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MATHEMATICS OF ANCIENT ARCHITECTURE (Original Title: Mayan Treasure: Space and Time Unified at Teotihuacan)

RESEARCH SUMMARY NO.6: 1971--2008

by Hugh Harleston, Jr.

[Reedited: 21 June 2008]

SECTION I: 2002 SECTION II: 2003 SECTION III: 2004 SECTION IV: 2004 SECTION V: 2005

[ [SECTION VI: 2008] ]

[See www.hharlestonjr.com]

(File Ref. AA-07T2 – 01-IX-08)

http://www.hharlestonjr.com/

© - Hugh Harleston, Jr. - 2008

ALL RIGHTS RESERVED. Without written permission from the author, no part of this Research Summary may be reproduced or copied in any form or by any means--graphic, electronic, or mechanical, including photo-copying, taping or information storing and retrieval systems, except for brief quotations, unless quoted by students of Mayan research, who on request will be given permission by the author.

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Teotihuacan figurine. Two double circles (1,512) multiplied by 9, the necklace beads, equals 13,608: the number of Jupiter/Saturn conjunctions in a Numerical Ark of height 57 STU (Fig.3, Sect.I.) 13,608x100 are 1,360,800 days: Mayan Long Count 9.9.0.0.0 marking 400 Saturns and 378 Jupiter synodic orbits, plus 378 additional days, (Sect.I, Fig.5.) Teotihuacan’s base is 378 units= Saturn’s synodic orbit. Its architecture = submultiples of factorial 9! and duplicates musical tone numbers. Hugh Harleston, Jr., P.O.Box 43-1192, SAN DIEGO, CA. 92143-1192

[e-mail: harleston13(at)yahoo.com]

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MATHEMATICS OF ANCIENT ARCHITECTURE

Section VI – Topics Guide

(1) Architectural dimensions of the site named “Teotihuacan” present a map of Mayan planetary orbital counts displayed in Standard Teoti-huacan Units of measure of one meter, 5.94(6) centimeters (“STU.”)

(2) The basic count, given by the largest quadrangle, is the synodic or-bit in earth revolutions (days and nights) of Saturn observed from earth, measuring 378 STU /side, a measure that repeats at the site.

(3) Teotihuacan’s dimensions and their mathematical relationships du- plicate four known ancient systems of musical tones charted by past civilizations: medieval, Pythagorean Greek, Chinese and Persian.

(4) Kepler’s 17th century diagram of forty Jupiter/Saturn conjunctions, rotating triangles taking 2,359 years to circle the zodiac, was known by Mayans and tabulated in the Dresden Codex.

(5) Teotihuacan’s dimensions in STU give areas or volumes that, when multiplied by the 260-day Tzolkin, have factors correlating orbital information of the sun, the moon, and seven planets. The mathematic relationships must be in STU, not in metric or English units..

(6) H.M.Calderon deciphered the Dresden Codex tabulation to give researchers exact values in Tzolkins, earth revolutions and stellar year counts of 364 days for Jupiter’s synodic within 0.0031% of the modern (1991) computer-derived orbit.

(7) Application of Dresden procedures to Teotihuacan show that the use of the Tzolkin as a secret multiplier guided dimensions and design of the architecture consistently in a “Ceremonial” Zone, which in reality were Mayan monuments to mathematical and astronomical registra- tion for extended periods of long-term calendars. Calderon estimated the information dates to approximately 4,500 BCE. His procedures are included in an English translation, Appendix 1, below.

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SECTION VI – ARCHAEOLOGICAL ARCHITECTURE

TEOTIHUACAN IN STD. UNITS OF 1.0594(6) METERS

Data sources:

(1) Teotihuacan Map/Univ.of Rochester/U.of Texas Press; (2) Interamer-ican Geodesic Services (IAGS), Mexico City; (3) Secretaria de la De-fensa, Mexico; (4) Defense Mapping Agency, Washington,D.C. via IAGS-Mexico; (5) Aerial Mapping, Comision de Estudios de los Te- rritorios Nacionales (CETENAL,) Mexico, D.F., 1974 -1998.

[Map repeated for convenience of students’ ]

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[Detailed drawing repeated for students’ convenience]

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INDEX

Topics Guide iii Map of Teotihuacan in Standard Teotihuacan Units (1998) iv Detailed Dimensional Map (1974, corr.1984) v Index vi Introduction vii Part 1: Geometrical Dividing Canon 1 Part 2: (a) Fig.3 -- Timaeus Locris Scale 7 (b) Fig.4 -- Chinese Lu Chromatic Scale 8 (c) Fig.5 -- Persian Enharmonic Scale 9 (d) Notes 10 (e) Fig.6 – Standard Particle Model and Notes 11 Part 3: (a) Fig. 7 – Trigon of Kepler and notes 14 (b) Fig. 8 – Dresden Codex, pp.71-73, notes-1989; 2008 16 (c) Fig. 9 – Jupiter Table, Dresden, pp.45 (78) 21 (d) Dresden Jupiter Table & The Tzolkin at Teotihuacan 22 Part 4: Mathematical Reflections 28 Part 5: Conclusions 31 Part 6: Conjectures and Suggestions for Future Research 32 Appendix 1: by H.M.Calderon, 1990: The Dresden Jupiter Table 33 Additional Bibliography 40

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SECTION VI – ARCHAEOLOGICAL ARCHITECTURE INTRODUCTION

My decision to end this project in 2007 was made after, once again, unexpected correlations were sent me. Were these “happenstances,” or events directed by a uni- verse that remains a speculative enigmatic mystery? The facts are: basic concepts that we use start with three immeasurable non-verbal streams of unspeakable paths, that we pretend we understand: life, existence, eternity. Humans are not equipped with systems that can explain these rivulets in an ocean of external materiality. Yet still there can be combined feeling, sensation and neuronal states that leave a taste for things that are true, as proposed by Henri Tracol. This Section invites a review of relationships. A cube of six – inches, centimeters, kilometers, miles – has an area and volume of 216 square or cubic units. In 1971 a small-scale Teotihuacan map led me to this study. I saw three proportional relation-ships: if the largest pyramid were four units, then the next largest would be three. A great square becomes seven, sum of the first two. In Standard Teotihuacan Units the measures are 216, 162 and 378, products of what I call the creation measure six: 6 x 36; 6 x 27; 6 x 63 (see map, p.iv.) Ceremonial Zone Elevations above sea level form a stairway: seven descending steps from the base of the “Moon” pyramid down to the “Citadel.” A map made by the Mexican Secretariat of Defense used higher magnification. Its elevation accuracy suggests that a seven-tone scale may have been used by architects. It also allows us to see that STU dimensions are Mayan calendar counts, astronomical cycles used to lay out monuments mathematically. Musicologist Mitzi de Whitt published five drawings listing 485 tones, whole numbers or factors, that match dimensions in STU’s at Teotihuacan. There may have been no interactions between four civilizations: Mayan, Greek, Chinese, Persian, which suggests that advanced ancient knowledge could have been registered worldwide and kept secret by ancient geniuses, hence therefore cannot be denied. Research of correlations in 2008 brought compelling evidence that the relationships calculated by Kepler in his 17th century Trigon of Jupiter/Saturn conjunctions is matched by a series of thirteen counts of Jupiter/Saturn tables in the Dresden Codex, astronomy known by Mayans long before today´s Common Era. I am convinced that the use of a special measure was applied by Mayans at Teotihuacan and that this explains dimensional knowledge evident in the site. If the time has arrived for these findings to reach a prepared audience the mathema-tical facts can allow corrections to be made of three basic units used for modern scientific measurements, while also serving as recognition of the reality of Mayan multidi-mensional vision. -vii- DISK: AA-07T2.DOC // HH // (23-VIII-07 reedited 01-IX-08)

SECTION VI – ARCHAEOLOGICAL ARCHITECTURE -- Part 1 Geometric Dividing Canon

This project began with musicology, for the purpose of defining dimensional proportions of Teotihuacan’s structures. The builders’ unit of measure in meters has mathematical significance. Architectural correlations correspond to Mayan time counts that were observed as sky returns of planets, seen as moving stars, when expressed in earth revolutions, or “days,” a term now used for a day and a night. The Parthenon, Section III, pp. 20–23, presents comparisons with a design measured in Pythagorean Diatonic Units (PDU) in 438 BCE. Greek builders used the same six basic numbers as those applied in STU of 1.0594(6) m. at Teotihuacan. One STU equals 318.36 PDU. Based on writers’ reports of related musical tones, used during medieval times, musicologist Mitzi de Whitt assembled the whole-number ta-bulation, Fig.1, titled “Geometric Dividing Canon.” The format is a Py- thagorean right triangle. Similar tabulations were believed to have been used by architects and constructors to make more accurate drawings. From left to right the numbers are a series of tonal octaves, multiples of “2”: 2, 4, 8, … 256, in which the pitch is doubled; for example, the frequency of vibration of a flute. It is well known that Mayans manufactured ceramic flutes using earth, water, air and fire. It is not so well known that based on research by Genoveva A. Escobar in Tepoztlan, Mexico, calibration of a Mayan basic tonality could have been confirmed by the response of special turtles from northwest Mexico. Land turtles found near Ceballos, Durango* have shells with equilateral triangles instead of the more common pentagons and hexagons. When a resonant tone sounds the turtle raises its head and tries to seek the source. During deep meditation the predominant brain wave in humans is resonant with F-sharp. An organ tube or a flute whose length is one STU will sound F-sharp. Teotihuacan’s architecture is resonant with the human brain’s alpha-wave. *“Zone of Silence.” Radio reception and transmissions fade or disappear, possibly due to a shift in the earth’s magnetic and/or gravitational field. DISK: AA-07T2A.DOC // HH // 08-IX-07 // edited 25-I-08 // p.1.

Section VI Archaeological Architecture (cont’d) The earth vibrates at an infrasonic tone resonant with B-natural, the note “Si.” The fifth tone above B-natural is F- sharp. Teotihuacan, by intention and/or intuition, commemorates the musicologist’s dream, a Pythagorean’s conviction that there is music of the spheres, mathematical connections to stars that obey laws of cosmic numbers. Fig.1 illustrates architectural dimensional lengths in STU with selected examples. Other numbers in four tabulations will be added later. Smal- ler dimensions in STU include: Dimension Location_ ½ = 52.9 cm.* = 20.85 inches Sea-shell mural, Moon Plaza* 1 = 105.946 cm. = 41.71 inches Multiple examples 2 = 211.893 cm. = 83.42 inches Height -- Platforms “Citadel” 3 = 317.839 cm. = 125.13 inches Height -- Platforms, Statues (*Two of these sculpted figures add to the STU of 105.9 cm. – see pp. 6)

Note: 1x2x3 = 1 + 2 + 3 = 6, the creation measure, a repeating factor at Teotihuacan in whole numbers. Below are listed several series with factors of “6” that appear in Teotihuacan’s architecture as dimensions, and as tones in the “Geometrical Canon.” Duplication repeats on three other tone diagrams, at archaeological sites whose locations and estimated epo-chs cover approximately 6,000 years before the present. On page 5 additional larger numbers and their factors are outlined. Fig. 1 lists 45 numbers. 28 tones are factors of “6.” 17 more are at Teo- tihuacan when whole-number factors are used. Eight are given by dimensions: 1, 2, 4, 8, 16, 32, 128 and 256, all multiples of “2”. A nineth tone -- “64”-- should be found, but I have not located it. Bolón--dimension “9,” Mayan number for Hunab Ku, repeats, horizontally and vertically. Seven more tones, factored, are dimensions in STU: 27 = 9x3 = 54 / 2 = 14+13. Steps, on the west side of the “Sun” pyramid plaza rise 14 ascending to the east, then 13 descending to the level inside a plaza that carries a platform 20 by 20 STU, one of the only two in Teoti- huacan to have these numbers. Its area is 400, perhaps orbits of Saturn. DISK: AA-07T2A.DOC // HH // 10-IX-07 // edited 25-I-08 // p.2.

Section VI Archaeological Architecture (cont’d.) The “Sun Plaza” elevation is 2,166 STU, lying 15 STU below the base of the “Moon” pyramid marking 2,181 STU. “400” also corresponds to a Mayan time count of 1.1.0.0.0 -- one Baktun (Niktekatun) plus one Katun: 144,000 + 7,200 days (and nights) -- total 151,200 revolutions of the earth. “1,512” = 4 x 378, perimeter of the “Citadel,” marked on a mural named “Plumed Shells” (Sect.V, pp.5,)* that correlates the Mayan time count of 400 synodic orbits of Saturn. 81 = 9 x 9, shown in the “Citadel” by platform spacing, and elsewhere. 243 = 3 x 81 = 3 to the 5th power = 3x3x3x3x3. Dimensioned in STU. 729 = 9 cubed = 9 x 81 = 3 to the 6th power. 2,187 = 3 times 729 = 9 x 243 = 27 x 81. 4,374 = 3 x 1,458 = 162 x 27 = (3x6x9) x (3x9) = 6 x 729. 6,561 = 81 squared = 9 x 729 = 27 x 243 =3 x 2,187 = 3 to the 8th power. The complete Fig.1 tone numbers, or their factors, appear in STU at Teo- tihuacan. It is significant that these are not approximate or rounded fractions, or poorly restored archaeological guesses. The dimensions are found in sculpted stone. We can see that Mayans used geometrical fig-ures to represent numbers that do not require speculative guesses for dimensional measures. A universal circle has a diameter of 120 units, no matter what the measuring system may be. This can explain how an alien system in Greece, utilizing Diatonic Units derived from a monochord, in which the tone frequency is precise, leads to stone columns that exhibit measures such as 144, 288 or 576 at the Parthenon as well as in the “Citadel,” a name that undoubtedly was not used by Mayans. A logical name could be Ain-Ek, the planet Saturn.

*(repeated below on pp.6 for the convenience of students.) DISK: AA07T2A.DOC // HH // 10-IX-07 edited 25-I-08 // p.3.

Section VI –Part 1, Fig.1, pp.4 Archaeological Architecture (cont’d)

© - Mitzi de Whitt -2006 By permission, from Gurdjieff, String Theory, Music, pp.54, shown as Fig.6

[Note: the number “6564” is a typographic error, and should be 6,561.]

The series of numbers outlined on pp.1 to 3, and below on p.5 permit veri- fication that the Dividing Canon evidences either direct Mayan dimensions at Teotihuacan or measurements of the factors that will confirm products that are the whole numbers tabulated. Of the above 45 numbers Mayan dimensions give, as linear or area or volume, 41 whole numbers.

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Section VI Archaeological Architecture (cont’d) (1.) Multiplication of the creation number “6” produces a first series: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108. Most appear as dimensions in STU. The series continues with: 114, 120, 126, 132,…144,…156,…162, 180,…192,…204,…216,… 222, 228, 234, 246, 252,…270,…288,…312,…324,...360,…378,… The numbers shown or their factors are STU dimensions. The last is the synodic orbit of Saturn. Significant ciphers are 144, 288, 312 (the Mayan “Short Count.”) “234” measures the Jupiter orbits in 13 Katuns –93,600 days,-- tabulated on page 35, Section I, Fig.12 (2002.) 234 STU is a major parameter of the Citadel’s patio. (2.) A second series: the number “40” appears below “Plumed Shells” (p.6), a sequence of black dots: 8, then 12, again 12, then 8; sum 40. Multiplication by “6” creates values found worldwide: 6x40 = 240; 240x6 = 1,440; then 8,640; 51,840; 311,040. The Hindu “Life of Bra- hma” is 311,040, the product of 864 x 360 “days and nights.” “864” is derived from 2 x 432. The value 51,840 = 3 x 17,280, ten cubes of sides 12, equal to two-thirds of 25,920, Plato’s “Great Year.” The area of the Great Pyramid of Egypt in square STU is 1944 x 10 times 4 sides = 77,760; the area of each face of the Great Pyramid of China (Urumchi) in square STU: 144x2160 = 77,760; x 4 = 311,040. (3.) A third series: At one time it was believed that Mayans only knew how to multiply by “20’s.” Multiplication by 6 shows us a series that starts with 120; then 720; 4,320; 25,920; 155,520, half of 311,040. (4.) Other values: the interlocked mathematical design of Teotihuacan shows that: 6 x 7776 = 46,656 = 216 squared. If there is a subterranean base underground, the Great Pyramid could stand on a square base 216 STU on a side like Egypt’s version. Other STU dimensions are: 7,776 = 6 x 1,296 = 648 x 2 x 6 = 108 x 12 x 6 = 144 x9 x 6 = 27 x 288 = 486 x 16. Encoded (west columns, Quetzapapalotl Patio) 7,776 x ten = 77,760 = area per face at Urumchi; times 4 = 311,040. DISK: AA07T2A.DOC // HH // 26-XII-07 // p.5.

Section VI, Part 1, Fig.2, p.6 Archaeological Architecture

p.6 Fig. 2

Mural of the “Plumed Shells” Palace of “Quetzalpapalotl” - Teotihuacan Four sets of bars and dots of 378 are 1,512


© - Mitzi de Whitt -2006 By permission, from Gurdjieff, String Theory, Music, pp.56, her Fig.7.

Tabulation of 36 whole number tones, all of which appear as either

STU dimensions or exhibited as factors of the number itself; for example, 10,368 = 192 x 54 = 96 x 108 = 48 x 216. All these factors appear as STU dimensions at Teotihuacan.

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© - Mitzi de Whitt -2006 By permission, from Gurdjieff, String Theory, Music, pp.56, her Fig.10.

Tabulation of 111 musical tones from the Chinese Lu scale thought to be approximately 2,700 BCE. It was reported that the duty of the Emperor’s Prime Minister was to verify proper tuning of stone organ pipes, to be resonant with the sound of the vibrating earth. Today’s physicists believe that the infrasonic tone corresponds to about 7.83 cycles per modern second, and that this is the resonance of the Grand Gallery / King´s Chamber of the Great Pyramid of Egypt. With that supposition, the human alpha-rhythm corresponds to 11.34 cycles per second and is F# sounded by an open pipe whose length is one STU.

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Section VI, Part 2, Fig.5, p.9 Archaeological Architecture (cont’d)

© -- Mitzi de Whitt – 2006

(by permission, from Gurdjieff, String Theory, Music, p.62, her Fig.11)

COMMENTARY

The Enharmonic Persian Scale, a tabulation of 245 whole-number tones, all of which, or their factors, appear as dimensions in STU. They are also seen at the Parthenon, Athens, Greece in Pythagorean Diatonic Units. De Whitt reports (personal communication) that there are experts who believe the “Persian” scale can be traced back to Sumeria cerca 4,000 years BCE. The octave is divided into 17 tones, used by Arabian musicians. In Hindu Sankhya “17” represents a body having finer frequencies internally, an immortality symbol, “outside of time.” The same concept was adopted by Christianity. Even more important, de Whitt tells us, in a Kurd sect (Ahl-i Haqq) and in other dervish and Turkish groups not only Sufis but Greeks, including Aristotle, gave importance to a 17-tone sound-octave. To my knowledge there have been no reports of the use in America of the Enharmonic Tone Scale, nor of the use outside Mexico of astronomical planetary registrations of Jupiter/Saturn conjunctions, combined with orbital correlations using 360 “days,” 7200 “days, ” 144,000 “days” nor 1,872,000 “days” to predict cycles of future celestial events. (One “day” is actually one earth revolution [see Notes continued on pp.10, below.]

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Section VI – Part 2, pp.10 Archaeological Architecture (cont’d)

COMMENTARY (CONT’D)

(1) Enharmonic Scale (Fig.5, p.9): the 9th column, 3rd row down, should be 576.

(2) Timaeus-Locris Scale (Fig.3, p.7.) Tabulates 36 numbers, ending at 10,368. The Teotihuacan pyramidal zone marks 36 levels its elevations consolidated

with precolumbian concrete termed “argamasa.” The basic elevation is a lava tunnel under the Great Pyramid, said to be a “ Sun “ pyramid, a term used by Aztecs in the 16th century, who had arrived in the 11th century. The elevation marked by the tunnel registers 2,160 STU above mean sea level, confirmed by the Uac-Kan Research Group with geodesical instruments, and by Mexican Defense Secretariat maps.

There are artifacts resembling wheels with 36 spokes. The final number has many factors. For example 10,368 = 192x54 = 96x108 = 48x216 = 24x432 = 12x864 = 36 x 288. All these factors appear as dimensions in STU. Also factorial 9! = 36 288 0 (in Mayan format,) obtained by repeated additions.

(3) The Chinese Lu step-pyramid (Fig.4, p.8) The inverted pyramid can be put inside a box, of base 18 by 18, height 18 x 12. This box has side areas 12 x 18 = 216. Four sides are 4 x 216 = 864. Two tops are 18 x 18 = 324, for a total area of 648. The Chinese Lu pyramid can be contained in a box whose area is 864 + 648 = 1,512. This number is carved in Mayan dot and bar code on the wall of the “Plumed Shells” mural (see Fig.2, p.6.)

(4) Anthropologist Bethe Hagens (personal communication) has called attention to a geometric construct, a rhombic triacontrahedron, formed by thirty rhom-

bic diamonds with sides having lengths that are functions of Phi, the “Gol- den Mean.” The Mayan world model area is 45,360 square STU. The area of each diamond = 45,360 divided by 30 = 1,512, carved in dot and bar codes on the “Plumed Shells” mural. This is also the perimeter of the Great Qua- drangle of Saturn: 4 times 378 = 1,512. Symbols: 3 dots and 3 bars count 18. The same figure at the next level signifies “ 360.” The total of the two is 378, Saturn’s synodic orbit in earth revolutions. There are four horizontal groups,

that form the mural, one level beneath the Patio of the Falcons, misnamed as a “Quetalpapalotl” i.e., Quetzal-Butterfly in modern Nahuatl. Study by profes- sional ornithologists identified the carved birds as falcons, with double circles on each side of their beaks. Each circle has a value of “378.” The symbol is unmistakeable: it is the number “1,512,” the earpieces of a Mayan Halach.

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Section VI, Part 2, Fig. 6, pp. 11 Archaeological Architecture (cont’d)

©-Mitzi de Whitt – 2006.

From Gurdjieff, String Theory, Music, pp.37, her Fig.1. This tabulation of 60 numbers and concepts leads me to conjecture that a civilization of Mayan characteristics could propel them to select numbers that correspond to multidimensional relationships. Trained in non-verbal meditative disciplines, Halach could have intuited the numbers and concepts as spiritual initiates, even though they lived an epoch whose infrastructure is deemed impossible for us to contact in view of today’s intellectual confrontations. The objective capacity of human thinkers has yet to be scientifically evaluated, and perhaps may never be possible to fathom.

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SECTION VI – ARCHAEOLOGICAL ARCHITECTURE -- Part 2-(e) Standard Particle Model, Fig.6, p.12

In depth study of Teotihuacan requires archaeology, ethnology, anthropology, mu-sicology, engineering, physics and other disciplines. De Whitt’s research created new, well-documented analogies. All categories, each with its conjectures, make a fun-damental assumption that, optimistically, half the theories may lead to material finds: artifacts, related dimensional proportions, physical evidence. None of these is capa-ble of predictions without errors, nor provable about events thousands to millions of years ago. They will forever remain educated guesses, some probable, for the time being. New discoveries led to posthumous cancellation of a Nobel prize when space science showed that erroneous assumptions had been applied at the time of allocating credit to researchers. De Whitt’s musicological interpretations of a 21st century Standard Particle Model will here, with her permission, be seen as applicable to Mayan dimensional correlations. Comparison gives rise to a need to modify a tendency to deny that past civilizations could reach apparently unlikely capabilities. Let’s not forget a precaution: avoid assuming that ancient sources were ignorant. Specialized knowledge kept se-cret cannot be denied. Secrecy today, especially military, can withhold vital data and label it nonexistent or confidential. How could Mayans have known advanced mathematics? Intelligent people are found worldwide. It should not be surprising that in the epochs believed to be Mayan several Halach could, among themselves, develop talents for mathematics and precision measuring capabilities. If no measuring “tools” have been found, this might mean that they utilized methods unknown today; for example identification by sensitive turtles of the frequency corresponding to F-sharp, described in Part 1, above. Some researchers joined the ranks of specialists promoting belief in diffusion, the transport of savants to distant areas to try to convince others that sources “must be” as speculated. A recent shift to DNA “proofs” postulates origin in Africa for biblical ideas of generation of all humanity from an original pair of beings. As this theory is being proposed the definition of humans has moved farther back, and at present is believed to be millions of years. A new discovery may find humans in the tertiary with dinosaurs, 65 million years ago. Would it be unthinkable to have humans in the Triassic, 144 million years before our present era? Continental drift was said to be impossible until Weggener’s finds were ridiculed in 1916, only later proved out by scientific publishing in 1939. After becoming familiar with De Whitt’s tone tabulations, it behooves us to become philosophers, as she suggests. Each family of particles presents sixteen numbers (see Fig.6, below) whose direct or factored values are examples in STU at Teotihuacan. DISK: AA-07T2A-2.DOC // HH // 12-XI-07 // p.12 // reedited 01-IX-08

Section VI, Part2, Fig.6, p.13 Archaeological Architecture (cont’d)

COMMENTARY (that refers to associated conjectures)

I. Family 1 Correlations of Teotihuacan Parameters .00054 54, 108, 162, 216, 270, 378, 432, 486, 648… .0047, .0074 141, 282…(earth’s orbital radius, diameter) 2/3, 1/3 Systems of 3… 1/2 Octave multiplier… 0 “Complete…” nothing missing Red Sunrise, dawn, light in darkness II. Family 2 .11 Saturn multiplier… 1.6, .16 Vertical, 16 only used twice 2/3, 1/3 Systems of 3… 1/2 Octave multiplier…

0 Completion concept… Green Life; not inert… III. Family 3

1.9 Jupiter synodic: 19 x 3 x 7 189 Half-cycle of Saturn… 5.2 (4x13) – planetary alignments… 2/3, 1/3 Systems of 3… 1/2 Octave multiplier… 0 Completion concept… Blue Above; clear sky We ask: Why were “colors” used for “charges?”

Can “neutrinos” really be defined? Why “up, down, charm, strange, top, bottom”? Do we really “know” why “life” is “green”? What happened to the “full-spin neutrino” visualized by Olivier Costa de Beauregard in the 1970’s to explain the transmutation of potassium 39 to calcium 40 in chickens, reported by Louis C. Kevran (France.) Here are 13 characteristics that appear in some form in Mayan Teotihua- can. Were their geniuses any less misunderstood than today’s intellectuals?

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SECTION VI, Part 3a, p.14 Archaeological Architecture JUPITER / SATURN CONJUNCTIONS (a) The Kepler Trigon In the 17th century Johannes Kepler (1571 – 1630 CE) formulated three mathematical laws for planetary orbits, defining them as being elliptical and accepting the heliocen- tric solar system of Copernicus. Kepler produced a diagram of 40 conjunctions of Jupiter and Saturn, each 19-2/3 solar years, when the two planets nearly touch in the sky. The fourth event is seen, however, in 59 years because the second two conjunctions are on the opposite side of the earth and not visible (see Fig.7, p.15.) Kepler demonstrated this with a series of rotating triangles –the Trigon– in numbered sequences: 1, the initial reference point; then 4,7, 10…40, a count of thirteen events; followed by 3,6,9,12…39, the second count of 13; and finally 2,5,8,11…38, the third. To move through one-third of the zodiacal great circle, spaced one triple Great Con- junction to the next, requires 786-1/2 years. To travel around the complete zodiac the time is (120) x (19.663) = 2,359.56 solar years, equal to 2,160 Jupiter orbits of 399. Comparing these measurements with Mayan astronomers’ registers, we find that they used a cycle interval between two conjunctions of one Katun less eighteen days: 7,200 days minus 18 = 7,182. In solar years of 365.2422 the Mayans marked 19.6637…a value 99.9969% of the averaged count. They knew that a whole-number assigned to the orbits of Jupiter (399 days) and Saturn (378 days) were off by minus 1/8th day for Jupiter and plus 1/11th day for Saturn, so corrections were made after eight counts were observed for Jupiter and eleven for Saturn.* This permitted them to tabulate planetary count bands in the Dresden Codex to make corrections. Their use of conjunction counts of 7,182 days was within 0.0031% of the averaged value of 7,181.78 days (99.997% over long periods.) The Trigon in Fig.7 shows in red the Mayan positions: the zero reference point is opposite the first triangular corner of the Conjunction Circle. The words for “zero re-ference point” in Mayan are “Mix Baal Holeistak,” an impressive term. Three sets of 13 corners total 39. The number of steps in the Citadel that form an ad-dition to the west of the pyramid are 39. The number “59” is a factor of the spacing of the platform marking the modern “San Juan River,” shown on my 1976 map, and repeated (page v, of this Section) as 9 x 59 = 531 STU. On the same map the distance from the Great Pyramid centerline E/W marks 8 x 59 = 472 STU. The Triple Great Conjunctions mark a count of 59 years. A conjunction is 18 Jupiter orbits of 399 = 7,182; and 19 orbits of Saturn times 378 = 7,182, the 19-year, 8-month count. *The first body of the first pyramid (“Moon”) is 11 STU high; its first add-on is three bodies, each 8 STU in height. In the “Citadel:” 8 platforms=N/S; the 6-step pyramid presents each “plumed serpent” with an 11-petalled design. DISK: AA-07TJS.DOC // HH // reedited 01-IX-08

Fig.7. THE KEPLER TRIGON Section VI, Part 3-(a), p.15 Archaeological Architecture

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Section VI, Part 3a, p.16 Archaeological Architecture (cont’d) Why does the largest square at Teotihuacan mark in STU the synodic orbit of Saturn in “days,” i.e., in earth revolutions? Why are the first and second pyramids (named “Moon” and “Sun”) spaced on centerpoints separated by two Saturn orbits in an area renamed by moderns “Ceremonial Zone,” an area covering two by six Saturn orbits? Recognized mythologists –Frazer, Santillana, Campbell – listed worldwide knowledge of the yellow-orange planet, indicating that ancients knew the clock-wise motion of earth’s axis of rotation requiring nearly 26,000 years to make one wobbly ellipse. We see our travel around the sun as “precession of the equinoxes” and our traditions use a circle of twelve major constellations separated by periods of 2,160 years to describe a “Platonic Great Year,” brought from Egypt by Plato’s uncle Solon. Mayans saw 13 constellations. Each sector was 101 Katunes of 7,200 days, so that 13 periods of 727,200 days totaled 9,453,600 days. Divided by 365.2422 is a period of 25,883 years, or 1,991 years per constellation. The number of Jupiter/Saturn cycles is 10.97. We are convinced that Mayan astronomer-mathematicians would have incor-porated the number “11” as not only sacred for Saturn’s orbital correction, but also for long-range Jupiter/Saturn meetings. They commemorated this carved in stone as eleven “petals” around each of the 348 “plumed serpents,” one of the alternative spec-ulations made for the pyramid in the Citadel, that could make the top building have a count of 12 “serpents” to total the Tun of 360 days. Some of the ancient names for Saturn are: in China, the yellow Emperor Huang-Ti; also the “pivot point,” god of the center. In Persia, the Shahs’ Royal Jubilee Festival is every thirty years of 360, or 10,800, the ancient sidereal orbit of Saturn, Zuwan akarana, meaning unlimited time. Egyptians’ old Pharoah was Ptah: Saturn. In Iran: Zurvan akarana. Finland called Saturn Waralden Olmay; Sumer’s name was me; for Babylon Saturn was the Star of Law and Justice. In Sanskrit the planet was Kala, also meaning time and blue-black death. Following we present Part 3b, Fig.7A, pp. 71-73 (51-53,) tabulated by E.Thompson as nothing more than an agricultural augury, that he called a mediocre attempt to pre-dict rainy weather to be expected over future dates, “not a multiplication table, with glyphs such as one-half of (the Venus glyph,) with ‘evil connotations’ that mean a scarcity of meat.”…”this almanac is clearly tied to weather, …solid evidence that the serpent numbers are not linked to any planet whatsoever.” The basic reason that recognition of the series of “54’s” became possible is that thous-ands of conversions of STU dimensions had prepared me with observations of repeat-ing whole-number sequences. Clue numbers are 108, 162, 216; 144, 288, 576; and multiples of 378 (756, 1,512, 2,268). These, added to Jupiter/Saturn combinations of 21,600 minus 54 define the triple conjunction time of 21,546 days. Let’s recall that the base of the Citadel’s pyramid is 60 by 60 STU. Its cube measures 216,000: half of a Venus cycle, whose positions form an invisible pentalfa in the sky. DISK: AA-07TJS.DOC // HH //reedited 01-IX-08.

Section VI, Part 3-b, p.17 Archaeological Architecture JUPITER/SATURN CONJUNCTIONS

(b) The Dresden Codex. A documented history of this Mayan book, held in Dresden, Germany, is highly spe-culative. There are reasons to believe, as some do, that the original copy was semi- destroyed, and may have been sent to Charles V of Spain by Cortes himself, possibly in 1,519 or 1,520 CE. It has been variously interpreted. In his commentaries (cf. Bibliography, Section I, p. 25) Eric Thompson declared that the book registers only religious ceremonies and agricultural auguries. A reason for this opinion could be if we are convinced that Mayans firmly believed history repeats in cycles of time defined by their calendar system. Fortunately, there are other theories available to demonstrate that Mayans have been maligned and misunderstood. An analysis of their count systems reveals a verifiable range of astronomical observations and mathematics, outlined below. The original was bought by C. Götze in January of 1,740, acquired from a private col-lector in Vienna. The first publication was made in 1,811. Then it was copied and reproduced by Lord Kingsborough in 1,831-1848, appearing in Vol. III of his nine-book Antiquities of Mexico. However, pagination was mixed up, numbers were changed. Scholastic research showed that a Baron Rocknitz used the Codex at Leipzig in 1,796.

Other editions appeared in 1,880 and 1,892. Subsequently Villacorta in Guatemala produced a color version in 1,930, later updated by Gates in 1,932, who renewed the drawings with his own images, ostensibly to achieve clarity. He eliminated variations that could permit the identification of the various scribes who had copied data from more ancient originals. Gates also “restored” glyphs without showing what he had actually done, plus he made over two dozen errors in the overall reproduction. A sixth edition was made in East Berlin in 1,962. But there had not been recognition of the astronomical data registered for Jupiter and for the Jupiter/Saturn conjunctions. Page 18 is Tabulation 8A, from E. Thompson (Op.Cit., p.208-209) listing information given in the Dresden Codex on pp.71-73, whose color original is reproduced in Fig.8, p.19, including the notes I made Nov.18, 1989. My first deductions theorized that the two circular glyphs with a twin-ribbon tail, said to be a “Ring Number,” is in reality numbering thirteen triple Jupiter/Saturn conjunctions. The interval between two events is one Katun of 7,200 days minus 18 = 7,182 days. Three events are 21,600 less 3 x 18 = 54. The series are corrections for triple events: 21,546 days, or 58.991 solar years. This explains why there are several dimensional examples of the number “59” as a significant factor (see p.14, above, and detailed map, 1976 & 1984, pp.v,) Mayan documentationn presents precision time periods, later rediscovered in the 17th

…cont’d pp.20 DISK: AA-07TJS4.DOC // HH // 21-III-08 // p.17

Section VI, Part 3b, p.18, Tabulation 8A Archaeological Architecture DRESDEN CODEX – pp.71-73 (51-53)

Codex Page / T’Ol Tzolkin Interval

Factors // Count

Dimensions given:

71a T1 71a T2 72a T3 72a T4 72a T5 72a T6 72a T7 72a T8 72a T9 73a T10 73a T11 73a T12 73b T13 Note:

11 Lamat 13 Ik 2 Cib 4 Oc 6 Kan 8 Edznab 10 Eb 12 Cimi 1 Ahau 3 Ix 5 Lamat 7 Ik 9 Cib dimensions

54 108 162 216 270 324 378 432 486 540 594 648 702 in STU

6 x 9 // 2.14 9 x 12 // 5.8 9 x 18 // 8.2 6 x 36 // 10.16 9 x 30 // 13.10 3 x 108 // 16.4 6 x 63 // 1.0.18 2 x 216 // 1.3.12 6 x 81 // 1.6.6 9 x 60 // 1.9.0 6x 99 //1.11.14 9x 72 // 1.14.8 6x117 //1.17.2 underlined

Pyramid -- Citadel Sun Pyr. & Citadel Moon Pyr.& Citadel SunPyramid/Various Citadel, Adosado Citadel, Grand Ave. Sun Pyr., Citadel Grand Avenue Shells; Citadel Pyramid - Citadel Lunar-2,920 Days Citadel; Ave; 3x216 Mercury; Citadel

Source: Thompson, J.Eric, “A Commentary on the Dresden Codex” (310 pp., Transl. Fondo de Cultura Económica, Mexico, D.F., 1988, pp. 208-209.) Original: A Maya Hieroglyphic Book, 1972, American Philosophical Society, Philadelphia, PA, USA. NOTES: ref.89-19HH, Mexico, D.F., as evidence to confirm the design of the pyram-idal complex of Teotihuacan was Mayan (see p.15B, below for original Codex.) OTHER REF: Apr., 1972, dimensional data in Standard Teotihuacan Units measure 108 / 216; 81 / 162; 54 / 108; 36 / 72; 18 / 36; 9 / 18: Congress of Americanists, 1974. Aug., 1972: “Citadel”defined 400.5 mtrs.= 378 STU; in days = synodic orbit of Saturn. 1991 data from Mexico Instituto de Astronomia, Fis. D. Flores Master’s dissertation corrects orbit to 378.095. Mayan correction (one day after 11 orbits) is 378.092 earth revolutions. COPIES: of the above tabulation were sent in 1989 to: H.M.Calderon-Mexico,D.F.; A.E. Schlemmer–Shreveport, La.; C.B.Milne-San Juan del Rio, Mexico.

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Section VI, Part 3b, p.19 FIG.8 Archaeological Architecture

DRESDEN CODEX - pp.71-73 (51-53) (with notes by H. Harleston, 18-XI-1989)

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Section VI, Part 3b, p.20 Archaeological Architecture (cont’d) century. These finds led me to a more impressive fact: Principal dimensions at Teotihuacan are multipliers for Tzolkins of 260 days, known to have been in use during the selection by Mayans of information to be displayed at the pyramidal complex. H.M.Calderon’s work identified messages appearing on the last page of the Dresden Codex, appended below (Part 3d,) together with its color reproduction: the Jupiter Table, [p.45 (78), Fig.9, Part 3c,] Calderon was impeccably scientific, his comments based on a profound understanding of Mayan procedures. He decoded various tables in the Dresden. First, some comments with respect to Jupiter / Saturn conjunctions: Tabulation pp.8A indicates factors that produce a series of the number “54,” a special number: 9, number of Hunab Ku, times the creation number 6 = 54. Each number in the Mayan long count system is noted, in which from right to left bars and dots stand for days (K’in,) the 20-day Uinal; 360 days (Tun,) 7,200 days (Katun,) 144,000 days (Niktekatun, or Baktun of 400 Tuns) and 1,872,000 days (an Oxlahkatun.) For example, the synodic orbit of Saturn -- 378 days -- is 6 x 7 x 9, coded 1.0.18, or 360 + 18. Two significant platforms in the “Ceremonial Zone” are 18 by 18 STU, with an area of 324 = 6 x 54, whose long count is 16.4 = 16 x 20 = 320, plus 4 days. There are only two platforms with sides of 20 STU, one in the “Moon” Plaza, the other in the plaza west of the Great Pyramid. Their area is “400.” A series of counts of 400 orbits of Saturn is tabulated in Section I, p.16 to register the zero reference point (3,114 B.C.) and a twelfth count in May of 1,855. The series began as 0.0.0.0.0, ends 12.12.0.0.0, and begins as the 13th zeroth point, a Mix-Baal-Holeistak. The interval “486” is the distance in STU between the center of a patio now named the Patio of Quetzalpapalotl, and the E/W centerline of the Great Pyramid. It not only has factors of 6 x 81, but measures a truncated cube of nine, cut off at a height of six, volume 486 cubic units, that can be used for drawing a universal pyramid whose side is the square root of 216, its apothem the square root of 162: base of the so-called “Moon” Pyramid, and the volume of a cube of sides 6, the creation measure (not days.) “216” repeats in a “Ceremonial” Zone measuring two by six Saturn orbits. Six orbits of Mercury in Mayan times were 702 = 6 x (9x13,) = 6 x 117 days and nights, repeated in the “Citadel” and near the Grand Avenue. The eleventh event, 594 = 6 x 99, contains a factor of five Venus counts: 99 moons of 29-1/2 days measures 8 vague years of our own orbit: 8 x 73x5 = 8 x 365 = 2,920 = 5 x 584. The twelfth event, 648 = 9 x 72 = 8 x 81. The west, south and north walls of the “Citadel” (the Great Quadrangle of Saturn) are 72 STU, so the three total a cube of six: 216, marked by the west baseline of the 6-body pyramid named “Quetzalcoatl” by moderns. DISK: AA-07TJS4.DOC // HH // 23-III-08 // p.20.

Section VI, Part 3-c, p.21 Archaeological Architecture

FIG. 9 – THE JUPITER TABLE

DRESDEN CODEX [45 (78) ]

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Section VI, Part 3-c, p.22 Archaeological Architecture

JUPITER TABLE AND THE TZOLKIN AT TEOTIHUACAN Students of Mayan astronomy are indebted to H.M.Calderon for his incisive analysis of the last undestroyed page of the Dresden Codex, Fig.9, above, p21. The upper por- tion of the page provides a formula 4.0.16.0 = 29,120 days = 112 Tzolkin of 260 days, 73 synodic orbits of Jupiter, divisible by a 364-day stellar year: 13 constellations of 28 days each, confirming Mayan counts conserved in the architectectural mathematics of Teotihuacan. Included as Appendix 1, by permission of his son Sergio, is my English translation of Calderon’s document that I hope may be useful to students. In order to appreciate the validity of these correlations, we begin with a partial list of the number “73,” used as factors by Mayan mathematician/astronomers: 73 x 5 = 365, the vague year, one Mayan Haab. 73 x 260 = 18,980 = 52 x 365 = 52 Haab mark planetary alignments. 73 x 8 = 584, synodic orbit of Venus. Mayans knew a precise value: 583.928 days. Our modern 583.921 days tells us that Venus has accelerated. 73 x 780 = 56,940 days = 219 x 260 = 219 Tzolkin, Mars’ synodic. 73 x 6 = 438; times 260 = 113,880 = 520 x 219 = 312 Haab, a short count of six 52-year periods; each 312 Haab Mercury Venus, Earth and Mars align in opposition. 73 x 398.9041 = 29,120 days, Jupiter’s orbit: 112 Tzolkins. In 1992 the orbit was 398.877 days (= 99.993%.) 73216000 x 378 x 756 = 16! = 2.092278989 x 10,000,000,000,000 may or may not have been known by Mayans. If they kept xponentials secret we may never know. Two cubes with sides of 378, Saturn’s Quadrangle, equal the “Ceremonial” Zone with a height of 63 STU, summit of the Great Pyramid without a building on top: 756 x 2,268 x 63 = two cubic Saturn Quadrangles: 2 x 378 x 378 x 378

--- 000 --- 000 --- 000 --- The first pyramid at Teotihuacan was erroneously named “Moon” by ignorant Aztecs in the 16th century. By applying Calderon´s procedures to this construction we may discover what Mayans planned. Dimensions drawn in 1984 for The Keystone, pp.121-122, Figs.11 & 12 (cf. Bibliogra-phy, Section I) were transferred from drawings given me by Ponciano Salazar of the National Institute of Anthropology and History (INAH.) Great care was taken to conserve accuracy within limits not to exceed those used for aerial photography con- version to governmental survey maps. Reliance rested on stone buildings and carved DISK: AA-07TJS7.DOC // HH // 10-IV-08 // p.22

Section VI, Part 3-c, Jupiter-Dresden-Tzolkin Archaeological Architecture artifacts. Field dimensions were remeasured with steel tape when there were doubts. The final base rectangle of the “Moon” was 144 by 162 STU: 23,328 sq.STU. Con-struction began with width 144 and north to south length 128 STU. But 144 x 162 times a Tzolkin = 6,065,280, that I will henceforth call the “Tz#.” This one will reappear at the Great Pyramid as a factor of a larger Tz#. It does not reappear in the Citadel. Tests were: first, to see if it can be divided evenly by the synodic orbit of Mars. It can. 780 x 7776 = 6,065,280. It can also be 78 x 77,760, a special number. It is the area in square STU of the four faces of the Great Pyramid of Egypt, and appears again as the area of each face of the Chinese pyramid at Urumchi. Why is 7,776 on each of the west columns of a patio with an Aztec name: Quetzalpapalot, named in the 1960’s (Sect.III, Part 6A, pp.23, tabulation 8, footnote.2) Ten columns are 77,760 –- 6 x 12,960 --- equal to one half a Platonic Great Year of 25,920, itself twelve cycles of 2,160 vague years. The second test was to check planets Mercury and Venus. Mercury´s orbit for BCE Mayans was 117 days, a significant 9 times 13. We divided the basic total of Tz# 6,065,280 by 117. It equals 51,840. This seemed familiar. It is. It is two Platonic Years; 2x25,920. It is also 351 x 17,280. The dimension “351” is marked in the Cita-del by the eastern three platform centers. “1,728” is a cube 12 units on a side. For Venus, whose rounded orbit is 584 days (8x73) I applied an ancient scheme of ad-ding or subtracting the number “one,” and found that 6,065,280 is 585 x 10,368, also familiar. It is 36 x 288. Mayan adepts’ knowledge surfaced: factorial Nine – 9! – is 362880. In Mayan format it can be 36 288 0. I now had Mercury, Venus and Mars. Did I have the stellar year of 364 days? No. I did not. Another test was that the constellation count should appear. It was located: instead of area we should look at a three-dimensional box, multiplying by the height of the pyramid without a building on top: the base rectangle 144 by 162 times 42. The box volume is 979,776 cubic STU. This is multiplied by the Tzolkin. I held my breath and divided Tz# 254,741,760 by 364. The answer is melodious: it is 699,840 -- an even product -- obtained by multiplying 9 by 77,760. Next I looked at the add-ons south of the main body of the “Moon.” The first addition is 4 by 96 STU, an area of 384 sq. STU, plus 18,432 sq.STU of the main base is 18,816; times 260, the Tzolkin. The product: Tz# 4,892,160 was divided by the zodiac number 364. The result: 13,440 equals 40 x 336. The Stellar year factor is confirmed, plus a square defined in Saturn’s Quadrangle: 336 by 336, which is 3 times 112 (Jupiter.) The number “40” is found displayed under the Plumed Shells on murals, that show a series of black dots: 8-12-12-8. DISK: AA-07TJS7.DOC // HH // 10-IV-08 // p.23

Section VI, Part 3-c, Jupiter-Dresden-Tzolkin Archaeological Architecture What happened when the total area was tested? I included the second southern addition that originally measured 49 STU east to west by 30 STU north to south, an area 1,470 sq.STU. The combined three structures’ area of 20,286 sq.STU is multiplied by 260, to form a Tz# of 5,274,360. This time the first test was to divide by the zodiac stellar year: 364. The result is 14,490 = (2 x 5 x 9 x 7) x 23 the eclipse multiplier. Next, Mars at 780 must be multiplied by 6762 = 6 x (23 x 49.) Mercury’s multiplier of 117x45,080 equals 40x(23x49.) Venus divides as 585x9016; factors= 8 x (23 x 49.) We can now see that the addition of dimensions of the first pyramidal installation and its subsequent expansions, were controlled by a set of parameters made to fit mathematical obligations that have numbers that were, and still are, cosmically significant. The Tzolkin was by no means a “sacred” number as it was labelled by sciences that did not appear in the modern world until the 19th century. The number 260 was a con-fidential term used by Mayan savants who were adepts in astronomy and knew accurate counts of planetary orbits. This should be recognized, via Calderon’s insights. He realized that Mayans could measure sidereal orbits by timing passage through the Pleiades, or, as they called these stars, the tail of the rattlesnake: Tzab. After scores of hypothetical calculations the Tzolkin scheme produced results. I moved on to the Great Pyramid itself, the second magna project, estimated to have been over 300 years in process. It may have taken from 216 BCE to 199 CE (cf. Sec- tion I, pp.16-18.) Applications of the Tzolkin show us that even though the first body begins in the lava cave below the Pyramid, the area and height that fit the tests imply an invisible subterranean square measuring 216 by 216 STU and a design height without building, that was 63 STU over a cave at 2160 STU above mean sea level. Alter-nate dimensions do not comply with all four tests. The apparent terrain around the Great Pyramid was leveled at 6 STU above the cave, or in Mayan terms 2,166 STU (proved by E.Matos’ excavations in the last century.) A mental “box” volume would be 216 x 216 x 63 = 46,656 x 63 = 2,939,328 cu. STU. On multiplying by 260, our Tz# is: 764,225,280. The tests:

Mars = 780 x 979,776 Mercury = 117 x 6,531840 Venus = 585 x 1,306,368 Saturn = 378 x 2,021,760

Short Count = 312 x 2,449,440 Stellar Year = 364 x 2,099,520 Tz# = (378 / 3) x 6,065,280 (Tz# “Moon,” p.23) The third major test area is the Great Quadrangle of Saturn. The square was vertical 6 STU, and on the east side it was sloped to 377 instead of 378. I decided to test 378 squared times 6 = 857,304; times 260 to produce Tz# = 222,899,040. DISK: AA-07TJS7.DOC // HH // 10-IV-08 // p.24

Section VI, Part 3-c, Jupiter-Dresden-Tzolkin Archaeological Architecture This Tz# is a revelation: more than five dozen factors tested are significant dimen-sions, that range from small to large numbers, including major demarcations. We can factor with Teotihuacan pi= (9x7 / 4x5 = 3.15) used throughout the “Ceremonial” Zone. The answer is 70761600. Selected factors below illustrate how architects checked, with a planned system, the dimensions they were marking. Special factors: 45,360 x 4,914; the area of the Mayan scale model of the earth, the icosahedral sphere of twenty equilateral triangles of area 2,268. Multiplier “4,914” is equal to 42 orbital counts of Mercury: 42 x 117. One-tenth the earth model’s volume factors our Citadel Tz# as 2,467 x 90,720. And 2,467 = (7x13) x (9x3) = 91 x 27, a cube wih sides of 3 units. multiplied by the 91 steps up the pyramid at Chichen-Itzá. In the first fifty factors that were checked (1 to 50) Tz# 222,899,040 can be divided by 32 numbers, or 64%, beginning with the first ten digits (1 to 10.) Below is a selection covering small, medium and large dimensional STU measurements that I propose also indicates with a Mayan format the possible satisfaction of a scribe, astronomer/mathe-matician as the 9-digit Tzolkin was being proved acceptable for the architectural crys-tallization into stone and carved panels that are still enigmas in the 21st century: MACRO NUMBERS STU Tz# / STU

MEDIUM DIMENSIONS STU Tz# / STU

SMALL DIMENSIONS STU Tz# / STU

2,268 98 28 0 1,872 11 90 70 1,080 20 63 88 936 23 81 40

756 29 48 40 378 58 96 80 336 66 33 90 312 71 44 20

16 13 93 11 90 13 171 46 080 9 24 76 65 60 8 27 86 23 80

In each case in the above selection, I have divided Tz#222,899,040 by a dimension in STU (cf. maps, 1974-1998, pp.iv & v, above, with details of factors given by analysis of the correlations.) The Mayan format of the result in each case may have been seen by the scribe who was making additions to obtain the products of multiplications. It appears acceptable to postulate that a scribe, adept in astronomy and mathematics, would find satisfaction when the Tzolkin procedure produced familiar friendly num-bers, such as: 98 = 2 x 49; 11 orbits of Saturn; 20, the number of triangles on an icos-ahedral sphere; 23, the eclipse multiplier (23 x 520 = 11,960 days in three eclipses); 48 & 96, displayed as important separations of the three east platforms of the Saturn Quadrangle; 66 = 132 / 2 at the First Pyramid (“Moon?”) and in the “Citadel;” 24, the eight north and south platforms in the “Citadel,”; 76 = 4 x 19, the Jupiter factor (21 x 19 = 399; 9x19= 171; 4x19= 76;) the cycle time of Dark Lord Yum-Eek = 65 days, reported by NASA over the South Pole. This tabulation can be extended to scores of examples that interested students could calculate to support the conviction that Mayans utilized these procedures at Teotihua-can, illustrated below by two more companion cases: Palenque and Chichen-Itzá. DISK: AA-07TJS7.DOC // HH // 11-IV-08 // p.25

Section VI, Part 3-c, Jupiter-Dresden-Tzolkin Archaeological Architecture For Chichen-Itzá the base of the pyramid was 21 STU–10 STU (staircase,) 21 STU, a total of 52 STU; squared, area is 2,704. Multiplied by a height of 22.5 STU the Tz# is 15,818,400. The Mars cycle is 780x20,280; Mercury is 117x135,200; Venus at 585 = 27,040. Strangely, Jupiter + 1 divides as 400 x 39,546: But the zodiac year of 364 does not fit here. This was a late site, near the end of Mayan domination, occupied by Toltec invaders from Tula (Tollan,) who instituted bloody practices. The factors indicate that probably there were still adepts at the site. Palenque, highly publicized for its unique tomb of a ruler misnamed “Pakal,” was terminated in the 8th century CE. Its dimensions nonetheless, are significant: a base 52 STU partially truncated in a low hill on which we find the Temple of the Inscrip- tions, whose 69 steps remind us of the eclipse factor (3x23= 69.) Without a building on top its height measures 22.5 to 23 STU. Therefore, the Tz# might have been the same as Chichen-Itzá. Once again the expertise may have been forgotten, so that the division by 364 does not work out. Or the researcher needs more reliable data. However, it is apparent that some of the significant STU measures are there. The tomb of the personage centers his remains at a height one STU above the floor, lying 66 steps of 35.3 cm. (1/3rd STU) descending inside the Temple. This places “Pakal” 21 STU below the floor of the Temple above him, commemorating the lag time of Jupiter behind Saturn when a cycle of conjunctions has run its course. It appears that by the 8th century CE the internal conflicts were increasing and by the 11th to 12th century of our calendar the Mayan domination had disappeared as Aztec power replaced it. This 37-year project terminates with poetry, following guidelines laid down by Santi- llana in “Hamlet’s Mill.” A conventional research supervisor would not pertmit this since it could be considered unduly personal. But this is not a conventional research document. It can be safely conjectured that there are no post-doctorate authorities with objective knowledge of Mayan architects nor their confidential methodology. It has been common practice to convert speculation into “probability.” As an understudy for twenty-five years with H.M.Calderon I was privileged to have access to and reread a number of research reports that converted some of my misun-derstandings to acceptable logic. One example can illustrate this: in the 1980’s Cal- deron reported on Jupiter / Saturn and their conjunctions, given in the Dresden Codex. He had not yet found the Jupiter Table, Fig.9, above. Reading and then rereading is the definition of “research.” Look, then look again and then once again. On the last page of his report he mentioned that for a Jupiter/Saturn conjunction to be observed again in the same constellation (such as Tzab, the Pleiades) there must be 43 events of 7,182 (one Katun minus 18): 308,826 days= 846 solar years. In 1976, I published a detailed map, that appears above, on p.v of this Section. It was again published in 1984 on p.123 of The Keystone. DISK: AA-07TJS7.DOC // HH // 14-IV-08 // p.26

Section VI, Part 3-c, Jupiter-Dresden-Tzolkin Archaeological Architecture The dimensions show us the factor “43” twice between the “Sun” pyramid and the south platform limit. It also shows “43” three times between the south limit, north to the Great Pyramid’s centerpoint/east-to-west-centerline. It was only this year (2008) that I recognized the emphasis given by the architects on the importance of 43 Jupiter -Saturn conjunctions. This example illustrates that a series of cosmic numbers can be poetic. Poetry combines intellectual knowledge with positive emotional and sensual experience, a musical triad. I salute the Mayan adepts and their teachings, that awakened admiration and fostered astonished appreciation.

ANCIENT MATH

With memory intellectual, emotional, sensational Predictability weaves a vision correlational, Unmaterialized futures more often than not,

At times random, seldom precise, soon forgot…

A polished block of granite between Sphinx’s paws, Reveals with authoritative tone three cosmic laws, A dozen million between snows of Hamlet’s Mill

Connect poet and troubadour with verity, instill

Objective conscience in an observer who sees, Cancels imaginary past, and will, in the now, free The wheel of drifting invisible raft, our passport To silent unnumbered companions, who resort

To intention, invited by each observer’s essence,

Liberated, with no need of a prompter’s presence. Can this miracle be attained without assistance? Intuition can insist, yet it still requires resistance.

FINIS

DISK: AA-07TKS7-DOC // HH // 14-IV-08 // ´P.27

Sect.VI, Part 4, pp.28 Archaeological Architecture MATHEMATICAL REFLECTIONS

Reflections can be defined in many ways. One definition is “light or sound returned from a surface.” Another is “an idea that forms from associations during meditation.” In 1987 Asunción Preisser of Mexico City invited me to her oral examination to qualify for the degree of Master of Arts in Philosophy of Science. Her dissertation was based on ideas of German mathematician Gottlob Frege, who postulated a theory to define the origin and nature of numbers. Preisser’s crystalline observations gave me tools to compare architecture of structures that were applications by Mayans to commemorate their knowledge of mathematical truths. The first principle Preisser stated is that neither are we able to explain satisfactorily the nature of mathematical knowledge, nor do we know the nature of thoughts, whose existence we cannot deny. It is recognized that truth in itself is neither spatial nor temporal. We could admit there can be an objective domain that is unreal even though logical psychology considers it to be simply subjective. In order for logic and mathematics to be true and objective, both disciplines have to be free of subjective doubts, required for having a relationship with external re-ality. Frege, Preisser tells us, finally recognized that arithmetic requires intuition for its demonstrations, although not for the physical event itself. Any science or theory experiences many questions that have no answers. We are not certain as to exactly how the logical notions are apprehended, nor exactly which affirmations and principles they describe, because the latter have not yet been completely justified. We should not be drawn into mixing philosophy with empirical research, nor lured into confusing facts with probability, in spite of advances achieved with ingenious new methodologies. Frege saw numbers as outside time and space, independent of the individual in the sense that numbers should be the same for all humans, and not objects of visual perception. Philosophy should not prescribe how any science should be, nor how scientific notions must be. Preisser realized that our experiences lead us to consider an objective world that is not perceived by the senses as the only response to our relationships. Perhaps numbers express objective connections, or they measure the results of objective processes, whether they are visible or not. Numbers may not be objective entities, but they could express something from an objective world. My work has made it evident that via Mayan architecture I can arrive at multidimensionality independent of a time frame, and reveal a matrix expressing whole-number relationships to unify space and time measurements, linking astronomy with artifacts as well as with ancient mathematics. DISK: AA-07T2-MRred.DOC // HH // reedited 04-VIII-08

Section VI, Part 4, pp.29 Archaeological Architecture (contd) The Mayan sound that signifies ONE is Hun, a sound that translates as a unified measure – Hun Naab: one hand, a specific width, a sound that also refers to any circle. The number TWO – Ca –represents duality, the doubling of sound to its resonant octave, played on a ceramic flute. THREE – Ox – symbolizes an equilateral triangle formed by three points, dividing a Mayan 378-degree circle that counts time and space, a great square speculatively named today a “Citadel,” that marks the number of days for Saturn to reappear in the sky above us. A vertical triangular nest – K’u – (symbolized by a pyramid) when inverted is the portal of entry into life, our doorway of birth. And FOUR – Kan – symbolizes the first born, nature, whose multiplication materializes the invisible in the form of a sentient five-fingered being. FIVE: Ho, symbol of Venus, is the number for Tepeu, the Former, the Shaper. Can there be groups of events separated by thousands of years? The answer is “yes.” Astronomers also register the invisible, for example infra-red, ultraviolet and X-ray radiation. Can we include objects that we are unable to imagine? Even “unity” is an unimaginable concept. How many objects are listed under the concept “earth’s satellite?” The earth has three moons: the largest; plus an asteroid named “Toro;” and a small piece of high radiation that orbits us in 65 days at a distance of 720,000 KSTU, twice the distance of our large “first” moon, marked at Teotihuacan as “720.” Mayans named this enigma “Great Darkness” (Yum-Eek,) and documented its cycle in the Dresden Codex, p.74(54), recognized by H.M.Calderon in Mexico City. The figure illustrates events with copious rainfall, with a humanoid dark personage throwing bolts of lightning downward. In the 1980’s NASA reported an interference with the Austral Aurora over the south pole caused by Yum-Eek. The moonlet was affecting the time of rotation of earth. NASA theorized that the object was a fragment of a neutron star, one possible explanation for its high radiation emission. Frege used the German word “Wert(h)verlauf.” “Wert” is “value,” or “appreciative.” “Verlauf” is “progress,” “reality,” “truth.” The combination can mean multidimensional value.” Other meanings are “valued pathway,” “worthy procedure” “meritorious progression.” A non-logical, non-verbal assembly of apparently unrelated concepts will be recognized when expressed via whole-number units of measure, the twelve-millionth part of earth’s polar axis, used by Mayans to lay out architecture today named “Teotihuacan’s Ceremonial Zone,” a rectangle measuring in earth revolution time the count of the reappearance of a planet now named “Saturn” by us, and “Ain-Ek,” the Crocodile Star that holds us prisoner, by Mayan Halach. DISK: AA-07T2-MRred.DOC // HH // reedited 04-VIII-08

Section VI, Part 4, pp.30 Archaeological Architecture cont’d. Preisser imagines Werthverlaufe in motion, moving, so as to become accessible to our restricted mental patterns. She posits “Werthverlauf ” as a masterpiece, a drawing that shows us all lines that connect all objects, including those that fall under the concept and those that do not. This is “multidimensional,” as if there were a diagram showing the links between abscissa and ordinates. This can mean an objective procedure with multidimensional values, a matrix. It has been conjectured that this cannot be demonstrated formally, perhaps because in 1902 Frege had no Mayan matrix that uses units selected such that there can be a language formed of related numbers to accurately illustrate relationships of “our ” solar system, perhaps even those of any part of a “multiverse,” if such “multiverses ” materially or objectively exist. The connections between the components of a Mayan multidimensional matrix do not follow customary logic, but rather definitions of units of measure: length, angles, time, the sums of repetitions of events observed in the heavens. They can be defined as groups or classes when we elect to buy fruit in the supermarket or as intelligible communications between mathematicians and physicists who wish to express rela-tionships of segments or resolve a gravitational acceleration problem. In 1976 I thought I had found how to show that the mass of a particle increases by a whole number (twice, three times, 1872 times its rest mass) when the vector angle is used to find the value of its sine as a function of the speed of light. This was sent to three researchers: Bucky Fuller, Andrija Puharich, and Alfred Schlemmer. There it rested. Two of them have left this planet. I dedicate Mathematical Reflections to my three friends. Hugh Harleston, Jr. Tijuana, B.C., Mexico September, 2008. DISK: AA-07T2-MRred.DOC // HH // reedited 04-VIII-08.

Section VI, Part 5, p.31 Archaeological Architecture CONCLUSIONS

1.) Correlations in this Section again confirm that the design of the Great Pyra-

mids of Teotihuacan was based on Mayan astronomy and mathematics. 2.) Empirical observations of repeating sky events – stars, planets and other celes-

tial bodies -- led to long term Mayan usage of counts registering the sun, the moon and seven or more planets, combining the synodic orbits of Jupiter, Sa- turn, and their conjunctions, the latter confirmed by the Dresden Codex, on pages 71-73, that registered 40 conjunctions as three events of 13 plus a zero reference origen, matching the Trigon calculated by Kepler in the 17th century.

3.) Mayan architects used a special confidential number: 260, the Tzolkin, as a multiplier to test dimensions and measures for conformity with preselected standards of orbital information: the synodic and sidereal counts in earth revolutions of Mercury, Venus, Mars, Jupiter, Saturn and possibly Uranus. (see data in Section II, 2003, pp.16, 17, 18.)

4.) Tests for acceptable architecture required a whole-number value: the stellar year: 364 revolutions = 4 times 91 = 13 Mayan constellations of 28 days. The base area, or a cubic value that included the height, was multiplied by 260 to produce a “Tzolkin” whole-number, that should be divisible by 364. 5.) The Earth was measured with the sun, in revolutions per orbit; i.e., a calendar solar year, that Mayans knew accurately: 365.242(2) days, in the Paris Codex. (see Section I, 2002, Fig.7, p.30.) 6.) The Dresden Codex, pp.45 (78) shows an accurate synodic orbit of Jupiter as 112 Tzolkin; i.e. 29,120 “days” divided by 73 = 398.9041 days. Semi-destroyed

values were decoded by H.M.Calderon in 1990 but unpublished. The modern orbital value is 398.87735 days (1991, Physicist Daniel Flores, Instituto de As- tronomia de La Universidad Nacional Autónoma de México, Mexico, D.F.)

DISK: AA-07T2-CONCL:DOC // HH // 17-IV-08 // p.31

Section VI, Part 6, p.32 Archaeological Architecture CONJECTURES

1.) Based on musical scales in China, Persia, Greece and Mexico it is conjectured that numerical values originated in more ancient civilizations that linked music and dimensions with astronomy.

2.) There can be additional discoveries inside the “Moon” pyramid, providing

further evidence that the pyramids of Teotihuacan were Mayan.

3.) Sacred Geometry (Lawlor, McClain, Schwaller) suggests Mayans knew the square roots of 2 and 3, and the Golden Mean, that they encoded in Teotihua-

can’s architecture, beginning with the first (“Moon”) pyramid. Three series of phi are visible, including the 14th number (377= 378 minus 1,) significantly appearing east-to-west at the “Citadel,” the Great Quadrangle of Saturn. FUTURE RESEARCH 1.) Apply the Tzolkin method (Tz#) to Mayan architecture (Tikal, Kobá, Tulum and other candidate sites.) 2-) A study of Chichen-Itzá to detect mistakes in restoration. Define the base with the sequence of 21 STU, then a staircase width of 10 STU, followed by the remaining 21 STU, total 52 STU. The height of 22.5 STU fits the Tzolkin test except for the zodiac year (see p.26, above.) 3.) Find whether Jupiter/Saturn conjunction data were recognized by Pythagore- ans in Greece.

4.) Make an analysis of the mathematical structure of each Mayan glyph; e.g., the “Ahau” (see Sect.III, Part 7, p.25 identifying 6x120 = 720; four circles = 1,512; etc.) All Mayan glyphs may hold hidden mathematical messages. 5.) Explore the corners of the Great Pyramid to determine if there is a material definition underground, NE, NW and SW. A cursory inspection on the SE corner was made in the 1960’s, and revealed nothing. An underground base may be invisible mathematics, known only to Mayan high-level initiates . 6-) The center of the Great Pyramid should be defined with a borescope from the lava cave terminus, 38 STU away. A possible find may be a square, vertically descending shaft at elevation 2,160 STU, downward 63 or 72 STU. DISK: AA-07T2.DOC // HH // 17-IV-08 // p.32 (reedited 01-IX-08)

Section VI, Appendix 1, p.33 Archaeological Architecture

THE DRESDEN CODEX JUPITER TABLE © -- By Hector M. Calderon – Sept. 01, 1990.

Due to compactness and the semi-blurry condition the last page of the Dresden Co- dex constitutes a challenge to the researcher of Mayan astronomy. The table is on page 78 (previously 45); it measures scarcely 6.5 by 9 centimeters, and this is where astronomers at the ending of the Classical Period have shown us their impressive and patient observations over a period of millenniums. The following research notes will tell us how many. [N.B.: The color copy of this Table appears under Fig.9, above. Calderon also com- pared the Gates modified version, that was executed with “improved” sketches of the Mayan version, which Calderon asserts are complements, and provide a basis that fa-cilitates glyphs that are difficult to identify, as well as those that are not well aligned horizontally. This allows us to distinguish K’ins, Uinals, Tuns, etc. and define where they end. To further complicate the attempt to decipher, there are omissions of some numbers, above all in the case of zeroes (in red) that most probably were blurred out over time. In spite of these obstacles, and utilizizing his experience with analyzing in the past other Tables (Mercury, Mars, eclipses) it became possible to reconstruct al-most completely this very important record.] What we can see and what is possible to infer (given in parentheses) is as follows: A B C D E F A’ ? 8 Keh Octé 0 1 this is not a ringnumber 10 Triple J/S conjunction [NBHH] ______

4AHAU

? T588b 8 17 11 3 (0) 13 OC

? (7,8,9) ------- 4 0 16 0 15 2 0 13 OC

? ? ? 0 12 ___ 0___ 10 2 ____0___ 4 0 15 (16) 13 KIMI

? ? ? ? 8 __ 0__ 5 1 __ 0___ 3 0 12 13 IK

? ? ? ? ? ___0___ 1 0 __(4)?__ (2)? (0)? 8 13EDZNAB

(1) (0) (4) 13HIIX

1 2 3 4 _______ 5 ----------- 6

[NBHH: Flying twin-ribbon, double-star glyph is tenth triple J/S conjunction; cf p.17] Starting with Column A. We can distinguish in the upper part (A2 and 3) two glyphs: AA-07T2-HMC.DOC // HH // 24-IV-08 // P.33 (translation by HH, reedited 01-IX-08)

Section VI, Appendix 1, p.34 Jupiter Table Archaeological Architecture 8 Keh, and Yocteil. The first is part of a calendar date wheel (the number and the Uinal of a Haab.) The second glyph we had already identified as the name of Jupiter. Its glyphic structure is T-33.765b:103 and it confirms the phonetic value of the suffix TE or TEIL. Under these glyphs we find the chronodistance of being “tied,” (also a “ring number”) which will relate to the “date of entry” of the Table with archaic information. The reference date of the archaic calendar is annotated in B2 by a glyph: T(588b: 140) 181. which announces it. This requires an explanation of the theory which postulates that in all calendars used in Mesoamerica the fundamental base was the so-called “calendar wheel” (xiumolpilli or buc-xoc) with two interlocking “gears”: the Tzolkin of 260 days and the Haab of 365 days, including the cycles of 52 Haab. I am convinced that even before the olme-cas or protomayas created their “long count” they had already registered position da-ta of all the planets and the moon, compiled in the midpoint of the fifth millennium prior to our era (the “CE,”) and had recorded this for each repetition of the 52-Haab cycle, precisely for the dates with Ahau on which they terminated. Whether it be for interpolation or by calculation, the Mayan astronomer could verify the position of any celestial body, on finalizing each Tzolkin and above all, for each cycle of 52 Haab. For that reason the Dresden tables begin by expressing a date that invariably is Ahau and, with that beginning point, by means of the chronodistance to “tie” it to the archaic ca-lendar, the date of entry into the table can be calculated. Let me describe this in a simpler manner. Let’s suppose that, in the case of Jupiter, a Mayan astronomer consulted an archaic codex in which they had registered for each wheel of 73 Tzolkins (52 Haab), the number of days [N.B: earth revolutions] before and after an opposition (of Jupiter.) He probably examined the wheel in question and also on that wheel the closest Tzolkin to his present time as well as the day assigned exclusively to the celestial body in which he was interested. He found that for example for Jupiter on the day 4 Ahau-13 Chen (the end of the Tzolkin) the planet would be 15 days before its opposition. He next found the 13 Oc nearest, and discovered that it is 30 days before the reference date; that is, 15 days before opposition. This is just what he needed: an Oc day, specially reserved for Jupiter, named in the planet’s honor, and would be the closest possible to the Opposition. He could give the date of the long count the 4 Ahau nearest which would have appeared in his tables. It was 8.17.11.3.0—4 Ahau, 13 Chen. He registered the instructions to follow to arrive at the date of entry in the Table, and “tie it” to the archaic calendar by means of subtracting from the reference date 30 days; which are 1.10 on the long count. That is what columns A and B are telling us, where the chronodistance to tie (1.10), and the archaic reference date 8.17.11.1.10 appears, which of course lacks the final zero (in red). This is a minor fault because we well know that the only dates that are always ended with zero are Ahau’s. DISK: AA-07T2-HMC.DOC // HH // 19-IV-08 // p.34

Section VI, Appendix 1, p.35 Jupiter Table Archaeological Architecture The result of the subtraction is to show us the remaining date 8.17.11.1.10 – 13 Oc, 2 Mol. With the time constant (HMC) 584,314 we find this is October 24, 387 CE (i.e. Julian Date 1,862,704,) exactly 14 days before Opposition No. 1810, given by the Insti- tute of Astronomy of the National University of Mexico. Because of his urge to be concise (one of the few advantages we enjoy when the writings are as complicated as the Mayan language) the astronomer has given us explicitly the entering date, just as done in other tables (Mars, Venus, Mercury, eclipses…) but in this case this is not important for those who have learned to calculate to check the answers. Next let’s look at columns C, D, E, and F. At the beginning we believed that the dates were over long time periods and would take us to millions of days. However, we were able to detect the separations of differing levels, guided by the zeroes, and realized that there are multiples of “364 days, “ as well as Tzolkins. We also discovered that a column is missing to the right of F…which evidently was page 79, now non-existent. At the bottom of this column – (A’) there should have been a “13 Hiish” in order to complete the sequence, not only the Tzolkin days, but also multiples of “364.” In fact from 13 Edznab we will arrive at 13 Ik by adding 364 days, the same as the count from 13 Ik to 13 Kimi plus from 13 Kimi to 13 Oc will require 364 days. However, if we add 364 days to 13 Oc we arrive at 13 Hiish, which does not appear on this table. If we add another 364 days we return correctly to 13 Edznab, thereby finalizing 7 Tzolkins ( = 1,820 days) and making it possible to recycle this table. [N.B.-HH: this duplicates five bands of 364 days = 1,820 = 7 x 260, shown on pp.23-24 of the Mayan Paris Codex.] By starting with the multiple 1.0.4 ( = 364 days) that we presume was in the hypotheti-ca1 column A5 on missing page 79, and working to the left, just as we found to be the method used on other tables, we can deduce that in F5 was a number: 2.0.8 = 2x364 = 728, but now we can only see the “8.” Also we can correct with certainty the three-bar “15” that appears in D5, because it must be “16” in order to give the date 13 Kimi. The box labelled F4 is a problem. If we study the position in the original Codex (on the right hand, pg. 1 (for Fondo de Cultura Económica version) we see that the space is for only three numbers between the zero and the “8.” This allows us to situate here 1.0.4 that is missing. But that does not correspond to the additional column A’ whose base should have been “13 Hiish.” A second alternate is that the “1” and the “0” seen there might be the ending of a larger number belonging to Box F3. A third hypothesis is that, with the Codex still in use, it suffered extreme damage that forced the Mayan astronomer to set up in this space the lost “1.0.4” because he knew perfectly well that it did not correspond to day 13 Edznab; instead it was only for 13 Hiish (that had disappeared.) Any apprentice whatsoever would have known this, but even more so a a specialist like whoever it was that registered these drawings. DISK: AA-07T2-HMC.DOC // HH // 22-IV-08 // p.35

Section VI, Appendix 1, p.36 Jupiter Table Archaeological Architecture The number “5.1.0” is very clear in Box E4. It supports our calculations for the other numbers in the columns. It is equal to 1,820 ( = 5 x 364.) Continuing to the left is the number “10.2.0” ( = 10 x 364) and is not a problem. We advance to Box C4, in which a step is formed, because it is the first number with four ciphers: 4.0.16.0, the number that allows us to discover the Mayan formula to relate the synodic period of Jupiter with Tzolkins and also with the 364-day period:

4.0.16.0 = 29,120 days: 80 periods of 364 = 112 Tzolkins = (precisely) 73 Jovian periods. The value Mayans assigned to the synodic orbital period can be calculated with the above. In decimals it is 398.9041…days. The 1991 modern count (by physicist Daniel Flores, Instituto de Astronomía, Universidad Nacional de México, published in his Master’s Thesis) is: 398.87735… a difference of +0.0066933 %, or 38-1/2 minutes shorter than the Mayan. We can now go to level 3, and see only the endings of larger figures. On studying the possibilities, I can suggest that the destroyed numbers could have been as follows:

BOX MAYAN NO. EQUIVALENT 364-DAY CYCLES

F3 E3 D3 C3

1.10.6.0 2.0.8.0 3.0.12.0 17.12.8.0

10,920 14,560 21,840 126,880

30 X 364 40 X 364 60 X 364 488 X 364

The last number was obtained with a commensurability program between the Jupiter cycle and the Tzolkins. It fulfills the requirement to end in 8.0, as well as the modern synodic orbit of 398.87735 days, but it does not fit the 364-day count, hence it remains doubtful. Summary: The Jupiter Table, p.78 of the Dresden Codex, supports the hypothesis that Mayan astronomers correlated four cycles to be able to follow the path of this planet: the 260-day Tzolkin; the stellar (zodiac) year of 364 days [N.B.HH: i.e., 28 days times 13 constellations,] the Jupiter synodic, and the multiplier “73.” We believe they also used other multiples of 364; for example, 238 x 364 = 86,632 that can permit calculation of the sidereal orbit time of 4,330 days = 86,632 / 20, plus a correction of 1.6 days. This, however, cannot be confirmed, since the numbers in the high range were obliterated from the Codex. Of course, we know how they used their own well-known technique to adjust slippage and periodically modified the entry date of their tables, but at the same time being careful that it always fell on the name-sign reserved for each celestial body. DISK: AA-07T2-HMC.DOC // HH // 22-IV-08 // p.36

Section VI, Appendix 1, p.37 Jupiter Table Archaeological Architecture As I worked with the Jupiter, it occurred to me that at some time in the remote past the entry name to the Jupiter Table might have been precisely the day 9 Oc, symbol- izing their Bolon-Tik’u, [N.B.: literally “Nine-Here-Nested.” Later, this was speculated to mean “Lords of the Night.”] This is congruent with “Bolon-Yocteil” given in the Chilam Balam de Chumayel (a star Registry.) The approximate slippage of the Mayan count of the whole-number Tzolkins and the actual observed orbital count made it necessary to change the entering day in the Table, which moved from 9-Oc to 2-Oc. When this changed the calendar, another ten days (beginning with 2-Oc) the entering day had to be “8-Oc,” in spite of an observed opposition ten days earlier. On completing the allowed movement over 10 days before and after the designated Oc day, the assigned number no longer applied, and the designated “Oc” had to deliver its “burden” to the following “Oc,” so that Jupiter “moved” from zero-Oc to 7-Oc, to finally arrive at 13-Oc in 387 CE (or A.D.), the entering date in the Dresden Codex. We can calculate exactly how long this took for the gradual change. If slippage was produced of 0.02056 days (29 min.-36 sec.) with respect to the real time of 398.8774, then the chronodistance in the Tzolkin from 9-Oc to 13-Oc is 90 days minimum and 110 days maximum, the adjustment necessary between 4,008 and 4,899 years before the Dresden entering date. From this we subtract 387 years (CE after the Table en-try) plus the 365 days of the year “zero” CE, ignored by modern calendars. We see that this is 3,620 to 4,611 BCE = 500 to 1,500 years before the present Mayan beginning date (13.0.0.0.0 = 3,114 BCE.) [N.B.HH: equaling 3,614 to 4,614 BCE.] This deduction is supported by the Mercury Table (Dresden) that gives witness to ob-servational astronomy before the last beginning Mayan count (3,166 BCE) and their Long Count of 5,125 years (an Oxlahkatun of 1,872,000 days.) Their Mercury Table registers the beginning date at Gregorian 704 CE (i.e., A.D.) so that Mayan statistics must have begun about 4,421 BCE. This is supported by recent excavations dated at the 4th to 5th millennium BCE [N.B.: Norman Hammond, “The Emergence of Mayan Civilization#, Sc.Amer, Vol.255, No.2, New York, Aug., 1986, and personal communication with HH.] We suspect the names given to the “Bolon-Ti-K’u” (Lords of Night) date to a time when the Mayan calendar was designed to correspond to original entering dates so that there could be no interference with other guardians in the Tzolkin. If Jupiter was exclusively assigned “Oc,” (one of his names,) then the same procedures gave Hiish to Mercury, Ahau to Venus, Lamat to Mars. This hypothesis and observations with respect to the four mentioned Tik’u correspond to ten signs (with even numbers) of the Tzolkin, starting with Ik, and these assist us to identify the Tables of the remaining 9 Lords. We are sure these include the moon, Saturn, and other celestial travelers that we may have possibly not imagined, such as the black satellite of the Table 4Eb, Dres- den, pp.70-73, and the Dark Lord Eek-Yum. DISK: AA-07T2-HMC.DOC // HH // 22-IV-08 // p.37

Section VI, Appendix 1, p.38 Jupiter Table Archaeological Architecture Calculation of slippage of the entering dates is simple, and it is helpful if we carry this out here as an exercise. We begin with the unexpressed but calculable 8.17.11.1.10 13-Oc, 2 Mol, Julian day 1,862,704 – the 24th of October, 387 A.D. This is 14 days before Opposition #1810 (by Institute of Astronomy, National University of Mexico.) It is probable that, on redrawing the Dresden Codex, the Mayan scribe-astronomer may have discovered that with violent events the end of 900 CE, the bases themselves were destroyed or mutilated in the Mayan society, and that this interrupted all astronomical observations, with cancellation of the Table in effect prior to his work, corresponding to 7-Oc, prematurely moved to 13-Oc, that caused a slippage of the initial “burden-carrier” of 14 days. To correct that, the scribe should have held 7-Oc effective for a longer time. But he didn’t do that. However, we can do so and restore one Uinal of 20 days, which puts us at the entering date of 8.17.11.2.10 (when 7-Oc was still effective.) From then forward we can subtract the chronodistance 4.0.16.0 registered in Box C4 of the Table. Note that on doing this the dates fall to less than ten days after Jupiter’s opposition, and slippage will gradually diminish to between one or two days for each subtraction of 29,120 days, until we arrive at Opposition exactly, then pass on to negative slippage. All this happens as we move into the past. An example: if we start at 8.17.11.2.10, 7-Oc (we don´t mention the Haab date [N.B.HH: the vague year] because this is being done with Tzolkins.) On this date Jupi-ter was 5 days after the opposition that we were using. If we now subtract 4.0.16.0 (i.e., 29,120 days) we find that on 8.13.10.4.10 (also 7-Oc) slippage was 4 days. If we again subtract 4.0.16.0 we are at 8.9.9.6.10 (7-Oc,) with an approximation of 2 days after the opposition. In this manner we can go back, changing the day Number of Oc each time that slippage gets to ten days. We learn that each “controller Oc” presides for 14 cycles of 29,120 days: i.e., approximately 1,116 years. The sequence, going from the present to the past is this: 8.17.11.1.10 the control of 13-Oc begins _________________________________________________________

8.17.11.2.10 the control of 7-Oc ends (adjustment) 8.5.8.8.10 full vigilence reached by 7-Oc; exact opposition

6.17.2.4.10 control of 7-Oc begins _________________________________________________________

6.17.2.5.10 end of vigilance by 1-Oc (adjustment) 5.8.16.1.10 exact opposition with 1-Oc [N.B.: 20-July-(-968 BCE)] 4.0.9.16.10 entering of 2-Oc

_________________________________________________________ 4.0.9.17.10 last day of 8-Oc (adjustment)

2.16.4.10.10 exact opposition with 8-Oc 1.7.18.8.10 entering of 8-Oc DISK: AA-07T2-HMC.DOC // HH // 23-IV-08 // p.38

Section VI, Appendix 1, p.39 Jupiter Table Archaeological Architecture

Sequence from 387 CE to past (continued)

1.7.18.8.10 last day of 2-Oc (adjustment) 3.13.1.10 full vigilance of 2-Oc (Jupiter opposition)

[Note: from here on the dates are based on 4 Ahau 8 Zotz] 11.15.6.15.10 entering of 2-Oc 11.15.6.16.10 ending of 9-Oc (adjustment made.) 10.7.0.12.10 peak moment for 9-Oc

8.18.14.8.10 the name of Bolon-Yocteil given to Jupiter, as well as a home in the sky. Gregorian date: July 3 of 4,716 BCE (1,550 years before the beginning of the calendar of

Ahaukatunes (3,166 BCE); 1,602 years before the theoretical invention of the “Long Count” (3,114 BCE.) What we have done here can be carried out for other planets. We have found that, supposing that Mayans christened with prehistoric names, then they may have also given each of them the number “9,” officially meaning “Bolon-Ti-K’u,” Lord of the Night. [N.B.HH: also meaning literally “nine-here-nested.” The nine figures on the walls of the tomb at Palenque were designated “Lords of the Night” by archaeologists in the 1950’s as a theoretical speculation.] Each time we resume our study of the Codices of Mayan sages we cannot but admire their grandeur, still unrecognized today as being the apex of all other civilizations in remote antiquity. H.M.Calderón, Mexico, D.F., September 01, 1990. [translation and editorial notes by H.Harleston, jr., / 2008, recognizing the genius of don Hector whose acuity demonstrated his profound immersement in Mayan truths.] DISK: AA-07T2-HMC.DOC // HH // 23-IV-08 // p.39

Section VI, Appendix 2, p.40 Archaeological Architecture

ADDITIONAL BIBLIOGRAPHY

ACOSTA, JORGE (and personal communications) 1964 El Palacio de Quetzalpapalotl, INAH, drawings: Manuel Gaitan, Mexico City CHAMBERS, DAVID W.

1965 “Did the Mayans know the Metonic cycle?” ISIS, Vol.56, 3, p.348, Historical. CALDERON, HECTOR M. (and personal communications) 1962 Clave Fonética de los Jeroglifícos Mayas, Ed.Orion, Mexico, D.F. DE NICOLAS, ANTONIO T. (and personal communications) 1976 Meditations Through the Rig Veda, Shambhala, Boulder, Colo. DE WHITT, MITZI (and personal communications) 2004 Aristoxenus’s Ghost, XLibris, Philadelphia, Penna. 2005 Nearly All and Almost Everything, XLibris, Philadelphia. 2006 Gurdjieff, String Theory, Music. XLibris, Philadelphia. FRAZER, JAMES GEORGE 1960 The Golden Bough, Macmillan Co., New York. FULLER, R. BUCKMINSTER (and personal communications)

1975 Synergetics I, Macmillan Co., New York. 1979 Synergetics II, Macmillan Co., New York.

GRANET, MARCEL 1934 Le Pensée Chinoise, Ed.Albin Michel, Paris, (English translation “Chinese Thoughts,”) pp.173-229 on Chinese numbers, e.g. 144, 189 = 378 / 2, etc.

HAGENS, BETHE (and personal communications) 2008 Comparative drawings Egyptian Zodiac, Louvre, Paris and Aztec (Toltec)

calendar wheel – stone carving, Mexico City. HAMMOND, NORMAN (and personal communications)

1986 “The Emergence of Mayan Civilization,” Sc.Amer., Vol.255, No.2, New York. LAWLOR, ROBERT. 1982 Sacred Geometry, Thames & Hudson, Ltd., London. LEE, THOMAS (and personal communications) 1985 Los Códices Mayas, Ed.Commemorativa, Aniversario, Univ.Autón.Chiapas. MARQUINA, IGNACIO (and personal communications) 1928 Estudio Arquitectónico Comparativo de los Monumentos Arqueológicos de México, Talleres Gráficos de la Nación, Mexico, D.F. para contribuir al XXIII Congreso de Americanistas, SEP. MCCLAIN, ERNEST G. (and personal communications)

1976 The Myth of Invariance (Origin of the Gods, Mathematics and Music from the Rig Vedas to Plato,) Nicolas Hays, Ltd., New York

1977 The Pythagorean Plato (Prelude to the Song Itself,) Nicolas Hays, Ltd.N.Y. 1980 Meditations Through the Quran (Tonal Images in an Oral Culture.) Nicolas

Hays, Inc., York Beach, Maine. DISK: AA-07T2-HMC.DOC // HH // 04-VIII-08 // p.40 (reviewed 01-IX-08)

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