While Chomsky's attempt to formalize a grammar is wonderful, the probabilistic approach (based on weights) to language advocated by Norvig is, it seems, more close to what is going on inside the brain.
Brain does not perform recursive algebraic simplifications (which is, probably, the most beautiful abstraction humans have produced - fixed points, Y-Combinator, etc), it performs structure-based pattern matching - "it looks like a duck".
Natural selection, it seems, would select a crudest, good-enough model, full of cues, short-cuts and heuristics learned from environment, instead of evolving a beautiful, universal recursive meta-circular evaluator, which MIT guys are worshiping (what else there is to worship, but a beauty?!)
And, of course, mutually recursive processes (physical processes which could be abstracted out and formalized that way) are everywhere in biology. It just happen that language is a pattern matching, not an algebra, like everything else in the brain. Algebras, like numbers, does not exist outside our heads.)
Algebra and pattern matching are basically the same thing, aren't they? To find a solution to an algebraic problem, you pattern match on the problem structure and see what falls out. To solve a pattern matching problem, you perform algebraic transformations to isolate the pattern being matched.
>Algebras, like numbers, does not exist outside our heads
Models are called models because they are not the things they model. Anything that is a model is an approximation. This doesn't mean they don't exist outside our heads. If that were true, there wouldn't be any computers.
The meaning of the term pattern-matching here is "mechanical" rather than "mathematical". Think of shapes of the proteins in an enzime. Their structure defines behavior of an enzime, and only a molecule that match (with physical shape and electro-chemical properties) will do the thing.
Similarly, it seems, a higher level behavior is defined by physical structure of neurons, a highly-specialized circuitry evolved by the process of trial and error, which happen to be good-enough for its purpose. There is no algebra involved. It is a electo-mechanical massive-parallel machine.
> Algebra and pattern matching are basically the same thing
The difference is that pattern matching is done on a model of the world provided by words, instead of applying it directly to senses.
In reinforcement learning there is an approach to model the world first, then run RL on top of the model, because that would provide a way for the agent to imagine possible outcomes without the need to try them first in actuality. Model based RL is a refinement of direct RL and is essential for thinking.
Brain does not perform recursive algebraic simplifications (which is, probably, the most beautiful abstraction humans have produced - fixed points, Y-Combinator, etc), it performs structure-based pattern matching - "it looks like a duck".
Natural selection, it seems, would select a crudest, good-enough model, full of cues, short-cuts and heuristics learned from environment, instead of evolving a beautiful, universal recursive meta-circular evaluator, which MIT guys are worshiping (what else there is to worship, but a beauty?!)
And, of course, mutually recursive processes (physical processes which could be abstracted out and formalized that way) are everywhere in biology. It just happen that language is a pattern matching, not an algebra, like everything else in the brain. Algebras, like numbers, does not exist outside our heads.)