“A and B” is equivalent to “B and A”, and the order matters
In math, I’m used to making no distinction between saying “A and B” and saying “B and A” — they each assert that both of the component statements are true. In fancy terms, we say that the conjunction “and” is commutative, like addition (a+b=b+a) and multiplication (ab = ba). Many mathematical operations are not commutative in general, […]
Binary compression of continuous data
“Which am I supposed to use: mean or median?” Early on in my stats classes, we talk about how to describe the distribution of a piece of numerical information — things like height, weight, age, income, and so on that can vary continuously. A good description should cover three aspects of the distribution: A measure […]
Maximal matching: What to do when?
My wife and I enjoy playing Wingspan, a beautiful strategy game about choosing birds to live in your bird sanctuary. This past week we played a few games together against the computer — she’s much better than I am, so I hoped to pick up some strategy tips from her for the next time we play against […]
Three tools for changing your mindset
One of my earliest posts here was about different meanings of “habit”: there are … … intentional habits, things you regularly choose to do, … automatic habits, things you do on autopilot, and … mindset habits, your default ways of thinking. Intentional and automatic habits look very similar — the difference is how much mental effort you […]
How to hope
Pessimism comes naturally to me. Choosing between optimism and pessimism is like asking whether I would rather be disappointed or pleasantly surprised; it just sounds safer to choose the latter. But over time, pessimism takes its toll on my mood and health, and I’ve been advised many times to be more hopeful. Until recently, I’ve had […]
Narratives Add
This year at Carleton I’ve gotten to teach one of my favorite parts of multivariable calculus, the multivariable chain rule. Despite its scary-sounding name, the multivariable chain rule seems to capture a fundamental principle about how the world works, a principle I call “narratives add.” I’ll walk you through how the multivariable chain rule works […]
Writing an academic paper with Scrum
Part of my job as an academic is to write up and share my research results with the rest of the mathematical community, but while I moderately enjoy writing, I don’t enjoy how long it takes me: I spend a lot of time rewriting whole sections to make a point slightly better, or having to […]
The game competitiveness spectrum
I really enjoy cooperative games: Pandemic, Forbidden Desert, and Hanabi are some of my favorites. But I remember realizing two related facts about competitive games: I’m happier when I’m able to benefit other players as I play, in a kind of semi-cooperative way, even if we’re really competing against each other. Some games definitely make […]
Self-referential spam
I have a contact page here on my website, which lets people get in touch with me without my having to make my email address public, and it’s come in handy several times—mostly for former students or readers of my academic papers who only have old contact info for me. It’s always attracted a little […]
Acceptance vs. “Loving what’s true”
To elide the distinction is to think that your only options are resignation and denial.