Last week I explained that my wife and I have learned that in the context of our three children and the chaos they generate, 1 + 1 + 1 = a lot more than 3. Put differently, the amigos’ collective rowdy effect is considerably more than the sum of their constituent parts. I also mentioned in last week’s column (“The New Math”) that a certain pattern is emerging in our family—a pattern which I refer to as the “Swensen sequence”. In the “Swensen sequence” each amigo takes roughly a two year turn as the primary (though by no means the sole) source of our concern and exasperation. Then that child yields to the next amigo in line, and that child serves a term as our primary headache (they’re a bit like members of Congress in that way), and so on until it’s the first child’s turn again. I noted in passing that the “Swensen sequence” shouldn’t be confused with the Fibonacci sequence, another fascinating mathematical phenomenon.
The Fibonacci sequence was first popularized in the West in the 13th century when Fibonacci (also known as Leonardo of Pisa) discussed it in detail in his book Liber Abaci (“Book of Calculation”). In order to flesh out the sequence one begins with the integers 0 and 1. From there one generates the next number in the progression by taking the sum of the immediately preceding two numbers. Thus, the sequence goes like this: 0, 1, 1 [0 + 1], 2 [1 + 1], 3 [1 + 2], 5 [2 +3], 8 [3+ 5], and so forth. The next set of numbers, then, would be: 13, 21, 34, 55, 89, etc. The next number is calculated by adding 55 and 89.
Meanwhile, dispassionate-yet-beautiful mathematics has given us the so-called “Golden Ratio”, an irrational number (that is, a real number that can’t be expressed as a simple fraction; its decimal will never repeat in a loop (like, say, 6/9) and it will never end). “Pi” is the best known example of an irrational number. The Golden Ratio is expressed precisely as 1 + square root of five, divided by 2. Rounded out to the nearest one hundred thousandth it comes to 1.61803, but it goes on forever. Someone somewhere, with an enormous brain and too much time on his hands, discovered this ratio by observing that two numbers (a larger number, A, and a small number, B) produce a “golden” ratio when the ratio of B to A is the same as the ratio of A to (A + B). Or, if you prefer, a golden ratio is expressed when A/B = (A + B)/A. Confused? Relax. Just rest in the knowledge that it (1) is pretty awesome in its own right; (2) is expressed in an astonishing array of venues and disciplines—architecture, nature, music, art, and others; and—getting back to Leonardo of Pisa for a moment—(3) the further one moves along the Fibonacci sequence (…144, 233, 377, 610….) the closer one inches closer to the golden ratio when one divides a larger number in the string by its immediately preceding (smaller) neighbor. The Golden Ratio (also known as “The Divine Ratio,” by the way) and the Fibonacci sequence are intertwined in a knot of mathematical wonder and beauty.
But what of the Swensen sequence? Is it inextricably connected to a similar, dazzling ratio of some sort? It’s tempting to conclude that our “Golden Ratio” is X (number of amigos) / Y (number of amigo parents) = 1. After all, when one amigo spends the night with a friend or cavorts about town with Grandma for the day, leaving Krista and me with the other two, it feels as if a two-ton weight has been lifted; the sun seems to shine with unparalleled clarity, angels weep in profound thanksgiving, rainbows flow across the sky, and unicorns gallop down Park Drive. There is peace. There is (I’m getting a little misty-eyed at the thought) quiet. But the truth is more subtle, more disorganized, and a lot less quiet.
Our actual Golden Ratio was not intended to resemble the meticulous pattern of spiral petal growth on a sunflower, dimensions found in the human body (including our DNA), or the spectacular and unexpected symmetry of quasi-crystals. No, no. On the contrary, our divinely bestowed ratio (two exhausted, occasionally frustrated, sometimes overjoyed, and immensely flawed parents divided by three mercurial, chatty, energetic, fiendishly clever children), while unique in its makeup of personalities, temperaments, and sub-relationships (among other facets), mirrors both the imperfections and grace found in other families. It was meant to produce occasional fits of anarchy, tears, anger, confusion, frustration, and mess amid episodes of clarity, unity, calm, insight, laughter, and elation. It was designed and delivered, I think, to elicit growth, forgiveness, and the expression of genuine, sacrificial love. Over and over and over and over again (like the never-ending decimal of an irrational number).
Or maybe I need to re-check my math.
Timothy Swensen is the author of the weekly column series Virtue and Mischief that is published every Tuesday in The Daily Advocate. He can be reached at firstname.lastname@example.org. Viewpoints expressed in these opinion pieces are the work of the author. The Daily Advocate does not endorse these viewpoints or the independent activities of the author.