Quite a lot of work is being produced by cognitive scientists about metaphor – what they are -what they do, how they shape thought – and I find it all interesting and provocative. The way in which metaphor shapes the way we see the world is the subject of James Geary’s book I Is an Other. Metaphor, as it is now understood, is said to transfer physical experience to psychological experience. Some quick writing from Geary can be found on his blog.
Metaphor has also been used to account for the complex weave of ideas in mathematics, as seen in the book Where Mathematics Comes From by George Lakoff and Raphael Nunez. It’s a way to see the purely conceptual being drawn out of the physical. A useful critique of the book appeared in 2001 in the Notices of the AMS.
But I can’t help but think that, given the ubiquitousness of metaphor in our experience, there is something of a ‘chicken or the egg’ problem here. Which comes first, the concept warmth or all warm things in our experience? The answer may not be as obvious as it seems. Abstraction does happen at the cellular level. There are specialized brain cells that respond preferentially to straight lines at a particular angle. There are cells that synthesize multiple views of an object into a “view-invariant” image. It is possible that the brain and the nervous system are primarily concept driven, or that their functions rely heavily on what we would think of as form rather than content, all being played out before anything even hits our awareness. This would certainly contribute to a discussion of what mathematicians find, when they find it ‘intuitively.’
Geary also brought up Watson, the Jeopardy champion, in one of his blogs.
What does this have to do with metaphor? Well, the kinds of things Watson and his human opponents will be parsing tomorrow are the same kinds of things that go into metaphors: loose associations, punning relationships, sidelong and sidereal correlations. Until now, computers have not been very good at making these kinds of intuitive connections, as the wealth of useless information thrown up by the simplest Google search demonstrates. If Watson can do it, though, that is one giant leap for computerkind…
But a recent post on Mashable gives us some inside info from a journalist who had access to Watson’s development. I grabbed this piece:
Q: Can you give us an example of a concept that was deceptively hard to teach Watson — something the researchers assumed would be straightforward but ended up being a challenge for the AI?
A: You mentioned the killer word in your question: concept. Watson and other machines don’t master concepts. A four-year-old child somehow figures out that a chihuahua and a great dane are both dogs. Conceptually, the two very different animals have something in common. Computers have to be taught such things. It’s a laborious process. (Watson, I should point out, hasn’t been taught such facts and relationships. It comes up with its responses by studying and analyzing data, most of it written English.)
While we may only be able to approximate the origin of what we call concept with our conscious minds, I’m sure it is a useful enterprise. In defense of the idea that concept is not derived, I’ll defer again to Poincare. This is from his discussion of Space and Geometry in his Science and Hypothesis:
It is seen that experiment plays a considerable role in the genesis of geometry; but it would be a mistake to conclude from that that geometry is, even in part, an experimental science. If it were experimental, it would only be approximative and provisory. And what a rough approximation it would be! Geometry would be only the study of the movements of solid bodies; but, in reality, it is not concerned with natural solids: its object is certain ideal solids, absolutely invariable, which are but a greatly simplified and very remote image of them. The concept of these ideal bodies is entirely mental, and experiment is but the opportunity which enables us to reach the idea.
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