PAIGI: Math, And How To Know What You Don’t Know

Blog Note: This might not seem completely all together, but I wanted to have this post out before the weekend and I didn’t want a half-finished draft to just disappear from view. I’m dealing with losing the family pet tonight so some things aren’t going to be smoothed out until later. My apologies for that.

This is in response to the Big Think video included below, which is less than four minutes long and is presented by Po-Shen Loh, associate professor of mathematics at Carnegie Mellon University.

Professor Loh starts out by saying, “I think that everyone in the world could be a math person if they wanted to,” which to my ears is a powerful statement. It is a statement that I want to believe in, because I am not a math person. I want to be one, but I currently am not one. And that is a problem.

Here’s the thing about physics: it’s really just a form of applied mathematics. It uses the foundations of math and turns it into visual theory that we can test and experiment with and form new ideas from. But that still doesn’t change the fact that to get physics, you have to, in one sense or another, get math.

(It’s the same, to a different extent, with math and computer programming, which is something I’ve been getting into recently, but that is quite the kettle of fish and something that can be addressed at another time.)

So the big point that Professor Loh makes during his video is that the reason people can’t just jump into math and learn it as they do history is because of a lack of access points. Where exactly do you start? Maybe that depends on how much math you really want to learn, and what kind, although as Loh points out, it’s all part of a chain, and to build the chain, you have to start with the first link. So what is the first link? Pre-algebra? Calculus? Elementary logic? Do we start high or low, concept-wise?

I would argue that history is just as complex a link system of learning as maths and science is, but again, that’s for another day.

So the question you have to ask yourself before jumping into the nearest access point is this: what do I not know? Ironically, I couldn’t figure out what I didn’t know until I started studying in all earnest. It’s only after I started going through my college physics textbook that I realized my maths background was lacking to the point that I was having issues understanding basic formulas about force and motion, all because I had stopped formally learning at the college algebra level and hadn’t gone back for almost five years.

I think Professor Loh would then agree with me: you won’t learn anything until you open yourself up to the possibility that there are things you will need to learn in addition to the thing you originally set out to conquer first. I won’t be able to learn physics until I review my algebra and actually (ugh!) learn calculus. The same might be for you, albeit for different concepts.

The important part is that we see how one field connects to another field in what Loh described as a series of links and what I’d describe as a complex series of webs, strands of disciplines crisscrossing through one another that eventually make something cohesive and strong and beautiful.

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