One small, but telling example of the latter is the belief that al Qaeda and Iraq are linked simply because of their common enmity toward the U.S. Many who believe this subscribe to some version of "An enemy of my enemy is my friend." But if this proverb were literally true, it would be impossible for there ever to be three mutual enemies since any two of them, by virtue of having a common enemy, would be friends.
In particular, since both we and Iraq have been enemies of al Qaeda, we might just as easily conclude from the proverb that we're friends with Iraq. This is absurd, but no more so than the simplistic either-or mentality that seems to underlie so much discussion of the war.
And just as we can have a variety of enemies, we can have a variety of friends, which suggests that excoriating traditional allies for not immediately signing on to war is most unhelpful.
What Is the Price?
Finally, what might the price of war be? Estimates for its costs and for the more arduous post-war occupation and rebuilding range from $100 billion to three-quarters of a trillion dollars over five years. (Compare this with average annual U.S. foreign aid of approximately $10 billion.)
No matter one's position on the war, one has to acknowledge that this money could buy a lot of Iraqi containment, not to mention homeland defense.
In addition to these monetary expenditures are a variety of imponderable costs associated with an American-led war that lacked a broad international consensus. These latter — increased terrorism, gas attacks on Israel, damage to the rule of law — can't be quantified, but may nevertheless be the more significant.
In short, although numbers may be helpful, what's really needed is wisdom for which, alas, there is no formula. Every course of action can lead to a variety of outcomes — some good, some bad — whose probabilities we can only guess at.
Professor of mathematics at Temple University and adjunct professor of journalism at Columbia University, John Allen Paulos is the author of several best-selling books, including Innumeracy, and the forthcoming A Mathematician Plays the Market, which will be published in the spring. His Who’s Counting? column on ABCNEWS.com appears the first weekend of every month.