Mathochism: Types of reasoning
One woman’s attempt to revisit the math that plagued her in school. But can determination make up for 25 years of math neglect?
My second geometry class was yesterday, and the professor continues to impress me. I have yet to come up with a nickname for him — doing something with the fact that he’s Russian is tempting, but unfortunately, that is a language I don’t speak, though I have wanted to learn for years.
Anyway, we continued to study the foundations of geometry, and I realized I still didn’t quite understand the difference between inductive and deductive reasoning. So I asked him, and he explained it to me by saying that, in his experience, teaching more than 45 students at a time is untenable. His coming to that conclusion, he added, was an example of inductive reasoning, which is based on personal experience or experimentation.
However, if he had made that decision using numerous other people’s experiences, as well as the general assumption by the educational establishment that smaller class sizes lead to better student and teacher performance, then he was using deductive reasoning.
(I finally understand why so many Internet arguments end with people saying: “Your personal experience doesn’t make something a fact!” They’re clearly touting the superiority of deductive over inductive reasoning. At the same time, though, how many women have to say they hate being ordered to smile by strangers until we establish that as a fact?)
Deductive reasoning is the preferred form of reasoning for geometry, and I understand that, but I disagree that inductive reasoning is not useful and that intuitive reasoning is useless.
Let me amend that: I think people often think they’re using intuitive reasoning when in fact they are using inductive or even deductive reasoning. For example, we talk about getting a “gut feeling” when we meet someone, but a lot of the time, what we’re really doing is reading micro-expressions or analyzing actions that have proven to us in the past that the person who does this is usually pleasant or unpleasant.
Gavin de Becker talks about this in his book “The Gift of Fear.” He describes how a woman escaped a killer who repeatedly told her, very calmly, that he wasn’t going to hurt her, that he was just going to rob her. She noticed, without really registering it consciously, that his actions contradicted his words, and by doing the opposite of what he said — don’t move — she survived.
That is not intuitive thinking, which is not predicated on anything logical, but closer to inductive and deductive reasoning. And, of course, she was right.
At any rate, my geometry instructor doesn’t pooh-pooh intuitive or inductive reasoning. “We use it every day,” he told us. Using it in class, though, might be a mistake. Or at least, that is what I have deduced so far.
All text copyrighted by A.K. Whitney, and cannot be used without permission.