Megalithic yard in Teotihuácan?

              Andrzej WIERCINSKI, Warsaw:
MEGALITHIC YARD IN TEOTIHUA.CAN?
1. Introductory remarks
In 1951 J. D. Wolfel suggested that the oldest megalithic cultures of the Near East or
the Iberian Peninsula created a formative matrix for ideologies and the resultant
monumental architecture of the great centers of civilization of the Ancient World.
The suggestion can now be further corroborated on the following grounds:
a) R. Muller ( 1970) and discussions concerning the Stonehenge problem demon­strated
the presence of a profound astronomical knowledge among the
"Megalithics" applied to time recording and predicting;
b) more elaborated megalithic structures needed previous detailed planning and
large, well-organized social labour forces directed by well-differentiated and
rigidly organized religious elites;
c) many megalithic structures served as both cul tic centers and astronomical
instruments.
An astrobiological vision of the world and man's well-defined position in it not
only flourished in the ancient centers of great civilisations but was their basic
ideological regulating system.
An extreme example of the regulating power of such an astrobiological world
model in archai"c society is found in Prehispanic Mexico.
From a series of anthropological studies dealing with intra- and interpopulational
racial differentiation of both ancient and modern Amerindian groups in Mexico
(A. Wiercinski, 1969, 1971, 1972, 1972a, 1972b) I derived a working hypothesis
according to which the "maternal" Mesoamerican Olmec civilisation was the product
of an infusion of megalithic ideas resulting from sporadic transatlantic migrations
from the western Mediterranean centers of megalithic cultures into the native
archaic Amerindian together with transpacific impulses from China during the time
between the Shang and Chou periods. The last detailed discussions and critiques of
this general idea (J. Comas, 1972, 1973) bolstered my anthropological findings
(A. Wiercinski, 1974) particularly in regard to the presence of Negroid components
among Olmec groups. In Almogaren III, Z. Krzak ( 1972: The problem of reconstruc­ting
an Afro-Iberian Ship from the Neolithic Age) proved the possibility of suficient
megalithic navigational skill to allow for the voyages necessary to establish the
validity of the hypothesis.
In this context, "megalithic ideas" connote initially the idea of monumental stone
architecture erected for both religious and astronomical functions.
If such an idea were brought to Preclassic Mexico from the western megalithic
cultures between the 3rd and 2nd millennia B.C., it could be expected that the
megalithic measuring unit, the "megalithic yard," which equals 0.829 m. according
271
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to A. Thom (1962) and R. Muller (1970), was used in at least some of the Mexican
centers of monumental architecture.
This paper discusses the possibility of the use of the megalithic yard in the
construction of the Sun Pyramid of Teotihuacan.
2. Analysis of dimensions of the Sun Pyramid
The most recent publication of the dimensions of the buildings of the sacral
complex at Teotihuacan is by H. Harleston (1974). He used photogrammetric data,
field measurements, and archeological plans deposited in the I.N.A.H., Mexico. His
data are burdened by some errors in his reconstruction, particularly his belief in a
common minimum linear unit bringing all Teotihuacan dimensions into integral
numbers. He holds that this unit is 1.059463 m., exactly 1/12 millionth of the
earth's polar diameter and assumes the theocratic elite of Teotihuacan knew this
diameter.
The following objections are advanced against this hypothesis:
a) there is no evidence that Teotihuacan priests knew anything about the earth's
diameter;
b) presence of a common divisor for Teotihuacan dimensions can mean only that
the architects built according to simple proportions;
c) dimensions given in Harleston's "Hunabs" have no relation to specific calendric
cycles coded in the structure of the buildings.
Harleston's data seem to approximate real dimensions to the error of 0.25%.
Converted to meters they serve as a base for this analysis. From them were selected
the horizontal dimensions of one of the most conspicuous buildings, the Sun
Pyramid.
The procedure accepted here included the following steps:
a) conversion of diameters to meters to diameters in megalithic yards by dividing
meters by 0.829;
b) calculation of diagonals of all squares formed by edges of particular bodies of
the Pyramid;
c) search for possible meaning of these figures in relation to established
Mesoamerican calendric cycles known to have played a principal role in
ideological regulating system;
d) if meanings were found, postulation of a means to refine dimensions;
e) conversion of accepted dimensions from megalithic yards back into meters;
f) comparison of these new metric figures with the base dimensions derived from
Harleston's data.
Results of the calculations are given in Table 1. They reveal striking and probably
non-random regularities.
The sum of both diagonals of the square formed by the lower edges of the first
body of the Sun Pyramid is very near to 780, the longest cycle of Mars (779.94
days), and equal to 3 x 260 Tonalpohualli days.
The diagonals of its upper edges total 650 m.y., corresponding to
260 x 2-1/2 Tonalpohualli days.
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The sum of the diagonals of the lower edges of the second body is near 585 m.y.,
very near to the Venus cycle minus one day, i.e., 583.92 days, and very near 20
lunations and 260 x 2-1/4 Tonalpohualli days. The 585 day cycle is in the Aztec
Stone Calendar as two runs between 4-0llin and 4-Ehecatl (R. Noriega, 1974 ).
The sum of diagonals of the square formed by the upper edges is near 460 or 463
m.y. It is dificult to explain in the context of "c)" above.
The diagonals of the square formed by the lower edges of the third body are near
390 m.y. and correspond to one half cycle of Mars, or to 260 x 1-1/2, while those
of its upper edges are about 292.5 m.y., nearly 10 lunations or half a Venus cycle.
The fourth body of the Pyramid requires more complicated considerations.
Diagonals of its lower edges are almost exactly 260 m.y., one sacral cycle of the
Tonalpohualli! The sum of the diagonals of the central edges is about 255 m.y.,
which is not readily interpreted in the context of "c)" above.
The sum of diagonals of the upper edges are about 255 m.y., which corresponds
to a doubled Mercury cycle (115, 88 days). It is possibly noted in the Aztec Stone
Calendar as the span of 11 7 days between 4-Ehecatl and 4-Quiahuitl. It is near to 40
lunations.
The remaining dimensions are astonishly near to being multiples of 780 or 260
day cycles.
The diagonals from the lower edges of the fifth body are almost 195 m.y.,
equalling 780 x 1/4, while those from the upper edges are nearly 130 m.y., precisely
half the Tonalpohualli cycle of 260 days. The diagonals formed by the lower edges
of the sixth body give a value near to 86. 7 m.y., corresponding to 1 /3 of 260, and
those of the upper edges equal 65 m.y., a well known division of the Tonalpohualli
day count into 4 segments.
The accepted, more refined dimensions of diagonals were rounded numbers, and
those of the edges of the bodies of the Sun Pyramid prove there was very little
"cosmetisation" in the calculations.
Circumferences of particular squares formed by the edges of Pyramid bodies were
also calculated. Here we point out only that the values obtained for the
circumferences of the lower and central edges of the fourth body equal 368 and 361
respectively, which gives an arithmetic mean of 365 !
The circumference of the square formed by the upper edges of the fourth body of
the Pyramid is 82.8 m.y. This value times 10 is the circumference of the square of
the lower edges of the second body. It may be connected with the Tonalpohualli
day count and possibly with Venus, Mercury, and Lunation cycles, although proof is
not yet demonstrable.
To look at the problem modo geometrico, an attitude playing a greater role in the
"Gestaltarithmetrics" of ancient peoples than it does in our more purely numerical
thinking, consider Figure 1. It may be interpreted as reflecting simple dependencies
between 82.8, 58.5, and 11.7, as well as between them and 260.
Minor changes in figures applied to particular measurements give 58.4, 11.6, and
200 and even permit establishment of their relations with 365 and 29.
This simple geometric device allowing for all sorts of relations to dimensions of
273
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the Sun Pyramid and known Prehispanic Mexican astronomical time cycles is left for
free play of the imagination of interested readers.
3. Conclusions
The possibility of the use of the megalithic yard, 0.829 m., in Prehispanic Mexican
architecture was demonstrated at one of the greatest buildings of one of the most
important cultic centres, Teotihuacan, by converting the dimensions of the Sun
Pyramid into megalithic yards and comparing sums of the diagonals of the six body
squares of the Pyramid with known coded calendric cycles, especially those of
Tonalpohualli, Mars, Venus, and Mercury. Possibilities for association with both
lunar and solar cycles exist.
I do not think it possible to believe that the numerous mathematical matches are
an illusion.
REFERENCES CITED
COMAS, J., 1972: Hip6tesis trasatlanticas sobre el poblamiento de America. Caucasoides y
Negroides. Instituto de Investigaciones Hist6ricas. UNAM, Mexico.
COMAS, J ., 197 3: Transatlantic hypothesis on the peopling of America: Caucasoids and Negroids.
Journal of Human Evolution, vol. 2, p. 75
HARLESTON, H., Jr.; 197 4: A mathematical analysis of Teotih uacan. XLI International Congress
of Americanists (reprint), Mexico D.F.
KRZAK, Z., 1972: The problem of reconstructing an Afro-Iberian ship from the neolithic age.
Almogaren, vol. 3, p. 14 7
MILLON, R., 1967: Teotihuacan. Scientific American, vol. 216, p. 40
MOLLER, R., 1970: Der Himmel iiber dem Menschen der Steinzeit. J. Springer, Heidelberg.
NORIEGA R., 1974: Interpretaci6n matematico astron6mica de la Piedra del Sol. XLI Congreso
de Americanistas (reprint), Mexico, D.F.
THOM, A., 1962: The megalithic unit oflength. Journ. Roy. Stat. Soc., vol. 125, p. 243
WIERCINSKI, A., 1969: Ricerca antropologica sugli Olmechi. Terra Ameriga, vol. 18-19, p. 17
WIERCINSKI, A., 1971: Afinidades raciales de algunas poblaciones ant{guas de Mexico. Anales de
INAH, vol. 2, p. 124
WIERCINSKI, A., 1972: An anthropological study on the origin of "Olmecs". Swiatowit, vol. 33,
p. 143
WIERCINSKI, A., 1972a: Inter- and intrapopulational racial diferentiation of Tlatilco, Cerro de
las Mesas, Teotihuacan, Monte Alban and Yucatan Maya. Swiatowit, vol. 33, p. 175
WIERCINSKI, A., 197b: Interpopulational diferentiation of the living Amerindian tribes in
Mexico. XXXIX Congreso Intern. de Americanistas, Lima, vol. 1, p. 213
WIERCINSKI, A., 1974: Some problems in taxonomy of past and living populations of
Amerindians. XLI Intern. Congress of Americanists, Proceedings/in press/.
W6LFEL, D. J., 1951: Die Religionen des vorindogermanischen Europa. In: Christus und die
Religionen der Erde, vol. 1 (Vienna)
ACKNOWLEDGEMENTS
The present author wants to express here his best thanks to Dr. James L. Swauger
from Carnegie Museum of Natural History, Pittsburgh, for this kind revision of the
manuscript and all the corrections.
274
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Table 1. The horizontal dimensions of the Sun Pyramid in meters and megalithic yards
l9
. Sl"' ,.:i
.§
"Cl -
. .<: 0 ':l
i: 0
0 "'
·.o 0
c., . ·cV .:c. "' . ., 0
o.E.
First body, lower edge /d11/
First body, upper edge /d12/
Second body, lower edge /d21/
Second body, upper edge fd22f
Third body, lower edge /d31/
Third body, upper edge /d31/
Fourth body, lower edge /d41 /
Fourth body, central edge /d42/
Fourth body, upper edge /d43/
Fifth body, lower edge /d51/
Fifth body, upper edge /d52/
Sixth body, lower edge /d61/
Sixth body, upper edge /d62/
.0
;.a - .0 -.i,.
V 0-
1! rl
􀀆􀘠 "',.. 0:i . .,.e .:"',.
.s 􀀟􁼠
-6􀀠􂀠
228.84
190.70
171.63
135.61
114.42
85.82
76.28
74.80
68.44
57.21
38.14
25.42
19.07
"'
>- -
. :a: s -5 °'
;:N
􀀍􀶫«?
<>e I,.:I
.s s
=􀀂􀈢 "Cl-
276.05
230.04
207.04
163.58
138.02
103.52
92.02
90.23
82.56
69.01
46.01
30.67
23.00
e
h.s
.;:i N 􀀡􂅬lo 􀂊􈨬,:; 0 N
390.38
325.33
292.80
231.34
195.19
146.40
130.14
127.60
116.76
97.59
65.07
43.37
32.53
􀀢􂈰0 ;
"Cl.,
.p,. 􀀎􀸮.
V e
< .s
390
325
292.5
230.
195
146.3
130
127.5
117
97.5
65
43.3
32.5
.00 􀂋􈬮 . "'
0 i: e g,
􀀅􀔠 ;a
780
650
585
460
390
292.5
260
255
234
195
130
86.7
65
' >-
<.) • e"' e0 -􀂍􈴺:i
t,h 􀀂􀈠
"Cl:,:; g"
] :a
"3"' "Cl,. -V"' .,.c,. U V
275.8
230.0
206.8
162.6
138.0
103.4
92.0
90.2
82.8
69.0
46.0
30.6
23.0
"'.... 0
., Vi::
)Q. "Cl. ::ir 􀂌􈱥e -.i­,.
:lV :;i:;j
.!:; C"' u "'
1104
920
828
650
552
414
368
361
332
276
184
122
92
i:
·;􀀢􂈠
"Cl .,. ."' :i> .,. 0 .,
V f:
0
-h='-s
228.64
190.67
171.44
134.80
114.40
85.72
76.27
74.78
68.64
57.20
38.13
25.37
19.07
,.."' .,. e
,.V ·􀂍􈴺:i 􀀣􂌮. ,"Cl:􀂎􈸠
􀂏􈼠 II
􀀤􂐀􀀥􂔀􀀦􂘠
+0.20
+.0.03
+0.19
+0.81
+0.02
+.0.10
+0.01
+0.02
-0.20
+o.01x/
+0.01
+0.06
0.00
u"',. 􀀧􂜢"'
>, i:
V 0
e .lf
-􀂍􈴠 "Cl
." .:<. .s g "Cl .. § 0 􀀨􂠠 e
􀀩􂤠 􀀪􂨠 􀀫􂬠
ci . e
u ..;:l .s
780 days of Mars cycle =
260 x 3 of the Tonalpohualli
260 x 2 1/2 of the Tonalpohualli
584 + 1 days of a Venus cycle =
260 x 2 1/4 of the Tonalpohualli
?
780 X 1/2 = 260 X 1 1/2
585 x 1/2 = near to 10 Lunations
260 days of the Tonalpohualli
approach to solar cycle?
116 + 1 days of a Mercure
cycle x 2 = nearly 40 Lunations
780 X 1/4
260 X 1/2
260 X 1/3
260 X 1/4
Remark: if R. Millon's (1967) assesment that some of the principal measurements in Teotihuac:in exhibit multiples of ea. 57 meters, it corresponds exactly to
one fourth of 228.8 what is 57.2 i.e. 69 m.y.=d51 which forms the square with diagonals = 195 i.e. one fourth of the cycle 780 days.
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􀀂􀉲rt>
-tJ<o
'b
from 2 .G? up to 275.s
Fig. 1: A simple geometric device for calculating calendaric cycles.
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