What I have to share today is a simple idea that I’ve found really motivating. When I feel like I’m stuck in a loop of choices I regret, each leading to the next in a vicious cycle, I remind myself that every vicious cycle can also be a virtuous cycle. For example, if I don’t … More Every vicious cycle is also a virtuous cycle
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, … More “A and B” is equivalent to “B and A”, and the order matters
“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 … More Binary compression of continuous data
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 … More Maximal matching: What to do when?
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 … More Narratives Add
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 … More Writing an academic paper with Scrum
I’ve been helping put together some materials for a new class we’re tentatively calling “Math and Public Life”, organized around ten or so concepts from higher mathematics and how they relate to the way we think about life and each other. One of the themes I’m hoping to show is that often as our understanding … More Better than binary: four kinds of false dichotomy
For a future blog post, I’ve been thinking about how sometimes, when we have two alternatives, one is really a special or “limiting” case of the other, the way a square is just a special case of rectangle. I’m still working on that post, but meanwhile I’ve been distracted by thinking about other shapes that … More A Quadrilateral Venn Diagram
A frequent reader of this blog sent me a link to this video on Facebook, of a side-by-side comparison between a traditional method for doing multidigit multiplication (which is over very quickly) and a new “grid” method (which takes a long time to explain): She wanted to know why anyone would use the long, drawn-out … More New Math vs Old Math
A recent Washington Post article has the title “When a danger is growing exponentially, everything looks fine until it doesn’t.” The article talks about how suddenly exponential growth seems to go from vanishingly tiny to passing a major threshold. This made me wonder if there is some natural moment in time at which we can … More Does an exponential curve have a corner?