Re: [agi] Conway's Game of Life and Turing machine equivalence
Vladimir Nesov wrote: On 10/5/07, Richard Loosemore [EMAIL PROTECTED] wrote: Vladimir Nesov wrote: On 10/5/07, Richard Loosemore [EMAIL PROTECTED] wrote: Mike Dougherty wrote: On 10/4/07, Richard Loosemore [EMAIL PROTECTED] wrote: All understood. Remember, though, that the original reason for talking about GoL was the question: Can there ever be a scientific theory that predicts all the interesting creatures given only the rules? The question of getting something to recognize the existence of the patterns is a good testbed, for sure. Given finite rules about a finite world with an en effectively unlimited resource, it seems that every interesting creature exists as the subset of all permutations minus the noise that isn't interesting. The problem is in a provable definition of interesting (which was earlier defined for example as 'cyclic') Also, who is willing to invest unlimited resource to exhaustively search a toy domain? Even if there were parallels that might lead to formalisms applicable in a larger context, we would probably divert those resources to other tasks. I'm not sure this is a bad idea. Perhaps our human attention span is a defense measure against wasting life's resources on searches that promise fitness without delivering useful results. I hear you, but let me quickly summarize the reason why I introduced GoL as an example. I wanted to use GoL as a nice-and-simple example of a system whose overall behavior (in this case, the existence of certain patterns that are stable or interesting) seems impossible to predict from a knowledge of the rules. You do predict that behavior by simulating the model. What you supposedly can't do is to find initial conditions that will lead to required global behavior. But you actually can - for example by enumerating possible initial conditions in a brute force way and looking at what happens when you simulate it. It's just very inefficient, and as a result you can't enumerate many initial conditions which will lead to interesting global behavior. And probably there are tricks to get better results, by restricting search space. You propose a framework which will help in efficient enumeration of low-level rules and estimation of high-level behavior, and restrain possibilities to as close as possible to existing working system - human mind. All along these same lines. Computational mathematics deals with this kind of thing all the time. Vladimir, You keep taking this example out of context! You are making statements that are completely oblivious to the actual purpose that the GoL example serves in the paper: Given that this purpose is what I'm trying to understand, being non-oblivious to it at the same time would be strange indeed. Okay, maybe I have been misunderstanding the level of apparent dismissiveness in your tone. I will try to reorient myself and address the issue as carefully as possible. everything you say above is COMPLETELY impractical if it is generalized to systems more complex than GoL. I disagree. It's not specific enough to be of practical use in itself, but it's general enough to be a correct statement about practically useful methods. Please don't misunderstand my intention: I find your way of presenting technical content rather obscure, so I'm trying to construct descriptions that apply to what you're describing, starting from simple ones and if necessary adding details. So if they are overly general, it's OK, but if they are wrong, please point out why. I started to reply to this directly, but now I think it is better to refer you to the answer I have given in a parallel post to Mike Dougherty, which addresses the core issue. Richard Loosemore. - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=50733913-b27ff0
Re: [agi] Conway's Game of Life and Turing machine equivalence
Mike Dougherty wrote: On 10/5/07, Richard Loosemore [EMAIL PROTECTED] wrote: My stock example: planetary motion. Newton (actually Tycho Brahe, Kepler, et al) observed some global behavior in this system: the orbits are elliptical and motion follows Kepler's other laws. This corresponds to someone seeing Game of Life for the first time, without knowing how it works, and observing that the motion is not purely random, but seems to have some regular patterns in it. Having noticed the global regularities, the next step, for Newton, was to try to find a compact explanation for them. He was looking for the underlying rules, the low-level mechanisms. He eventually realised (a long story of course!) that an inverse square law of gravitation would predict all of the behavior of these planets. This corresponds to a hypothetical case in which a person seeing those Game of Life patterns would somehow deduce that the rules that must be giving rise to the patterns are the particular rules that appear in GoL. And, to be convincing, they would have to prove that the rules gave rise to the behavior. with GoL you started with the rules and try to predict the behavior. with planetary motion you observe the behavior and try to discover the rules. I'm going to stop you here and deal with this alone. Strictly speaking this is only half the story, because with planetary motion you try to discover the rules and then you have to show that the the hypothesised rules do indeed predict the behavior. (Several other people besides Newton, if you remember, also suspected the inverse square law, but Newton trumped them by inventing calculus and proving that the inverse square law predicted elliptical orbits, etc). Explanation in general is a two part process: hypothesise the mechanism, then demonstrate that the mechanism really does give rise to the behavior. In my use of GoL in the paper I did emphasize the prediction part at first, but I then went on (immediately) to talk about the problem of finding hypotheses to test. Crucially, I ask if it is reasonable to suppose that Conway could have written down the patterns he *wanted* to see emerge, then found the rules that would generate his desired patterns. It is *that* question that is at the heart of the matter. That is what the paper was all about, and that issue is the only one I want to defend. It is so important that we do not lose sight of that context, because if we do ignore that (as many people have done), we just go around in circles. So, yes, i did say that it is extremely hard (read: impossible) to predict or explain the patterns in GoL, given the rules ... but what is happening right now, in the general discussion going on in this thread, is that some people are trying to broaden the sense of predict or explain so that it could be said that the patterns in GoL really can be xplained or predicted. (In particular, Josh is obstinately trying to insist that just doing lots of simulations and searching for the patterns is the same thing as explaining or predicting them). The problem is that this kind of distorted, special-case interpretation of explanation is not only atypical of scientific explanations in general, but also completely useless in the context of the question I raised in the paper: If Conway had had the goal of inventing GoL rules that would generate a specific set of patterns, what good would it have done if the only way to predict the patterns from the rules was the kind of prediction or explanation that Josh insists on (simulate and test)? If there had been any way at all to find a compact explanation of that relationship, the existence of that compact relationship would have offered the hope that Conway could have worked backward from his patterns to the rules that would generate them. Similarly, if there did not exist any compact explanation for the shape of planetary orbits, Newton would never have been able to guess the rules that gave rise to the orbits. Just imagine that the orbits were the result of a massive combination of exhange-interactions between five million species of subatomic particles, and that orbits were not elliptical, but some other bizarre shape: if the only way to find out the shape was to simulate the five million different types of subatomic interactions, how would Newton ever have come up with a hypothesis to test? The existence of compact low-level to high-level relationship was what made it possible for him to do that. The two directions involved in the process of explanation (hypthesising, which is going from high level to low level, and testing, which is going from low level to high level) are interrelated. My emphasis on the testing phase of this process, in the specific case of GoL, was part of a larger plan to consider its impact on the whole explanation process. And that, in turn, was part of a larger goal about thinking about the process
Re: [agi] Conway's Game of Life and Turing machine equivalence
Linas Vepstas wrote: On Thu, Oct 04, 2007 at 11:06:11AM -0400, Richard Loosemore wrote: In case anyone else wonders about the same question, I will explain why the Turing machine equivalence has no relevance at all. Re-read what you wrote, substituting the phrase Turing machine, for each and every occurrance of the phrase GoL. The semantics of the resulting text is unchanged, and states nothing particularly unique or original that isn't already (well-)known about Turing machines. You continue to distort the meaning of the argument by taking it out of context.. Richard Loosemore. You can even substitute finite state machine or pushdown automaton at every point, and you argument would still be unchanged (although the result would not actually be Turing complete). That's because some finite automata are boring (cyclic in trivial ways), and some are interesting (generating potentially large and complex patterns). Most randomly generated finite automata will be simple, i.e. boring, and some will exhibit surprisingly complex behaviours. To be abstract, you could subsitute semi-Thue system, context-free grammar, first-order logic, Lindenmeyer system, history monoid, etc. for GoL, and still get an equivalent argument about complexity and predicatability. Singling out GoL as somehow special is a red herring; the complexity properties you describe are shared by a variety of systems and logics. --linas - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?; - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=50734307-79d28c
Re: [agi] Conway's Game of Life and Turing machine equivalence
Andrew Babian wrote: Honestly, it seems to me pretty clearly that whatever Richard's thing is with complexity being the secret sauce for intelligence and therefore everyone having it wrong is just foolishness. I've quit paying him any mind. Everyone has his own foolishness. We just wait for the demos. Why make insulting personal remarkss instead of explaining your reasoning? Richard Loosemore - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=50734636-a1e889
Re: [agi] Do the inference rules of categorical logic make sense?
Major premise and minor premise in a syllogism are not interchangeable. Read the derivation of truth tables for abduction and induction from the semantics of NAL to learn that different ordering of premises results in different truth values. Thus while both orderings are applicable, one will usually give more confident result which will dominate the other. On 10/6/07, Edward W. Porter [EMAIL PROTECTED] wrote: But I don't understand the rules for induction and abduction which are as following: ABDUCTION INFERENCE RULE: Given S -- M and P -- M, this implies S -- P to some degree INDUCTION INFERENCE RULE: Given M -- S and M -- P, this implies S -- P to some degree The problem I have is that in both the abduction and induction rule -- unlike in the deduction rule -- the roles of S and P appear to be semantically identical, i.e., they could be switched in the two premises with no apparent change in meaning, and yet in the conclusion switching S and P would change in meaning. Thus, it appears that from premises which appear to make no distinctions between S and P a conclusion is drawn that does make such a distinction. At least to me, with my current limited knowledge of the subject, this seems illogical. - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=50749379-2a7926
Re: [agi] Schemata
Josh, I have no idea how new the idea is. When Schank was talking about scripts ... From the MIT Encyclopedia of the Cognitive Sciences (p729): Schemata are the psychological constructs that are postulated to account for the molar forms of human generic knowledge. The term *frames*, as introduced by Marvin Minsky (1975) is essentially synonymous, except that Minsky used frame as both a psychological construct and a construct in artificial intelligence. *Scripts* are the subclass of schemata that are used to account for generic (stereotyped) sequences of actions (Schank and Abelson 1977). Josh, Yes but the image schema of Mark Johnson co, are literally outline graphics - something like, say, a point or blob - an arrow - and another point or blob - for X journeys to Y [a goal] . [See The Body in the Mind] The schemata of Minsky co, as I understand, are networks of symbolic concepts - and haven't worked. And - correct me, because I only have a vague knowledge here - my impression is that everyone who is currently trying to draw analogies - e.g. Hofstadter, Gentner, Ben - is also relying on some form of symbolic networks. This whole area is v. confused and difficult to discuss, precisely because it involves visual images. For example, Johnson Laird's mental models, as I understand, partake of both visual elements and symbolic concepts - but it often isn't clear which. It also often isn't always clear in Minsky's work whether he might not mean something more visual by scripts, though in fact he definitely works just with symbols. I - and perhaps Johnson co - am arguing that this whole area is extremely important. You could say that image schema/ graphics are the mind's informal geometry - and are central to its power to do almost all the things that AGI is currently incapable of - like drawing analogies, visual object recognition and visual thinking AND NLP - and, one might add, the mind's technically extraordinary ability to construct altogether new visual scenes and scenarios in dreams. (I - again, I think, Johnson co - don't think the mind works with just image schemas, but also with more detailed images - as the example of dreams indicates. Schema/graphics are the visual and sensory storyboard which allows the mind to then flesh in more detailed images). - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=50765092-85047a
Re: [agi] Do the inference rules of categorical logic make sense?
Right. See concrete examples in http://nars.wang.googlepages.com/NARS-Examples-SingleStep.txt In induction and abduction, S--P and P--S are usually (though not always) produced in pair, though usually (though not always) with different truth values, unless the two premises have the same truth-value --- as Edward said, it would be illogical to produce difference from sameness. ;-) Especially, positive evidence equally support both conclusions, while negative evidence only deny one of the two --- see the Induction and Revision example in http://nars.wang.googlepages.com/NARS-Examples-MultiSteps.txt For a more focused discussion on induction in NARS, see http://www.cogsci.indiana.edu/pub/wang.induction.ps The situation for S-P is similar --- see comparison in http://nars.wang.googlepages.com/NARS-Examples-SingleStep.txt Pei On 10/6/07, Lukasz Stafiniak [EMAIL PROTECTED] wrote: Major premise and minor premise in a syllogism are not interchangeable. Read the derivation of truth tables for abduction and induction from the semantics of NAL to learn that different ordering of premises results in different truth values. Thus while both orderings are applicable, one will usually give more confident result which will dominate the other. On 10/6/07, Edward W. Porter [EMAIL PROTECTED] wrote: But I don't understand the rules for induction and abduction which are as following: ABDUCTION INFERENCE RULE: Given S -- M and P -- M, this implies S -- P to some degree INDUCTION INFERENCE RULE: Given M -- S and M -- P, this implies S -- P to some degree The problem I have is that in both the abduction and induction rule -- unlike in the deduction rule -- the roles of S and P appear to be semantically identical, i.e., they could be switched in the two premises with no apparent change in meaning, and yet in the conclusion switching S and P would change in meaning. Thus, it appears that from premises which appear to make no distinctions between S and P a conclusion is drawn that does make such a distinction. At least to me, with my current limited knowledge of the subject, this seems illogical. - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?; - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=50765665-44f7f5
RE: [agi] Do the inference rules of categorical logic make sense?
If you are a machine reasoning from pieces of information you receive in no particular order how do you know which is the major and which is the minor premise? Edward W. Porter Porter Associates 24 String Bridge S12 Exeter, NH 03833 (617) 494-1722 Fax (617) 494-1822 [EMAIL PROTECTED] -Original Message- From: Lukasz Stafiniak [mailto:[EMAIL PROTECTED] Sent: Saturday, October 06, 2007 4:30 AM To: agi@v2.listbox.com Subject: Re: [agi] Do the inference rules of categorical logic make sense? Major premise and minor premise in a syllogism are not interchangeable. Read the derivation of truth tables for abduction and induction from the semantics of NAL to learn that different ordering of premises results in different truth values. Thus while both orderings are applicable, one will usually give more confident result which will dominate the other. On 10/6/07, Edward W. Porter [EMAIL PROTECTED] wrote: But I don't understand the rules for induction and abduction which are as following: ABDUCTION INFERENCE RULE: Given S -- M and P -- M, this implies S -- P to some degree INDUCTION INFERENCE RULE: Given M -- S and M -- P, this implies S -- P to some degree The problem I have is that in both the abduction and induction rule -- unlike in the deduction rule -- the roles of S and P appear to be semantically identical, i.e., they could be switched in the two premises with no apparent change in meaning, and yet in the conclusion switching S and P would change in meaning. Thus, it appears that from premises which appear to make no distinctions between S and P a conclusion is drawn that does make such a distinction. At least to me, with my current limited knowledge of the subject, this seems illogical. - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?; - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=50766573-29b233
RE: [agi] Do the inference rules of categorical logic make sense?
So is the following understanding correct? If you have two statements Fred is a human Fred is an animal And assuming you know nothing more about any of the three terms in both these statements, then each of the following would be an appropriate induction A human is an animal An animal is a human A human and an animal are similar It would only then be from further information that you would find the first of these two inductions has a larger truth value than the second and that the third probably has a larger truth value than the second.. Edward W. Porter Porter Associates 24 String Bridge S12 Exeter, NH 03833 (617) 494-1722 Fax (617) 494-1822 [EMAIL PROTECTED] -Original Message- From: Pei Wang [mailto:[EMAIL PROTECTED] Sent: Saturday, October 06, 2007 7:03 AM To: agi@v2.listbox.com Subject: Re: [agi] Do the inference rules of categorical logic make sense? Right. See concrete examples in http://nars.wang.googlepages.com/NARS-Examples-SingleStep.txt In induction and abduction, S--P and P--S are usually (though not always) produced in pair, though usually (though not always) with different truth values, unless the two premises have the same truth-value --- as Edward said, it would be illogical to produce difference from sameness. ;-) Especially, positive evidence equally support both conclusions, while negative evidence only deny one of the two --- see the Induction and Revision example in http://nars.wang.googlepages.com/NARS-Examples-MultiSteps.txt For a more focused discussion on induction in NARS, see http://www.cogsci.indiana.edu/pub/wang.induction.ps The situation for S-P is similar --- see comparison in http://nars.wang.googlepages.com/NARS-Examples-SingleStep.txt Pei On 10/6/07, Lukasz Stafiniak [EMAIL PROTECTED] wrote: Major premise and minor premise in a syllogism are not interchangeable. Read the derivation of truth tables for abduction and induction from the semantics of NAL to learn that different ordering of premises results in different truth values. Thus while both orderings are applicable, one will usually give more confident result which will dominate the other. On 10/6/07, Edward W. Porter [EMAIL PROTECTED] wrote: But I don't understand the rules for induction and abduction which are as following: ABDUCTION INFERENCE RULE: Given S -- M and P -- M, this implies S -- P to some degree INDUCTION INFERENCE RULE: Given M -- S and M -- P, this implies S -- P to some degree The problem I have is that in both the abduction and induction rule -- unlike in the deduction rule -- the roles of S and P appear to be semantically identical, i.e., they could be switched in the two premises with no apparent change in meaning, and yet in the conclusion switching S and P would change in meaning. Thus, it appears that from premises which appear to make no distinctions between S and P a conclusion is drawn that does make such a distinction. At least to me, with my current limited knowledge of the subject, this seems illogical. - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?; - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?; - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=50767228-6b318e
Re: [agi] Do the inference rules of categorical logic make sense?
The order here isn't the incoming order of the premises. From M--S(t1) and M--P(t2), where t1 and t2 are truth values, the rule produces two symmetric conclusions, and which truth function is called depends on the subject/predicate order in the conclusion. That is, S--P will use a function f(t1,t2), while P--S will use the symmetric function f(t2,t1). Pei On 10/6/07, Edward W. Porter [EMAIL PROTECTED] wrote: If you are a machine reasoning from pieces of information you receive in no particular order how do you know which is the major and which is the minor premise? Edward W. Porter Porter Associates 24 String Bridge S12 Exeter, NH 03833 (617) 494-1722 Fax (617) 494-1822 [EMAIL PROTECTED] -Original Message- From: Lukasz Stafiniak [mailto:[EMAIL PROTECTED] Sent: Saturday, October 06, 2007 4:30 AM To: agi@v2.listbox.com Subject: Re: [agi] Do the inference rules of categorical logic make sense? Major premise and minor premise in a syllogism are not interchangeable. Read the derivation of truth tables for abduction and induction from the semantics of NAL to learn that different ordering of premises results in different truth values. Thus while both orderings are applicable, one will usually give more confident result which will dominate the other. On 10/6/07, Edward W. Porter [EMAIL PROTECTED] wrote: But I don't understand the rules for induction and abduction which are as following: ABDUCTION INFERENCE RULE: Given S -- M and P -- M, this implies S -- P to some degree INDUCTION INFERENCE RULE: Given M -- S and M -- P, this implies S -- P to some degree The problem I have is that in both the abduction and induction rule -- unlike in the deduction rule -- the roles of S and P appear to be semantically identical, i.e., they could be switched in the two premises with no apparent change in meaning, and yet in the conclusion switching S and P would change in meaning. Thus, it appears that from premises which appear to make no distinctions between S and P a conclusion is drawn that does make such a distinction. At least to me, with my current limited knowledge of the subject, this seems illogical. - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?; - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?; - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=50767869-3791d3
Re: [agi] Do the inference rules of categorical logic make sense?
On 10/6/07, Edward W. Porter [EMAIL PROTECTED] wrote: So is the following understanding correct? If you have two statements Fred is a human Fred is an animal And assuming you know nothing more about any of the three terms in both these statements, then each of the following would be an appropriate induction A human is an animal An animal is a human A human and an animal are similar Correct, though for technical reasons I don't call the last one induction but comparison. It would only then be from further information that you would find the first of these two inductions has a larger truth value than the second and that the third probably has a larger truth value than the second.. Right, though the rules immediately assigns truth values to the conclusion, based on the evidence provided by the current premises. The role of further information is to revise the previous truth values. In this way, the system can always form a belief (rather than waiting for enough information), though the initial beliefs will have low confidence. Pei Edward W. Porter Porter Associates 24 String Bridge S12 Exeter, NH 03833 (617) 494-1722 Fax (617) 494-1822 [EMAIL PROTECTED] -Original Message- From: Pei Wang [mailto:[EMAIL PROTECTED] Sent: Saturday, October 06, 2007 7:03 AM To: agi@v2.listbox.com Subject: Re: [agi] Do the inference rules of categorical logic make sense? Right. See concrete examples in http://nars.wang.googlepages.com/NARS-Examples-SingleStep.txt In induction and abduction, S--P and P--S are usually (though not always) produced in pair, though usually (though not always) with different truth values, unless the two premises have the same truth-value --- as Edward said, it would be illogical to produce difference from sameness. ;-) Especially, positive evidence equally support both conclusions, while negative evidence only deny one of the two --- see the Induction and Revision example in http://nars.wang.googlepages.com/NARS-Examples-MultiSteps.txt For a more focused discussion on induction in NARS, see http://www.cogsci.indiana.edu/pub/wang.induction.ps The situation for S-P is similar --- see comparison in http://nars.wang.googlepages.com/NARS-Examples-SingleStep.txt Pei On 10/6/07, Lukasz Stafiniak [EMAIL PROTECTED] wrote: Major premise and minor premise in a syllogism are not interchangeable. Read the derivation of truth tables for abduction and induction from the semantics of NAL to learn that different ordering of premises results in different truth values. Thus while both orderings are applicable, one will usually give more confident result which will dominate the other. On 10/6/07, Edward W. Porter [EMAIL PROTECTED] wrote: But I don't understand the rules for induction and abduction which are as following: ABDUCTION INFERENCE RULE: Given S -- M and P -- M, this implies S -- P to some degree INDUCTION INFERENCE RULE: Given M -- S and M -- P, this implies S -- P to some degree The problem I have is that in both the abduction and induction rule -- unlike in the deduction rule -- the roles of S and P appear to be semantically identical, i.e., they could be switched in the two premises with no apparent change in meaning, and yet in the conclusion switching S and P would change in meaning. Thus, it appears that from premises which appear to make no distinctions between S and P a conclusion is drawn that does make such a distinction. At least to me, with my current limited knowledge of the subject, this seems illogical. - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?; - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?; This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?; - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=50768597-1784af
Re: [agi] Do the inference rules of categorical logic make sense?
On 10/6/07, Pei Wang [EMAIL PROTECTED] wrote:
On 10/6/07, Edward W. Porter [EMAIL PROTECTED] wrote:
So is the following understanding correct?
If you have two statements
Fred is a human
Fred is an animal
And assuming you know nothing more about any of the three terms in both
these statements, then each of the following would be an appropriate
induction
A human is an animal
An animal is a human
A human and an animal are similar
Correct, though for technical reasons I don't call the last one
induction but comparison.
BTW, in the future you can easily try it yourself, if you want:
(1) start the NARS demo by clicking http://nars.wang.googlepages.com/NARS.html
(2) open the inference log window by select View/Inference Log from
the main window
(3) copy/paste the following two lines into the input window:
Fred {-- human.
Fred {-- animal.
then click OK.
(4) click Walk in the main window for a few times. For this example,
in the 5th step the three conclusions you mentioned will be produced,
with a bunch of others.
There is a User's Guide for the demo at
http://nars.wang.googlepages.com/NARS-Guide.html
Pei
-
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Re: [agi] Conway's Game of Life and Turing machine equivalence
Linas Vepstas said: To amplify: the rules for GoL are simple. The finding what they imply are not. The rues for gravity are simple. Finding what they impl are not. And I would argue that the rules of Friendliness are simple and the finding what they imply are not. - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=50769549-f05ef8
RE: [agi] Do the inference rules of categorical logic make sense?
Thanks. So as I understand it, whether a premise is major or minor is defined by its role of its terms relative to a given conconclusion. But the same premise could play a major role relative to once conclusion and a minor role relative to another. Edward W. Porter Porter Associates 24 String Bridge S12 Exeter, NH 03833 (617) 494-1722 Fax (617) 494-1822 [EMAIL PROTECTED] -Original Message- From: Pei Wang [mailto:[EMAIL PROTECTED] Sent: Saturday, October 06, 2007 8:20 AM To: agi@v2.listbox.com Subject: Re: [agi] Do the inference rules of categorical logic make sense? The order here isn't the incoming order of the premises. From M--S(t1) and M--P(t2), where t1 and t2 are truth values, the rule produces two symmetric conclusions, and which truth function is called depends on the subject/predicate order in the conclusion. That is, S--P will use a function f(t1,t2), while P--S will use the symmetric function f(t2,t1). Pei On 10/6/07, Edward W. Porter [EMAIL PROTECTED] wrote: If you are a machine reasoning from pieces of information you receive in no particular order how do you know which is the major and which is the minor premise? Edward W. Porter Porter Associates 24 String Bridge S12 Exeter, NH 03833 (617) 494-1722 Fax (617) 494-1822 [EMAIL PROTECTED] -Original Message- From: Lukasz Stafiniak [mailto:[EMAIL PROTECTED] Sent: Saturday, October 06, 2007 4:30 AM To: agi@v2.listbox.com Subject: Re: [agi] Do the inference rules of categorical logic make sense? Major premise and minor premise in a syllogism are not interchangeable. Read the derivation of truth tables for abduction and induction from the semantics of NAL to learn that different ordering of premises results in different truth values. Thus while both orderings are applicable, one will usually give more confident result which will dominate the other. On 10/6/07, Edward W. Porter [EMAIL PROTECTED] wrote: But I don't understand the rules for induction and abduction which are as following: ABDUCTION INFERENCE RULE: Given S -- M and P -- M, this implies S -- P to some degree INDUCTION INFERENCE RULE: Given M -- S and M -- P, this implies S -- P to some degree The problem I have is that in both the abduction and induction rule -- unlike in the deduction rule -- the roles of S and P appear to be semantically identical, i.e., they could be switched in the two premises with no apparent change in meaning, and yet in the conclusion switching S and P would change in meaning. Thus, it appears that from premises which appear to make no distinctions between S and P a conclusion is drawn that does make such a distinction. At least to me, with my current limited knowledge of the subject, this seems illogical. - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?; - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?; - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?; - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=50771155-cc051f
RE: [agi] Do the inference rules of categorical logic make sense?
Great, I look forward to trying this when I get back from a brief
vacation for the holiday weekend.
Edward W. Porter
Porter Associates
24 String Bridge S12
Exeter, NH 03833
(617) 494-1722
Fax (617) 494-1822
[EMAIL PROTECTED]
-Original Message-
From: Pei Wang [mailto:[EMAIL PROTECTED]
Sent: Saturday, October 06, 2007 8:51 AM
To: agi@v2.listbox.com
Subject: Re: [agi] Do the inference rules of categorical logic make sense?
On 10/6/07, Pei Wang [EMAIL PROTECTED] wrote:
On 10/6/07, Edward W. Porter [EMAIL PROTECTED] wrote:
So is the following understanding correct?
If you have two statements
Fred is a human
Fred is an animal
And assuming you know nothing more about any of the three terms in
both these statements, then each of the following would be an
appropriate induction
A human is an animal
An animal is a human
A human and an animal are similar
Correct, though for technical reasons I don't call the last one
induction but comparison.
BTW, in the future you can easily try it yourself, if you want:
(1) start the NARS demo by clicking
http://nars.wang.googlepages.com/NARS.html
(2) open the inference log window by select View/Inference Log from the
main window
(3) copy/paste the following two lines into the input window:
Fred {-- human.
Fred {-- animal.
then click OK.
(4) click Walk in the main window for a few times. For this example, in
the 5th step the three conclusions you mentioned will be produced, with a
bunch of others.
There is a User's Guide for the demo at
http://nars.wang.googlepages.com/NARS-Guide.html
Pei
-
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Re: [agi] Do the inference rules of categorical logic make sense?
On 10/6/07, Edward W. Porter [EMAIL PROTECTED] wrote: Thanks. So as I understand it, whether a premise is major or minor is defined by its role of its terms relative to a given conconclusion. But the same premise could play a major role relative to once conclusion and a minor role relative to another. Exactly (though I usually don't use the terms major and minor). Furthermore, the same belief can be used as premise in various types of inference (deduction, induction, abduction, comparison, analogy, revision, ...), and plays different roles in each of them. Pei Edward W. Porter Porter Associates 24 String Bridge S12 Exeter, NH 03833 (617) 494-1722 Fax (617) 494-1822 [EMAIL PROTECTED] -Original Message- From: Pei Wang [mailto:[EMAIL PROTECTED] Sent: Saturday, October 06, 2007 8:20 AM To: agi@v2.listbox.com Subject: Re: [agi] Do the inference rules of categorical logic make sense? The order here isn't the incoming order of the premises. From M--S(t1) and M--P(t2), where t1 and t2 are truth values, the rule produces two symmetric conclusions, and which truth function is called depends on the subject/predicate order in the conclusion. That is, S--P will use a function f(t1,t2), while P--S will use the symmetric function f(t2,t1). Pei On 10/6/07, Edward W. Porter [EMAIL PROTECTED] wrote: If you are a machine reasoning from pieces of information you receive in no particular order how do you know which is the major and which is the minor premise? Edward W. Porter Porter Associates 24 String Bridge S12 Exeter, NH 03833 (617) 494-1722 Fax (617) 494-1822 [EMAIL PROTECTED] -Original Message- From: Lukasz Stafiniak [mailto:[EMAIL PROTECTED] Sent: Saturday, October 06, 2007 4:30 AM To: agi@v2.listbox.com Subject: Re: [agi] Do the inference rules of categorical logic make sense? Major premise and minor premise in a syllogism are not interchangeable. Read the derivation of truth tables for abduction and induction from the semantics of NAL to learn that different ordering of premises results in different truth values. Thus while both orderings are applicable, one will usually give more confident result which will dominate the other. On 10/6/07, Edward W. Porter [EMAIL PROTECTED] wrote: But I don't understand the rules for induction and abduction which are as following: ABDUCTION INFERENCE RULE: Given S -- M and P -- M, this implies S -- P to some degree INDUCTION INFERENCE RULE: Given M -- S and M -- P, this implies S -- P to some degree The problem I have is that in both the abduction and induction rule -- unlike in the deduction rule -- the roles of S and P appear to be semantically identical, i.e., they could be switched in the two premises with no apparent change in meaning, and yet in the conclusion switching S and P would change in meaning. Thus, it appears that from premises which appear to make no distinctions between S and P a conclusion is drawn that does make such a distinction. At least to me, with my current limited knowledge of the subject, this seems illogical. - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?; - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?; - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?; - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?; - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=50771875-8eff2f
Re: [agi] Conway's Game of Life and Turing machine equivalence
Andrew Babian said: Honestly, it seems to me pretty clearly that whatever Richard's thing is with complexity being the secret sauce for intelligence and therefore everyone having it wrong is just foolishness. I've quit paying him any mind. Everyone has his own foolishness. We just wait for the demos. Try the following rephrasing: Richard believes and is trying to convince others that complexity is a necessary pre-condition for intelligence. If that is correct, then virtually every system to date cannot rise to intelligence (since they are not complex). Where I personally find Richard's statements a little strong (mainly in emphasis) is that those systems are certainly useful in the same way that Newton's Laws are useful -- as a necessary precondition to the next step -- and I think that Richard comes across as a bit too negative for his ideas to get as much traction as they would on their own merits. On the other hand, if yo don't slap people upside the head, they frequently don't listen. A corollary of Richard's statements that is less obvious is that he is very much a proponent of bottom-up systems whereas most previous systems are mostly to-down. Top-down designed systems, unless over-hauled or *much* less regulated than is usual, generally aren't going to manage to be complex. I, personally, am very much a proponent of bottom-up systems and can understand Richard's complexity point but feel that it is actually a sidelight to what I believe is his actual best point (which he's not succeeding in getting to :-). P.S. Your e-mail did come across as somewhat insulting in my perception -- but I'm frequently guilty of that as well. - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=50773032-d4390b
Re: [agi] Religion-free technical content breaking the small hardware mindset
Edward W. Porter wrote: It's also because the average person looses 10 points in IQ between mid twenties and mid fourties and another ten points between mid fourties and sixty. (Help! I'am 59.) But this is just the average. Some people hang on to their marbles as they age better than others. And knowledge gained with age can, to some extent, compensate for less raw computational power. The book in which I read this said they age norm IQ tests (presumably to keep from offending the people older than mid-forties who presumably largely control most of society's institutions, including the purchase of IQ tests.) I disagree with your theory. I primarily see the IQ drop as a result of the Flynn effect, not the age. - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=50774160-ad0d02
Re: Economic libertarianism [was Re: The first-to-market effect [WAS Re: [agi] Religion-free technical content]
Linas Vepstas wrote: My objection to economic libertarianism is its lack of discussion of self-organized criticality. A common example of self-organized criticality is a sand-pile at the critical point. Adding one grain of sand can trigger an avalanche, which can be small, or maybe (unboundedly) large. Despite avalanches, a sand-pile will maintain its critical shape (a cone at some angle). The concern is that a self-organized economy is almost by definition always operating at the critical point, sloughing off excess production, encouraging new demand, etc. Small or even medium-sized re-organizations of the economy are good for it: it maintains the economy at its critical shape, its free-market-optimal shape. Nothing wrong with that free-market optimal shape, most everyone agrees. The issue is that there's no safety net protecting against avalanches of unbounded size. The other issue is that its not grains of sand, its people. My bank-account and my brains can insulate me from small shocks. I'd like to have protection against the bigger forces that can wipe me out. I am skeptical that economies follow the self-organized criticality behavior. There aren't any examples. Some would cite the Great Depression, but it was caused by the malinvestment created by Central Banks. e.g. The Federal Reserve System. See the Austrian Business Cycle Theory for details. In conclusion, economics is a bad analogy with complex systems. - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=50774944-955341
[agi] How many scientists?
Does anyone know of any decent estimates of how many scientists are working in cog-sci related fields, roughly AI, psychology, and neuroscience? Josh - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=50789647-287dda
Re: Economic libertarianism [was Re: The first-to-market effect [WAS Re: [agi] Religion-free technical content]
On 10/6/07, a wrote: I am skeptical that economies follow the self-organized criticality behavior. There aren't any examples. Some would cite the Great Depression, but it was caused by the malinvestment created by Central Banks. e.g. The Federal Reserve System. See the Austrian Business Cycle Theory for details. In conclusion, economics is a bad analogy with complex systems. My objection to economic libertarianism is that it's not a free market. A 'free' market is an impossibility. There will always be somebody who is bigger than me or cleverer than me or better educated than me, etc. A regulatory environment attempts to reduce the victimisation of the weaker members of the population and introduces another set of biases to the economy. A free market is just a nice intellectual theory that is of no use in the real world. (Unless you are in the Mafia, of course). BillK - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=50792589-4d8a77
Re: [agi] Conway's Game of Life and Turing machine equivalence
On 10/6/07, Richard Loosemore [EMAIL PROTECTED] wrote: In my use of GoL in the paper I did emphasize the prediction part at first, but I then went on (immediately) to talk about the problem of finding hypotheses to test. Crucially, I ask if it is reasonable to suppose that Conway could have written down the patterns he *wanted* to see emerge, then found the rules that would generate his desired patterns. It is *that* question that is at the heart of the matter. That is what the paper was all about, and that issue is the only one I want to defend. It is so important that we do not lose sight of that context, because if we do ignore that (as many people have done), we just go around in circles. Is it reasonable: I doubt precisely stating your goal is enough to reach it. (that is, unless you're Oprah and believe very strongly in The Secret) I just realized your question is if Conway could have written two frames of cells, then reverse-engineered the transformations that move from A to B. That transformation would be absolutely correct in getting from A to B, however as a candidate for the Universal ruleset, it would have to apply to every transformation from B to C or X to Y. Probably this candidate would prove unusable outside the fragile case for which is was written. I can write a very simple loop to output the records of a table with known fields, it takes much more consideration to generalize the solution to any number of unknown fields. Consider states T1 and T5. Use the same transformation hypothesis generator employed in the paragraph above. Given four steps from T1 to T5, there may have been one complete transform and three static states or four 'normal' transformations. How can a T1 to T5 transformation rule be written? Consider a cyclic behavior with a period of 4 - the transformation rule would have to observe a static state because it's observation moments are not granular enough to detect the changes. A glider with a period below the observation interval would give rise to a transformation rule describing, Given this collection of cells, the next observation in open space it will appear to have moved one unit left Of course that rule requires open space, the number of configurations of impact with other cells during the observation interval give rise to an explosion of possibility. The hypothesis generation algorithm will have a computational complexity that is orders of magnitude larger than the classical GoL rules making observations/computes at each 1 unit of time. To pull back from the simplistic GoL example, consider the planetary motion example. I think I better understand the rules prediction you were talking about - the true planetary motion rules are as unavailable to Kepler as an observer in the GoL world. So by observation, he detects a regularity to the moon's path around the earth and works out a theory for why that happens. Then he uses the theory to predict the future state of the moon - and he's right. Has he found the absolutely Truth in planetary motion? No. He has found a good enough approximation for the purpose of predicting local observed phenomenon. Is there an extra term in the True formula, for which our local observation conveniently sets a value of 1 in a multiplication process? Then this predictive function has limitations on use. it is still sufficiently useful when the hidden variable maintains the value of 1 (for our locally observable universe) Think of a multidimensional motion function that has been curried down from higher dimensions, leaving only those dimensions Kepler could observe. I initially thought we were discussing the patterns than can arise from examining the actual rules, rather than trying to discover the rules from observation of states. In the context of AGI research, I think the discovery of explanations is a much more interesting problem. I think resource limitations make brute force compute every possible permutation approaches to hypothesis generation absolutely unfeasible. Even with only a few known parameters, the combinatorial explosion will cripple the largest machine we have - but with an unknown number of parameters, the task of finding every permutation is impossible. So the ability to reason about classes and test hypothesis by proof (without requiring exhaustive search) is important to working intelligence. I feel there is a great deal of value in reasoning about AGI as a class of computation rather than a single solution or program. - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=50795592-49b3a8
Re: [agi] Conway's Game of Life and Turing machine equivalence
Richard, Any problem can be stated as search for results that satisfy given constraints. What you state here doesn't seem to contradict what I wrote before. In following paragraph you describe it: On 10/6/07, Richard Loosemore [EMAIL PROTECTED] wrote: In my use of GoL in the paper I did emphasize the prediction part at first, but I then went on (immediately) to talk about the problem of finding hypotheses to test. Crucially, I ask if it is reasonable to suppose that Conway could have written down the patterns he *wanted* to see emerge, then found the rules that would generate his desired patterns. So, you ask if it's possible to find local rule given global behavior. It's obviously possible to get global behavior once you have local rules. Which essentially what I wrote before, and what Josh exemplified by his brute force initial conditions enumerator. I try not to be 'dismissive', which suggests kind of oversight, but I also try not to ignore inconsistencies. On 10/5/07, Vladimir Nesov [EMAIL PROTECTED] wrote: You do predict that behavior by simulating the model. What you supposedly can't do is to find initial conditions that will lead to required global behavior. But you actually can - for example by enumerating possible initial conditions in a brute force way and looking at what happens when you simulate it. It's just very inefficient, and as a result you can't enumerate many initial conditions which will lead to interesting global behavior. And probably there are tricks to get better results, by restricting search space. You propose a framework which will help in efficient enumeration of low-level rules and estimation of high-level behavior, and restrain possibilities to as close as possible to existing working system - human mind. All along these same lines. Computational mathematics deals with this kind of thing all the time. -- Vladimir Nesovmailto:[EMAIL PROTECTED] - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=50812333-d89460
Re: [agi] Conway's Game of Life and Turing machine equivalence
William Pearson wrote: On 05/10/2007, Richard Loosemore [EMAIL PROTECTED] wrote: William Pearson wrote: On 05/10/2007, Richard Loosemore [EMAIL PROTECTED] wrote: We have good reason to believe, after studying systems like GoL, that even if there exists a compact theory that would let us predict the patterns from the rules (equivalent to predicting planetary dynamics given the inverse square law of gravitation), such a theory is going to be so hard to discover that we may as well give up and say that it is a waste of time trying. Heck, maybe it does exist, but that's not the point: the point is that there appears to be little practical chance of finding it. A few theories. All states which do not three live cells adjacent, will become cyclic with a cycle length of 0. Or won't be cyclic if you reject cycle lengths of 0. Similarly all patterns consisting of one or more groups of three live cells in a row inside an otherwise empty 7x7 box will have a stable cycle. Will there be a general theory? Nope, You can see that from GoL being Turing complete. ^^ Sorry, Will, but this not correct, and I explained the entire reason just yesterday, in a long and thorough post that was the beginning of this thread. Just out of interest, did you read that one? Yup, and my argument is still valid, if this is the one you are referring to. You said: Now, finally: if you choose the initial state of a GoL system very, VERY carefully, it is possible to make a Turing machine. So, in the infinite set of GoL systems, a very small fraction of that set can be made to implement a Turing machine. But what does this have to do with explaining the existence of patterns in the set of ALL POSSIBLE GoL systems?? So what if a few of those GoL instances have a peculiar property? bearing in mind the definition of complexity I have stated above, how would it affect our attempts to account for patterns that exist across the entire set? You are asking about the whole space, my argument was to do with a sub space admittedly. But any theory about the whole space must be valid on all the sub spaces it contains. All we need to do is find a single state that we can prove that we cannot predict how it evolves to say we will never be able to find a theory for all states. I have a question for you, Will. Without loss of generality, I can change my use of Game of Life to a new system called GoL(-T) which is all of the possible GoL instantiations EXCEPT the tiny subset that contain Turing Machine implementations. Nothing changes in my arguments: all the known patterns/creatures are still observed (except the TM pattern), there are still an infinite number of instantiations, the patterns are still just as hard to explain for my purposes GoL(-T) is as good an example as GoL. So now, my question to you is this: tell me exactly how the existence of the TM implementation in those other instantiations, which are now outside the GoL(-T) system, have any effect on questions about the explicability of the patterns in GoL(-T)? Could you please specify the precise way that the TMs now have some impact on GoL(-T). As far as I can see (and this was my original point, of course), they have no impact. Please remember that it is my particular use of the explanation concept, in the context of the paper, that has to be referenced. Thankyou, Richard Loosemore If it was possible to find a theory, by your definition, then we could use that theory to predict the admittedly small set of states that were TMs. I might reply to the rest if I think we will get anywhere from it. - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=50850372-722294
Re: [agi] Conway's Game of Life and Turing machine equivalence
I am sorry, Mike, I have to give up. What you say is so far away from what I said in the paper that there is just no longer any point of contact. Best wishes, Richard Loosemore Mike Dougherty wrote: On 10/6/07, Richard Loosemore [EMAIL PROTECTED] wrote: In my use of GoL in the paper I did emphasize the prediction part at first, but I then went on (immediately) to talk about the problem of finding hypotheses to test. Crucially, I ask if it is reasonable to suppose that Conway could have written down the patterns he *wanted* to see emerge, then found the rules that would generate his desired patterns. It is *that* question that is at the heart of the matter. That is what the paper was all about, and that issue is the only one I want to defend. It is so important that we do not lose sight of that context, because if we do ignore that (as many people have done), we just go around in circles. Is it reasonable: I doubt precisely stating your goal is enough to reach it. (that is, unless you're Oprah and believe very strongly in The Secret) I just realized your question is if Conway could have written two frames of cells, then reverse-engineered the transformations that move from A to B. That transformation would be absolutely correct in getting from A to B, however as a candidate for the Universal ruleset, it would have to apply to every transformation from B to C or X to Y. Probably this candidate would prove unusable outside the fragile case for which is was written. I can write a very simple loop to output the records of a table with known fields, it takes much more consideration to generalize the solution to any number of unknown fields. Consider states T1 and T5. Use the same transformation hypothesis generator employed in the paragraph above. Given four steps from T1 to T5, there may have been one complete transform and three static states or four 'normal' transformations. How can a T1 to T5 transformation rule be written? Consider a cyclic behavior with a period of 4 - the transformation rule would have to observe a static state because it's observation moments are not granular enough to detect the changes. A glider with a period below the observation interval would give rise to a transformation rule describing, Given this collection of cells, the next observation in open space it will appear to have moved one unit left Of course that rule requires open space, the number of configurations of impact with other cells during the observation interval give rise to an explosion of possibility. The hypothesis generation algorithm will have a computational complexity that is orders of magnitude larger than the classical GoL rules making observations/computes at each 1 unit of time. To pull back from the simplistic GoL example, consider the planetary motion example. I think I better understand the rules prediction you were talking about - the true planetary motion rules are as unavailable to Kepler as an observer in the GoL world. So by observation, he detects a regularity to the moon's path around the earth and works out a theory for why that happens. Then he uses the theory to predict the future state of the moon - and he's right. Has he found the absolutely Truth in planetary motion? No. He has found a good enough approximation for the purpose of predicting local observed phenomenon. Is there an extra term in the True formula, for which our local observation conveniently sets a value of 1 in a multiplication process? Then this predictive function has limitations on use. it is still sufficiently useful when the hidden variable maintains the value of 1 (for our locally observable universe) Think of a multidimensional motion function that has been curried down from higher dimensions, leaving only those dimensions Kepler could observe. I initially thought we were discussing the patterns than can arise from examining the actual rules, rather than trying to discover the rules from observation of states. In the context of AGI research, I think the discovery of explanations is a much more interesting problem. I think resource limitations make brute force compute every possible permutation approaches to hypothesis generation absolutely unfeasible. Even with only a few known parameters, the combinatorial explosion will cripple the largest machine we have - but with an unknown number of parameters, the task of finding every permutation is impossible. So the ability to reason about classes and test hypothesis by proof (without requiring exhaustive search) is important to working intelligence. I feel there is a great deal of value in reasoning about AGI as a class of computation rather than a single solution or program. - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?; - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your
Re: [agi] Conway's Game of Life and Turing machine equivalence
Vladimir, I say the following without meaning to be critical. In what I wrote yesterday, I was trying to establish the first point in the sequence of points that make up the argument in my paper. What is happening, in this discussion, is that you are trying to ask me to present the entire argument that was in the paper, but only one step at a time. That seems fair enough, by itself, except that . This is having the unfortunate side-effect that as each point is presented, you are interpreting it and (especially) running on ahead with it in directions that do not have any relation to my argument. The paper I wrote was a single coherent whole, and this process of breaking it up is getting crazy. I find myself continually trying to explain that this or that argument has nothing to do with what I wrote. Please ignore the paper. It is intended for a different audience than most of the people on this list. Richard Loosemore Vladimir Nesov wrote: Richard, Any problem can be stated as search for results that satisfy given constraints. What you state here doesn't seem to contradict what I wrote before. In following paragraph you describe it: On 10/6/07, Richard Loosemore [EMAIL PROTECTED] wrote: In my use of GoL in the paper I did emphasize the prediction part at first, but I then went on (immediately) to talk about the problem of finding hypotheses to test. Crucially, I ask if it is reasonable to suppose that Conway could have written down the patterns he *wanted* to see emerge, then found the rules that would generate his desired patterns. So, you ask if it's possible to find local rule given global behavior. It's obviously possible to get global behavior once you have local rules. Which essentially what I wrote before, and what Josh exemplified by his brute force initial conditions enumerator. I try not to be 'dismissive', which suggests kind of oversight, but I also try not to ignore inconsistencies. On 10/5/07, Vladimir Nesov [EMAIL PROTECTED] wrote: You do predict that behavior by simulating the model. What you supposedly can't do is to find initial conditions that will lead to required global behavior. But you actually can - for example by enumerating possible initial conditions in a brute force way and looking at what happens when you simulate it. It's just very inefficient, and as a result you can't enumerate many initial conditions which will lead to interesting global behavior. And probably there are tricks to get better results, by restricting search space. You propose a framework which will help in efficient enumeration of low-level rules and estimation of high-level behavior, and restrain possibilities to as close as possible to existing working system - human mind. All along these same lines. Computational mathematics deals with this kind of thing all the time. - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=50853083-ef3499
Re: [agi] Conway's Game of Life and Turing machine equivalence
On 07/10/2007, Richard Loosemore [EMAIL PROTECTED] wrote: I have a question for you, Will. Without loss of generality, I can change my use of Game of Life to a new system called GoL(-T) which is all of the possible GoL instantiations EXCEPT the tiny subset that contain Turing Machine implementations. As far as I am concerned it is not that simple. Turing completeness has nothing to do with any particular implementation of a TM in that system. It is a property of the system. That is the ability to be organised in such as way as to compute whatever a turing machine could. And there are many, many potential ways of organising a Turing complete system to compute what a TM could. To take an analogous example. Lets say you wanted to take C and make it no longer turing complete. Well the simple way, you would remove loops and recursion. Then to be on the safe side self-modifying code in case it wrote in a loop for itself. Why such drastic measures? Because otherwise you might be able to write a java/ruby/brainfuck interpreter and get back to Turing completeness. So maybe I am throwing the baby out with the bath water. But what is the alternate method of getting a non-Turing complete subset of C. Well, you would basically have to test each string to see whether it implemented a UTM of some variety or other. And discard those that did. It would have to be done empirically. Automatic ways of recognising strings that implement UTMs would probably fall foul of Rice's theorem. So in imagining GoL-T, you are asking me to do something I do not know how to find simply without radically changing the system, to prevent looping patterns. And if I do the complex way of getting rid of UTMs, I don't know what the states left over from the great UTM purge would look like. So I can't say whether it would still be Complex afterwards, to know whether the rest of your reasoning holds. Will Pearson - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=50866846-9589ac
Re: [agi] Conway's Game of Life and Turing machine equivalence
On 10/6/07, Richard Loosemore [EMAIL PROTECTED] wrote: I am sorry, Mike, I have to give up. What you say is so far away from what I said in the paper that there is just no longer any point of contact. oh. So we weren't having a discussion. You were having a lecture and I was missing the point. That's fine. This is a form of entertainment for me. I don't have anything to prove. thanks for your consideration. - This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244id_secret=50875268-6eac9d
