With a full decade of teaching under my belt, I thought I had a handle on saying things out loud. I’ve tried to capture students by bringing the strange history of mathematicians to liven up even the driest of lessons. For the last few years, I’ve been presenting game theory ideas to packed houses at conventions across the country, and I’ve even performed with Gosh Darn Fiasco at even more. I mean, I’ve sat down at tables for years playing RPGs with total strangers and bringing to life weird and fantastical stories for hours at a time. I thought I had this.
I was not prepared to stand up and tell a story all about myself for Story Collider.
I really thought I was. I’d scripted out the entire ten minute story. I’d faithfully memorized the text and really annoyed my fellow teachers by closing my door and reciting between classes. But when it came down to it, I just wasn’t ready for the emotion that would come from talking about my own personal stories. By being open and honest about a pretty ridiculous time in my life, I felt a real sense of warmth and worth. The other speakers were also smart and charming and wonderful. Being part of Story Collider was an incredible experience, which was certainly helped by the fact that I made it all about game theory.
It’s difficult for me to think back to a time when my world did not revolve around the topics of mathematics and education. I’ve been a teacher for twelve years, so by this point, I feel like I confidently state that I have heard every single stereotypical story about math experiences. I’ve worked in schools specifically to help kids who have troubles in math. I’ve spoken to their parents. And their friends. And my friends. And complete strangers, because as I have learned, there are few things that unite us as a people quite as much the dislike of mathematics, either algebra or geometry, depending on the person.
To break down the story, it’s often a deep and abiding love and/or hatred for a specific textbook or a lesson or a teacher, with a few variations. I’ve made bingo cards just for the first conversation I have with anyone after they learn that I am a math teacher. Surprise, everyone wins.
I’m here to say that, after years watching stories about school where the math teacher is a villain, I get it. We taught you the bad math. Please don’t tell anyone I called it the bad math. We’re trained to teach a very binary kind of math which must be taught in a specific sequence and is always right or wrong. It’s easy to teach and assign homework and test and grade. But it is hardly the math of our everyday lives.
For example, though I didn’t know it at the time, I had my first real mathematical breakthrough in middle school.
I grew up on the mean streets of Portland, Oregon. But then we packed up and moved to the suburbs. And then again out to the country.
So imagine this ten year old future math teacher, showing up in a new school and trying really hard to make a good first impression like he’s a cool kid from the city. Turns out, my first day was also school picture day and I doubt I had ever looked more pathetic. I have since, sure, but this may have been the first time I truly felt pathetic. My dad had passed away at the start of the summer, and I was trapped in this new terrible school without any friends at all. I was like a little sadness sponge, and if you pushed or squeezed me too much, a torrent of tears would just burst out. Which was often tested by my new classmates while playing football at recess.
And that was the start of my year as The Crying Kid. Every school seems to have one, and once upon a time, it was me.
Things got better over time, but then, in seventh grade, I found myself at a middle school dance. Even now, I feel a little ripple in my stomach just thinking about it. But these were the moments that could supposedly help a weird kid make friends, or at least that’s what my mom kept telling me as she pushed me out the door of our Jeep Cherokee.
I have no idea how to dance, so I find myself wandering the school. I enter a long, empty hallway, getting about halfway down when I see a familiar face come around the corner. She smiles, waves, and says “Hello.”
Here’s where my math brain kicked in for the first time. A basic social interaction.
Most likely, she was simply expecting me to respond in a normal way. You know, like a human. And yet, I wondered, what if she wasn’t talking to me? Sure, we were the only two people in the hallway, but consider this. Earlier, the hallway had zero people. Then there was just me. Now there were two people. Clearly, it was just as likely that a third person had stepped into the hall behind me because that’s how math works.
Does this guy even have a Fields Medal?
As the most famous mathematician in the world once said, “Life finds a way.” And yeah, it’s a little weird that the most famous mathematician in the world is Jeff Goldblum in Jurassic Park.
Anyway, there I was, trapped in the middle of the hallway faced with a decision about whether to respond to a polite Hello with a Hello of my own. Perchance a Hi.
Very quickly, I built up a mental construct which could weigh the consequences of my possible choices in order to determine the best possible outcome. Also, like a human.
Overall, the best outcome is what you’d expect. Two young people being cautiously friendly. But if she was actually talking to someone else, then I was very eager to avoid the most embarrassing option which would be to give an enthusiastic HEYYYY…
So, if she were talking to someone else, my best outcome would be to assume that and stay quiet.
Taking a situation like this and applying a construct called a utility matrix to gauge decisions is a branch of mathematics called Game Theory. I love game theory! It was designed as a way to understand economics, but it can really be applied to any kind of conflict. By simulating an opposed set of actions, we can develop strategies that lead all players, or at least all friendly players, to their greatest reward.
One possible outcome of this hallway encounter was a happy, normal, human conversation. A solid outcome for a tortuous middle school dance. The second possibility is the one I feared the most; as I replied with hello, two people would start to laugh at me for thinking anyone might ever want to talk to me. I would live my life in shame, and my only friends would be the animals on our farm. We’d wander the forest together, solving forest crimes, whatever those might be.
The third outcome is the one I expected, where I’d be silent, and those two people would go be happy together. I would be ignored, but safe.
Of course what actually happened was the fourth option. Instead of replying, I turned around to see who she could actually be talking to, assuming that it wasn’t me. In that moment, I heard a noise that is clearly weighing on me almost three decades later. She said “Awwww. I was saying hi to you!”
The good news is that this meant that my mother was right and this dance might be some kind of transition from being the Crying Kid to maybe more like who I was going to be as a person.
Years later, I began studying Game Theory, and realized just how many of my personal interactions could have been simulated and analyzed.
One major game theory interaction is called Chicken. Traditionally, it’s Rebel Without A Cause, racing cars towards the edge of the cliff, each racer unwilling to be the chicken and swerve away first. However, if neither swerves away, they both die. And yet, the winning strategy is to continue towards the edge of the cliff! That’s wild to me. But since I’m not legally allowed to discuss my sordid cliff racing histories, let’s talk about my college roommates and our general disdain for common chores.
I don’t want to do my dishes, so I stack them by the sink. So does everyone else. We all know that the dish supply is limited, and we’ll soon be forced to eat our greasy delivery pizza right from the cardboard box. Eventually, Kim is going to call a house meeting and lay down some new rules, and I’m forced to nod and say sure, sure, I’ll do the dishes as long as everyone else around here pulls their weight too, and then Ryan is going to get those big wild eyes and demand an apology because he did the dishes last week and he will be damned before he does the dishes twice in a row, and soon enough everyone is way too mad to play Smash Brothers like we do every single night, or did before the dishes ruined our lives.
So I did some of the dishes. And then Ryan did some of the dishes. And then, we Smashed.
Anyway, that story is also the Cuban Missile Crisis.
Being able to relate a huge, global conflict to my college kitchen is what makes Game Theory so powerful. It’s about conflict, and humanity happens to be really, really good at conflict.
For example, I was once locked into an important conflict about llamas. We had a pair of them growing up, for important high-elevation backpacking reasons, but a fun moment happened right before my Senior Prom. My mom wanted me to take a picture standing in my tux, right next to Hobie the Wonder Llama. At the time, as one might imagine, I was not very excited about this particular photo shoot. I was worried that every single human in the world would laugh at me, and began to consider choosing my teenage dignity over my mom’s desires. On the other hand, my mom wanted us to work together to make something potentially amazing. But, she could have been wrong.
This is actually Mister Goodbar, but Hobie was always my favorite Wonder Llama.
So to break it down, I was worried that a large group experiment would fall through, and I was considering the option of backing out. This is a problem we call Stag Hunt. We can all play a fun game together, but if I take my ball and go home, at least I still have my ball while the rest of you have nothing.
Fortunately for me, when my mom has a plan, I try to cooperate. So now I have one of the greatest prom photos ever taken in a pasture in Oregon.
Looking back, I can’t help but wonder what would have happened if young me had been taught about game theory. What if I’d been taught to weigh the rewards and consequences of my choices and actually learn how to think in the moments before I act? It could have been transformative. Instead, I got an A in Pre-Algebra.
Let’s be honest, I got an A in every math class.
The best I can do these days is to help spread this knowledge to others because I want to make math relevant to our lives. And someday, I want to throw away those bingo cards as our experiences with math truly become something fun and personal and truly worth sharing in a positive way. It certainly isn’t just us weird kids and sadness sponges who need to think about conflict and choices.
Speaking of weird kids, my mom was right. The girl in the hallway and I did become friends. We ended up being dance partners and worked on the high school newspaper together, and she’s doing quite well today. I might even send her a copy of this story, after I complete a thorough analysis of the possible benefits and consequences, just like a real human.