At a deeper level, however, subtraction raises a much more disturbing issue, one that never arises with addition. Subtraction can generate negative numbers. If I try to take 6 cookies away from you but you only have 2, I can’t do it — except in my mind, where you now have negative 4 cookies, whatever that means.
Subtraction forces us to expand our conception of what numbers are. Negative numbers are a lot more abstract than positive numbers — you can’t see negative 4 cookies and certainly can’t eat them — but you can think about them, and you have to, in all aspects of daily life, from debts and overdrafts to contending with freezing temperatures and parking garages.
Still, many of us haven’t quite made peace with negative numbers. As my colleague Andy Ruina has pointed out, people have concocted all sorts of funny little mental strategies to sidestep the dreaded negative sign. On mutual fund statements, losses (negative numbers) are printed in red or nestled in parentheses, without a negative sign to be found. The history books tell us that Julius Caesar was born in 100 B.C., not –100. The subterranean levels in a parking garage often have names like B1 and B2. Temperatures are one of the few exceptions: folks do say, especially here in Ithaca, that it’s –5 degrees outside, though even then, many prefer to say 5 below zero. There’s something about that negative sign that just looks so unpleasant, so … negative.