Today's event at the opening of the George W. Bush Presidential Library brought together all of the living presidents in his honor. Which prompted us to wonder: At what point were the most presidents alive at once?

The answer is a bit of a fudge. It's hard to know, after all, since there are more than five presidents alive today — some of whom have not yet been elected president. By that standard, there could be a dozen presidents alive today. It's impossible to know.

But it's still unlikely we'll match the high point of living presidents. That was reached between August 1833 and June 1836 — between the birth of Benjamin Harrison and the death of James Madison. At that point, there were no fewer than eighteen living presidents: Madison, Jackson, Adams, Harrison, Van Buren, Taylor, Tyler, Buchanan, Polk, Fillmore, Pierce, Johnson, Lincoln, Grant, Hayes, Arthur, Garfield, and Harrison. Of course, most of them hadn't yet been elected; several hadn't even reached adulthood.

We graphed the lifespans of each president, highlighting the moment at which the most were alive. The top of each bar represents the date on which the president was born; the bottom, the date of his death.

There are fewer presidents alive today than at any other point in history — but, again, that's only because we don't know who's next.

It's even possible, in fact, that there were more than five living presidents at the ceremony today. At the funeral of Sam Rayburn, in 1961, there were four presidents in attendance: Kennedy, Johnson, Eisenhower, and Truman. But Johnson was still vice president at that point.

In the audience today, for example: Jeb Bush. Who knows?