A year ago, I wrote about “the Alexandrian solution” to the Gordian Knot. I saw this as a metaphor for all instances in which genius lies in espying the simplicity hiding in a complex situation.
It just occurred to me that Carl Friedrich Gauss was, at the age of 10, just such an Alexander the Great. (Alexander was young, too, of course. In espying simplicity, it seems to help to be young — ie, intellectually daring, unspoiled by the complexity of life, et cetera.)
In about 1787, the young Carl Friedrich sat in class when the teacher told the kids to find the sum of the numbers 1 through 100. In other words:
1 + 2 + 3 … + 100 = ?
Think of this as the Gordian Knot. The teacher assumed that the kids would be busy for a long time, practicing their addition skills. Gauss reacted just as Alexander would have (I take poetic license):
This is too f***ing boring. There must be a simpler way.
Did Gauss get nervous as the other kids pulled ahead adding numbers, while he was still at 1, searching for simplicity? I don’t know. But he found it:
He realized that the numbers came in pairs:
1 + 100 = 101
2 + 99 = 101
3 + 98 = 101
(and so on until:)
50 + 51 = 101
So the sum of the numbers is simply (simply!)
50 x 101, or 5,050
You might, if you’re a regular on The Hannibal Blog, be guessing that I’m much less interested in sums of numbers than in, shall we say, Gordian Knots and Alexandrian Solutions in general — meaning in other, preferably surprising, walks of life.
If you can think of any instances in which daring simplicity blasted through mind-numbing complexity, drop me a line.