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 … More Three tools for changing your mindset

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 … More How to hope

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 … More Narratives Add

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 … More Self-referential spam

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 … More Better than binary: four kinds of false dichotomy

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 … More New Math vs Old Math