Writing and logic
I haven’t been writing. I’m applying to graduate school, to study something related but different from what I’ve worked on all these years, and between reading and talking to people and researching programs in psychology of language, psycholinguistics, etc, it’s consuming most of my time and energy. It’s very exciting though, because no amount of reading and talking to people and researching programs has made me any less convinced that this is really what I want to do. As someone who’s experienced numerous seeming breakthroughs about What I Want To Be When I Grow Up that only held up for a few hours or days or weeks, I find this incredibly reassuring.
A couple days ago, I was making a vague attempt to study for the GRE, and the prep book I was using included a reminder in the math section that anything raised to the power of 0 is 1 (x^0=1). Of course, this is something I learned in middle school and used in many subsequent math classes, but I realized I didn’t actually know why the answer is always 1. The GRE study book didn’t explain it, and I don’t think any of my teachers ever explained it either, which was a big problem in my entire public school math education. Math, even relatively easy math like algebra and geometry, was often presented as a set of esoteric formulas to memorize, not as a rational system we the students could actually understand. We were very rarely required to prove the formulas we learned, just to spit them back out on the exam.
So I texted Mitsu to ask why anything to the 0 is 1. And he called me back, from his car, where he was driving somewhere with Sue, and both of them tried to explain it to me.
“What’s x-squared times x-to-the-third?” Mitsu asked.
“x-to-the-fifth.” I said
“Right,” he said. And then he tried to explain why that same rule of addition of exponents meant that x-to-the-0 had to be 1, but I didn’t understand what he was saying. Sue tried too, but I still wasn’t getting it, and finally Mitsu just said, “Write this down.”
So I got a pen, and he dictated the equation to me: x^(a+0)=x^a*x^0.
“Oh!” I said, looking at what I’d just written on the corner of my GRE workbook, “I get it now!”
The exact same words I hadn’t been able to understand over the phone, when written out in front of me, seemed totally clear.
“Text me if you have any more math questions,” he said.
Yesterday, I read this in an essay by George Miller, in the book Language by Ear and by Eye: The Relationships between Speech and Reading (which is actually the proceedings from a conference held in 1971):
“The written proposition is a tangible representation of an act of thought. It is a physical thing, an object, and it can be reacted to as any other object can. Thus writing made it possible to react to one’s own thoughts as if they were objects, so the act of thought became itself a subject for further thought. Thus extended abstraction became possible, and one of the brilliant abstractions recognized by the Greeks concerned the form of valid arguments. And so, out of writing, was logic born.”