William H. Calvin's HOW THE SHAMAN STOLE THE MOON (chapter 2)
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William H. Calvin
UNIVERSITY OF WASHINGTON
SEATTLE, WASHINGTON   98195-1800   USA
How the Shaman Stole the Moon

Copyright ©1991 by William H. Calvin.

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2

How Does Stonehenge Work?

[The stones of Stonehenge] are as prodigious as any tales I ever heard of them, and worth going this journey to see. God knows what their use was!
     Samuel Pepys, Diary, 11 June 1668

Pilgrims to Stonehenge may call themselves tourists these days, I thought as I drove along the valley in Salisbury Plain, but I felt more like a pilgrim myself. The paved highway overlies a well-worn footpath from pilgrimages past. To the ancient traveler, not having been prepared by picture postcards or television specials, the first sight of upright stones in the distance must have been particularly intriguing.

      Stonehenge sketch Their size is hard to judge, lacking adjacent trees to which you might compare a stone’s height. That some of the upright stones are capped by bridging stones is obvious, even from the distance. And they were once extensively capped, huge lintels hoisted aloft and carefully positioned, creating a stone circle in the sky. As you get closer to Stonehenge and begin to see people in the vicinity, you realize just how tall the stones are. To the ancient pilgrim, not accustomed to multistory buildings, they probably seemed enormous as well as exotic.

      I suspect that the pilgrims had to stop and prepare themselves before entering the ancient precincts, just as I had to stand in line for the opportunity to contribute a few coins to the present government of the island. At least the ancient pilgrims didn’t have to walk under a highway and then hike up out of a tunnel before approaching the now-silent stage.

      In its beginning the site was a simple, circular earthwork or "henge," an open space bordered by a chalk bank and large enough to hold several hundred people. Outside the entrance stood a weather-roughened stone, the well-known Heel Stone. For a thousand years, forty or more unremembered generations, this earthwork continued to be the meeting-place of native farmers, unaltered except for the digging-out of a circle of pits, the Aubrey Holes, just within the banks.
      Then, as late as 2200 BC, people brought some Welsh bluestones to the site, started to set them up in two circles, one inside the other, and constructed an avenue, undeviatingly straight, up the northern hillside towards the henge’s entrance. Abruptly the work stopped. The bluestones were removed and in their place dozens of massive sarsens were dragged a score of heavy miles from the Marlborough Downs. A horseshoe-shaped setting of five archways, the trilithons, was erected. Around it, enclosing it in a ring of dark stone, the pillars of the outer circle were raised, lintels lifted and laid along their tops... Later, the bluestones were restored, set up in a circle, dismantled, arranged differently.... The work gangs eventually gave up 2000 years after their ancestors had begun....

      Aubrey Burl, The Stonehenge People, 1987
      I heard people marveling at the engineering feats, saying the same things as do the crowds surrounding the pyramids of Egypt. Stonehenge was built about the same time, almost five thousand years ago, long before wheels and cranes and hydraulic lifts. Those big upright sarsen stones had to be hauled in from Marlborough Downs (and there is a major river valley to descend and ascend). The smaller bluestones were transported from far beyond the distant western horizons: they come from the Preseli Mountains in southwest Wales. While glaciers might have carried along the stones and scattered them hereabouts, the traditional assumption is that the Stonehenge builders barged them most of the way. In either eventuality, they had to be hauled uphill to Stonehenge. Why build here? Why not build your ceremonial center down near the banks of the River Avon, between the plateau of Salisbury Plain and that of Marlborough Downs?

**Fig. 2-1P  Trilithons photo**

      Perhaps this site was chosen because the view is better up here. This area is called Salisbury Plain, but it isn’t exactly flat. The "plain" has a number of deep depressions created by the water runoff over the millennia, which has cut down into the chalk bedrock that lies just beneath a surface layer of soil and grass. The roads seem to follow the grooves. And so the travelers’ view can be limited until one is close enough to Stonehenge to make out some of the details, such as those lintels. As you arrive at Stonehenge, your obstructed view expands. It extends without limit to all horizons, though not really like the view from a mountain top I was reminded of being at sea, flat horizons all around (give or take a wave or two), and no obstructions except those big, exotic stones.

      One reason that you can see so far is that the chalk underneath the thin layer of surface soil isn’t very hospitable to tree roots. Indeed, the subsurface chalk is why these stones are still standing. Many sarsens have stayed upright all these millennia because the builders dug foundation holes into the chalk, rather like sockets for teeth, in which to seat the stones. That makes them hard to topple, though many a stonemason in search of nice raw material has tried to quarry at Stonehenge over the years. They occasionally succeeded, which is why so much of Stonehenge is missing. If the authorities were to permit you to walk around probing the ground with a fencing foil after some heavy rains, you’d discover a number of places where you could sink it in, up to the hilt (usually, you’d encounter the hard chalk within a knife’s length). Over a hundred such empty stone sockets are hidden from view beneath the grass. **Fig. 2-2  Heel Stone and Aubrey Holes sketch**

      Some of them form rings around the central collection. There is a ring of 30 so-called "Z Holes" and, just outside it, another ring of 30 "Y Holes." Farther out, just inside the bank, is a ring of smaller stones, older than the others: those 56 "Aubrey Holes" were named for John Aubrey, the seventeenth century explorer of Stonehenge.

      Stonehenge is surrounded by a low earthen bank, beyond which is a ditch. Hardly large enough to qualify as a moat, the ditch is difficult to see anymore. Several large stones are outside the ditch perimeter in the northeast, such as the "Heel Stone." The "Avenue" leading to these outlying stones is bordered by its own bank and ditch, but it was a late addition.

      In between the few modern trees on the horizon (analysis of ancient pollen suggests that there used to be many more), you see some odd-shaped mounds, especially to the north. They too are human in construction, and about as old as the earliest Stonehenge in the vicinity of 5,000 years old. Simply nothing else around the countryside fixes your eye; this isn’t like the ancient Greek temples, situated to impress the visitor by the vistas they command as well as by the view seen by the visitor looking at the temple from the approach path. What made the view here so worthwhile?


MAYBE THE ANCIENT BUILDERS instead liked the view of the night skies. It is often suspected that the heavens were much closer to the interests of our ancient ancestors, back when after-dark entertainments were more restricted.

      Yet the view of the heavens would have been almost as good from down by the river’s edge. Getting rid of minor low-lying obstructions usually isn’t worth it, as the stars near the horizon are already obscured by that extra-long path through the atmosphere. Building Stonehenge down near the River Avon would have avoided the long haul for both the stones and the drinking water. And avoided the wind.

      Maybe the view was part of the scene-setting for ceremony, the way that Delphi has long views from its cliff-edge sites. But here the view (outside of Stonehenge itself) seems unexceptional to me, certainly little different from other places around Salisbury Plain.

      One possibility that remains is that the view was for doing science. Stonehenge has somehow become the universally-recognized symbol of scientific sophistication in prehistoric times, just as the caves at Lascaux, Niaux, and Altamira have become the symbols of Ice Age sophistication in art. The 25,000-year-old cave art tends to speak for itself, however; the 5,000-year-old Stonehenge does not. We have a rather superficial understanding of how those stones functioned. Were they useful in cataloging the heavens? Keeping a calendar? Or predicting eclipses, a step on the road to saving Christopher Columbus’s skin?

      Whose eyes should we attempt to see through? If we are to attempt to look at Stonehenge through the eyes of the earliest scientists, how far back should we go? Instead of thinking in terms of record-keeping agricultural civilizations such as Sumer or Babylon, perhaps we need to try to see the world through the eyes of the hunter-gatherers who preceded them, or those of the early agriculturalists who first settled down in one place. The hunter-gatherer societies of today are notably supernaturalistic in their approach to natural phenomena; if they are any indication of what a prehistoric society thought like, an eclipse prediction scheme that worked only half of the time would probably have been a great success, because of feeding on wishful thinking. I doubt that our ancestors had our modern attitudes regarding how good a scientific explanation needs to be in order to be judged successful.



  **Fig. 2-3  Sightline closing up sketch** AS I WALK AROUND STONEHENGE, I look between the stones. Whenever two stones line up, I sight along their edges. If I use the right side of one stone, and the left side of a more distant stone, the view becomes needle thin, pointing a well-defined direction. Gunsights tend to use grooves and needles, but the two opposing edges may have been the early version of defining a sightline. And where do such sightlines point? At Stonehenge, they merely point to different places on the distant horizon, none of which seem (to me) to be very interesting.

      At least, those places on the horizon are not very interesting in the middle of the day, when Stonehenge is open to visitors. Were I here at sunrise, wandering among the long shadows, peering through reddish-tinged stones, I might see the sun framed at the end of my sightline. But that would occur only on certain days, such as the shortest day of the year in late December which, for reasons that I will avoid elaborating upon, is also when sunrise reaches its extreme position on the southeastern horizon. The sun turns around the next day and, with each successive sunrise, heads back north.

**Fig. 2-4  Plan of Stonehenge**

      Another interesting day is the longest day of the year in late June, when the sun turns around from its northeastern extreme. Actually, the view of the sunrise remains the same for a week or more, as the day-to-day movement in the sun’s position on the horizon alters very slowly at those times of the year (that’s why they are called the winter and summer solstices, solsticederiving from the Latin for the "sun-standing" still). Halfway between the solstices, near the equinoxes in March and September, the place where the sun rises virtually gallops from day to day, jumping more than a full sun diameter along the horizon from one morning to the next, leaving space in between untouched by rising sun.

      Other Stonehenge sightlines are to the extreme sunset positions in the southwest and northwest. And there are some to extreme positions of moonrise and moonset. The moon isn’t often seen at the end of such sightlines, since the moon’s cycle is close to 18.61 years long. (Why? The "precession of the nodes" of the moon’s tilted orbit takes that long to complete. Rounded up, it’s 19 years; three such cycles are about 56 years.)

This island... is situated in the north, and is inhabited by the Hyperboreans, who are called by that name because their home is beyond the point whence the north wind (Boreas) blows; and the land is both fertile and productive of every crop, and since it has an unusually temperate climate it produces two harvests each year.... The account is also given that the god visits the islands every nineteen years, the period in which the return of the stars to the same place in the heavens is accomplished; and for this reason the nineteen-year period is called by the Greeks the "year of Meton."
     the ancient Greek historian Hecataeus, ca. 500 B.C.

SIGHTLINES created by the stones are the conventional "explanation" of the Stonehenge architectural plan; the first such suggestion was made four centuries ago, noting that the Avenue to the outlying Heel Stone was also the observation path to sunrise for the longest day of the year. Indeed, we now know that many megalithic monuments around the British Isles can function in a similar manner. What makes Stonehenge special is the claim of various archaeologically inclined astronomers that the Stonehenge architecture was used to predict eclipses of the sun and moon, that Stonehenge "functions" by design as a neolithic computer.

      Astronomers and historians usually assume that record-keeping was the way that the secret of eclipses was discovered: Carefully noting the cycles of the moon, how they correspond with the eclipses of moon and sun, and then noting that eclipses repeat on a cycle of 6585.3 days (the Saros cycle of 18 years and 11 days). By extrapolating ahead, one should be able to predict the dates of future eclipses from the record of past ones.

      Fred Hoyle’s complicated eclipse-prediction scheme for Stonehenge focuses on this eclipse repeat cycle, using those 56 Aubrey holes in the ring that surrounds (and antedates) the central megaliths. He hypothesizes several movable markers, transferred from stone to stone around the ring (and presumably heavy enough to resist mischievous youths and strong winds for 56 consecutive years). One "counts down" to the next eclipse, using such a computing scheme. Gerald Hawkins’ original scheme is much more simple; he suggested that the Stonehenge astronomers were counting off eclipse "seasons" which recur about every six months.

      The only hard evidence for any of the intriguing theories are those 56 holes in the earliest stone ring at Stonehenge and 19 in one of the later ones. They’re not predicted by the theory, only some of the many assumptions that go into the theory. And so many learned disputes among archaeologists and astronomers have appeared in the pages of Nature and Science, trying to make the most of the unavoidably thin evidence. In science as elsewhere, there is a tendency that, the thinner the evidence is, the more vehemently expressed are the opinions. One of early archaeological criticisms of the astronomer Gerald Hawkins’s book Stonehenge Decoded called it "tendentious, arrogant, slipshod and unconvincing" which, in retrospect, it has proved not to be. In particular, it provided a big surprise: the Stonehenge people were observing the moon’s horizon cycle, as well as the sun’s.

      The various 56-hole schemes are complicated enough that even someone with my training in spherical trigonometry and astronomy has to study them for a while before they begin to make sense. I cannot imagine trying to explain them to someone else without the aid of some complicated three-dimensional diagrams showing the orbit of the moon around the earth, and of the earth-moon combination around the sun. Someone, somewhere, likely used one of those three schemes involving 56-year-long record keeping, even if it turns out that the operators of Stonehenge didn’t. Surely these complicated schemes are not stumbled into, just by accident which is why I think that they are candidates for some intermediate stage in astronomy, but not an early one. How did eclipse prediction get started? Maybe with a method that only worked some of the time, but using simple observations, simple record keeping, simple reasoning?


RETRACING MY STEPS through the underpass, I reflected that whether or not the Stonehenge priests actually accomplished eclipse prediction, it is clear that, at some stage, various other peoples did. For example, the Greek philosopher Thales somehow predicted the 585 B.C. solar eclipse and the Babylonian astronomers seemed to know a lot about eclipses (though lacking a geometrical model).

      Even the natives of the Americas, probably isolated from any Eurasian protoscience for more than 10,000 years, managed to predict eclipses. And the evidence for the New World people doing it is better than that for the Old World peoples: The Dresden Codex (which is made of bark, not porcelain) is named for the German museum where the painted text now resides, and it is one of only about four sizeable examples of Mayan writing found in Mexico that survived the Catholic priests. Once its inscriptions were deciphered and analyzed, it became apparent that the Maya knew all about eclipses of the sun. This table, covering the period A.D. 755-788, didn’t miss a single one of the 77 partial or total solar eclipses of that period.

      So were the Maya great observers, compiling a "Mayan Almanac" from extensive eyewitness accounts? No. Only four of those 77 solar eclipses could have been observed in Mexico and, however good their communications system, it could not have been good enough: some of the listed eclipses were visible only in Antarctica. And most partial solar eclipses are never noticed. So this "Mayan Almanac" is a worldwide prediction table, not a list of observations. The Maya knew the sun-moon cycles well enough to be alert for an eclipse, even though they probably didn’t know where on Earth it would be seen.

      The Dresden Codex can be interpreted to predict about 98 percent of lunar eclipses as well. This near-perfection suggests that the Codex was probably designed for solar eclipses, and that another bark record existed, since lost (or burned by the pious Spaniards), specifically for predicting lunar eclipses. With the appropriate corrections, the Dresden Codex can even be made to work to predict modern eclipses: if those shipwrecked modern astronomers had a tourist replica of that ancient Mayan bark text, they too could predict eclipses without a reference library.


BUT THIS IS SURELY NOT how predicting eclipses got started, I reflected while driving north on the road up to another megalithic monument. Less than an hour north of Stonehenge by modern highway, Avebury was a long day’s journey for the ancient pilgrim. It is atop another chalky landscape called the Marlborough Downs; the pilgrim would have had to hike down into the Vale of Pewsey, across the River Avon, and then back uphill. The pilgrims probably stopped at enormous man-made mounds along the way such as Silbury Hill.

      From any one island, solar eclipses are often 400-800 years apart. Even if you have widespread communications so that word of distant solar eclipses reaches you, you would have to keep careful records for a long time in order to discover the repeat patterns. Yet most civilizations are fragile. Uprisings destroy the orderly records of events; plagues kill off the scribes; religious and philosophical differences frequently cause records to be destroyed. The priests accompanying the Spanish explorers were, of course, probably worried about accusations of being "soft on pagan religions" by their local chapter of the Inquisition.

      Knowledgeable people were lost as well: the earliest recorded solar eclipse was probably the one of 22 October 2134 B.C. Ancient Chinese records note that "the Sun and Moon did not meet harmoniously." The two Chinese royal astronomers, Hsi and Ho, failed to predict it and were executed by the unhappy emperor. Other major, long-lasting civilizations such as ancient Egypt and medieval Europe sometimes didn’t record a single mention of eclipses. This suggests that eclipses might have been too sacred to mention. While an oral tradition among the select few is one good way to keep the eclipse prediction method secret, it also makes it possible to lose the secret if several people die suddenly.

      Record-keeping a table of observations of eclipses has to be pretty good before it is of much use for eclipse prediction. Gaps in a record can be a big problem unless one knows exactly how long the hiatus was. When comparing records from different observers, one also needs a universal calendar so that a "date" truly represents the same day in both locations. We have enough trouble converting from the Julian to our Gregorian calendar; it was even worse in Roman days when a complicated moon-based calendar was in style. Voltaire once quipped that, while the Roman generals always won, they never knew what day it was when the victory occurred. Back in the Dark Ages, scribes lost track of a year every now and then, which is why the birth of Jesus is now placed in about 6 B.C. The time of year also seems to have been moved from springtime back to a few days after the winter solstice.

      Perhaps there is another early method for predicting eclipses aside from historical records, with the observation table coming later as record-keeping became better, after which someone figured out the repetition cycle. Perhaps the tables merely codified the knowledge that built up from the careful attention paid to eclipses, thanks to the successes of a more primitive prediction method. But what is that method, if the modern astronomers can’t figure it out?

      Recognizing that lunar eclipses only occurred at the full moon, when moonrise occurs near sunset, was likely the first step. Perhaps the new moon was similarly known as a danger period for solar eclipses. Eclipses simply never occur when the moon is waxing or waning. Surely in the months following a lunar eclipse, each full moon was carefully watched.


**Fig. 2-2P  Avebury stones, ditch, and bank PHOTO**THE PICTURE POSTCARDS show Avebury as a great circle, with a high earthen bank. Unlike Stonehenge, Avebury has an inner ditch (which rather detracts from the notion that these ditches were protective moats). Avebury is several city blocks in diameter, and the aerial views make it look like some sort of prehistoric particle accelerator buried in the earth. But its high circular bank is now split in four places to accommodate modern roads; there is, incredibly, a crossroads pub in the middle of the Avebury circle, and an adjacent village that has obliterated part of the great bank-and-ditch in recent centuries.

      In each "quadrant" created by the roads, upright stones are seated in chalk sockets, Indeed, the Avebury stones often look like incisors, bicuspids, and molars. Marlborough Downs, too, is underlain by chalk. So is much of England, as one can see at those white cliffs of Dover.

      The Avebury stones march along in stately procession too far apart to be bridged by lintels, in the Stonehenge fashion. Two small rings of stones are in the center of the large Avebury circle but, unlike the concentric rings at Stonehenge, these small rings are adjacent. Like Stonehenge, there are no obvious sightlines at Avebury or rather there are too many, with so many stones that the lines between them serve to point a great many directions. Even if a few should point to a solstice or a lunar extreme, what are all the others for? To disguise the purpose of the few?

      Whoever finds significance in a selected sightline may simply be imposing one’s own preconceptions on the place it helps believability if there are only a few sightlines and most are sun or lunar extremes. Stonehenge has at least ten such sightlines among its earliest stones, including the particularly obvious major axis through the Heel Stone in the direction of summer solstice sunrise; if you use the more modern stones, they provide Stonehenge sightlines in every which direction, not just the extreme positions of sun and moon on the horizon. So too at Avebury sightlines to everywhere.

      The size of Avebury and its many arcs of stately stones make one realize that Stonehenge once had stones in those Aubrey Holes. And that Stonehenge too had a significant bank and ditch surrounding it. The bank at Avebury is several stories high above the bottom of the ditch, far higher than anything at Stonehenge. Remaining sections of the bank can appear level and so the viewer standing near the central stones is treated to an artificially leveled horizon, one that obscures the distant hills and trees that might create irregularities in the perceived horizon. Was that an intended function of the bank, to smooth the observer’s horizon by elevating it a little?

      Exhibit A: A smooth horizon. For what is it so handy?


ANOTHER MOMENT IN PREHISTORY upon which I would happily eavesdrop would be the first time that someone watching an eclipse of the moon said, "Aren’t these happening awfully often? When was the last eclipse? It wasn’t all that long ago." And so people would have argued about the previous eclipse, correcting one another with examples of the events associated with each of the recent full moons. Exactly how often might a diligent observer see another eclipse?

      I puzzled over this while flying home, and finally realized that there was a way to answer this question without undertaking years of observation. On my way to the physics-astronomy library is one of the most impressive of modern sightlines: a pedestrian walkway and parkland on a northwest-southeast axis downhill through the University of Washington’s campus. It points to Mount Rainier. In Seattle, when one sees an elongated open space, one automatically looks at the horizon to see if the great white volcano is visible through the clouds. I suppose that’s why I was disappointed with the horizon at Stonehenge: a vista with a missing view.

      I sat down near the library windows with some big books from Vienna that list all of the eclipses since 2,002 B.C. Though called the "canons," they aren’t great leather-bound tomes in Germanic typefaces but rather softbound computer printouts. They list nearly 20,000 eclipses so where does one start? First I picked a region where the observers might have lived: one place is as good as another, as far as seeing eclipses is concerned (clouds excepted!). Since I’m interested in the Anasazi of the American Southwest about A.D. 700 for other reasons, I picked that time and place. Then I started entering the lunar and solar eclipses into my laptop computer — not all of them, just the eclipses that they might have seen then and there.

      I got tired of this after 125 years, so I tabulated the statistics. During the period between A.D. 700 and 824, an observer could have seen as many as 56 total and 57 partial lunar eclipses. There were 14 solar eclipses where more than half of the solar disk was obscured. You don’t usually notice a partial solar eclipse, so I only counted the occasions where totality occurred nearby; I was assuming that rumors of a total eclipse will spread a few hundred miles to my hypothetical observer in the Four Corners (where the modern states of Arizona, New Mexico, Colorado, and Utah meet).

      This means that about one potentially-observable eclipse occurs in an "average year." However, as I noticed scanning down my list, eclipses are not evenly distributed: sometimes a series of three or four eclipses can be seen in a two-year period; other times, no eclipses can be observed for about four years. So they cluster. There was often a second lunar eclipse on the sixth full moon after the first. Now, wasn’t that nice!

      If moonrise is carefully watched for a partial eclipse ending, the vigil maintained all night while most people sleep, and moonset watched near sunrise the next morning for signs of a partial eclipse beginning, the diligent observer would see many more eclipses than seen by the modern evening-only spectator. Given such diligent observers and unclouded viewing conditions, one gets a 56 percent chance of another lunar eclipse at the sixth full moon after an eclipse, an 11 percent chance at the twelfth, 8 percent at the seventeenth, and 5 percent at the eighteenth. If cloudiness or sleepiness causes the observer to miss an eclipse at the sixth full moon, the eclipse interval may appear to be twelve instead.

      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 readily get the reputation of being particular danger periods. Count to six, and then count 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.

      About 67 percent of all lunar eclipses occur at either the sixth or twelfth full moon following an observed eclipse, so by itself the clenched fist method is going to work two-thirds of the time. However, when no eclipses have been observed for a year, it gets slightly more complicated. While lunar eclipses do occur on the later multiples of six (18, 24, 30, etc.), many occur a month earlier than that (17, 23, 29, 35, and 53 months for the A.D. 700-824 lunar eclipses). Such eclipse intervals longer that a year account for 33 percent of the total; simply treating the late eclipse-danger periods as two months wide (17-18, 23-24, etc.) will encompass essentially all cases.

      Solar eclipses, I discovered from the canons, also occur on the same six-month spacing as the lunar eclipses. They’re just a half-month earlier or later than the lunar eclipse danger zone, occurring at the new moon that precedes or follows the full moon eclipse alert. But solar eclipses are reported (on my mostly covered criterion, word traveling a few hundred miles) about eight times less frequently. And probably even less so; this fraction, unlike the one for lunar eclipses, probably varies with the particular century and observation site. Thus you need not get started on solar eclipse prediction by observing one solar eclipse and counting new moons thereafter. You can get synchronized by observing even a partial lunar eclipse, counting by sixes (and making allowances after a year of no eclipses), and watching out for the new moons that precede and follow the lunar eclipse alerts. Because of this lunar-to-solar linkage, learning to predict commonly observed lunar eclipses was likely the path of discovery for solar eclipse prediction.

      So eclipse prediction is potentially quite easy, so long as you can be wrong half of the time. And the beliefs associated with intermittent reinforcement suggest that being wrong occasionally is, paradoxically, a psychological advantage.

      This clenched-fist counting scheme is uncomplicated, easy to discover (I may have discovered it with the aid of modern computers but anyone curious about when the last eclipse happened could have guessed the rule within a few years) and even easier to operate over the years.

      Of course, I mused (when the excitement of discovery wore off), solar and lunar extremes on the horizon have nothing to do with my counting-by-sixes eclipse prediction scheme. Nor do movable-marker 56-hole counting schemes. Indeed, clenched-fist doesn’t need horizon observations at all, certainly not the artificially flattened horizon that so impressed me at Avebury. Ironically, I’ve "explained" something without using any of the pieces of the puzzle that anyone has identified, thus far.

      But having found one simple scheme for predicting eclipses, I am led to ask: Are there other simple schemes? Could equally simple schemes make use of observations of the sun and moon sitting on a flat horizon, of the sort that the Stonehenge builders made and so immortalized in its architecture?

Anyone who has lived
through an English winter
can see the point
of building Stonehenge
to make the sun come back.

     the ethologist Alison Jolly, 1988
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