by bisby | 2025-04-20 03:40:59+00:00
Have you ever watched a video of a highly skilled tetris player? Where they fill the screen most of the way to the top and then suddenly they just combo the whole thing down and everything wraps up cleanly, and then they start fresh.

The feeling of "oh yeah, that was nice watching that mess turn into something clean and squared away" is where I get a lot of my joy from math.

But also, there are uses to math that you might be able to play with through every day, but you've never thought of those scenarios in a mathematical way.

I was walking today, and on the street there is a right angle turn. The inner portion of the turn is just a square right angle, but the outside of the turn is a radius. I started wondering to myself, if I want to be on the outside of the turn going into and exiting the turn, what would be different ways I could walk this, and what would the distance differences be.

Crossing directly across, to the inner corner and crossing directly across to the outer side again, would be 2w (for the width of the road w). Following the edge of the radius would (assuming perfectly circular), be 1/4 of a circle, so 1/42piw = 1/2 pi * w. The shortest route is a straight line, which would make a right triangle, so w^2 + w^2 = c^2, 2w^2 = c^2, sqrt(2) w = c

So crossing twice is 2w, following the edge is 1/2piw, and shortest path is sqrt(2)*w. Not super applicable, and I didn't need to do math to figure it out, but I was walking and bored, so I found joy in it. The fact that they all boil down to having w as a factor means I could figure out a nice ratio between all of them. And then I needed to mentally figure out what 1/2 pi was. 3.14/2 = 1.57... And I know that sqrt(2) is roughly 1.41 ish.

So now I know that crossing twice has a cost of 2, following the edge is 1.57, and direct line is 1.41. Following the edge is vaguely close enough to the ideal path to warrant not walking into the street to optimize the route, 1.57 / 1.41 is about ~110%. Whereas by defintion, a cost of 2 is going to be sqrt(2) times sqrt(2), so ~141% more than shortest path.

A few things to note here. First off, I'm aware that not everyone finds the same joy in doing simple mental math and thinking about problems mathematically even when there is no need to do it, but trying to think of things more minor trivial things mathematically may cause you to at least appreciate it more, which can grow into joy. And second, I wasn't doing any complicated math in my head. I just thought to myself "is it faster to cut to the inside corner and then cut back out... of course not, right?" and I was able to answer that definitively to myself. Did it matter? Was the answer probably obvious anyway? Probably, but I was able to _prove_ that. And I value facts. Finding joy in the simple things lets you build up more of a familiarity and view it more as a problem solving tool than a tedious thing to rote memorize.

A great way to build up math familiarity and see how other people find joy in mathematics would be to watch Numberphile videos on YouTube[0]. It's a bunch of mathematicians sharing things they find interesting about math. Some times are REAL hard to grasp, but some are just very interesting puzzles[1]. The puzzles don't always have clear immediate usefulness, but can often be described as "a mathematician wanted to know an answer, so they did some math to find out and prove something to themself."

Sorry, end of spiel.

tl;dr - find the joy in the simple things and use math as a tool to answer (even simple) questions to help highlight the usefulness.

0: https://www.youtube.com/channel/UCoxcjq-8xIDTYp3uz647V5A 1: https://youtu.be/ONdgXYEBihA