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Sunday, October 25, 2009

Social Interactions, Theory of Grammar, and Geometry of Debate

Related Link » The Third Culture, Chapter 9, Roger Schank, "Information Is Surprises"
“There was a rather acrimonious debate between [Roger Schank] and [Noam] Chomsky's followers in the 1970s. But a lot of that energy may have been wasted, because they were talking past each other. [...] This was unfortunate. Much of the debate between Chomsky and Schank is another case of the blind men and the elephant. They're asking different questions, so the answers they come up with aren't really contradictory. Chomsky, in my opinion, is right in saying that there's an autonomous mental organ for grammar and that a child can acquire grammar only if the basic design of the grammar of the world's languages is in some sense built in. Roger is right in that actual use of language, in conversation or understanding, involves a lot more than grammar — such as knowledge of how people interact with one another in typical situations — and that therefore to tell the whole story about how conversation works, you can't simply have a theory of grammar but you must embed it in a theory of knowledge about the world and social interactions.” [emphasis added]
— Steven Pinker, commenting on Schank's and Chomsky's acrimonious debates’
Related Link » You talkin' to me? To debate or not to debate, that is the question
“There are basically two kinds of debates, having distinct objectives: resolution or victory. And these two distinct types are orthogonal. Orthogonality, and its opposite parallelism, are geometric concepts; nevertheless, they can provide graphical insight for understanding some non-mathematical situations. In the issue under discussion, if we represent these two types of debate by a pair of normalized vectors then resolution would be perpendicular to victory, because these goals are completely at odds with one another, in the sense that neither participant can derive any value from a debate in which they have different objectives. The mathematical expression for such a condition is: the cross product of orthogonal unit vectors is another unit vector orthogonal to both original vectors (graphically demonstrating that the originals are completely at odds to one another), and their dot product is zero (demonstrating that the measure of their efficiency is nil). On the other hand, if both participants have the same objectives (either both victory or both resolution), the analogous mathematical situation is a pair of parallel unit vectors. Here we have a cross product of zero (the participants' objectives are not at odds but, rather, in complete harmony), and the dot product is magnitude one (the debate will be 100% efficient, since each participant will derive the maximum value for their efforts, either resolution for both, or the thrill of confrontational competition for both).”
— ‘TheBigHenry’
Steven Pinker seems inclined to believe that the Schank-Chomsky debate was wasted energy, but I think such a conclusion may be debatable. It all depends on what the objectives of both Schank and Chomsky were in their debate.

My sense is that their mutual animosity was such that mere victory was insufficient; they both wanted to demolish the other's position. In which case both of them derived the maximum value from their flame war — the thrill of confrontational debate was win-win.

Post #978 Social Interactions, Theory of Grammar, and Geometry of Debate

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