Negativity

Sean Carroll excerpts an anecdote from a memoir of literary critic Lorna Sage:

Hanmer school left its mark on my mental life, though. For instance, one day in a grammar school maths lesson I got into a crying jag over the notion of minus numbers. Minus one threw out my universe, it couldn’t exist, I couldn’t understand it. This, I realised tearfully, under coaxing from an amused (and mildly amazed) teacher, was because I thought numbers were things. In fact, cabbages. We’d been taught in Miss Myra’s class to do addition and subtraction by imagining more cabbages and fewer cabbages. Every time I did mental arithmetic I was juggling ghostly vegetables in my head. And when I tried to think of minus one I was trying to imagine an anti-cabbage, an anti-matter cabbage, which was as hard as conceiving of an alternative universe.

There follows a discussion of how difficult and remarkable the human ability to abstract numbers from cabbages really is. I like commenter Jennifer's notion that people who are disturbed when they encounter a new idea like negative numbers are probably experiencing it most fully. Had Sage been learning arithmetic as a meaningless rote exercise, as too many people do, she wouldn't have blinked.

But I mostly quoted this because I remember having precisely the opposite crying jag. My father, who had a degree in mathematics, taught me about negative numbers one evening when I had been learning about subtraction in school. He told me that you got a negative number when you subtracted a larger number from a smaller one. My teacher, however, continued to insist that you simply couldn't subtract a larger number from a smaller one, and I came home in tears, distraught that the teacher was lying.

In hindsight it was my first encounter with the notion of a discussion being restricted to a universe of discourse, and with the existence of what Terry Pratchett calls "lies-to-children," deliberate oversimplifications made for a pedagogical purpose. Ever since then I've struggled with lies-to-children when trying to educate people; I don't like them and never have, but it seems impossible to do away with them entirely without overwhelming the student with an avalanche of quibbles and qualifications. When I was working as a teaching assistant for Melissa Franklin, she called me "Mr. Second-Order" because I kept bringing up exceptions to everything in class that threatened to derail the discussion.

Feynman at the blackboard

Via The Poor Man: Streaming video of Richard Feynman (RealVideo) giving the 1979 lectures in New Zealand that were the basis for his book QED: The Strange Theory of Light and Matter.

I never had the opportunity to hear him talk, and it's interesting to see the way he fumbles around at the beginning of a lecture before something seems to engage and he's off. I know the feeling. I think he described that somewhere as "the physics taking over".