HOW TO COUNT SHEEP WITHOUT FALLING ASLEEP

Suppose that the whole development of our number system had occurred inside the head of one bright shepherd. Leighton's and Feynman's shepherd starts out with a notched stick and then, to allow for the loss of a sheep, with a sack full of rocks (one for each); he soon steps up to chipping tallies in stone, with Xs for units of ten and minus signs for sheep that die. The authors have the same shepherd inventing a series of slide rules, still mumbling ""There must be a better system,"" and finally--to help the tax collector add and subtract--switching from Roman to Arabic numbers and breaking through with zero. There are appended directions for making your own ""adding and subtracting machine,"" along with the promise that like the shepherd you won't need it for long, as you'll soon know all the combinations by heart. This represents no big step forward in introducing the system, but it could add up as a classroom supplement.