Decades ago, I was at a Thanksgiving dinner and the person across from me was wearing a pin that flashed “Jesus is the Reason for the Season” throughout the entire meal. In addition, all of the talk during the dessert course was of how they planned to get up early and cross the state line to avoid sales tax for the Black Friday deals. There were so many things wrong with all of this but I couldn’t wrap my head around which was the most repugnant to me.
Let’s go back several thousand years, way before Christianity, and let’s put ourselves deep in the Northern hemisphere (where Berlin, Germany currently is, perhaps). What happened between what we now call June 21st and December 21st? The same thing that still happens in the second part of the calendar year; each day was shorter than the day before until by early December there were only about 8 hours between sunrise and sunset. Without modern conveniences such as electricity and central heating, IT WAS DARK AND COLD. Cultures celebrated the Winter Solstice because it marked the time when the amount of daylight was at a minimum (here comes the math) and then started to increase. These celebrations were often tied to rituals involving parties, light, and/or worship. When Christians looked for ways to spread their religion, it was natural to fold Christian holy days, such as the birth of Jesus, into preexisting celebrations, such as the Romans’ Saturnalia or the Jews’ Hanukkah or even prehistoric sun worship as seen at Stonehenge. No one knows what time of year Jesus was actually born, but most biblical scholars agree it was likely in the spring since shepherds were tending their flocks (Luke 2:7-8), which wouldn’t happen in December.
Now, I am a mathematician, not a historian (so please forgive my perhaps too brief and mostly un-footnoted musings above). When I teach trigonometry, my students calculate, by hand, the amount of daylight in various cities on January 21st, February 21st, March 21st, and so on … all the way to December 21st. There are plenty of great websites where you can obtain this data — I personally like the U.S. Naval Observatory site. If anything, it is a good exercise for students in unit conversion. It is also an eye opener for how much less (or how much more) daylight there is in a place like Fairbanks, Alaska, relative to where we live in Mississippi. Some of my students are inevitably surprised, “How do they really know that the sun will come up at that time six months from now?!” Once the data is collected and the amount of daylight calculated, I have them hand-draw graphs with the days along the horizontal axis and the amount of daylight along the vertical axis. This is likely their first introduction to a periodic function. We can then discuss salient characteristics such as amplitude, period, phase shift, and vertical translation before we ever look at a graph of y=sinx or y=cosx. We also discuss the meaning of the intersection points (equinoxes), and the extreme values (maxima and minima). [Of course this can all be done with the aid of technology from a modeling perspective too, but I tend to do this exercise the way I would have taught it 28 years ago; sometimes the technology is too fast IMO and the students don’t have time to process what just happened.] For a free copy of this project, click here.
So there you have a little glimpse into my head. Whenever I hear or see, “Jesus is the reason for the season,” I think about the northern hemisphere daylight graph and the minimum value around December 21st. I think about the place where there is a horizontal tangent since for that one moment in time, the amount of daylight is neither increasing nor decreasing. I think about why we have different amounts of daylight at different times of the year — because Earth has an axial tilt of about 23.5 degrees, and because I don’t happen to live on the Equator. And I think about how the early Christians, in an effort to spread Christianity, folded their new holidays into preexisting traditions. So there you have it! Happy Winter Solstice! Io Saturnalia! Happy Hanukkah! Happy Kwanza! Merry Christmas!
Here we are today in Mississippi… around the point (355, 9.7).