A nice exposition, Will. Sadly, our brains are evolved to cope with the relatively simple world inhabited by our ancestors and are generally very poor at abstract reasoning. Some years ago, a class taking Physics 101 in their first year of undergraduate study was given the relevant equations and all successfully utilized them to prove that objects of different mass will indeed (in a vacuum) fall at the same rate. But then, when the teacher immediately afterward said that a ball of lead and a tennis ball will fall at the same rate, most of the class laughed at the joke....