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Thinkable Models

The broader availability of technical training and its vigorous application have created an explosion in the quantity of knowledge available. The successes of relatively few at research are leaving the many behind. Increasing sophistication of machines creates tougher job competition for people, more of whom are becoming economically obsolete. We have reached a Malthusian imbalance, for the rate of knowledge growth outpaces the ability of teachers to absorb and communicate what is discovered. Skills developed through schooling are often obsolete or irrelevant before students are in a position to apply them. Beyond the arena of instruction waits another problem, pervasive but less well recognized: commonsense knowledge is becoming harder to acquire. We are all served by tools more complex than we understand. The objects we depend on "contain no user serviceable parts"; if they did, few of us would have the experience to know what to do with them. A second source of impenetrability is the increasing complication of life by rules, even at the simplest level. If children must learn to calculate percentage sales taxes before understanding sums involved in simple purchases, we need not wonder at the decline of interest in and competence with arithmetic calculation. The decreasing accessibility of common sense knowledge makes the instructional contribution even more critical than it has been in the past.

We need to increase the effectiveness of education by understanding more profoundly how humans such as we are can better adapt to the volatile world we are creating through the information revolution. I hope to contribute to this end by addressing these questions:
1. A powerful idea in early Logo research was giving children the experience of being a mathematician as opposed to teaching them some mathematical ideas. How can this approach be extended across the broader spectrum of the technical disciplines ? Can we analyze knowledge and human learning so that the outcome will suggest directions for development of computer based learning environments ?
2.An objective for popular technical education is that people should have in their minds "thinkable models" -- representations of things and processes simple enough that they can be used in thought experiments. The organization of cognitive structures for technical knowledge could be imagined to reflect a network of appropriately connected thinkable models. AI, as the science of representations, has focused in the main on language-like representations. How can we enlarge our vision of representations to include the greater variety of ways of thinking that are useful to people ?
3.The hope is to broaden access to scientific ideas. Can thinkable models help us reach out to students now left behind by current instructional methods? How can learning environments be designed to communicate a broad range of introductory technical knowledge ?

What People Do Well
Feynman's Story: If our objective is to get usable knowledge in people's minds, we should ask what they are good at. What do people do really well, at their best ?

When I was a young man, it was once my privilege to spend an evening with a man, Richard Feynman, known more for his work in physics than in psychology. Nonetheless, what Feynman said about thinking and learning deserves consideration. When asked how he got to be so good at solving problems, Feynman offered a description of his practice as an undergraduate student which is fundamental to the view developed in this paper. He recalled that whenever he actually solved a new problem -- by whatever method he could manage -- his exploitation of that small victory had only begun. He would then step back from the problem and try to see what other ways of looking at it were possible and to ask in what other formalism one might describe the problem. He would then work through the "same" problem to its solution in those secondary formalisms using the primary solution for guidance.
Feynman's reflection upon these different schemes of representation, his developing understanding of the relation of one to another and the details of their intertranslatability led to his mastery of selection among and application of varieties of descriptions and formalisms.

A new division of labor: In Feynman's story, we can see a way of looking at the balance between algorithm execution and problem recognition. Depth is needed to push through analysis with rigor. Breadth pays. The exploration of alternative representations and prosecution of problem solving in their terms is the activity which leads to mastery of individual representations and understanding of which is the best fit among those possible. This suggests the possibility of a new division of labor. We people need all the help we can get. Whatever help machine intelligence can give us should be exploited for the exhaustive exploration of fecund problems in order that the human learner can improve the ability to recognize problems and select the best representational framework for addressing any new problem encountered. Excessive dependency on mechanized knowledge can be avoided by following a proposal of Feurzeig (in Artificial Intelligence and Education, Lawler and Yazdani, Eds.,1987) to design intelligent microworlds; such are learning environments which permit the user to decide whether the computer is to execute some function in its repertoire (whether understood by the user or not); to demonstrate its means of solving a particular problem or class of problems; or even to provide coaching and challenging problems when the user wants that guidance and testing. If we are more and more willing to relegate to machines, even conditionally, computationally burdensome algorithmic knowledge, what is left for people to know ? What can be their contribution to solving problems ?

Thinkable Models
People are best at recognizing problems and classifying situations (the kind of logical process that C.S. Peirce called "abduction", 1878). Some might call it speculation; theory building is a fancier name. The process is one of making hypotheses to answer some question which will not go away. How can we support what is naturally strongest in human capability ? It would serve people well to own a collection of valid thinkable models; thinkable models are descriptions of things and relations simple enough for use as tools for thought and as the basis of thought experiments. The full text of the article continues with a simple taxonomy and then attempts to relate such models to existing knowledge. The particular example pursued is a collection of various methods of proving the pythagorean theorm.

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| Learning and Computing | Education | Computing | Psychology | Artificial Intelligence |