When you’ve been arguing with the religious right over gay marriage for a while, you get used to having certain comparisons thrown your way: gay marriage is like calling a circle a square, it’s like calling a tail a leg, calling a cat a dog, yada yada yada.
Here’s another common one: gay marriage is like saying 2 + 2 = 5.
The idea is that the Church, and the wiser elements of society, are supposed to reject that sort of funny math and stand up for the good old square arithmetic that we all learned in grammar school. Rod Dreher lays it out here in an exchange last year with Andrew Sullivan:
We have been over and over and over this, and all the vehemence and foot-stomping in the world will not change basic Christianity on this point, and certainly will not change Roman Catholicism. Two plus two will always equal four in Catholicism.
Dreher, in Dreherian fashion, follows that with a dig at my church: “There is a church that takes Andrew’s line on sex; it’s called the Episcopal Church.” No surprise there.
Now, I’ve got really smart readers, so what follows may not be news to many of you, but I’m not a math guy, and this blew me away when I read it last year in Jordan Ellenberg’s “How Not to Be Wrong” column at Slate. Ellenberg, a mathematician at the University of Wisconsin, asks, “Is the repeating decimal 0.999… equal to 1?” And he answers yes, it is.
Here’s the reasoning:
Everyone knows that
0.333… = 1/3
Multiply both sides by 3 and you’ll see
0.999… = 3 / 3 = 1
If that doesn’t sway you, try multiplying 0.999… by 10, which is just a matter of moving the decimal point one spot to the right.
10 x (0.999…) = 9.999…
Now subtract the vexing decimal from both sides.
10 x (0.999…) – 1 x (0.999…) = 9.999… – 0.999…..
The left-hand side of the equation is just 9 times (0.999…), because 10 times something minus that something is 9 times the aforementioned thing. And over on the right-hand side, we have managed to cancel out the terrible infinite decimal, and are left with a simple 9. So we end up with
9 x (0.999…) = 9.
If 9 times something is 9, that something just has to be 1—doesn’t it?
Ellenberg ties his answer to a handful of fascinating paradoxes, including Grandi’s series, named after the 18th Century mathematician who argued that, despite appearances, the sum of the series 1 – 1 + 1 – 1 + 1 – 1 +… equals ½.
Like I said, I this blew my mind. And then, when I read a) that Guido Grandi was a Benedictine monk who tied his findings to the mysteries of creation and b) that divergent series like Grandi’s have been called “the invention of the devil,” my parabolic mind got to work.
Because there is a lesson in there, and I think the lesson is this: the Church’s job is not to teach 2 + 2 = 4. If that’s all she does, then what’s her point? You can learn that counting on the skeletal fingers of Christopher Hitchens’ inanimate corpse.
[Sorry for the image, but it’s the least church-y thing I could come up with.]
The Church’s more important job is to teach how .999…—which never can be 1—is, in fact, 1. The problem is that this is risky work: it opens the Church to a certain type of criticism. Ellenberg notes that this type of thinking might look like relativism; it seems to move away from objective truth. But running that risk is precisely the Church’s job; that’s what makes her indispensable.