What an excellent discussion. As a layman trying to grasp physics equations (e.g. F=ma), I often get tripped up by what is actually happening to the units being manipulated mathematically, and what they actually "mean" in the real world. The analogy of multiplying bananas by umbrellas to get a grandfather clock (mentioned in the article cited by michel123456) especially resonated with me. Thanks to everyone who has contributed; I hope this bump gets more people to chime in.