Shadow Time

Shadows tell time badly. This is their advantage. A clock tells you it's 2:47 PM and you think: I have thirteen minutes before the meeting. A sundial tells you it's mid-afternoon and you think: the light is moving west and the garden is warm and the meeting can wait. I build sundials. Not for a living — you can't make a living building sundials, and I know this because I've tried. I'm a maths teacher. The sundials are what I do with the mathematics that school doesn't let me teach, which is most of the interesting mathematics. A sundial is a solved equation made of stone. The gnomon — the part that casts the shadow — has to be angled to your latitude. I'm at 51.5 degrees north, which means my gnomon tilts at 51.5 degrees from horizontal, aimed at the celestial pole, and the shadow it casts sweeps across a set of hour lines that I calculate using the arctangent function, which is the only time I've seen trigonometry justify itself outside a textbook. My first sundial was wrong by forty minutes. I'd calculated for the wrong longitude. This is the sundial equivalent of a typo and it bothered me in the way that only a mathematical error can bother someone who is supposed to teach mathematics. I ground it down and redid the lines. Twenty minutes off. Closer. The third attempt was accurate to within five minutes, which for a sundial is excellence and for a clock is a sacking offense. The thing about sundials that people forget is that they don't measure clock time. They measure solar time, which is different. Solar noon — when the sun is highest — happens at a different clock time every day because the earth's orbit is elliptical and its axis is tilted. The difference is called the equation of time, and it swings by about sixteen minutes across the year. A sundial tells the truth. A clock tells a useful fiction. We chose the fiction, and here we are. I have four sundials now. One in the garden, which is limestone and reads accurately from March to October. One on the south wall of the house, which is slate and which my wife tolerates because it's flush with the brickwork and visitors think it's decorative. One portable one I bring to classrooms, made of brass, which gets the attention of approximately three students per class, which is enough. And one I'm still working on — an analemmatic sundial where you stand on the date and your own shadow tells the time, which requires an ellipse set in paving stones and which my wife has not yet agreed to. She will. The garden is large. The equation of time is persuasive. And shadows don't need batteries, which is the best argument I have for anything.