RE: [agi] Compressed Cross-Indexed Concepts
An agent can only flip so many bits per second. If it gets stuck in a computational conundrum it will waste energy that should be used for survival purposes and the likelihood for agent death increases. Avoidance behavior for impossible computation is enforced. Mathematics is a type of database for computational energy storage. All of us multi-agent intelligences, mainly mathematicians, contribute to it over time. How long did it take to invent the wheel, but once the pattern is known, it takes just a few bits to store. That's one obvious method of the leveraging, but this could be, and is, used all over the place. John From: Jim Bromer [mailto:jimbro...@gmail.com] John How would a mathematical system that is able to leverage for unnecessary or impossible computation work exactly. What do you mean by this? And how would this work to produce better integration of concepts and better interpretation of concepts? On Fri, Aug 13, 2010 at 4:25 PM, John G. Rose johnr...@polyplexic.com wrote: -Original Message- From: Jim Bromer [mailto:jimbro...@gmail.com] On Thu, Aug 12, 2010 at 12:40 AM, John G. Rose johnr...@polyplexic.com wrote: The ideological would still need be expressed mathematically. I don't understand this. Computers can represent related data objects that may be best considered without using mathematical terms (or with only incidental mathematical functions related to things like the numbers of objects.) The difference between data and code, or math and data, sometimes need not be as dichotomous. I said: I think the more important question is how does a general concept be interpreted across a range of different kinds of ideas. Actually this is not so difficult, but what I am getting at is how are sophisticated conceptual interrelations integrated and resolved? John said: Depends on the structure. We would want to build it such that this happens at various levels or the various multidimensional densities. But at the same time complex state is preserved until proven benefits show themselves. Your use of the term 'densities' suggests that you are thinking about the kinds of statistical relations that have been talked about a number of times in this group. The whole problem I have with statistical models is that they don't typically represent the modelling variations that could be and would need to be encoded into the ideas that are being represented. For example a Bayesian Network does imply that a resulting evaluation would subsequently be encoded into the network evaluation process, but only in a limited manner. It doesn't for example show how an idea could change the model, even though that would be easy to imagine. Jim Bromer I also have some issues with heavily based statistical models. When I was referring to densities I was really meaning an interconnectional multidimensionality in the multigraph/hypergraph intelligence network, IOW a partly combinatorial edge of chaos. There is a combination of state and computational potential energy that an incoming idea, represented as a data/math combo, would result in various partly self-organizational (SOM) changes depending on how the key - the idea - effects computational energy potential. And this is balanced against K-complexity related local extrema. For the statistical mechanisms I would use for more of the narrow AI stuff that is needed and also for situations that you can't come up with something more concrete/discrete. John --- 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 http://www.listbox.com/ 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 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=8660244-6e7fb59c Powered by Listbox: http://www.listbox.com
Re: [agi] Compressed Cross-Indexed Concepts
On Thu, Aug 12, 2010 at 12:40 AM, John G. Rose johnr...@polyplexic.comwrote: The ideological would still need be expressed mathematically. I don't understand this. Computers can represent related data objects that may be best considered without using mathematical terms (or with only incidental mathematical functions related to things like the numbers of objects.) I said: I think the more important question is how does a general concept be interpreted across a range of different kinds of ideas. Actually this is not so difficult, but what I am getting at is how are sophisticated conceptual interrelations integrated and resolved? John said: Depends on the structure. We would want to build it such that this happens at various levels or the various multidimensional densities. But at the same time complex state is preserved until proven benefits show themselves. Your use of the term 'densities' suggests that you are thinking about the kinds of statistical relations that have been talked about a number of times in this group. The whole problem I have with statistical models is that they don't typically represent the modelling variations that could be and would need to be encoded into the ideas that are being represented. For example a Bayesian Network does imply that a resulting evaluation would subsequently be encoded into the network evaluation process, but only in a limited manner. It doesn't for example show how an idea could change the model, even though that would be easy to imagine. Jim Bromer On Thu, Aug 12, 2010 at 12:40 AM, John G. Rose johnr...@polyplexic.comwrote: -Original Message- From: Jim Bromer [mailto:jimbro...@gmail.com] Well, if it was a mathematical structure then we could start developing prototypes using familiar mathematical structures. I think the structure has to involve more ideological relationships than mathematical. The ideological would still need be expressed mathematically. For instance you can apply a idea to your own thinking in a such a way that you are capable of (gradually) changing how you think about something. This means that an idea can be a compression of some greater change in your own programming. Mmm yes or like a key. While the idea in this example would be associated with a fairly strong notion of meaning, since you cannot accurately understand the full consequences of the change it would be somewhat vague at first. (It could be a very precise idea capable of having strong effect, but the details of those effects would not be known until the change had progressed.) Yes. It would need to have receptors, an affinity something like that, or somehow enable an efficiency change. I think the more important question is how does a general concept be interpreted across a range of different kinds of ideas. Actually this is not so difficult, but what I am getting at is how are sophisticated conceptual interrelations integrated and resolved? Jim Depends on the structure. We would want to build it such that this happens at various levels or the various multidimensional densities. But at the same time complex state is preserved until proven benefits show themselves. John --- 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=8660244-6e7fb59c Powered by Listbox: http://www.listbox.com
Re: [agi] Compressed Cross-Indexed Concepts
It would be easy to relativize a weighted network so that it could be used to include ideas that can effectively reshape the network (or at least reshape the virtual network) but it is not easy to see how this could be done intelligently enough to produce actual intelligence. But maybe I should try it sometime just to get some idea of what it would do. Jim Bromer --- 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=8660244-6e7fb59c Powered by Listbox: http://www.listbox.com
RE: [agi] Compressed Cross-Indexed Concepts
-Original Message- From: Jim Bromer [mailto:jimbro...@gmail.com] On Thu, Aug 12, 2010 at 12:40 AM, John G. Rose johnr...@polyplexic.com wrote: The ideological would still need be expressed mathematically. I don't understand this. Computers can represent related data objects that may be best considered without using mathematical terms (or with only incidental mathematical functions related to things like the numbers of objects.) The difference between data and code, or math and data, sometimes need not be as dichotomous. I said: I think the more important question is how does a general concept be interpreted across a range of different kinds of ideas. Actually this is not so difficult, but what I am getting at is how are sophisticated conceptual interrelations integrated and resolved? John said: Depends on the structure. We would want to build it such that this happens at various levels or the various multidimensional densities. But at the same time complex state is preserved until proven benefits show themselves. Your use of the term 'densities' suggests that you are thinking about the kinds of statistical relations that have been talked about a number of times in this group. The whole problem I have with statistical models is that they don't typically represent the modelling variations that could be and would need to be encoded into the ideas that are being represented. For example a Bayesian Network does imply that a resulting evaluation would subsequently be encoded into the network evaluation process, but only in a limited manner. It doesn't for example show how an idea could change the model, even though that would be easy to imagine. Jim Bromer I also have some issues with heavily based statistical models. When I was referring to densities I was really meaning an interconnectional multidimensionality in the multigraph/hypergraph intelligence network, IOW a partly combinatorial edge of chaos. There is a combination of state and computational potential energy that an incoming idea, represented as a data/math combo, would result in various partly self-organizational (SOM) changes depending on how the key - the idea - effects computational energy potential. And this is balanced against K-complexity related local extrema. For the statistical mechanisms I would use for more of the narrow AI stuff that is needed and also for situations that you can't come up with something more concrete/discrete. John --- 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=8660244-6e7fb59c Powered by Listbox: http://www.listbox.com
RE: [agi] Compressed Cross-Indexed Concepts
-Original Message- From: Jim Bromer [mailto:jimbro...@gmail.com] Well, if it was a mathematical structure then we could start developing prototypes using familiar mathematical structures. I think the structure has to involve more ideological relationships than mathematical. The ideological would still need be expressed mathematically. For instance you can apply a idea to your own thinking in a such a way that you are capable of (gradually) changing how you think about something. This means that an idea can be a compression of some greater change in your own programming. Mmm yes or like a key. While the idea in this example would be associated with a fairly strong notion of meaning, since you cannot accurately understand the full consequences of the change it would be somewhat vague at first. (It could be a very precise idea capable of having strong effect, but the details of those effects would not be known until the change had progressed.) Yes. It would need to have receptors, an affinity something like that, or somehow enable an efficiency change. I think the more important question is how does a general concept be interpreted across a range of different kinds of ideas. Actually this is not so difficult, but what I am getting at is how are sophisticated conceptual interrelations integrated and resolved? Jim Depends on the structure. We would want to build it such that this happens at various levels or the various multidimensional densities. But at the same time complex state is preserved until proven benefits show themselves. John --- 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=8660244-6e7fb59c Powered by Listbox: http://www.listbox.com
Re: [agi] Compressed Cross-Indexed Concepts
[from: Concept-Rich Mathematics Instruction] Teacher: Very good. Now, look at this drawing and explain what you see. [Draws.] Debora: It's a pie with three pieces. Teacher: Tell us about the pieces. Debora: Three thirds. Teachers: What is the difference among the pieces? Debora: This is the largest third, and here is the smallest . . . Sound familiar? Have you ever wondered why students often understand mathematics in a very rudimentary and prototypical way, why even rich and exciting hands-on types of active learning do not always result in real learning of new concepts? From the psycho-educational perspective, these are the critical questions. In other words, epistemology is valuable to the extent that it helps us find ways to enable students who come with preconceived and misconceived ideas to understand a framework of scientific and mathematical concepts. Constructivism: A New Perspective At the dawn of behaviorism, constructivism became the most dominant epistemology in education. The purest forms of this philosophy profess that knowledge is not passively received either through the senses or by way of communication, just as meaning is not explicitly out there for grabs. Rather, constructivists generally agree that knowledge is actively built up by a cognizing human who needs to adapt to what is fit and viable (von Glasersfeld, 1995). Thus, there is no dispute among constructivists over the premise that one's knowledge is in a constant state of flux because humans are subject to an ever-changing reality (Jaworski, 1994, p. 16). Although constructivists generally regard understanding as the outcome of an active process, constructivists still argue over the nature of the process of knowing. Is knowing simply a matter of recall? Does learning new concepts reflect additive or structural cognitive changes? Is the process of knowing concepts built from the bottom up, or can it be a top-down process? How does new conceptual knowledge depend on experience? How does conceptual knowledge relate to procedural knowledge? And, can teachers mediate conceptual development? | Concept-Rich Mathematics Instruction Is Learning New Concepts Simply a Mechanism of Memorization and Recall? Science and mathematics educators have become increasingly aware that our understanding of conceptual change is at least as important as the analysis of the concepts themselves. In fact, a plethora of research has established that concepts are mental structures of intellectual relationships, not simply a subject matter. The research indicates that the mental structures of intellectual relationships that make up mental concepts organize human experiences and human memory (Bartsch, 1998). Therefore, conceptual changes represent structural cognitive changes, not simply additive changes. Based on the research in cognitive psychology, the attention of research in education has been shifting from the content (e.g., mathematical concepts) to the mental predicates, language, and preconcepts. Despite the research, many teachers continue to approach new concepts as if they were simply addons to their students' existing knowledge-a subject of memorization and recall. This practice may well be one of the causes of misconceptions in mathematics. Structural Cognitive Change The notion of structural cognitive change, or schematic change, was first introduced in the field of psychology (by Bartlett, who studied memory in the 1930s). It became one of the basic tenets of constructivism. Researchers in mathematics education picked up on this term and have been leaning heavily on it since the 1960s, following Skemp (1962), Minsky (1975), and Davis (1984). The generally accepted idea among researchers in the field, as stated by Skemp (1986, p. 43), is that in mathematics, to understand something is to assimilate it into an appropriate schema. A structural cognitive change is not merely an appendage. It involves the whole network of interrelated operational and conceptual schemata. Structural changes are pervasive, central, and permanent. The first characteristic of structural change refers to its pervasive nature. That is, new experiences do not have a limited effect, but cause the entire cognitive structure to rearrange itself. Vygotsky (1986, p. 167) argued, It was shown and proved experimentally that mental development does not coincide with the development of separate psychological functions, but rather depends on changing relations between them. The development of each function, in turn, depends upon the progress in the development of the interfunctional system. From: Jim Bromer Sent: Monday, August 09, 2010 11:11 PM To: agi Subject: [agi] Compressed Cross-Indexed Concepts On Mon, Aug 9, 2010 at 4:57 PM, John G. Rose johnr...@polyplexic.com wrote: -Original Message- From: Jim Bromer [mailto:jimbro...@gmail.com] how would these diverse
