Message #434:
From: AzTeC SW Archaeology SIG
To:   "'Matthias Giessler'" 
Subject: Surveying in the Anasazi Southwest
Date: Tue, 31 Dec 1996 15:56:28 -0700
Encoding: MIME-Version: 1.0


FROM:	William H. Calvin WCalvin@U.Washington.edu
	    Just to confuse everyone, I have *two* new books this year, HOW BRAINS
        THINK (BasicBooks) and THE CEREBRAL CODE (MIT Press)

http://weber.u.washington.edu/~wcalvin/gnomon.htm
A method for surveying a very long north-south line without modern
instruments

William H. Calvin, University of Washington, Seattle WA 98195-1800 USA

The archaeologist Stephen H. Lekson has noted that three ancient sites
lie within a kilometer of a 700-km-long line, the meridian of longitude
at 107°57'W. Many similarities have been noted between the pre-Columbian
Anasazi cultures of the Four Corners area (a region centered on 37°N and
109°W, where the states of Colorado, New Mexico, Arizona, and Utah meet)
and the ruins further south in Mexico. Now  Lekson suggests, in an
article in Archaeology magazine (from whose website your web browser is
now downloading the adjacent map by Lynda  D‚Amico), that three of the
largest ancient towns were all constructed to be exactly north-south of
one another. 

The misnamed Aztec Ruins are the most northerly, and are connected by an
ancient road to Chaco Canyon 88 km to their south, a road that is mostly
straight north-south. The Lekson meridian passes through the
northwestern part of Chaco where two large mesa-top sites (Pueblo Alto
and Tsin Kletzin) lie on a north-south line that includes, in the valley
itself, the great kiva of Casa Rinconada (the two other largest ruins in
the valley, Chetro Ketl and Pueblo Bonito, straddle this same
north-south line). 

Also near the Lekson meridian is Casas Grandes 624 km further to the
south, in the Mexican state of Chihauhua. Because of the architectural
similarities between the sites, it has long been assumed that the
Anasazis (who are among the ancestors of the remaining Pueblo Indians)
built them all in the centuries spanning AD 900-1500, moving north from
Chaco to Aztec Ruins and then far south to Casas Grandes. The Acoma
people, Pueblo Indians living 30 km east of this meridian, have a legend
of their leaders taking journeys north and far south.

Long north-south alignments date back even earlier in China. They
featured the gnomon, a vertical column whose shortest shadow was used to
measure seasonal changes in the elevation of the noontime sun. To quote
Krupp (1983): 

          By A.D. 725 a series of field stations -- each equipped with
		  an 8-foot gnomon and all strung
          out like widely spaced beads on a single meridian longitude
		  over a span of nearly 2,200 miles -- was
          set up by a Chinese Buddhist monk, I Hsing.

My brief purpose here is to suggest a method for surveying long
north-south lines, using several gnomons at a time. Many peoples have
used gnomons, such as Borneo tribesmen, Babylonians, and Ionian Greeks.
Though I know of no Anasazi use of the gnomon, they did carry long,
straight cedar and pine trees for great distances, judging from those
remaining as beams in the Chaco ruins.

I suggest that an experienced team of "utility pole" haulers could stand
the pole on end, temporarily holding it in a vertical position with a
few guy ropes. Given two such teams facilitates an interesting surveying
method.

Surveying a Long North-South Line

1. Balance a pole on end, guying it so that observations can be repeated
on successive days. 
2. Use a long radial rope, loosely tied around the pole base, to follow
the pole tip's shadow throughout the day. Find the shortest shadow
length (which occurs at local noon) and stake the spot. Better yet, find
a pair of points in the morning and afternoon where the shadow is the
same longer length -- say, the 0900-1500 points when the pole's shadow
reaches the rope's end. Stake this pair and then stretch out another
rope between the pair (this defines an east-west line); bisect this line
by folding the rope to find the midpoint. Stake the center. The noon,
0900-1500 center, and gnomon pole should form a line. If they don't line
up, repeat tomorrow with more morning/afternoon pairs, using knots along
the radial rope to mark the standard lengths. The result should be a
true north-south line. 
3. Send your second team south with the other tall pole. Have them hold
it up as far away as a sight line can be maintained, such as atop a
ridgeline. 
4. Standing north of the noon stake, the surveyor sights past the
center-line stakes and the local pole, ignoring outliers, and judges if
the distant pole (or the smoke plume from a signal fire) is in
alignment. If not, the surveyor signals the second team to relocate east
or west. A good signal for particularly long legs (one ridge line to
another could be 20-30 km) would be a blanket tied to the top of the
local pole, a rope (in the manner of a flag halyard or a jib sheet)
being used to shift this flag from east to west as the surveyor directs. 
5. Once alignment is achieved, the first team bypasses the second to
become the third, etc. The second team guys their pole in place and
repeats the previous steps to extrapolate another line to the south. Via
such leapfrogging gnomons, a long north-south line can be surveyed.

Practical Considerations

Poles would surely be selected to look straight; otherwise, they will
not balance well on end. Without a wind, they ought to have been able to
tune the guys for equal (and minimal) tension. 

The pole top should be thick, in the manner of modern utility poles, to
produce a sharp shadow. Even with a squared-off top, the shadow will
taper to a point at a distance (from the top of the pole) of about a
hundred times the pole's width at the top, thanks to the 0.5°-wide sun.
For example, for a three-story-high pole of 10 meters and a diameter of
14 cm, the square-tipped noon shadow will become a point when the
afternoon sun reaches an elevation of 45°. Fastening a broad object to
the top of the pole would be useful when trying to detect the tip of a
long shadow.

Errors can be either to the east or the west on any given leg but,
unless there is some cumulative bias (say, always sighting along the
same side of the post, or always folding the east-west rope in the same
direction), errors ought to average out and a line will form bracketing
a meridian line -- though not necessarily the one that began the series.
Shorter legs would keep errors from being amplified. On any one leg,
assuming autumn long shadows, the pole-to-noon leg is about 70% longer
than the pole, but the surveyor can stand farther back to judge the
center-stake alignments, so that's the judgment that governs the error;
the farther back, the less the width of the nearby pole will obscure
errors in the placement of the distant one. 

The method would not work well in forests, where sightlines can be hard
to maintain. But surveyors would tend to leap over valleys, going from
one ridge line to the next, clearing any trees on the ridgeline that
interfere with extending the sightline north and south. However, because
the land is not approximately flat near ridgelines, there will be errors
in using shadow lengths along the ground. An artificial horizontal plane
would be useful in most locales.

Given a vertical pole to rotate about, there is a simple method for
generating a horizontal plane. Two radial ropes are used, one rotating
about the base of the pole and the other about a higher point, both
being defined by pegs or circumferential grooves that keep the
respective rope loops from sliding along the pole. The far ends of the
two ropes are knotted together, thus fixing their elevation relative to
the pegs when held taut, and this would be true along any radial. When
the triangle is rotated about the pole, the knot's travels thus define a
plane perpendicular to the pole's axis -- and this is horizontal if the
pole is indeed vertical. The practicalities of keeping a heavy pole
balanced guarantees a vertical alignment, in line with gravity, if they
avoided support from the sides of a hole; the pole could be placed on a
large slab of stone to keep it from holing the ground. 

For the gnomon application, tie a series of N knots in the lower radial
rope, then tie the two rope ends together at a comfortable elevation --
say, waist height. As the gnomon shadow rotates, follow it with the
ropes, holding them taut at all times via the end knot. Each of the
knots will then be rotating in its own horizontal plane. In the morning,
when the shadow shortens enough to reach the rope  end, drop a long
stake to mark the spot. When the Kth knot is reached, stake that
position as well. And so on in the afternoon, as shadows lengthen. When
the Kth knot is again reached, use another rope to make a line to its
morning partner, bisect it via folding, and drop another center-line
stake. Once discovered (and the circular architecture and leveled
benches of kivas suggest the Anasazi knew such a rotating rope triangle
technique), the rope triangle would surely have been used in preference
to clearing and leveling ground around a temporary gnomon.

DISCUSSION

Were a leapfrogging gnomon method used along the Lekson meridian,
107°57'W, it seems likely that the poles would have been left somewhere
along the line rather than carried back home. Even if they were not
permanently erected as gnomons, such valuable timber would likely have
been incorporated into structures. Examining tree ring series at the
Casas Grande ruins might, for example, discover beams whose decadal
weather profiles match those of forests far to the north.

The surveyors might not, of course, have stopped at Casas Grande,
continuing south in search of the spot when the pole's shadow
disappeared at noon on the summer solstice. The Tropic of Cancer is,
alas, offshore in the Pacific Ocean at that meridian, but they could
have gotten within a degree by the time that 107°57'W reached the
coastline, near the modern city of Culiacán. Given that the pole is
tapering, it would be difficult to detect such a shadow at the base of
the pole, so the coastline at 107°57'W might well have seemed the right
spot, the final destination. 

REFERENCES

E. C. Krupp, Echos of the Ancient Skies (Harper and Row, NY, 1983). If
true, 2,200 miles is a distance equal to that of a north-south line
running down 100°W from the US-Canadian border at 49°N, though North
Dakota, South Dakota, Nebraska, Kansas, Oklahoma, Texas, and all the way
through Mexico to Acapulco at 17°N -- five times longer than the
distance suggested for the Anasazi. But this may be an error in
translating units of length, as modern China is not that long, from
north to south.

Stephen H. Lekson, "Rewriting Southwestern Prehistory," Archaeology
Volume 50 Number 1 January/February 1997 

Story in New Scientist, 14 December 1996.

Salt Lake Tribune story, 2 December 1996.

BACKGROUND

Lekson, Stephen H. Great Pueblo Architecture of Chaco Canyon. University
of New Mexico Press, 1986.

Lekson, Stephen H., Editor. The Architecture and Dendrochronology of
Chetro Ketl. Reports of the Chaco Center, No. 6, Division of Cultural
Research, National Park Service, Santa Fe. 

Curtis F. Schaafsma, "The Casas Grandes Interaction Sphere," excerpted
from a paper presented at the Durango Conference on Southwest
Archaeology, September 16, 1995.

W. J. Judge et al., "The Chaco Canyon Community", Scientific American
July 1988, p. 72.

John Kanter, "An Evaluation of Chaco Anasazi Roadways," webbed research
paper and graphics presented to the Society for American Archaeology in
1996.

----------- 

William H. Calvin is neither a surveyor nor an archaeologist. He has
written about the Anasazi in two books, The River That Flows        
Uphill (Sierra Club Books 1987) and How the Shaman Stole the Moon
(Bantam 1991). The latter is about prehistoric astronomy, a dozen
entry-level methods for predicting eclipses of the sun and moon, and it
contains much more on the use of constructed sightlines for making
measurements of high accuracy. He is better known as a theoretical
neurophysiologist and for his books on brains such as How Brains Think
(Basic Books 1996) and The Cerebral Code (MIT Press 1996). Original
elements ©1996 W. H. Calvin