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July 20, 2009

how to spell heuristics

Posted in: behaviour,coaching and teaching,life the universe and everything

The idea of the egg and spoon race was, I’m guessing, to teach children balance, poise and concentration versus speed. Handicap all participants with a brittle object so that they develop a skill other than moving fast; break the egg and, as the computer says, Game Over. Heuristically speaking, slow and steady wins the race.

But various concerns, such as the risk of salmonella, forced the real egg in the egg-and-spoon race to withdraw. Its place was taken by the hard-boiled, ceramic or wooden egg, even the surrogate potato or stone. Casting notions of fragility aside, winning now depends on the participant navigating the course fastest with only the closest approximation to following the rules whilst under observation: a very different competition, more akin to modern banking.

Perhaps educationalists should think twice (another heuristic?) before deciding to dilute an educational activity to the point where its original purpose is lost. There may be another post on this subject in which we will investigate together a new sports day phenomenon: the synthetic sack race, where you find that the winner, in a surprise turn of events, is your local supermarket.

Back in the classroom, sheltering from the rain, other rules of thumb are sitting in the corner with the dunce’s hat on.  Michael Quinion, who runs the site and email list World Wide Words and has just published Why is Q Always Followed by U?: Word-Perfect Answers to the Most-Asked Questions About Language, points to a recent document sent to all primary schools in which the government is now recommending that the spelling rule “i before e except after c” no longer be taught because it doesn’t work. Quinion takes exception for pragmatic reasons, rather than bemoaning a fall in standards as the Opposition has. He says that, while not universal, it is a small, useful aid on the journey to good spelling. In fact, he notes from the document itself that there is a refined definition of the rule that delivers even fewer exceptions: “i before e except after c when the sound is ee”. The point is that the rule is approximate, and there is a subsidiary learning process in absorbing the exceptions to the rule.

I’ll take Quinion’s word for it on its value in spelling: it helped me. But there may be another reason not to drop so readily a rule of thumb that has proven its worth to so many generations of children, whether you are in the business of advocating spelling reform or not. The teaching to children of how to apply rules of thumb may itself be a useful pedagogical exercise for our modern times, and perhaps is even a first order imperative; the kids would be better equipped to face a complex future than we turned out to be. If I have this right, rules of thumb can work very well for those who will never master quantitative methods. Moreover, rules of thumb can operate as an antidote for those whose mastery of the quantitative, or dependence on the technological, makes them slaves to the same; something liable to get them, and the rest of us, into trouble.

Maybe schools are doing this anyway, and it’s just that I’m not seeing it yet. My gut feeling is that they are not.

Well, even from the giddiest of academic heights there does seem to be a problem according heuristics the respect they deserve. This is what Dan Goldstein at Decision Science News wrote recently:-

All smart statisticians use rules of thumb. DSN has noticed that as soon as one statistician codifies or pronounces a rule of thumb, smart alecs come along with special cases that violate the rule thereby “proving” the rule and the person who articulated it “wrong”. (Smart alecs love to pretend that those who impart rules of thumb are so dumb as to believe that the rules work in all circumstances).

This leads me, if not you, back to Quinion, and an entry in his earlier book Port Out, Starboard Home: And Other Language Myths on the subject of the phrase “the exception that proves the rule,” a phrase often uttered by smart alecs in the corollary to Dan’s example i.e. when they themselves might have been otherwise proved wrong. Quinion shows how this is a corruption of its original meaning, wrapped as it is in heuristic value.  The phrase really comes from a medieval Latin legal principle:-

exceptio probat regulam in casibus non exceptis

Which Quinion translates for me as:-

the exception confirms the rule in the cases not excepted

In practice, what this means is that when you see a sign “Parking prohibited on Saturdays” you are seeing an exception to a rule which can be inferred as “parking is allowed at all other times”.

In the meantime, I note that the heuristics literature has always had its skeptics:-

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