Sean Carroll on parallel parking and the non-commutation of vector fields

I remember vividly, there’s this wonderful little book on differential geometry by Walter Burke, where he gives an explanation for why people are… Find it difficult to get an intuitive grasp of parallel parking. He says it’s because it involves the non-commutation of vector fields…. Because you have the operation of moving forward or backward, you have the operation of turning your wheels right or left, and they don’t commute, it really matters which you do first. And if you understand that perfectly well, it helps you parallel park.

source: Episode 39: Malcolm MacIver on Sensing, Consciousness, and Imagination Sean Carroll