An Aging Mind Grapples with Euler, Diderot, and Biological Clocks

I typically start my days by hobbling into the kitchen and staring through the window at the bird feeder, waiting for both my mind and my eyes to come into focus. This can be more complicated than it sounds; eyes and mind are not automatically coordinated at that time of day, and it may take a while to get them both on the same topic. For example, today I was staring at a flock of pine siskins. They are northern relatives of the common goldfinch, only a bit smaller and covered with black stripes. In ordinary times they rarely are seen around here but this winter they are abundant, and I should have been marveling at them. But instead my mind was on my daughter, who was born on this date 52 years ago. That was really something to marvel about… little things, like holding her for the first time and wondering how she could have her grandmother's dimple in her cheek, a trait that is caused by a dominant gene and that I do not have (I hadn't learned about gene penetrance at that time). Or big things, like growing up in the '60s, and how she seemed to turn out all right in spite of all the things we didn't know about parenting…. That's a lot for a mind to deal with when it isn't quite awake yet.

Aging has strange effects on the mind. By the time you become aware of how much you do not know, you begin to forget what you do know. Also, at some point you begin to realize that a lot of what you thought you knew is wrong. For example, the northeastern section of the country had a major snowstorm on March 1, and I had planned to begin this article by writing that March had come in like a lion; then I learned that the old expression has nothing to with the weather. According to Dr. Wooten's piece on "The Night Sky of March" in the last issue of the Chronicle, the saying originated because the constellation Leo, the lion, is rising at that time, and Aries, the ram (who used to be a lamb) is rising at the end of the month… in like a lion, out like a lamb, regardless of temperature and precipitation. Checking the internet, the only thing I found in support of the weather was a children's poem by Lorie Hill:

"March roars in like a lion so fierce,
The wind so cold it seems to pierce.
The month rolls on and Spring draws near,
And March goes out like a lamb so dear."

Lion or not, the storm left about three inches of snow in our yard, and the next morning there under the bird feeder was a fox sparrow. It is a beautiful bird, the largest of our sparrows, with a dark spot surrounded by heavy brown stripes on its breast, a soft gray on its back, and a warm, russet-brown color on its tail. Unlike the pine siskins, I see it every year in the first week of March; it is migrating from its winter home in the southern states to its breeding grounds in Newfoundland or Labrador. It does not travel in flocks; usually I see only one at a time. It stayed two days, and then was off; although the storm was still raging in New England, it had no choice in the matter. Back when it was enjoying the warm sun in Alabama or Florida, its biological clock detected the lengthening of the days and sent signals to its endocrine system to start pumping out reproductive hormones and get on the road north. Come lions, lambs or high water, it was Newfoundland or bust.

The fox sparrow sent my mind wandering back to the 1960s, when we were just beginning to understand biological clocks. To show my class how day length changes, I recorded the time of sunrise and sunset from the Frederick News-Post for a year and made a graph of the results. The line on the graph went up and down in a regular pattern that mathematicians call a sine wave; it is the series of peaks and valleys you get if you tape a magic marker to a wheel and roll it along a wall (take my word for it… don't try it in your home). The lowest point on the graph, representing the shortest day of the year, is the winter solstice (around December 21, but not exactly the same date each year because the year isn't exactly 365 days long). The longest day, or summer solstice, around June 21, is the highest point. The equinoxes, Vernal around March 21 and Autumnal around September 21, are the points where day and night lengths are equal. The graph shows that the period of light changes by only a few seconds each day around the solstices, but it changes about two minutes a day around the equinoxes. This is enough to be detected by the biological clock in the brain, and it is the same every year; the graph I made in 1966 is still accurate today. Thus in the spring and fall, when other aspects of the weather vary widely from one day to the next, day length is a reliable factor to use for timing activities like migration and breeding.

Sine waves are important in biology; they describe a wide variety of things, from day length to the change in blood pressure between heartbeats. I was sure I had learned the formula for the sine wave in some course or other, but while watching the fox sparrow I realized that I had forgotten it, so I got the textbook and looked it up. It didn't look familiar at all. There were notes in my handwriting and calculations in the margin of the page which showed that I had mastered it at the time… but looking at it now, it might as well be written in Chinese.

Thinking about the formula as I went back to watch the fox sparrow again, my mind drifted to a story of a debate in the court of Catherine the Great, between the Swiss mathematician, Leonhard Euler, and the French philosopher, Denis Diderot, who was an atheist. (It was around 1760, and television hadn't been invented yet, so I suppose they had to have something to do in the evenings.) The topic of the debate was whether God existed, and Euler began, "Sir, (a + b)^n/z = x; therefore, God exists. Respond!" Diderot was speechless, the audience laughed him off the stage, and he left in disgrace, so the story goes. I thought I remembered the French words: "Monsieur, (a + b)^n/z = x; donc Dieu existe; repondez!" but I decided I'd better look that up too, since I fared so poorly with the sine wave formula. I couldn't remember which book it was in, so I looked on the internet; and there I found that the whole story was a fabrication. The debate never really happened; it was made up by an enemy of Diderot's.

I found it ironic that the one thing I could remember never happened, and I thought my wife might sympathize if I told her about it; but, wrong again. She just shook her head and walked away, muttering "Another child left behind."