Learning how to ride a horse has always been a tricky business. Xenophon pondered it in the fifth century BCE. So did the famous Renaissance riding master Federico Grisone. Even today, book shops have plenty of titles on learning how to ride (Figure 1). To put it a bit bluntly, riding a horse is about more than just sitting on a creature that moves. Unlike walking a dog or hunting with a hawk, horse riding is not only an activity shared by a human and an animal actor but entails actual co-movement. Whereas a dog or a falcon is instrumentally conditioned to fulfill a specific function according to human commands, horse riding is a physically shared co-activity based on (ideally) harmonious movement.