Time and space in the Sun Pyramid from Teotihuacan

Andrzej Wierciński

Time and space in the Sun Pyramid

from Teotihuacan

Contributions in New World Archaeology nr 1, 87-103

POLISH CONTRIBUTIONS IN NEW WORLD ARCHAEOLOGY Kraków 1977

ANDRZEJ WIERCIŃSKI

TIM E A N D SPACE IN TH E SU N P Y R A M ID F R O M TEO TIH U A C A N

1. EXPLANATION OF THE PROBLEM

The purpose o f this paper is to present a study on num erical represen­ tatio n o f astronom ical calendric cycles in the m ain architectonical dimensions o f the Sun Pyramid from Teotihuacan.

The analysis of this problem departs from the set o f the following premis­ ses :

1.1: there exists a certain dependence between architectonic style and a central ideological m otivation in the development of various ethno-cultural systems;

1.2: the socio-cultural activities o f the people in all the centers o f ancient civilisations, with Prehispanic Mexico as the m ost extreme example, were ideologically regulated by astro-biological religions;

1.3: the very nucleus o f these religions was everywhere the same and, it had been unrooted in the fram e of the oldest megalithic cultures, somewhere in the W estern o f N ear Eastern M editerraneum , wherefrom came a stimulation tow ards constructing m onum ental architecture which served bo th; for cultic an d astronom ical purposes;

1.4: this architectonic inspiration, together with the linear measuring unit equal to 0.829 m (so called: “megalithic yard”), was brought to Mexico by, a m ore or less, sporadic transatlantic m igration, in the tim e between III and II millennium B. C. which departed from a centre belonging to the W estern wing o f megalithic cultures.

Owing to all these premisses, it is probable th at the Sun Pyram id as one o f the m ost m onum ental and conspicous buildings o f the sacral complex from Teotihuacan will reveal in its architectonic structure a reflection o f the astronom ical calendric cycles which played so im portant role in the astro- biological religion o f the ancient Mesoamerica. Precisely, this statement

should be demonstrated in this paper. However, before showing an attem pt

a t such a dem onstration, it seems reasonable to give some m ore explanations o f the premisses listed above. They may run as follows.

A d 1.1) The hum an program m ing o f any cultural product needs suitable

inform ation and em otional m otivation. Any m onum ental architecture which is built for a long-termed, public and ritualised use demands a huge and well

A M D B Z E J W I E R C I Ń S K I

organized social labour, as well as, its previous detailed program ming. Jf so, its spatial structure and decoration can not be a product o f a free, random play of determining factors but, both these constituents must represent the cultural information and motives stemming from the ideological subsystem (i.e. social, general model of the world with defined position o f m an within it) which organizes the normo type currently impregnating hum an m entality and regulating hum an behaviour within a given ethno-cultural system (see: Kos- secld 1973 and 1975).

A t once, worthy o f m entioning is, for example, a very general corre­ spondence between interiorised Christian religion and the construction o f the churches closed completely from the above and all the sides in which the public ritual performances proceed and, the interrior o f which is m ost richly decorated versus a correspondence between exteriorised ritualism o f various ancient pre-Christian religions celebrated around and/o r on the surface o f the huge iemple-pyramids with decorated façades, w hat was associated with vivication, personification and deification o f many different objects and processes o f the external environment. Such an opposition between the two extreme examples: a Gothic church and a tempie-pyramid, m ay be con­ sequently filled up with different types o f half-open temples with a colonnade, richly decorated outside and inside.

On the other hand, all these sacral buildings, the program m ing o f which and m otivation descend from a religious ideology may be excellently contrasted w ith the public buildings o f the m odem architecture characterised by an abstractous simplicity of their external form and an economical functionality o f the interior, devoided o f any richer, symbolistic decorativeness.

A nd no wonder, since the m entality o f the contem porary m an o f a “new deal” o f Europo-American technocracy is, m ore and m ore, m otivated by a narrow ideology o f life’s com fort and economy, included in a rationalistic, rather superficial scienticism.

A d 1.2) The astrobiological model o f the world which constituted the

essential nucleus of ancient religions, in the fram e o f which appeared the structure o f grave (or tempie-pyramid), may be most briefly characterised in the following way;

2.1 : the reality is permanently variable, vivified, personificated and deified, being subdued to periodical and cyclical transform ations; the objects are only the time cross-sections o f the processes—are their states in the time strata (the principle of the universal, psychological, processual variation);

2.2 : at the base of this variation lies a dynamical unity o f the pairs o f interacting polarised opposites which manifest themselves as: male and female principles light and darkness, heat and cold, day an d night, life and death, Heaven and Underworld, right and left, creation and destruction, Summer and Winter, Sun and M oon, to p and base of the pyram id, etc. etc. (the principle o f dually polarised Centre);

T IM E A N D S P A C E I N S U N P Y 3 A M I D ₈₉

according to the cardinal points which constitutes a universal, organising frame of reference in all the things and processes; as the cosmic system o f coordinates, it is denoted by the Polar Star, the Centre of the E arth and, by 4 cardinal directions; this 4-fold division may manifest itself as: 4 Ele­ ments, 4 parts of the day, 4 seasons o f the year, 4 phases o f the hum an life, 4 Cosmic Eras, 4 symbolic colours, 4 quartern o f the town, 4 -sides or 4 edges o f the pyramid etc. etc.; together with the centre in the plane or, with the vertical axis in the space, it passes into 5-fold division (the principle of the field o f 4( + l) cardinal points);

2.4: all the processes on the E arth are generated and regulated by the interplay o f the rhythmical activities o f the cosmic forces, the ordering o f which is reflected in the movements o f coelestial bodies on the firmament, first o f all, those of the Sun, M oon and visible Planets, in reference to the distinguished star constellations and the points o f the horizon (the principle o f the creative and regulating role o f the stable cosmic rhythms exerted on the biorhythms) ;

2.5: the world around m an is divided into 3 main regions: upper or the Heavens, the living surface of the E arth and the lower i. e. the Underworld ; in turn, these regions are further subdivided into m ore zones along the vertical axis o f the cosmic system o f coordinates; there is a connexion between the yearly round of the Sun and the divisions into 9 or 12 (+.1 representing the Highest Centre) or 6 (again + 1 ) heavenly zones; it was giving the possibility o f calculating the covariation in the movements o f coelestial bodies in the astronomical count of time (the principle of the division into W orld’s Zones) ; 2.6: m utually interacting opposites create a universal, all vivifying and developing bu t also destructing energy o f Fire, the portioning o f which decides about the time order in the structure of the processes; this Fire may manifest itself in the light of heavenly bodies, the athm ospheric lightnings, volcanic fire o f the Earth, as well as, in the fire of house hearths, animal and hum an blood, in the hum an emotions or sacrificies ; its transition into a Segmented Serpent o f Time represents the time ordering o f the states of a process (the principle o f the unity o f the universal energy o f Fire and Time) ;

2.7: the development o f the W orld in all its particular manifestations is previously informationally program m ed in the highest (7th -th or 13th) zone o f the Heaven; this program me is hierarchically ordered and idealised in the form o f a Cosmic Calendar o f Events; its realisation produces the world from a state o f a maximum homogeneity (Primordial W aters o f Chaos), causes its evolution and, in turn, its implosion (the principle o f .hierarchical descendance o f the W orld’s Program m e);

2.8: in the cyclically conceived processes, the energy o f the universal Fire must be preserved and suitably distributed ; the hum an Fire-Soul which is a portion o f the Cosmic Fire, can be timely imprisoned after the death in the Underworld or may pass into- a given Heavenly Zone and, then, it descends back into the other body; from this results the idea of reincarnation

9 0 A N D R Z E J W I E R C I Ń S K I

and of effectiveness of bloody sacrificies or, the autodeprivation o f emotions, as well as, the idea o f the elem entary cataclysms caused by the hum an sins (the principle o f preservation o f the energy o f Universal Fire) ;

2.9: the hum an being living on this E arth m ost fully reflect the M acro­ cosmos; man is conceived as he would be a com plicated lense which con­ centrates different cosmic forces and, so, his psychophysical construction is Imago M undi (the principle o f equivalency between M an as Microcosmos and, the M acrocosmos as an Anthropocosmos).

This shortly sketched above astrobiologica! w orld’s m odel o f ancient religions was being visualised in the iconic-numerical code o f concentrically organised M andalas (of which the richest example is the famous Aztec Stone Calendar!), as a Cosmic Tree or, m ore poorely, in the form of a grave or temple-pyramid as a Cosmic M ountain (see: Eliade 1966, Schwabe 1951, Tucci 1961, and Wierciński 1974).

It could be also dynamically represented in the system o f complicated ritualisms o f cyclical, public feasts, with very high em otional m otivation derived from their dram atic theatraiism , program m ed in the order o f the sacral calender which resulted from the astronom ical com patibility o f p ar­ ticular cosmorhythms.

A d 1.3 and 1.4) The present author shares the general idea of D. J. Wol-

fel (1951) th at the oldest megalithic cultures from the Iberian Peninsula or Near East have constituted a com m on, formative m atrix for ideologies and monum ental architecture o f great centers o f civilisation o f the Ancient W orld.

Nowadays, this hypothesis can be further corroborated on the following grounds:

a) R. M üller (1970) and the whole discussion around the Stonehenge problem and also a larger review article o f E. C. Baity (1973) have supplied new evidences for the presence o f rather profound astronom ical knowledge

am ong “Megalithics”, related to the count o f tim e; .

b) all the more elaborated megalithic structures which needed detailed programming and a good organisation o f the public works implies clearly the rise of already well differentiated and rigidly organised theocratic elite;

c) a good num ber o f these megalithic structures served bo th for cultic (at least sépulcral) practices and as astronom ical instruments.

Thus,

it is quite natural to expect an evolution o f a system o f feedbacks

between the astronomical count o f time which necessitated some mathematics and geometry and social stratification on one hand and, the development of agriculture with cattle breeding as a m ain subsistence economy and the rise of larger more densely populated settlements, on the other. F rom all these emerged the astrobiological vision o f the world which reorganised previous more primitive religions, the m onum ental architecture and the be­ ginnings of the urbanisation. The way from the oldest dolm en grave with a porthole and earthly m ound to the grave or tem ple-pyram id has been opened!

T IM E A N D S P A C E I N S U N P Y R A M ID 91

However, how to connect the temple-pyramids from Prehispanic Mexico with megalithic cultures of the M editerraneum ? In order to answer this delicate question, first of all, worthy of emphasize are the papers o f J. Alcina Franch (1969 and 1971) which attem pted to show a series o f possible a r­ chaeological links between neo-enolithic Europe and America. Secondly, the present author has published a series of anthropological studies dealing with intra — and interpopulational racial differentiation of both, ancient and m odern Am erindian groups in Mexico (Wierciński 1969, 1971, 1972a and 1972b). They permitted to advance the working hypothesis th at the Olmec civilisation, m aternal for Mesoamerica, has been the product of an infusion of megalithic ideas, brought by a- sporadic transatlantic m igration from th e W estern M editerranean centers of megalithic cultures, into the native, creative and archaic Amerindian background, interm ingled with transpacific impulses from China o f a transition between Shang and B shou Periods. The last, m ore detailed discussion with the critics published by I. Comas (1972 and 1973) did not discredit but even strengthened the anthro­ pological findings o f the present writer (Wierciński 1974), at least, as regards the presence of Negroid components among the Olmecoid groups. Also, Z. K rzak (1972) has shown the navigation’s possibilities existing in the frame of megalithic cultures o f the Mediterraneum.

Consequently, the present writer has assumed th at if a megalithic in­ spiration was brought to Mexico from the Western wing o f megalithic cultures, between III and II millennium В. C., it might be reasonably expected that, at least, in some of the Mexican centers of the ancient m onum ental architec­ ture, the megalithic measuring unit was used (i.e. megalithic yard = 0.829 m), as discovered by A. Thom (1962) and still more dem onstrated by R. M üller (1970).

A nd indeed, a first preliminary analysis o f the dimensions o f the horizontal edges of the six bodies of Sun Pyram id from Teotihuacan, based on the data published by H arleston (1974) and converted into megalithic yards, revealed striking numerical coincidencies with the duration o f several astro­ nomical cycles, especially, with the sacral calendar of 260 days (Wierciński

1974—75).

This finding encouraged further analysis o f the Sun Pyram id which will be presented below.

2. DIMENSIONS OF THE SUM PYRAMID AND THEIR ANALYSIS

As it was mentioned above, the main body o f dimensions of the Sun Pyramid, as well as, those of the other buildings o f the sacrai complex from Teotihuacan has been recently published by H . H arleston (1974). He ad­ vantaged in his study the photogram etric data, field measurements and

92 A N D R Z E J W I E R C I Ń S K I

archaeological plans deposited in I. N. A. H., in the light of R. M illon’s reconstruction (1970).

Of course, H arleston’s data are burdened by some, though, probably not very great errors of his geometrical reconstruction (what is a great m erit of tins author), guided by his belief in a com m on minimum linear unit which brings all the dimensions of Teotihuacan objects into the integral numbers.

He has found it equal to 1.059463 m and called it: “H u n ab ”. Strangely enough, it is exactly 1/12 milionth of E arth ’s polar diameter. Thus, H ailesto n assumed that the theocratic elite who program m ed the construction o f Teo­ tihuacan knew tjjis diameter.

However, there is a complete lack of any scrap of evidence th at the Teo­ tihuacan priests knew anything about E arth ’s polar diam eter and, the finding of a common divisor of Teotihuacan dimensions may also denote only that its architecture was built according to some simple proportionalities.

In any case, H arleston’s data seem to approxim ate well the real, possible dimensions of the Sun Pyramid up to the error of 0.25% perm, and, con­ verted into meters again may serve as the departure m aterial for the purpose o f this analysis.

The table I yields this departure m aterial of dimensions of the Sun Pyramid together with the lengths of diagonals calculated for the squares formed by the edges of particular bodies of the Pyramid, in order to show their coincidencies with the calendric cycles. In turn, the table II represents the duration of possible calendric cycles, the data of which will appear useful in our analysis.

However, in order to study now m ore thoroughly the architecture of the Pyramid also the heights of its bodies m ust be considered. Their respective values are presented in the table III.

It may be immediately seen th at the length of the edge of the highest 6th body equal to 23 m .y. is repeated again as the height of the lowest, 1st body. M oreover, the upper edge o f the 1st body measures exactly

10 X 23 m.y.

Secondly, the elevation of-the 6th body is alm ost exactly 1/6 of 23 m .y. and, it corresponds accurately to the time cycle of 13 (sic!) lunar m onths divided by 100 (13 x 29.5 = 383.5 days).

I f we connect these findings with the simple proportionalities found by H arleston and, the observation that the length of the upper edge o f the 4th body near to about 82.8 m .y. times π gives roundly the num ber 260, it seems reasonable to suspect a very clever geometry which probably program m ed the spatial structure of our Pyramid in relation to particular calendric cycles.

Since, the measuring error should be the lowest for the small objects and, at any rate, we deal with the Pyramid, let us start from its Top!

Thus, we may assume that the vertical elevation o f the highest 6th body, so nicely corresponding to the round o f 13 synodical m onths (surely well

T a b le I. The h o r i z o n t a l d i m e n s i o n s of the Sun P y r a m id in m e t e r s and m e g a l it h ic y a r d s T IM E A N D S P A C E IN S U N P Y B A M ID 9 3 <D О я Я Ό υ с г? О υ & .а 4 ) 1 ч о Я 3 о о ■w ci =3 -С о а Н X П| >· I S £ X X X N г -1 i X с-· c s м д Д оЗ 's 's д rC О О о п ; a а , 13 1 3 1 3 to С о о О h H f-1 X X X e n τ η ■r i· ■-η ł-T Cf t 1 3 с т ? о т о u n u n un u n О С ,-н о u n n i о n i CÛ о о u n о о NO O N O N .S О S-. п -N O un Г П Ш О u n τ η u n О O u n 1 S > > N С . О С / СО с О * л C S Ή < П \J D c n e s o n e n o n ^ τ η τ η < Ν Щ Μ i— ■I Ο τη u n N O [X un τη n i « σ \ ό ^ т о ■ -S ■ 6 α ο Jjß Ъ ον % 1 ES Й 1 Л ' t Τ ) · G O Γ ΐ N η η Ό η p © © u n ρ u n ρ n i u n © Ν Ο Ο f X Т П С О Т П η ! Ο П -l Ο Ν Γ~ ~· Т П Ο N O m Ο O N O N C G N O N n l N n -и и О О Cft 4> о s ' о 4 ) 0 Û C *3 '_{T о} i ■rl* n .S ·— о О oj O N " ί Μ ffi en Т П T -! n s n ~ ,_ i 00 r-i T— 1 чЧ г -Т Г O en n i oo O N flf T i­ n i о °° . n n o N O p °° . n i C -; T T n i **f r n -od © P u n fli* un N O 00 * fX e d un © n i n i O N n ~ τη 00 r -r -N O un τ η n i O n " a N ? _i * β & (J Μ Ό № a a Ή ^ a ω -α » -α Ό 4> Ο £ s-^ J g J u ϋ ö R ω of op ω τι Ό Ό Ό y Ο ο <ϋ i) u ö Й з л и и о о · ,-Д 4 ) 4) LT -. C L г л г л т з -а о о •о ^ о о P*« >> >, >n >> ТЗ Д Т З TO О О О О X ) Æ Æ Л д Д Л -Й й ί£ .Ή .Ή E l , fe 'е й

T a b le I I . A lis t o f s o m e c a l e n d r ic cycles (in d a y s)

Synodical mouth 29 A

Mercure cycle 116

Tonalpohualli (sacral calendar) Solar year without additional Nemonteni

260

days 360

Common Solar year 365

13 months “Lunar year” ■ 383 Va

Saturn cycle 376

Jupiter cycle 399

Venus cycle 584

Mais cycle 780

Table III. The vertical dimensions of the Sun Pyramid in meters and megalithic yards

Description of dimensions hi in meters (according to H. Harlestone, 1974) hi in megalithic yards

First body, vertical elevation 19.070 23.004 Second body, vertical elevation A2 15.892 19.170 Third body, vertical elevation hs 12.714 15.337 Fourth body, vertical elevation

(lower) й4(!) 2.119 2.556

Fourth body, vertical elevation

(upper) A4(2) 4.238 5.112

Fifth body, vertical elevation й5 9.535 11.502 Sixth body, vertical elevation h% 3.178 3.834

known in Mesoamerica), will be one o f the key-lengths for the remaining dimensions o f the Pyramid.

Having some degrees of freedom in the measuring error for particular dimensions and accepting the principle of possibly simple proportions, there were calculated little refined new values of bodies’ heights as multiplicities of 3.835 m .y. (see: table IV). The deviations o f the new heights in reference to prim ary H arleston’s data appeared to be alm ost none. The greatest height h[, previously equal to 23.004 m.y. now became 23.010 m .y. what is only 5 m m of the difference! The same regards to all the other heights h\.

Strikingly enough, num ber 23.010 is divisible without any rest by 2.60 (23.010:2.60 = 8.850).

Also, it is worthy of a great emphasize that 23.010 = 2.950 x7.80 and th at: 3.600 x 23.010 = 82.836 s : 260/π ^ diZ (look for astronom ical coinci- dencies at the table II!).

Consequently:

T IM E A B D S P A C E IN S U N PYBAM ID 95

Table ÏY, The vertical dimensions of the Sun Pyramid derived from 3.835 m.y.

Description of dimensions Primary heights hi in megalithic yards Refined heights hi in megalithic yards Difference in meters i h - h ' d

First body, ve/tic- ! elevation h. 23.004 23.010 0.005 Second body, vertical elevation A2 19.170 19.175 0.004 Third body, vertical elevation h3 15.337 15.340 0.003 Fourth body, vertical elevation

(lower) hi{l) 2.556 2.550 0.005

Fourth body, vertical elevation

(upper) A4(2) 5.112 5.120 0.006

Fifth body, vertical elevation hs 11.502 11.505 0.003 Sixth body, vertical elevation hs 3.834 3.835 0.001

F urtherm ore :

,,, Л1П _ 5.84 x 1 1 6 2.60 x260 _ 116x 11 6 _ 5 2 x 2 6 0

~ 29.5 = 29.5 = 584 = 584 '

Having a t disposal the num bers: 3.835, 23.010 and 82.836 m .y., so pregnant w ith concordances with calendric cycles, it would be difficult n o t to fall to tem ptation to see their relations with particular h[.

Table V. The refined vertical dimensions o f the Sun Pyramid related to 828.36, 23.01, 3.835 and 2.60 Description of dimensions Refined heights hi in 828.36 23.01 hi hi megalithic . yards hi hi 3.835 2.60

First body, vertical elevation hx 23.010 36 1 6 8.850

Second body, vertical elevation кг 19.175 43.20 1.20 5 7.375

Third body, vertical elevation hs Fourth body, vertical elevation (lower)

15.340 54 3.50 4 5.900

A(i>

Fourth body, vertical elevation (upper)

2.550 324 9 0.67 0.981 *

A4(2) 5.120 162 4.50 1.33 1.969

Fifth body, vertical elevation hs 11.505 72 . 2 3 4.425

Sixth body, vertical elevation A6 3.835 216 6 1 1.475

* This is only one height which is not divisible by 2.60 without a rest.

The table ¥ represents in full extent this 'question. A t the same time, it shows th a t all the heights hi, generated by 3.835 m .y. are divisible without any rest by 2.60, corresponding to Tonalpohualli sacral calender of 260 days, with the exception o f h'm .

9 6 A M D F .Z E J W I E H C m s K Ï

But, h'i{1) is simply 1/9 c f 23.010 m .y. and:

^(1)+Äl(2) = 7.67 = 2 X 3.835 .

Can we approach a calendric meaning o f the proportions:

* Ц = ^ - < Х « 6 6 . . . ar.d: ! & = £ * - M M . . . ,

A possible reply is the following one:

I ? = 0. 666. . . and: B A 1.336!

A t present, after so promising results with the heights o f particular p lat­ forms, let us see whether it will be possible to derive from them the values o f all the horizontal dimensions (d-j) o f the edges, if we shall accept the con­ ditions that they should be nearest to prim ary di} and simply proportional to 82.836, 23.010, 3.835 and 2.60.

Thus, it should be noticed that:

Σ h[ = 21 X 3.835 = 80.535 = 82.836-2.30 1 ^ diZ 1 Then, consequently: 82.836+ 4 x 2 .3 0 1 = 92.04 ^ da 92.04 + 5 x 2.301 = 103.54 ^ ds2 103.54 + 1 5 X 2.301 = 138.06 ^ dn ' 138.06 + 1 2 X 2.301 = 165.67 ^ dzz 165.67 + 1 8 X 2.301 = 207.09 ^ dzl 207.09 + 1 0 X 2.301 = 230.10 ^ d a

(notice here th at: 230.10 = 100 x2.301 and: 230.10+ 13 x 2.301 = 260 !!!),

230.10 + 2 0 x 2.301 = 276.12 a* 4 · And : 8 2 .8 3 6 -6 x 2.301 = 69.03 *=* d ix 69.03 - 1 0 x 2.301 = 46.02 ^ d6z 4 6 .0 2 -6 .6 6 7 x 2.301 = 30.68 ^ dn 82.836 — 26.0(î) x 2.301 = 23.01 as daz

There remains only diZ = 90.23 m .y. which can not be so simply approxi­ mated.

Assuming that it m ust obey our rule of being totally divisible by 2.60, the nearest solution will be:

T IM E AN D S P A C E IN S U N P Y B A M ID _{9 7}

Ultimately, all the accepted dimensions o f the edges o f particular platform s, together with calculated diagonals and relations to π, 828.36, 23.01, 3.835 and 2.60, represents table VI.

There were also calculated the relations o f the circumferences o f squares

4 4 to 13 day “weeks” o f Tonalpohualli. In connexion with this, it is worthy

o f notice th at the remaining rests o f the latter "ones after dividing 4 ^ /1 3 correspond exactly to integral products o f the divisions; <77/23.01 or, if they are n o t integral, they approach 1/2 or 1/4 o f 23.

O f course, the very slight deviations from the prim ary H arleston’s data (with one only strange exception o f d f ) have caused the fact th at all the previously observed coincidences (Wierciński, 1974—75) between sums o f diago­ nals and the know n calendric cycles persisted w ithout any essential change, i.e. those o f M ars ( = 781 — 1), Venus ( = 585 — 1), Tonalpohualli ( = 260), M ercure ( = 4 — 117(— Î) or 2 X 117(— 1)) and the simple divisions- o f Tonal­ pohualli.

In this way, the total architectonic structure o f the Sun Pyram id fro m Teotihuacan could be expressed-as the simple derivation fro m 260, 360 and 383.5, i.e. the Tonalpohualli, Solar and Lunar cycles.

It is easy to see th at such simple and concordant results will not be obtained w ith any other o f the calendric cycles, listed in the table II.

M oreover, some further calendric coincidences with the dimensions o f the Sun Pyramid (when expressed in megalithic yards) should be stressed |

d'1± = 4d'bl = 276.12 m .y. => 276 days, the time span between Spring and

A utum n Equinox,

4d& = 184.08 m .y. => 183 and h alf days between Summer to W inter Solstice,

4d f = 122.72 m .y. => 383.5 — 260 days,

4dg2 = 92.04 m .y. => 92 days between Spring Equinox, and Summer Solstice,

4d'a + 4 d ^ — 368.16 m . y . + 361.92 m .y. = 730.08 m .y. => 2 x 365 days o f

full complete cycles,

d4'2 = 90.48 m .y. => —-jwmr— a correspondance with M ars and M ercure

JL UUU

cycle.

One m ay w onder th at the different and m ore complicated shape of the 4th platform with 3 edges is the richest, in direct coincidencies with calendric cycles, i.e .: with Tonalpohualli (all edges, diagonals o f 4d'a and, by π with

d'f), M ercure (diagonals o f 4d(3), M ercure and M ars (d(2), L unar (d'f) and

Solar (4^4! and 4d ’f) .

Also, shall we be to o far reaching, if we would emphasize that 13 x 29.5 x 29.5 (Moon)

π ^ --- -— — —— --- = 3.142, what could correspond to a num

en-— - 3 6 0 x 10 (Sun) v

Table VI. Full analysis of the horizontal dimensions of the Sun Pyramid g o S .s ’* x C S

s

S

·

-|8 890 Ό 0.050 0.045 1.729 0.029 со © © 0.020 0.210 ' 0.225 0.015 0.009 0.007 0.005 C S β© ч— Ч O S 1r s C S 40 m c s M -in 40 e n C S Γ-; y-i T -Ι­ 4 -+ 4-4* + 4 _ 4-+ 4 -4" *43 * O O ο t-e n Ч О © У П c s SÎ -© c n

a

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rlfi j яХ i.' , j·

T IM E A N D S P A C E IN SU N P Y R A M ID 99

cai and geometrical expression of the “M ystical M arriage between Sim and M oon”, so im portant in the ancient religions?

However, in Prehispanic Mexico the n value could be approxim ated also very closely by the equation:

260

ж ~ --- = 3.139

~ 7.80 x 2.95 x 3.60

M oreover, the strict correspondance between the num ber o f 13 edges which limit, in fact, 7 bodies (if a temple suggested on the top will be accounted) o f the Sun Pyramid and the division into 13 and 7 Heavenly Zones ought to be noticed. Now, we need only an archaeological discovery o f a richly endowed tom b at a base or near to it...

23my.= 19.4 m.

Fig. 1. The idealized architectonic structure of the Sun Pyramid from Teotihuacan

In order to m ake m ore complete this m oderate analysis, the lengths o f the side-edges together with respective angles have been calculated on the basis o f h[ and d'u, w hat represents table V II and fig. 1.

Table VII. The remaining rest of the measurements of the Sun Pyramid calculated on the basis o f d[j and hi

Description of the measurement

Side edge of the body’s wall

(in m.y.) Height of the body’s wall (in m.y.) Angle of inclination of the wall Angle of inclination of the side edge

First body 39.854 32.541 45° 54°44'

Second body 34.730 28.242 42°46' 54°24'

Third body 28.830 23.092 37°11' 53°14'

Fourth body, lower part 2.779 2.667 72°57' 73°41'

Fourth body, upper part 7.444 6.388 5346' 59°6'

Fifth body 19.928 16.271 45° 54°44'

IGO AIMiDBZHJ W I E H C I H S K I

A t the end, it should be stated that the whole picture o f our time-numerical reconstruction o f the Sun Pyramid will remain almost intact, i f more rounded vaines fo r its dimensions would be accepted.

3, CONCLUSIONS

The present author is fully aware th at the results o f this analysis represent merely a working hypothesis since they are based on H arleston’s data of only approximative value in reference to equally conjectural reconstruction of R. Milion. However, the heights o f elevations o f particular bodies of the Sun Pyramid should be the nearest to real dimensions and precisely out of them started our study.

The discovery of so many and specific for M esoamerica numerical com­ patibilities between time and space in the architectonic structure o f the Sun Pyramid was possible only thanks to the convertion o f its dimensions into megalithic yards. This result is nothing strange, i f the idea o f the Cosmic M ountain will be applied in the interpretation. Perhaps, the other similar pyramid structures in Prehispanic Mexico m ight be explained in the same way. In connexion with this statement, for example, a legendary 9 stepped pyramid of king Nezaualcoyotl from Texcoco or the famous “Castillo” from G lichen Itza with 365 stairs may be quoted. I f the Sim Pyramid from Teotihuacan will be interpreted as the Cosmic M ountain which codes the m ain assumptions o f an astrobiological religion, the following conclusions should be inferred:

3.1 : Top and base of the Pyramid, as well as, its surface and interior

may reflect the idea o f polarisation into pairs o f oppositions (see: 2.2); 3.2: its stepped surface seems to correspond to hierarchic descendance of the W orld's Programme being, at the same time, a kind o f a “frozen” Firm am ent while, its central or lower interior belongs to the Underworld (see: 2.4 and 2.5);

3.3: four sides and four side-edges correspond to the 4-fold division of the field o f the cardinal points (see: 2.3); in this respect, the Sun Pyramid, together with the pyramid from Tenayuca, as well as the complex of Tula and G lichen Itza belong: to the 17° system o f F. Tichy (Tichy 1974);

3.4; the num ber o f platforms or bodies o f the Pyramid, together with a temple on the top, as well as, their horizontal edges, correspond to the division into: 7 and 13 Heavenly Zones (see: 2.5);

3.5: the main dimensions o f the ledges and elevations o f the Pyramid reflect numerically the principle of creative and regulating role o f the cosmo- rhythms exerted on the E arth and H er Biosphere and as such, they are strictly compatible with the calendric cycles, first of all, with solar round o f 360 days,

T I M E A N D S P A C E IN STJN P Y 3 A M I D _{1 0 1}

lunar cycle of 1 3 x 2 9 .5 days and, especially, with the sacral calendar of 260 days, so specific for the ancient Mesoam erica (see: 2.4).

This hypothetical interpretation of the symbolical m eaning o f the Sun Pyram id m ay be, m ore or less, easily verified by the similar analysis of the dimensions o f analogical architectonic creations both, in Prehispanic M eso- america and in the Old W ordl, provided that they can be expressed in the native length-units of measure.

The present author expects th at these other pyramids will also show exact, num erical correspondance o f their dimensions to the used calendric cycles, especially, to the solar of 360 days and, at least, some lunar cycle.

In Egypt, a representation of the Syrius cycle may be suspected. A con­ viction th a t the solar cycle of 360 days could play such a great role in or­ ganizing the m ain dimensions of the ancient grave or temple-pyramids as the representations o f the Cosmic M ountain, is based on the striking finding th at equally in M esoamerica, as well as, in ancient Egypt, Athens or Iran, there existed the idea of 5 “evil” or “unnecessary” days, additional to “regular”

360 round. s

In ancient M esopotam ia the Star Day was divided into 360 parts. In connexion with the idea o f the Cosmic M ountain and this area, so rich in the ziggurats-pyramids of 1, 3, 4, 5 and 7 platform s, the sacred names of these structures are o f a special interest. They run, for example, as follows: “House of the F oundation of the Heaven and E arth ” (Babylon), “Houghty H ouse o f Z ababa and Innina the H ead of Which Is So High As Heaven” (Kish), “House of the Seven Guides of Heaven an d E arth” (Birs N im rad), “H ouse of Chins Between Heaven and E arth” (Larsa), “House of the M oun­ tain ” (Nippur) or, exactly, “House of the M ountain of the Universe” in Assur (see: P arrot 1968). O f course, it would be rather unwise to see in the Sun Pyramid a faithfull copy of the Sumerian or Babylonian ziggurat or th at of the 6-platformed pyramid from Sakkara. We w ant to suggest here only a common formative, megalithic soure of inspiration which m aturated notionally and architectonically in the form o f a variety of the Pyramids- Cosmic M ountains.

A t the very end of this paper, the present author has fallen to tem ptation o f showing that:

a) a lengthy natural m an’s step is around 0.829 m ;

b) the duration o f the norm al gestation’s period corresponds to 9-10 x29.5 lunar m onths (251-299 days) being near 260 or 292 days which is exactly 1/2 cycle of Venus.

Acknowledgements. The author is much indebted to M r Jan Grządzieisld for His valuable suggestion about the dependence between numbers 82.8, 260 and π. Also, best thanks should be expressed to the au tho r’s son Krzysz­ to f Wierciński for His help in calculations.

1 0 2 A N D H Z E J W I E K C I K S K I

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T IM E A N D S P A C E I N S U N P Y B A M ID 103

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