Driving on Route 7 in Northern Virginia in late November poses a special challenge. There are a few days when the sun rises directly in line-of-sight down the road. Because it is so early in the morning the sun is low in the sky and blinds drivers. Traffic slows down as you come over certain hills or go around certain curves. The problem doesn’t last for more than a week or so, and even on the days when it is present the minutes of trouble shift a bit each day. 

Commuters.Hate.This. It’s dangerous.

Years ago, Route 7 was a little narrower, and there were trees planted down the median strip. They were enough to shelter people from most of this problem. As the road widened and changed, the problem has become acute, for those few days.

The cause of the problem is that the sun is constantly changing its position in the sky. It rises and sets, but it doesn’t rise and set from the same point all the time. And it rises higher in the sky in the summer and lower in the winter. This is a link to a fascinating picture that demonstrates the principle involved.

https://apod.nasa.gov/apod/ap190621.html  (Analemma with extra pictures of the sun showing how the equinox is NOT at the crossing point of the analemma and how the position of sunset changes.)

Even people who never pay attention to the sun are occasionally brought face to face with this fact/phenomenon. This constant change in the position of the sun means is that everyone might have a bit of personal Stonehenge in their lives if they looked around. 

My church used to have clear round windows up high, and stained glass saints down lower. I could sit in church and watch the reverse shadow, the lighted image of a round window move across a west wall. One morning in October, outside the church, I looked at a window and saw the face of Saint Agnes shining at me. This was a little freaky since, normally, stained glass from the outside shows nothing except the leading between colors. That moving light, from the round window up high, was shining at exactly the right slant to strike the face of Saint Agnes in the window, and only her face.

It happened the next day, October 13, as well, at which point someone else saw it. By the following day the light was below the saint’s face, and the window was dark enough that nothing appeared. I watched for this phenomenon the following year, and I worked out when it might occur in March, and then the church filled in the clear glass and the effect vanished.  

However, some people have created effects like this deliberately. Smithsonian magazine documented various special lighting line-ups in a December 21, 2017 article about various mission churches in Mexico and the southwest US. 

The Tower of the Wind in the Vatican has a famous hole in the wall which is used to determine the spring equinox. The light slips through the hole in the wall and strikes a marked spot on the opposite wall. This is how the Vatican knew that the Julian calendar was slipping away from reality. When the calendar said March 11 and the wall said March 21, there was a problem.

I have heard of two other examples. 

MIT has a set of buildings that are oriented (accidentally) to allow a shaft of light down a long set of buildings at sunset at the end of January. The light illuminates a corridor which runs for 825 feet through several buildings. The sudden illumination of the walls of the corridor for one or two minutes is considered quite the sight. The picture shows the illumination and the website at MIT has more discussion of it. https://web.mit.edu/planning/www/mithenge.html

A church in England (which I cannot now trace) had a blocked up window in an attic. When the church was refurbished and the window was unblocked it was positioned exactly to shine a direct light on the crucifix on the opposite side of the church at 3 p.m. on March 25. 

The analemma, pictured on the APOD site, was the favorite shape of an Italian Catholic scientist, Giuseppe Fagnano, in the early 1700’s. He was so in love with it that he wanted it inscribed on his gravestone. The mathematics, of many of the Catholic scientists from that time on, is way above my head. Francois Vieta described algebra, using ‘x’ for a number, in equations, in the 1500’s. After that, it’s a problem. (He also had Mary, Queen of Scots, for a client on his lawyer side.)

However, if you’d like to read the biography of another Catholic mathematician I give you this one from my favorite math people website. https://mathshistory.st-andrews.ac.uk/Biographies/Evans/