### “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

### 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

### 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

### The three varieties of habit

I like habits. I think chipping away a little at a time is a great way to make a big dent in something, and I’m always looking for ways to break down big problems into little solutions I can effect over time. But I’ve noticed in my readings that not everyone has the same idea … More The three varieties of habit

### Discrimination or just consequence?

Recently on Facebook, a friend of a friend mentioned that the police routinely pull him over because he is a man with long hair, and claimed that this makes him the target of discrimination. I had two conflicting thoughts about that: Seriously? If having long hair as a man is correlated with more unsavory activities, … More Discrimination or just consequence?

### When is a mixture better than a middle?

We often optimize by looking for a nice middle partway along a spectrum: Exercising means challenging your body enough to respond but not so much that you hurt yourself. Astronomers look for potentially habitable planets in the”Goldilocks zones” around other stars, the bands where it’s not too hot and not too cold. It’s appropriate to … More When is a mixture better than a middle?

### On not exuding confidence

I’m what you could call shy. Here’s what happens when I am in a conversation with people I don’t know very well. My joints start to feel stiff and my breath gets shallow. Everything feels hard to move and I have to concentrate on breathing normally and not clutching one arm with the other. When … More On not exuding confidence

### "I feel stupid."

“I should hang onto this piece of paper, but I don’t want to get out the filing stuff…” “I should get out the packing list and double-check, but I’m pretty sure I’ve got everything…” “If I leave now, I’ll be early, so I’ll get back on the computer and try to just check one thing … More "I feel stupid."

### Health is not a virtue

I was a healthy child. I had a healthy immediate family, too. We all got sick occasionally, and my sisters and I have all broken a bone at some point, but we just weren’t the sort of people to have chronic ailments or other serious health concerns. At least, that’s the best I could muster … More Health is not a virtue