Hiking upriver two hours after sunrise, I looked back from my first rest stop — and had difficulty even locating the Cardenas hilltop amidst the other shapes of the Grand Canyon.

     It had become cloudy but remained shirt sleeve hiking weather. The mild winter temperatures in the bottom of the Grand Canyon can be compared to a marine climate like that of Seattle or San Francisco, where the sea temperature usually keeps adjacent land from cooling down to freezing even in winter. As temperate zone winters go, conditions are pleasant. The animals know it too, judging from the footprints that you occasionally see, leading down to the shores of the Colorado River. Still, you can look up at the North Rim and see tall snow drifts.

     The fact that there are so many eclipse methods suggests that there are multiple routes to this kind of knowledge base, that it need not require the specialized roles and record-keeping that we imagine existing only after the settled existence associated with agriculture. Indeed, one can even argue that hunter-gatherer eclipse-warning success might have promoted a settlement near useful horizon features, the shaman reluctant to move very far away from where the methods seemed to work — and that agriculture was promoted by such settlement.

     Was supernaturalism part of all this? Supernaturalism is merely the social give-and-take metaphor, carried to extremes. For nearly all humans, that’s the “mechanism” that they know best: they learn it from their siblings, they often consciously use it as young adults in trying to make their way in a world where older adults control the resources. When you have to deal with something that you don’t understand, you don’t invent something out of the clear blue sky. The first thing that you try is a familiar analogy — and for most people, that’s social give-and-take. These days, many of us have additional mechanistic metaphors: we apply plumbing (“He’s stuck”), photographic (“A virtual snapshot in time”), automotive (“She’s a real self-starter”), and sailboat analogies (“He keeps flip-flopping on the issue”) that not only broaden our social analyses but also allow us insights into harder-to-understand physical systems such as electricity, aerodynamics, computers, and ocean currents. In science, we have gradually developed an extensive repertoire of analogies, handy for trying out on new situations to see if they will give some insight, even if they won’t work exactly: even mentally, you can’t make something out of nothing, so you start with new combinations of old concepts.

     Praying before an eclipse was just another supernatural application — but, with a forecast to trigger the supplicants, there would have been rapid feedback (that partial eclipse reversing instead of becoming total) before you forgot the antecedents. The role of the priests with the skills to warn of eclipses would come to be recognized, in a way with few parallels in the usual supernaturalistic pleading for rainfall, for prey animals to come one’s way, and so forth. That’s a lot of incentive for the priests to improve their predictive skills.

     The only other shamanistic activity with a good parallel to eclipse forecasting is the physician’s good fortune, being able to take credit for the patient spontaneously getting better. As all physicians eventually learn, most illnesses — at least, at the stage when the patient initially seeks out a physician — really are better the next morning, even without treatment (that’s why you always have to compare a new therapy to the “natural course” of the disease if left untreated — and disease symptoms often fluctuate). So too, after most ritual forms of healing, the shaman probably got a lot of undeserved credit from patients who spontaneously improved.

     The age of the Cardenas ruin continued to intrigue me, as I hiked uphill. One millennium versus ten is certainly an enigmatic aspect of the Cardenas levered sightline. But the significance of the Cardenas lever — as well as that at Perfect Kiva and anywhere else with a good corner in which to fit the sun — doesn’t really depend on age. It’s all those implications for how early instrumented science could have evolved, could have provided some metaphors that would serve as new building blocks: counting, comparison, measurement. One tends to credit curiosity about how nature works, but most societies were probably not like the ancient Greeks in that regard. Environmental situations that shape discovery — so that you can "back into" a method without really intending to — may represent an earlier stage of protoscience than intellectual curiousity about the nonedible aspects of nature.

     Shadows are “light levers,” the shadow edge rotating about a fulcrum as the sun rises. With long lever arms, one might expect considerable sensitivity to small-angle changes in solar declination near the solstice. Yet shadows per se have their problems, even in a large room such as a great kiva. The penumbra of the half-degree-wide sun is nearly one percent of the lever arm, blurring the shadow boundary as distance increases. That’s why I think that all those shadow tricks using caves and rock art are analogous to toy sundials. Maybe they were used, and were part of the learning curve before more precision methods were invented, but most shadow spectacles are likely imitations of a sort.

     A major improvement is to watch the sun rather than the shadow, framing it somehow to get the advantages of leverage. The open frame, such as winter solstice sunrise at the Hungo Pavi kiva, does have a problem (though it is minor, compared to watching shadows). Because framing the side and bottom of the exposed sun is possible only at elevations near the horizonal, the results are going to vary with the weather. Cold, dense air serves to bend light better; when the sun appears to be sitting on the local horizon (which itself is not particularly bent), it is actually farther below the horizontal than usual — and therefore farther north. Conversely a heat wave can move the sunrise southeasterly, even make you think that the solstice has arrived prematurely. It must have been embarrassing for a Sun Priest when, in retrospect, the solstice was celebrated on the wrong day.

     Obscuring frames mean that the measurement can be made with the sun 15° high in the sky as at Perfect Kiva and Cardenas, where daily fluctuations in temperature, pressure, and humidity will produce little effect (because the light path through the atmosphere is much shorter). Combining obscuring-frames with pivoting-to-a-standard-view seems to be a particularly nice combination: it creates a uniform horizon (at least for the months that the frame and observation arc is useful), it avoids the aforementioned refraction fluctuations, and it allows just one unclouded morning in the week before the solstice to pinpoint the exact day, provided you can count on your fingers.

     With lever arms the length of the Cardenas sightline, you can even detect leap-year-type fluctuations. You establish markers for the tenth, ninth, eighth, etc., mornings before the solstice. You use different colored stones the next year, and discover the drift. Which continues until, on the fourth year, you find yourself back over the original markers.

     It started raining early the next morning. Jim stayed a lot drier than the rest of us. In the morning light, we could see the fresh snow falling at higher elevations — up where we were heading.

     Alan intentionally didn’t stir the pot where the oatmeal was cooking, just long enough to demonstrate how the surface would become furrowed into six-sided cells. Having seen some lava that had formed hexagonal columns, he wanted to demonstrate how six-sided columns simply emerged as a solution to a packing problem when there was a temperature gradient. Crystals do the same thing.

     There were some big, wet snow flakes drifting down into the coffee cups. And surely sticking up higher along the trail. I talked to Katherine on the radio: She had been surveying some little-known Anasazi ruins that overlook this part of the Canyon, set back slightly from the South Rim — a summer home for the Cardenas Anasazi rather like those on the North Rim could have served for the Unkar Delta people?

     And, she said, it’s supposed to snow until Christmas Day.

     The shaman as healer surely has its origins in mothering. The identification and use of natural medicines seems to be present even in chimpanzees; again, I would tend to expect that women were the experts because they spend a lot more time foraging for plant foods in most present-day preagricultural societies.

     A lot of spatial intelligence is required for most of the eclipse methods; such mental abilities tend to be better developed in modern males than females — though the many female airline pilots with the requisite skills for one of the most spatially demanding tasks of the modern world (and a lot of men who can’t find their car in the airport parking lot) demonstrate that gender isn’t a reliable guide to expertise. Women tend to excel in verbal intelligence and, to the extent that storytelling was important to the role, might have been somewhat more likely to become a shaman than males.

     Another aspect is the use of eclipse knowledge to dominate others. In the apes, males tend to use spectacular feats to manipulate the whole troop. Among the wild chimps at Gombe, Mike’s charging display using the noisy tumbling of the tin cans is the classic example of attracting “respect” with a novel act. While there is a separate dominance hierarchy among chimp females, status is largely acquired by being born to a high-ranking mother, not by marvels that manipulate (though such tentative conclusions are always being overturned; when the number of observation hours doubles again, perhaps we will have seen some contrary examples).

     Who has the spare time to devote to experimenting with sun and moon observation? Men tend to have more leisure time (certainly in the Pueblos), and are better able to go wandering around the countryside without having to worry about dependent children. Many native societies (and some major world religions, such as Islam) severely restrict the mobility of females with culturally imposed rules.

     I’m not so much interested in whether the protoscientific shamans were mostly male or mostly female, but I am interested in how a mix of skills coalesced into a part-time occupational specialization called “shaman.” Among the useful talents are spatial-reasoning skills, plan-ahead skills, dominance-seeking tactics, methods for intimidating enemies, healing techniques, finding and using medicinal plants, weather forecasting, orchestrating spectacular performances, fortune-telling, spellbinding story-telling — and, of course, skills special to evoking the religious experience in listeners. But not every shaman would possess all such skills. Was there once a healing shaman (often female) and a separate spectacle-orchestrating shaman (often male) as the cultural niche started to evolve?

     And when did a shaman become known as a prophet or seer (with their foresight connotations)? Surely the occasional success of eclipse forecasting must have lent authority to whatever the prophet had to say about other subjects. But it’s a two-edged sword: some people erroneously infer cause-and-effect, equivalent to blaming a geologist for an earthquake simply because the scientist predicted it. It’s a version of the “bearer of bad news” effect: after something unusual happens, people tend to associate it unfavorably with the unusual things that happened even earlier. Post hoc, ergo propter hoc seems to apply even to predictions that precede the predicted event, in people without a more advanced understanding of cause and effect. If you predict good things, and they happen, you become associated with something good; a successful prediction of something bad is a little risky, and one suspects that prophet-protoscientists often insulated themselves by claiming to be messengers rather than power brokers like Columbus.

     The purveyors as a group are now somewhat different from when those subjects were part of the more general intellectual mainstream, back before things split apart into philosophy, religion, 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 they were recognized as 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 were useful for warning of total 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).

     What we see now are remnants of the former spectrum of subject matter. Religion too is a remnant; if you can manage to ignore their creeds and concentrate instead on their deeds, you may notice that religions (television evangelists excepted) manage to provide civilizing services to the community that the snake-oil purveyors do not.

     Why do people pay attention to the pseudoscientific fringe? Perhaps they perceive the power of knowledge but missed out in school on a decent science education — pseudoscience may be the best substitute that they can easily find, without going back to school (rather the way that comic books provide a refuge for the adult illiterate). I consider the popularity of pseudoscience (and those 94 percent levels of “scientific illiteracy”) a reproach to the scientists, for our failure to convey the excitement of our subject in understandable terms, and a rebuke to the shortsighted legislators who starve our educational systems.

     Science is often perceived as “difficult stuff,” considerably worse than balancing your checkbook. That’s a classic error: many mathematicians can’t balance their checkbooks either. Besides, what most people want is an understanding of the world around them, not an ability to solve homework problems or dissect dead frogs, and so can be tempted by the shortcuts that pseudoscience claims to possess.

     We also see how susceptible modern humans are to pseudoscientific claims: there is a niche for many of the aforementioned beliefs, one that continues to be exploited (sometimes cynically) by those who offer illusory shortcuts to knowledge and power. An orientation toward the future does bring with it a susceptibility to the false hopes raised by fortune-tellers. Our future-perfect thinking increases worry and suffering and gambling — but it is also a basis for our ethics.

     To predict something without understanding why the prediction works may seem more like magic than science. But, it must be recalled, the same can still be said of most medical treatments for most diseases — aspirin was used for a hundred years before we even began to get some hints about how it functioned in the nervous system. While an eclipse prediction scheme such as “Clenched Fist” is crude by modern scientific standards, one presumes that combinations of several of these methods could have substantially improved the accuracy of prediction.

     Were we to see that an ancient culture had invented a form of gunpowder, we might reasonably conclude that it augmented the forms of social organization associated with warfare — though, lacking specific evidence, a stubborn skeptic could always argue that explosive power led to nothing more than firecrackers. Should the archaeologists see the features of these modestly accurate eclipse forecasting practices in an ancient culture, it will be interesting to debate what uses were made of predictive power. Perhaps such techniques only served to line the pockets of fortune-tellers rather than serving to manipulate masses of people, facilitate the beginnings of large-scale social organization, and reinforce religious practices. But I think it reasonable to assume that eclipse forecasting could have triggered some such changes.

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, potentially back in hunter-gatherer times, during the long haul of the ice ages when the hominid brain was still enlarging and reorganizing.

     And I didn’t even have to find a path through these cliffs, only follow in the snowy footprints of the others up ahead. The first Indian to climb these cliffs had a much harder job than Alan, who was in the lead. When there’s no trail, you use your knowledge of other trails — perhaps remembering that switchbacks are a good way to handle a steep gradient, rather than going straight up.

     Yet what happens if you have never climbed a similar cliff before, don’t have an instructor? And you don’t know about switchbacking? Or about testing a handhold to make sure it will hold your weight (but looking first to make sure that your hand isn’t going to disturb a rattlesnake)? Or about planning a tentative route or two, when you’re still far enough back from the cliff to have a good view, rather than up close with a limited perspective?

     Protoscience, without a body of tested methods to draw on, must have found it difficult going too. Many an explorer of the eclipse methods must have given up in disgust, rather like the naive hiker retreats after the first section of a cliff, feeling totally frustrated by the dead ends and all the backtracking, worried about those shaking legs that had to hold too much weight for too long.

     Modern science has a wonderful collection of methods and metaphors that often carry over from one field to another. I’m not thinking so much of the way my psychiatrist friends can gain insights into neurosis from the default settings of computer software (and how inappropriate settings cause machine equivalents of tunnel vision, premature closure, and other strange behaviors). Or the insight psychiatrists can gain from the strengths and limitations of the peacemaking techniques that primates are observed to use during times of social upheaval — that sort of animal model is pretty direct analogy, at least in comparison to the more abstract analogies and metaphors that sometimes develop. Some of the ways of thinking that oceanographers have developed to model the abrupt climate changes in Europe have certainly influenced my thinking about sudden mood changes in mental illness, those unfortunate patients whose violent behavior just seems to explode rather than gradually develop as anger builds. And the hardware and software problems of computers have given the new generation of neurologists some fresh ways of thinking about various other kinds of brain disorders.

     Protoscience and modern science differ in some profound ways. As the biologist Mahlon B. Hoagland noted, modern science “is the natural searching within ourselves and in our surrounds for explanations. It is the process of making comprehensible, by discovering and explaining with simple laws, that which had been dark — and often frightening — mystery.” But protoscience may well have been in the business of creating mystery instead, keeping secrets rather than explaining to others. In some fields, there is a post-modern reversion going on: for lack of sufficient public funding, basic biological research is becoming privatized in the biotechnology companies, with new knowledge closely held rather than released in the public interest and widely discussed, as has been the academic tradition for basic research.

     And that might have been enough to enable someone to rediscover eclipse prediction. The ritual itself might contain most of the building blocks needed for forecasting. The new Sun Priest might reformulate the rules a little differently than the dead ones, and so shift from one of the warning methods to another in the process. But the priestly power conferred by successful eclipse warning might reinvest the priesthood with a wide influence over whole tribes, even permit them to frighten off enemies with tales of their powers over the sun and moon. Without reading and writing, ritual and storytelling are what carry along the more abstract aspects of the culture.

     Climbing out of the Grand Canyon is such a fitting metaphor for the ascent of science. As you reach the end of the path up the steep cliffs, you can indeed see farther — but the narrow path also starts to widen out onto a plateau. It’s an accessible land of opportunity, with lots of new choices for your next step.