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Combinatorial Explosion
January 6, 2009 by Anonymous, 45 weeks 5 days ago
Comment id: 33640
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The problem that I see with Pinker's "Combinatorial Explosion" is that he is presupposing a computational method by which possibilities are being tested -- i.e. in some serial assessment: "the child is looking for correlations".
However, the "learning procedure" is not only distributional, but the processing is as well. Every sentence an infant hears is being processed by literally the same wetware which acts as both processor and storage. The child does not need to *look* for correlations as though pulling examples from some internal database and comparing them one-by-one. Incoming utterances are processed; the act of processing, alters the processor. Over time, correlations reinforce each other and fall out of the system by virtue of the process.
I see language learning as a process, something much more akin to a genetic algorithm, another distributed computational method. The "Traveling Salesman" becomes computationally intractable when approached serially because of combinatorial explosion; GAs solves it quite easily.
Pinker suffers from an overly 'digital CPU' concept of the brain (and language). Here's a 'great' Pinker quote:
“On the order of 40 million base pairs differ between chimpanzees and humans, and we see no reason to doubt that universal grammar would fit into these 10 megabytes with lots of room left over, especially if provisions for the elementary operations of a symbol-manipulation architecture are specified in the remaining 99% of the genome.†(Pinker and Bloom, 1990: 726)
Even in 1990, it was asinine to suggest any such quantification is possible and it betrays much about how Pinker believes DNA and brains function and how information in them is stored and processed. In reality brains and genomes do not store digital information, even though superficial similarities can be observed of a single neuron firing or of a single allele.
That being said, I don't disagree that there has to be innate structure. That's equally apparent; otherwise chimpanzees would be telling us about their days, their aspirations and their disappointments. However, that innateness is likely to be much more high level and structural than Pinker believes; and more likely derived from perception/action and cognitive salience than from specifying features and rules.