“It has become almost a cliche to remark that nobody boasts of ignorance of literature, but it is socially acceptable to boast ignorance of science and proudly claim incompetence in mathematics.”
— Richard Dawkins
I must ask you to bear with me today. I am going to try to teach you something about mathematics. I know in some of you this inspires a fear akin to jumping out of an airplane or wrestling a polar bear. I hope that you come out the other side having decide it was worth it.
I wrote my senior paper on something called the Goldbach Conjecture. It’s simple. It says that all even numbers can be written as the sum of two prime numbers. If you need a reminder, a prime number is any positive whole number than can only be divided by itself and 1 (if you need a reminder of what an even number is, you may be beyond my help). Some examples to help jog your memory are 5, 11, 37, and 91.
Now, it’s easy to see that 8 = 5 + 3, or that 14 = 7 + 7. With me so far?
Before long, people realized that the bigger your even number, the more ways you can express it in this way. For example, 6 has only one such expression: 3 + 3. 10 has two, 30 has three. At some point, someone had the brilliant idea to make a graph of the number of different ways you could write each number this way. Here are the first few:
At the moment, this looks like nothing special. Just a chaotic cluster of dots, kinda slowly getting bigger. Bob Dylan said, however, “Chaos is a friend of mine.” Apparently God agrees. This is what it looks like if you keep this process going a million or so more times:
This is called Goldbach’s comet, and its image has been known to put audible gasps in the throats of freshman math students everywhere.
I am showing you this for two reasons. One, it is beautiful, and beautiful things are worth sharing. Two, it is helpful for me to remember that it can be hard to see a pattern developing if it is complex enough. But the Composer of Life does not specialize in simple melodies. So step back and look ahead. What at one moment looked like a chaotic mess can suddenly reveal itself to be a stunning image of perfect clarity. To paraphrase our Lord, if God can paint such a stunning picture with the disorganized mess of prime numbers, can He not so much more with you?