This week, I've had the time to delve into my math studies in earnest. It was a little rough getting back into it as there had been an almost year-long hiatus, but once I reacquainted myself with it, I remembered why I wanted to do it in the first place: it's fun.
Part of what made this week's math (nth-Order Linear Homogeneous Differential Equations with Constant Coefficients, in case you were wondering) enjoyable was...factoring. You know how everyone complains about the quadratic formula, i.e.
x= (-b +/- (b^2 - 4ac)^1/2)/2a ?
After playing with 6th order equations and trying to factor them, the quadratic formula looks like a relative luxury (which of course is only available for 2nd order equations). It will not help you (at first) with something like:
x^6-5x^4+16x^3+36x^2-16x-32=0
So you've got to go in and play with groupings, guess at what value of x might make the equation zero out, and you're going to go down a couple of rabbit holes for a little bit until you do, finally, factor down to a quadratic equation, which is going to be a necessity when you find yourself dealing with complex (a combination of real and imaginary) numbers. And it's tedious, but then you remember that it is the tedium that makes it fun. At no point did I wish that there was an equation similar to the quadratic for, say, 4th-level equations.
This kind of work hit a sweet spot for me: it required me to pull on skills I already have but use them in a different way, but wasn't so unfamiliar that I could only touch the perimeter of the problem. It was solvable, but it was a challenge, and it's exactly the kind of thing I'm happy to lose myself in for a couple of hours. (But as I told my husband several times, really, don't worry, I can stop any time I want.)
This is work that I find enjoyable, in no small part because I don't have a deadline attached to it, except what I assign to myself. I'm not getting paid to do it by someone who wants me to solve thousands of these equations in a day. I don't have to be productive, I don't have to be efficient; I am doing it for its own sake. I am doing it because it's fun, and making the work go faster would not make it more fun, but less.
This freedom followed me into Korean language study as well. (Yes, I'm using Duolingo right now, just like everyone else.) I kick myself for what I don't know and always get upset when I don't have something memorized, or I have it memorized for the wrong reason. It's so hard for me to Do It Right, and this is probably the primary reason why I have shied away from formal language study my entire life.
But yesterday as I was playing with conjugations and reminding myself of vocabulary, completely not the way you're supposed to, I had a little epiphany: I was also having fun playing with the language, and even if that owl and its little mob of animated characters didn't approve, I was also, bit by bit, learning something. I might not ever be fluent, and I might always need subtitles on K-dramas and K-movies, but oh well. I can play with words for their own sake--just as I can play with numbers for their own sake--and it's okay if I don't "master" it. I can learn for its own sake--and seriously, what parlor tricks would anyone want to see me perform with math or Korean at this point anyway?
For many things, there is no correct way; in many cases, there are multiple means by which we can achieve a goal--but maybe a limited number of them will we enjoy. It bothers me now to think of all the years I didn't play with certain subjects because I wasn't going to do it Just So, causing my very brain to miss out on activity that can keep it healthy, and my soul (if I have one) to miss out on things that could make it soar. Well...ugh.
I'll let people with more time on their hands engage in pedagogical debates; I've got some math, Korean, and chemistry to get to.
Deb in the City
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