These sidewalk sines make this walking path in Santa Monica look almost grooved. I definitely had recurring moments of disorientation as I walked along!
Resources Teaching
Why Winning in Rock-Paper-Scissors (and in Life) Isn’t Everything — Quanta Magazine
My latest column for Quanta Magazine explores the concept of a Nash equilibrium in the simple game of Rock-Paper-Scissors.
A Nash equilibrium occurs in a game when each player employs a strategy that can’t be improved upon. That is, in a Nash equilibrium, no player can improve their individual outcome by changing their strategies. John Nash proved that in all games involving a finite number of players and a finite number of options, a Nash equilibrium must exist. This result revolutionized game theory and economics, and earned Nash the Nobel Prize in 1994.
My column explores the nature of Nash equlibria in the context of a game everyone is familiar with: Rock-Paper-Scissors.
So, what does a Nash equilibrium look like in Rock-Paper-Scissors? Let’s model the situation with you (Player A) and your opponent (Player B) playing the game over and over. Each round, the winner earns a point, the loser loses a point, and ties count as zero.
Now, suppose Player B adopts the (silly) strategy of choosing Paper every turn. After a few rounds of winning, losing, and tying, you are likely to notice the pattern and adopt a winning counterstrategy by choosing Scissors every turn. Let’s call this strategy profile (Scissors, Paper). If every round unfolds as Scissors vs. Paper, you’ll slice your way to a perfect record.
The guaranteed existence of Nash equilibria dramatically impacts the way we study economic incentives, treaty negotiations, network analysis, and many other things. However, a recent paper suggests that even though Nash equilibria must exist, it may be unwise to assume players will always find them! You can learn more by reading the full article at Quanta Magazine.
Resources
Quantized Academy Columns Now Featured in WIRED
I’m excited to announce that my column for Quanta Magazine, Quantized Academy, is also being featured in WIRED magazine.
You can find my pieces on pentagonal tilings, symmetry and group theory, and gerrymandering there. And there was actually a brief window where my column on the efficiency gap was among the most popular articles on WIRED, which was a cool surprise!
You can find all my Quantized Academy articles at Quanta Magazine, and those that appear on WIRED can be found here.
Resources
MfA and Story Collider
I am excited to be taking part in a Story Collider event this April!
The Story Collider’s mission is to bring true, personal stories about science to life through their live storytelling shows, and Math for America is partnering with the Story Collider to create an evening of teacher storytelling.
I’ll be joining five other MfA teachers to tell our stories about our classrooms, professional lives, and journeys through teaching. This is yet another example of the incredible professional opportunities that Math for America creates for its teachers to learn, to lead, and to be heard.
You can find out more about the Story Collider here, including links to their podcasts and a schedule of upcoming events.
Related Posts
Teaching
What Will They Be Doing?
When planning a lesson, start with the question “What will the students be doing?”
I received this piece of advice as a pre-service teacher and it has stuck with me my entire career.
Before you get too excited, my answer to this question is usually pretty straightforward; most often, it’s “Working on a problem I’ve shared” or “Thinking about a question I’ve asked“. But making this activity explicit in the planning process reminds me to focus on those things that matter most in my lesson: the specific questions I want to ask and the specific problems I want students to engage with.
Asking myself this simple question also helps keep the focus of my planning where it belongs. Instead of starting from “How do I understand this?”, I start from “How will my students come to understand this?” This is a small shift that makes a big difference.