Who’s Afraid of Big Numbers?

Pretty much everyone. But it doesn’t have to be that way, two mathematicians contend.

“Billions” and “trillions” seem to be an inescapable part of our conversations these days, whether the subject is Jeff Bezos’s net worth or President Biden’s proposed budget. Yet nearly everyone has trouble making sense of such big numbers. Is there any way to get a feel for them? As it turns out, there is. If we can relate big numbers to something familiar, they start to feel much more tangible, almost palpable. For example, consider Senator Bernie Sanders’s signature reference to “millionaires and billionaires.” Politics aside, are these levels of wealth really comparable? Intellectually, we all know that billionaires have a lot more money than millionaires do, but intuitively it’s hard to feel the difference, because most of us haven’t experienced what it’s like to have that much money. In contrast, everyone knows what the passage of time feels like. So consider how long it would take for a million seconds to tick by. Do the math, and you’ll find that a million seconds is about 12 days. And a billion seconds? That’s about 32 years. Suddenly the vastness of the gulf between a million and a billion becomes obvious. A million seconds is a brief vacation; a billion seconds is a major fraction of a lifetime.