From the Hopi’s Third Mesa, you look west and see the Grand Canyon on the horizon — at least, on a clear day. A sulphurous haze is becoming common, thanks to the smokestacks of the giant coal-burning power plant just north of the Hopi Reservation.

      South of Third Mesa, you can see the canyon of the Little Colorado River making its way northwest toward the Grand Canyon. A few miles before the confluence of the Little Colorado with the Colorado River inside Grand Canyon is a hot springs dome to which the Hopi trace their origins. In Hopi cosmology, people emerged from the underworld through that very "sipapu" and the dead return to the underworld through it (there is a symbolic sipapu — a hole in the floor — in every kiva). Shrines are located all along the route from the Hopi villages to the Grand Canyon, where the final shrine is located in some small alcoves on the banks of the Colorado River. Undertaking a journey to visit these places can be part of growing up Hopi.

      Just around the corner, as it were, from that final shrine in the Grand Canyon are Anasazi agricultural sites. The canyon opens out into bottomlands for a dozen miles on both sides of the river, finally narrowing again just below Unkar Delta. Has the Pueblo tradition forgotten this part of their Anasazi heritage (which seems to date from about A.D. 700 to about 1100)? Or do they merely avoid mentioning them to outsiders? If they visit further downriver than Mile 64, the Hopi certainly don’t leave behind prayer sticks and other offerings.

      I was particularly curious about that Cardenas Hilltop Ruin at Mile 71, across the river from Unkar Delta where I saw the lunar eclipse. The view from there provided a wonderful horizon calendar because of all those notches in the eastern rim of the Grand Canyon. When I had projected some color slides at home, that had been taken at my request from that hilltop by Larry Stevens, an ecologist working nearby, I noticed that the southeast skyline had a hole in it, through which you could see blue sky. That turned out to be where my calculations said that winter solstice sunrise ought to be: shining through the hole in the wall. But I couldn’t be precise about where you stood to see it: it was surely someplace along that southwest ridgeline on the Cardenas hilltop. Was the ruin the "Right Spot" to stand? I couldn’t be sure, just from the map. But the map is not the territory; I’d just have to consult the territory.

      And, of course, I couldn’t resist going to see the winter solstice sunrise from the ruin — with a little help from my friends.

      Lipan Point is where the trail begins, dropping down into the Grand Canyon. It was snowing lightly as we started out, but it was the old ice on various sections of the trail that caused us to be cautious. Robert Euler, the Park Service anthropologist at the Grand Canyon, was the only one of us who had the foresight to bring along instep crampons, handy for such icy patches. Bob went along with us just for part of the first day, returning to his South Rim office to remain in radio contact with us; he’s the expert on Cardenas Ruin, having dated the pottery fragments found near it to about A.D. 1100. My wife, Katherine Graubard, stayed on the rim and ran the radios for the five days of the expedition, keeping us supplied with weather forecasts.

      Hiking down, Bob explained that the Paleo-Indians were in the Canyon for many millennia before the Anasazi, that some caves were sites where they left split-twig figurines, presumably as offerings. A willow branch is split for most of its length, then folded into the shape of an animal, the willow ends tucked in to create the appearance of a spear embedded in the animal. Some are dated to 4,000 years ago.

      We camped halfway down the trail, far enough down in altitude to be rid of the ice but still likely to be snowed upon during the night. Our camp was not far from an old Anasazi campsite, judging from all the pottery fragments that Bob Euler had analyzed from this hilltop. We enjoyed a wonderful sunset view — not only of the Grand Canyon itself, but also of its east rim, known as the Palisades of the Desert, a series of vertical scallops in the cliffs above us, tinted red by the sunset.

      Over dinner we discussed yet another scheme for eclipse warning, which could have used those scallops in the cliffs. I’d worked it out back in rainy Seattle, while planning the expedition. In reading about Pueblo lore, I’d been struck with their notion of an underworld — and decided that the concept might substitute in some ways for what we call solid geometry. I even found a practical use for their underworld.

      The Hopi calendar in use in the nineteenth century had a peculiarity that fits well with yet another lunar-eclipse-warning scheme. In the old Hopi calendar, the winter months were called by the same names as the summer months. You may remember in the Pekwin story that the Zuni’s sun god said, "At the end of the year when I come to the south, watch me closely; and in the middle of the year in the same month..., watch me closely" (my emphasis). To illustrate, the first month after each solstice was called Pa-muya at Hopi. It is as if we were to call both January and July by the same name (say, "Januly"), both February and August by another name ("Febgust"), etc. ("Marctember, Aprilober, Mainov, Junecember").

      That is a very odd arrangement, since Hopi ceremonies throughout the year are scheduled by when the sun rises or sets over some horizon feature (with some modification by what the moon is doing that year). Yet these month names do not directly correspond to horizon positions — Pa-muya occurs when the sunrise is in both the most extreme southeast and the extreme northeast sectors of the swing in sunrise between 120 and 60, but only in the month after the solstice, not before it (when the sunrise is also in the same sector). Such peculiar month names suggest a second calendar system superimposed upon the sensible horizon calendar system. Why?

      Horizon calendars are rather like measuring the eastern horizon with a ruler, marked off with the days since the last solstice. When the sun rises over this ruler, you read off the date. It’s not a linear scale (the 31 days of March will occupy far more space than the 31 days of January, for example), but linearity is important only if you need to add and subtract. If you just want to compare two arcs that each start from a solstice, so as to pronounce them same-or-different, the nonlinearity won’t bother you.

      Now, suppose that you treat the full moon as if it were the rising sun, and read off its "date" from the horizon scale: you merely measure the full moon with the sun’s ruler. "The moon’s in the middle of March," as we could say if the moonrise was nearly due east, where the sun rises in mid-March. Given the similarity in size and shape between the sun and the full moon, one can see how this practice might have gotten started without an intent to predict eclipses — especially given that underworld notion. If the moon’s date (the number of "days" from the other solstice extreme) is the same as the sun’s current date, eclipses will tend to occur: the moon’s "date" is simply the angle from the other solstice, just as the sun’s date is the angle from the most recent solstice.

      Suppose that it were a month after the winter solstice, and that the moon rose where the sun does a month after the summer solstice: the "date" of each is the "last day of Januly." Since the "Januly" month is just a stand-in for an angle, you’ve got the condition for an eclipse.

      Thus a simple eclipse warning scheme, requiring no understanding of Hoyle’s equal angles principle, is to measure the full moon with the sun’s ruler and watch out for "identical" dates. It’s nothing more than Method #7 ("The Arm’s-Length Necklace") but using the most recent solstice rather than the nearest solstice, using the horizon’s features rather than a necklace. Ambiguity has its uses, in Method #12: "Measuring the Moon with the Sun’s Horizon Calendar."

      Comparing dates circumvents the usual problem of correcting the sunrise angle for the local horizon elevation — or of leveling the horizon, which would defeat the naming of those notches that prove so handy for a horizon calendar. You’re not literally measuring the angle between sunrise and solstice sightline, in the manner of holding a necklace up, but using the date as a stand-in for the true angle. Indeed, the bumpier the horizon the better, as the ruler will require less interpolation between named features.

      You could, I suppose, create a series of 183 marks, one for each day, and number them somehow, starting at the winter solstice ("Number 1") so that "Winter-Spring #183" was at the summer solstice sunrise rising position. For convenience, put them all on one side of the well-trodden path, say the side facing the pivot. Then create another series of 183 stones for summer-autumn on the back side of the path, numbered with the days after the summer solstice until reaching the winter solstice stone, "Summer-Autumn #183"). Your observer path is bordered by numbered stones. If the sun rises when the priest is standing at Winter-Spring stone 67, then the eclipse-prone position for moonrise will be near Summer-Autumn stone 67. Well, you could be off by a day because of the earth’s elliptical orbit, but I suppose that this counts as Method #13, "Moon Date Equals Sun Date" (though I’d bet that a name involving a coincidence with underworld happenings would be more likely, were the Anasazi using the method).

      Furthermore, you need not count the 183 days of the half-year in an unbroken string. Any scheme of subdividing the half-year will do (such as the Januly-type names), so long as it begins and ends with a solstice. The descriptions of the old Hopi calendar certainly come close to these requirements, though the overlay of new moon considerations complicates the issue (like the Romans, the Hopi tried to incorporate new moons somehow into a solar-synchronized calendar).

      This potential use of the old month-naming scheme makes me wonder if the Hopi or their ancestors managed to find a method that merged an eastern-horizon-only eclipse-warning scheme (that ordinarily requires a flattened horizon) with the otherwise desirable bumpy-horizon seasonal calendar for agriculture. Compromises for calendar reform, which somehow merge the features of two calendar systems, have taken many generations to work out in European cultures. No one knows how long the Maya spent trying to mesh their 260-day ceremonial calendar (arguably related to magic number schemes) with the 365.24-day seasonal calendar — but one speculates that it stimulated their need for more and better mathematical methods. If the Anasazi merged a bumpy-horizon seasonal calendar with a flat-horizon eclipse-forecasting system, the feat surely ranks high among prehistoric intellectual accomplishments.

      If the Pueblo peoples warn of eclipses using this horizon calendar scheme (or any other), they have successfully kept it a secret from the anthropologists. Whenever I think of Pueblo secrecy in ritual matters, I am reminded of the Pythagoreans, whose penalties were severe for disclosing even the existence of the dodecahedron. There is, of course, the possibility that the natives did tell the anthropologists — but that the anthropologists knew less astronomy than the natives, and so were never able to make sense of the explanations offered (such has occurred in matters biological, where natives accurately distinguish between sibling species of plants that most knowledgeable observers lump together). Indeed, even if a knowledgeable Pueblo shaman had undertaken to explain all to an astronomer, the explanation might have gone unappreciated, as approximate methods are unknown to most modern astronomers.

      The curtain of light drifts downward in a stately manner, revealing more and more of the nighttime canyon still in shadow. Dawn in the Canyon is a world of red cliffs, of whitened spires, of chocolate-colored buttes shaped like temples and castles. Sunrise can take more than an hour to sweep down from rim to river. It is a special hour when the air is still and clear, where the rich colors and long shadows contrast, emphasizing the depth and detail of the Canyon.

      Sunrise follows Unkar Creek down from its beginnings below Cape Royal, slowly bringing a new day to one after another of the dwelling places of the Anasazi; their corn patches were scattered all along the length of that creek, wherever a seep provided enough water. Eventually the sun reaches the sandy slopes near the river at Unkar Delta.

      Then the sun illuminates Cardenas hilltop across the river. Inside the mile-deep Canyon, this is a minor hill, distinguished only by its enigmatic ruin. The hilltop’s view is sweeping and spectacular, a panorama of the Canyon and its rims. But its exposed position, atop a windswept ridge well away from water supplies, is hardly the sensible building site usually favored by the Anasazi. It’s too large for a mere scout’s lookout and, although the Pueblo peoples do build prayer shrines in distant places, well away from their habitations, I’ve never heard of one quite so large. A kiva for Unkar Delta peoples?

      Even without having visited Cardenas hilltop at sunrise, I can tell you (thanks to topographic maps and computers) that something very special happens near that place. Each day in midwinter, about the time that the descending curtain of sunlight reaches the river’s edge, a narrow beam of light begins to shine on the hilltop. Like a dim and diffuse spotlight beaming down on a stage, a circle of sunlight illuminates the hilltop near the ruin. Each day as the winter solstice approaches, this spot of light brings a new day to the hilltop for a few special minutes before the wave of sunshine marching across the canyon reaches the hilltop. The next day, the spot of light comes a step or two closer to the ruin.

      Looking up at the rocks that block the about-to-rise sun, observers would have seen a humanlike facial profile in the skyline, looking rather like an Indian chief gazing up into the sky. His "eye" would appear to be brightly lit (that’s what causes the spotlight), and a "halo" appears around his "head." This probably did not escape the notice of the Anasazi, judging by the fascination that the winter solstice sunrise has for their descendants in the Pueblos, forty generations later. Did the beam of sunlight illuminate a waiting group of Anasazi, and signal the start of a solstice celebration?

      With levered sightlines pivoting about a foresight, where the observer moves every day to maintain a standard view of the rising sun, you can imagine a corral that marks the end of the line, the place where the Sun Priest stands still for days. A modern analogy would be the end-of-the-line turntable used to reverse a trolley car on its tracks — the trolley barn as kiva? Might the Cardenas Hilltop Ruin be such a turnaround? It all depends on whether the "eye" is indeed the pivot, part of an obscuring frame that forces the rising sun into a well-defined corner.

      Could this have been a special kiva for the winter solstice — the Sun’s Winter House? A real structure after all?

      Alan Fisk-Williams is the boatman (and lately high school science teacher) who introduced me to the place — and also introduced me to Bob Euler, who proved so helpful with anthropological background of the Grand Canyon’s Anasazi. Alan organized the logistics, all that food for hungry people.

      John DuBois is my oldest continuous friend, dating back to grade school near Kansas City, continuing through high school, through undergraduate years at Northwestern University; we even both did Ph.D. degrees in somewhat similar subjects, John in bioengineering and I in neurophysiology. John (who more recently has been designing instruments for orbiting satellites) was my source for all the computer programs that ran the heavens backwards to tell me what things looked like in the past, ran them forward to tell me when to be where, if I wanted a good view. John’s teenaged son Jim also came along from Boston; I’m not sure I’d want to do this as my first major hike, as it might make subsequent hikes pale by comparison.

      Jack Bunn is another old friend from graduate school; we suffered through qualifying exams together. A Seattle eye surgeon, Jack has an ophthalmologist’s eye for visual spectacle (as will become apparent). Two of his friends, Lynn Lively and Karen Kepler, were readily persuaded to come along as additional observers.

      As we hiked down, we all kept a lookout for that hole-in-the-wall in Cardenas Butte. It couldn’t be resolved on the topographic map, and the aerial photographs weren’t much help either. What we saw were some blocky chunks of Supai formation in the shape of a letter "G"; no matter how hard we looked, we couldn’t find an enclosed "O" in that rock formation.

      Lunch was taken in the Precambrian layers, sitting on rocks that were 800 million years old. Then on to the Colorado River, with a stop to refill the canteens. A few more miles downriver was our intended campsite, the same one that Alan and I had stayed in, back that night of the long lunar eclipse.

      I was curious whether a sunset sightline might exist at winter solstice, so Jim and I hurried to get up to the ruin before the sunset — which is rather early in the depths of the Grand Canyon in midwinter. Alan had told me about a shortcut trail that led directly up a ridgeline, beginning in back of the camp, and I quickly found it and puffed my way uphill. When I crested the top, I saw the Cardenas Hilltop Ruin in the late afternoon sunlight, looking even larger than it had in the pictures, certainly more sizable than I had remembered seeing it in the fading moonlight before that extra long lunar eclipse.

      And there was the Cardenas Butte hole-in-the-wall, standing above the ruin in the southeast, blue sky clearly visible through it, even without the aid of binoculars. The rocks surrounding it were perfectly lit by the setting sun, as clear a view as we ever had. The hole-in-the-wall, I realized, was indeed the "G" we had seen from the trail during our descent. From down here, the view of it was so oblique that the "G" appeared closed like an "O." The hole-in-the-wall that isn’t. But in this case, the appearance is what counts, not the name — a virtual hole, perhaps? Maybe just "window" will do.

      The sunset itself was considerably less interesting. It merely set into the side of a butte, at no special place. We checked in with the others by radio; they had arrived at camp too late to start uphill. And I talked with Katherine up on the rim, who said the weather ought to be good tomorrow morning — but maybe not the day after, the exact day of the winter solstice. Another storm system was coming.

      Dinner was hurried. Briefing for the morning’s activities was done by flashlight, over the sound of the rushing river.

      The next day, I discovered that my shiny metal spoon was missing. That was one determined packrat; I’m surprised that it didn’t try to acquire Alan’s flashlight for its collection. The archaeologists are rather fond of packrats, at least in the abstract: they hoard seeds and nuts (and anything shiny, for unknown reasons), but don’t always consume them. So the archaeologists can mine their middens, dating them with radiocarbon techniques, using the plants that were growing in the various millennia as an indicator of ancient climate change.

      Maybe some future archaeologist will find my spoon, stashed away in some recess in the rocks. We carried lots of extra batteries — for the cameras, for John’s little computer, for the flashlights, for the two handheld radios, for the little tape recorders — but not an extra spoon. Eating breakfast cereal with a fork is not my idea of fun.

      As best as I could tell from the calculations, the ruin wasn’t the best place to see the sunrise spectacle anymore: that was surely somewhere to the southwest of it. Even if the ruin were the best place a thousand years ago, the 0.1 reduction in the tilt of the earth’s axis since then would have shifted the final viewpoint about 10 meters to the southwest.

      What we might see could be predicted to some extent: The Cardenas Butte skyline, elevated 15 from the ridgeline, has a U-shaped "notch" to the north of the hole-in-the-wall (the "window"). The sun would peek through this notch, while otherwise remaining obscured behind the rocks, and this might last for a half-minute if the observer didn’t move. Then the window would brighten. After some seconds of the brilliant silhouette of the facial profile with the gleaming window, the sun crests the butte to the right of the window ("crest") and the scene becomes too bright to view. If one were to stand too close to the ruin, the sun would merely rise over the notch, and the scene would be too bright for further viewing; you’d have to move to your right to keep from being blinded. If you moved too far right, you’d never see the window lighted before the sun crested the butte. So in between, you should be able to keep the sun obscured except for that window.

      John and I both had small tape recorders on wrist straps and good telephoto lenses; we planned to move around to try and find the best view. Rather than fiddling with maps or aerial photos, we decided to mark the spots at which we shot pictures or dictated observations by dropping numbered coins on the ground; that would allow us to reconstruct the sunrise scene afterwards. The other five stationary observers were scattered over 140 meters of the ridgeline.

Aerial photo of Cardenas Hilltop. The ruin is at the cusp. The ridgeline for observations runs at about four o'clock from that center.

      I stayed near the ruin myself, looking at the brightening ridgeline with the big telephoto lens on my camera. But I guessed wrong. Jack Bunn shouted "Notch!" and then sidestepped to the southwest for a better view, while John and I ran toward him. Soon the sun crested the butte, and it was all over. Most of us had missed the view. Everyone commented on the strong "halo" around all of the skyline features near the sun — and maybe something spiky in addition.

      Jack had dropped a Canadian five-cent coin on the ground before he moved; it turned out to be 79 meters from the ruin. He thought that the best place to view the lighted window was several meters southwest along the ridgeline. And Jack had picked the 79 meter spot by a different criterion from mine. I’d been busy, watching the brightening skyline. He turned around and watched the shadow line moving toward our ridgeline, spotted the distorted features of the skyline we were watching, and maneuvered himself near to where he thought the window view would be. I never thought to look behind me; scientists often become fixated on a plan, but lots of the interesting discoveries come from just keeping alert, looking around for incidental things, like creeping shadows.

      So, we now knew where to stand tomorrow, a line of observers closely spaced, far from the ruin. After debriefing was complete, we hiked over to see the Colorado River from atop the cliffs. Unkar Delta across the river was newly bathed in morning sunlight, and Alan pointed out the ruins and where the Anasazi had irrigated fields of corn and squash. But I was restless to get back to camp, wanting to use John’s computer to figure out the significance of that 79 meter distance. It was far longer than I had guessed, and it was a good thing that I’d spread the observers widely rather than clustered them near my preliminary estimated position, about 10 meters from the ruin.

      Essentially, the question was: How much more must the earth’s axis be tilted to move Jack’s observer position inside the ruin? Was it too much, more than the known estimates of the earth’s range of tilt fluctuations (24.6 is about the greatest)? That would certainly scuttle the Sun’s Winter House hypothesis for the Cardenas Hilltop Ruin. John and I sat on a log next to the river and tapped the numbers into the handheld computer in order to get a rough estimate. It said that the tilt would have to be nearly a degree beyond the present 23.43. So, while uncomfortably large (i.e., a long, long time ago), not entirely impossible.

      We had a radio schedule to talk with Bob Euler up on the South Rim, and I reported our preliminary findings. And got the revised weather forecast: probably clear tomorrow for the solstice, but with snow arriving soon after. That suggested that we weren’t going to get a third morning at the ruin, that we would need to hike out starting tomorrow, after the sunrise.

      If an observer could detect the difference that half a meter made, then the exact day of the winter solstice could be determined, even before the reversal, just because you’d reach the daily markers left from previous turnarounds. The sensitivity of the viewing position was the other important thing we’d need to find out, in our one remaining morning; it tells you how big a circle that you need for a pivot calendar (as in Method #13) that can discern each and every day of the year via a stone circle.

      Part of the day was spent measuring distances from ruin to ridgeline, calibrating the aerial photographs that Katherine and I had taken from a small airplane several days earlier. And we looked around the ruin and along the ridgeline for ancient markers of any sort: carved rocks would have been nice, but I would have settled for tally marks. Nothing. Of course, a rock cairn will suffice for a century and, given the way that the turnaround (and all the other daily markers) would have drifted away from the ruin at the rate of about one meter per century, rock inscriptions would have become inaccurate here in only a few generations of Sun Priests. At sites such as Perfect Kiva, where the lever arm is 19-fold shorter (and thus the daily movements, and the century movements), viewer positions would have likely seemed eternal.

      Archaeologists have never excavated Cardenas hilltop, so we have no idea what the rock underlying the ruin might contain. Perhaps there are little buried offerings in some recesses in the rock floor, analogous to the prayer sticks (containing many bird feathers) that the Pueblo peoples leave at isolated shrines? Then too, the packrats might have created a time capsule: I keep hoping that the pre-Pueblo prayer sticks contain materials attractive to packrats — perhaps crystal or mica? Maybe a piñon nut necklace, so that a packrat might save a radiocarbon-datable nut with flattened ends and a hole through it? I could learn to like packrats.

      Now that we knew approximately where to stand along the ridgeline, we could cluster. I tried for several meters apart, hoping to answer the sensitivity questions. John and I synchronized our watches with my camera back that imprinted the time on each color picture that I took. We tested our pocket tape recorders, making sure that everyone’s voice could be heard.

      This time I used Jack’s trick, watching the sunrise shadow creeping slowly across the Colorado River, then up toward us. It’s sure hard to see the "spotlight" itself, in the manner of Delicate Arch’s; with 3 kilometer distances, the shadow edges become pretty fuzzy, as I should have guessed. But the horizon’s "profile" can be identified from the shadow line and so you can guess where to stand.

      About that time, I realized that this sunrise spectacle on the hilltop is also visible from down below, on the river bank. The right place would be just a mile or so upriver from Unkar Delta, and on the route to the other agricultural sites on that side of the river. Back before the Glen Canyon Dam started regulating river flows, the river thinned down considerably in midwinter, and the exposed river channel would have dried out and made an excellent footpath through this part of the Grand Canyon, an Anasazi "Main Street." Maybe that’s how they discovered this halo-and-window spectacle, just walking along the river, anytime in the month before or the month after the winter solstice. Perhaps the priests reserved the hilltop for themselves after trying to build the Sun’s Winter House where the spring floods washed it away.

      Alan, standing farther toward the ruin than the rest of us, caught the first glimpse of the sun but soon all observers were reporting the sun in the notch. One minute later, John reported seeing the sun in all three places: notch, window, and crest. But just 2.1 meters southwest of John, I saw none of this — yet 15 seconds later, I saw (and photographed) a magnificent sight: Only the window was brightly lit, with wispy curls silhouetting the rest of the "facial profile." Solar corona? Karen and Lynn, standing 1.3 meters further southwest than I was, saw only the bright wisps, without the window lit.

      Then everyone was reporting "crest" and we stopped looking. I handed the camera with the telephoto to Alan, who was wearing his running shoes rather than his climbing boots. We wanted a photograph of sunrise from the ruin, just to show how far off sunrise position was from the interesting spectacle. He took off for the ruin, making the trip in only 36 seconds — then had to wait for two minutes before the sun finally rose at the ruin. Sunrise there was considerably to the left of the low point in the horizon.

      Anticlimax. We began debriefing each observer, then measuring the positions of the numbered coins that marked their various positions along the ridgeline. As the roving observer, I had dropped six coins, announcing each into the tape recorder.

      A moving observer would have about 90 seconds to position the sun behind the rocks: one is forced southwest because the left edge of the sun peeks out and becomes too bright to view. If one goes too far southwest, the window isn’t lit. If I were an Anasazi observer trying to define a standard view to use each morning, I’d first find a place where only the notch is illuminated, then move right just far enough to keep it dimly lit. The notch would darken as the window brightened. Finally, the window would wink out before the sun finally crested the butte.

      My guess is that an experienced observer (and they got lots of practice, in the month before and after the solstice) could become pretty good at finding the viewpoint for this sequence: he could sidestep left, and recognize the view as a bit wrong; sidestep a bit right, only to correct back. It’s an empirical question, but I’ll bet that less than a 0.5 meter uncertainty in "the right place" would remain after a little practice, thanks to how well the notch-window-crest combination serves to precisely corner the half-degree-diameter sun in an obscuring frame.

      That suggests a standstill of several days, when the observer can’t be sure if reversal has occurred — but if the observer had a series of rock cairns marking a week of viewing positions from a prior year of unclouded sunrises, then just one unclouded sunrise would suffice to predict the exact day of turnaround. When the daily sidesteps are several meters, and the positioning uncertainty is less than a meter, it’s pretty easy to know which presolstice day you’re at.

      And this also suggests that 3,100 meters is sufficient as the lever arm, if you want to create one of those pivot calendars with an observer path that is lined with 183 stones on each side. Expert observers might get by with much shorter distances to the pivot.

      The turnaround is currently 82.3 meters along the path from the nearest corner of the ruin, using my proposed standard view. To run things back in time, I had to allow for the ruin being 7.4 meters lower in elevation than the ridgeline viewpoint (which I estimated from photographs), and for the Anasazi being 0.3 meters shorter (on average) than I am. But the result was that the present site of the ruin could indeed have been a turnaround during the period since Paleo-Indians began visiting the high desert Southwest. It could be a Sun’s Winter House, a place where the Sun Priest stood still.

      But it would have to be a very old one. The date suggested is back within a millennium of when the tilt of the earth’s axis was near its most recent maximum, 9,500 years ago. Since then, the winter solstice viewpoint has been slowly drifting away from the site of the ruin; the tilt cycle is 41,000 years long and so it will continue to flee the ruin for some time yet.

      The ruin surrounds the turnaround of all turnarounds (whether or not the Paleo-Indians knew it), the Ultimate Turnaround. The Kiva of all kivas? The holiest of the Holy?

      I certainly doubt that the present ruin is 9,500 years old. Bob Euler has compared photographs taken a century ago with the present state of the ruin, and thinks that there is little change from a century’s wear and tear. Still, I’d expect it had to be rebuilt every millennium or so, just from the windstorms; the walls are only piled-up slabs of stone (from a nearby outcrop) that a few workers could build in a few days. No mortar, no roof — more like a New England rock fence. The issue is whether this might be a traditional site, preserved and occasionally maintained, even though the solstice turnaround kept drifting farther away.

      It’s not as improbable as it initially seems. Paleo-Indians were around the higher elevations of the Southwest by that date, the Clovis-Folsom hunters that were likely Arctic-adapted prior to the opening of the ice-free corridor through Canada about 12,000 years ago. About 10,000 years ago, the transition from big-game hunting to foraging occurred, as the megafauna disappeared. The mild temperatures, plus the good hunting and gathering, would have surely attracted them into this part of the bottom of the Grand Canyon during the winter storms. And the lighted window in Cardenas Butte is a visual spectacle that is easily discovered for several months of midwinter, just walking along the river’s "Main Street" about sunrise. So it’s not unlikely that the Paleo-Indians viewed winter solstice sunrise hereabouts, not unlikely that they saw the spectacle.

      Thus, for the ruin to be a Sun’s Winter House, it would have to be a particularly old one. The archaeoastronomy suggests that the rock crevasses around Cardenas hilltop might be a good place to search by more traditional archaeological methods. I just hope that the ancient Paleo-Indians (or the ancient packrats) left us some time capsules.