I should start by apologizing to all Southern Hemisphere readers for my descriptions of sun and moon directions that assume a Northern Hemisphere viewpoint. Readers in the tropics, even of the Northern Hemisphere, will also know that my descriptions of the sun's path through the sky will fail the test of generality in certain seasons. Most non-Northern-Temperate-Zone readers can, I suspect, make the relevant translations more reliably than the author, leading to my decision to leave these problems as "exercises for the reader."

I would like to thank Robert Euler, Dabney Ford, Astrida Blukis Onat, and Donald Keller for anthropological advise; Blanche Graubard, Leslie Meredith, and Katherine Graubard for editorial suggestions; Laurance Doyle, John DuBois, and Woody Sullivan for suggestions on the archaeoastronomy; Larry Stevens for a preliminary photographic survey of Cardenas, and the members of the Cardenas Solstice Expedition (Jack Bunn, John and Jim DuBois, Alan Fisk-Williams, Katherine Graubard, Karen Kepler, Lynn Lively) for their extensive help. The underground architect, Malcolm Wells, is responsible for converting my vague descriptions into valuable illustrations.

Web note: There is a useful summary of astronomy measurement principles in the context of Anasazi archaeoastronomy at http://www.hao.ucar.edu/public/education/archeoslides/appendix.html.

xi Mihaly Csikszentmihalyi, Flow: The Psychology of Optimal Experience (Harper and Row, 1990), pp.136-137.

4 Brian Brewer, Eclipse 2d edition (Earth View, Seattle, 1991), p.21. Partially reprinted in F. Richard Stephenson, "Computer Dating," Natural History 96(1):24-29 (January 1987). Note that the old woodcut illustration of Columbus and the Indians has the classic error committed by artists: the moon crescent should be rotated a quarter-turn anti-clockwise.

5 The 29 February 1504 full moon was partially eclipsed for 103 minutes, totally eclipsed for 48 minutes, then took 103 minutes to uncover. At the midpoint of the eclipse, it stood over latitude 40N, longitude 70W. From J. Meeus and H. Mücke, Canon of Lunar Eclipses -2002 to +2526 (Astronomisches Bro, Vienna, 1979). This implies that the eclipse began shortly before sunset/moonrise in Jamaica.

10 For some background on "after this, therefore because of this," see the Aplysia chapter in my book, The Throwing Madonna (Bantam, 1991).

10 Elman R. Service, The Hunters (Prentice-Hall, 1966).

17 Aubrey Burl, The Stonehenge People (Dent, 1987), p. 4.

20 Hunter-gatherers supernaturalistic: Service, p. 65.

23 Hacataeus, as quoted by the Sicilian historian Diodorus about 44 B.C.

24 R. J. C. Atkinson, "Decoder misled?" Nature 210:1302 (1966).

24 Gerald S. Hawkins and John B. White, Stonehenge Decoded (Dell, 1965).

25 Gerald Hawkins, "Stonehenge Decoded," Nature 200:306-308 (1963); Fred Hoyle, On Stonehenge (Freeman, 1977); H. C. Hostetter, in Archaeoastronomy 4:29-30 (1981); C. A. Newham, The Astronomical Significance of Stonehenge (John Blackburn, 1972); for a review, see Douglas C. Heggie, Megalithic Science: Ancient Mathematics and Astronomy in North-west Europe (Thames and Hudson, 1981), pp. 101-104. Hoyle has an excellent appendix on the geometry. Hawkins' use of the 56 holes is actually a warning scheme rather than a countdown; his eclipse seasons identify the same every-six-moons tendency for eclipses as my modulo-6 counting, and the 56 holes are used to count off the movement of the critical positions of full moonrise along the horizon.

26 Anthony F. Aveni, Skywatchers of Ancient Mexico. University of Texas Press (1980). Harvey M. Bricker and Victoria R. Bricker, "Classic Maya prediction of solar eclipses," Current Anthropology 24(1):1-24 (February 1983).

28 Dating the Christmas supernova: Nigel Henbest, "New stars for old," New Scientist, p. 764 (18/25 December 1980).

32 Readers exposed to the New Math will recognize "Clinched Fist" as a modulo-6 scheme; digital computers tend to use modulo-8 "octal" and modulo-16 "hexadecimal" schemes for internal computation, before translating the result to decimal. There is a very slight chance of seeing two partial lunar eclipses in a row (see Brewer, p.50).

34 Alison Jolly, "The evolution of purpose." In Machiavellian Intelligence, edited by Richard W. Byrne and Andrew Whiten (Clarendon Press, 1988), pp. 363-378 at p. 367.

38 I also saw a near-miss near sunset: a solar eclipse didn't occur but one could see the shadow of the moon in the atmosphere, starting at the horizon and expanding slightly before reaching the zenith. This cone shadow was visible for nearly a half-hour on the U.S. East Coast at the new moon in early February 1989; a partial solar eclipse occurred one month later, visible on the West Coast at midday.

41 The Pueblo peoples use crystals in kivas to reflect light entering through the smoke hole entry: A. M. Stephen, Hopi Journal of Alexander M. Stephen, edited by E. C. Parsons, Columbia University Contributions to Anthropology 23:959-962 (1936).

The Delicate Arch "spotlight" is present for a month before and after the summer solstice, whenever the sun's azimuth exceeds 293.50 but the sun is above 3.00 elevation; on first appearance, the spotlight is quite high and on Delicate Arch's stocky pillar to the north of the speaker's platform. Nearer the solstice, it starts below the pillar and angles up toward the speaker's platform. At the solstice, it starts well below the pillar (by about as much as the arch's height).

49 Robert C. Euler, George J. Gumerman, Thor N. V. Karlstrom, Jeffrey S. Dean, and Richard H. Hevly, "The Colorado plateau: Cultural dynamics and paleoenvironment." Science 205:1089-1101 (14 September 1979). And Jeffrey S. Dean, Robert C. Euler, George J. Gumerman, Fred Plog, Richard H. Hevly, and Thor N. V. Karlstrom, "Human behavior, demography, and paleoenvironment on the Colorado Plateau," American Antiquity 50:537-554 (1985).

51 Ray A. Williamson, Living the Sky: The Cosmos of the American Indian (Houghton Mifflin, 1984).

51 The Chaco Canyon "Sun Dagger" story is summarized by Anna Sofaer, Rolf M. Sinclair, and L.E. Doggett, "Lunar markings on Fajada Butte, Chaco Canyon, New Mexico," in Archaeoastronomy in the New World, edited by A.F. Aveni (Cambridge University Press, 1982), pp. 169-181; the sun-only part of the story may be found in A. Sofaer, V. Zinser, and R.M. Sinclair, "A unique solar marking construct," Science 206:283-291 (1979). See Williamson (1984) for a commentary and contrast to another Anasazi "Sun Dagger" at Hovenweap. Some doubts about the Sofaer et al. interpretation are expressed by Michael Zeilik, Science 228:1311-1313 (1985) and Jonathan E. Reyman, Science 229:817 (1985).

51 J. C. Brandt, S. P. Maran, R. Williamson, R. S. Harrington, C. Cochran, M. Kennedy, W. J. Kennedy, and V. D. Chamberlain. "Possible rock art records of the Crab nebula supernova in the western United States." In: Archaeoastronomy in Pre-Columbian America, edited by A. F. Aveni (University of Texas Press, 1975), pp. 45-58. Carl Sagan's Cosmos has a photograph of the Chaco Canyon pictograph on p. 232. The first report, from the area east of the Grand Canyon, was William C. Miller, "Two possible astronomical pictographs found in northern Arizona," Plateau (Museum of Northern Arizona) 27(4):6-13 (1955).

51 Anasazi as astronomers: See John A. Eddy, "Archaeoastronomy in North America: Cliffs, mounds, and medicine wheels," chapter 4 In Search of Ancient Astronomies, edited by E. C. Krupp (Doubleday, 1978); and Williamson (1984). Other rock shelters and Anasazi art, see the Preston's discoveries in Arizona Highways Magazine, pp. 22-25 (February 1983).

53 Pamela Hansford Johnson, The Unspeakable Skipton (Scribner's, 1981).

56 D. W. Schwartz, R. C. Chapman, and J. Kepp, Archaeology of the Grand Canyon: Walhalla Plateau (School of American Research Press, Santa Fe, 1980-81).

56 Monsoon season, see Arthur M. Phillips III, "And then came the rains: Wildflowers in response to climate." Plateau 58(3):3-7 (1987).

61 Point of measurement of shadow would be when the sun's center is aligned with the celestial horizon; knowing about parallax and the atmospheric bending of light (which amounts to more than a sun/moon diameter near the horizon), a modern observer might want to use the point at which the sun's lower edge is a half-diameter above the horizon. By the time that the sun sits on the horizon, it has already set by a true horizontal.

62 The astronomer Gerald Hawkins noted the "moonrise not long before sunset" rule while awaiting a lunar eclipse at Stonehenge (see Stonehenge Decoded, p. 146) and suggests that one might predict the hour of the eclipse from the decreasing interval between moonrise and sunset on the nights preceding the full moon rise. My "more than a few diameters" rule requires some explanation. For the 6 August 1990 lunar eclipse, the moon's upper limb was at 1.80 when the sun's lower limb was on the western horizon; the eclipse started eight hours later, shortly before moonset. In the winter, when the full moon can be above the horizon twice as long as in summer, a greater range would be needed than four diameters. But "more than 3-4 diameters" should suffice to rule out lunar eclipses that might happen before midnight, and the occasional surprises would only be seen by the dedicated observers that stayed up all night watching.

63 The straight-line rule won't work for eclipses that are due to happen in the hours before dawn; the moon moves enough in its orbit during the night to shift the angles about eight moon diameters. For example, the evening of the lunar eclipse of 6 August 1990, which was seen in Seattle only in the hours just before sunrise, the moon rose across the celestial horizon at an azimuth of 119.20 and seven minutes later, the sun set across the opposite celestial horizon at 295.60 (so that the center of its shadow cone was at 115.60, about 3.60 north of where the moon rose. But simultaneous measurements, as in the shining streaks and shadows, would have had a separation of 4.90 for most of the time between moonrise and sunset. On most occasions when ten diameter separations occur, eclipses don't happen.

63 When an eclipse is due, the moonrise will often occur when the moon is in the penumbra, already getting less sunlight and with much of what it gets filtered through the earth's atmosphere. Thus the moon may appear redder than usual.

66 Observer's criterion: for example, when the rising moon is symmetrically positioned behind the sun priest, the setting sun should come to be symmetrically positioned behind the moon priest. Either upper limb or lower limb on the horizon will work, as long as the two observers have the same rule; note that the judgments are not made simultaneously but moonrise first, then sunset when it occurs.

If the horizons are truly flat (i.e., the celestial horizon, perpendicular to the vertical), equal rules for both observers are needed. But if the eastern horizon is elevated a little, the moonrise will occur slightly southeast of the true position; similarly an elevated western horizon also shifts the sunset angle to the southwest, creating a dog-leg rather than a straight line between moonrise and sunset. One way to correct for a half-degree elevation difference (that's the approximate diameter of the sun and the moon) is to use the first glimpse of the moon (the "upper limb") but the sun when its bottom ("lower limb") is sitting on the horizon.

Two observers can evolve a correction for a larger elevation difference (given a standard observation site, say a high mesa) by introducing some lateral asymmetry. For example, the moon priest positions himself so that the rising moon's north side is touching the south side of the sun priest, as if framed in an L. The sun priest then watches to see if the setting sun touching the south side of the moon priest to form another L. If they stand far apart from one another, this sun-moon angle will be just short of 1800; if they move closer, the angle will shift down to 1750, etc. Thus a tradition might evolve of standing at a certain distance apart, just to create a correction angle that works locally for predicting eclipses. It's not something that you might stumble into, for discovering the straight-line method initially, but a tribe that moved from its original locality to the plains or mesas might discover that some slight changes in their original symmetrical method would still function correctly. Unless the horizon elevation is uniform (as I postulate for bank-and-ditch at the megalithic monuments), the correction would vary with the seasonal change in the direction of the sunset.

66 E. C. Parsons, Pueblo Indian Religion (University of Chicago Press, 1939), pp. 86, 181.

66 Florence H. Ellis, in Archaeoastronomy in Pre-Columbian America, edited by Anthony F. Aveni (University of Texas Press, 1975), pp. 82-83.

67 I first mentioned (though rather cryptically; it was a note added in page proof) some eclipse methods in The River that Flows Uphill: A Journey from the Big Bang to the Big Brain (Macmillan, 1986), p. 113.

71 Horizon calendars: See Williamson (1984) and Stephen C. McCluskey, "Historical archaeoastronomy: The Hopi example," in Archaeoastronomy in the New World, edited by A.F. Aveni, (Cambridge University Press, 1982), pp. 31-57.

SUPPLEMENTARY REFERENCE: William H. Calvin (1997), "Leapfrogging Gnomons" survey method for meridian lines, at http://WilliamCalvin.com/1990s/1997gnomon.htm.

75 Jacob Bronowski, The Origins of Knowledge and Imagination (Yale University Press, 1967 lecture, published in 1978), p. 9.

77 One of the great misnomers in naming apes is due to the preoccupation with cavemen. The common chimpanzee's Latin name is Pan troglodytes. The common chimp and the bonobo ("pygmy" chimpanzee, Pan paniscus) are certainly the most versatile of the extant apes - but have never been observed to live in a cave, except at a zoo. Sleeping nests in trees are more their style. There are also some birds with species name troglodytes, but they really do live in holes or caves.

78 Typical topics of cave art: the anthropologist Dale Guthrie, in a talk at University of Washington (17 February 1988).

86 Pocket transit measurements are not considered adequate evidence by themselves; magnetic anomalies due to iron in the sandstone are always a possibility, and hand-held instruments are not as accurate as those mounted on a stable surveyor's platform. The best evidence is a picture of sunrise or sunset in the inferred location; if one cannot return at the winter solstice (and Anasazi Valley's steep approaches can be dangerously icy in the winter), a surveyor's instrument (a theodolite) can be used to measure the angles, and a sun sight can be taken (calculations are easily done to determine its azimuth and elevation at any time of day) to use as a reference direction for the measurements of the corners. Unfortunately, you can't see the sun from many of the sites in the summer, because of those shadowing overhangs. At the more open sites such as Chaco, I did take sun sights to correct for local magnetic anomalies, rotating the pocket transit atop a level table (a plastic plate atop a camera tripod) from the sun's direction (known from calculations based on latitude, longitude, and time) to the sightline, using the magnetic bearing differences to infer its azimuth. In the light of the subsequent successes with solstice alignments from kivas, the uncorrected measurements from the pocket transit at Anasazi Valley may well be reasonably close.

91 The roof of Perfect Kiva is not entirely original; it had to be repaired by the archaeologists. And probably strengthened against foolish visitors. Many decades ago, a large horseback party of tourists came down Anasazi Valley - and all 40 of them had their group photograph taken while standing atop Perfect Kiva. The thousand-year-old roof cracked.

92 Perfect Kiva sunrise and sunset views: While winter solstice photographs are the best way to settle the uncertainties of pocket transit measurements, one must also remember that the tilt of the earth's axis has decreased somewhat in the last thousand years, about 0.10 (one-fifth of the sun's diameter). The estimates are close enough so that they can "be made to fit," the usual expedient being making an assumption about what the Anasazi used as their point of measurement. Upper limb "first gleam"? Or lower limb visible? Or nicely nestled into a corner? I develop the latter idea subsequently, at Chaco Canyon, but the sun is so high in the sky (150) by the time that it rises behind the staircase that framing the exposed sun on its bottom and left side won't work at Perfect Kiva. An obscuring frame must be used, and the horizon feature at 1350 seems perfectly suited to the purpose.

93 Examples of posts or pillars as foreground sights for pivoting about: The Stonehenge heel stone is perhaps the best-known foreground sight, though daily movements about a standard sight are seldom mentioned in the megalithic literature. For the Anasazi, see the analysis of pivoting by Michael Zeilik and Richard Elston, "Wijiji at Chacho Canyon: A Winter Solstice Sunrise and Sunset Station," in Archaeoastronomy 6:66-73 (1983), briefly summarized by Ray A. Williamson, Living the Sky: The Cosmos of the American Indian (Houghton Mifflin, 1984). Proposals for levered sunset sightlines to the offshore islands of neolithic Scotland explicitly include the notion of daily sidesteps: A. Thom and A. S. Thom, in In Search of Ancient Astronomies, edited by E. C. Krupp (Doubleday, 1977), pp. 55-65.

95 Elman R. Service, The Hunters. (Prentice-Hall, 1966), p. 68.

105 "Too many kivas": There was a time when any round subterranean room was called a kiva, but it is now clear that 1) some kivas were rectangular and above-ground (such as the one at Turkey Pen Ruin), and 2) some round foundations are not kivas in the Pueblo sense of a ceremonial room and clubhouse. Kivas tend to have a ventilation shaft down their south wall, drawing air down to a fire pit beneath the ladder through the roof opening; there is usually a deflector plate in the floor at the end of the air shaft, so that the flames are not blown sideways into the room. Round rooms without such features are more likely to have been storage rooms, etc.

107 One has to do this probability analysis for each site, and the analysis in the text is predicated on a situation such as Stonehenge, with panoramic views. At Betatakin, for example, there are only 2-3 nice features in the west that could be used. But there isn't a 600 spread on both east and west horizons from which to choose, as the alcove faces south and severely constrains the view of both southeast and southwest horizons from anywhere in the alcove, so the one chance in 120 is more like one in 25. The text also doesn't mention moonrise and moonset extremes, which tend to expand those 600 sectors by another 80 on each end, at least at the latitude of the Four Corners sites.

108 Driving north from Phoenix along the freeway, one comes upon a particularly striking mesa. The road signs indicate that it is named Table Mesa. I always imagine the many Mexican-Americans living in Arizona as having a good laugh as they drive by; whoever named it seems not to have known that he was repeating himself.

110 Velma Garcia-Mason, "Acoma Pueblo," in Handbook of North American Indians, volume 9, edited by Alfonso Ortiz (Smithsonian, 1979), pp. 450-466.

110 Quote from Ward A. Minge, Acoma: Pueblo in the Sky (University of New Mexico Press, 1976).

114 Paul R. Ehrlich, The Machinery of Nature, (Simon and Schuster, 1986), p. 234.

114 The Hopi-Navajo contrast suggests looking at the two populations for twinning rates and other data that might indicate some evolutionary specialization along the r-K spectrum that I discussed in The Ascent of Mind: Ice Age Climates and the Evolution of Intelligence (Bantam, 1990), Chapters 6 and 7.

115 Some Native American tribes reconciled the lunar and solar calendars by adding (as the Jewish calendar does today) a thirteenth lunar month every three years. The best evidence is Alexander Marshack's "A lunar-solar year calendar stick from North America," American Antiquity 51(1):27-51 (1985).

116 Ruth F. Benedict, Zuni Mythology, vol. 2, pp.66-67 (AMS Press, New York, 1969).

117 R. W. Effland, Jr., A. T. Jones, and R. C. Euler, The Archaeology of Powell Plateau: Regional Interaction at Grand Canyon (Grand Canyon Natural History Association, monograph 3, 1981).

118 The Hopi history is from Stephen C. McCluskey, "Historical archaeoastronomy: The Hopi example," in Archaeoastronomy in the New World, edited by A. F. Aveni, (Cambridge University Press, 1982), pp. 31-57.

120 Crow Wing (1925), cited by McCluskey (1982), p. 38.

126 Chris Kincaid, editor, Chaco Roads Project, Phase I: A Reappraisal of Prehistoric Roads in the San Juan Basin (U.S. Department of the Interior, Bureau of Land Management, Albuquerque, 1983). I thank the Chaco archaeologist Dabney Ford for her interest and advise.

131 Robert H. Lister and Florence C. Lister, Chaco Canyon: Archaeology and Archaeologists (University of New Mexico Press, 1981), Figure 80.

133 I saw a possibility for accurately measuring summer solstice at the North Rim of the Grand Canyon: at summer solstice, the rising sun on the far-distant horizon is framed by a cliff a few miles to the northeast of Cape Royal, at least if you stand in the right place. The horizon is quite low, allowing Open Frame (as well as Obscuring Frame). The distance means that the day-to-day sidestepping is considerable, even near the standstill. There used to be a ruin in the vicinity of the summer solstice turnaround, but all is now a parking lot for Angel's Window.

135 The equinox yes-or-no is all part of a general principle of measurement, applicable to anything that varies back and forth: measure it when it is rapidly changing, not when it has slowed down to reverse direction. For example, to determine noontime when the sun is highest in the sky, don't sit there measuring the length of a shortening shadow and waiting for it to begin lengthening. Instead note the time when the sun is partway up in midmorning, and then note the time in the afternoon when the sun is back down to the same elevation angle and thus casting a shadow of the same length as in the morning. Halfway between the two times was noon, when the sun was highest in the sky. It's probably what the Hopi are doing when they second-guess the Sun Priest: they watch the sun pass a characteristic horizon feature weeks before the solstice, and again weeks after the solstice, and so they know that halfway in between was the exact day of the solstice. And, hopefully, their Soyal celebration was indeed held that day.

134 The great kiva's perfect north-south alignment is reviewed by Ray A. Williamson, "Casa Rinconada, a twelfth century Anasazi kiva," in Archaeoastronomy in the New World, edited by A. F. Aveni, (Cambridge University Press, 1982), pp. 205-219.

Despite the north-south symmetry, the four large pillars that supported the great kiva's roof (which no longer exists) are in the solstice sunrise and sunset directions, at least when the sun is about 15-160 high in the sky (see Williamson's Table 1). I would note that, were there a center smokehole in the roof in the manner of Hadrian's Pantheon, an oblique sunspot would cross a pillar several hours after dawn; one imagines a band around Post D in the northwest, above which the sunspot never reached, the maximum height being reached on the winter solstice sunrise (and similarly for sunset on Post A in the northeast). In the days before the summer solstice, the sunspot would descend Post C in the southwest, reversing when reaching a band at the same height. And similarly for sunset on Post B.

135 The sun cornered, touching an edge plus the horizon at bottom, is a very different criterion than first gleam (sun's upper limb, as tabulated in almanacs). Since the sun rises along a line tilted about 400 to the horizon at winter solstice, this also means that the first gleam is in the corner. The main problem with using that first gleam as the criterion is that, unlike the case of a flat horizon, you don't know what part of the sun's rim you're seeing - until the sun rises a little farther and more of the circle can be seen. The main problem with so framing the sun is that you have to look at the entire sun, which can be rather bright. And so such framing only works near the horizontal, when the sun's brightness is filtered by the extra-long path through the atmosphere. At higher elevations, it would never work.

139 Member of Taos Pueblo, quoted by Jeannette Henry, Vine Deloria, Jr., M. Scott Momaday, Bea Medicine, and Alfonzo Ortiz, editors, Indian Voices: The First Convocation of American Indian Scholars (The Indian Historical Press, San Francisco, 1970), p. 35.

148 The necklace beads would also make a good ruler, a route into counting.

149 The equal-angles rule works exactly only at the celestial horizon, since the sun rises at a shallower angle to the horizon in the southeast than the northeast; at a 50 uniform horizon elevation, the maximal error is 10 (two sun/moon diameters along the horizon). But the overnight changes are often much larger than this, and so tend to be the limiting factor in determining "how close" is close.

150 The observer's path also needs to be horizontal; if it goes uphill and down, it will destroy the virtues of the bank's elevated-but-level horizon. I'd recommend digging a shallow ditch along the observer's path, filling it with water and a little chalk. And then after the water evaporates or drains, fill the ditch with rocks, up to the height of the high water line. You also need a standard-height observer (sighting along the mark on a staff) or each observer having his own solstice markers.

153 Actually, what you want is symmetry of the observer's path around the sightline to equinox sunrise, and that isn't really due east because of the elevated horizon. So in looking for leveled observer paths (and this applies as well to the north-south room walls discussed later), one might hope to see a few degrees offset from a perpendicular to due east. Not compensating would, however, cause so little error that the failure to find such offsets means nothing.

154 The slit-shadow method is also inaccurate because it uses a shadow line rather than direct viewing of the sun/moon. Shadow lines are fuzzy, especially if the window is far away; move your eye into the shadow and you'll start to see the edge of the sun; continue moving and the rest of the sun will uncover. That penumbra, due to the half-degree diameter of the sun, is why any serious comparison of arcs is going to be hard. While longer levers would nominally improve things, they will also spread out the penumbra more. So looking directly at the sun/moon, and positioning it in a frame, is far more accurate. If you don't have room to put your head in the path, reflecting the light via a crystal seems a likely substitute.

154 Lack of evidence for sun-watching from kivas: M. Zeilik, in Archaeoastronomy 7:76-81 (1984).

159 Arlette Frigout, "Hopi ceremonial organization," in Handbook of North American Indians, volume 9, edited by Alfonso Ortiz (Smithsonian, 1979), pp. 574.

161 Fred B. Eiseman, Jr., "The Hopi salt trail." Plateau 32(2):25-32 (October 1959).

163 Split-twig figurines: R. C. Euler and A. P. Olsen, Science 148:368-369 (1965).

164 Mischa Titiev, "Old Orabi: A Study of the Hopi Indians of Third Mesa," in Papers of the Peabody Museum of American Archaeology and Ethnology (Harvard University), 22(1) (1944).

67 The Hopi month names are discussed by S. C. McCluskey (1982), pp. 44-46.

? Since perihelion is currently in January and the earth travels faster in its elliptical orbit then, the two half-years (from solstice to solstice) are an unequal number of days, but this potential error will make little difference in warning of lunar eclipses in the several hours after sunset.

166 Only horizon positions associated with the "sun's ruler" are relevant; when full moon rises outside the sunrise extremes, eclipses are impossible.

168 Alexander M. Stephen, 1893 letter to J. Walter Fewkes quoted by McCluskey (1982).

169 D. W. Schwartz, R. C. Chapman, and J. Kepp, Archaeology of the Grand Canyon: Unkar Delta (School of American Research Press, Santa Fe, 1980-81).

169 Prayer shrines may be well away from habitations: McCluskey (1982), p. 34.

175 Pack rats: Donald F. Hoffmeister, Mammals of the Grand Canyon (University of Illinois Press, 1971), pp. 137-139.

183 A reading error of about 0.5 meters would still make the Cardenas levered sightline quite a scientific measuring instrument: that's about 20 arcsec of declination. And without metal, just an objet trouvé.

184 The ancient axial tilts (obliquities) are calculated from the Fourier series given by Andre Berger in Nature 269:44-45 (1977). With a declination decrease of 0.830 (corresponding to 1.380 along the horizon at 360 latitude) since the maximum tilt 9,500 years ago, and allowing for the ruin being 7.4 meters below the ridgeline viewing position, the 3,100 meter distance to the window yields a turnaround position of 84.5 meters toward the ruin from the present site 82.3 meters from its nearest corner. This also includes minor corrections for the observers being 0.3 meters shorter (based on Mesa Verde Anasazi) than myself and for the 1982 solstice occurring 12 hours after the observations were made. The 82.3 meters measured along the contours of the hiking path overestimates the straight-line horizonal distance by about 3.0 meters, suggesting that the ancient turnaround was 5.2 meters inside the ruin, whose diagonal is 9.2 meters.

185 Wear and tear at Cardenas hilltop ruin: Besides weather, there is that from contemporary visitors; not only is there a major hiking path passing the ruin, but boatloads of river-runners camp just below, every night during the summer. For someplace not accessible by automobile, this ruin has a lot of visitors annually - one reason why the archaeology ought to be done soon.

185 R. H. Lister and F. C. Lister, Those Who Came Before (University of Arizona Press, 1983), p. 16.

185 The turnaround of all turnarounds: The Cardenas hilltop ruin's site might merely have been the first such turnaround that was observed, 9,000-10,000 years ago (and even this date is subject to what part of the ruin corresponds to turnaround - the south edge, the center, etc.). To say that they knew it was the turnaround of all turnarounds is a considerably greater claim, one that I am not making; that would have required them to be around a few thousand years earlier, watched their winter turnaround viewpoints marching further and further northeast, and then seen them reverse drifting, leaving a structure at the extreme location.

187 James Clerk Maxwell, quoted in The Sciences (July 1986), p. 9.

194 Richard W. Wrangham and Jane Goodall, "Chimpanzee use of medicinal leaves," in Understanding Chimpanzees, edited by Paul G. Heltne and Linda A. Marquardt (Harvard University Press, 1989), pp. 22-37.

195 "Respect" via novel act: Jane Goodall, The Chimpanzees of Gombe (Harvard University Press, 1986).

195 Female chimpanzee hierarchies: Frans de Waal, Chimpanzee Politics: Power and Sex Among the Apes (Harper and Row, 1982). See also Goodall (1986) and Toshisada Nishida, "Social interactions between resident and immigrant female chimpanzees," in Understanding Chimpanzees (1989), pp. 68-89. And for the ape language debate, see Sue Savage-Rumbaugh, "Language acquisition in a nonhuman species: Implications for the innateness debate," Developmental Psychobiology 23:599-620 (1990).

200 Mahlon B. Hoagland, The Roots of Life (Houghton Mifflin, 1977), p. viii.

200 Frans de Waal, Peacemaking Among Primates (Harvard University Press, 1989).

202 Thomas Goldstein, Dawn of Modern Science (Houghton Mifflin, 1980).