“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, … More “A and B” is equivalent to “B and A”, and the order matters

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

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