I woke up last night in the wee small hours — around 3 a.m. to be precise, which is even more wee than I usually wake up — thinking about math. Specifically, I was thinking about how much math humans have worked out and how remarkable it all is.
Did you know most people can’t accurately tell how many objects they’re looking at if the number is higher than five? It’s true. Scientists call it subitizing, and it’s what you do when you look at three cookies on a plate and instantly know it’s three and not five. Of course, you can look at larger groupings and tell how many objects are in your field of vision (say, a referee looking at how many players are on one side of a football field) but your brain uses different mechanisms to accomplish that, so you aren’t actually recognizing as much as you’re counting very quickly.
Of course, we can always count. But how high can you count? Pretty high, you might say. If by high you mean 1,000 I’ll agree. But in the scope of the numerical world that’s awfully small. It would take you longer than ten days to count to a million, and that’s if you never lost track. And anyway, what do those numbers even mean to you when they’re that high? No one can look at a stack of 872,561 ball bearings and tell that it’s not 872,562 or even a nice round 900,000.
Now, all of this is just counting. We haven’t gotten into manipulating these numbers by addition, subtraction, multiplication, division, to say nothing of trigonometry, calculus, and so on. The numbers involved in these operations, as far as our brains are concerned, are completely imaginary (no, not √-1). In effect, if you think about it (especially at 3 a.m.) all of these numbers are just words, and we’ve applied a very specific set of rules to how those words work together. That has to be the case, because we can’t actually think about them in any coherent way.
Except that’s not the case. We know that’s not the case because we’ve sent men to the moon. We bounce cell phone signals off satellite dishes. We build computers and cars and houses. Math works. Which is such a miracle that if you didn’t know it and trust it because you’ve been surrounded by it all your life you’d think it was too improbably to believe.
It gets better. There’s no explanation from fitness for humans understanding math the way we do. In other words, Grog the caveman didn’t need the capacity to divide 1,000 by 4 in order to outrun the cave bear and live another day to make a bunch of baby Grogs. We have the capacity, built into our minds, to comprehend things of such complexity that they nearly defy description and allow us to understand and predict in great detail the workings of the universe — for no reason at all.
To me, that’s a compelling reason to believe in God. I’m not going to sell you a line about which God to believe in. I have a line on that, but I’m not going to try to pitch it to you. Believe what you want, but whatever you believe pause for a moment and think about it, and wonder.