The Analemma: Eternity’s Crazy Eight

By Curtiss Clark

This year the 13th of April falls on a Friday, and under the special rules of superstition Friday somehow compounds the unlucky properties of the number 13 to make it a date of watchfulness and caution. So we watch where we step: not under a ladder, not in the path of a black cat, not on a crack for the sake of mother’s back. But if you dare, stop for a moment this Friday the 13th, say at noon, and lift your face to the sun to bask in a special solar alignment.

On every day of the year except two, April 13 and August 31, the sun occupies a unique position in the sky at noon. But at noon on April 13 and noon on August 31, the sun will be at the same point in the dome of the sky. It is a phenomenon that almost no one celebrates.

When most of us think of the movement of the sun through the sky, we think of its daily trip from the eastern horizon to the western horizon. That’s because we experience the sun in the continuum of time, which on this spinning planet of ours we measure in days — one spin. But if, like the spinning figure skater, we want to keep our bearings in our dizzying day-to-day relationship to the sun, we should do as the spinning skater does: keep our focus on just one point in the revolution and not on the whole turn.

Photographer Wojtek Rychlik has accomplished this feat for us in the multiple exposure photo you see here. He trained is camera on the same point in the sky at his home in Cascade, Colorado and exposed his film at the same time every day for 365 days. (There are few cloudy days at this altitude, but when there were, Mr Rychlik extrapolated.)  As you can see from this spinning skater’s perspective, the sun traces a figure eight in the sky over the course of the year. The crossover point occurs in the middle of April and the end of August.

This figure is known as the analemma. It reveals that the sun not only moves north and south in the sky over the course of the year (its declination, as indicated by the height of the figure eight), it also moves east and west (as indicated by the width of the figure eight). This east-west movement is measured by “the Equation of Time,” which apparently was named by a wizard.

The Equation of Time works this way: When your watch says noon, stand facing south and raise your arm straight into the sky. Clock time says that the sun should be located somewhere on the meridian that runs from the North Pole to the South Pole, through the point in the sky above your fingertips. If sun time (where the sun actually is) is to the east of your fingertips, it is said to have a negative value in the Equation of Time; if it is to the west, it has a positive value.

Knowing about the analemma, the Equation of Time, and the sun’s position in the sky was essential to mariners navigating the seas. That’s why, by tradition, older globes of the world have an analemma and the Equation of Time printed on them at the equator in the blank expanse of the Pacific Ocean. This figure eight shows the position of the sun for every day of the year.

Navigators on the open seas, knowing the date, can calculate their latitude on the globe by using a sextant to measure the angle of the sun to the horizon at a given time. But what if you know where you are, but you don’t know what the date is?

With nothing more than a rod to stick in the ground (or a south-facing wall) and a little time on your hands at the same time of day for the next year, you can create an analemma calendar. If you make a mark at the end of the shadow cast by the rod at the same time each day, let’s say noon again (adjust appropriately for Daylight Saving Time), the accumulation of marks over the course of a year will trace the figure eight shape of the analemma. Today’s mark, April 13, will be at the crossover point this year and next year and the next. (Actually, since our rotation around the sun is 365¼ days, the crossover point drifts into April 12 and August 30 in some years.) You can make 365 marks, or just 12 marks — one on the first day of each month. The resulting analemma will give you a pretty good calendar on into eternity, or until the earth fails to hold its current orbit around the sun, whichever comes first.

In the symbolism of mathematics, the analemma shape has another name: the lemniscate, from the Latin lemniscus, which means ribbon. It is the symbol for infinity.

Year after year, the sun traces this endless shape in the sky and in every shadow upon the earth. So no matter what our luck on this unlucky day, or on August 31, or on any other date of our choosing, we should remember that all of life is turning lazy, crazy eights. Luck changes right along with everything else. And when you’re walking along a ribbon with no beginning and no end, the occasional stumble means nothing. Watch your step if you want to. But consider, for once, looking up. Face the sun. Take a few courageous steps along the path of eternity.