In a Calculus class, the instructor talked about the difference between a formal, written proof and an explanation with a lot of hand waving.

I do like the formal written proofs when I need to look back to remember it fully. Formal proofs allow me to review each of their steps.

But I also like the hand waving when I’m trying to get an initial understanding of a new concept. Along with all of the other body language of the speaker, it seems faster and easier to get the point across.

Usually, if you can see the hand waving, then the speaker can also see you. This means that the speaker can get a better idea of whether the speaker’s point is getting across or if the speaker should elaborate.

I once had a long email conversation with an IT manager in Mexico. He’d described his problem and I thought that I’d solved it for him. This email conversation took months. When we met 6 months later, we had a 5-minute conversation face to face. In that 5 minutes, he figured out where he misunderstood me, I figured out where I misunderstood him, and the problem was really solved at long last.

I was recently reading a book on linguistics. (Don’t get too impressed. It was Linguistics for Dummies) I was surprised to find that, despite its name, a branch of linguistics called Phonology includes the study of gestures.

In the same way that you’re not always aware of the mechanics of making the sounds of your speech, you’re rarely aware of the gestures made as you talk.

I don’t have a better reason for waving my hands when I’m on the phone.