[From Bill Powers (2012.11.19.1440 MST)]
Addendum. Here's a simple experiment to try. While walking in an open space where several other people are walking, pick a person out and walk in such a way that the person remains 45 degrees (or any other constant angle) to the right or left of your direction of walking. Pick right or left according to which way the person is moving. If nobody else is there, bring a friend along.
If no obstacles get in the way and you can move fast enough, you will collide with that person. You will see that this is inevitable long before you actually get close to the person,