K Klingensmith's Friday post reminded me of one of the more useful heuristic concepts in my little arsenal of ideas: Ted's Law.

Ted's Law was invented by my friend "Ted" when he was about 10 years old. His class was studying mathematical powers (you know, where 10³ equals 10 x 10 x 10 equals 1000), and Ted came up with a way of explaining that rule in plain English for his classmates. His formulation, which I can't quite remember, was immortalized on a piece of construction paper that hung on the wall of his classroom, and later found its way into his attic (now, since Ted and Ted's mom are very good about not throwing things away, it's probably in the basement of his parents' house).

This is kind of what it looked like:

click to enlarge

"The number on the top right is the number of times the number on the bottom left is multiplied by itself": anyone who's gone through school has at some point internalized this logic, but the reason Ted's Law merited being called a law was that in some sense Ted discovered it for his peer group.

Like K's pseudo-inventions, about which "there were enough clues in the world, enough of the components of these incipient objects already in use, that the 'invention' was less an invention than the vision of a slightly modified existing object or combination of objects," Ted's Law is the putting together in clear language--the invention, perhaps, of a representation--of something everyone already knows (and which had, presumably, been put together in different but less felicitously clear language by Ted's teacher earlier that same day).

This sort of thing happens all the time, and not just in school. Everyone knows that if you take your time doing something you're less likely to have to go back later and fix your mistakes. But "a stitch in time saves nine" not only gets the job done faster, it also saves you the time thinking up a way to say that same thing yourself (which leaves more time for stitching carefully). And figuring out a way to say something well is often a way of really coming to understand it--anyone who's ever taught anyone anything knows that teaching is a great force for clarity, because you have to understand things well enough to explain them to someone who is not you.

One of the poignant things about being a teacher, however, is watching students go through some version of the discovery that led, those many years ago, to Ted's Law: coming up with something to say about a literary text that is already, if the text is canonical, part of a longstanding critical tradition. What makes such moments painful for me is the difference between the student's genuine excitement at discovery and the knowledge that I have (and the student does not) that what looks like a general discovery is really just a local one: Ted's Law. I usually don't know what to do when such a thing happens: does telling someone that their idea has already been had ruin the sense of power and pleasure they get from coming up with something that was new to them? Should I have been clearing space, instead, on my classroom walls?

I suppose those are two different models of what teaching should do. A pedagogy insensitive to the local thrill of discovery would simply rush its students through a series of lessons designed to get them to the point where they might discover something genuinely new (though of course that process takes, for most fields of knowledge, 18 years of school, 4 years of college, and 5 to 10 more of graduate school). Whereas a pedagogy designed to teach students how to learn would allow them space to make their own discoveries, would in some sense try to establish the right starting conditions from which a series of false discoveries could be made (here are a few pieces of information: deduce a theory from their conjunction; or, here is a set of rules: explain them clearly; or, here is a text: describe its workings).

I imagine most people prefer the second model--it's got more of a "teach a man to fish" feel to it. But of course the second model always depends on the first--you have to be given bases from which to make your discoveries, and every discovery depends on a wealth of material that must be assumed in order to make the jump possible. What a culture shares, more than anything, is a set of bases that establish the possible directions of its discoveries and inventions, a common framework that means that really good inventions (the internet, the CD-Rom) seem to emerge from a number of places all at once, not so much the product of a single brilliant leap, as K said on Friday, as the result of where things were going for everyone.

And at the same time--here is the mystery--not everyone comes up with everything. Of all the people who invented CD-Roms or the phrase "what's the haps," only one of them followed through on the idea and patented it, or used it in a song. Invention--real invention, the kind that results in new products or new laws or new readings--requires, it seems, more than an active imagination: somewhere beyond the realm of thought, every invention is sustained by a whole host of factors that move it from the mind to the real: money, surely; a compatible skillset, or access to someone who has one; enough faith in the idea to do the work of convincing others to build it, write it down, or pay you to do those things; 500 a year and a room of your own; a sheet or two of construction paper.