What's Your Number?

"Consider, first, large numbers, starting with an example that has no political overtones. In his excellent book Innumeracy: Mathematical Illiteracy and Its Consequences, John Allen Paulos, a mathematics professor at Temple University, tells the following true story. A blurb on the box containing a Rubik cube states that there are more than three billion possible combinations. Paulos notes that the actual number is about 4.3 times 1019. Is 4.3 times 1019 greater than 3 billion? Yes; the blurb is correct. But it’s so much greater than 3 billion, which has only 9 zeroes after it rather than 19, that the blurb is uninformative. As Paulos writes, it’s like having a sign at the entrance to the Lincoln Tunnel stating “New York, population more than 6.”

The Rubik cube blurb is just a “toy” example, right? Well, sure, but think about similar confusions about big numbers in the real world of government budgets. Many congressional Republicans say they’re worried about annual federal budget deficits that range between $500 billion and $1 trillion, and that they want to cut spending. Then look at some of their talking points and it’s rare for them to advocate cutting any particular program by at least $1 billion. Instead, they will castigate this or that federal agency for much smaller expenditures. Former Senator Jeff Flake of Arizona, for example, criticized the National Science Foundation for “spending millions of dollars to determine why yawning is contagious, if drunk birds slur when they sing, and if cocaine makes honey bees dance.” He was probably right to make that criticism. Those grants do seem wasteful. But they are rounding errors on $1 billion, let alone $1 trillion.

By contrast, consider what would happen if instead of increasing Social Security benefits by 1.6 percent for 2020, the federal government had increased them by “only” 1.5 percent. Social Security expenditures for Fiscal Year 2020 are expected to be $1.102 trillion. Cutting that $1.102 trillion by 0.1 percent would yield budget savings of $1.102 billion. That’s still a small number in a $4.747 trillion budget. But it swamps the effect of cutting expenditures on studying yawns, drunk birds, and waltzing bees."