Every vicious cycle is also a virtuous cycle
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 […]
“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 […]
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 […]
Better than binary: four kinds of false dichotomy
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 […]
A Quadrilateral Venn Diagram
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 […]
New Math vs Old Math
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 […]
Does an exponential curve have a corner?
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 […]