agi@v2.listbox.com Betreff: Re: AW: AW: [agi] Re: Defining AGI You and MW are clearly as philosophically ignorant, as I am in AI. But MW and I have not agreed on anything. Hence the wiki entry on scientific method: Scientific method is not a recipe: it requires intelligence, imagination, and creativity http://en.wikipedia.org/wiki/Scientific_method This is basic stuff. And this is fundamentally what I was trying to say. I don't think of myself as philosophically ignorant. I believe you've reversed the intention of my post. It's probably my fault for choosing my words poorly. I could have conveyed the nuances of the argument better as I understood them. Next time! --- 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 --- 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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
Re: AW: AW: [agi] Re: Defining AGI
On Tue, Oct 21, 2008 at 10:38 AM, Mark Waser [EMAIL PROTECTED] wrote: Oh, and I *have* to laugh . . . . Hence the wiki entry on scientific method: Scientific method is not a recipe: it requires intelligence, imagination, and creativity http://en.wikipedia.org/wiki/Scientific_method This is basic stuff. In the cited wikipedia entry, the phrase Scientific method is not a recipe: it requires intelligence, imagination, and creativity is immediately followed by just such a recipe for the scientific method A linearized, pragmatic scheme of the four points above is sometimes offered as a guideline for proceeding:[25] Yes, but each of those steps is very vague, and cannot be boiled down to a series of precise instructions sufficient for a stupid person to consistently carry them out effectively... Also, those steps are heuristic and do not cover all cases. For instance step 4 requires experimentation, yet there are sciences such as cosmology and paleontology that are not focused on experimentation. As you asked for references I will give you two: Paul Feyerabend, Against Method (a polemic I don't fully agree with, but his points need to be understood by those who will talk about scientific method) Imre Lakatos, The Methodology of Scientific Research Programmes (which I do largely agree with ... he's a very subtle thinker...) ben g 1.. Define the question 2.. Gather information and resources (observe) 3.. Form hypothesis 4.. Perform experiment and collect data 5.. Analyze data 6.. Interpret data and draw conclusions that serve as a starting point for new hypothesis 7.. Publish results 8.. Retest (frequently done by other scientists) - Original Message - From: Dr. Matthias Heger [EMAIL PROTECTED] To: agi@v2.listbox.com Sent: Monday, October 20, 2008 5:00 PM Subject: AW: AW: AW: [agi] Re: Defining AGI If MW would be scientific then he would not have asked Ben to prove that MWs hypothesis is wrong. The person who has to prove something is the person who creates the hypothesis. And MW has given not a tiny argument for his hypothesis that a natural language understanding system can easily be a scientist. -Matthias -Ursprüngliche Nachricht- Von: Eric Burton [mailto:[EMAIL PROTECTED] Gesendet: Montag, 20. Oktober 2008 22:48 An: agi@v2.listbox.com Betreff: Re: AW: AW: [agi] Re: Defining AGI You and MW are clearly as philosophically ignorant, as I am in AI. But MW and I have not agreed on anything. Hence the wiki entry on scientific method: Scientific method is not a recipe: it requires intelligence, imagination, and creativity http://en.wikipedia.org/wiki/Scientific_method This is basic stuff. And this is fundamentally what I was trying to say. I don't think of myself as philosophically ignorant. I believe you've reversed the intention of my post. It's probably my fault for choosing my words poorly. I could have conveyed the nuances of the argument better as I understood them. Next time! --- 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 --- 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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
RE: [agi] Who is smart enough to answer this question?
Ben, In my email starting this thread on 10/15/08 7:41pm I pointed out that a more sophisticated version of the algorithm would have to take connection weights into account in determining cross talk, as you have suggested below. But I asked for the answer to a more simple version of the problem, since that might prove difficult enough, and since I was just trying to get some rough feeling for whether or not node assemblies might offer substantial gains in possible representational capability, before delving more deeply into the subject. Ed Porter -Original Message- From: Ben Goertzel [mailto:[EMAIL PROTECTED] Sent: Monday, October 20, 2008 10:52 PM To: agi@v2.listbox.com Subject: Re: [agi] Who is smart enough to answer this question? But, suppose you have two assemblies A and B, which have nA and nB neurons respectively, and which overlap in O neurons... It seems that the system's capability to distinguish A from B is going to depend on the specific **weight matrix** of the synapses inside the assemblies A and B, not just on the numbers nA, nB and O. And this weight matrix depends on the statistical properties of the memories being remembered. So, these counting arguments you're trying to do are only going to give you a very crude indication, anyway, right? ben On Mon, Oct 20, 2008 at 5:09 PM, Ed Porter [EMAIL PROTECTED] wrote: Ben, I am interested in exactly the case where individual nodes partake in multiple attractors, I use the notation A(N,O,S) which is similar to the A(n,d,w) formula of constant weight codes, except as Vlad says you would plug my varaiables into the constant weight formula buy using A(N, 2*(S-0+1),S). I have asked my question assuming each node assembly has the same size S for to make the math easier. Each such assembly is an autoassociative attractor. I want to keep the overlap O low to reduce the cross talk between attractors. So the question is how many node assemblies A, can you make having a size S, and no more than an overlap O, given N nodes. Actually the cross talk between auto associative patterns becomes an even bigger problem if there are many attractors being activated at once (such as hundreds of them), but if the signaling driving different the population of different attractors could have different timing or timing patterns, and if the auto associatively was sensitive to such timing, this problem could be greatly reduced. Ed Porter -Original Message- From: Ben Goertzel [mailto:[EMAIL PROTECTED] Sent: Monday, October 20, 2008 4:16 PM To: agi@v2.listbox.com Subject: Re: [agi] Who is smart enough to answer this question? Wait, now I'm confused. I think I misunderstood your question. Bounded-weight codes correspond to the case where the assemblies themselves can have n or fewer neurons, rather than exactly n. Constant-weight codes correspond to assemblies with exactly n neurons. A complication btw is that an assembly can hold multiple memories in multiple attractors. For instance using Storkey's palimpsest model a completely connected assembly with n neurons can hold about .25n attractors, where each attractor has around .5n neurons switched on. In a constant-weight code, I believe the numbers estimated tell you the number of sets where the Hamming distance is greater than or equal to d. The idea in coding is that the code strings denoting distinct messages should not be closer to each other than d. But I'm not sure I'm following your notation exactly. ben g On Mon, Oct 20, 2008 at 3:19 PM, Ben Goertzel [EMAIL PROTECTED] wrote: I also don't understand whether A(n,d,w) is the number of sets where the hamming distance is exactly d (as it would seem from the text of http://en.wikipedia.org/wiki/Constant-weight_code http://en.wikipedia.org/wiki/Constant-weight_code ), or whether it is the number of set where the hamming distance is d or less. If the former case is true then the lower bounds given in the tables would actually be lower than the actual lower bounds for the question I asked, which would correspond to all cases where the hamming distance is d or less. The case where the Hamming distance is d or less corresponds to a bounded-weight code rather than a constant-weight code. I already forwarded you a link to a paper on bounded-weight codes, which are also combinatorially intractable and have been studied only via computational analysis. -- Ben G -- 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 | https://www.listbox.com/member/archive/303/=now Archives https://www.listbox.com/member/archive/rss/303/ | https://www.listbox.com/member/?; Modify Your Subscription http://www.listbox.com _ agi | https://www.listbox.com/member/archive/303/=now Archives
Re: [agi] Who is smart enough to answer this question?
makes sense, yep... i guess my intuition is that there are obviously a huge number of assemblies, so that the number of assemblies is not the hard part, the hard part lies in the weights... On Tue, Oct 21, 2008 at 11:18 AM, Ed Porter [EMAIL PROTECTED] wrote: Ben, In my email starting this thread on 10/15/08 7:41pm I pointed out that a more sophisticated version of the algorithm would have to take connection weights into account in determining cross talk, as you have suggested below. But I asked for the answer to a more simple version of the problem, since that might prove difficult enough, and since I was just trying to get some rough feeling for whether or not node assemblies might offer substantial gains in possible representational capability, before delving more deeply into the subject. Ed Porter -Original Message- *From:* Ben Goertzel [mailto:[EMAIL PROTECTED] *Sent:* Monday, October 20, 2008 10:52 PM *To:* agi@v2.listbox.com *Subject:* Re: [agi] Who is smart enough to answer this question? But, suppose you have two assemblies A and B, which have nA and nB neurons respectively, and which overlap in O neurons... It seems that the system's capability to distinguish A from B is going to depend on the specific **weight matrix** of the synapses inside the assemblies A and B, not just on the numbers nA, nB and O. And this weight matrix depends on the statistical properties of the memories being remembered. So, these counting arguments you're trying to do are only going to give you a very crude indication, anyway, right? ben On Mon, Oct 20, 2008 at 5:09 PM, Ed Porter [EMAIL PROTECTED] wrote: Ben, I am interested in exactly the case where individual nodes partake in multiple attractors, I use the notation A(N,O,S) which is similar to the A(n,d,w) formula of constant weight codes, except as Vlad says you would plug my varaiables into the constant weight formula buy using A(N, 2*(S-0+1),S). I have asked my question assuming each node assembly has the same size S for to make the math easier. Each such assembly is an autoassociative attractor. I want to keep the overlap O low to reduce the cross talk between attractors. So the question is how many node assemblies A, can you make having a size S, and no more than an overlap O, given N nodes. Actually the cross talk between auto associative patterns becomes an even bigger problem if there are many attractors being activated at once (such as hundreds of them), but if the signaling driving different the population of different attractors could have different timing or timing patterns, and if the auto associatively was sensitive to such timing, this problem could be greatly reduced. Ed Porter -Original Message- *From:* Ben Goertzel [mailto:[EMAIL PROTECTED] *Sent:* Monday, October 20, 2008 4:16 PM *To:* agi@v2.listbox.com *Subject:* Re: [agi] Who is smart enough to answer this question? Wait, now I'm confused. I think I misunderstood your question. Bounded-weight codes correspond to the case where the assemblies themselves can have n or fewer neurons, rather than exactly n. Constant-weight codes correspond to assemblies with exactly n neurons. A complication btw is that an assembly can hold multiple memories in multiple attractors. For instance using Storkey's palimpsest model a completely connected assembly with n neurons can hold about .25n attractors, where each attractor has around .5n neurons switched on. In a constant-weight code, I believe the numbers estimated tell you the number of sets where the Hamming distance is greater than or equal to d. The idea in coding is that the code strings denoting distinct messages should not be closer to each other than d. But I'm not sure I'm following your notation exactly. ben g On Mon, Oct 20, 2008 at 3:19 PM, Ben Goertzel [EMAIL PROTECTED] wrote: I also don't understand whether A(n,d,w) is the number of sets where the hamming distance is exactly d (as it would seem from the text of http://en.wikipedia.org/wiki/Constant-weight_code ), or whether it is the number of set where the hamming distance is d or less. If the former case is true then the lower bounds given in the tables would actually be lower than the actual lower bounds for the question I asked, which would correspond to all cases where the hamming distance is d or less. The case where the Hamming distance is d or less corresponds to a bounded-weight code rather than a constant-weight code. I already forwarded you a link to a paper on bounded-weight codes, which are also combinatorially intractable and have been studied only via computational analysis. -- Ben G -- 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
Re: AW: [agi] Language learning (was Re: Defining AGI)
This really seems more like arguing that there is no such thing as AI-complete at all. That is certainly a possibility. It could be that there are only different competences. This would also seem to mean that there isn't really anything that is truly general about intelligence, which is again possible. I guess one thing we're seeing here is a basic example of mathematics as having underlying separate mechanisms from other features of language. The Lakoff and Nunez talk about subitizing (judging small numbers of things at a glance) as one core competancy, and counting as another. These are things you can see in animals that do not use language. So, sure, mathematics could be a separate realm of intelligence. Of course, my response to that is that this kind of basic mathematical ability is needed to understand language. Of course, people who favor language use my not exercise their mathematical ability and it can become weak, but I think it generally has to be there for full competance. And there are some more abstract concepts that could be hard for people to get, and maybe some people don't have what it takes to get some concepts, so the don't have infinite potential. andi Matthias 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: agi@v2.listbox.com 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 --- 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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
Re: [agi] constructivist issues
Ben, Unfortunately, this response is going to be (somewhat) long, because I have several points that I want to make. If I understand what you are saying, you're claiming that if I pointed to the black box and said That's a halting oracle, I'm not describing the box directly, but instead describing it in terms of a (semi)formal system in my head that defines halting oracle. This system is computable. This seems to fit back with the comment I made about William Pearson's system: we don't assume that the universe is computable, instead we just assume that our mental substrate is. But, we need to be careful about what computable means here. Things like a mandelbrot set rendering are computably enumerable, which is formally separated from computable, but still easily implemented on a computer. The same is true of first-order theories that describe halting oracle and related notions. Technically these are not computable, because there is no halting criteria (or, in the case of the mandelbrot renderer, no halting criteria *yet*, although many mathematicians expect that one can be formulated.) We can list positive cases (provably halting/nonhalting programs, provably escaping points) but we have no way of deciding when to give up on the stubborn points. A third type of computability is computably co-enumerable, which is what the halting problem is. I imagine you know the definition of this term already. So, halting-related things such as halting oracles have no computable description, but they do have a description-implementable-on-a-computer. Unfortunately, AIXI does not use models of this variety, since it only considers models that are computable in the strict technical sense. But, worse, there are mathematically well-defined entities that are not even enumerable or co-enumerable, and in no sense seem computable. Of course, any axiomatic theory of these objects *is* enumerable and therefore intuitively computable (but technically only computably enumerable). Schmidhuber's super-omegas are one example. Concerning your statement, It is not clear what you really mean by the description length of something uncomputable, since the essence of uncomputability is the property of **not being finitely describable**. That statement basically agrees with the following definition of meaning: A statement is meaningful if we have a (finite) rule that tells us whether it is true or false. The idea of finite rule here is a program that takes finite input (the facts we currently know) and halts in finite time with an output. This agrees with the formal definition of computable, so that meaningful facts and computable facts are one and the same. Here is a slightly broader definition: A statement is meaningful if we have a (finite) rule that tells us whether it is true. This agrees instead with the definition of enumerable. Or, the scientific testability version: A statement is meaningful if we have a (finite) rule that tells us whether it is false. This of course agrees with the definition of co-enumerable. Now here is a rather broad one: A statement is meaningful if we have a (finite) rule that tells us how we can reason if it is true. So, each statement corresponds to a program that operates on known statements to produce more statements; applying the rule corresponds to using the fact in our reasoning. So the direct consequences of a statement given some other statements are computable, but the truth or falsehood is not necessarily. As it happens, this definition of meaning admits horribly-terribly-uncomputable-things to be described! (Far worse than the above-mentioned super-omegas.) So, the truth or falsehood is very much not computable. I'm hesitant to provide the mathematical proof in this email, since it is already long enough... let's just say it is available upon request. Anyway, you'll probably have some more basic objection. --Abram On Mon, Oct 20, 2008 at 10:38 PM, Ben Goertzel [EMAIL PROTECTED] wrote: On Mon, Oct 20, 2008 at 5:29 PM, Abram Demski [EMAIL PROTECTED] wrote: Ben, [my statement] seems to incorporate the assumption of a finite period of time because a finite set of sentences or observations must occur during a finite period of time. A finite set of observations, sure, but a finite set of statements can include universal statements. Ok ... let me clarify what I meant re sentences I'll define what I mean by a **descriptive sentence** What I mean by a sentence is a finite string of symbols drawn from a finite alphabet. What I mean by a *descriptive sentence* is a sentence that is agreed by a certain community to denote some subset of the total set of observations (where all observations have finite precision and are drawn from a certain finite set). So, whether or not a descriptive sentence contains universal quantifiers or quantum-gravity quantifiers or psychospirituometaphysical quantifiers, or whatever, in the end there are some observation-sets it
AW: [agi] Language learning (was Re: Defining AGI)
I agree. But the vaguely-human-mind-like-architecture is a huge additional assumption. If you have a system that can solve problem x and has in addition a human-mind-like-architecture then obviously you obtain AGI for *any* x. The whole AGI-completeness would essentially depend on this additional assumption. A human-mind-like-architecture even would imply the ability to learn natural language understanding - Matthias Ben wrote 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: agi@v2.listbox.com 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/? 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/? 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 | https://www.listbox.com/member/archive/303/=now Archives https://www.listbox.com/member/archive/rss/303/ | https://www.listbox.com/member/?; 7 Modify Your Subscription 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:
Re: [agi] constructivist issues
But, worse, there are mathematically well-defined entities that are not even enumerable or co-enumerable, and in no sense seem computable. Of course, any axiomatic theory of these objects *is* enumerable and therefore intuitively computable (but technically only computably enumerable). Schmidhuber's super-omegas are one example. My contention is that the first use of the word are in the first sentence of the above is deceptive. The whole problem with the question of whether there are uncomputable entities is the ambiguity of the natural language term is / are, IMO ... If by A exists you mean communicable-existence, i.e. It is possible to communicate A using a language composed of discrete symbols, in a finite time then uncomputable numbers do not exist If by A exists you mean I can take some other formal property F(X) that applies to communicatively-existent things X, and apply it to A then this will often be true ... depending on the property F ... My question to you is: how do you interpret are in your statement that uncomputable entities are? ben --- 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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
Re: [agi] Language learning (was Re: Defining AGI)
OK, I guess the term architecture is poorly defined. Let me say it this way, then: I suspect that if you have a system that a) has a generally dog/chimp/pig like cognitive architecture (which we humans certainly do) b) can learn to understand and generate human language this this system will also be able to learn basic human math... -- Ben G On Tue, Oct 21, 2008 at 11:53 AM, Dr. Matthias Heger [EMAIL PROTECTED]wrote: I agree. But the vaguely-human-mind-like-architecture is a huge additional assumption. If you have a system that can solve problem x and has in addition a human-mind-like-architecture then obviously you obtain AGI for **any** x. The whole AGI-completeness would essentially depend on this additional assumption. A human-mind-like-architecture even would imply the ability to learn natural language understanding - Matthias Ben wrote 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: agi@v2.listbox.com 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
Re: [agi] constructivist issues
Ben, My discussion of meaning was supposed to clarify that. The final definition is the broadest I currently endorse, and it admits meaningful uncomputable facts about numbers. It does not appear to get into the realm of set theory, though. --Abram On Tue, Oct 21, 2008 at 12:07 PM, Ben Goertzel [EMAIL PROTECTED] wrote: But, worse, there are mathematically well-defined entities that are not even enumerable or co-enumerable, and in no sense seem computable. Of course, any axiomatic theory of these objects *is* enumerable and therefore intuitively computable (but technically only computably enumerable). Schmidhuber's super-omegas are one example. My contention is that the first use of the word are in the first sentence of the above is deceptive. The whole problem with the question of whether there are uncomputable entities is the ambiguity of the natural language term is / are, IMO ... If by A exists you mean communicable-existence, i.e. It is possible to communicate A using a language composed of discrete symbols, in a finite time then uncomputable numbers do not exist If by A exists you mean I can take some other formal property F(X) that applies to communicatively-existent things X, and apply it to A then this will often be true ... depending on the property F ... My question to you is: how do you interpret are in your statement that uncomputable entities are? ben agi | Archives | Modify Your Subscription --- 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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
AW: AW: AW: [agi] Re: Defining AGI
Marc Walser wrote Science is done by comparing hypotheses to data. Frequently, the fastest way to handle a hypothesis is to find a counter-example so that it can be discarded (or extended appropriately to handle the new case). How is asking for a counter-example unscientific? Before you ask for counter examples you should *first* give some arguments which supports your hypothesis. This was my point. If everyone would make wild hypotheses and ask other scientists to find counter-examples then we would end up in a explosion of number of hypotheses. But if you would first show some arguments which support your hypothesis then you give reasons to the scientific community why it is worth to use some time to think about the hypothesis. Regarding your example with Darwin: Darwin had gathered signs of evidence which supports his hypothesis *first* . First, I'd appreciate it if you'd drop the strawman. You are the only one who keeps insisting that anything is easy. Is this a scientific discussion from you? No. You use rhetoric and nothing else. I don't say that anything is easy. Second, my hypothesis is more correctly stated that the pre-requisites for a natural language understanding system are necessary and sufficient for a scientist because both are AGI-complete. Again, I would appreciate it if you could correctly represent it in the future. This is the first time you speak about pre-requisites. Your whole hypothesis changes with these pre-requisites. If you would be scientific you would qualify what are your pre-requisites. So, for simplicity, why don't we just say scientist = understanding Understanding does not imply the ability to create something new or to apply knowledge. Furthermore natural language understanding does not imply understanding *general* domains. There is much evidence that the ability to understand natural language does not imply to the understanding of mathematics. Not to speak from the ability to create mathematics. Now, for a counter-example to my initial hypothesis, why don't you explain how you can have natural language understanding without understanding (which equals scientist ;-). Understanding does not equal scientist. The claim that natural language understanding needs understanding is trivial. This wasn't your initial hypothesis. - Original Message - From: Dr. Matthias Heger [EMAIL PROTECTED] To: agi@v2.listbox.com Sent: Monday, October 20, 2008 5:00 PM Subject: AW: AW: AW: [agi] Re: Defining AGI If MW would be scientific then he would not have asked Ben to prove that MWs hypothesis is wrong. The person who has to prove something is the person who creates the hypothesis. And MW has given not a tiny argument for his hypothesis that a natural language understanding system can easily be a scientist. -Matthias -Ursprüngliche Nachricht- Von: Eric Burton [mailto:[EMAIL PROTECTED] Gesendet: Montag, 20. Oktober 2008 22:48 An: agi@v2.listbox.com Betreff: Re: AW: AW: [agi] Re: Defining AGI You and MW are clearly as philosophically ignorant, as I am in AI. But MW and I have not agreed on anything. Hence the wiki entry on scientific method: Scientific method is not a recipe: it requires intelligence, imagination, and creativity http://en.wikipedia.org/wiki/Scientific_method This is basic stuff. And this is fundamentally what I was trying to say. I don't think of myself as philosophically ignorant. I believe you've reversed the intention of my post. It's probably my fault for choosing my words poorly. I could have conveyed the nuances of the argument better as I understood them. Next time! --- 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 --- 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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
Re: AW: AW: [agi] Re: Defining AGI
Yes, but each of those steps is very vague, and cannot be boiled down to a series of precise instructions sufficient for a stupid person to consistently carry them out effectively... So -- are those stupid people still general intelligences? Or are they only general intelligences to the degree to which they *can* carry them out? (because I assume that you'd agree that general intelligence is a spectrum like any other type). There also remains the distinction (that I'd like to highlight and emphasize) between a discoverer and a learner. The cognitive skills/intelligence necessary to design questions, hypotheses, experiments, etc. are far in excess the cognitive skills/intelligence necessary to evaluate/validate those things. My argument was meant to be that a general intelligence needs to be a learner-type rather than a discoverer-type although the discoverer type is clearly more effective. So -- If you can't correctly evaluate data, are you a general intelligence? How do you get an accurate and effective domain model to achieve competence in a domain if you don't know who or what to believe? If you don't believe in evolution, does that mean that you aren't a general intelligence in that particular realm/domain (biology)? Also, those steps are heuristic and do not cover all cases. For instance step 4 requires experimentation, yet there are sciences such as cosmology and paleontology that are not focused on experimentation. I disagree. They may be based upon thought experiments rather than physical experiments but it's still all about predictive power. What is that next star/dinosaur going to look like? What is it *never* going to look like (or else we need to expand or correct our theory)? Is there anything that we can guess that we haven't tested/seen yet that we can verify? What else is science? My *opinion* is that the following steps are pretty inviolable. A. Observe B. Form Hypotheses C. Observe More (most efficiently performed by designing competent experiments including actively looking for disproofs) D. Evaluate Hypotheses E. Add Evaluation to Knowledge-Base (Tentatively) but continue to test F. Return to step A with additional leverage If you were forced to codify the hard core of the scientific method, how would you do it? As you asked for references I will give you two: Thank you for setting a good example by including references but the contrast between the two is far better drawn in For and Against Method (ISBN 0-226-46774-0). Also, I would add in Polya, Popper, Russell, and Kuhn for completeness for those who wish to educate themselves in the fundamentals of Philosophy of Science (you didn't really forget that my undergraduate degree was a dual major of Biochemistry and Philosophy of Science, did you? :-). My view is basically that of Lakatos to the extent that I would challenge you to find anything in Lakatos that promotes your view over the one that I've espoused here. Feyerabend's rants alternate between criticisms ultimately based upon the fact that what society frequently calls science is far more politics (see sociology of scientific knowledge); a Tintnerian/Anarchist rant against structure and formalism; and incorrect portrayals/extensions of Lakatos (just like this list ;-). Where he is correct is in the first case where society is not doing science correctly (i.e. where he provided examples regarded as indisputable instances of progress and showed how the political structures of the time fought against or suppressed them). But his rants against structure and formalism (or, purportedly, for freedom and humanitarianism snort) are simply garbage in my opinion (though I'd guess that they appeal to you ;-). - Original Message - From: Ben Goertzel To: agi@v2.listbox.com Sent: Tuesday, October 21, 2008 10:41 AM Subject: Re: AW: AW: [agi] Re: Defining AGI On Tue, Oct 21, 2008 at 10:38 AM, Mark Waser [EMAIL PROTECTED] wrote: Oh, and I *have* to laugh . . . . Hence the wiki entry on scientific method: Scientific method is not a recipe: it requires intelligence, imagination, and creativity http://en.wikipedia.org/wiki/Scientific_method This is basic stuff. In the cited wikipedia entry, the phrase Scientific method is not a recipe: it requires intelligence, imagination, and creativity is immediately followed by just such a recipe for the scientific method A linearized, pragmatic scheme of the four points above is sometimes offered as a guideline for proceeding:[25] Yes, but each of those steps is very vague, and cannot be boiled down to a series of precise instructions sufficient for a stupid person to consistently carry them out effectively... Also, those steps are heuristic and do not cover all cases. For instance step 4 requires experimentation, yet there are sciences such as cosmology and
Re: AW: AW: [agi] Re: Defining AGI
Marc Walser wrote Try to get the name right. It's just common competence and courtesy. Before you ask for counter examples you should *first* give some arguments which supports your hypothesis. This was my point. And I believe that I did. And I note that you didn't even address the fact that I did so again in the e-mail you are quoting. You seem to want to address trivia rather than the meat of the argument. What don't you address the core instead of throwing up a smokescreen? Regarding your example with Darwin: What example with Darwin? First, I'd appreciate it if you'd drop the strawman. You are the only one who keeps insisting that anything is easy. Is this a scientific discussion from you? No. You use rhetoric and nothing else. And baseless statements like You use rhetoric and nothing else are a scientific discussion. Again with the smokescreen. I don't say that anything is easy. Direct quote cut and paste from *your* e-mail . . . . -- From: Dr. Matthias Heger To: agi@v2.listbox.com Sent: Sunday, October 19, 2008 2:19 PM Subject: AW: AW: [agi] Re: Defining AGI The process of translating patterns into language should be easier than the process of creating patterns or manipulating patterns. Therefore I say that language understanding is easy. -- Clearly you DO say that language understanding is easy. This is the first time you speak about pre-requisites. Direct quote cut and paste from *my* e-mail . . . . . - Original Message - From: Mark Waser [EMAIL PROTECTED] To: agi@v2.listbox.com Sent: Sunday, October 19, 2008 4:01 PM Subject: Re: AW: AW: [agi] Re: Defining AGI I don't think that learning of language is the entire point. If I have only learned language I still cannot create anything. A human who can understand language is by far still no good scientist. Intelligence means the ability to solve problems. Which problems can a system solve if it can nothing else than language understanding? Many or most people on this list believe that learning language is an AGI-complete task. What this means is that the skills necessary for learning a language are necessary and sufficient for learning any other task. It is not that language understanding gives general intelligence capabilities, but that the pre-requisites for language understanding are general intelligence (or, that language understanding is isomorphic to general intelligence in the same fashion that all NP-complete problems are isomorphic). Thus, the argument actually is that a system that can do nothing else than language understanding is an oxymoron. - Clearly I DO talk about the pre-requisites for language understanding. Dude. Seriously. First you deny your own statements and then claim that I didn't previously mention something that it is easily provable that I did (at the top of an e-mail). Check the archives. It's all there in bits and bytes. Then you end with a funky pseudo-definition that Understanding does not imply the ability to create something new or to apply knowledge. What *does* understanding mean if you can't apply it? What value does it have? --- 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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
AW: AW: [agi] Language learning (was Re: Defining AGI)
Andi wrote This really seems more like arguing that there is no such thing as AI-complete at all. That is certainly a possibility. It could be that there are only different competences. This would also seem to mean that there isn't really anything that is truly general about intelligence, which is again possible. No. This arguing shows that there are very basic features which do not imply necessarily from natural language understanding: Usage of knowledge. The example to solve a equation is just one of many examples. If you can talk about things this does not imply that you can do things. I guess one thing we're seeing here is a basic example of mathematics as having underlying separate mechanisms from other features of language. The Lakoff and Nunez talk about subitizing (judging small numbers of things at a glance) as one core competancy, and counting as another. These are things you can see in animals that do not use language. So, sure, mathematics could be a separate realm of intelligence. It is not just mathematics. A natural language understanding system can talk about shopping. But from this ability you can't prove that it can do shopping. There are essential features of intelligence missing in natural language understanding. And that's the reason why natural language understanding is not AGI-complete. Of course, my response to that is that this kind of basic mathematical ability is needed to understand language. This argumentation is nothing else than making a non-AGI-complete system AGI complete by adding more and more features. If you suppose for a arbitrary still unsolved problem P that everything is which is needed to solve AGI is also necessary to solve P then it becomes trivial that P is AGI-complete. But this argumentation is similar to the doubters of AGI who essentially suppose for an arbitrary given still unsolved problem P that P is not computable at all. -Matthias Matthias 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: agi@v2.listbox.com 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:
RE: [agi] Who is smart enough to answer this question?
Vlad, Thanks. In respone to your email I tried plugging different values into the Excel spread sheet I sent by a prior email under this subject line, and, and low and behold, got some interesting answers for the number A of assemblies (or sets) of nodes of uniform size S you can create from N nodes where no two assemblies have more than O overlapping nodes: N S OA == 100K 20 12.5x10^2 100K 20 21.3x10^5-10% overlap 100K 20 31.2x10^8 == 100K 50 23.3x10^3 100K 50 34.4x10^5 100K 50 47.9x10^7 100K 50 51.8x10^10-10% overlap == 100K 88 23.5x10^2 100K 88 31.4x10^4 100K 88 48.1x10^5 100K 88 55.7x10^7 100K 88 65.6x10^9 100K 88 75.2x10^11 100K 88 86.3x10^13-9.09% overlap == 50K88 68.2x10^7 50K88 81.6x10^11-9.09% overlap == 25K88 61.4x10^6 25K88 81.1x10^9-9.09% overlap From this data, it is clear that for a given N, increasing S (as least when S is small relative to N), increases the number of nodes that have a given percent of maximum overlap, such as 5% or 10% max overlap. Doubling N from 25k, to 50K, to 100K, provides a little less than two orders of magnitude in increases in the number of cell assemblies of size 88 having overlaps of 6 or 8 at each doubling. 88 was the largest number S that Excel could produce a C(100K,S) for, enabling the calculations to be made. BUT EVEN AT THIS LIMIT WITH 100K NODES, YOU COULD CREATE 57 MILLION NODE ASSEMBLIES WITH AN OVERLAP OF LESS 5.7%. This is a 570x increase in the number of states that could be represented, relative to representing states with individual nodes. Since it is clear that the number of possible assemblies relative to percent overlap, grows with N and with S, it is likely that one could produce even larger multiplicative increases in number of assemblies relative to the number of nodes having even lower percentage overlap, with larger Ns and/or Ss. The one thing I don't understand is how you derived the formula I used in this spreadsheet, the one you described in your Thu 10/16/2008 7:50 PM email (with the position of the variables in the combinations function switched). Switching the variables in the combinatorial formula to the convention more commonly used in America this formula that is as follows: A =C(N,S)/T(N,S,O) Where T(N,S,O)= C(S,S) +C(S, S-1)*C(N-S, 1) +C(S, S-2)*C(N-S, 2) +... +C(S, O)*C(N-S, S-O) (note the first term in T(N,S,O), i.e., C(S,S), is the equivalent of C(S,S-0)*C(N-S,0) since C(X,0)=1, oddly enough, which makes all the terms in T(N,S,O) have the same form, differing only by the value of the iterator which goes from 0 to O) THE ONE PROBLEM I HAVE, IS THAT I DON'T UNDERSTAND THE DERIVATION OF THIS FORMULA, SO I CAN'T KNOW HOW MUST FAITH OR ACCURACY I SHOULD ATTRIBUTE TO ITS ESTIMATION OF A LOWER BOUND. If it is possible to give an explanation of why this formula is a proper lower bounds, in a little more detail than in the email in which you first presented it, I would appreciate it very much, it would let me know how much faith I should put into the above numerical results. Ed Porter -Original Message- From: Vladimir Nesov [mailto:[EMAIL PROTECTED] Sent: Tuesday, October 21, 2008 1:14 AM To: agi@v2.listbox.com Subject: Re: [agi] Who is smart enough to answer this question? On Tue, Oct 21, 2008 at 12:07 AM, Ed Porter [EMAIL PROTECTED] wrote: I built an excel spread sheet to calculate this for various values of N,S, and O. But when O = zero, the value of C(N,S)/T(N,S,O) doesn't make sense for most values of N and S. For example if N = 100 and S = 10, and O = zero, then A should equal 10, not one as it does on the spread sheet. It's a lower bound. I have attached the excel spreadsheet I made to play around with your formulas, and a PDF of one page of it, in case you don't have access to Excel. Your spreadsheet doesn't catch it for S=100 and O=1, it explodes when you try to increase N. But at S=10, O=2, you can see how lower bound increases as you increase N. At N=5000, lower bound is 6000, at N=10^6, it's 2.5*10^8, and at N=10^9 it's 2.5*10^14. -- Vladimir Nesov [EMAIL PROTECTED] http://causalityrelay.wordpress.com/
[agi] natural language - algebra (was Defining AGI)
Matthias wrote: Your claim is that natural language understanding is sufficient for AGI. Then you must be able to prove that everything what AGI can is also possible by a system which is able to understand natural language. AGI can learn to solve x*3 = y for arbitrary y. And AGI can do this with Mathematica or without Mathematica. Simply prove that a natural language understanding system must necessarily be able to do the same. Here's my simple proof: algebra, or any other formal language for that matter, is expressible in natural language, if inefficiently. Words like quantity, sum, multiple, equals, and so on, are capable of conveying the same meaning that the sentence x*3 = y conveys. The rules for manipulating equations are likewise expressible in natural language. Thus it is possible in principle to do algebra without learning the mathematical symbols. Much more difficult for human minds perhaps, but possible in principle. Thus, learning mathematical formalism via translation from natural language concepts is possible (which is how we do it, after all). Therefore, an intelligence that can learn natural language can learn to do math. I have given the model why we have the illusion that we believe our thoughts are build from language. . snipped description of model My model explains several phenomena: 1. We hear our thoughts 2. We think with the same speed as we speak (this is not trivial!) 3. We hear our thoughts with our own voice (strong evidence for my model!) 4. We have problems to think in a very noisy and loud environment (because we have to listen to our thoughts) I believe there are linguistic forms of thought (exactly as you describe) and non-linguistic forms of thought (as described by Einstein - thinking in 'pictures'). I agree with your premise that thought is not necessarily linguistic (as I have in previous emails!). Your model (which is quite good at explaining internal monologue) - and list of phenomena above - does not apply to the non-linguistic form of thought (as I experience it) except perhaps for (4), but that could simply be due to sensorial competition for one's attention, not a need to hear thought. This non-linguistic kind of thought is much faster and obviously non-verbal - it is not 'heard'. It can be quite a struggle to express the products of such thinking in natural language. This faculty for non-linguistic mental manipulation is most likely exclusively how chimps, ravens, and other highly intelligent animals solve problems. But relying on this form of thought alone is not sufficient for the development of the symbolic conceptual framework necessary to perform human-level analytical thought. Terren --- 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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
Re: [agi] Who is smart enough to answer this question?
C(N,S) is the total number of assemblies of size S that fit in the N nodes, if you forget about overlaps. Each assembly overlaps in X places with other C(S,X)*C(N-S,S-X) assemblies: if another assembly overlaps with our assembly in X places, then X nodes are inside S nodes of our assembly, which gives C(S,X) possible combinations, and the remaining S-X of the nodes are outside the assembly, in remaining N-S nodes, which gives C(N-S,S-X) combinations, totaling to C(S,X)*C(N-S,S-X). Thus, the total number of assemblies that overlap with our assembly in O to S places (including our assembly itself) is T(N,S,O)= C(S,S)*C(N-S,S-S)+ C(S,S-1)*C(N-S,S-(S-1))+ ...+ C(S,O)*C(N-S,S-O) Let's apply a trivial algorithm to our problem, adding an arbitrary assembly to the working set merely if it doesn't conflict with any of the assemblies already in the working set. Adding a new assembly will ban other T(N,S,O) assemblies from the total pool of C(N,S) assemblies, thus each new assembly in the working set lowers the number of remaining assemblies that we'll be able to add later. Some assemblies from this pool will be banned multiple times, but at least C(N,S)/T(N,S,O) assemblies can be added without conflicts, since T(N,S,O) is the maximum number of assemblies that each one in the pool is able to subtract from the total pool of assemblies. -- Vladimir Nesov [EMAIL PROTECTED] http://causalityrelay.wordpress.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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
Re: [agi] constructivist issues
On Tue, Oct 21, 2008 at 4:53 PM, Abram Demski [EMAIL PROTECTED] wrote: As it happens, this definition of meaning admits horribly-terribly-uncomputable-things to be described! (Far worse than the above-mentioned super-omegas.) So, the truth or falsehood is very much not computable. I'm hesitant to provide the mathematical proof in this email, since it is already long enough... let's just say it is available upon request. Now I'm curious -- can these horribly-terribly-uncomputable-things be described to a non-mathematician? If so, consider this a request. --- 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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
AW: AW: AW: [agi] Re: Defining AGI
Mark Waser answered to I don't say that anything is easy. : Direct quote cut and paste from *your* e-mail . . . . -- From: Dr. Matthias Heger To: agi@v2.listbox.com Sent: Sunday, October 19, 2008 2:19 PM Subject: AW: AW: [agi] Re: Defining AGI The process of translating patterns into language should be easier than the process of creating patterns or manipulating patterns. Therefore I say that language understanding is easy. -- Clearly you DO say that language understanding is easy. Your claim was that I have said that *anything* is easy. This is a wrong generalization which is usually known in rhetoric. I think, often you are less scientific than those people who you blame not to be scientific. I will give up to discuss with you. --- 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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
Re: [agi] META: A possible re-focusing of this list
Matt. On 10/20/08, Matt Mahoney [EMAIL PROTECTED] wrote: The singularity list is probably more appropriate for philosophical discussions about AGI. Only those discussions that relate AGI to singularity. Another one for Ben's list: *Basic Economic Feasibility: It has been proposed that intelligent but not super-intelligent machines may have great economic value. Others have said that we already have way too many such biological machines, making more such intelligence worthless. This has been countered by arguments that there are hazardous and/or biologically impossible environments where only an intelligent machine could work. This seems to fall into the realm of basic business plan projections, where the cost of engineering and manufacture is returned by sales through market penetration. An abbreviated business plan showing quantitatively how a profit might be made would go a LONG way to settling this argument.* Steve Richfield --- 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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
Re: [agi] constructivist issues
Try Rudy Rucker's book Infinity and the Mind for a good nontechnical treatment of related ideas http://www.amazon.com/Infinity-Mind-Rudy-Rucker/dp/0691001723 The related wikipedia pages are a bit technical ;-p , e.g. http://en.wikipedia.org/wiki/Inaccessible_cardinal On Tue, Oct 21, 2008 at 2:27 PM, Russell Wallace [EMAIL PROTECTED]wrote: On Tue, Oct 21, 2008 at 4:53 PM, Abram Demski [EMAIL PROTECTED] wrote: As it happens, this definition of meaning admits horribly-terribly-uncomputable-things to be described! (Far worse than the above-mentioned super-omegas.) So, the truth or falsehood is very much not computable. I'm hesitant to provide the mathematical proof in this email, since it is already long enough... let's just say it is available upon request. Now I'm curious -- can these horribly-terribly-uncomputable-things be described to a non-mathematician? If so, consider this a request. --- 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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
Re: [agi] natural language - algebra (was Defining AGI)
Here's my simple proof: algebra, or any other formal language for that matter, is expressible in natural language, if inefficiently. Words like quantity, sum, multiple, equals, and so on, are capable of conveying the same meaning that the sentence x*3 = y conveys. The rules for manipulating equations are likewise expressible in natural language. Thus it is possible in principle to do algebra without learning the mathematical symbols. Much more difficult for human minds perhaps, but possible in principle. Thus, learning mathematical formalism via translation from natural language concepts is possible (which is how we do it, after all). Therefore, an intelligence that can learn natural language can learn to do math. OK, but I didn't think we were talking about what is possible in principle but may be unrealizable in practice... It's possible in principle to create a supercomputer via training pigeons to peck in appropriate patterns, in response to the patterns that they notice other pigeons peck. My friends in Perth and I designed such a machine once and called it the PC or Pigeon Computer. I wish I'd retained the drawings and schematics! We considered launching a company to sell them, IBM or International Bird Machines ... but failed to convince any VC's (even in the Internet bubble!!) and gave up... ben g --- 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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
Re: [agi] Re: Value of philosophy
Ben, Hey, maybe I FINALLY got your frame of mind here. Just to test this, consider: Suppose we change the format NOT to exclude anything at all, but rather I/you/we set up a Wiki that includes EVERYTHING. Right next to a technical details may be a link to a philosophical point, and right next to a philosophical point may be a link to a technical detail. Then, on this forum, people would only post pointers to new edits and information that they EXPECT would disappear into the bit bucket by tomorrow. We would include identified buzz phrases to be able to pull important but disjoint things together, as I have been using the buzz phrase Ben's list with my various distilled philosophical (read that feasibility) points. This way, everything ever related to a given subject would be pulled together and organized. I would be happier because the feasibility issues would all be together for anyone entering AGI to consider, and you would be happier because your technical section would be undisturbed by philosophical discussion, except for a few hyperlinks sprinkled therein. Does this work for everyone? Steve Richfield = On 10/20/08, Ben Goertzel [EMAIL PROTECTED] wrote: Just to clarify one point: I am not opposed to philosophy, nor do I consider it irrelevant to AGI. I wrote a book on my own philosophy of mind in 2006. I just feel like the philosophical discussions tend to overwhelm the pragmatic discussions on this list, and that a greater number of pragmatic discussions **might** emerge if the pragmatic and philosophical discussions were carried out in separate venues. Some of us feel we already have adequate philosophical understanding to design and engineer AGI systems. We may be wrong, but that doesn't mean we should spend our time debating our philosophical understandings, to the exclusion of discussing the details of our concrete AGI work. For me, after enough discussion of the same philosophical issue, I stop learning anything. Most of the philosophical discussions on this list are nearly identical in content to discussions I had with others 20 years ago. I learned a lot from the discussions then, and learn a lot less from the repeats... -- Ben On Mon, Oct 20, 2008 at 9:06 AM, Mike Tintner [EMAIL PROTECTED]wrote: Vlad:Good philosophy is necessary for AI...We need to work more on the foundations, to understand whether we are going in the right direction More or less perfectly said. While I can see that a majority of people here don't want it, actually philosophy, (which should be scientifically based), is essential for AGI, precisely as Vlad says - to decide what are the proper directions and targets for AGI. What is creativity? Intelligence? What are the kinds of problems an AGI should be dealing with? What kind(s) of knowledge representation are necessary? Is language necessary? What forms should concepts take? What kinds of information structures, eg networks, should underlie them? What kind(s) of search are necessary? How do analogy and metaphor work? Is embodiment necessary? etc etc. These are all matters for what is actually philosophical as well as scientific as well as technological/engineering discussion. They tend to be often more philosophical in practice because these areas are so vast that they can't be neatly covered - or not at present - by any scientific. experimentally-backed theory. If your philosophy is all wrong, then the chances are v. high that your engineering work will be a complete waste of time. So it's worth considering whether your personal AGI philosophy and direction are viable. And that is essentially what the philosophical discussions here have all been about - the proper *direction* for AGI efforts to take. Ben has mischaracterised these discussions. No one - certainly not me - is objecting to the *feasibility* of AGI. Everyone agrees that AGI in one form or other is indeed feasible, though some (and increasingly though by no means fully, Ben himself) incline to robotic AGI. The arguments are mainly about direction, not feasibility. (There is a separate, philosophical discussion, about feasibility in a different sense - the lack of a culture of feasibility, which is perhaps, subconsciously what Ben was also referring to - no one, but no one, in AGI, including Ben, seems willing to expose their AGI ideas and proposals to any kind of feasibility discussion at all - i.e. how can this or that method solve any of the problem of general intelligence? This is what Steve R has pointed to recently, albeit IMO in a rather confusing way. ) So while I recognize that a lot of people have an antipathy to my personal philosoophising, one way or another, you can't really avoid philosophising, unless you are, say, totally committed to just one approach, like Opencog. And even then... P.S. Philosophy is always a matter of (conflicting) opinion. (Especially, given last night's
Re: AW: AW: [agi] Re: Defining AGI
Hmm... I think that non-retarded humans are fully general intelligences in the following weak sense: for any fixed t and l, for any human there are some numbers M and T so that if the human is given amount M of external memory (e.g. notebooks to write on), that human could be taught to emulate AIXItl [see http://www.amazon.com/Universal-Artificial-Intelligence-Algorithmic-Probability/dp/3540221395/ref=sr_1_1?ie=UTF8s=booksqid=1224614995sr=1-1, or the relevant papers on Marcus Hutter's website] where each single step of AIXItl might take up to T seconds. This is a kind of generality that I think no animals but humans have. So, in that sense, we seem to be the first evolved general intelligences. But, that said, there are limits to what any one of us can learn in a fixed finite amount of time. If you fix T realistically then our intelligence decreases dramatically. And for the time-scales relevant in human life, it may not be possible to teach some people to do science adequately. I am thinking for instance of a 40 yr old student I taught at the University of Nevada way back when (normally I taught advanced math, but in summers I sometimes taught remedial stuff for extra $$). She had taken elementary algebra 7 times before ... and had had extensive tutoring outside of class ... but I still was unable to convince her of the incorrectness of the following reasoning: The variable a always stands for 1. The variable b always stands for 2. ... The variable z always stands for 26. She was not retarded. She seemed to have a mental block against algebra. She could discuss politics and other topics with seeming intelligence. Eventually I'm sure she could have been taught to overcome this block. But, by the time she overcame every other issue in the way of really understanding science, her natural lifespan would have long been overspent... -- Ben G On Tue, Oct 21, 2008 at 12:33 PM, Mark Waser [EMAIL PROTECTED] wrote: Yes, but each of those steps is very vague, and cannot be boiled down to a series of precise instructions sufficient for a stupid person to consistently carry them out effectively... So -- are those stupid people still general intelligences? Or are they only general intelligences to the degree to which they *can* carry them out? (because I assume that you'd agree that general intelligence is a spectrum like any other type). There also remains the distinction (that I'd like to highlight and emphasize) between a discoverer and a learner. The cognitive skills/intelligence necessary to design questions, hypotheses, experiments, etc. are far in excess the cognitive skills/intelligence necessary to evaluate/validate those things. My argument was meant to be that a general intelligence needs to be a learner-type rather than a discoverer-type although the discoverer type is clearly more effective. So -- If you can't correctly evaluate data, are you a general intelligence? How do you get an accurate and effective domain model to achieve competence in a domain if you don't know who or what to believe? If you don't believe in evolution, does that mean that you aren't a general intelligence in that particular realm/domain (biology)? Also, those steps are heuristic and do not cover all cases. For instance step 4 requires experimentation, yet there are sciences such as cosmology and paleontology that are not focused on experimentation. I disagree. They may be based upon thought experiments rather than physical experiments but it's still all about predictive power. What is that next star/dinosaur going to look like? What is it *never* going to look like (or else we need to expand or correct our theory)? Is there anything that we can guess that we haven't tested/seen yet that we can verify? What else is science? My *opinion* is that the following steps are pretty inviolable. A. Observe B. Form Hypotheses C. Observe More (most efficiently performed by designing competent experiments including actively looking for disproofs) D. Evaluate Hypotheses E. Add Evaluation to Knowledge-Base (Tentatively) but continue to test F. Return to step A with additional leverage If you were forced to codify the hard core of the scientific method, how would you do it? As you asked for references I will give you two: Thank you for setting a good example by including references but the contrast between the two is far better drawn in *For and Against Method*http://en.wikipedia.org/w/index.php?title=For_and_Against_Methodaction=editredlink=1(ISBN 0-226-46774-0http://en.wikipedia.org/wiki/Special:BookSources/0226467740 ). Also, I would add in Polya, Popper, Russell, and Kuhn for completeness for those who wish to educate themselves in the fundamentals of Philosophy of Science (you didn't really forget that my undergraduate degree was a dual major of Biochemistry and Philosophy of Science, did you? :-). My view is
Re: [agi] Re: Value of philosophy
This is basically the suggestion to move to a forum-type format instead of a mailing list It has its plusses and minuses... you've cited one of the plusses. ben On Tue, Oct 21, 2008 at 2:46 PM, Steve Richfield [EMAIL PROTECTED]wrote: Ben, Hey, maybe I FINALLY got your frame of mind here. Just to test this, consider: Suppose we change the format NOT to exclude anything at all, but rather I/you/we set up a Wiki that includes EVERYTHING. Right next to a technical details may be a link to a philosophical point, and right next to a philosophical point may be a link to a technical detail. Then, on this forum, people would only post pointers to new edits and information that they EXPECT would disappear into the bit bucket by tomorrow. We would include identified buzz phrases to be able to pull important but disjoint things together, as I have been using the buzz phrase Ben's list with my various distilled philosophical (read that feasibility) points. This way, everything ever related to a given subject would be pulled together and organized. I would be happier because the feasibility issues would all be together for anyone entering AGI to consider, and you would be happier because your technical section would be undisturbed by philosophical discussion, except for a few hyperlinks sprinkled therein. Does this work for everyone? Steve Richfield = On 10/20/08, Ben Goertzel [EMAIL PROTECTED] wrote: Just to clarify one point: I am not opposed to philosophy, nor do I consider it irrelevant to AGI. I wrote a book on my own philosophy of mind in 2006. I just feel like the philosophical discussions tend to overwhelm the pragmatic discussions on this list, and that a greater number of pragmatic discussions **might** emerge if the pragmatic and philosophical discussions were carried out in separate venues. Some of us feel we already have adequate philosophical understanding to design and engineer AGI systems. We may be wrong, but that doesn't mean we should spend our time debating our philosophical understandings, to the exclusion of discussing the details of our concrete AGI work. For me, after enough discussion of the same philosophical issue, I stop learning anything. Most of the philosophical discussions on this list are nearly identical in content to discussions I had with others 20 years ago. I learned a lot from the discussions then, and learn a lot less from the repeats... -- Ben On Mon, Oct 20, 2008 at 9:06 AM, Mike Tintner [EMAIL PROTECTED]wrote: Vlad:Good philosophy is necessary for AI...We need to work more on the foundations, to understand whether we are going in the right direction More or less perfectly said. While I can see that a majority of people here don't want it, actually philosophy, (which should be scientifically based), is essential for AGI, precisely as Vlad says - to decide what are the proper directions and targets for AGI. What is creativity? Intelligence? What are the kinds of problems an AGI should be dealing with? What kind(s) of knowledge representation are necessary? Is language necessary? What forms should concepts take? What kinds of information structures, eg networks, should underlie them? What kind(s) of search are necessary? How do analogy and metaphor work? Is embodiment necessary? etc etc. These are all matters for what is actually philosophical as well as scientific as well as technological/engineering discussion. They tend to be often more philosophical in practice because these areas are so vast that they can't be neatly covered - or not at present - by any scientific. experimentally-backed theory. If your philosophy is all wrong, then the chances are v. high that your engineering work will be a complete waste of time. So it's worth considering whether your personal AGI philosophy and direction are viable. And that is essentially what the philosophical discussions here have all been about - the proper *direction* for AGI efforts to take. Ben has mischaracterised these discussions. No one - certainly not me - is objecting to the *feasibility* of AGI. Everyone agrees that AGI in one form or other is indeed feasible, though some (and increasingly though by no means fully, Ben himself) incline to robotic AGI. The arguments are mainly about direction, not feasibility. (There is a separate, philosophical discussion, about feasibility in a different sense - the lack of a culture of feasibility, which is perhaps, subconsciously what Ben was also referring to - no one, but no one, in AGI, including Ben, seems willing to expose their AGI ideas and proposals to any kind of feasibility discussion at all - i.e. how can this or that method solve any of the problem of general intelligence? This is what Steve R has pointed to recently, albeit IMO in a rather confusing way. ) So while I recognize that a lot of people have an antipathy to my personal
RE: [agi] Who is smart enough to answer this question?
Ben, You're right. Although one might seem to be getting a free lunch in terms of being able to create more assemblies than the number of nodes from which they are created, it would appear that the extra number of links required not only for auto-associative activation withn an assembly, but that would be required to activate an assembly from the outside with a signal that would be distinguishable over the cross talk, may prevent such a use of node assemblies from resulting in any actual saving. If Vlad's forumula for a lower bound is correct, the one that I used in the Excel spreadsheet I sent out earlier under this thread, then it is clear one can create substantially more assemblies than nodes, with maximum overlaps below 5%, but it is not clear the increased costs in extra connections would be worth it, since it is not clear that the cost of a node, need be that much higher than the cost of a link. Ed Porter -Original Message- From: Ben Goertzel [mailto:[EMAIL PROTECTED] Sent: Tuesday, October 21, 2008 11:28 AM To: agi@v2.listbox.com Subject: Re: [agi] Who is smart enough to answer this question? makes sense, yep... i guess my intuition is that there are obviously a huge number of assemblies, so that the number of assemblies is not the hard part, the hard part lies in the weights... On Tue, Oct 21, 2008 at 11:18 AM, Ed Porter [EMAIL PROTECTED] wrote: Ben, In my email starting this thread on 10/15/08 7:41pm I pointed out that a more sophisticated version of the algorithm would have to take connection weights into account in determining cross talk, as you have suggested below. But I asked for the answer to a more simple version of the problem, since that might prove difficult enough, and since I was just trying to get some rough feeling for whether or not node assemblies might offer substantial gains in possible representational capability, before delving more deeply into the subject. Ed Porter -Original Message- From: Ben Goertzel [mailto:[EMAIL PROTECTED] Sent: Monday, October 20, 2008 10:52 PM To: agi@v2.listbox.com Subject: Re: [agi] Who is smart enough to answer this question? But, suppose you have two assemblies A and B, which have nA and nB neurons respectively, and which overlap in O neurons... It seems that the system's capability to distinguish A from B is going to depend on the specific **weight matrix** of the synapses inside the assemblies A and B, not just on the numbers nA, nB and O. And this weight matrix depends on the statistical properties of the memories being remembered. So, these counting arguments you're trying to do are only going to give you a very crude indication, anyway, right? ben On Mon, Oct 20, 2008 at 5:09 PM, Ed Porter [EMAIL PROTECTED] wrote: Ben, I am interested in exactly the case where individual nodes partake in multiple attractors, I use the notation A(N,O,S) which is similar to the A(n,d,w) formula of constant weight codes, except as Vlad says you would plug my varaiables into the constant weight formula buy using A(N, 2*(S-0+1),S). I have asked my question assuming each node assembly has the same size S for to make the math easier. Each such assembly is an autoassociative attractor. I want to keep the overlap O low to reduce the cross talk between attractors. So the question is how many node assemblies A, can you make having a size S, and no more than an overlap O, given N nodes. Actually the cross talk between auto associative patterns becomes an even bigger problem if there are many attractors being activated at once (such as hundreds of them), but if the signaling driving different the population of different attractors could have different timing or timing patterns, and if the auto associatively was sensitive to such timing, this problem could be greatly reduced. Ed Porter -Original Message- From: Ben Goertzel [mailto:[EMAIL PROTECTED] Sent: Monday, October 20, 2008 4:16 PM To: agi@v2.listbox.com Subject: Re: [agi] Who is smart enough to answer this question? Wait, now I'm confused. I think I misunderstood your question. Bounded-weight codes correspond to the case where the assemblies themselves can have n or fewer neurons, rather than exactly n. Constant-weight codes correspond to assemblies with exactly n neurons. A complication btw is that an assembly can hold multiple memories in multiple attractors. For instance using Storkey's palimpsest model a completely connected assembly with n neurons can hold about .25n attractors, where each attractor has around .5n neurons switched on. In a constant-weight code, I believe the numbers estimated tell you the number of sets where the Hamming distance is greater than or equal to d. The idea in coding is that the code strings denoting distinct messages should not be closer to each other than d. But I'm not sure I'm following your notation exactly. ben g On Mon, Oct 20, 2008 at 3:19 PM, Ben
Re: [agi] constructivist issues
Russell, The wikipedia article Ben cites is definitely meant for mathematicians, so I will try to give an example. The halting problem asks us about halting facts for a single program. To make it worse, I could ask about an infinite class of programs: All programs satisfying Q eventually halt. If Q is some computable function that accepts some programs and rejects others, it is only a little worse than the halting problem; Call this halting2. If Q is more difficult to evaluate than that, say if Q is as hard as solving the halting problem, it's more difficult; call problems like this halting3. If Q is as hard as halting2, then call that halting4. If Q is as hard as halting3, then call the resulting class halting4. And so on. This is a somewhat odd way of constructing it, but I hope it is understandable. Other references: http://en.wikipedia.org/wiki/Hypercomputation http://en.wikipedia.org/wiki/Arithmetical_hierarchy --Abram On Tue, Oct 21, 2008 at 2:27 PM, Russell Wallace [EMAIL PROTECTED] wrote: On Tue, Oct 21, 2008 at 4:53 PM, Abram Demski [EMAIL PROTECTED] wrote: As it happens, this definition of meaning admits horribly-terribly-uncomputable-things to be described! (Far worse than the above-mentioned super-omegas.) So, the truth or falsehood is very much not computable. I'm hesitant to provide the mathematical proof in this email, since it is already long enough... let's just say it is available upon request. Now I'm curious -- can these horribly-terribly-uncomputable-things be described to a non-mathematician? If so, consider this a request. --- 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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
Re: [agi] constructivist issues
Abram Demski wrote: Ben, ... One reasonable way of avoiding the humans are magic explanation of this (or humans use quantum gravity computing, etc) is to say that, OK, humans really are an approximation of an ideal intelligence obeying those assumptions. Therefore, we cannot understand the math needed to define our own intelligence. Therefore, we can't engineer human-level AGI. I don't like this conclusion! I want a different way out. I'm not sure the guru explanation is enough... who was the Guru for Humankind? Thanks, --Abram You may not like Therefore, we cannot understand the math needed to define our own intelligence., but I'm rather convinced that it's correct. OTOH, I don't think that it follows from this that humans can't build a better than human-level AGI. (I didn't say engineer, because I'm not certain what connotations you put on that term.) This does, however, imply that people won't be able to understand the better than human-level AGI. They may well, however, understand parts of it, probably large parts. And they may well be able to predict with fair certitude how it would react in numerous situations. Just not in numerous other situations. The care, then, must be used in designing so that we can predict favorable motivations behind the actions in important-to-us areas. Even this is probably impossible in detail, but then it doesn't *need* to be understood in detail. If you can predict that it will make better choices than we can, and that it's motives are benevolent, and that it has a good understanding of our desires...that should suffice. And I think we'll be able to do considerably better than that. --- 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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
AW: [agi] natural language - algebra (was Defining AGI)
Here's my simple proof: algebra, or any other formal language for that matter, is expressible in natural language, if inefficiently. Words like quantity, sum, multiple, equals, and so on, are capable of conveying the same meaning that the sentence x*3 = y conveys. The rules for manipulating equations are likewise expressible in natural language. Thus it is possible in principle to do algebra without learning the mathematical symbols. Much more difficult for human minds perhaps, but possible in principle. Thus, learning mathematical formalism via translation from natural language concepts is possible (which is how we do it, after all). Therefore, an intelligence that can learn natural language can learn to do math. The problem is not to learn the equations or the symbols. The point is that a system which is able to understand and learn linguistic knowledge is not necessarily able to use and apply its knowledge to solve problems. - Matthias --- 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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
Re: AW: AW: [agi] Re: Defining AGI
Mark, As you asked for references I will give you two: Thank you for setting a good example by including references but the contrast between the two is far better drawn in *For and Against Method*http://en.wikipedia.org/w/index.php?title=For_and_Against_Methodaction=editredlink=1(ISBN 0-226-46774-0http://en.wikipedia.org/wiki/Special:BookSources/0226467740 ). I read that book but didn't like it as much ... but you're right, it may be an easier place for folks to start... Also, I would add in Polya, Popper, Russell, and Kuhn for completeness for those who wish to educate themselves in the fundamentals of Philosophy of Science All good stuff indeed. My view is basically that of Lakatos to the extent that I would challenge you to find anything in Lakatos that promotes your view over the one that I've espoused here. Feyerabend's rants alternate between criticisms ultimately based upon the fact that what society frequently calls science is far more politics (see sociology of scientific knowledge); a Tintnerian/Anarchist rant against structure and formalism; and incorrect portrayals/extensions of Lakatos (just like this list ;-). Where he is correct is in the first case where society is not doing science correctly (i.e. where he provided examples regarded as indisputable instances of progress and showed how the political structures of the time fought against or suppressed them). But his rants against structure and formalism (or, purportedly, for freedom and humanitarianism snort) are simply garbage in my opinion (though I'd guess that they appeal to you ;-). Feyerabend appeals to my sense of humor ... I liked the guy. I had some correspondence with him when I was 18. I wrote him a letter outlining some of my ideas on philosophy of mind and asking his advice on where I should go to grad school to study philosophy. He replied telling me that if I wanted to be a real philosopher I should **not** study philosophy academically nor become a philosophy professor, but should study science or arts and then pursue philosophy independently. We chatted back and forth a little after that. I think Feyerabend did a good job of poking holes in some simplistic accounts of scientific process, but ultimately I found Lakatos's arguments mostly more compelling... Lakatos did not argue for any one scientific method, as I recall. Rather he argued that different research programmes come with different methods, and that the evaluation of a given piece of data is meaningful only within a research programme, not generically. He argued that comparative evaluation of scientific theories is well-defined only for theories within the same programme, and otherwise one has to talk about comparative evaluation of whole scientific research programmes. I am not entirely happy with Lakatos's approach either. I find it descriptively accurate yet normatively inadequate. My own take is that science normatively **should** be based on a Bayesian approach to evaluating theories based on data, and that different research programmes then may be viewed as corresponding to different **priors** to be used in doing Bayesian statistical evaluations. I think this captures a lot of Lakatos's insights but within a sound statistical framework. This is my social computational probabilistic philosophy of science. The social part is that each social group, corresponding to a different research programme, has its own prior distribution. I have also, more recently, posited a sort of universal prior, defined as **simplicity of communication in natural language within a certain community**. This, I suggest, provides a baseline prior apart from any particular research programme. However, I still don't think that a below-average-IQ human can pragmatically (i.e., within the scope of the normal human lifetime) be taught to effectively carry out statistical evaluation of theories based on data, given the realities of how theories are formulated and how data is obtained and presented, at the present time... -- Ben --- 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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
Re: AW: AW: [agi] Re: Defining AGI
I think I see what's on the table here. Does all this mean a Bayes net, properly motivated, could be capable of performing scientific inquiry? Maybe in combination with a GA that tunes itself to maximize adaptive mutations in the input based on scores from the net, which seeks superior product designs? A Bayes net could be a sophisticated tool for evaluating technological merit, while really just a signal filter on a stream of candidate blueprints if what you're saying is true. --- 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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
Re: AW: AW: [agi] Re: Defining AGI
But, by the time she overcame every other issue in the way of really understanding science, her natural lifespan would have long been overspent... You know, this is a *really* interesting point. Effectively what you're saying (I believe) is that the difficulty isn't in learning but in UNLEARNING incorrect things that actively prevent you (via conflict) from learning correct things. Is this a fair interpretation? It's also particularly interesting when you compare it to information theory where the sole cost is in erasing a bit, not in setting it. - Original Message - From: Ben Goertzel To: agi@v2.listbox.com Sent: Tuesday, October 21, 2008 2:56 PM Subject: Re: AW: AW: [agi] Re: Defining AGI Hmm... I think that non-retarded humans are fully general intelligences in the following weak sense: for any fixed t and l, for any human there are some numbers M and T so that if the human is given amount M of external memory (e.g. notebooks to write on), that human could be taught to emulate AIXItl [see http://www.amazon.com/Universal-Artificial-Intelligence-Algorithmic-Probability/dp/3540221395/ref=sr_1_1?ie=UTF8s=booksqid=1224614995sr=1-1 , or the relevant papers on Marcus Hutter's website] where each single step of AIXItl might take up to T seconds. This is a kind of generality that I think no animals but humans have. So, in that sense, we seem to be the first evolved general intelligences. But, that said, there are limits to what any one of us can learn in a fixed finite amount of time. If you fix T realistically then our intelligence decreases dramatically. And for the time-scales relevant in human life, it may not be possible to teach some people to do science adequately. I am thinking for instance of a 40 yr old student I taught at the University of Nevada way back when (normally I taught advanced math, but in summers I sometimes taught remedial stuff for extra $$). She had taken elementary algebra 7 times before ... and had had extensive tutoring outside of class ... but I still was unable to convince her of the incorrectness of the following reasoning: The variable a always stands for 1. The variable b always stands for 2. ... The variable z always stands for 26. She was not retarded. She seemed to have a mental block against algebra. She could discuss politics and other topics with seeming intelligence. Eventually I'm sure she could have been taught to overcome this block. But, by the time she overcame every other issue in the way of really understanding science, her natural lifespan would have long been overspent... -- Ben G On Tue, Oct 21, 2008 at 12:33 PM, Mark Waser [EMAIL PROTECTED] wrote: Yes, but each of those steps is very vague, and cannot be boiled down to a series of precise instructions sufficient for a stupid person to consistently carry them out effectively... So -- are those stupid people still general intelligences? Or are they only general intelligences to the degree to which they *can* carry them out? (because I assume that you'd agree that general intelligence is a spectrum like any other type). There also remains the distinction (that I'd like to highlight and emphasize) between a discoverer and a learner. The cognitive skills/intelligence necessary to design questions, hypotheses, experiments, etc. are far in excess the cognitive skills/intelligence necessary to evaluate/validate those things. My argument was meant to be that a general intelligence needs to be a learner-type rather than a discoverer-type although the discoverer type is clearly more effective. So -- If you can't correctly evaluate data, are you a general intelligence? How do you get an accurate and effective domain model to achieve competence in a domain if you don't know who or what to believe? If you don't believe in evolution, does that mean that you aren't a general intelligence in that particular realm/domain (biology)? Also, those steps are heuristic and do not cover all cases. For instance step 4 requires experimentation, yet there are sciences such as cosmology and paleontology that are not focused on experimentation. I disagree. They may be based upon thought experiments rather than physical experiments but it's still all about predictive power. What is that next star/dinosaur going to look like? What is it *never* going to look like (or else we need to expand or correct our theory)? Is there anything that we can guess that we haven't tested/seen yet that we can verify? What else is science? My *opinion* is that the following steps are pretty inviolable. A. Observe B. Form Hypotheses C. Observe More (most efficiently performed by designing competent experiments including actively looking for disproofs) D. Evaluate Hypotheses E. Add Evaluation to Knowledge-Base (Tentatively) but continue to test
Re: [agi] natural language - algebra (was Defining AGI)
As unpopular as philosophical discussions are lately, that was what this is - a debate about whether language is separable from general intelligence, in principle. So in-principle arguments about language and intelligence are relevant in that context, even if not embraced with open arms by the whole list. Terren --- On Tue, 10/21/08, Ben Goertzel [EMAIL PROTECTED] wrote: OK, but I didn't think we were talking about what is possible in principle but may be unrealizable in practice... It's possible in principle to create a supercomputer via training pigeons to peck in appropriate patterns, in response to the patterns that they notice other pigeons peck. My friends in Perth and I designed such a machine once and called it the PC or Pigeon Computer. I wish I'd retained the drawings and schematics! We considered launching a company to sell them, IBM or International Bird Machines ... but failed to convince any VC's (even in the Internet bubble!!) and gave up... ben g agi | Archives | Modify Your Subscription --- 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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
Re: [agi] natural language - algebra (was Defining AGI)
Yes, I find this thread relevant to practical AGI work ... although, I wouldn't precisely say it's addressing the separability of language from general intelligence: that would be an even broader question!! ben On Tue, Oct 21, 2008 at 5:23 PM, Terren Suydam [EMAIL PROTECTED] wrote: As unpopular as philosophical discussions are lately, that was what this is - a debate about whether language is separable from general intelligence, in principle. So in-principle arguments about language and intelligence are relevant in that context, even if not embraced with open arms by the whole list. Terren --- On Tue, 10/21/08, Ben Goertzel [EMAIL PROTECTED] wrote: OK, but I didn't think we were talking about what is possible in principle but may be unrealizable in practice... It's possible in principle to create a supercomputer via training pigeons to peck in appropriate patterns, in response to the patterns that they notice other pigeons peck. My friends in Perth and I designed such a machine once and called it the PC or Pigeon Computer. I wish I'd retained the drawings and schematics! We considered launching a company to sell them, IBM or International Bird Machines ... but failed to convince any VC's (even in the Internet bubble!!) and gave up... ben g agi | Archives | Modify Your Subscription --- 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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
Re: AW: AW: [agi] Re: Defining AGI
On Tue, Oct 21, 2008 at 5:20 PM, Mark Waser [EMAIL PROTECTED] wrote: But, by the time she overcame every other issue in the way of really understanding science, her natural lifespan would have long been overspent... You know, this is a *really* interesting point. Effectively what you're saying (I believe) is that the difficulty isn't in learning but in UNLEARNING incorrect things that actively prevent you (via conflict) from learning correct things. Is this a fair interpretation? I think that's a large part of it Incorrect things are wrapped up with correct things in peoples' minds However, pure slowness at learning is another part of the problem ... It's also particularly interesting when you compare it to information theory where the sole cost is in erasing a bit, not in setting it. - Original Message - *From:* Ben Goertzel [EMAIL PROTECTED] *To:* agi@v2.listbox.com *Sent:* Tuesday, October 21, 2008 2:56 PM *Subject:* Re: AW: AW: [agi] Re: Defining AGI Hmm... I think that non-retarded humans are fully general intelligences in the following weak sense: for any fixed t and l, for any human there are some numbers M and T so that if the human is given amount M of external memory (e.g. notebooks to write on), that human could be taught to emulate AIXItl [see http://www.amazon.com/Universal-Artificial-Intelligence-Algorithmic-Probability/dp/3540221395/ref=sr_1_1?ie=UTF8s=booksqid=1224614995sr=1-1, or the relevant papers on Marcus Hutter's website] where each single step of AIXItl might take up to T seconds. This is a kind of generality that I think no animals but humans have. So, in that sense, we seem to be the first evolved general intelligences. But, that said, there are limits to what any one of us can learn in a fixed finite amount of time. If you fix T realistically then our intelligence decreases dramatically. And for the time-scales relevant in human life, it may not be possible to teach some people to do science adequately. I am thinking for instance of a 40 yr old student I taught at the University of Nevada way back when (normally I taught advanced math, but in summers I sometimes taught remedial stuff for extra $$). She had taken elementary algebra 7 times before ... and had had extensive tutoring outside of class ... but I still was unable to convince her of the incorrectness of the following reasoning: The variable a always stands for 1. The variable b always stands for 2. ... The variable z always stands for 26. She was not retarded. She seemed to have a mental block against algebra. She could discuss politics and other topics with seeming intelligence. Eventually I'm sure she could have been taught to overcome this block. But, by the time she overcame every other issue in the way of really understanding science, her natural lifespan would have long been overspent... -- Ben G On Tue, Oct 21, 2008 at 12:33 PM, Mark Waser [EMAIL PROTECTED] wrote: Yes, but each of those steps is very vague, and cannot be boiled down to a series of precise instructions sufficient for a stupid person to consistently carry them out effectively... So -- are those stupid people still general intelligences? Or are they only general intelligences to the degree to which they *can* carry them out? (because I assume that you'd agree that general intelligence is a spectrum like any other type). There also remains the distinction (that I'd like to highlight and emphasize) between a discoverer and a learner. The cognitive skills/intelligence necessary to design questions, hypotheses, experiments, etc. are far in excess the cognitive skills/intelligence necessary to evaluate/validate those things. My argument was meant to be that a general intelligence needs to be a learner-type rather than a discoverer-type although the discoverer type is clearly more effective. So -- If you can't correctly evaluate data, are you a general intelligence? How do you get an accurate and effective domain model to achieve competence in a domain if you don't know who or what to believe? If you don't believe in evolution, does that mean that you aren't a general intelligence in that particular realm/domain (biology)? Also, those steps are heuristic and do not cover all cases. For instance step 4 requires experimentation, yet there are sciences such as cosmology and paleontology that are not focused on experimentation. I disagree. They may be based upon thought experiments rather than physical experiments but it's still all about predictive power. What is that next star/dinosaur going to look like? What is it *never* going to look like (or else we need to expand or correct our theory)? Is there anything that we can guess that we haven't tested/seen yet that we can verify? What else is science? My *opinion* is that the following steps are pretty inviolable. A. Observe B. Form Hypotheses C. Observe
Re: AW: AW: [agi] Re: Defining AGI
On Tue, Oct 21, 2008 at 10:31 PM, Ben Goertzel wrote: Incorrect things are wrapped up with correct things in peoples' minds However, pure slowness at learning is another part of the problem ... Mark seems to be thinking of something like the checklist that the ISP technician walks through when you call with a problem. Even when you know what the problem is, the tech won't listen. He insists on working through his checklist, making you do all the irrelevant checks, eventually by a process of elimination, ending up with what you knew was wrong all along. Very little GI required. But Ben is saying that for evaluating science, there ain't no such checklist. The circumstances are too variable, you would need checklists to infinity. I go along with Ben. BillK --- 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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
Re: AW: AW: [agi] Re: Defining AGI
Wow! Way too much good stuff to respond to in one e-mail. I'll try to respond to more in a later e-mail but . . . . (and I also want to get your reaction to a few things first :-) However, I still don't think that a below-average-IQ human can pragmatically (i.e., within the scope of the normal human lifetime) be taught to effectively carry out statistical evaluation of theories based on data, given the realities of how theories are formulated and how data is obtained and presented, at the present time... Hmmm. After some thought, I have to start by saying that it looks like you're equating science with statistics and I've got all sorts of negative reactions to that. First -- Sure. I certainly have to agree for a below-average-IQ human and could even be easily convinced for an average IQ human if they had to do it all themselves. And then, statistical packages quickly turn into a two-edged sword where people blindly use heuristics without understanding them (p .05 anyone?). A more important point, though, is that humans natively do *NOT* use statistics but innately use very biased, non-statistical methods that *arguably* function better than statistics in real world data environments. That alone would convince me that I certainly don't want to say that science = statistics. I am not entirely happy with Lakatos's approach either. I find it descriptively accurate yet normatively inadequate. Hmmm. (again) To me that seems to be an interesting way of rephrasing our previous disagreement except that you're now agreeing with me. (Gotta love it :-) You find Lakatos's approach descriptively accurate? Fine, that's the scientific method. You find it normatively inadequate? Well, duh (but meaning no offense :-) . . . . you can't codify the application of the scientific method to all cases. I easily agreed to that before. What were we disagreeing on again? My own take is that science normatively **should** be based on a Bayesian approach to evaluating theories based on data That always leads me personally to the question Why do humans operate on the biases that they do rather than Bayesian statistics? MY *guess* is that evolution COULD have implemented Bayesian methods but that the current methods are more efficient/effective under real world conditions (i.e. because of the real-world realities of feature extraction under dirty and incomplete or contradictory data and the fact that the Bayesian approach really does need to operate in an incredibly data-rich world where the features have already been extracted and ambiguities, other than occurrence percentages, are basically resolved). **And adding different research programmes and/or priors always seems like such a kludge . . . . . - Original Message - From: Ben Goertzel To: agi@v2.listbox.com Sent: Tuesday, October 21, 2008 4:15 PM Subject: Re: AW: AW: [agi] Re: Defining AGI Mark, As you asked for references I will give you two: Thank you for setting a good example by including references but the contrast between the two is far better drawn in For and Against Method (ISBN 0-226-46774-0). I read that book but didn't like it as much ... but you're right, it may be an easier place for folks to start... Also, I would add in Polya, Popper, Russell, and Kuhn for completeness for those who wish to educate themselves in the fundamentals of Philosophy of Science All good stuff indeed. My view is basically that of Lakatos to the extent that I would challenge you to find anything in Lakatos that promotes your view over the one that I've espoused here. Feyerabend's rants alternate between criticisms ultimately based upon the fact that what society frequently calls science is far more politics (see sociology of scientific knowledge); a Tintnerian/Anarchist rant against structure and formalism; and incorrect portrayals/extensions of Lakatos (just like this list ;-). Where he is correct is in the first case where society is not doing science correctly (i.e. where he provided examples regarded as indisputable instances of progress and showed how the political structures of the time fought against or suppressed them). But his rants against structure and formalism (or, purportedly, for freedom and humanitarianism snort) are simply garbage in my opinion (though I'd guess that they appeal to you ;-). Feyerabend appeals to my sense of humor ... I liked the guy. I had some correspondence with him when I was 18. I wrote him a letter outlining some of my ideas on philosophy of mind and asking his advice on where I should go to grad school to study philosophy. He replied telling me that if I wanted to be a real philosopher I should **not** study philosophy academically nor become a philosophy professor, but should study science or arts and then pursue philosophy independently. We chatted back and forth a little after
Re: AW: AW: [agi] Re: Defining AGI
AI! :-) This is what I was trying to avoid. :-) My objection starts with How is a Bayes net going to do feature extraction? A Bayes net may be part of a final solution but as you even indicate, it's only going to be part . . . . - Original Message - From: Eric Burton [EMAIL PROTECTED] To: agi@v2.listbox.com Sent: Tuesday, October 21, 2008 4:51 PM Subject: Re: AW: AW: [agi] Re: Defining AGI I think I see what's on the table here. Does all this mean a Bayes net, properly motivated, could be capable of performing scientific inquiry? Maybe in combination with a GA that tunes itself to maximize adaptive mutations in the input based on scores from the net, which seeks superior product designs? A Bayes net could be a sophisticated tool for evaluating technological merit, while really just a signal filter on a stream of candidate blueprints if what you're saying is true. --- 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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
Re: AW: AW: [agi] Re: Defining AGI
Incorrect things are wrapped up with correct things in peoples' minds Mark seems to be thinking of something like the checklist that the ISP technician walks through when you call with a problem. Um. No. I'm thinking that in order to integrate a new idea into your world model, you first have to resolve all the conflicts that it has with the existing model. That could be incredibly expensive. (And intelligence is emphatically not linear) But Ben is saying that for evaluating science, there ain't no such checklist. The circumstances are too variable, you would need checklists to infinity. I'm sure that Ben was saying that for doing discovery . . . . and I agree. For evaluation, I'm not sure that we've come to closure on what either of us think . . . . :-) - Original Message - From: BillK [EMAIL PROTECTED] To: agi@v2.listbox.com Sent: Tuesday, October 21, 2008 5:50 PM Subject: Re: AW: AW: [agi] Re: Defining AGI On Tue, Oct 21, 2008 at 10:31 PM, Ben Goertzel wrote: Incorrect things are wrapped up with correct things in peoples' minds However, pure slowness at learning is another part of the problem ... Mark seems to be thinking of something like the checklist that the ISP technician walks through when you call with a problem. Even when you know what the problem is, the tech won't listen. He insists on working through his checklist, making you do all the irrelevant checks, eventually by a process of elimination, ending up with what you knew was wrong all along. Very little GI required. But Ben is saying that for evaluating science, there ain't no such checklist. The circumstances are too variable, you would need checklists to infinity. I go along with Ben. BillK --- 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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
Re: AW: AW: [agi] Re: Defining AGI
Post #101 :V Somehow this hit the wrong thread :| --- 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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
Re: AW: AW: [agi] Re: Defining AGI
Post #101 :V --- 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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
RE: [agi] Who is smart enough to answer this question?
Vlad, Thanks for your below reply of Tue 10/21/2008 2:17 PM. I have spend hours trying to understand your explanation, and I now think I understand much of it, but not all of it. I have copied much of it word for word below and have inserted my questions about its various portions. If you could answer the following questions I might understand all of it. If your formula works, it is important, and if possible I would like to understand it Thank you! =quote from Vlad's reply with my comments =Vlad C(N,S) is the total number of assemblies of size S that fit in the N nodes, if you forget about overlaps. Each assembly overlaps in X places with other C(S,X)*C(N-S,S-X) assemblies: if another assembly overlaps with our assembly in X places, then X nodes are inside S nodes of our assembly, which gives C(S,X) possible combinations, [=EWP: --I understand this --- for any first given set of S nodes, there would be C(S,X) different sub-combinations of X node from that given set of S nodes] =Vlad and the remaining S-X of the nodes are outside the assembly, in remaining N-S nodes, which gives C(N-S,S-X) combinations, [EWP: --I interpret this as saying: for a given fixed sub-combination of X nodes from the many possible such subcombinations C(S,X), let us determine the number of combinations C(N-S, S-X) of length S-X that can be created from the N nodes minus the S nodes in the first given set, and that can be added to said given combination of X nodes to create different sets of length S --- is this correct?] =Vlad totaling to C(S,X)*C(N-S,S-X). [=EWP: --I interpret this as saying: --sum the following over each of the sub-combinations C(S,X) of length X that can be selected from the first given set of S nodes, -the number of each possible combination C(N-S,S-X) of length S-X, described above, that when added to the X nodes from a given one of such sub-combinations would form another set of length S --this was counter intuitive to me at first, because I subconsciously rejected the notion that each sub-combination of X nodes from the first given set of length S could occur in all C(N-S,S-X) possible complimentary combinations of length S-X, so I kept thinking there must be something wrong with it, but now I realize there is no reason they shouldn't be allowed to --For each given sub-combination of X node in the first given set of length S, all other sets of length S are complementary and include the same sub-combination of X nodes. --Am I correct in assuming that over all possible sub-combinations of X nodes in the first given set of length S, all possible sets of length S that have an exact overlap of length X with the first given set will be counted?] =Vlad Thus, the total number of assemblies that overlap with our assembly in O to S places (including our assembly itself) is T(N,S,O)= C(S,S)*C(N-S,S-S)+ C(S,S-1)*C(N-S,S-(S-1))+ ..+C(S,O)*C(N-S,S-O) [=EWP: --this is equivalent to the formula for T(N,S,O) that I used in my spread sheet that I derived from your email of Thu 10/16/2008 7:50 pm, after having switched the positions of the combination function variables --I have rewriten this formula below to make its structure easier to see at a glance T(N,S,O)= +C(S, S-0)*C(N-S, 0) (= 1) +C(S, S-1)*C(N-S, 1) +C(S, S-2)*C(N-S, 2) +... +C(S, O)*C(N-S, S-O) OR T(N,S,O) = SUM FROM X = 0 TO S-O OF C(S, S-X)*C(N-S, X) Comparing this to C(S,X)*C(N-S,S-X) --- it appears that T(N,S,O) is equal to the number of all combinations calculated by C(S,X)*C(N-S,S-X) where X is greater than O, Thus it is an attempt to enumerate all such combinations in which the overlap is more than O and thus which should be excluded from A. --Thus it would seem A should equal C(N,S) - T(N,S,O), not C(N,S) / T(N,S,O). Why isn't this correct] =Vlad Let's apply a trivial algorithm to our problem, adding an arbitrary assembly to the working set merely if it doesn't conflict with any of the assemblies already in the working set. Adding a new assembly will ban other T(N,S,O) assemblies from the total pool of C(N,S) assemblies, thus each new assembly in the working set lowers the number of remaining assemblies that we'll be able to add later. Some assemblies from this pool will be banned multiple times, but at least C(N,S)/T(N,S,O) assemblies can be added without conflicts, Since T(N,S,O) is the maximum number of assemblies that each one in the pool is able to subtract from the total pool of assemblies. [=EWP: --I don't understand this. --First, yes, each new assembly of length S added to the working set lowers the number of remaining assemblies that we'll be able to add later, but adding a
FW: [agi] Who is smart enough to answer this question?
Ben, Upon thinking more about my comments below, in an architecture such as the brain where connections are much cheaper (at least more common) than nodes, cell assemblies might make sense. This is particularly true since one could develop tricks to reduce the number of links that would be required between assemblies representing different concepts for the implication between such concepts to a number not more than two to four times the value of O, of the maximum overlap allowed between assembly populations. This could be done by having assemblies that are activated enough to be transmitting synchronize their firing, so that their inputs to another concept node could be filtered out from background noise, and if such synchronized input were above a given threshold, the assembly receiving them could be activated. Perhaps it would be valueable to have the communication between two concept nodes first blast a very strong synchronized signal to allow inputs above cross talk to be identified, and then have a more variable signal reflecting the degree of the input, which could be lower, since the nodes receiving them would know from which links to expect such a signal. Since in a brain like computer you want a fair amount of redundancy in your connections, for reliability of connections in a noisy setting, and to enable variable values to be transmitted with reasonable degree of statistical smoothing, the cost of the extra connection required to exceed the maximal cross talk between concept assemblies, might not be above that which would be desired for such other purposes. Ed Porter -Original Message- From: Ed Porter [mailto:[EMAIL PROTECTED] Sent: Tuesday, October 21, 2008 3:09 PM To: agi@v2.listbox.com Subject: RE: [agi] Who is smart enough to answer this question? Ben, You're right. Although one might seem to be getting a free lunch in terms of being able to create more assemblies than the number of nodes from which they are created, it would appear that the extra number of links required not only for auto-associative activation withn an assembly, but that would be required to activate an assembly from the outside with a signal that would be distinguishable over the cross talk, may prevent such a use of node assemblies from resulting in any actual saving. If Vlad's forumula for a lower bound is correct, the one that I used in the Excel spreadsheet I sent out earlier under this thread, then it is clear one can create substantially more assemblies than nodes, with maximum overlaps below 5%, but it is not clear the increased costs in extra connections would be worth it, since it is not clear that the cost of a node, need be that much higher than the cost of a link. Ed Porter -Original Message- From: Ben Goertzel [mailto:[EMAIL PROTECTED] Sent: Tuesday, October 21, 2008 11:28 AM To: agi@v2.listbox.com Subject: Re: [agi] Who is smart enough to answer this question? makes sense, yep... i guess my intuition is that there are obviously a huge number of assemblies, so that the number of assemblies is not the hard part, the hard part lies in the weights... On Tue, Oct 21, 2008 at 11:18 AM, Ed Porter [EMAIL PROTECTED] wrote: Ben, In my email starting this thread on 10/15/08 7:41pm I pointed out that a more sophisticated version of the algorithm would have to take connection weights into account in determining cross talk, as you have suggested below. But I asked for the answer to a more simple version of the problem, since that might prove difficult enough, and since I was just trying to get some rough feeling for whether or not node assemblies might offer substantial gains in possible representational capability, before delving more deeply into the subject. Ed Porter -Original Message- From: Ben Goertzel [mailto:[EMAIL PROTECTED] Sent: Monday, October 20, 2008 10:52 PM To: agi@v2.listbox.com Subject: Re: [agi] Who is smart enough to answer this question? But, suppose you have two assemblies A and B, which have nA and nB neurons respectively, and which overlap in O neurons... It seems that the system's capability to distinguish A from B is going to depend on the specific **weight matrix** of the synapses inside the assemblies A and B, not just on the numbers nA, nB and O. And this weight matrix depends on the statistical properties of the memories being remembered. So, these counting arguments you're trying to do are only going to give you a very crude indication, anyway, right? ben On Mon, Oct 20, 2008 at 5:09 PM, Ed Porter [EMAIL PROTECTED] wrote: Ben, I am interested in exactly the case where individual nodes partake in multiple attractors, I use the notation A(N,O,S) which is similar to the A(n,d,w) formula of constant weight codes, except as Vlad says you would plug my varaiables into the constant weight formula buy using A(N, 2*(S-0+1),S). I have asked my question assuming each node
Re: [agi] Who is smart enough to answer this question?
(I agree with the points I don't quote here) General reiteration on notation: O-1 is the maximum allowed overlap, overlap of O is already not allowed (it was this way in your first message). On Wed, Oct 22, 2008 at 3:08 AM, Ed Porter [EMAIL PROTECTED] wrote: T(N,S,O) = SUM FROM X = 0 TO S-O OF C(S, S-X)*C(N-S, X) To match with the explanation of the size of the overlap, I intended T(N,S,O)= C(S,S)*C(N-S,S-S)+ C(S,S-1)*C(N-S,S-(S-1))+ ...+C(S,O)*C(N-S,S-O) to be parsed as T(N,S,O) = SUM FROM X =O TO S OF C(S,X)*C(N-S,S-X) Comparing this to C(S,X)*C(N-S,S-X) --- it appears that T(N,S,O) is equal to the number of all combinations calculated by C(S,X)*C(N-S,S-X) where X is greater than O, Thus it is an attempt to enumerate all such combinations in which the overlap is more than O and thus which should be excluded from A. I don't exclude them from A, as I don't know which of them will go to A and which will get banned multiple times. I exclude them from overall pool of C(N,S). --First, yes, each new assembly of length S added to the working set lowers the number of remaining assemblies that we'll be able to add later, but adding a given new assembly will ban not T(N,S,O) assemblies, but rather only all those assemblies that overlap with it by more than O nodes. But T(N,S,O) IS the number of all those assemblies that overlap with a given assembly by O or more nodes (having from X=O to X=S nodes of overlap). --Second, what are the cases where assemblies will be banned multiple times that you mentioned in the above text? It's one of the reasons it's a lower bound: in reality, some of the assemblies are banned multiple times, which leaves more free assemblies that could be added to the working set later. --Third --- as mentioned in my last group of comments --- why doesn't A = C(N,S) – T(N,S,O), since C(N,S) is the total number of combinations of length S that can be formed from N nodes, and T(N,S,O) appears to enumerate all the combinations that occur with each possible overlap value greater O. It's only overlap with one given assembly, blind to any other interactions, it says nothing about ideal combination of assemblies that manages to keep the overlap between each pair in check. --Fifth, is possible that even though T(N,S,O) appears to enumerate all possible combinations in which all sets overlap by more than O, that it fails to take into account possible combinations of sets of size S in which some sets overlap by more than O and others do not? --in which case T(N,S,O) would be smaller than the number of all prohibited combinations of sets of length S. Or would all the possible sets of length S which overlap be have been properly taken into account in the above formula for T? T doesn't reason about combinations of sets, it's a filter on the individual sets from the total of C(N,S). --Sixth, if C(S,X)*C(N-S,S-X) enumerates all possible combinations having an overlap of X, why can't one calculate A as follows? A = SUM FROM X = 0 TO O OF C(S,X)*C(N-S,S-X) Because some of these sets intersect with each other, you can't include them all. -- Vladimir Nesov [EMAIL PROTECTED] http://causalityrelay.wordpress.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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
Re: AW: AW: [agi] Re: Defining AGI
Mark W wrote: What were we disagreeing on again? This conversation has drifted into interesting issues in the philosophy of science, most of which you and I seem to substantially agree on. However, the point I took issue with was your claim that a stupid person could be taught to effectively do science ... or (your later modification) evaluation of scientific results. At the time I originally took exception to your claim, I had not read the earlier portion of the thread, and I still haven't; so I still do not know why you made the claim in the first place. ben --- 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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
Re: [agi] constructivist issues
Charles, You are right to call me out on this, as I really don't have much justification for rejecting that view beyond I don't like it, it's not elegant. But, I don't like it! It's not elegant! About the connotations of engineer... more specifically, I should say that this prevents us from making one universal normative mathematical model of intelligence, since our logic cannot describe itself. Instead, we would be doomed to make a series of more and more general models (AIXI being the first and most narrow), all of which fall short of human logic. Worse, the implication is that this is not because human logic sits at some sort of maximum; human intelligence would be just another rung in the ladder from the perspective of some mathematically more powerful alien species, or human mutant. --Abram On Tue, Oct 21, 2008 at 3:29 PM, Charles Hixson [EMAIL PROTECTED] wrote: Abram Demski wrote: Ben, ... One reasonable way of avoiding the humans are magic explanation of this (or humans use quantum gravity computing, etc) is to say that, OK, humans really are an approximation of an ideal intelligence obeying those assumptions. Therefore, we cannot understand the math needed to define our own intelligence. Therefore, we can't engineer human-level AGI. I don't like this conclusion! I want a different way out. I'm not sure the guru explanation is enough... who was the Guru for Humankind? Thanks, --Abram You may not like Therefore, we cannot understand the math needed to define our own intelligence., but I'm rather convinced that it's correct. OTOH, I don't think that it follows from this that humans can't build a better than human-level AGI. (I didn't say engineer, because I'm not certain what connotations you put on that term.) This does, however, imply that people won't be able to understand the better than human-level AGI. They may well, however, understand parts of it, probably large parts. And they may well be able to predict with fair certitude how it would react in numerous situations. Just not in numerous other situations. The care, then, must be used in designing so that we can predict favorable motivations behind the actions in important-to-us areas. Even this is probably impossible in detail, but then it doesn't *need* to be understood in detail. If you can predict that it will make better choices than we can, and that it's motives are benevolent, and that it has a good understanding of our desires...that should suffice. And I think we'll be able to do considerably better than that. --- 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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
Re: [agi] constructivist issues
I am completely unable to understand what this paragraph is supposed to mean: *** One reasonable way of avoiding the humans are magic explanation of this (or humans use quantum gravity computing, etc) is to say that, OK, humans really are an approximation of an ideal intelligence obeying those assumptions. Therefore, we cannot understand the math needed to define our own intelligence. Therefore, we can't engineer human-level AGI. I don't like this conclusion! I want a different way out. *** Explanation of WHAT? Of your intuitive feeling that you are uncomputable, that you have no limits in what you can do? Why is this intuitive feeling any more worthwhile than some peoples' intuitive feeling that they have some kind of absolute free will not allowed by classical physics or quantum theory?? Personally my view is as follows. Science does not need to intuitively explain all aspects of our experience: what it has to do is make predictions about finite sets of finite-precision observations, based on previously-collected finite sets of finite-precision observations. It is not impossible that we are unable to engineer intelligence, even though we are intelligent. However, your intuitive feeling of awesome supercomputable powers seems an extremely weak argument in favor of this inability. You have not convinced me that you can do anything a computer can't do. And, using language or math, you never will -- because any finite set of symbols you can utter, could also be uttered by some computational system. -- Ben G On Tue, Oct 21, 2008 at 9:13 PM, Abram Demski [EMAIL PROTECTED] wrote: Charles, You are right to call me out on this, as I really don't have much justification for rejecting that view beyond I don't like it, it's not elegant. But, I don't like it! It's not elegant! About the connotations of engineer... more specifically, I should say that this prevents us from making one universal normative mathematical model of intelligence, since our logic cannot describe itself. Instead, we would be doomed to make a series of more and more general models (AIXI being the first and most narrow), all of which fall short of human logic. Worse, the implication is that this is not because human logic sits at some sort of maximum; human intelligence would be just another rung in the ladder from the perspective of some mathematically more powerful alien species, or human mutant. --Abram On Tue, Oct 21, 2008 at 3:29 PM, Charles Hixson [EMAIL PROTECTED] wrote: Abram Demski wrote: Ben, ... One reasonable way of avoiding the humans are magic explanation of this (or humans use quantum gravity computing, etc) is to say that, OK, humans really are an approximation of an ideal intelligence obeying those assumptions. Therefore, we cannot understand the math needed to define our own intelligence. Therefore, we can't engineer human-level AGI. I don't like this conclusion! I want a different way out. I'm not sure the guru explanation is enough... who was the Guru for Humankind? Thanks, --Abram You may not like Therefore, we cannot understand the math needed to define our own intelligence., but I'm rather convinced that it's correct. OTOH, I don't think that it follows from this that humans can't build a better than human-level AGI. (I didn't say engineer, because I'm not certain what connotations you put on that term.) This does, however, imply that people won't be able to understand the better than human-level AGI. They may well, however, understand parts of it, probably large parts. And they may well be able to predict with fair certitude how it would react in numerous situations. Just not in numerous other situations. The care, then, must be used in designing so that we can predict favorable motivations behind the actions in important-to-us areas. Even this is probably impossible in detail, but then it doesn't *need* to be understood in detail. If you can predict that it will make better choices than we can, and that it's motives are benevolent, and that it has a good understanding of our desires...that should suffice. And I think we'll be able to do considerably better than that. --- 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
Re: [agi] constructivist issues
On Wed, Oct 22, 2008 at 11:21 AM, Ben Goertzel [EMAIL PROTECTED] wrote: Personally my view is as follows. Science does not need to intuitively explain all aspects of our experience: what it has to do is make predictions about finite sets of finite-precision observations, based on previously-collected finite sets of finite-precision observations. I can do one better than that. If you don't believe that AGI is possible then bugger right off. We don't want your mysticism around here. Is it too much to ask that the people on this list be interested in the topic? If you don't think it's possible, go back to your cave and pray for our souls or something. Trent --- 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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
Re: [agi] constructivist issues
Ben, This is not what I meant at all! I am not trying to make an argument from any sort of intuitive feeling of absolute free will in that paragraph (or, well, ever). That paragraph was referring to Terski's undefinability theorem. Quoting the context directly before the paragraph in question: I am suggesting a broader problem that will apply to a wide class of formulations of idealized intelligence such as AIXI: if their internal logic obeys a particular set of assumptions, it will become prone to Tarski's Undefinability Theorem. Therefore, we humans will be able to point out a particular class of concepts that it cannot reason about; specifically, the very concepts used in describing the ideal intelligence in the first place. To re-explain: We might construct generalizations of AIXI that use a broader range of models. Specifically, it seems reasonable to try models that are extensions of first-order arithmetic, such as second-order arithmetic (analysis), ZF-set theory... (Models in first-order logic of course could be considered equivalent to Turing-machine models, the current AIXI.) Description length then becomes description-length-in-language-X. But, any such extension is doomed to a simple objection: (1) We humans understand the semantics of formal system X. (2) The undefinability theorem shows that formal system X cannot understand its own semantics. That is what needs an explanation. The one we can all agree is wrong: Humans are magic, we're better than any formal system. The one Charles Hixon is OK with, but I dislike: Humans approximate a generalization of AIXI that satisfies the above assumptions; therefore, the logic we use is some extension of arithmetic, but we are incapable of defining that logic thanks to the undefinability theorem. --Abram On Tue, Oct 21, 2008 at 9:21 PM, Ben Goertzel [EMAIL PROTECTED] wrote: I am completely unable to understand what this paragraph is supposed to mean: *** One reasonable way of avoiding the humans are magic explanation of this (or humans use quantum gravity computing, etc) is to say that, OK, humans really are an approximation of an ideal intelligence obeying those assumptions. Therefore, we cannot understand the math needed to define our own intelligence. Therefore, we can't engineer human-level AGI. I don't like this conclusion! I want a different way out. *** Explanation of WHAT? Of your intuitive feeling that you are uncomputable, that you have no limits in what you can do? Why is this intuitive feeling any more worthwhile than some peoples' intuitive feeling that they have some kind of absolute free will not allowed by classical physics or quantum theory?? Personally my view is as follows. Science does not need to intuitively explain all aspects of our experience: what it has to do is make predictions about finite sets of finite-precision observations, based on previously-collected finite sets of finite-precision observations. It is not impossible that we are unable to engineer intelligence, even though we are intelligent. However, your intuitive feeling of awesome supercomputable powers seems an extremely weak argument in favor of this inability. You have not convinced me that you can do anything a computer can't do. And, using language or math, you never will -- because any finite set of symbols you can utter, could also be uttered by some computational system. -- Ben G On Tue, Oct 21, 2008 at 9:13 PM, Abram Demski [EMAIL PROTECTED] wrote: Charles, You are right to call me out on this, as I really don't have much justification for rejecting that view beyond I don't like it, it's not elegant. But, I don't like it! It's not elegant! About the connotations of engineer... more specifically, I should say that this prevents us from making one universal normative mathematical model of intelligence, since our logic cannot describe itself. Instead, we would be doomed to make a series of more and more general models (AIXI being the first and most narrow), all of which fall short of human logic. Worse, the implication is that this is not because human logic sits at some sort of maximum; human intelligence would be just another rung in the ladder from the perspective of some mathematically more powerful alien species, or human mutant. --Abram On Tue, Oct 21, 2008 at 3:29 PM, Charles Hixson [EMAIL PROTECTED] wrote: Abram Demski wrote: Ben, ... One reasonable way of avoiding the humans are magic explanation of this (or humans use quantum gravity computing, etc) is to say that, OK, humans really are an approximation of an ideal intelligence obeying those assumptions. Therefore, we cannot understand the math needed to define our own intelligence. Therefore, we can't engineer human-level AGI. I don't like this conclusion! I want a different way out. I'm not sure the guru explanation is enough... who was the Guru for Humankind? Thanks, --Abram
Re: [agi] constructivist issues
Abram, To re-explain: We might construct generalizations of AIXI that use a broader range of models. Specifically, it seems reasonable to try models that are extensions of first-order arithmetic, such as second-order arithmetic (analysis), ZF-set theory... (Models in first-order logic of course could be considered equivalent to Turing-machine models, the current AIXI.) Description length then becomes description-length-in-language-X. But, any such extension is doomed to a simple objection: (1) We humans understand the semantics of formal system X. (2) The undefinability theorem shows that formal system X cannot understand its own semantics. That is what needs an explanation. It doesn't, because **I see no evidence that humans can understand the semantics of formal system in X in any sense that a digital computer program cannot** Whatever this mysterious understanding is that you believe you possess, **it cannot be communicated to me in language or mathematics**. Because any series of symbols you give me, could equally well be produced by some being without this mysterious understanding. Can you describe any possible finite set of finite-precision observations that could provide evidence in favor of the hypothesis that you possess this posited understanding, and against the hypothesis that you are something equivalent to a digital computer? I think you cannot. So, your belief in this posited understanding has nothing to do with science, it's basically a kind of religious faith, it seems to me... '-) -- Ben G --- 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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
Re: [agi] constructivist issues
It doesn't, because **I see no evidence that humans can understand the semantics of formal system in X in any sense that a digital computer program cannot** I agree with you there. Our disagreement is about what formal systems a computer can understand. (The rest of your post seems to depend on this, so I will leave it there for the moment.) Whatever this mysterious understanding is that you believe you possess, **it cannot be communicated to me in language or mathematics**. Because any series of symbols you give me, could equally well be produced by some being without this mysterious understanding. Can you describe any possible finite set of finite-precision observations that could provide evidence in favor of the hypothesis that you possess this posited understanding, and against the hypothesis that you are something equivalent to a digital computer? I think you cannot. So, your belief in this posited understanding has nothing to do with science, it's basically a kind of religious faith, it seems to me... '-) -- Ben G agi | Archives | Modify Your Subscription --- 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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
Re: [agi] constructivist issues
Ben, How accurate would it be to describe you as a finitist or ultrafinitist? I ask because your view about restricting quantifiers seems to reject even the infinities normally allowed by constructivists. --Abram --- 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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
Re: [agi] constructivist issues
On Tue, Oct 21, 2008 at 10:11 PM, Abram Demski [EMAIL PROTECTED]wrote: It doesn't, because **I see no evidence that humans can understand the semantics of formal system in X in any sense that a digital computer program cannot** I agree with you there. Our disagreement is about what formal systems a computer can understand. (The rest of your post seems to depend on this, so I will leave it there for the moment.) Actually our disagreement seems to be about the meanings of words like exist or understand To make things clearer for you, I'll introduce new words existP = exist pragmatically understandP = understand pragmatically I will say that A existPs iff there is some finite Boolean combination C of finite-precision observations so that C implies (A existPs) ~C implies ~(A existPs) Similarly, I will say that A understandPs B iff there is some finite Boolean combination C of finite-precision observations so that C implies (A understandPs B) ~C implies ~(A understandPs B) That is what I mean by exist and understand in a science and engineering context. In essence, this is Peircean pragmatism (more general than strict verificationism), as summarized e.g. at http://www.iep.utm.edu/p/PeircePr.htm#H4 What do you mean by the terms? -- Ben G --- 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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
Re: [agi] constructivist issues
I am a Peircean pragmatist ... I have no objection to using infinities in mathematics ... they can certainly be quite useful. I'd rather use differential calculus to do calculations, than do everything using finite differences. It's just that, from a science perspective, these mathematical infinities have to be considered finite formal constructs ... they don't existP except in this way ... I'm not going to claim the pragmatist perspective is the only subjectively meaningful one. But so far as I can tell it's the only useful one for science and engineering... To take a totally different angle, consider the thought X = This is a thought that is way too complex for me to ever have Can I actually think X? Well, I can understand the *idea* of X. I can manipulate it symbolically and formally. I can reason about it and empathize with it by analogy to A thought that is way too complex for my three-year-old past-self to have ever had , and so forth. But it seems I can't ever really think X, except by being logically inconsistent within that same thought ... this is the Godel limitation applied to my own mind... I don't want to diss the personal value of logically inconsistent thoughts. But I doubt their scientific and engineering value. -- Ben G On Tue, Oct 21, 2008 at 10:43 PM, Abram Demski [EMAIL PROTECTED]wrote: Ben, How accurate would it be to describe you as a finitist or ultrafinitist? I ask because your view about restricting quantifiers seems to reject even the infinities normally allowed by constructivists. --Abram --- 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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
Re: [agi] constructivist issues
On Wed, Oct 22, 2008 at 3:11 AM, Abram Demski [EMAIL PROTECTED] wrote: I agree with you there. Our disagreement is about what formal systems a computer can understand. I'm also not quite sure what the problem is, but suppose we put it this way: I think the most useful way to understand the family of algorithms of which AIXI is the best-known member, is that they effectively amount to: create (by perfect simulation) all possible universes and select the one that exhibits the desired behavior. Suppose we took a bunch of data from our universe as input, if the amount of data were large enough to be specific enough, our universe (or at least one with the same physical laws) would be created and selected as producing results that match the data. So the universe thus created would contain humans, and therefore contain all the understanding of mathematics that actual humans have. Of course, this understanding would not be contained in the original kernel. But this should not be surprising. Consider a realistic AI which can't create whole universes, but can learn about mathematics. Suppose the kernel of the AI is written in Lisp, does the Lisp compiler understand incomputable numbers? No, but that's no reason the AI as a whole can't, at least to the extent that we humans do. Does this help at all? --- 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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
Re: [agi] constructivist issues
Russel, I could be wrong here. Jurgen's Super Omega is based on what I called halting2, and while it would be simple to define super-super-omega from halting3, and so on, I have not seen it done. The reason I called these higher levels horribly-terribly-uncomputable is because Jurgen's super-omega is at least defined in terms of things computable in the limit. As he says, he is pushing the boundaries of the constructivist program. Higher omegas than the one he defines would obviously not be constructivist. Well, I'm calling it a night. I will reply to Ben's further comments at a later date. --Abram On Tue, Oct 21, 2008 at 10:55 PM, Russell Wallace [EMAIL PROTECTED] wrote: On Tue, Oct 21, 2008 at 8:13 PM, Abram Demski [EMAIL PROTECTED] wrote: The wikipedia article Ben cites is definitely meant for mathematicians, so I will try to give an example. Yes indeed -- thanks! The halting problem asks us about halting facts for a single program. To make it worse, I could ask about an infinite class of programs: All programs satisfying Q eventually halt. If Q is some computable function that accepts some programs and rejects others, it is only a little worse than the halting problem; Call this halting2. If Q is more difficult to evaluate than that, say if Q is as hard as solving the halting problem, it's more difficult; call problems like this halting3. If Q is as hard as halting2, then call that halting4. If Q is as hard as halting3, then call the resulting class halting4. And so on. Right -- if I understand correctly, this is equivalent to the line of reasoning I came up when I first saw the proof of the incomputability of the halting problem: suppose you have an oracle that can solve the halting problem, can that answer all questions? No, because by the same logic you can show that to predict the behavior of an oracle requires a super oracle. But I was under the impression this is just the same as the super Omegas? And that you were talking about something beyond that? --- 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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
Re: [agi] constructivist issues
I disagree, and believe that I can think X: This is a thought (T) that is way too complex for me to ever have. Obviously, I can't think T and then think X, but I might represent T as a combination of myself plus a notebook or some other external media. Even if I only observe part of T at once, I might appreciate that it is one thought and believe (perhaps in error) that I could never think it. I might even observe T in action, if T is the result of billions of measurements, comparisons and calculations in a computer program. Isn't it just like thinking This is an image that is way too detailed for me to ever see? Charles Griffiths --- On Tue, 10/21/08, Ben Goertzel [EMAIL PROTECTED] wrote: From: Ben Goertzel [EMAIL PROTECTED] Subject: Re: [agi] constructivist issues To: agi@v2.listbox.com Date: Tuesday, October 21, 2008, 7:56 PM I am a Peircean pragmatist ... I have no objection to using infinities in mathematics ... they can certainly be quite useful. I'd rather use differential calculus to do calculations, than do everything using finite differences. It's just that, from a science perspective, these mathematical infinities have to be considered finite formal constructs ... they don't existP except in this way ... I'm not going to claim the pragmatist perspective is the only subjectively meaningful one. But so far as I can tell it's the only useful one for science and engineering... To take a totally different angle, consider the thought X = This is a thought that is way too complex for me to ever have Can I actually think X? Well, I can understand the *idea* of X. I can manipulate it symbolically and formally. I can reason about it and empathize with it by analogy to A thought that is way too complex for my three-year-old past-self to have ever had , and so forth. But it seems I can't ever really think X, except by being logically inconsistent within that same thought ... this is the Godel limitation applied to my own mind... I don't want to diss the personal value of logically inconsistent thoughts. But I doubt their scientific and engineering value. -- Ben G On Tue, Oct 21, 2008 at 10:43 PM, Abram Demski [EMAIL PROTECTED] wrote: Ben, How accurate would it be to describe you as a finitist or ultrafinitist? I ask because your view about restricting quantifiers seems to reject even the infinities normally allowed by constructivists. --Abram --- 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 | Modify Your Subscription --- 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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
[agi] If your AGI can't learn to play chess it is no AGI
It seems to me that many people think that embodiment is very important for AGI. For instance some people seem to believe that you can't be a good mathematician if you haven't made some embodied experience. But this would have a rather strange consequence: If you give your AGI a difficult mathematical problem to solve, then it would answer: Sorry, I still cannot solve your problem, but let me walk with my body through the virtual world. Hopefully, I will then understand your mathematical question end even more hopefully I will be able to solve it after some further embodied experience. AGI is the ability to solve different problems in different domains. But such an AGI would need to make experiences in domain d1 in order to solve problems of domain d2. Does this really make sense, if every information necessary to solve problems of d2 is in d2? I think an AGI which has to make experiences in d1 in order to solve a problem of domain d2 which contains everything to solve this problem is no AGI. How should such an AGI know what experiences in d1 are necessary to solve the problem of d2? In my opinion a real AGI must be able to solve a problem of a domain d without leaving this domain if in this domain there is everything to solve this problem. From this we can define a simple benchmark which is not sufficient for AGI but which is *necessary* for a system to be an AGI system: Within the domain of chess there is everything to know about chess. So if it comes up to be a good chess player learning chess from playing chess must be sufficient. Thus, an AGI which is not able to enhance its abilities in chess from playing chess alone is no AGI. Therefore, my first steps in the roadmap towards AGI would be the following: 1. Make a concept for your architecture of your AGI 2. Implement the software for your AGI 3. Try if your AGI is able to become a good chess player from learning in the domain of chess alone. 4. If your AGI can't even learn to play good chess then it is no AGI and it would be a waste of time to make experiences with your system in more complex domains. -Matthias --- 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=8660244id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
