New Directions in American Archaeoastronomy: Pt.46 9780860545835, 9781407347394

Table of contents :
Cover
Copyright
Contents
List of Contributors
Introduction
Archaeoastronomy and Dynastic History at Tikal
The Observatory at Dzibilchaltun
Astronomical Images and Orientationsin the Architecture of Chichen Itza
The Relationship between the Venus Table and an Almanac in the Dresden Codex
Measurement of Angles in Mesoamerica. Necessity and Possibility.
Astronomia Primitivaentre los Tainos y los Caribes de las Antillas
The pillars of Cuzco: Which two dates of sunset did they define?
Directionality as a Conceptual Model for Zuni
Astronomy and Ritual: The Rhythm of the Sacred Calendar in the U.S. Southwest

Citation preview

Proceedings

4 6 Congreso Internacional de Americanistas International Congress of Americanists Amsterdam, Netherlands 1988

New Directions in American Archaeoastronomy

edited by Anthony F. Aveni

BAR International Series 454

1988

B.A.R. 5, Centremead, Osney Mead, Oxford OX2 ODQ, England.

GENERAL EDITORS A.R. Hands, B.Sc., M.A., D.Phil. D.R. Walker, M.A.

BAR -S454, 1988: 'Iew Directions in American Archaeoastrono:my'

© The Indi vi dual Authors, 1988 The authors’ moral rights under the 1988 UK Copyright, Designs and Patents Act are hereby expressly asserted.

All rights reserved. No part of this work may be copied, reproduced, stored, sold, distributed, scanned, saved in any form of digital format or transmitted in any form digitally, without the written permission of the Publisher. ISBN 9780860545835 paperback ISBN 9781407347394 e-book DOI https://doi.org/10.30861/9780860545835 A catalogue record for this book is available from the British Library This book is available at www.barpublishing.com

CONTENTS L ist o f Contributors Introduction 1 .

vii

A rchaeoastronomy and Dynastic History a t Tikal Anthony F .

2 .

Aveni

a nd Horst Hartung

The Observatory a t Dzibilchaltun Clemency Chase Coggins and R .

3 .

1

David Drucker

Astronomical Images and Orientations Architecture o f Chichdn I tzä

i n the

Susan Milbrath 4 .

5 .

5 7

The Relationship between the Almanac i n the Dresden C odex Victoria R . Measurement o f Possibility

Venus

Table

Bricker Angles i n Mesoamerica:

Necessity and

1 05

Astronomia Primitiva entre de l as Antillas

l os

Tainos y

l os C aribes

Sebastiän Robiou-Lamarche 7 .

The Pillars o f Cuzco: They Define? R .

8 .

M . 9 .

1 21

Which Two Dates o f Sunset Did

Tom Zuidema

Directionality a s Expressive Behavior

a nd an

8 1

Franz Tichy 6 .

1 7

1 43 a

Conceptual

Model

f or

Jane Young

Zuni

1 71

A stronomy & R itual: The Rhythm Calendar i n the U .S. Southwest Michael Z eilik

o f

the

S acred

1 83

i ii

L IST OF CONTRIBUTORS Anthony F . Aveni, Russell B . Colgate Professor o f Astronomy & Anthropology, C olgate University, Hamilton, New York 1 3346, USA Victoria B ricker, P rofessor o f Anthropology, University, New Orleans, Louisiana 7 0118, USA C lemency C hase Coggins, Peabody Museum o f Ethnology, Harvard University, Massachusetts 0 2138, USA R .

David Drucker, G eochron Massachusetts 0 2138, USA

Horst

Hartung, Faculty o f Guadalajara, Mexico

Susan

Milbrath, Florida Florida, Gainesville,

S ebastiän P .R. Franz

M .

Robiou-Lamarche, 0 0903, USA

Archaeology & Cambridge,

Enterprises,

Architecture,

Tulane

Cambridge,

University

o f

S tate Museum, University Florida 3 2611, USA

o f

Aptdo.

Tichy, P rofessor für Erlangen-Nürnberg, Kochstr.

Postal

1 626,

San Juan,

Geographie, Universität 4 , D 8 520 Erlangen, RFA

Jane Young, A ssociate P rofessor o f American Studies, University o f New Mexico, Albuquerque, New Mexico 8 7131, USA

Michael Z eilik, P rofessor o f Astronomy, University o f New Mexico, Albuquerque, New Mexico 8 7131, USA R .

Tom Zuidema, I llinois,

P rofessor o f Anthropology, Urbena, I llinois 6 1801, USA

University o f

I NTRODUCTION These papers a re among s ome three dozen f rom twelve countries r ead a t a j oint symposium entitled " Etnoastronomia y Arqueoastronomia en l as Americas", chaired by Edmundo Magai la a nd Anthony F . Aveni, and held a t the 4 6th International Congress o f Americanists in Amsterdam, July 1 988. When collection and editing o f the f ull complement o f papers proved unwieldy, i t was j udged to be more r ealistic to undertake to publish the a rchaeoastronomy papers s eparately; thus the present volume. A s was the case with a s imilar symposium held at the 4 4th I CA i n Manchester in 1 982 ( B.A. R. 1 74, 1 983), the editor's principal goal has been t o disseminate r esults o f current r esearch i n the g rowing i nterdisciplinary f ield o f a rchaeoa stronomy both expediently and e fficiently t o our i ntere sted colleagues. Most o f t he contributors to this volume will be f amiliar t o those who have r ead earlier collected works on a rchaeoastronomy i n the Americas; however, the careful r eader will note the g rowth and advancement o f the i nterd iscipline indicated by the i ncreased depth and breadth o f i nquiry undertaken by each o f the authors into problems t hey had a lready dealt with to s ome extent in earlier publications. Thus, Zuidema has more f inely honed his a rguments concering the placement o f the sun pillars on the horizon o f Inca C uzco, Aveni and Hartung have r e-examined t heir earlier s tudies o f the placement and o rientation o f the major t emples o f Tikal i n the l ight o f r ecently a cquired knowledge concerning the dynastic s equence that r uled the g reat Maya c ity, and Bricker has begun t o bring t ogether the edges o f the hazy gap between written Maya a stronomical ephemerides and a lmanacs. The a rguments o f C oggins & Drucker and Milbrath concerning the orientation o f buildings a t D zibilchaltun and Chichdn I tzä, r espectivel y, a re s et upon t he more s olid f oundations o f the bases o f evidence provided by the Maya written and i conographic r ecord. Three o f t he n ine papers in the collection address broader questions that t ranscend the s tudy o f s ingle s ites a nd perhaps even i ndividual culture g roups. P resentations by Z eilik and Young on the native American people o f t he US s outhwest and t he paper by Tichy on Mesoamerica i nquire i nto the rhythmic nature o f the calendar, concepts o f d irectionality a nd notions o f angular measurement i n g eneral. The appearance o f s uch overview papers in a p roceedings volume r eflects the degree to which contributing s cholars a re thinking well beyond the more narrow, i ndividualized r esearch approaches that characterized our i nterdiscipline a g eneration ago. A rchaeoastronomy has i ndeed s et upon n ew d irections that carry i t well beyond vii

a lignment hunting! While Mesoamerica dominates the p resent volume ( four papers s pecifically address Maya a stronomy), we a re pleased to s ee i mportant contributions r epresenting South America and the U .S. s outhwest appearing under the s ame roof. And we a re e specially grateful t o Robiou-Lamarche f or s ubmitting his work on the Antilles, a new a stronomical horizon f or most s tudents o f a rchaeoastronomy. The editor i s grateful t o Lorraine R . Aveni a nd J im McCoy f or their t echnical a ssistance i n the p resentation o f this collection. Anthony F . Aveni 1 November 1 988

v iii

" ARCHAEOASTRONOMY AND DYNASTIC H ISTORY AT T IKAL" A . Aveni & H . Hartung In t he 1 970's, Hartung ( 1975, 1 977) proposed a number o f l ogical a nd s tructural hypotheses by which deliberate o rientation and planning s chemes, particularly o f a n a stronomical nature, may have been i ncorporated i n Mesoamerican c eremonial c enters. Over the next two decades he and Aveni s urveyed l arge numbers o f Mesoamerican a rchaeo logical s ites with a v iew toward t esting and applying s ome o f these hypotheses. These s tudies helped t o develop the broader d iscipline o f a rchaeoastronomy, which f ocuses on understanding the nature o f ancient a stronomical practice utilizing both t he written and the unwritten r ecord. More r ecently, Aveni & Hartung ( 1986) have r eviewed Maya c ity planning a s i t p ertains t o f unctional orientations that r elate to the e stablishment o f environmental calendars, wherein t he movement o f celestial bodies a t the horizon, particularly the s un and Venus, s erved a s t iming devices, thereby indicating where c ertain s tructures ought to be placed and how they s hould be o riented. A portion o f o ne o f these s tudies ( Hartung 1 977, pp 1 12-118) d eals w ith the ruins o f Tikal. The data were based i nitially upon the f orm a nd a rrangement o f buildings gleaned f rom a s tudy o f t he Tikal map ( Carr & Hazard 1 961). Though we had only l ittle knowledge o f Tikal chronology a t t hat t ime, our e arly s tudies nevertheless r evealed the existence o f s everal e lements that suggest i ntentional planning. Alignment data were collected with s urveying equipment by the a uthors at t he s ite i n January 1 975. They were supplemented by further precise measurements made i n January 1 978 and J anuary 1 987. In t he past d ecade-and-a-half, much i nscriptional and a rchaeological e vidence has come t o l ight r egarding the dynastic history o f Tikal and we now have a much c learer, though not yet f ully comprehensive, i dea o f the chronology o f the building c omplexes and even o f s ome o f the individual buildings. Moreover, we know and i n s ome i nstances can make educated g uesses about which members o f the royal l ine a re buried beneath the different s tructures. For example publications by Coggins ( n.d.), Jones ( 1977), and Jones & S atterthwaite ( 1982), s tress the valuable h istorical i nterpretations o f the hieroglyphs at Tikal. These data have s timulated f urther s tudies on Tikal, and i n particular i nquiries r elating t o the p lacement o f buildi ngs. Based on the l atest inscriptional and a rchaeological evidence, the building s equence, a s best we c an l ay i t out, i s g iven i n Table 1 .

1

TABLE 1 .

BUILDING S EQUENCE AT T IKAL

No. Acropolis - * 5D33-1st, 5 D33-3rd & 2 nd

T II & T I p robably conceived c ommemorative pair

a s a

v4 - i v+ - v i 4--

( or IV Notes to Table:

V )

A .

But s ee Coe ( 1967) who has I and V c ontemporary ( with I V f ollowing about 1 c entury l ater) because I was f inished a fter the death o f A , while at the same t ime the initiation o f V could have t aken place.

B .

Coe ( 1967) s ays that I II follows I by 1 00 years, based on dates on St. 2 4. I f A s tarted building I before his death ( in AD 7 22 o r 7 34), then I II could have b een built 1 00 years l ater, based on the S t. 2 4 dates.

I n this paper we r e-examine o ur earlier ideas on t he r ole o f a stronomy and geometry i n the planning o f Tikal, g iving particular a ttention to the n ew data concerning the genealogical a rguments. The major portion o f s uch a rguments deals with the construction by the dynasty s tarting with Ruler A ( nick-named Ah Cacau) a t the end o f t he s eventh c entury. The dominant ( approximately 1 0° E o f N ) orientation a t Tikal i s embedded in the North Acropolis: i t i s the same o rientation a s that o f Temples I and I I ( Figs. 1 & 2 ), which confront one another immediately t o the s outh and delimit the G reat Plaza on the e ast and west. Temples IV a nd V I ( although facing west) a lso have the same approximate o rientation and the north f ront o f Temple V deviates only a l ittle more than 1 0 degrees E o f N . Only Temple I II i s d ifferent f rom the others, l ying 1 8°16' o ff cardinal north to the east. No convincing explanation f or these deviations, a stronomical o r o therwise, has been o ffered s ince their peculiarity was f irst pointed out by Tozzer ( 1911: 1 06), but we believe the s olar z enith passages a t Tikal may have played a r ole ( see summary i n Table 2 ). The s ix l arge pyramids ( Temples I -VI) were built over a l ittle more than one hundred years by the dynasty t hat began with Ruler A . An i nauguration date on L intel 3 o f Temple I r eads 9 .12.9.17.16 5 C ib 1 4 Z otz ( AD 6 82) on F 8E 9, preceding the g lyph o f " seating." A t F 10-F11 the names o f Ruler A and the Tikal emblem glyph a re g iven. Burial 1 16, t he tomb i n Temple I , contains t he r emains o f t his ruler, while Temple I I may have b een dedicated t o his wife ( Coggins n .d.: 4 55), though no burial has been f ound there. One o f t he o riginal f ive beams o r wooden l intels o f t he middle doorway o f t his t emple s hows a person, who may r epresent this woman. 2

Fig. 1 : Temple I viewed ( Photo by Hartung).

from

the

F ig. 2 : View f rom the doorway of ( foreground) and t o Temples I II and by Hartung). 3

doorway

o f

Temple

I I

Temple I to Temple I I IV ( background) ( Photo

Recently, M . Miller ( 1985) has examined the s patial organization o f the Late C lassic T ikal pyramids in t erms o f the s tructure o f the ruling f amily. She interprets T I and T II t o be personifications o f husband a nd wife, the f emale being " shorter, squatter, and broader than the male" ( p. 8 ). She a lso r efers to the d ramatic breaking, by the eastwest orientation o f T I and T II, o f the pattern o f the s tructures built on the North A cropolis by the Early C lassical rulers a s the concrete i mage o f a new order ( p. 8 ). S ince t he beginning o f Tikal ( around 6 00 BC), the North Acropolis, with i ts particular f unerary architecture, had been the s acred burial g round o f the Tikal rulers. But n ear the end o f the Early C lassic P eriod s igns o f change began to o ccur. Some s cholars have a rgued that a cyclical rule o f s uccession gave way t o a dynastic political system.' This t ransition i s said t o have occurred with Curl Nose ( AD 3 79-426), a possible usurper who may have come f rom the south, and his son S tormy Sky ( AD 4 26-457). The t omb o f the f irst o f the n ew dynasty rulers may be Burial 4 8 at the southern l imit o f t he North Acropolis and on i ts axis ( but s ee Note 1 ). A s mall t emple ( Structure 5 D-33-3rd) was built above i t, which l ater, in the middle o f the f ifth century, was covered by 5 D-33-2nd, possibly constructed by Curl Nose's s on. This structure r epresents the most o rnate example o f Early C lassic Tikal f unerary a rchitecture and i t persisted l argely unchanged until the end o f t he s eventh c entury, when i t was partially dismantled a nd covered by the conspicuous, tall pyramid 5 D3 3-1st. Apparently Ruler A e rected 5 D-33-1st a s h is f irst major building a fter taking power a t Tikal in AD 6 82. The i ntention o f this building was two-fold: f irst, t o r eaffirm his relation to his ancestors Curl Nose and Stormy Sky ( Coggins n .d.: Table 4 ; Jones 1 977: 6 2) and s econd, t o commence a new k ind o f a rchitectural expression s uitable to h is dynasty. Meanwhile, s tructure 5 D-33-2nd was r elatively l ow ( about 1 2 m high including the " cresteria"); its f acade was a ccentuated by r ectangles enclosing s tucco polymorphic r eliefs. The s eventh c entury pyramid, 5 D-33-1st, anticipates the form o f Temples I I and I that would f ollow i t ( particularly the l atter with i ts v ertical a ccent). We consider S tructure 5 D-33-1st t o be o f vital i mportance in the planning s cheme o f Tikal. It embodies a l ink between the a rchitectural p ast and t he r evolutionary i deas o f the f uture dynasty. Tradition s eems s tronger a t t his l ocation, where the tomb o f t he founder o f the dynasty i s f ixed on a xis with the t emples o f the North A cropolis. A lso, S tela 3 1 r epresenting S tormy Sky, which may have been

4

positioned i n f ront o f 5 D-33-2nd, was placed i nside the t emple o f 5 D-33-2nd when Ruler A covered t his s tructure o ver with 5 D-33-1st. I t i s important to r ealize that today, the l arger part o f 5 D-33-1st i s n o l onger s tanding; thus the v iew i s l eft open f rom the G reat Plaza t o the North A cropolis' ( Fig. 3 ). The earlier building o f Ruler A had previously closed o ff this v iew, thus l ending importance to the future spatial r elations between t he Great Plaza and Temples I and I I.

F ig. 3 : Tikal d iorama viewed f rom the east, " An Artist's Conception o f Tikal a t AD 1 000" ( 1986) ( with permission).

adapted f rom i n A . Miller

Judging f rom the Tikal map o f 1 961, a l ine between the doorways o f Temples I and I I l ies a t 9 0 0 to the approximate N-S axis o f the North Acropolis. The distance f rom the c rossing point o f both l ines t o Temple I I i s somewhat l arger than to Temple I , which may be due t o an a lignment r eference o f Temple I I to the c entral pyramid ( 5D-104) o f the South Acropolis, an earlier construction. Archaeological data suggest that Temple I I was constructed ( around 7 00 AD) before Temple I , where Ruler A was buried. I f, a s i t s eems, the wooden l intels o f Temple I were elaborated i n the l ifetime o f Ruler A , one can s uppose that he a lso p repared the construction o f the pyramid and even may have initiated i t. 4 Ruler A a lso i nitiated a n ew type o f building: the Twin-Pyramid C omplex. The f irst o f t hese, Complex M ( or 3 D-1), i s s ituated e xactly north o f o f 5 D-33-1st, while the s econd, Complex N ( or 5 C-1), i s l ocated exactly t o t he west, each o f these d irections d eviating n oticeably f rom 5

e . c . , „ e ' , 0 e g a t e w„ l e w i 4 e v

‘

„ i „4 7 47d "e l ! : . 2 1q

; .

'

1

i ä1 4 / e . \ \ - -.

e

e

„

. 0

' : 7 i .2 •1 II I "/ AA a l

l xt

,

e r

e \ 1 1 1 1

9

A

7a

t e l e t et . • e g e e i l ie T .

. . .temK -

Fig. 4 : 4 :The Tikal Map ( Carr & Hazard 1 961) showing r eference l ines and s cale added by the authors. Vertical grid l ines f ixed to magnetic north, which deviates approximately 5 1° to the east o f a stronomical north.

6

the dominant a xis o f the North A cropolis, a s can be s een in F ig. 4 . Cases o f r ight angles between two notable d irect ions s uch a s t hese can be detected i n other examples a s well. I n placing both complexes, the r eference was t aken f rom t he c enter o f the G reat Plaza. The visibility o f C omplex N f rom 5 D-33-1st s eems to have been important and t he v isual l ine t aken f rom the earlier Complex M a nd d irected toward the S outh a lso appears to be decisive. I t s hould be noted that i n Complex M we f ind Altar 1 4 with the katun-ending d ate 9 .13.0.0.0 8 Ahau 8 Uo and Stela 3 0 with the e arliest r epresentation o f Ruler A . C omplex N has the e laborate Stela 1 6 and Altar 5 . As i f t o a ccentuate the north-south a xis, the s ides ( and the axis) o f the northern part o f the Maler Causeway ( leading t o the North Z one) a lso a re d irected exactly to the north ( see r ight-most solid l ine i n F ig: 4 ). The southern s egment o f the causeway ( dashed l ine) i s d irected parallel to the axis o f the North A cropolis. The two parts j oin at a point where the twinpyramid complexes Q and R extend to t he east, and Complex 0 t o the west.' The l ater C omplex 0 has by s eriation a n a ssigned date o f 9 .15.0.0.0 = AD 7 31. The monuments in the North enclosure ( Stelae P 55 and a ltar P 47) a re plain. I f one a ccepts the l ast date on an o ffering i n Burial 1 16 a s the day o f t he death o f Ruler A , then he would have died i n 9 .14.11.17.3 = AD 7 22. There could have f ollowed a t ime o f t ransition until his s on, Ruler B , took o ffice i n AD 7 34 ( his i nauguration date appears on S tela 2 1 in f ront o f Temple V I, more than 1 200 meters t o the s outheast o f the G reat P laza). Between these two dates 1 2 years l apsed, during which a k atun ( 9.15.0.0.0 = AD 7 31) was completed; t hus the n ecessity to build a complex.' I f Ruler A had d ied in 7 22, his Temple I surely would have been completed by 7 31, and even i f i t was not, the position o f t he entrance t o the t emple s hould have been d ecided, i n order to define, exactly toward t rue north, the c enter-point o f t he eastern ( and more important) pyramid o f C omplex 0 . The placement o f the western, four-stairway pyramid o f C omplex 0 also may have been the r esult o f c onscious planning, s ince i t l ies exactly t rue north a s s een f rom Temple V . This pyramid has not yet been exc avated, a lthough i t i s generally supposed that i t e ither i mmediately preceded o r s ucceeded Temple I V. In this case, Temple V ( Fig. 5 ) may have been constructed in the a forementioned t ime o f t ransition and would f it with the choice o f the p lace o f t he Western pyramid i n C omplex 0 ( in AD 7 31). There a lso exists an i nteresting connection between TV a nd T IV, a s s een f rom the doorway o f T I. F rom T I, l ines t o T IV a nd TV ( solid i n F ig. 4 ) l ie a t an a lmost-perfect r ight angle to o ne another ( our 1 975 measurement g ives 8 9°57'), each l ine deviating c lockwise f rom the cardinal d irections by 1 4° ( consult Table 2 f or details). 7

F ig. 5 : View f rom the doorway o f T I t o TV ( left) South Acropolis ( unexcavated mound at t he r ight).

and the

Temple V may have been visualized with 3D-43, i ts s omewhat smaller counterpart to the n orth, i n mind. The importance o f this south-facing structure i s underlined by the d iscovery o f a tomb beneath i t in 1 985, with an extraordinary s tone monument o f a human f igure in the full round ( seated c ross-legged, the head missing). The shoulders and the back o f the torso o f this l ife-sized s tatue a re covered by a vertically-arranged hieroglyphic text, containing calendric information and Tikal emblem glyphs. Interpretations are pending but should bring forth useful data ( Mayer 1 988). A visual l ine between V and 3D4 3 ( dashed in Fig. 4 ), which passes over a distance o f nearly 1 200 meters, i s parallel to t he main axis o f the North Acropolis. As t raced from the c orresponding pyramids o f Complex 0 , this same orientation may have been employed to determine the l ocation of the two pyramids o f the l ater Complex P o f AD 7 51, immediately w est o f and adjacent to 3 D-43. There a re at l east two other i ndications that s uggest a dependency o f the placement and o rientation o f Temple IV upon earlier s tructures. F irst, t he direction f rom the doorway o f Temple I to the doorway o f Temple IV ( solid l ine in Fig. 4 ) corresponds to the position o f s unset on 1 2-13 Aug, the back-calculated commencement date o f the Maya l ong count. The doorway o f Temple IV a lso a ligns a t 9 00 t o the axis o f the North A cropolis a nd faces the n o-longer-extant but once most i mportant pyramid 5 D-33-1st.

IV,

S econd, a l ine perpendicular t o the f ront o f Temple taken f rom i ts doorway, l eads t o t he small platform 5 E8

2 5 ( about 3 00 meters east o f Temple I ), which i s s ituated i n t he c enter o f a g reat platform base ( Structures 5 E2 3/28, o f d imensions 1 00 x 1 20 meters and over 1 0 meters high) ( This l ine i s dashed and dotted i n Fig. 4 ). The platform i s quite s imilar to the one that s upports Temple I V a nd could have s erved a s a platform for a s imilar pyramid. " This might have become the biggest t emple o f a ll" s aid Guillemin ( 1968: 3 3). Could this have been t he project o f Ruler C , who built the two Twin-Pyramid C omplexes Q and R i mmediately to the north? The l ocation f or Temple I II, the l ast o f the g reat t emples o f the Ruler A dynasty, must have been carefully s elected, f or we f ind a t l east f our l ines that s tart o r end here that might r elate i t to earlier pyramids. P erhaps most s ignificant o f a ll i s the precise east-west direction ( 269°54') c oming f rom the doorway o f Temple I and passing through t he center o f t he doorway o f Temple I II ( solid in F ig. 4 ). This distance, n early 3 20 meters, a lso f orms the baseline o f an i sosceles t riangle with i ts point o f departure a t the doorway o f S tructure 5 D-104, a high t emple-pyramid inside o f the S outh Acropolis ( Hartung 1 977, p . 1 13). 8 Note a lso in F ig. 4 that this equinoctial a lignment i s parallel to the l ine between the c enter o f Complex N and Structure 5 D-33. From the doorway o f Temple I II, a l ine ( solid in F ig. 4 ) points exactly s outh to the doorway o f Temple 5 D-90, a building on the s outh s ide o f the Court o f the S even Temples. This d istance i s about the same a s that f rom Temple I II t o Temple I , and i t r epresents another i sosceles t riangle with the point o f departure a t the doorway o f Temple I II ( the two equal s ides l ie i n the cardinal directions a nd f orm a r ight ang1e). 8 Finally, the doorway o f Temple I II can b e r elated t o the c entral doorway o f Structure 5 D-71, a building on the s outh s ide o f the Great Plaza that confronts S tr. 5 D-33 on i ts north s ide, and which l ies on axis with the North Acropolis. The direction t o Temple I II ( dashed i n F ig. 4 ) l ies a t 9 0° to the l atter ( the f ront o f 5 D-33 s eems t o have the s ame d irection). I f a ll f our o f the l ines we have suggested a re considered a s valid and deliberate constructions, then Temple I II emerges a s an exceptional example o f t he s election o f a " special" place. The particular problem would have been t o l ocate i t in a c enter a lready built-up, r ather l ate in T ikal's h istory, a ssuming the e rection o f S tela 2 4 in f ront o f Temple I II ( 9.19.0.0.0 = AD 8 10) r efers to the inauguration o f that pyramid. Up t o n ow, t his has been the extent o f s tudies o f planning, a rrangement and the o rientation o f buildings a t Tikal. Whether t he l ines we posited a d ecade-and-a-half ago were d eliberate o r coincidental was i n no r eal s ense t estable a t the t ime a nd owing t o the absence o f o ther s upport evidence f or t he g eometrical/astronomical hypo9

thesis the s ituation for a l ong t ime has r emained inconclusive. Today we believe Guillemin's ( 1968: 1 -5) remark that " orientation would be a more r eligious concept than an urbanistic form" does not a pply to the l ayout o f Tikal. No l onger i s one j ustified i n implying that mathematical and g eometrical exactitude were never a consideration and even i f considered, were a lways s eparated f rom r eligion i n the Maya mentality. Just a s in the codices, r itual and s cientific v iews a ct together; they r einforce one another. M . Miller's 1 985 novel a rguments about the idea o f e stablishing order and f orm in an urban p lan based upon principles o f family r elationships i n a dynastic s equence may be j ust a s t enuous a s those a rising f rom the method whereby one l ooks for purely g eometrical/astronomical r elationships; however, when the r esults o f each independent method a re compared, i t i s possible t o f ind a number o f points o f convergence. Accordingly, the most s alient fact to emerge f rom M . Miller's a nd our own s tudy o f t he planning and a rrangement o f the monumental structures a t Tikal i s the c entral role o f T I a nd its ancestral t ies t o 5 D-33. Though by no means the l argest s tructure a t Tikal, T I nonetheless emerges a s pivotal i n both t he genealogy and in the geometrical/astronomical analyses. The new order expressed by the axis T I - I I a nd l ater T I - I II and T IIV runs counter to the north-south oriented Early C lassic complex on the North Acropolis. T I i s the center o f the r ight angle T IV-I-V, which may imply that TV was placed exactly where we f ind i t, not only to g ive an expansive view but a lso to t ie i t directly t o the g enealogical l ine IV-I. T I i s also the pivot o f the t riangle T III - T I - 5 D1 04. ( At the present t ime we can s ay nothing more about complex 5 D-104 g enealogically.) And f inally, i t i s the principal end o f the west-east T III-TI axis. These l inks among specific Tikal s tructures a re consistent with M . Miller's ( 1985: 1 3) conclusion that none o f the other t emples was a llowed to obstruct the view o f the f ront elevation o f T I." Despite the great number o f constructions, not one interferes with the most important s tructure o f a ll. " All others only revere and imitate T I, to whom a ll others l ook." We could go further by suggesting that in the spirit o f the concreteness o f dynastic imagery characteristic o f the Ruler A dynasty, l ater rulers s ought very definite ways t o t ie t heir s tructures to T I by placing them a long s ignificant a nd prominent visual and a stronomical l ines. " F inally, i t i s important t o n ote that a rchaeologists now have begun to take quite s eriously the " new data and i nterpretations bearing on the n ature o f calendrical and cosmological r ites i n s o f ar a s t hey may i nfluence s ite planning that have emerged in r ecent years" ( Ashmore 1 986). Thus, Ashmore ( n.d.) has outlined t he principal components o f cosmological patterns including the use o f ballcourts 1 0

a nd causeways. A t Tikal, the cardinal d irections f ind an i mportant expression i n the twin-pyramid group a s depicting " the Maya cosmos i n miniature" ( Ashmore n .d.: 4 ). A shmore ( n.d.: 6 ) also a cknowledges that "Ah C acau 's constructions c learly emphasized the microcosmic l ayout o f both the Great P laza complex a nd the twin-pyramid groups". In sum, we have t ried t o demonstrate that quite r ecently t he data concerning persons r elated to s pecific buildings a t T ikal have provided s everal s trong points o f r einforcement o f earlier ideas we had posited solely on the basis o f apparent geometrical and a stronomical r elations hips among these buildings. Because we practice our d isciplines i n a world in which the written historical r ecord t akes precedence on t he l adder o f evidence, we believe that i t would be valuable t o continue to r eexamine, i n . the way we have exemplified i n this paper, the a rchaeoastronomical a rguments a lready proposed a t other Maya s ites.

A cknowledgments: We a re grateful t o C lemency Coggins and Chris Jones f or their helpful advice and comments i n the preparation o f this paper.

1 1

TABLE 2 . Summary o f Possible A stronomically-Related Alignments a t Tikal

Alignment

A zimuth 1 04°

Remarks The sunrise dates a re 1 4 F eb & 2 9 Oct. Whether these s till might have any l ocal agricultural s ignificance i s not known. They do d ivide the year i nto 2 57/108 day periods, close to 2 60/105.

I II ( Facade)

1 08°16'

Faces g enerally east, but does not l ook directly a t T I; a lso faces sunr ise on anti zenith passage. The same deviation o f 1 8°16' S o f E t aken t o the north ( i.e. 1 8°16' N o f E ) goes d irectly to 5 D-33. This i s the d irect ion o f s unrise on the day i t passes t he z enith. Note ( Aveni & Hartung ( 1986), Table 3 ) the special r elation that obtains between the s olstices and the z enith passage dates i n the Pet8n a rea.

I II

8 9°54'

Equinox s unrise.

2 80°35'

Faces west. S olar dates corresponding to this direction a re 1 8 Apr and 2 5 Aug. Twenty days before f irst solar z enith passage would correspond to an a zimuth o f 2 81°44'. I f one l ooked over the top o f T II ( see Fig. 2 ) there would be a very s light adjustment for e levation.

- I

I ( Facade)

Note: The a zimuths quoted i n a rc-minutes were obtained with surveyor's transit and sun-fix a t Tikal. These a re a ccurate to 5 a rc minutes.

1 2

NOTES 1 .

The most u p-to-date t able o f the chronology o f rulers a t T ikal i s g iven by Jones ( 1982: Table 6 ), a v ersion o f which appears in A . Miller ( 1986). Jones ( p.c. 1 /15/88) adds the f ollowing comments: ( a) Under S tormy Sky, Jones d isagrees with the a ssignment o f Bu. 4 8 to Curl Nose. ( b) Under Ruler B , S t. 2 1 o f TVI i s the inaugural monument o f this r uler. ( c) Under Ruler C , the man depicted on S t. 2 4 in f ront o f T III i s Ruler C .

2 .

Though there i s no wide agreement, s ome s cholars reason that t he Late C lassic t emples o f Tikal were part o f a master plan dedicated to the Ruler A dynasty, with r ulership now being expressed in the form o f concrete visual images rather than the more abstract images o f the cyclicity o f t ime employed in the C lassic ( see e .g. A . Miller 1 986: 6 0).

3 .

Berlin's ( 1967) c ritique o f the dismantling o f 5 D3 3-1st i s based s trictly on a rchaeological grounds. See the r eplies by Rainey et a l ( 1967) and Thompson ( 1967). These works deviated a ttention f rom the early observations o f Maler and Tozzer by concluding that " the l oss to mankind i s not . .. s erious."

4 .

In contrast, M . Miller ( 1985) proposes that the l intel o f T I ( as well a s that o f T IV) depicts the dead ruler i n an underworld confrontation. Jones' interpretation, that the ruler, very much alive, s its upon his throne on a wooden l itter in celebration o f a war victory, i s based upon dates carved on t he l intels that f all well within the l ifetime o f t he ruler in each case.

5 .

That the doorways o f TI and TV may have s erved a s a departure .point for a pair o f l ines that l ead northward to t he Twin Pyramids o f Complex 0 was f irst suggested by Hartung ( 1977). Extended northward, t hese l ines l ead to complex P , which i s s imilarly a rranged. While these l ines a re not perfectly north-south, they do have the same direct ion a s the p rincipal axis o f the North Acropolis. These complexes have l ong been r egarded a s symbolic o f the quadripartite expression o f the Maya cosmos ( Jones 1 977; C oggins n .d. and 1 980). We measured the axes o f C omplexes Q and R and f ound them to l ie in d irections 2 °10' and 5 °28' E o f N , r espectively; i .e. quite c lose to the t rue N-S direction. Additional observations on possible g eometrical r elat ions a t Tikal were contributed i n an unpublished paper by Sanford ( details r eported by Hartung 1 977: 1 17-118). 1 3

6 .

Coggins ( p.c. 8 /23/88), c iting t extual support in the T IV i nscriptions, believes Ruler A died c lose to 9 .15.2.0.0 and that T IV commemorates one l ahuntun s ince his death. She s uggests that Ruler B built T IV and that his mother i s buried inside i t.

7 .

Miller places Ruler B in Temple IV ( but s ee Note 1 ); his pyramid i s s aid to have been s ituated to keep t he buildings o f his parents in s ight. Thus, T IV s eems to be " in dialogue" w ith T I, the smaller TII deferring t o them ( indeed, h is mother's back i s l iterally turned to him). Thus, T IV g ives r eference a t a d istance f rom T I, even though i t i s l arger. I t " addresses" and i t " does not chall enge." Ruler C , to whom Miller a ssigns T III, l ies under the " sheltering shadow" o f his f ather's TIV and j ts i nscriptions make many r eferences to his father. But the v iew f rom T III a lso encompasses T I and T II; again, they a re t he primary r eferents. Thus, T III i ndicates the family r elationship to both s ets o f f orebears; i t l ies i n t he " bosom o f the dynasty." Given the placement o f these s tructures, M . Miller goes on ( p. 1 3) to s peculate about the ruler to whom the e ccentrically l ocated TV i s dedicated. She a ssigns Ruler AB ( first s on o f Ruler A ), i n one o f the date g aps between A and B , to this s tructure.

8 .

Today the S outh Acropolis i s c overed with high t rees ( Hartung 1 977: 1 17, F ig. 9 .3), but in f ormer t imes, S tr. 5 D-104 would have been a very conspicuous building, a s F ig. 3 shows.

9 .

Might the different o rientation o f Temple I II ( in comparison t o the other g reat t emples) have been chosen f or a better visual r elation with respect to the i sosceles t riangle?

1 0.

Though the a rchitectural t radition i s quite diff erent, the s ituation i s r eminiscent o f the tomb o f Pacal and the Temple o f the Inscriptions a t Palenque. Pacal d ied i n AD 6 83 and s urely had cons tructed his t emple, while Ruler A had his inaugura tion i n AD 6 82 and might have built 5 D-33-1st, though not yet his t omb and the t emple on top o f i t. In both cases, the doorways ( the central one at Palenque) were the r eference points, but a t Palenque the tomb l ies e xactly below, while a t Tikal i t i s north o f the central axes. I t would be rather unorthodox to obstruct the view o f the f ront e levation o f T I, a nd s o i t perhaps became more correct to t ie one's s tructure to TI by placing i t a long prominent v isual and a stronomical l ines.

1 4

REFERENCES Ashmore, W . 1 986 "Pet8n Cosmology in the Maya Southeast: An Analysis of Architecture and Settlement Patterns at Classic Quirigua", The Southeast Maya Periphery, ed. P . Urban and E . Schortmann, University o f Texas Press, Austin, pp. 3 5-49. Ashmore, W . n .d. "Deciphering Maya Architectural Plans", Paper presented at symposium on "New Theories o f the Ancient Maya", University o f Pennsylvania Museum, Philadelphia, 1 987. Aveni,

A . & H . Hartung 1 986 Calendar", Trans. Am.

"Maya City Planning Phil. Soc. 7 6 ( Part 7 ):

Berlin, H . 1 967 " The Destruction of Tikal", Am. Antq. 3 2: 2 41-2. Carr,

Coe,

Structure

and the 1 -81.

5D-33-1st

R . & J . Hazard 1 961 "Map o f the Ruins o f Pet6n, Guatemala", Tikal Reports, no. 1 1, of Pennsylvania Museum, Philadelphia.

at

Tikal, El University

W . 1 967 "Tikal: a Handbook o f the Ancient Maya Ruins", University o f Pennsylvania Museum, Philadelphia.

Coggins, C . n .d. "Painting & Drawing Styles at Tikal: An Historical Iconographic Reconstruction" ( Diss.) University o f Michigan Microfilms, Ann Arbor, 1 975. Coggins, C . 1 980 "The Shape o f Time: Implications of a Four Part Figure", 7 39.

Some Political Am Antq 4 5: 7 27-

Guillemin, E . 1 968 "Tikal: Development the Tikal Ceremonial Center", Ethnos

and 3 3:

Function o f 1 -35.

Hartung, H . 1 975 "A Scheme o f Probable Astronomical Projections in Mesoamerican Architecture", in Archaeoastronomy in Pre-Columbian America, ed. A .F. Aveni, University o f Texas Press, Austin pp. 1 912 04. Hartung, H . 1 977 "Ancient Maya Architecture and Planning: Possibilities and Limitations for Astronomical Studies", in Native American Astronomy, ed. A .F. Aveni, University o f Texas Press, Austin, pp. 1 111 29. Jones,

C . 1 977 Rulers of

" Inauguration Dates of Three Late Classic Tikal, Guatamela", Am Antq, 4 2: 2 8-60.

1 5

Jones,

C . and L . Satterthwaite 1 982 " The Monuments a nd Inscriptions o f Tikal: The Carved Monuments", Tikal Report No. 3 3, University o f P ennsylvania Museum, Philadelphia.

Mayer,

K .H. 1 988 " Tikal: Exhibit", Mexikon 1 0,

Miller, A . 1 986 Pennsylvania Museum,

A Unique Maya No. 3 : 4 9-50.

" Maya Rulers Philadelphia.

o f T ime",

S culpture on

University o f

Miller, M . 1 985 " Tikal, Guatemala: A Rationale for t he Placement o f the Funerary Pyramids", Expedition, 2 7, No. 3 : 6 -15. Rainey, F ., A . Kidder I I, L . Satterthwaite, " Reply to Berlin", Am Antg, 3 2: 2 42-4. Thompson, 3 2:

J .E.S. 2 44.

1 967

"A Third

W .

Coe 1 967

Party Comment",

Am Antq,

Tozzer, A . 1 911 " Preliminary Study o f t he Guatemala", Mem. Peabody Museum, Cambridge, Massachusetts.

1 6

&

Ruins o f T ikal, Harvard 5 (2),

THE OBSERVATORY AT C lemency Chase

Coggins

DZIBILCHALTUN and R .

David

Drucker

Introduction At Dzibilchaltun two distant groups of structures that are connected by a ceremonial roadway are the halves of a single observatory. The eastern half of this macroassemblage has been excavated and reconstructed ( Andrews IV and Andrews V 1 980:82-148), its stucco decoration analyzed and i ts observatory function proposed ( Coggins 1 983:7); in this paper Coggins further proposes that the architectural form and serpent iconography of the eastern temple which combine Teotihuacan with Maya symbolism a lso encode observational and calendric data from the solar year, the Venus cycle, and the Maya Long Countand that these were synchronized for a s ingle day in Maya history: the completion of katun thirteen, 9 . 13.0.0.0 8 Ahau 8 Uo, or the Gregorian date March 1 6, A . D. 6 92. ( 1) D zibilchaltun i s located in the dry northwestern corner of the Yucatan Peninsula 2 3 km from the Gulf of Mexico at 21 deg. 5 ' 45 " North latitude. It is the first important site encountered traveling inland from the coast to the north and west ( Kurjack 1 979:13-15). Komchen, a site 6 km northwest of the center of D zibilchaltun, was chosen for settlement i n Middle Formative times ( Ca. 700-400 B . C.) by people who were in contact, probably by sea, with the Olmec of La Venta to the southwest on the Gulf of Tabasco ( Andrews V 1 986:34-42), while greater D zibilchaltun was populated until the Spanish Conquest, and may always have played some role in coastal trade. In the seventh c entury more than a millenium after the founding of the Formative settlement a small structure ( Str. 612) was built in the style of Teotihuacan 7 km southwest of the center of D zibilchaltun. This cardinallyoriented single room building had a talud-tablero on its western, principal, facade ( Andrews IV and Andrews V 1 980:68-80). The talud-tablero is the hallmark of Teotihuacan architecture and no other such architecture is known from the northern Maya lowlands. About two centuries after this a massive west-facing structure ( Str. 3 8) was built with " open-ended" talud-tablero terraces that suggest central Mexican or Cholulan inspiration ( Andrews IV and Andrews V 1 980:162). This unMaya construction, located at the central plaza of the site, was contemporary with the adoption of a widespread central Mexican 1 7.2 degrees east of north building orientation at Dzibilchaltun ( Andrews V 1 979).

1 7

The Observatory Assemblage Sometime in the seventh century the ritual concourse of D zibilchaltun was laid out with the Cenote Xlacah a s i ts f ocus ( Figure 1 ). The site's main axis i s a s acbe, or ceremonial roadway, that extends east-west f or 2 ,263 m on a line that i s just 3 .5 degrees south o f east, or 9 3 deg. 3 0' a zimuth. ( 2) A radially symmetrical temple ( Str.66) at the west end of this sacbe had a s ingle room, four doorways and four stairways, with two range buildings located to i ts east on either side of the sacbe axis. These three buildings are enclosed by a wall except on the east where the sacbe leads 200 m to a radial p latform ( Str. 6 3) with the plain Stela 2 1. Over 2 .5 km east at the opposite e nd of the axial s acbe another symmetrically radial temple ( Str. 1 -sub) mirrors the western one ( Figures 1 -4); it has four unusually wide doorways ( 235 cm wide) and four s tairways, and i s a lso enclosed by a wall, but this temple has a single range building to its east, and three pairs of such s ingle-room buildings to i ts west, while a radial platform ( Str. 1 2) with the plain Stela 3 i s located 1 35m west of the group a long the sacbe. Although they differ in details the east and west groups are twins, complementary halves of a s ingle, entirely contemporaneous a ssemblage. In the Coggins report on the architectural decoration of the eastern buildings it was postulated that these widely s eparated groups were part of an equinoctial a ssemblage and analogous to the twin pyramid complexes of Tikal, and that l ike them i ts principal purpose was the celebration of the completion of a katun, and specifically of the katun ending at 9 .13.0.0.0, in A . D. 6 92 ( 1983:52-54). Since no s telae or informative inscriptions date f rom this period at D zibilchaltun these hypotheses were based entirely on the stylistic and iconographic traits o f the architecture and its stucco decoration, and of associated ceramics. Form and Decoration of the Eastern Temple. The f orm of the eastern temple ( Str. 1 -sub), with i ts f our-part radial symmetry i s the three-dimensional equivalent of Mesoamerican s igns that denote the completion of cycles: solar, planetary and c alendric ( Figures 3 , 5 ; Coggins 1 980, 1 983:36-58). It i s a lso the equivalent of the quincunx, or f ive-point s ign that may denote Venus ( Figure 5c). The upper f acade of the temple had a stucco frieze with eight projecting heads located at the corners and at the center of each s ide a ll joined by two crisscrossing undulating serpentine f orms that are studded with perforated discoidal e lements ( Figure 6 ). The heads have a curl at the corner of the upper j aw, and no l ower jaw, a lthough a tongue or beard-like e lement projects downward. They once had protruding noses. Their eyes are square with cross-eyed pupils, and each had a waterlily knotted on i ts f orehead. In the Coggins analysis these were called " Chak" heads, or the head of God B which has a long nose and i s 1 8

usually a ssociated with agriculture and the solar year. On the facade these serpentine forms swim in the sea and i t was proposed that this represented the waters of the underworld from which the sun would r ise directly to the east of this equinoctially-oriented temple ( 1983:7, 2 6, 2 7). Fragments of stucco from the " tower" of Str. 1 -sub and f rom other buildings in this group indicate such discs tudded serpentine f orms with waterlilies and Cauac signs were once part of their ( long gone) friezes as well, and that the central east-facing Str. 7 may have had a f eathered serpent on i ts upper f acade. Teotihuacan Antecedents While evidence of central Mexican contact at D zibilchaltun i s embedded in the local Maya cultural matrix certain of these traits will be identified here as background for an understanding of the observatory a ssemblage at the heart of the site. For instance, while very rare in the Maya Lowlands feathered serpents were commonly represented at Teotihuacan. The Temple of Quetzalcoatl in the Ciudadela at Teotihuacan i s decorated with disc-studded tableros that contain feathered serpents, with different f ront and rear heads, that swim in a watery environment while s ingle-headed feathered serpents swim a long the taludes below ( Figure 7 ). These f eathered s erpents probably represent Quetzalcoatl, the Venus creator deity who swam i n the primordial sea; the differentiated heads of these Venus serpents correspond to the Morning ( front head) and Evening ( rear head) Star aspects of the planet and thus together denote Venus cycles ( Coggins 1 986b, 1 987c, d). The Temple of Quetzalcoatl i s a west-facing eastern pyramid located within a walled precinct that i s matched by another precinct on the western side of the main axis of Teotihuacan. Coggins has suggested that this serpentine eastern pyramid of Quetzalcoatl and its matching precinct served as a conceptual model for the east-west D zibilchaltun observatory assemblage which was built f ive hundred years later ( 1983:42, 4 3) a model both in orientation and i n symbolism since the eastern D zibilchaltun temple i s s imilarly decorated with Venus serpents that swim in the ( primordial?) sea. It i s also located within a walled precinct and it i s matched by a mirroring western precinct although i f there was ever a temple in the western precinct at Teotihuacan no evidence of i t remains. Probably equally important in a search f or antecedents i s the scale of the east-west sacbe at D zibilchaltun which i s two and one quarter kilometers long. The only other centrally located c eremonial roadway in a ll of Mesoamerica that i ts ambition and scale can be compared i s the northsouth Street of the Dead at Teotihuacan. Measured from 1 9

the Pyramid of the Moon to the southern edge of the Ciudadela this i s a hundred meters shorter than the D zibilchaltun sacbe, although the Street of the Dead continues as f ar south again within the confines of the city ( Millon 1 973:42, f ig. 6 b). The orientations are different but the idea of l aying out a road of such length as part of the preliminary planning of a sacred place i s known in only these two instances. It i s the idea of a vast ceremonial axis with mirrored precincts dedicated to Venus serpents that i s f ound at both Teotihuacan and D zibilchaltun. Another important central Mexican concept that Coggins has postulated was integrated into Maya calendric celebration i n the Early C lassic was the f undamental organization of time i nto periods of 2 60, or of thirteen times twenty, units. This was the structure of the pan-Mesoamerican ritual calendar and it was given new emphasis in Maya Long Count celebrations through the influence of Teotihuacan emigrants at or near Tikal in the fourth century A . D. where it was expressed in a cycle of thirteen katuns which comprised thirteen twenty tun periods f or a cycle of 2 60 tuns ( Coggins 1 979,1980). These new practises were numerologically evident in the particular symbolic significance of the numbers 1 3, 2 0 and 2 60 which later played key roles in the i conographic program of Str.1-sub at D zibilchaltun built to commemorate the completion of the thirteenth katun. In this thirteen katun cycle 2 60 tuns had been completed s ince the critical baktun completion date 9 .0.0.0.0 8 Ahau 1 3 Ceh ( Dec.11 4 35). ( 3) The

Iconography of the Eastern Temple

The Long Count Dedicatory Date. There are no contemporary inscriptions at D zibilchaltun but the commemorative date 9 .13.0.0.0 8 Ahau 8 Uo was encoded in Mayan i conography and language in the stucco decoration of Str. 1 -sub for all to read ( Figure 6 ). First, there are the serpents which Coggins has described as Chak-like water-lily serpents swimming in the waters of the underworld ( 1983:26,27,445 2); these have more recently been identified by Karl Taube as " an avian water serpent - a creature occurring a s the personified tun glyph and as a head variant of the number thirteen" ( 1986:66,67; and see Hellmuth 1 987:160-163; Thompson 1 960:88, 1 36, 1 44). ( 4) In other contexts these serpents, their s inuous bodies l ined with precious disc s igns, connote the number thirteen while they are at the same time the personification of the tun, or 3 60 day year ( Figure 8a,b). Each of the heads on the D zibilchaltun f acade once had a knotted water-lily on i ts forehead. ( 5) Such knotted f orehead devices ( in this case a water-lily which serves to identify the number thirteen, Figure 8a) may be read phonetically as the Yucatec Mayan syllable k 'a from the verb k 'ax, to tie or knot ( Coggins 1 987b, 1 988b) and i n association with the overlapping tun connotation these serpents could be read a s k 'atun, ( 6) and as " thirteen katuns", or the katun ending commemorated by the 2 0

construction of the temple. The Calendar Round date 8 Ahau 8 Uo could probably a lso be read on this f acade. There were eight serpent heads and the eight displayed the characteristics of the day and month s igns. Unlike most such long-nose serpents the eight had the l arge square eyes with inward-focussed pupils of the sun god, the supreme lord, or Ahau - thus 8 Ahau may have been expressed, while Ahau was also the day that denoted the completion of the cycle. The serpents also had crossed bands on an e lement that projected downward in place of a lower jaw, and cross-hatched spots that were affixed to the s ides of their eyes. The cross-hatched spots could be read, in Yucatecan, as ek' for black, and the crossed bands as k 'at ( Fox and Justeson 1 984:48). Together these two e lements combine to form the glyph for the month Uo ( Figure 8c). In sum, the f orm of this temple expressed the completion of a cycle while the stucco decoration stated, both logographically and phonetically that the date of completion as thirteen katuns, 8 Ahau 8 Uo. Solar and Venus Symbolism. The i conography of the f acade of Str. 1 -sub suggests other cycles besides those of the Maya Long Count. The long-nosed serpent i tself may represent Chak, or God B of the codices, who presides over the 3 65 day solar and agricultural year as well as over a 2 60 day cycle that i s synchronized with Venus ( Bricker, this volume). The masks on this structure are also the earliest extant examples of the later common Chak f acade masks of Yucatan and Campeche. At least f our such masks crowned the f our doorways of the circular Caracol at Chichen Itza, eight masks decorated the corners of Temple 2 2 at Copan, and Chak masks were arranged in groups of f ive on the upper f acade of the Governor's Palace at Uxmal - these are the only three Maya structures that have been demonstrated to be Venus observatories ( Aveni, Gibbs and Hartung 1 975;, C loss, Aveni and Crowley 1 984; Aveni 1 980, pp. 2 73-277). ( 7) The presence of Chak masks need not designate an observatory but Maya observatories may a ll have Chak masks. At D zibilchaltun the serpents on the upper f acade of Str. 1 -sub are explicitly identified with Quetzalcoatl, Venus, and the sun, and they might have been read phonetically as kukulkan. In Yucatec Mayan the word f or wavy or undulating i s kukul while the word for serpent i s kan. Kukulkan, undulating serpent, i s a pun f or K ' uk'ulkan the Maya name f or Quetzalcoatl. Both names mean feathered serpent, or bird-serpent, whether i n Mayan or i n Nahuatl. If we look into s ome of the other Maya associations f or the number eight a combined Venus/solar reading f or this temple becomes even more obvious. Eight solar cycles equal f ive Venus cycles and the temple a lludes to this f ormula i n i ts e ight s erpent program, i n i ts combined quadrilateral and quincunx f orm, and i n i ts equinoctial and, as we shall 2 1

see, Venus-viewing f unctions. The walled eastern group can a lso be viewed as containing eight structures i f the doubled western buildings are counted separately, and as having f ive structures i f they are c ounted jointly ( Figure 3 ). Eight i s a lso the median, and canonical, number of days that Venus disappears at i nferior conjunction before i ts heliacal rise as Morning Star, as the Maya knew well. And for the Maya the e ighth day i s L amat - " the day of the Venus God" ( Thompson 1 960:77). The Venus Serpent. Tikal. The serpents that decorate Str. 1 -sub are f ound in other Late C lassic Maya contexts that confirm their Venus identity. One of these i s an i ncised bone from the tomb of Ah Kakaw at Tikal. This fragmentary bone depicts a Maya canoe with f ive anthropomorphic passengers ( Figure 9 ). The boat i s a pparently paddled, i n the stern, by a f igure wearing a crocodile headdress. In f ront of him a toad f aces f orward while a Maya l ord, a monkey(?) and a mammal seated in the bow a ll face backward ( Coggins 1 975:480-483). The prow of the canoe i s carved i nto a serpent head which has a a curl at the corner of i ts upper jaw and a bearded crossed bands emblem in place of a lower jaw. The beard streams forward as i f the canoe were being paddled backward. The canoe has Lamat, or Venus, glyphs along i ts side and the head at the bow belongs to the Venus serpent. This craft i s further identified as a Venus boat by the presence, at the beginning of an i nscription immediately above, of the "Venus over the earth" glyph which, with a repeated Calendar Round date ( 6 Akbal 1 6 Zac), i s also f ound on other bones with canoe s cenes f rom this same burial ( Coggins 1 975:469-479). It has been suggested that this glyph indicates the the date of warfare and the sacrifice of prisoners - possibly occuring at elongations or f irst appearances of Venus as Evening Star ( Lounsbury 1 982). Of the two possible Long Count dates f or this inscription, 9 .11.19.4.3, September 2 6, 6 71 and 9 .14.11.17.3, September 1 4, 7 23, the earlier date i s 1 8 days before Venus' Last Appearance as Morning Star. The later one i s about 4 0 days before Venus' heliacal set as Evening Star, but not an e longation point; either date might be correct within the context of the burial. Whatever their s ignificance the Venus connotations of this boat are c lear in the Lamat glyphs, the "Venus over the earth" glyph, and the crossed bands " lower jaw" emblem which defines this aquatic s erpent. Copan. A second relevant example of this Venus s erpent i s f ound on Stela N at Copan. ( Figure 1 0) Versions of i ts head f orm the headdress of the f igure on the south f ace of the stela - a f igure that i s a lmost i dentical to the f igure on the north. The two represent the Venus twins ( the Morning and Evening Stars) on a stela that i s dedicated to the Venus day One Ahau ( Coggins 1 988:99,100,107; 1 986a). The twins wear Venus " serpent" headdresses with curls at the corner of the upper jaw, and w ith water l ilies knotted 2 2

on the f orehead, l ike the D zibilchaltun f acade serpents. On the south f igure smaller versions of this same head, a lso with the knotted water l ilies and f ish, and jaw curls, have crossed bands emblems in place of lower jaws as do the Tikal bone and the D zibilchaltun serpent heads. However, just as important as the shared Venus significance of this i conography i s the calendric relationship between Copan Stela N and Str. 1 -sub at D zibilchaltun. They are dedicated to period endings 3 1 /2 katuns apart: Str. 1 -sub to 9 .13.0.0.0 8 Ahau 8 Uo, March 1 6, 6 92; Stela N to 9 .16.10.0.0 1 Ahau 3 Zip, March 1 5, 7 61. The two monuments are distinguished by the mechanisms they devised to commemorate both the Long Count date and the Spring Equinox. At D zibilchaltun both dates ( March 1 6 and March 2 0) were marked architecturally ( Figure 1 1). On Stela N the Initial Series inscription records the equinox as well as the expected lahuntun ending which should read 9 .16.10.0.0. 1 Ahau 3 Z ip ( March 1 5,761). The inscription actually reads 1 Ahau 8 Z ip, f ive days later, or March 2 0 ( the equinox). A third example of this type of commemoration i s the Castillo at Chichen Itza which, 3 1 /2 katuns later, celebrated the completion of the baktun ( 10.0.0.0.0 7 Ahau 1 8 Z ip) on March 1 3, 8 30 ( Coggins 1 983:55-57; 1 986a, 1 988b). The Castillo i s almost as well known as an equinox marker ( Rivard 1 969) as it i s f or i ts f eathered serpent i conography which i s usually read as Kukulkan, or Venus, symbolism. Unlike at D zibilchaltun and Copan we do not know how the seven day i nterval between March 1 3 and 2 0 was registered in the Castillo, but these three March period endings, s eparated by 3 1 /2 katuns, share Long Count, equinoctial, and Venus symbolism. If Str. 1 -sub was not the f irst of its kind the katun ending 9 .6.0.0.0 9 Ahau 3 Uayeb must have been commemorated somewhere in analogous fashion, s ince i t fell on March 2 0. The association between the Spring equinox and Venus may have had to do with the even balancing of the year between halves that were metaphorically analogous to the Morning and Evening Star phases of Venus, whereas the c lose association with the period endings was cyclic ( during the Classic period). It i s possible to read in i ts form and decoration the exact Long Count date f or which Str. 1 -sub was built as well as to deduce that the temple was probably involved in Venus and solar related ritual. This information a lone might be enough to date i t - but when we consider some of the astronomical phenomena that the D zibilchaltun Maya could have observed i n this observatory there can be no question of the specific dedicatory date. Astronomical

Observation and the Eastern Temple

Solar. In previous work on Str. 1 -sub Coggins suggested this eastern temple was used as a sunrise f oresight when viewed from Str. 6 6 on the west ( 1983:7). This was 2 3

e specially l ikely because Str. 1 -sub has f our doorways a ligned on the east-west axis with visibility through to the eastern horizon, and the axial doorways are f lanked by windows, to the north and south, which a lso give views through to the f ar horizon ( Figures 2 -4,11). Few, i f any, vaulted structures existed at D zibilchaltun when the s acbe was laid out and the twin temples built ( Andrews IV and Andrews V 1 980:123-124), and thus no big buildings or natural f eatures obstructed the views to the f lat eastern or western horizons. The doubled assemblage was probably built to create calibrated horizons f or the recording of astronomical events where there was no significant natural topography that might be used for this purpose. When Hartung and Aveni measured the sight l ine from Str. 6 6 on the west to Str. 1 -sub on the east they f ound this axis was skewed 3 .5 degrees to the south of east. and they f ound the same deviation when they s ighted through the Str. 1 -sub doors from the stela 3 platform ( Str. 1 2) just to the west of the eastern group. They f elt confident such a consistent deviation was deliberate ( Figures 2 ,3). From either vantage point the sun would have risen through the f our axial doorways f our days before the spring equinox, whereas i t rose through the two a ligned southern windows s ix days before, and through the two a ligned northern windows two days before the equinox. On this same day the sun would probably a lso have risen above the center of the temple tower ( Figure 1 1). ( 8) The windows apparently served as anticipatory, or predictive, markers f or the sun's appearance in the doorway at a time of year when i t was moving most rapidly, and was thus hardest to " catch". ( 9) In the f all this sequence of events would have been reversed; as the sun approached the tower from the north i t would have been visible in the windows and doorways s ix, f our, and two days after the f all equinox. While the Aveni and Hartung measurements confirmed the equinoctial functions of this building they did not explain the 3 .5 degree skew, beyond i ts predictive character. Their measurements did, however, reveal other possible observational uses f or this eastern group ( Figure 3 ). E . Wyllys Andrews V informs Coggins that as Strs. 6 -7 are reconstructed only the very top of the Str. 1 -sub doorways, and not the windows, would have been visible from the Stela 3 platform ( Str. 1 2). Thus solar viewing eastward Through the doorways was probably only possible f rom Str. 6 6, on March 1 6, f our days before the equinox. Much of the eastward horizon viewing probably took place on the Stela 3 platform. ( Figure 3 ; Table 1 ) After the equinox, March 2 0, the f irst z enith occurred on May 2 5, and the second, after an i nterval of 5 2 days, on July 1 7 ( Chart 1 ). ( 10) The two z enith sunrises would have been visible ( from Stela 3 ) to the north of the three symmetrical pairs of f acade buildings above the center of the smaller Str. 1 0 which had been added to the group ( Figures 3 , 1 1). When i t was built the architectural f orm of Str. 1 0 was most 2 4

unusual s ince i t consisted of a s ingle room with f our cardinally placed doorways. The western one was 2 50 cm wide, wider than the Str. 1 -sub doorways; i t was later narrowed and the other three were f illed in ( Andrews IV and Andrews V 1 980:132). Str. 1 0 was a lso unlike other buildings in the group in having had glyphic sun-related ahau and kin elements in i ts stucco f acade decoration ( Coggins 1 983:29-31). The corners of this building, the east-west doorways, and some parts of the roof decoration served as markers f or z enith and summer solstice sunrises. The 5 2 day i nterval between the equinoxes i s s ignificant because f ifty two i s one of the most numerologically important mesoamerican numbers ( 2 x 2 6, 4 x 1 3, and the number of years in a Calendar Round cycle); Milbrath reports that agricultural calendars in the Maya Madrid Codex are laid out in 5 2 day periods ( 1979:278-279). Observation of the two z enith passage dates, which vary according to latitude, were also particularly significant in ancient Mesoamerica and this 5 2 day interval may have been instrumental i n determining the location of this observatory group ( in Yucatan to the east, Motul, and less precisely Tizimin and Culuba, had this same interval between zenith passages). Copan, f ar to the southeast, has an interval twice as long ( Aveni 1 977:fig. 1 .5). On the south side of the group winter solstice may have been marked over a small platform that was added to the south end of the two southwestern buildings ( Strs. 4 -5), or possibly from Structure 5 itself over Structure 3 , while the actual solstice sunrise might have been s ighted from the l ater higher Str. 1 1, to the southwest, along the north wall of the strangely skewed Str. 2 at the eastern edge of the group. Long Count commemoration. Observation and celebration of the predictable structure of the solar year was only one of the purposes of this group - and it was possibly the least important. It i s the 3 .5 degree deviation from east that gives the conclusive c lue to the dedicatory date and paramount commemorative purpose of the eastern temple. The sun rises through the f our aligned doorways f our days before the vernal equinox, or on March 1 6 which in A . D. 6 92 was the day 8 Ahau 8 Uo, 9 .13.0.0.0. that commemorated the completion of the thirteen katun cycle of 2 60 tuns s ince the beginning of baktun nine. Str. 1 -sub was built to capture this particular sunrise, as was the whole macroassemblage, and this date probably signified the C lassic period f ounding of D zibilchaltun. This dedicatory date could have been celebrated in this way only until Str. 1 -sub was superseded perhaps a century after i ts construction, although observations of the stations of the solar year did not become obsolete, and the exteriors of Structures 4 -9 were never modified. ( 11) Venus as Morning Star. The solar observations were keyed i nto another calendric observation that, i n view of the 2 5

serpentine decoration of the f acade, must be viewed as having been as important as the katun commemoration. This involved tracking the Morning Star appearances of Venus which i s so c losely tied to the course of the sun. As noted above f ive Venus cycles equal eight solar cycles, and each Venus cycle includes a period as Morning Star and a period as Evening Star. In discussing these appearances Anthony Aveni recently i llustrated his paper with charts that show the height reached each day by Venus and the configuration these positions make during each period of appearance ( Aveni 1 986); see Figure 1 2 f or the f ive Morning Star phases of the Venus cycle that began in November 6 91. ( 12) In the Dresden Codex, the best source for evidence of the Maya observation of Venus, the number of days assigned for the eastern ( morning) and western ( evening) appearances ( 236 and 2 50 respectively) are probably of numerological significance s ince they are not observationally correct. Aveni argues that each interval was actually understood to last 2 60 days since the mean period i s 2 63 days. Two hundred s ixty days i s a lso the length of the ritual calendar, and 2 60 tuns the length of a katun cycle. The importance of this number was noted above, and Aveni plausibly proposes that i t was known as the length of each Venus appearance as well. The F ive cycles. The striking Venus configurations on the charts ( Figure 1 2) trace the distance from the sun that Venus attained at f ive day intervals during the course of i ts approximately 2 63 days of appearance as Morning Star: Venus would have been visible at only one of these points at a time so that while rise points might easily be marked a long the horizon ( real or man-made) relative e levation would be much more difficult to record. During the course of i ts f ive cycles Venus traces f ive different patterns in the eastern morning sky, and f ive i n the western evening sky. These have markedly different characters. The one we will consider the f irst of the f ive at D zibilchaltun began with the heliacal rise of Venus late in November to the south of east and ended i n August with rise to the north, thus including the vernal equinox, f irst and second z enith passages, and summer solstice i n i ts period as Morning Star ( Figures 1 2a,13; table 1 ; chart 2 ). The second cycle began early i n July, 5 84 days ( one Venus cycle) after the f irst, with heliacal rise to the north of east and ended with rise in February to the south, thus including second z enith passage and the autumnal equinox and winter solstice ( Figure 1 2b) The third began with a February heliacal rise to the south of east and ended to the north i n October; i t inlcuded both equinoxes, both z eniths, and summer solstice ( Figure 1 2c). The f ourth began i n September with heliacal rise just north of east and ended l ate i n April not f ar from the same horizon point; i t i ncluded both equinoxes and the winter s olstice ( Figure 1 2d). The f ifth began i n April with heliacal r ise 2 6

to the north of east and ended with December rise to the south; i t included both zeniths, summer s olstice, f all equinox, and possibly winter solstice ( Figure 1 2e). Each of these periods of eastern ( and of western) appearance traces i ts own characteristic pattern i n the sky, with e longations and retrograde motion creating l oops that, a long with each distinctive seasonal character, helps explain the differentiated personalities ascribed to the f ive periods i n the i llustrations of the Dresden Venus Table ( Thompson 1 972: ms. pp. 4 6-50). ( 13) The f act that over the f ive periods the heliacal rise shifts along the horizon f rom south of east to north of east, to south, to north, and f inally to north again adds to the distinctiveness of these appearances and would have keyed them into the architecture of the eastern group at D zibilchaltun where I believe they were tracked. ( 14) If the tracks of the f ive Morning ( and Evening) star phases were superimposed, on paper or in the minds of the observers, they would appear to criss-cross, or interweave because f our of the f ive consecutive paths a lternate north to south and south to north. Coggins proposes that this was symbolized by the criss-crossing bodies of the Venus serpents on the f acade of the temple ( Figure 6 ), and a lso by the serpents' crossed bands emblems. The crossed-bands glyph, T552, i s often part of the sky g lyph, T561c, and i s regularly part of " sky bands". It was probably read k 'at, " crossing", in Yucatecan ( Kelley, 1 976:152), and refers to the apparently erratic path of planets, particularly of Venus. Such an i nterpretation would a lso explain the importance of the a ssociation of Venus on Str. 1 -sub with the month Uo whose glyph, as noted above, could be read ek k 'at in Yucatecan. This name may mean " black crossing", or it could mean " star crossing", and thus serve as a name f or Venus. The evidence f or tracking Venus as Morning Star in this group ties the heliacal rise of D zibilchaltun Venus cycle 1 to the group's March 1 6 dedicatory date and to the end of the katun cycle ( Table 1 ; Figure 1 1). On March 1 6, 6 92, Venus rose at the same horizon point that i t had 8 3 days before i n its heliacal rise. But perhaps the most extraordinary a spects of this Morning Star period are the Venus cycle's critical Calendar Round dates. In D zibilchaltun cycle 1 Venus appears to have f ollowed an ideal pattern and this particular cycle might therefore have served as a canonical model ( Chart 2 ). Heliacal Set as Evening Star. The last appearance of Venus as Evening Star occurred on November 1 7, 6 91. ( 15) This was the numerologically s ignificant Long Count date 9 .12.19.12.0 5 Ahau 1 3 Kankin which i s 1 3 completed days after the thirteenth mesomonth of the Calendar Round. I t was also the beginning of the thirteenth uinal in the c losing katun thirteen. Thirteen was a lso personified i n the temple's Venus serpent decoration, as noted above. The 27

glyph f or the month, Kankin, in which the last appearance occurred, represented the dog that s ignified Venus as Evening Star ( Closs 1 979, p . 1 63); the day s ign Ahau denoted Lord, while the day number, f ive, was the quintessential Venus number as Aveni has pointed out ( 1986). Heliacal Rise. After this last appearance the Venus period of disappearance at i nferior conjunction lasted exactly eight days as i t i s canonically described in the Dresden Codex. This i s the median, but the period may be as short a s z ero and as long as twenty days ( Aveni 1 986). The heliacal rise of Venus in D zibilchaltun cycle 1 was November 2 5, A . D. 6 91 i n the Morning Star phase that was to include the March 1 6 completion of katun thirteen and the presumed dedication of the architectural assemblage. This Long Count date was 9 .12.19.12.8 1 3 L amat 1 Muan. Like the heliacal set date this one combines thirteen with a Venus name since Lamat i s the day and g lyph a ssociated with Venus. Intermediate Points. During this cycle as Morning Star Venus returned to i ts 1 08 degree heliacal rise position on the dedicatory day 8 Ahau 8 Uo, 9 .13.0.0.0, after having risen almost as f ar south as the winter solstice rise point and then looped back toward the north. On both those days Venus rose over the center of the southern Structures 4-5 ( Figures 3 ,11; Table 1 ). The equinox was f our days later. On April 2 1 Venus rose through the doorway of Str. 1 -sub. This was f our days before the end of the 4 0 day ( two uinal) period s ince March 1 6; ( 16) this i s another example of the use of a f our day anticipatory interval. On May 1 7 Venus rose over the the northern Structures 89 . This was f our days before May 2 1 which was the heliacal r ise of the P leiades, visible through the axial doorways of Str. 1 0 ( fig. 1 1). These two dates may have been of particular historical s ignificance at D zibilchaltun because May 1 7, f irst z enith passage at Teotihuacan, had coincided with the heliacal rise of the P leiades when the Teotihuacan orientation was laid out - while at that time the P leiades a lso set on the Teotihuacan orientation line ( Aveni and Gibbs 1 976:516). An additional f our days later, May 2 5, was f irst z enith sunrise at D zibilchaltun. Like the P leiades the z enith sun rose on the axis of Str. 1 0. This relationship, memorialized in this bulding at A . D. 6 92, l inked the P leiades and the Zenith - perhaps in emulation of the Teotihuacan relationship. Str. 1 0's east doorway may have been c losed off when the P leiades were no longer visible there - a century or more later. Last Appearance. On the day of i ts l ast appearance Venus rose at the s ame horizon point i t had on May 2 5 ( First D zibilchaltun z enith passage). Last Appearance occurred 2 60 days after heliacal rise, on August 1 0, 6 929 .13.0.7.7 1 2 Manik 1 5 Chen. This date completes the ideal 2 60 day Morning Star period i n the same period as the 2 8

completion of the 2 60 tun katun cycle. Whereas the next day, 1 3 Lamat 1 6 Chen was August 1 1, "Maya Creation Day", or the solar anniversary of 4 Ahau 8 Cumku the date of the beginning of the L ong Count in 3 114 B . C., 9 .13.0.0.0 baktuns earlier, at the end of the preceding 1 3 baktun cycle. That mythical earlier cycle was the ultimate thirteen date, one that was perhaps invoked by the K 'uk'ulkan f acade s erpents i f they were understood as swimming in the primordial seas of the creation ( Coggins 1 986). "Maya Creation D ay", August 1 1, i s a lso a Teotihuacan orientation day ( one of the two days on which the sun sets on the orientation axis as viewed from the Pyramid of the Sun), while i t i s a lso second zenith passage at I zapa, Kaminaljuyu and Copan ( Drucker 1 977). We suggest that sunset on August 1 1-12 may be the basis f or the " 17 degree f amily of orientations " ( Aveni 1 975:166-168) f ound throughout Mesoamerica. Sunset on August 1 1-12 may have determined the location of Temple IV, relative to Temple I , at Tikal ( Aveni and Hartung, this volume), and further research may reveal the s ignificance of this date for orientation purposes throughout Mesoamerica. The following period of superior conjunction at D zibilchaltun was 5 2 days l ong i f Venus' f irst appearance as Evening Star was celebrated on October 2 , 6 92, which was 9 .13.0.10.0 1 3 Ahau 8 Ceh, another important thirteen date ( although Venus may have appeared two days earlier). ( 17) In sum, this Venus cycle consisted of eight days at i nferior conjunction, 2 60 days as Morning Star, 5 2 days at superior conjunction and 2 64 days as Evening Star. These may have been canonical Venus periods that were authorized i n 6 92 by the construction of this D zibilchaltun observatory. The Evening Star appearances of Venus were surely also tracked for this particular cycle but the ruined western group must be measured from its stela platform to understand how i t may have worked. Observatories The eastern half of the D zibilchaltun observatory was the l arger group with a bigger pyramidal structure and i t was located closer to the center of the s ite ( Figure 1 ). The smaller western half, which was probably observed from both Str. 1 -sub and f rom i ts associated stela platform, was a lso constructed differently in that there were only two range buildings between it and the platform. Thus i t would have been possible to s ight between the buildings from this platform and through Str. 6 6 i f i t had axial doorways l ike Str. 1 -sub. While they differed i n detail, the two ends of this macroassemblage were reciprocally related - l ike the opposing differentiated heads of the bicephalic serpent ( Figure 7 ). The e astern " head" connoted the r ising sun and Venus as Morning S tar and the western " head" the s etting s un and the Evening Star. 2 9

No other observatory l ike this one i s known f rom any date. The preclassic equinox and solstice observatories at Tikal ( Fialko 1 988) and Uaxactun ( Aveni and Hartung 1 986b) a lso sighted eastward with the a id three small a ligned s tructures, but from l arge radial pyramidal structures. As at D zibilchaltun the solstices were s ighted at the northern and southern edges of the eastern group and the equinox may have been viewed through an axial doorway at an early stage of their use, but the pyramidal structures i n a ll of these groups eventually became so high that horizon viewing could not have i nvolved i ntermediary buildings as f oresights. Instead backsights were probably incoporated i nto the sighting structure as was later done with the windows of the Caracol ( Aveni, Gibbs and Hartung 1 975), or an interior wall was used as in the Temples of the Jaguars at Chichen Itza ( Milbrath, this volume). As katun . commemorating complexes the twin pyramid complexes at Tikal are symbolically analogous to the D zibilchaltun observatory s ince they i nclude east-west mirroring radially symmetrical pyramids ( Coggins 1 983, pp. 4 0-41). If they were observatories the horizons might have been viewed from the two large pyramids i n the same way as f rom the later enlarged pyramids at Tikal, Uaxactun, and D zibilchaltun, or they could have s erved as f oresights f or each other. Early Maya observatories were oriented toward the east ( Ruppert 1 940), whereas the Pyramid of the Sun and the Temple of Quetzalcoatl at Teotihuacan, as well a s the much later Caracol at Chichen Itza were oriented toward the west. The twin pyramid complexes at Tikal may have f ormalized dual observation, the observatory at D zibilchaltun may have refined the idea, and at Chichen Itza, the Castillo, may have institutionalized it. The Temple of Quetzalcoatl at Teotihuacan could have been used for observation of the eastern horizon from the radial platform to its west, a s at D zibilchaltun, or possibly from the pyramid i tself and across the three small structures on the eastern wall of the compound, a s F ialko proposes, ( 1988, pp. 1 9, 2 0). But when f oresight structures are smaller than the viewing pyramid, a s at Teotihuacan, in the l ater phases of the Tikal and Uaxactun groups, or at either end of the D zibilchaltun assemblage, then it i s l ikely that i t was the nearby low axial radial platforms that served as the viewing sites. The stela platforms at D zibilchaltun, located at some distance down the sacbe from the eastern and western groups were evidently viewing platforms f or their associated temples. Each had a plain stela that may also have served some s ighting purpose as well as f unctioning as z enith gnomons, and as commemorative of the 9 .13.0.0 0 date f or which the assemblage was built. Conclusions The observatory at D zibilchaltun was built with a f our day predictive capacity that s erved to synchronize the 3 0

solar, Long Count and Venus dramas that were enacted there. The f act that the primary f ocus of the assemblage was a date, and not just an a stronomical event, was probably true for the orientation of a ll Mesoamerican religious structures. Anniversaries such as "Maya Creation Day" ( August 1 1-12) which had scriptural s ignificance f or a ll Maya as well as historic s ignificance at Teotihuacan might determine orientations just as the completion of a major calendric period, i n conjunction with a solar event like spring equinox, might combine with an i deal Venus cycle to determine the l ayout of a sacred place where the interval between zenith passages was exactly 5 2 days. This paper has sketched only some of the more obvious horizon events at Str. 1 -sub where a ll the stars were players in the heavenly dramas f or which the Maya had constructed the proscenium.

ACKNOWLEDGEMENTS Much of the raw data f or this paper was supplied by others to whom we are exceedingly grateful. Anthony Aveni and Horst Hartung made the measurements at D zibilchaltun and offered suggestions for possible solar s ight lines. Owen Gingerich and Barbara Welther of the HarvardSmithsonian Center f or Astrophysics generously created and provided the Venus cycle charts. Victoria Bricker, E . Wyllys Andrews V , and Horst Hartung also made valuable comments on the f irst draft.

NOTES

1 .In this paper Gregorian dates are used with the Thompson 1 1.16.0.0.0 correlation and Julian day number 5 8423.

2 . Azimuth measurements in this paper were planned and made by Anthony Aveni and Horst Hartung. They differ by 1 deg. from the D zibilchaltun site map which was laid out in reference to this east-west sacbe at 4 .5 deg. east of true north ( Kurjack 1 979, p . 4 ).

3 . The completion of the ninth baktun at 9 .0.0.0.0 8 Ahau 1 3 Ceh ( A. D. 4 35, December 1 1), and the tenth at 1 0.0.0.0.0 7 Ahau 1 8 Z ip ( A. D. 8 30, March 1 3), were historically associated with Teotihuacan influenced Maya prophecy ( Coggins in press b ).

3 1

4 . Karl Taube a lso points out that the personification of the number thirteen i s depicted i n a graffito on the f loor of Str. 1 -sub ( 1986:67). In i ts published i llustration ( Andrews IV and Andrews V 1 980: f ig. 1 10) this head i s not c lear because the f igure i s turned 9 0 deg. counter-clockwise. 5 . Only s ix of the eight masks retained decoration, but these fragments suggest the were i conographically equivalent ( Coggins 1 983: 2 6,27). 6 . K 'atun signifies both the tying up of the well as denoting 2 0 tuns s ince k 'ax means means 2 0 ( Coggins 1 987b).

any stucco eight masks

tun cycle as tie and k 'al

7 . Herbert Spinden noted the associations of Chak ( the long-nose deity) with Venus, the sun ( kin s ign), the bicephalic monster, and the manikin scepter deity ( God K ) ( 1913:61-69; and see Kowalski 1 987:187-202). The same c luster of associations may be made here since the f irst three are i nherent in the symbolism of the D zibilchaltun observatory assemblage. The manikin scepter i s not evident and probably only later became important at Dzibilchaltun ( Coggins in press, in preparation). 8 .

The

original

height

of this

reconstructed tower

9 . Real windows l ike these are otherwise unknown architecture ( Andrews IV and Andrews V 1 980:95).

i s unknown. in Maya

1 0. Drucker calculated z enith dates from the American Ephemeris and Nautical Almanac ( 1968) using the solar declinations after leapday f or the f irst year of f our. 1 1. Str. 1 -sub. was built with an experimental annular vault that may have collapsed and the building was covered by the much larger radially symmetrical Str. 1 ( Coggins 1 983, pp. 7 ,8,56). 1 2. Owen Gingerich provided Coggins with sets of configurations f or Venus cycles i n the years A . D. 6 89-698 and 7 21-730, while Anthony Aveni s hared his A . D. 5 00-509 and 6 50-659 sets. These were a ll prepared by Barbara Welther and Owen Gingerich of the Harvard-Smithsonian Center f or Astrophysics from a program devised by Barbara Welther, Owen Gingerich, and Beth Collea. 1 2. 1 3. These cycles are not f ixed in the year, although the configurations change very l ittle. D zibilchaltun cycle 1 was about twelve days l ater i n A . D. 6 51-652 than i t was i n 6 91-692 and i t was ten days earlier i n 7 23-724, while the r ise points were a degree to the s outh in 6 51 and a degree north i n 7 23 ( 109-107 degrees a zimuth i n 9 cycles, or 7 2 years).

3 2

1 4. This pattern of Venus r ises to the north and to the s outh of east ( and a lso of west) i s i llustrated in the wall paintings of the Upper Temple of the Jaguars at Chichen I tza where the east and west axes of the paintings are c learly designated by two f igures that apparently s ignify the sun and Venus. At the s ame time Venus i s shown rising in separate paintings just to the north and south of these axial portraits. Venus i s shown at superior conjunction on the north wall of this temple room and at inferior conjunction on the s outh, so that the cycle of paintings corresponds to a complete Venus cycle of 5 84 days ( Coggins 1 984, pp.156-165). 1 5. Drucker consulted Tuckerman's tables with corrections from Neugebauer ( 1938).

( Tuckerman

1 964),

1 6. See Drucker 1 977, Aveni 1 977, and Aveni and Hartung 1 986a for calendric uses of twenty and forty day intervals. 1 7. f or

9 .13.0.10.0 1 3 Ahau 8 Ceh would have been desirable i ts period ending and f or its 1 3 and 8 coefficients.

3 3

1 .

Heliacal

Rise

of Venus,

2 .

Winter Solstice,

December

Platform,

5 .*

Sunrise.

6 .

Spring Equinox,

7 .

Pleiadei Rise,

8 .

First Zenith Passage, May 2 5. Center Str. 1 0. Venus Rise, May 2 5. Between Strs. 8-10 ( see Aug

March May

windows, 2 0.

21.

N .

Axial

Second

Zenith

1 1.

Venus Last Appearance, ( see May 2 5).

1 2.

Sunrise,

1 3.

Fall

Maya

Equinox,

Passage,

July

4 .

1 -sub.

Str.

Str.

doorways

1 -sub.

1-sub.

Str.

1 0.

1 0).

corner Str. 1 0. S . window Str. 1 -sub. 1 7.

August

Axial

1 0.

Creation Day,

August

September

N .

2 3.

Str.

4 .

1 -sub.

tower,

corner

Summer Solstice, June 2 1. N . * Orion Epsilon rise, June 2 6.

1 0.

Str.

S .

Sunrise. March 1 6. Axial doorways, Str. Venus Rise March 1 6. Center Str. 4 . N .

windows,

Center Str.

4 .*

1 8.

S .

6 91.

6 91.

Sunrise.

March

1 4,

21,

25,

3 .*

9 .

March

November

doorways

Between

11.

N .

corner Str.

Strs.

S tr. 10. 8 -10.

end Str.

8 .

1 -sub.

Table 1 . Postulated observations of astronomical horizon events at the Str.1- sub group, 6 91-692 A . D. Starred ( *) sightings visible from Str. 6 6, a ll others from Str. 12.

3 4

B IBLIOGRAPHY Andrews

IV,

1 980

E .

Wyllys

and Andrews V ,

E .

Wyllys

Excavations at D zibilchaltun, Yucatan, Mexico. Middle American Research Institute Publication Tulane University, New Orleans.

Andrews V ,

E .

4 8,

Wyllys

1 979

Early Central Mexican architectural traits at Dzibilchaltun, Yucatan. Actes, 4 2nd International Congress of Americanists, VIII:237-249, Paris.

1 986

Olmec jades from Chacsinkin, Yucatan and Maya ceramics f rom La Venta, Tabasco. In Research and Reflections in Archaeology and History, editor E . W. Andr ws V ., Middle American Research Institute Publication 5 7, pp. 1 1-47, Tulane University, New Orleans.

Aveni,

Anthony

F .

1 975

Possible astronomical orientations in ancient Mesoamerica. In Archaeoastronomy in Pre-Columbian America. ed. A . F. Aveni, pp. 1 63-190. University of Texas Press, Austin.

1 977

Concepts of positional astronomy employed in ancient mesoamerican architecture. In Native American Astronomy. ed. A . F. Aveni, pp. 3-19. University of Texas Press, Austin.

1 980

Skywatchers of Ancient Mexico. Press, Austin.

1 986

The real Venus-Kukulcan in the Maya inscriptions and alignments. Sixth Mesa Redonda de Palenque. University of Oklahoma Press, Norman. In press.

Aveni, 1 975

Aveni, 1 976

Aveni,

Anthony

F .,

S .

The Caracol astronomical 9 77-985. Anthony

F .,

L .

Gibbs,

and H .

University of

Texas

Hartung

tower at Chichen Itza: an ancient observatory? Science, 1 88 ( 4192):

Sharon

L .

Gibbs

On the orientation of ceremonial centers in Central Mexico. American Antiquity, 41:510-517. Anthony

F .,

Horst Hartung

1 986a Maya city planning and the calendar. Transactions: American Philosophical Society vol. 76, part 7 :18 7. 3 5

1 986b Uaxactun, Guatemala, Group E and similar assemblages: an archaeoastronomical reconsideration. In World Archaeoastronomy, editor, A . F . Aveni. Cambridge University Press. In press. d oss,

Michael

1 979

Class, 1 984

Coggins,

P .

Venus in the Maya world: glyphs, gods and associated astronomical phenomena. In Tercera Mesa Redonda de Palenque, vol. IV, editors M . G . Robertson and D . C . Jeffers. Herald, Monterey. pp. 1 47-165. Michael

P .,

A . F.

The planet Venus 9 :221-248. Clemency

Aveni,

and B .

and Temple

2 2,

Crowley Copan.

Indiana,

Chase

1 975

Painting and Drawing Styles at Tikal: an Historical and Iconographical Reconstruction. Ph. D. dissertation, Harvard University. University Microfilms, no. 76-3783. Ann Arbor.

1 979

A new order and the role of the calendar: some characteristics of the Middle C lassic period. In Maya Archaeology and Ethnohistory, editor Norman Hammond. University of Texas Press, pp. 3 8-50.

1 980

The shape of time: some political implications of a four-part figure. American Antiquity, 45:727-739

1 983

The Stucco Decoration and Architectural Assemblage of Str. 1 -sub, D zibilchaltun, Yucatan, Mexico. Middle American Research Institute Publication 4 9, Tulane University, New Orleans.

1 984

Catalogue.In Cenote of Sacrifice: Maya Treasures From the Sacred Well at Chichen Itza. editors C . C . Coggins and O . C. Shane I II. University of Texas Press, Austin.

1 986a New Sun at Chichen Itza.In World Archaeoastronomy. editor, A . F. Aveni. Cambridge University Press. In press. 1 986b Reflections on Teotihuacan. P aper presented at the Society for American Archaeology meetings, New Orleans.

3 6

1 987a New f ire at Chichen Itza. Memorias del Primer Coloquio Internacional de Mayistas, ( 1985), Universidad Nacional Autonoma de Mexico, pp. 4 27-484. 1 987b The names of Tikal. Primer Simposio Mundial sobre Epigrafia Maya, Asociacion Tikal, Guatemala. pp. 2 3-45. 1 987c Quetzalcoatl, Teotihuacan, and the Maya. Paper presented at the Society for American Archaeology meetings, Toronto. 1 987d Names of Quetzalcoatl at Teotihuacan and in Maya regions. Paper presented at the American Anthropological Association meetings, Chicago. 1 988a On the historical significance of decorated ceramics at Copan and Quirigua and related Classic Maya sites. In The Southeast Classic Maya Zone, editors E . H. Boone and G . R. Willey. Dumbarton Oaks, Washington, D . C., pp. 95-123. 1 988b The birth of the baktun at Tikal and Seibal. In Vision and Revision in Maya Studies, editors F . Clancy and P . D. Harrison. University of New Mexico Press. In press. Drucker, 1 977

Fialko, 1 988

Fox,

R .

David

A solar orientation for Teotihuacan. Los Procesos de Cambio ( en Mesoamerica y areas circunvecinas). XV Mesa Redonda, Sociedad Mexicana de Antropologia y Universidad de Guanajuato. vol. 2 : 2 77-284. Vilma Mundo perdido, Tikal: un e jemplo de Complejos de conmemoracion astronomica. Mayab 4 : 13-21. Madrid.

James A .

1 984

Kelley, 1 976

Justeson

Polyvalence in Mayan hierogolyphic writing. In Phoneticism in Mayan Hieroglyphic Writing, editors J .S. Justeson and L . Campbell. Institute for Mesoamerican Studies, State University of New York Publication 9 : 1 7-76. Albany.

Hellmuth, 1 987

and John S .

Nicholas

The lily-pad headdress monster, Monster und Menschen i n der Maya-Kunst. Graz. pp. 1 60-163. David H . Deciphering Maya Press, Austin.

Script.,

3 7

University

of

Texas

Kowalski, 1 987

Jeff

Karl

The House of the Governors: a Maya Palace at Uxmal, Yucatan, Mexico. University of Oklahoma Press, Norman.

Kurjack, 1 979

Edward

B .

Introduction to the Map of the Ruins of D zibilchaltun, Yucatan, Mexico. Middle American Research Institute Publication 4 7, Tulane University, New Orleans.

Lounsbury, 1 982

Floyd G .

Astronomical Knowledge and i ts uses at Bonampak, Mexico. In Archaeastronomy and the New World, editor, A . F. Aveni. Cambridge University Press, pp. 1 43-168.

Milbrath,

Susan

1 981 Astronomical imagery in the s erpent sequence of the Madrid Codex. In Archaeastronomy in the Americas, editor R . A. Williamson. Balena Press, Anthropological Paper no. 2 2, Los Altos, CA. Millon,

Rene

1 973

The Teotihuacan Map, Part I : Text. In Urbanization at Teotihuacan, Mexico, editor R . Millon, University of Texas Press, Austin.

Neugebauer, 1 938

P . V.

Tafeln zur Berechnung der Jahrlichen auf- und unter-gange de planeten. Astronomische Nachrichten 264(6331): 3 13-322. Kiel.

Ruppert, Karl 1 940 A special assemblage of Maya structures. Maya and Their Neighbors. editors C . Hay Appleton-Century, N . Y. pp. 2 22-231. Spinden, 1 913

Taube, 1 986

In The et al.

Herbert A Study of Maya Art. Memoirs vol. VI. Harvard University,

of the Peabody Museum Cambridge, MA.

Karl The

Teotihuacan

cave

of

3 8

origin.

Res

1 2:

51-82.

Thompson,

J .

Eric

S .

1 960 An Introduction to Maya Hieroglyphic Writing, University of Oklahoma Press, Norman. 1 972

A Commentary on the Dresden Codex. Philosophical Society Memoirs vol. Philadelphia.

Tuckerman, 1 964

U .S.

American 9 3,

B .

Planetary, Lunar, and Solar Positions, A . D. 2 A . D. 1 649 at 5 Day and 1 0 Day Intervals. American Phlosphical Society Memoirs vol. 5 9, Philadelphia.

Government printing Office

1 968

American Ephemeris and nautical Almanac. Government Printing Office, Washington, D . C.

3 9

Ma rch 1 6

Ma rch 2 0 -e s - S p r ing E qu inox 7 1 d ays

May 2 5 Z en ith # 1

r i 3 S um me r c n S o ls t ice 0 9< c i )

W in te r S o ls t ice

J u ly 1 7 Z en i th # 2

7 3d ays

S ep t . 2 7

Chart

1 .

S e p t .2 3 . 6 F a l l E qu inox

Postulated divisions of the solar year at Dzibilchaltun ( 21 deg. 5 '45 " North latitude).

4 0

S upe r io r C on junct ion 9 . 13 .0 .10 .0 1 3 Ahau 8C eh O c t . 26 92

9 . 13 .0 .7 .7 1 2 Man ik 1 5C hen Aug . 1 0 6 92

F A E S

E ven ing S ta r

Mo rn ing E S ta r

W

HS /ES

9 . 12 .19 .12 .0 5Ahau l 3K ank in Nov . 1 7 6 9 1

HR / MS

S

9 . 12 . 19 .12 .8 1 3La ma t 1Muan Nov .2 5 6 9 1

I n fe r io r C on junc t ion Chart

2 .

A Canonical

Venus

cycle

41

at

Dzibilchaltun.

e r r

c t ) D

_

0

c e

7 12

_

0

' o

, -

. c '1 l ac t e . . . 7

0

r • I

1

-

._ j , T Y = e,

2 E ' 0 • . . . . . r i 0-

D w

e

Il e

\55

i

'

0 ]

O M

a 0

( %

i .

'

L

" ---r-7 t e zt

r

. :

r o

o

=r i ..

F = it '

L I

0

0

I

‘ , \ _.

c r ,

,

. ,

i

q 0

00

0

, -, , •p .' , d i

•

0

4

0 .

C

C o g i n s 1 9 8 3 ,

.

, r : Pi i0

E l

.

e d

M 3

ti lU ee-

1 1

=

• r -L - I r

L I

0

a

*

o

o

m • .i n '

•. n

•

0

r _ E d i

•c, I8 I I

e o

.

: eh • P : • 0 0°

I

_

_

[33

-em ir

• 0 ,

e ie 4

r s_ i

. 4 '• c

o

. ,

›

. .

•

o . .

. 7 t y i i

Q

.

D 0

,c p

0 Ä . -. .-

0

•A . 0

D

a

-L I

—

.. o o9 0 t0A

ou . • s o u

•:

_

.

• I F -

d )

—

.. ,

e o

—

G:

0

*

.

o

! . _ /

•, _ ,

Ce

n

0 l i r

. .

.

1 .

•2

a

A '

i i n

I A ?

• I l l

. . . . .z '

,0 _

g

.

i n . •g ä a i l

. ;

0

c r )

4 2

•

ü

-

c

.

0

°•

.

4 3

[115°] #2

......,._-z.--------

50m 3. str. 1-sub group with bearings measured from stela 3, on Str. l. Azimuths in parentheses are postulated.

44

9 3 t x , 4 . ) P K 1 0 u ) a ) 43 •0 r i l 4 ) — I a )4 ) t r u l P O H c l ) 0

0

> 1

L I ( I ) a ) t r u l • a ) 0 3 P R I C Z 0

• . . . . 0 .ri

P •a ) gio e 0 P a ) 2 31• ) 9 3 . C 1 i d • -. A

t aZ t , 4 41 •0 ) . 4 4 ) > c a u ) a ) 4 ) 0 0 4 0 0 • -• -1 O H

r i 0 4 ) N 0 • • 4 ) U )

0 3 t r •-I r n

O f a O w a ) ,A

r ZF A e

4 5

a

b

C

f

e 5 .

d

Mesoamerican four-part signs that denote the completion of cycles. a . Kan cross b . Kin s ign ( one day) c . Lamat ( Venus) d . Teotihuacan f lower emblem ( xochitl?) e . Katun completion sign f . Codex Fejervary-Mayer, page 1 ( calendar cycle) ( From Coggins 1 983, fig. 3 3)

4 6

4 13

a

I s _ i •1

"

i e . .

. ) . 2 / .

00 CM At e,bz 0L25 emmam

6 .

Structure 1 -sub. Remaining stucco decoration on the a . South f acade b . East facade c . North facade. ( From Coggins 1 983, f igs. 7-10)

4 7

7 .

Temple of Quetzalcoatl, Teotihuacan. Facade decoration. Drawing by Barbara Page. ( From Coggins 1 983, f ig. 3 6)

4 8

a

b 1 6

1 5

U o C 8 a .

1 0

1 2

1

1 3

1 5

Head variant of the number thirteen ( From Thompson 1 960, f ig. 2 5:9). b . Full f igure variants of the number thirteen and of the tun. 1 5. "Thirteen tuns" 1 6. "Five tuns" ( From Thompson 1 960, fig. 2 8: 1 5,16). C . Glyphs for the month Uo ( From Thompson 1 960, f ig. 1 6:10-15)

4 9

5 0

1 0.

Copan Stela N , I , pl. 8 2)

south

f ace.

5 1

( From Maudslay

1 889-1901,

r

C D

& )

4

i n

I

I

1

i N

r • J

E Q U I N O X S U N R I S E

r z i

t o ( 1 )

C D

U ,

a c i r t unv 5 2

3 5

1

1

1

1

1

1

1

1

VENUS EAST 1 II

1

T ill

a

3 0

2 5

7 0

8 0

9 0

1 00

AZ I MUTH 1 2.

1 10

1 20

1 30

N OV

The f ive configurations of Venus as Morning Star. Charts show the greatest height of Venus at f ive day intervals. The sun i s 1 5 degrees below the horizon on these charts a lthough Venus i s visible when as close as 7 degrees to the sun. The amended chart i n f ig. 1 3 i llustrates the f ull Venus period ( Courtesy of Owen G ingerich, Harvard-Smithsonian Center for Astrophysics). a . D zibilchaltun cycle 1 . November 2 5-August 1 0, A . D. 6 91-2. b . Cycle 2 . JulyFebruary, 6 93. c . Cycle 3 . February-October, 6 95. d . Cycle 4 . S eptember-April, 6 96-7. e . Cycle 5 . AprilDecember, 6 98.

5 3

b

V ENUS E AST -2

3 5

3 0

2 5

C I

2 0

1 0

5

o

6 0

7 0

8 0

9 0

1 00

10

1 20

C

V ENUS EAST -3

3 5

1 30

F EB

A Z IMUTH

J UN

3 0

2 5

w 0

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F RANZ T ICHY Mea su r em en to f Ang l e si n Me soame r ica . Nece s s i ty a nd P o s s ib i l i ty . 1 .N e c e s s i ty o fm e a su r em en to fa ng l e s . I nt h ea r ch i t e c tu r eo fM e so am e r i c ab o th i nt h eg r oundp l an so fb u i ld ing sa nd i nt h es e t t l em en t a nd f i e ld p a t t er n ss e v e r a lc l e a r ly d i s t ing u i sh ab l ea l i gnm en t sh av eb e en d i s cov e r ed .A n thony A v en i a nd H o r s tH a r tung h av ed e t e rm in ed t h ed i r e c t ion s ,i . e .t h eb e a r ing so fm any b u i ld ing s ,c ol e c t ed f u r th e rd a t aa nd l a id t h ef o und a t ion sf o rf a r th e rr e s e a r ch ( s e eA v en i 1 9 80 a pp end ix A ;A v en ia nd H a r t ung 1 9 86 ) .T h eb e s tk nown i st h e1 51 / 2 0 Eo fN d i r e c t ion o ft h eT eo t ihu a c an g r id i nac l o ckw i s e d i r e c t ion .O th e r ss u ch a st h ea x i so fC ho lu l ai ss k ew ed c l o ckw i s e2 5-26 °a nd t h ep a t t e rn o ft h et own a nd T emp lo M ayo ro fT eno ch t i t l an -M ex i co w i th t h e7 °d ev i a t ion Eo fN a r ea l so r em a rk ab l e . T h eg r e a tv a r i e ty o fa l i gnm en t si nt h eM ay ar e g ion i sc on f u s ing ,i ts t i l lr em a in ss oa f t e rA v en ia nd H a r t ung ' sn ew i n v e s t ig a t ion sp ub l i sh ed i n1 9 86 .T h e r ea r es t i l lm any u n an sw e r ed q u e s t ion s .H ow w a s t h e T eo t ihu a can d i r e c t ion t r an s l a t ed t os u ch d i s t an t p l a c e s t ot h e T rop i c o fC an c e r a nd t o G u a t em a l a ? Why w e r et h e r es om any d i f e r en ta l i gnm en t s ? Wh a td o e st h ed i f e r ing a ng l e ss i gn i f y a nd w hy i si ta lmo s ta lw ay s ac l o ckw i s ed ev i a t ion ?A r ea lt h eb e a r ing sc onn e c t ed w i th t h ec a l end a r ? H ow w a st h ep l ann ed a x i sf i x ed a tt h ep l a c ew h e r e ab u i ld ing w a se r e c t ed o r as e t t l em en te s t ab l i sh ed ? A nd t h i sr e qu i r eo b s er v a t ion so ft h es u ne v e ry t i m eo n ap a r t i cu l a rd ay ,o rw e r et h e r ep ro c edu r e sa nd i mp l em en t st om e a su r et h ea n g l e ?T od ay Is h a l lt r yt oa n sw e rt h el a s tq u e s t ion w h i l et o u ch ing u pon o t h e r s . T h ef l a to ro n ly s l i gh t ly h i l ly r e g ion o f No r th Y u c a t an m ak e si tp o s s ib l et oo b s e r v es u n r i s ea nd s u n s e to nt h eh o r izon i ft h e r ei sn oc l oud .I ti sp o s s ib l et of i xt h es u n r i s eb yu s ing ap a i ro fc r o s s ed s t i ck s ,f o re x amp l e ,o rw i th p o l e s .T h ea pp rop r i a t ed ay i sd e t e rm in ed b yt h en umb e ro fd ay st ot h e n ex tp a s s ag e o ft h e s u n a c ro s st h e z en i th . O b s e r v a t ion o ft h i si se a sy i nt h eT rop i c s ( Av en i a nd H a r tung 1 9 8 1 ;T i chy 1 9 80 :1 3 2 ) .F l a tg r ound p e rm i t st h en v e ry p r e c i s ea l i gnm en t sw i th am a rg in o f e r ro ro fa tl e a s t1 ° .E v en w h e r et h eg r ound i sn o ts of l a t ,w h e r em oun t a in so r ar a ng eo fm oun t a in s o b s cu r et h eh o r i zon ,a si nt h eb a s in so fC en t r a lM ex i co ,t h ev a r iou sb e a r ing sa r ee a sy t od i s t ingu i sh . T h i sr a i s ing o ft h e h o r izon a pp a r en t ly d i dn o th av em u ch e f e c to nt h ep a t t e rn so fb u i ld ing sa nd s e t t l em en t s . D i r e c to b s e r v a t ion o ft h e s u n w a sn o ta lw ay s u nd e r t ak en t od e t e rm in et h er e qu i r ed p a t t e rn . G r e a ti mpo r t an c e w a s a t a ch ed t oa s t ronom i c a l o b s e r v a t ion sf o r s om e e s p e c i a l ly s i gn if i c an t b u i ld ing si nc e r emon i a lc e n t e r s . S om el a rg ea r e a sw i th t h e i rs e t t l em en t sa nd f i e ld si nt h eb a s in so f P u eb l a -T l ax c a l a( T i chy 1 9 74 ) ,M ex i co ( T i chy 1 9 76a ,b )a nd O ax a c a( S to r ck 1 9 80 )a l so h av ep r e c i s e b e a r ing s .P a th sa nd f i e ld b ound a r i e sg oi nt h es am ed i r e c t ion f o rv e ry l o ng d i s t an c e su n t i la na r e aw i th ad i f e r en tb e a r ing i sr e a ch ed .T h e s ea r ep rob ab ly t h ef o rm e rt e r r i to r i e so ft r i b e so rr u l e r sw h i ch a r e e xp l i c i t ly d i s t ingu i sh ed i nt h i sw ay ( s e ef i g . 1 ) . I ti sh a rd ly l i k e ly t h a tt h es u nw a so b s e r v ed r e p e a t ed ly o nt h er e l ev an td ay si no r d e rt ok e ep t o t h e r e qu i r ed d i r e c t ion . We c a n , h ow ev e r , a s sum e t h a t c e n t r a l r a i s ed p o in t s w e r e u s ed a s o b s e r v a to r i e s ,f r om w h i ch e x a c to b s e r v a t ion sw e r em ad es oa st ot r an s l a t et h e s ea l i gnm en t so nt ot h e s u r round ing l a nd . I nl a rg ea r e a s ,s u ch a st h ei n n e rb a s in o fP u eb l a ,w h e r eC ho lu l ad e t e rm in e st h es y s t em o fo r i en t a t i on ,t h e r ew e r ec on s id e r ab l ed e v i a t ion s .T h i sw a sn o tt h ec a s ei ns m al e ra r e a s . F o re x amp l e ,t h e T ep e a c a -T e cam a ch a l co p l a in ee a s to fP u eb l al i k eC ho lu l ai sd e t e rm in ed b yt h es un r i s eo ft h ew in t e r s o l s t i c e( 2 5 —2 6 ° ) ,b u t mu ch m o r ep r e c i s e ly ( s e ef i g . 2 ) . I fac e r t a in a x i a ld i r e c t ion h ad t ob ef i x ed ,w i thou ti tb e ing p o s s ib l et oo b s e r v es u n r i s eo rs u n s e t o no n eo ft h ef o u rr e l evan td ay si nt h el o c a lh o r izon w i th n oo rl i t t l ee l ev a t ion ,t h ea ng l em u s th av e 1 05

b e en m e a su r ed s om ehow .T h i sr e qu i r e s af i x ed p o in ta tt h eh o r izon ,a na g r eed u n i to fm ea su r emen t a nd s ome k i nd o fd ev ic e . We c a na s sume t h a ti tw a sn ec e s s a ry a nd c ommon t om ea su r ea ng l e si n M e soame r ic a . B u th ow w a si td on e ? 2 . Way st om e a su r ea ng l e s . How c ou ld i th av eb e en d on eb yt h ee a r ly n omad i cp eop l ei nt h ef i r s ts t ag e so fc i v i l iz a t ion ? No s u i t ab l e i mp lemen th a sb e en d i s cove r ed b y a r ch a eo log i s t s . T h ep r e cu r so ro fa ni mp l em en tc ou ld h av eb e en am ea su r et a k en f r om t h eh um an b ody ,l i k et h eu n i t sy a rd a nd f o o t .A tf i r s ti tw a sp robab ly p o s s ib l et oi n d ic a t ed i s t an c eo nt h eh o r izon u s ing t h ee x t end ed a rm w i th s p r e ad f i ng e r s . W i th t h e w id th o ff i v es p r ead h and s Ic a nc ov e r ar i gh ta ng le , a bou t 1 8 0p e rh and . U s ing af i x ed o r i en t a t ion p o in t ,t h et o po f amoun t a in a s at o pog r aph ica lf i x ed p o in t ,o rw h e r e t h e s un r i s e s o r s e t s , as o l s t i c e p o in t , ad i r ec t ion c a n b e i n d i c a t ed mo r e o rl e s s a c cu r a t e ly a nd c ommun i ca t ed t oo t h e r si n ag r oup o fh un t e r so rg a th e r e r s . U s ing t h ei n d iv idu a ls p r e ad f i ng e r s Ic a nd i v id et h e1 8 0u pi n to 5 0 ,90 o r1 3 0. I nt h i sw ay w i th my o u t s t r e ch ed a rm Im e a su r eo nt h eh o r izon o ra nywhe r ee l se a na ng l eo f aq u a r t e ro ft h eo p en p a lm o ra t w en t ie th o ft h e r i gh ta ng le —4 . 5° o r 5d e c ima ld eg r e e s ( s e ef i g . 9 ) . S i n ce m yf i r s to b s er va t ion so fo r ien t ed s e t t l emen t si nC en t r a lM ex ico , Ih av ea s sumed t h a tt h i si s t h em e soame r i can u n i to fa ng le s .B u t Ih av ea sy e tp r e s en t ed t o ol i t t l ee mp i r i ca le v id en c et os uppo r t t h i sh ypo th e s i s . Ih op et od ot h i st o day i no rd e rt or e fu t et h ec r i t ic i sm m ad eo f my h ypo the s i s . Ou t s id eM e soam e r i ca t h er i gh ta ng le h a sa l so b e en r e p r e s en t ed i nt w en t i e th p a r t sa nd i nr e la t ion t ot h eh uman b ody —a tav e ry e a r ly s t ag eo fh uman c i v il iz a t ion .T h eZ ü r i ch e ng in ee r Amandu s We i s s f o und o ne o ft h e s er e p r e sen t a t ion sa bove t h ep i c tu r eo f ab i son ( s e ef i g . 3 )i nt h eL a s c aux c a ve .H e b e l i ev e st h a tt h en om ad i ch un t e r sh ad ak i nd o fc omp a s s1 7 ,000 y e a r sa go w h i ch t h ey c ou ld r e p r e sen t o nt h ee a r th a ss oon a st h en o r th p o in th ad b e en f i x ed .J u s ta bov et h eb i son a2 5c mw id ea r co f ac i r c l e g o e sa c ro s st h ew ho l el e ng th o ft h ep i c tu r e .I ti sm ad eu po f1 2t o1 5f i ne s ho r ts c r a t ch e so n en ex tt ot h e o t h e r . On t h ep i c tu r ei tc a nb es e en e x t end ing o ve r 4m e t r e s .F r om t h i sa r ct h e r ea r e3 . 5m e t r el o ng t h in l i ne se qu id i s t an tf r om e a ch o t h e ra nd r unn ing t owa rd st h ec e n t r eo ft h ea r c . 3 . 5 m e t r e si st h e e qu iv a l en to f 5s t ep se a ch 7 0c ml o ng .T h er a d i a ll i n e sa r e2 8c m ,i . e .o n ef o o t ,a p a r tw h en t h ey r e a ch t h ea r c .I nt h i sq ua r t e rc i r c l et h e r ea r e2 0o ft h e s er a d ia ll i n e s ,t h a ti st os a yt h er i gh ta ng l ew a sd i v id ed i n to 2 0p a r t sa nd e v e ry f o o t l eng th c o r r e spond ed t oe x a c t ly f i v ed e c ima ld eg r e e so rg r ad i an s( W e i s s 1 9 84 : 3 16 ) . I fad i r e c t ion -d e t e rm in ing i mp l emen to ft h i s k i nd w a s k nown t ot h e v e ry e a r l i e s th un t e r so f E u rop e a nd b eyond E u rope i nE u r a s i a , i ti sr e a son ab l e t oa s sume t h a t i tw a s o n e o fM an ' s f i r s t t e chn i ca la ch iev emen t si nt h en o r th e rn h em i sph e r ea nd t h a ti tw a st a k en f r om E u r a s i at o Ame r ic a .S o f a rn o r i gh ta ng l e d i v id ed i n to 2 0 p a r t s o r ac i r c l e d i v id ed i n to 8 0 p a r t s h a s b e en f o und i n No r th Am e r ic aa l though t h e r ea r es ome c i r c l e sw i th r a d ia l s . T he r ea r et h e " m ed ic in ew h ee l s " ,s u ch a st h eo n ei nB i gH o rn , Wyom ing w h i ch i s2 7m e t r e s a c ro s sa nd h a s2 8s p ok e s( Eddy 1 974 ) ." P e ck ed c i r c le s "f o rm ed a sr ow so fd o t so ns t on eh ave b e en d i s cov e r ed ( Av en i ,H a r tung a nd B uck ingham 1 9 78 ;A v en ia nd H a r tung 1 9 80 ;A v en i ,H a r tung a nd K el ey 1 9 82 ;s e ea l so f i g . 4aa nd 4b) .T h ey c ou ld b er e g a rd ed a ss ymbo l so f ac omp a s sw h i ch a ng l e s w e r e m e a su r ed a tt h i s p o in t . We a r e s t i l l l o ok ing f o r e v id en c e f o r t h e u s e o ft h e a n c i en ta ngu l a r m e a su r em en tu n i t4 . 5° , w h i ch i si na c co rd an ce w i th t h ev i g e s ima l s y s t em o fA n c i en t Ame r ic a . T h e a ngu la r m ea su r em en t u n i t w h ich Ip o s tu la t e r e su l t ed f r om t h e s t a t i s t i c a l t r e a tm en t o f d i r e c t iona lv a lu e si nt h eb a s in so fC en t r a lM ex i co . B e s id et h ev a lue so ft h er e la t ive ly f ew a nd w el s u r v ey ed p y r am id s Iu s ed t h ea x i a ld i r e c t ion so ft h ec hu r ch e s ,t h ec o lon ia ls u c ce s so r so ft h et emp le si n t h eh i gh land s ,w h ich w e r es e t t l ed i ne a r ly t i m e s .T he s ea r ea tt h es ame t i m et h ea x ia ld i r ec t ion so ft h e s e t t l em en t s ,t h ev i lag e sw i th t h e i rf i e ld s .T h eh i s tog r am o ft h ea x e so f2 77 c hu r ch e si nt h eM ex i co b a s in r e ve a l ed t h a tt h ea x ia ld i r ec t ion sa r ec on c en t r a t ed a r ound a s t ronom i ca le a s tt os o u th w i th t h e c l o ckw i s e d ev ia t ion 1— 2 °7 ° 1-12° 1 6 ° 2 0° a nd 2 5° ( s ee T i chy 1 9 76a , b ;s e e t o o f i g . 5 ) . T h e c onn e c t ion w i th t h em ovem en to ft h es u nc a nb es e en i nt h es o l s t ic i a ld i r ec t ion ( 2 5° ) ,t h eb e a r ing so f 1 06

s u n s e to nt h ed ay so ft h ep a s s ag eo ft h es u nt h rough t h ez en i th o n1 9 0N .L .( 2 0 ° )a nd t h es o c al ed m idy e a rd ay sn e a rt h ee qu inox e s( 10) .T h e1 ° ,7 °a nd 1 6 °d i r e c t ion sa r ee xp l a in ed b yt h ef i r s td ay so f t h ep e r iod so f2 0d ay si n ah ypo th e t i c a lf i x ed s un c a l end a rp o s i t ed a c co rd ing t ot h ed e s c r ip t ion b y S a h ag un f o r1 5 64-1567 i nT l a t e lo l co ( T i chy 1 9 80 ) .F o rs e v e r a lr a r ea l i gnm en t si nt h eh i gh l and sj u s t A f o r1 °n oe x p l an a t ion h a sa sy e tb e en f o und .I ts e em sc l e a rt h a tt h eb a s i si sn o ts i mp ly t h ec a l end a r b u t a l so ag e om e t r i c s y s t em t h a t c on s i s t s o fa r i thm e t i c a l a ngu l a r s e r i e s w i th 4 . 5 ° i n t e rv a l s . T h e s e qu en c e o fa n g l e s d i s cov e r ed i nC en t r a lM ex i co c a nh av e e i th e rt h e s o l s t i c i a l p o in t s i nt h e e a s t ( 9 0 +2 5 ° ) o ri nt h ew e s t( 2 70 +2 5° ) a sf i x ed p o in t so nt h eh o r izon ,b e c au s et h e s ea r ei ne v e ry i n s t an c ec l o ckw i s ed ev i a t ion s .T h i sf a c tr e v e a l st h eg r e a ti mpo r t an c eo ft h e s ep o in t sa nd d i r e c t ion sa s c a rd in a lp o in t sa nd c a rd in a ld i r e c t ion so fm e so am e r i c an c o smo logy . U s ing t h e i ro wn a nd d a t ap r e s en t ed b yo t h e rs c ho l a r sr e l a t ing t ob u i ld ing s ,A v en ia nd H a r t ung ( 1 986 ) h av ef o und t h e s am ea ngu l a rv a lu e s i ns om ec a s e s . I nm o s tc a s e s , h ow ev e r , t h e i rv a lu e s , c o l l e c t ed i nt h eM ay ar e g ion ,o c cu rv e ry r a r e ly i nt h eH igh l and so fC en t r a lM ex i co .I na dd i t ion t ot h e d ev i a t ion s a r ound 1 °7 °1 ° 1 6 ° a nd 2 5 ° a l r e ady m en t ion ed w h i ch o c cu r ed l e s sf r equ en t ly ,t h ey f o und v a lu e so f5 °9 °1 4 °1 8 °a nd 2 °i nt h eM ay aa r e a( s e ef i g .6 ) .I nc ommon w i th t h eM ex i co s e r i e s , t h i sM ay ao r i en t a t ion s e r i e sa l so h a sa ngu l a rv a lu e sd ev i a t ing b y4 °t o5 ° .T h i sf a c ta l so l e nd ss u ppo r t t ot h e h ypo th e s i s t h a t t h e r e w a s am e so am e r i c an a ng u l a r m e a su r em en t u n i t o f4 . 5 ° . On ly t h e d i r e c t ion s1 °7 °9 °1 4 °1 6 °a r ec onn e c t ed w i th t h eh ypo th e t i c a ls o l a rc a l end a rw i th 2 0d ay p e r iod s— t h eO r i en t a t ion C a l end a ra c co rd ing t oA v en ia nd H a r t ung —b u tt h e r ei sa l so a ne xp l an a t ion c ov e r ing b o th s e r i e sa tt h es am et i m e —n am e ly ah ypo th e t i c a lS o l a rC a l end a rw i th 1 3 d ay p e r iod sw h i ch i s p r e s en t ed i nt h et a b l e( T i chy 1 9 88b ) . Ic a nno th e r eg oi n to m o r ed e t a i la bou ti tb u t Ia s sum et h a ti ti s v a l id f o r , a nd c a nb ea pp l i ed t o ,t h ew ho l eo fM e so am e r i c a ( s e et a b l ea nd f i g . 7 ) . A n i n s t r um en t i sn e ed ed t om e a su r e a ng l e s a nd a r c s i nt h e s k y o ro n t h e h o r izon m o r e a c cu r a t e ly .I ts h ou ld m ak ei tp o s s ib l et om e a su r ed if e r en c e sb e tw e en t h ep o s i t ion so fs t a r so rb e tw e en t h ep o in t sw h e r et h es u nr i s e sm o r ea c cu r a t e ly t h an w i th t h eo u t s t r e ch ed a rm w i th s p r e ad f i ng e r s . P e rh ap st h i sd ev i c el o ok ed l i k et h es t r ang eo b j e c th e ld b y af i gu r ei nt h eC od ex S e ld en ( s e ef i g .8 ) . A v en i( 1 980 ,f i g . 7 )c a l l si t" ap r o long ed i mp l em en tw i th s t a r sp e r ch ed o ni t " . My r e ad ing o ft h i s p i c tu r ei st h a ti tr e p r e s en t s ah and h o ld ing o u t at e nd r i lw i th 3o r 4p r ong so r ab und l eo ft w ig s .T h e t i p so ft h et w ig sa r ee qu id i s t an tf r om e a ch o t h e r .T h es t a r ss u gg e s tt h a tt h ed ev i c ew a su s ed f o rt h e o b s e r v a t ion o fs t a r s . H ow f a ra p a r tm u s tt h et i p so ft h et w ig sb ew i th t h eo u t s t r e ch ed a rm h o ld ing t h ed ev i c ev e r t i c a l ly t om e a su r et h ea s sum ed 4 . 5 °a n g l e ?I nm yc a s ew i th t h ed i s t an c eb e tw e en e y ea nd i n s t r um en tb e ing a bou t5c mt h ed i s t an c ei s= t a n4 . 5° x 5 c m =4 . 3c m( s e ef i g .9 ) .W i th f o u rt i p st h ed ev i c ew ou ld b e1 2 .9 c ma c ro s sa tt h et o pa n dw ou ld p e rm i tt h eo b s e r v e rt os e e3 /20 o ft h er i gh ta ng l eo r1 3 .5 ° .T h i s i se x a c t ly h ow m u ch t h a tc a nb es e en w i th t h ef o u rs p r e ad f i ng e r so ft h eh and .T h i si n s t rum en t ,i fi ti s o n e ,s e em st oh av ec a l ib r a t ed o rs t and a rd iz ed t h eh and a sau n i to fm e a su r em en tf o ro b s e r v ing a ng l e s . W i th t h i sd e v i c ea nd u s ing af l a tp i e c eo fs uf i c en t ly d a rk o b s id i an a sp ro t e c t ion f o rt h ee y e s a g a in s tt h es u n ,i tw il h av eb e en p o s s ib l et om ak eo t h e ro b s e r v a t ion so ft h es un .T h ef a c tt h a tb e low 1 9 °N .L .a tn oon o nJ un e2 1 s t ,t h es umm e rs o l s t i c e ,t h es u nr e a ch e si t sh i gh e s tp o in t —a r ound 4 . 5 ° f r om t h e z en i th t ow a rd s t h e N o r th — m u s t c e r t a in ly h av e b e en k nown a nd m u s t h av e h ad c on s id e r ab l e s i gn if i c an c e f o r s u ch i mpo r t an t c e r emon i a l c e n t r e s a s C ho lu l a , C a c ax t l a a nd X o ch i c a l co ,w h i ch a r ec l o s et ot h i sp a r a l l e lo fl a t i tud e . A na dv an c ed c i v i l iz a t ion w i th s u ch o u t s t and ing a c h i ev em en t si na s t ronomy w i l ln o to n ly h av e h ad s u i t ab l eo b s e r v a to r i e ss u ch a st h eC a r a co lo fC h i ch en I t z äa nd t h eb u i ld ing o n Mon t eA lb an ( Av en i1 9 80 :2 49-286 )o rs o l a ra nd c a l end a ro b s er v a to r i e ss u ch a st h eg r oup Eo fU ax a c tun o rt h e g r oup C a nd D o fX o ch i c a l co t of i xt h er e l a t ion sh ip so fa ng l e so nt h eh o r izon ( s e eT i chy 1 9 85 :1 0 2 ) . T op l an a nd p u tu p ab u i ld ing o fa ny s i gn if i c an c e ,t op l an t own sa nd s e t t l em en t s ,i n c lud ing t h e s ei nt h e o p en c oun t ry , e v e ry th ing h ad t ob e m ad e p a r t o f as y s t em o fo r i en t a t ion c onn e c t ed w i th a n o r i en t a t ion c a l end a r .H av ing a s c e r t a in ed t h a tt h e r ew a sv e ry p rob ab ly am e so am e r i c an a ngu l a ru n i t o f1 / 20 th o f ar i gh ta ng l e , as u i t ab l ei n s t r um en tc a nb er e con s t ru c t ed o w ing t h ei l u s t r a t ion si nc od i c e s ( T i chy 1 988a ) .P e rh ap so n ew i l lb ef o und o n ed ay a l though t h ey w e r ev e ry p rob ab ly m ad eo fw ood 1 07

w h i ch w ou ld r o t . E ven i ft h i s l i nk i nt h e c h a in o fp roo fi sm i s s ing , w e h av e m ad e c on s id e r ab l e p rog r e s s t ow a rd s e xp la in ing t h e m any a l ignmen t s i n t h e a r ch i t e c tu r e o f Me so am e r ic a a nd u nde r s t and ing t h ep r a c t ica l r e a l i s a t ion o fs u ch p l an s . I nf u t u r ew h en g i v ing a ng le si nc onn ec t ion w i th t h ec u l tu r e so f Me so ame r ica ,w es h ou ld u s et h e n ew d ec im a l g r adua t ion w i th t h e 4 00 d ec ima l d eg r ee s ( g r ad i an s ) n ow e mp loy ed i ns u r vey ing i n p r e f e r en c et ot h eo l d3 60 0 d eg r ee s y s t em . Me a su r emen to ft h ef r on t i sp e a c eo ft h e Mendoz aC od ex w h i ch r e p r e s en t st h el e g end o ft h ef o unda t ion o fT eno ch t i t l an p rodu ced as u rp r i s ing r e su l t( s ee f i g . 1 0 ) .T h ed i agon a l sc r o s sa ta ng le so f9 0gand 10 g r ad ien s ,t h a ti s1 8a nd 2 m e soam e r i c an u n i t s .T he d i agon a l ly o ppo s i t ep a i r so fa ng le so ft h er e c t ang le a r e4 5 gand 5 g r e sp e c t ive ly , 9a nd 1 o ft h e s eu n i t s . T h i sc onf i rm sm ei n my a s sump t ion st h a tt h eu n i tp o s tu la t ed w a su s ed .T he r ei sac l e a rc onn e c t ion w i th t h ep ropor t ion so ft h es i d e so ft h er e c t ang le —6: 7 .T h e s ep ropor t ion sa r ef o und v e ry f r equ en t ly i nT eo t ihu a can ( t he i n ne r c our tya rd o ft h e C iudad e la i n c lud ing t h e Que tz a l co a t l P y r am id , t h e g r ound p l an o ft h e p a la ce s o n b o th s i d e s o ft h i s p y r am id , t h e c our ty a rd i nt h e b u i ld ing s b eyond M i cc ao t l i ( t h e R o ad o ft h e D ead ) a nd i ns e v e r a l c ou r ty a rd c omp lex e si nT e t i t la ) . T h eb a s eo ft h e Qu e tz a l co a t lP y r am id i nX och i ca lco a l so h a st h es ame p ropo r t ion 6: 7 .O th e rr e c t angu l a rg r ound p l an s ,s t e l e sa nd h i e rog lyph s t on es l ab sh ave d i agon a la ng l e sw ho s er ound ed v a lu e sc a nb ee xp r e s s ed i ng r ad ian s . Wh en t h es i d e sa r ei np ropor t ion 1: 2i ti s3 0g , 1: 32 0 g , 5: 74 0g . Is ugg e s tt h a ti tw ou ld b e w o r thwh i l et of o l low u p t h e se r e la t ion sh ip s .

R e f e rence s A ven i , A .F . 1 980 S kywa t che r so fA n c i en tM ex i c o . Un iv e r s i ty o fT ex a sP r e s s , A u s t in a nd L ondon . A ven i , A .F . , S .L . G ibb s a nd H . H a r tung 1 975 T h eC a r a co lT ow e ra tC h i ch en I t z a :A nA n c ien tA s t ronom i c a l Ob s er v a to ry ?S c i enc e1 8 8 : 9 77 -985 . A ven i , A .F . a nd H . H a r tung 1 976 I n ve s t ig ac iön p r e l im ina r d e l a s o r ien t ac ion e s a s t ronöm ic a s d e C op än . Y axk in 1 :8 13 . T eguc ig a lp a . I n s t i tu to Hondu r e f io d eA n t ropo log i a eH i s to r i a . A ven i , A .F . a nd H . H ar tung 1 98 1 T h e Ob se r v a t ion o ft h e S un a tt h eT ime o fP a s s ag et h rough t h eZ en i th i nM e so ame r i c a . A r cha eoa s t r onomy N r . 3 ,S upp l emen tt oJ ou rn a lf o rt h eH i s to ry o fA s t ronomy 1 2 : 5 1 -70 . A ven i ,A .F . a nd H . H ar tung 1 986 May aC i ty p l ann ing a nd t h e C a l end a r . T r an sa c t i on so ft h e Am e r i c an P h i l o s oph i c a lS o c i e t y 7 6 . P a r t7 :1 87 .

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A v en i , A .F . , H . H a r tung a nd B .B uck ingh am 1 978 T he P ecked C ro s s S ymbo l i nA n c i en t Me so am e r i c a . S c i en c e2 02 : 2 67 -279 . A ven i , A .F . , H . H a r tung a nd J .Ch . K e l ley 1 982 A l t a V i s t a ( Cha lch ihu i t e s ) , A s t ronom ic a l I mp l i c a t ion s o f aM e soame r i c an C e r emon i a l Ou tpo s ta tt h eT rop i c o fC anc e r . Am e r i c an A n t iqu i ty 4 7 : 3 16 -335 . E ddy ,J .A . 1 974 A s t ronom ic a l A l ignm en to ft h eB i g Ho rn M ed i c in e Wh e e l . S c i enc e 1 84 : 1 0 35 1043 . S t o r ck , K . -A . 1 980 D i eO r i en t i e rung v on O r t s -u nd F l u rg rund r i s s en i mB e ck en v on O axa ca /Mex iko .L a t e in a me r ika -S tud i en 6 :1 39 163 . Mün ch en . T i chy , F . 1 974 D eu tung v on O r t s -u nd F l u rne tz en i m Ho ch l and v on Mex iko a l sk u l t r e l ig iö se R e l ik t fo r m en a l t ind ian i sche rB e s i ed lung . E rd kund e 1 8 : 1 9 4 -207 . B onn . 1 08

T ichy ,F . 1 976a O rdnung u nd Z uo rdnung v on R aum u nd Z e i t i m We l tb i ld A l t ame r ik a s . My tho so d e r W i rk l ichk e i t ? l b e r o -Am e r ikan i s ch e sA r ch iv N .F . 2 : 13 154 . B e r l in . T i chy , F . 1 976b O r i en t a c iön d el a sp i r äm id e s ei g l e s i a se ne lA l t ip lano Mex ic ano .S up l e r r z en t o C omun i c a c i on e sI V : P ueb l a . F unda c iön A leman ap a r al aI nve s t ig a c iön C i en t if i ca . T i chy ,F . 1 980 D e rF e s tk a l end e rS ah agun ' s .E in e ch t e rS onn enka lend e r ?I nW i r t s chaf tu nd g e s e l l s chaf t l i che s B ewuß t s e in i nM ex i c os e i td e rK o l on i a l z e i t ,e d i t ed b yH . -A .S t eg e ru nd J .S chne id e r ,p p . 15 1 37 . L a t e iname r ik a -S tud i en 6 ,W i lh e lm F ink V e r lag , Mün ch en . T i chy , F . 1 976/8 1 O rd e r a nd R e l a t ion sh ip s o fS p ac e a nd T ime i n Me soam e r i ca : My th o r R ea l i ty ? I n D umb e r t on O ak sC onf e r en c eo nM e soame r i c an S i t e sa nd W o r ld V i ew s ,e d i t ed b yE .P .B en son , p p . 2 17 -245 . Wa sh ing ton D .C . 1 976 , C opy r igh t 1 98 1 . T i chy , F . 1 982 T h eA x i a lD i r ec t ion o f Me so ame r i c an C e r emon ia lC en t e r so n1 7 0No r th o f We s ta nd t h e i r A s so c i a t ion st oC a l end a ra nd C o smov i s ion .I nS pa c ea nd T ime i nt h eC o smov i s ion o fM e so a me r i c a , e d i t ed b yF .T i chy ,p p . 6 3 -83 . L a t e in ame r ik a -S tud i en 1 0 ,W i lh e lm F i nk V e r lag , Mün ch en . T i chy , F . 1 985 S onn enb eoba ch tung en u nd A g r a rk a l end e r i n Me soam e r ik a . I n G ed enk s ch r if tf ü r G e rd t K u t s ch e rT e i l2 ,e d i t ed b yA . Mönn i ch ,B .R ie s eu nd G .V olm e r ,p p .9 9 112 .I nd ian a 1 0 . B e r l in . T ichy , F . 1 9 88a D e rF uß z u rL äng enme s sung i n Me so am e r ik a ,d i eH and z u rW ink e l ang ab e ?I nF e s t s ch r if t f ü rT homa sB a r th e lz um 6 5 . G ebur t s t ag , e d i t ed b yV . H a rm s . T üb ing en . T i chy ,F . 1 988 bO r ien t i e rung sk a l end e ri nMe soam e r ik a . Hypo th e s en ü b e rA u f bau ,A nwendung u nd V e r b r e i tung . ( M s . ) . We i s s ,A . 1 9 84 O r i en t i erung d e r Wand e r jäg e r i m P a l äo l i th ikum . N a tu rw i s s en s chaf t l i ch e R und s chau 3 7 : 3 12 -3 19 .

1 09

Hypo the t ica l So la r O r ien ta t ion Ca lenda r w i th 1 3 -day Weeks b eg inn ing w i th W in ter So ls t ice a nd t he s equences o f a ng les w i th t he d i f ference o f 4 ,5 0. i st

day

1 3-day

of

astronomical

week

agrarian

events

clockwise sunset in

cycle .

sunrise

deviation from W or summer half-year

in

winter

half-year

Lat.15 ° N Winter

22/12 4

2 5

Solstice

/1

Beginning Agrarian

Cycle

25/2 10/3 Mid-year

23/3

Day

(Vern.Equinox)

6

5/4

/ /

1 8/4 1 /5

1 .

Solar Zenith Lat. 15 ° N

Passage

2 5 °0 8'

2 3 °3 5'

2 4 °0 7'

2 4 °2 2'

22

22 ° 1 4'

1 .

Solar Zenith Lat. 2 1 o1 6'

Passage

14 /5 27/5 9/6

Summer

22/6 5/7 1 8/7

2 .

Solar Zenith Lat. 2 1 o1 6' N

Passage

2 .

Solar Zenith Lat. 1 5 °N

Passage

3 1 /7 1 3/8

26 /8

2 1/9

Mid-year

Day

(Aut.

/1 0

9

1 7/10 3 0/10

Conclusion

Agrarian

Cycle

1 2/11

1 03'

6° 1 5'

6° 2 3'

60 2 7' 4

°

1 1'

(Maya)

Summer

( Central

Triangles: Calculati an refraction the

Orientation Mexico)

Difference based of

on

astronomical

Serie:

1 9 °4 3'

1 9 °5 5' 4

2 2 °3 4'

2 2 °4 8'

2 3 °4 7'

2 4 °2 0'

2 4 °3 4'

1°04,

1 1 0 10,