oded@WISDOM.BITNET (Oded Maler) (07/26/88)
From: Oded Maler <oded%WISDOM.BITNET@CUNYVM.CUNY.EDU> Date: Sun, 24 Jul 88 09:06 EDT To: ai-list@ai.ai.mit.edu Subject: What can we learn from computers What Can We Learn From Computers and Mathematics? ================================================= A few digests ago Gilbert Cockton raised the above rhetoric question as part of an attack on the computationally-oriented methodologies of AI research. As a side remark let us recall that many AIers see their main question as "What can we teach computers?" or "What are the limits to the application of Mathematics to real-world modeling?" Although I consider a lot of Cockton's criticism as valid, his claim about the non-existent contribution of Mathematics and Computers to the understanding of intelligence is at least as narrow-minded as the practice of those AI researchers who ignore the relevance of Psychology, Sociology, Philosophy and disciplines alike. I claim that experience with computers, machines, formal systems, in all levels, (starting from typing, programming and hacking, through computer science and up to pure mathematics) can teach a person (and a scientist) a lot, and may build relevant intuitions, metaphors and perspectives. Some of it cannot be gained through a life-long traditional humanistic scholarship. Just imagine what a self-aware person can learn from using a word-processor by introspecting his own performance: Context-sensitive interpretation of symbols, learning by analogy (when you move from one WP to another), reversible and unreversible operations, eye-brain-hand coordination. I'm sure Mr. Cockton's thoughts have benefited from such an experience, so think of those who were using or designing such devices for some decades. And what about programming? Algorithms, nested loops, procedures and hierarchical organization, stacks and recursive calls, data-structures in general, input and output, buffers, parameter passing and communication, efficiency of programs, top-down refinement, and the most important experience: debugging. No time before in history had so many people and so often been involved in the process of making theories (about the behavior of programs), watching them being refuted, fixing them and testing again. It is very easy to criticize the simplistic incorporation of such paradigms into models for human thinking, as many hackers and so-called AI researchers often do, but to think that these metaphors are useless and irrelevant to the study of intelligence is just making an ideology out of one's ignorance. And let's proceed to theoretical computer science: the limits of what is computable by certain machines, the results from complexity theory about what can be performed in principle and yet is practically impossible, the paradigm of a finite-state machine with input, output and internal states, mathematical logic and its shortcomings, the theory and practice of databases, the research in distributed systems, the formal treatment of knowledge and belief: is none of these relevant to the humanities? Not the mention the mathematical ideas concerning sets, infinity, order relations, distance functions, convergence, algebraic structures, the foundations of probability, dynamical systems, games and strategies and many many others. Mr. Cockton was implicitly concerned with the following question: "What is the best selection of formal and informal experience, a scientist must have during his/her (hopefully ongoing) development, in order to contribute to the advance of the cognitive sciences?" Excluding experiences of the above kind from the candidate list is not what I expect from adherents of scholar tradition. Every scientist grows within some sub-sub-discipline, learns its methodologies, tricks, success criteria and its most influential bibliographic references. When we turn later to inter-disciplinary areas, we cannot go back to the kindergarten, and start learning a new discipline as undergraduates do. We must learn to discover those parts of other disciplines that are essential and relevant to our object of study. Because of our inherent limitations (complexity..) we are doomed to neglect and ignore a lot of work done within other disciplines and even within our own. C'est la vie. I agree with Mr. Cockton that by reading some AI work one gets the impression that history begun just around the production of the paper: no references to prior work and to past philosophical and psychological treatments of the same issues. But going the other extreme, by adopting the scholar (and sometimes almost snobbish) tradition to the modern cognitive sciences is ridiculous too. Does a physicist or a chemist need to give references to pre-Newtonian works, to astrology or alchemistry? (I'm not speaking of the historian or philosopher of science). I got the impression that Mr. Cockton views informaticians and mathematicians in a rather stereotyped way: technocrats, misantropes that can only deal with machines, persons that want to put the lively world into their cold formulae and programs, individuals who are insensitive to the arts and to human-human interaction. All this might be partially true with respect to a certain fraction, but to generalize to the whole community is like saying that humanists are nothing but a bunch of guys, incapable of clear and systematic thinking, who use the richness and ambiguity of natural language in order to hide their either self-evident or vacuouss and meaningless ideas. I don't want to continue this local-patriotic type of propaganda, but one can fill several screens with similar deficiencies of the current traditions in the humanities. The applicability of such descriptions to any fraction of the ongoing work in the humanities, still does not justify a claim such as "What Can We Learn from (say) Sociology?". To conclude, I think that a good cognitive scientist can learn A LOT from mathematics and computers. A humanist may still do important work in spite of his mathematical ignorance, but I suspect that in some fields this will become harder and harder. Oded Maler Dept. of Applied Mathematics Weizmann Institute Rehovot 76100 Israel oded@wisdom.bitnet