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Do-It-Yourself Eclipse Prediction

IF YOU ARE IN a tight spot, you may find yourself wishing for a solar eclipse to turn day into night, as in A Connecticut Yankee in King Arthur's Court. If you knew the eclipse was going to happen (but others didn't), you could pretend to "command the heavens." While Mark Twain's solar eclipse was an invention, his inspiration was probably a real-life incident involving Christopher Columbus in 1504, where the explorer "stole the moon" to get himself out of a sticky situation in Jamaica.

I doubt that Columbus was the first to pretend to manipulate the heavens (and since lunar eclipses are seen far more frequently than solar eclipses, they were probably the typical target). One imagines that eclipse prediction was a standard tool of the prehistoric priesthoods, back in the days before it was commonly understood that the clockwork orbits of earth and moon were all that eclipses involved, and that neither seems to be modified by prayers and offerings. A shaman who could appear to move the heavens might have been able to dominate neighboring tribes as well and oft-fulfilled prophesies might convert a shaman into a full-fledged prophet, lending authority to what the shaman had to say on other subjects.

Columbus probably had a nautical almanac that listed upcoming eclipses but remember that 1504 was long before Galileo or Newton, well before those orbits were understood. The astronomical lore of the times probably used a list of magic numbers, rather like that of the Mayan astronomers who wrote the Dresden Codex. (No, it's not written on porcelain that's just the German museum where the bark now resides, one of the few pieces of "pagan" writing to have escaped the Inquisition-haunted Spanish priests, who zealously destroyed what they couldn't understand.)

Back before record-keeping, however, there were likely some simple methods for eclipse prediction. Knowledge of them seems to have been lost to modern astronomers, who might be unable to impress the natives if shipwrecked on some island without their computers and reference books. The manufacture of stone tools was also forgotten when metal tools became popular; only recently have archaeologists such as Nick Toth rediscovered how to make an Acheulean hand ax or a Clovis-style spear point. Similarly, I have been trying to recover prehistoric methods of eclipse prediction, methods far simpler than orbital calculations or lists of magic numbers. Having discovered a dozen methods so far, I have concluded that warning of imminent eclipses is far easier than it first appears. Here I will give a short course in how to do it, emphasizing how success can be improved by using crystals, necklaces, and suitably placed windows. In How the Shaman Stole the Moon: Inventing Eclipse Prediction, Prayer, Priestly Power, and Protoscience (to be published later this year by Bantam), I explain why the methods work, relate them to ar-chaeoastronomy sites such as Stone-henge and those in the American Southwest, and discuss the origins of protoscience.


Total solar eclipses are impressive but rare. A partial solar eclipse is hard to see, even if you know when it is going to happen; the only one I've ever seen via naked eye happened to occur just before sunset, as the sun and moon set together over the Olympic Mountains as viewed from Seattle. You can sometimes study the sun's shape just before sunset, as its brightness is filtered enough by the long path through the atmosphere so as to permit brief glimpses. And that evening as the sun neared the horizon, it obviously had the moon just in front of it, obscuring its lower left; the three-dimensionality was quite striking. But most solar eclipses don't occur so conveniently close to the horizon.

Any fan of eclipses has heard of pinhole cameras, producing an inverted image of the eclipsing sun on a screen. Pinhole images are far easier than you might think; this isn't a matter of needing a darkened tent with a hole in the roof. Pinhole images occur in nature, as you can discover lounging in the shade of a tree whose leaves have been perforated by insects. Likely someone remembered those little round spots of light that had inexplicably turned into crescents before the world darkened. Odd-shaped spots, all facing the same way, are certainly striking; you feel as if "something is happening." Warped reality.

Just hold a perforated leaf at arm's length toward the sun. Look down at your chest at the leafs shadow, and see the little crescent of light in the midst of the shadow. As you move the leaf farther away, the light spot changes from the shape of the insect's hole to the shape of the eclipsing sun. The smaller the hole, the sharper the image. If leafless, .merely cross your fingers to produce a small opening and inspect your hand's shadow for a little crescent.


Crystals, at least those with many small-but-flat reflecting surfaces, also ought to be useful for viewing eclipses; a small facet serves to combine the pinhole with a mirror. Just pull the shades except for a small opening, lay your crystal or jewel on the window sill in the sunlight, and walk up to inspect the crescent spots reflected onto the walls. And watch them slowly change. Spangles embedded in a plaster wall can-produce the same effect, if small enough (a square millimeter is about right).

Once you've learned one of the pinhole methods, you can give an hour's warning of a solar eclipse, know it's happening long before anyone else notices that the sun is dimming. Still, you can't spend all your time watching pinholes for solar eclipses, on the off chance that one might happen. Solar eclipses can happen only at the new moon, and a superstitious wariness about new moons probably developed into an important bit of astronomical lore for the prehistoric shaman. When the crescent moon can no longer be seen before dawn, watch out for the next several days. When the crescent moon can again be seen above the sunset (a day especially important in some religions, such as Islam), you can relax your vigil.


Similarly, lunar eclipses only happen at the full moon. But the moon looks full for several nights; which one is it? Back before orbits were understood, "full moon" was likely defined as the night that the moon rose just before sunset, looking especially large and rosy (that's the night when there's a chance of a lunar eclipse; it is often the night before your calendar indicates a full moon).

There are ways to narrow down a likely solar eclipse even further by paying attention to the more common lunar eclipses. Following a lunar eclipse, there's no chance of another for the next five full moons, but then there is a 56 percent chance of another eclipse on the sixth full moon. If one doesn't occur then, there is still an 11 percent chance of a lunar eclipse on the twelfth full moon. If you raise the alarm every sixth and twelfth full moon following an observed eclipse, you've got two chances out of three of acquiring a reputation for foreknowledge.

You can imagine how this might have been discovered, back before careful records were kept. Surely a second lunar eclipse within a year of another would be cause for some observers to discuss when the previous one occurred, counting backward to discover that it had been either six or twelve full moons ago. And so the sixth and the twelfth full moon after an eclipse could readfly get the reputation of being particular danger periods. One counts to six, and then counts to six again.

Too bad we only have five fingers, you say? Contrary to the usual decimal notions, one can readily count to six and twelve on the fingers. On the sixth full moon, you close down those five extended fingers and clench your fist. On the seventh, you pick up the count on the other hand, extending one finger and so on to two clenched fists upon the twelfth full moon. That makes the full moons coinciding with a clenched fist the "dangerous ones," threatening to disappear. After a year with no eclipses, the danger zones expand to include the full moon preceding a multiple of six, i.e., 17 &. 18, 23 & 24, 29 &. 30, etc.

Solar eclipses also occur on the same six-month spacing as the lunar eclipses. They're at the new moon which precedes or follows the full-moon eclipse alert. Thus you need not get started on solar eclipse prediction by observing one solar eclipse and counting new moons thereafter: you get synchronized by observing even a partial lunar eclipse, counting by sixes, and watching out for the new moons that precede and follow the lunar eclipse alerts.

So lunar eclipse prediction is potentially quite easy, so long as you can be wrong a certain amount of the time. The method is crude, compared to modern scientific theories, but it could have been quite successful for an interesting reason.


The psychology of intermittent reinforcement suggests that being wrong occasionally wasn't a problem; it was an advantage (at least, to the shaman). What would you do if you feared eclipses, but were solemnly told that one was coming and by someone who was right last time? Trying to prevent eclipses through fervent prayer, before and during an eclipse, surely must have seemed to work most of the time. After all, many of the predicted eclipses didn't happen (the methods were crude, so there were a lot of what are now called "false positives"); this could have led a lot of people to believe that their prayers had prevented the eclipse; and many of the predicted eclipses that nonetheless happened were partial, allowing someone to conclude that the prayers had reversed the moon in its tracks, preventing a total eclipse.

So prayer was powerfully reinforced it seemed to work. If the priestly predictions had been nearly always wrong, of course, the announcements would have soon lost their credibility. If the predictions had been always right, eclipses would soon have lost their fascination. Being right just enough of the time is what makes some situations so attractive, as gambling illustrates.

I can see how large groups of people would have been psychologically trapped, how predicted eclipses would have made them believe in the power of wishful thinking. A control experiment that would have omitted prayers after half of the eclipse warnings, would have shown them that eclipses occurred independently of their prayers. Again, priestly credibility would have suffered. But the control experiment is a recent scientific innovation, invented after scientists discovered that they were fooled too often by mere coincidence.

I'm not surprised that people were fooled by post hoc ergo propter hoc the classical fallacy of "after this, therefore because of this," a fallacy that fools us every day even when we're alert to it. Despite its unreliability, one thing following another is a powerfijl way in which we learn our way around our environment, especially when dealing with the unfamiliar, such as a rare event.

Partial eclipses might have gotten prayer started back before prediction was discovered, wishfijl thinking during the . initial phases being credited with the avoidance of a total eclipse. And given something (the shaman's warning) to trigger the prayers a few hours or days ahead of time, belief in the power of prayer to move the heavens was sure to emerge and, of course, prediction itself would have become valued by the leadership, a powerful incentive to more and better science.

Often-successful eclipse prediction would have helped the shaman with everyday matters as well. Forget for a moment the Ijterary depiction of the shaman as some sort of psychedelic guru and consider what the anthropologists say about the shaman's range of skills. Besides predicting weather, the shaman of most known hunter-gatherer tribes is supposed to be able to cure illness and bring down illness upon enemies (or at least appear to do so). Given the strength of the placebo effect (for pain, it is now estimated that one of every two sufferers gets some temporary relief just from the power of suggestion), one can easily imagine that a shaman who had just manipulated the moon or sun would have even more success than usual at relieving pain.

Even if the leadership was blind to the Columbus-style possibilities for manipulation, even if the healers didn't know about eclipses, the prediction aspect itself would still have been handy to a fortune-teller and we humans seem to have an inordinate appetite for predictions about what the future might bring. While eclipses might be unrelated to "You will meet a tall, dark stranger" and other such staples of the repertoire, a fortune-teller's ability to occasionally predict eclipses would be a powerfijl validation of her or his abilities. (If she's right about the moon disappearing for an hour, then surely she has a powerful pipeline to the spirits and maybe we'd better make her a nice gift).


"Reach out and touch the moon" if you can (but usually you can't). The only times when the full moon rises in your sunset shadow are, however, spectacular they tend to be followed by lunar eclipses in the next several hours. Like the leaves and crystals that give an hour's warning of a solar eclipse in progress, the shadow directions are capable of being used for a few hours' warning of a lunar eclipse.

It's all because the earth's shadow, narrowing like a cone, stretches out into space; you can't see it, but it is just to the left of the rising moon. (Should your sunset shadow point to the right of the moon, you can be sure that no eclipse will happen, as the moon moves left during the night in its orbit.)

You need not understand that to invent a simple rule, to watch out for those full moons when the sunset shadows point at the rising moon. If your sunset shadow points at the moon when it is already a half-dozen diameters above the horizon, that doesn't count. If the moon rises after sunset (assuming that you haven't some hills in the way, elevating the horizons), you're safe too. It is when the full moon is no more than a few diameters off the eastern horizon at sunset that an eclipse is possible provided the Pointing Shadow is somewhat to the left of the moonrise.

But what about all of those hazy sunsets over the Pacific, where the shadows are pretty hard to see? You can solve such problems (and those associated with the fuzzy edges of shadows) by looking directly at the setting sun, getting your line of sight from an edge of the sun itself rather than from a shadow. And how can you do that, if you also have to look at the rising moon? Yes, I know that you can turn around but how do you know that you've turned exactly half a circle, short of using a modern surveying instrument?


The low-tech solution is to get a friend to help: use two observers, standing some distance apart from one another. Observer A stands still while Observer B moves around until the rising moon is located just behind A. Then B remains standing there, and Observer A (continuing to stand still) sights past, him toward the setting sun. If the setting sun is indeed behind B, then the observers must be on the line from sun to moon.

Now it seems unlikely that prescien-tific peoples would have formulated the rule as a "straight line" relationship. They'd have personified things, if folk culture is any clue. They might have called Observer A the "Sun Priest" because he watched the sunset, and called Observer B the "Moon Priest." They would have watched for those occasions when the sun "touched" the Moon Priest in the same manner as the rising moon had "touched" the Sun Priest. Symmetry, no less. How close is close? For lunar eclipses in the evening, several diameters (the sun and moon are both about half a degree); for eclipses after midnight, warnings will be pretty unreliable.

You can also use the Two Priests method to determine the day of the equinox; this will be left as an exercise for the reader's ingenuity.


The Pointing Shadow and Two Priests methods require that you get the hills out of the way. From an island or peninsula, you can usually find a beach with a view, giving a flat horizon to both east and west (my favorite is that promontory southeast of Athens, where the Temple of Poseidon is). Most people, living in most places, don't have such nice viewpoints with their opposite views. Their shaman would search for methods that would allow successful warnings from observations involving only half a horizon: northeast-to-southeast, for example, without any need for a view to the west.

I have a variety of solutions to that problem; they're not entry-level in quite the manner of the others, but they are far simpler than the intermediate-level magic numbers and the high-level orbital calculations. These low-level methods all involve using a familiar viewpoint and knowing a reference direction or two.

Lacking the proper sunset view, you have to make do with the sunrise view that morning. To use an example from autumn or winter, sunrise is as far south of due east as the sunset will be south of due west. Therefore the earth's shadow cone that evening at sunset will be equally north of due east. A moonrise which is as far north of due east as the sunrise was south of due east is an eclipse warning.

All fine and good, provided that you've already discovered how to determine due east from the equinox (one of the outcomes of that reader's exercise). But there is an easier way: just use the extreme position of sunrise in the southeast (which occurs on the winter solstice) and the other extreme sunrise position in the northeast (from the summer solstice). They're both the same distance from due east. Thus, all you need do is to note the position of today's sunrise relative to the nearest extreme (winter solstice sunrise in this example); if moonrise tonight is equally far from the other extreme, you have an eclipse warning.


How do you compare those angles or arcs (as we post-Euclidian types would say)? The nicest way I know is to hold a string of beads at arm's length, say an unfastened necklace with a little slack so that the beads can slide a ways (to start, force all the beads over to the right end). Hold it up to the sunrise with the necklace's right end at the well-known winter solstice sunrise direction, which you have memorized (or because you have erected a marker, though it need not be as elaborate as those megaliths at Stonehenge). Slide your left hand over to point at the rising sun and take hold of the bead under the sun. Let the other beads slide down the slack.

Maintain that separation between the two sets of beads (tie a knot or something) until evening, when you observe the moonrise. Hold the end of the necklace to line up with the summer solstice sightline and see if the moon rises over the last bead in the tightly packed group from the morning's observation. If it comes close, there's your eclipse warning.

Solstice directions are actually useful for eclipses. My guess is that's why the architects of sites such as Stonehenge were so fond of immortalizing sight-lines to the winter and summer solstice sunrises. Their use as anchors for a calendar has always seemed illogical because the sunrise position on the horizon changes so slowly from day to day; you can miss the reversal day by a week, especially when it's cloudy in winter, and that's no way to run a calendar.

A necklace, of course, isn't required; you can use any old stick, breaking it to the right length to preserve the data until moonrise. Note that you only have to make a very simple comparison it's not really measurement, doesn't really require a knowledge of geometric concepts such as angle. But you can see how the fancier concepts might have followed, once a shaman discovered how useful such a technique was. In particular, the necklace beads (pinon nuts are favored by the Indians as they have a soft core that can be punched out after grinding off the ends, handy for stringing onto a long hair) would make a good calibrated ruler, a nice way into inventing the counting and record-keeping needed for intermediate-level magic-number schemes.

We've solved the lunar-eclipse warning problem for those folk living on an eastern coastline, having a sea horizon but only to the east. What about those poor folks inland, with a nice even horizon that is, alas, elevated several degrees? The method will still work, surprisingly enough. There are problems with the Two Priests and Pointing Shadow methods where horizons are elevated: since the sun rises at an angle to the vertical, a sunrise delayed by a hill is a bit to the south of where it would have been if you had removed the hill. Elevated horizons can change a straight line into a dogleg, because a delayed sunrise appears slightly to the south and a premature sunset is also shifted south.

If both horizons are equally elevated, the error doubles.

But such problems are minor when dealing with only an eastern horizon. Both sunrise and moonrise are shifted around toward the south, but since you're always taking differences with the solstice directions (also shifted), the errors cancel. The horizon just needs to be uniformly elevated.


One way to smooth out a bumpy horizon is to build a level bank nearby, preferably in an arc around the observer's traditional viewing position. Thus both summer and winter sunrises are equally delayed, as are moonrises. An enigmatic feature of the megalithic monuments in the British Isles (seen most impressively at Avebury, a hour's drive to the north of Stonehenge) is a circular ditch and bank, the former likely the source of the latter. For the elevated-horizon scheme to work, only a fraction of a circle is actually needed, from northeast to southeast.

An easy way to level such a bank is after the winter rains have filled the ditches: use the high-water mark, making the top of the bank some fixed height above it. This should have been easy at Stonehenge and Avebury, as they dug through the thin soil and well into the underlying chalk; a floating scum of chalk powder leaves behind an excellent bathtub ring. The do-it-yourselfer might prefer to utilize the top of a fence.


Before anyone digs a ditch or builds a fence, let me point out a far simpler method: just pivot around a pinnacle (such as a tall fence post), keeping the rising sun hidden behind it (move back until just a little of the left and the right side of the sun peek out on each side). You will have to keep moving north as the sun rises, to maintain the two-point view. The sun finally crests, showing three pinpoints of sun around the obscuring pinnacle. The sun then becomes too bright to look at, so you look at your feet and mark the final viewing position for the day.

From one day to the next, the observer's final position will change, eventually reaching a northerly extreme at winter solstice, then reversing. The southern end of the path traced by the diligent observer will mark the summer solstice viewing position. Maintaining the two-point view will cause you to create a circular arc centered on your pivot (you have, after all, created a light lever, seesawing with the seasons); the arc described by the observer's path will be about as long as the distance to the pivot.

After sunrise, lay a long stick along the ground (or rope, or lengthy necklace) from your final viewing position to the nearest turnaround. Then take it over to the other extreme, laying it out along the observer's path. Observe the full moon that evening, marking the observer position when the moon begins to crest the pinnacle. If it is in the predicted place marked by the end of the stick, solemnly pronounce your eclipse warning. You can do the same thing, holding a forked stick against the nearest solstice marker.

Instead of a standard observer watching the sunrise move every day along the horizon, one has a moving observer obtaining a standard view of sunrise every day. The observer's position becomes the measurement. Best of all, the pinnacle pivot saves you leveling the horizon: the top of the pinnacle is the standard elevation at which both sunrise and moonrise are observed. Like the fence, the lower the better: pinnacles little higher than the tallest bump on the horizon are to be preferred. The observer's arc needs to be fairly level; shorelines and old lake beds are ideal (and a parking lot will do). A pier piling off an east-facing shoreline would make a good pivot.


The longer the distance to the obscuring pinnacle, the more the daily position jumps. With a lever arm of several miles, you can create an excellent calendar without any need for counting days, since there will be a unique observer position for each day of the half-year. If it isn't cloudy, you'll always know what day it is from your marks on the observer path, which will also need to be several miles long.

Actually, pinnacles aren't essential for either calendar or eclipse uses: any cliff profile or building edge will suffice (you keep one edge of the sun or moon in sight until it crests). Nor is a circular path essential for eclipse warning: a straight-line path that is approximately north-south will do (and for calendar-only use, even that requirement can be relaxed).

You can also use levered sunset views for a calendar, though not for eclipses.

Creating a good calendar is easier than predicting eclipses, thanks to the "mechanical advantage" of light levers.


The most familiar levered sightline is, of course, the shadow. The sun rises in the east and, as it gets higher in the sky, also moves south. Given a window on an eastern wall, the patch of sunlight on your western wall starts high on the wall and moves down but also north. It is as if the corner of the window fi-ame was the fulcrum of a lever.

For simplicity, imagine a window that is merely a thin vertical slit (as when a thin sliver of light sneaks in past the window shade to awaken you in the morning). First a "sun dagger" appears high on your wall, slowly moving down and to the right. When it reaches the floor, mark the spot. Tomorrow the spot will be different, as the sun's path through the sky changes with each passing day. The solstice sunrises will mark two extreme positions on the floor. Lay out a belt (or stick) from the spot reached by today's sunrise and move it over to the other extreme position, to predict a position for the full moon's rise tonight. Watch the "moon dagger" move down the wall to the right, and see if it reaches the floor at the same spot on the belt.

Simplicity. If the bottom of the window is high above the floor, you'll want to build a level shelf halfway up the wall, so that measurements are made when both sun and moon are still low in the sky but higher than the tallest obstruction. For ordinary windows that produce rather wide daggers, use where the lower right corner hits the floor (or shelf) as your criterion. Any north-south wall opposite an eastern window will do; it can even be rounded, like that of the Navajo hogan (with its east-facing doorway), so long as it is symmetrical around an east-west line.

Ultimately, such shadow schemes cannot be very accurate in comparison to the other eclipse techniques that directly observe an edge of the sun (and even they are likely to fail one time in three); long levers, as in the great kivas of the Anasazi at Chaco Canyon, tend to be defeated by the shadows' fuzzy edges. Small sundials aren't very accurate at telling time either, but people often decorate their homes with them, imitating the big ones. A lot of the rock art in southwestern caves that is illuminated by "sun daggers" or shadow edges may be similarly decorative, with the shaman making the serious eclipse and seasonal determinations elsewhere.


I'd recommend doing something to improve those sometimes-faint moon daggers. You can always position your head along the floor, and look to see where the moon first appears. But that's awkward.

Fortunately, you can reflect moonbeams (and sunbeams) around the room. Line up a series of crystals along the floor, watching to see which is the first to glow. Making a necklace out of crystals is even better. Lay out the necklace from the extreme nearest the sunrise in the morning, marking the first one illuminated (just slide the extras away from it). Then move it over to the other extreme and come back at moonrise; see which crystal catches the moonbeam first. Rhinestone belts might serve the purpose, if you're not up to drilling holes in crystals.


Shamanistic protoscience should not be confused with the modern versions of astrology, crystal power, numerology, fortune-telling, faith healing, and the like. Eclipse methods do indeed touch upon some practices for which a fascination still persists in many societies; it makes one curious about why humans are so much more intrigued than are the apes by predicting the future, collecting shiny jewels, and watching the heavens. There is an occupational niche created by this fascination; it is presently exploited by the purveyors of a variety of rather tiresome fringe enterprises, many with pseudoscien-tific pretensions.

Their purveyors as a group are now different than back in the days when those subjects were part of the more general intellectual mainstream, before things split apart into philosophy, religion, medicine, science, and fringe. The intellectual giants used to participate in the now-fringe discussions (Isaac Newton is a classic example from three centuries ago), back before so many were recognized as illusory dead ends. Improvements in eclipse prediction by Newton, for example, might have taken some of the fascination out of crystals (to the extent that they had been useful for warning of solar and lunar eclipses) and out of numerology (to the extent that some numerology was validated by those lists of magic numbers used by the Maya and the authors of Columbus's nautical almanac).

Selling an illusory shortcut to power seems to be the modern motivation of the purveyors, not the advance of knowledge though one must acknowledge that the fringe would be considerably less popular (and its purveyors considerably poorer) if scientists did a better job of making their subject accessible to the 94 percent of the U.S. population who cannot pass a simple test of "scientific literacy." While there is now an educated sub-population that is relatively immune to their claims of power, their purveyors have media assistance in propagandizing the less experienced (besides all their paid advertising, try comparing the column-inches that your local newspaper devotes weekly to astrology and to basic science).

To predict something without understanding why the prediction works may seem more like magic than science at least in the turn-the-rational-crank view of science. Textbooks emphasizing the rational over the creative aspect of science are one reason why many people imagine "doing science" to be about as much fun as balancing their checkbook. It should be emphasized that, on the frontiers of research, one is often investigating some creative scheme that seems to work, though you don't yet know why. We tend to find out why (or forget about the scheme) within decades, but that's on the modern time scale of scientific advance; in protoscience, such schemes surely persisted for many generations without any advance in understanding, tantalizing but entangled with the irrelevant, passed along as tradition.

Whether any of the present eclipse-prediction methods are, indeed, reinventions of prehistoric methods remains for archaeological analysis to evaluate. That there are so many methods suggests that there are many potential routes to this kind of knowledge base. Not only could predictive physical science have developed before the mathematics and geometry of the ancient Greeks and Chinese, but it could have flourished long before organized record-keeping even back in hunter-gatherer times, during the long haul of the ice ages when the hominid brain was still enlarging, and reorganizing.