MAYAN TREASURE:
Space and Time Unified at Teotihuacan
RESEARCH SUMMARY: 1971--2006
by Hugh Harleston, Jr.
> SECTION V: 2005 <
Was 9! the Mathematical Base of Mexico’s Great Pyramids?
[Posted www.harleston13.com – 2006]
MAP OF TEOTIHUACAN IN STD. UNITS OF 1.0594(6) METERS
Data sources:
(1) Teotihuacan Map/Univ.of Rochester/U.of Texas Press; (2) Interamerican Geodesic Services (IAGS), Mexico City; (3) Secretaria de la Defensa, Mexico; (4) Defense Mapping Agency, Washington,D.C. via
IAGS-Mexico; (5) Aerial Mapping, Comision de Estudios de los Territorios Nacionales (CETENAL,) Mexico, D.F., 1974 -1998.
ii
SECTION V – FURTHER CORRELATIONS
INDEX
Map of Teotihuacan in Standard Units of 1.0594(6) m.
Map—Detailed, 1974 & 1984 data with corrections
Index
Introduction
Part 1: Mathematical Design Base was 9-factorial?
Supplemental Geodetic Sources
Tabulations 1 & 2: Space-Time Factors of 9!
Figure 1. Plumed Shells Mural: 1,512 & Venus Counts
ii
iii
iv
v
1
3
4
5
Part 2: Prime Numbers (recognized: 1974 to 2005)
Factorial Limits
Tabulation 3: Prime Numbers as dimensional factors
6
7
8
Part 3: Mayan Decimals?
Multiples of 17,280 vague years. Factors of 25,920
9
10
Part 4: Redundancy Cubed; Triangular Numbers
Fig.2 – The “Citadel” – 1984
Overlapping Numbers
Fig.2A – Map 2, 1984 with notes 2005
11
12
13
13A
Part 5: Vertical Visions: Measured Heights
“Sun” pyramid: Jupiter Numbers
“Moon” pyramid: Jupiter, Saturn, Eclipse numbers
Multidimensional Awareness
Figure 3: the “Moon” 630 B.C. to 216 B.C.?
14
15
17
18
19
Part 6: Conclusions
Predictions
Planned Future Research
Beyond the Speed of Light
20
22
23
24
iv
SECTION V - INTRODUCTION
The definition of “research” can be to investigate thoroughly,
reexamine carefully, revise accepted theories in the light of new facts.
It can also mean to study again, and again,… and still again. Italian
philosopher Benedetto Croce said that an artist sees the landscape; the
rest of us surmise what it ought to be. Marcel Proust tells us that a real
journey of discovery is not new landscapes, but having new eyes.
This section presents conclusions applied to data accumulated in and related to the Valley of Teotihuacan. Three basic attitudes were experienced: physical, that stores evidence of the senses; emotional, that
observes sentiments generated by contact with the site itself and with
colleagues whose paths were shared; intellectual associations, thoughts
evolving like rotating kaleidoscopes. There can be a mixture of two or
more kinds of experience.
These mixtures generated Section V of Mayan Treasure, that includes
mathematical correlations, new research possibilities and an invitation
to consider Mayan contributions to replace obsolete speculative
theories. The value of seeing differing viewpoints is that they can reveal
some of the limitations in today’s assumptions with respect to scientific
measurements and interpretations of art.
This may open new doorways. As Cousineau tells us, mythology is to
religion as mathematics is to physics. Both mythology and mathematics
use technical languages that access realms that cannot be described in
everyday language. This project has taught me to follow Emerson’s
dictum, “Adopt the pace of nature: her secret is patience.”
Emerson encouraged me to relive findings of the 1940’s, 1970’s and the
new millennium. This led to a better understanding of unexpected
correlations that evolved at “nature’s pace.” It is my hope that the
suggestions assembled here will bear fruit for other researchers.
Hugh Harleston, Jr.
Tijuana, B.C., Mexico
20 November 2005.
v
SECTION V – Part 1
TEOTIHUACAN’S MATHEMATICAL BASELINE*
In August, 2005 I found a Mayan milestone, a marker on the road to unified space
and time. The marker: a mathematical “factorial,” the product of all positive
whole numbers from the number one to a selected number.
Factorial three, symbolized by 3!, is one times two times three, equal to the number
six. If we continue multiplying, factorial five is the number one hundred twenty.
5! is one times two times three times four times five.
A number can mean whatever is assigned to it. If it’s minutes, then 120 is two
hours. Worldwide agreement is to make our clocks move sixty seconds per minute
and sixty minutes per hour. This holds true if we continue to agree.
If a value is assigned to a piece of ceramic or stone used as the ruler for laying out
the Great Pyramids at Teotihuacan, then 120 rulers will be a precision model of
earth’s polar diameter, reduced one hundred thousand times. If a sphere is divided
into twenty equal surface triangles, these can be subdivided into only six smaller
triangles, each curved like a child’s balloon. The triangles are not duplicates. Sixty
of them have to be bent backwards to fit over the others.
If we use Teotihuacan’s rod each smaller triangle has an area of six times seven
times nine. If the units assigned are earth revolutions --“days” -- the area of each
triangle counts the reappearance of the planet Saturn overhead in the sky in almost
the same place after six times seven times nine: 378 days.
Mayan vision does not end here. A great Quadrangle was built, with sides of six
times seven times nine Mayan STU. Six of these sides measure the length from
north to south of the rectangle that defines the Monumental Zone area, a rectangle
whose width is two Great Squares. The area that archaeologists call “Ceremonial
Zone” covers twelve squares, shown by what could be renamed the Quadrangle of
Saturn. Mayans combined space and time measures. Teotihuacan’s Monumental
Zone measures two by six Saturn orbits, seen from earth. That’s nearly 192 square
city blocks, two million square meters, or 475 English acres.
Wonder grew when it was found that twenty times six orbits of Saturn equals the
number for the surface area of the earth model. But then, twenty earth model
areas become a number that measures the planet’s volume in cubic units.
-- 1 -*Also see A Mayan Milestone, website http://earthmatrix.com/harleston/index.html, 31/aug/2005
[edited 10-VIII-2006]
Harleston
Teotihuacan’s Mathematical Baseline
Even more impressive: that volume divided by six is the number of days in four
hundred orbits of Saturn. Each time period of 400 Saturns, registered on carved
Mayan stones called stelae, is equal to one hundred walks around the Great
Quadrangle of Saturn. Each walk is four times 378: one thousand five hundred
and twelve STU. This number, in Mayan bar-and-dot code, is sculpted on the wall
of a Teotihuacan mural in the chamber beneath a multi-columned patio assigned a
speculative Aztec name by last century’s restorers: Palace of the Quetzal Butterfly.
(see Fig.1, p.5 below, “Plumed Shells” mural, its numbers made visible.)
What does this have to do with factorials? The study of Teotihuacan’s architecture
confirms that the mathematical basis for Mayan measurements of space and time
given by the dimensions of the Great Pyramidal Zone, a time-count model of our
solar system, was probably factorial 9! …namely: 362,880
Or, in Mayan format: 36 288 0
Our solar system, like life itself, is a mathematical game played by Hunab Ku,
Giver of Unified Measurement. Teotihuacan is a monument to mathematical
truths that unify Space and Time, as well as truths beyond space and time.
In order to reach this conclusion thousands of conversions were made to map the
“Ceremonial Zone” in Standard Teotihuacan Units (see p.ii, above.) The first
technical paper (September, 1974,) confirmed there are repeating distances. Of 127
factors of 9! tested, 56 are principal dimensions. Tabulations 1 and 2 (p.4) present
some of these statistics. All twelve dates of Mayan Long Counts for the spaced 4,800
Saturn orbits are linked to five counts of factorial nine: 1,814,400 days. In Mayan
format: 18 144 00. Underlines show STU dimensions marked at Teotihuacan.
Registered Mayan Long counts are whole numbers that can produce the six-digit
factorial 9! They also fit higher values of factorials. This supports the conjecture
that 9! was the mathematical base for Teotihuacan’s architecture.
Page 3 is an explanation of map accuracies, a summary of salient points in Mayan
Treasure.
Students are invited to review the construction of a Mayan
Multidimensional Matrix (Section III, Part 4, pp.12-14.) The map of Teotihuacan
(1998) in Standard Teotihuacan Units (STU) of 1.0594(6)…meters, was redrawn
from data accumulated between 1974 and 1998. The majority of these dimensions
appeared in the Sept. 1974 technical paper (listed under Section I, p.23, A
Mathematical Analysis of Teotihuacan, Bibliography. Also see p.iii, with map, above,
in this Section.)
=0000=o=0000=o=0000=o=0000=o=0000=o=0000=
-- 2 –
Harleston
Teotihuacan’s Mathematical Baseline – Supplemental Clarification
The Mayan Treasure Project is research of dimensional data published between 1974 and
2006. Principal parameters of measurements at Teotihuacan were presented in A Mathematical Analysis of Teotihuacan, 1974, with minor corrections in subsequent publications.
It is pertinent that topographical maps made by Mexican Government Survey Studies were
machine-corrected from aerial photographs (scale 1:50,000.) Linear dimensions on the
Teotihuacan high plateau are shown plus or minus 50 centimeters.
Rounding of these data obeyed my policy of not exceeding the accuracy of the maps. Field
confirmations were made with steel tape, and defined in many cases by cut stone
dimensions, including smaller sculptures that give the base unit of measure: one meter,
5.94(6) centimeters, or namely 1.0594(6) meters ( = 3.476 feet.)
The data included maps made by the Mexican Defense Ministry on a scale of 1:2,000 that
present contour lines for elevations plus or minus 50 centimeters. These maps were
obtained from the Interamerican Geodesic Service (IAGS) in Mexico City. The IAGS also
provided geographical coordinates from U.S. Defense Mapping sources, Washington, D.C.,
for the bronze plate on the southwest corner of the fifth body of the largest pyramid,
assigned the name of “Sun” pyramid by the Mexican Institute of Anthropology and History
(I.N.A.H.) Naming has been Aztec (the Nahuatl language,) not Mayan.
Coordinates were corrected by steel tape measurements to the center of the sixth “body,” a
formless lump of stones and mortar refilled by I.N.A.H. It was not possible to define the
sixth structure, although paintings by Mexican professional J.Velasco had in the 19th
century demonstrated that there were six stages, not four. Corrected coordinates were
published in a technical paper I presented in 1976 at the Congress of Americanists in Paris,
France, to define the center of the Great Pyramid with an accuracy of plus or minus 0.08
seconds of an arc Latitude and Longitude: viz., North Latitude 19 degrees-41 minutes30.8285 seconds; West Longitude 98 degrees-50 minutes-35.8122 seconds. (See Section I,
Bibliography, A Probable Geodesic… System…Tepoztlan, Harleston, et al, 1976, Note 9, p.8.)
The center is defined within plus or minus 2.5 meters. Coordinates published by the
Official Map (Rochester Univ./University of Texas Press, 1973) are N.19d-41m-30s and
W.98d-50m-30s, obtained by graphical approximation without GPS. They show a point
that lies 25 meters to the south and 179 meters east of the vertical centerpoint of the Great
Pyramid. Even today GPS for civilians does not permit the accuracy enjoyed by the
Defense Departments of Mexico and the U.S.A.
These notes emphasize that the mathematical model of the Ceremonial Zone is supported
by evidence in stone and by reliable data that has not been arbitrarily molded by subjective
thinking. Comparison with data from Greece, Egypt and nine other world locations has
borne out the conjecture that in the remote past a high technology civilization could have
been a reality on this planet. Students are invited to evaluate correlations in Mayan
Treasure with critical review.
Hugh Harleston, Jr.
Tijuana, B.C., Mexico, November, 2005 [edited 10-august-2006]
-- 3 --
Harleston
Teotihuacan’s Mathematical Baseline
TABULATION 1.
FACTORS OF 9-FACTORIAL
TABULATION 2.
FACTORS OF (5) x 9-FACTORIAL
362,880
1,814,400
Space and Orbital Counts
Counts of 400 Saturns
Divisor
Factor
Divisor
2
3
4
8
16
18
20
24
36
48
63
72
96
181,440
120,960
90,720
45,360
22,680
20,160
18,144
15,120
10,080
7,560
5,760
5,040
3,780
126
144
162
189
216
252
360
378
504
720
756
1,512
2,268
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
Factor
Long Count
Multiplier x 9-factorial
2,880
2,520
2,240
1,920
1,680
1,440
1,008
960
720
504
480
240
160
12.12.0.0.0
11.11.0.0.0
10.10.0.0.0
9. 9.0.0.0
8. 8.0.0.0
7. 7.0.0.0
6. 6.0.0.0
5. 5.0.0.0
4. 4.0.0.0
3. 3.0.0.0
2. 2.0.0.0
1. 1.0.0.0
---
5
55/12
25/6
15/4
10/3
35/12
5/2
25/12
5/3
5/4
5/6
5/12
---
x
x
x
x
x
x
x
x
x
x
x
x
9!
9!
9!
9!
9!
9!
9!
9!
9!
9!
9!
9!
---
NOTES: Tabulation 1.
(1) Thirteen relatively small dimensions and thirteen larger dimensions
selected as divisors, are significant repeating modules given in the
“Ceremonial Zone.” (2) All divisors are Teotihuacan’s dimensions in
STU of 1.0594(6) meters (3) Factors include 1/10th of earth’s scale model volume; model area of 45,360 sq. STU; 1/10th the time in days for
12 counts of 400 Saturn orbits; Jupiter’s synodic orbital count (720 x
399 = 287,280 days) to cross one-third of the Zodiacal circle; and onetenth the day-count (151,200 days) for 400 Saturn orbits of 378 days.
NOTES: Tabulation 2.
(1) Twelve time counts, multiples of 400 Saturns (151,200 days,) are
whole number factors of five times 9!, or 1,814,400 days, which is also
10! divided by two. (2) We see here the same values for each Long
Count. The first number is multiplied by a Baktun of 144,000 days; the
second number by a Katun of 7,200 days) shown in tabulation Fig.5,
p.16 of Mayan Treasure, Section I, April 12, 2000. This correlation was
recognized Sept.1, 2005 [edited 10-august-2006.]
-4–
Fig. 1
Mural named “Plumed Shells”
Palace of “Quetzalpapalotl” - Teotihuacan
Four sets of bars and dots of 378 are 1,512,
the perimeter of the Great Quadrangle of Saturn
-- 5 --
SECTION V – Part 2
PRIME NUMBERS AND FACTORIAL LIMITS
My first technical paper (A Mathematical Analysis of Teotihuacan (1974,
Bibliography, Section I, p.23)--presented a theoretical map that registered prime
numbers in four orientations. Some of these primes appear in Tabulation 3.
Publication (1984) of The Keystone corrected minor errors in the 1974 map.
It
was important to see that four western platforms of the “Citadel” were centered on
108 STU. These platforms were spaced 54 STU center-to-center, a total of 162 STU
(3x54,) a measure shown also at the Great Pyramid and the “Moon” pyramid.
The sequence 108—162—108 (= 378) suggests a Mayan expression: “OX PAK,” that
means “between two numbers,” or “doubles.” Three 54’s becomes “OX-MUK” or
“OX-P’EL” meaning “tripled.” Another example is at the “Moon” pyramid, with its
first adosado, each 8 STU (a Jupiter orbital corrector) vertically, a triple 8—8—8.
This led to a series of Mayan words that define positions of similar quantities, to be
detailed in Section VI, 2006, with reasons why a reexamination needs to be made of
the Maya-Quiché sacred book – the Popol Vuh – that may reveal why current
theories describing “mythological twins” are only partly acceptable. The book was
translated by specialists who apparently ignored Mayan mathematics and
astronomical wisdom, not to mention the Mayan passion for multiple meanings.
The Popol Vuh is a combination of both kinds of knowledge. A limited vision can
convert mythology into religion, and overlook mathematics that explain
astronomical physics. I propose that a corrective translation may demonstrate this.
H. M. Calderon found that the Chilam Balam of Chumayel, classified by others as a
semi-mythological work, was in reality a three-level star register, that not only
presents a second-level problem but on a third level provides solutions with Mayan
synonyms recognized by Calderon. The text reveals double and triple meanings.
Domingo Martinez Paredez explained double meanings of words pointing to nonverbal realities as well as to astronomical events such as solar and lunar eclipses,
that were registered with high precision in the Mayan Dresden Codex.
The importance of the prime “59” is that this factor is required for the first eclipse
count of 9,204 days = 59 x 13 x 12 = 177 x 52. The second count is 1,424 days = 16 x
89 = 178 x 8, or a sum of (177 + 1) x 8. The third count is 36 x 37 = 1,332 days, the
distance in STU from the center of the Great Pyramid to the south side of the last
wall, lying 18 STU beyond the “Citadel’s” apparent termination. The 1 STU wall
was excavated in 1986, ten years after I made a map based on soundings registered
in the ‘60’s [edited 10-august-2006.]
6
Harleston
Prime Numbers and Factorial Limits
Triple eclipse counts are the elapsed days between repeating eclipses. They sum
11,960 days, a count also found by multiplying 520 by 23, another prime number.
The distance from the E/W centerline of the Great Pyramid to pyramidal ruins that
are on the Avenue, partly restored in the ‘60’s, is 520 STU. The spacing of 177 STU,
or 3 x 59, is given by the eight platforms in the Citadel. A repeat use of the prime is
also shown at the west side of the Citadel: 207 + 324 = 531 = 9 x 59.
Mayans registered eclipse counts in the Dresden Codex. They show multiples of 177
days (59 x 3) as well as 148 days (4 x 37) a distance marked by the first wall crossing
the Solar Avenue. The crosswall at that distance is 8 STU wide, so that the north
edge marks 144 STU and the southern edge marks 152 STU, a “Jupiter” number,
because it is 8 x 19. The only planet that requires the number “19” has a seenfrom-earth orbit (the synodic) of 399 days: 21 x 19.
The exact Jupiter synodic orbit was known to Mayans by waiting 8 orbits before
subtracting one day. Division by 8 of [(8 x 399) – 1] = 3,191 / 8 = 398.875 days.
Jupiter returns now in 398.877 days. We are indebted to H.M.Calderon for
deducing this and finding the table for Jupiter in the Dresden Codex. We are also
grateful to Daniel Flores of UNAM-Astronomy Institute for modern corrected
orbits, both synodic and sidereal, of all the planets. We can now safely say that
exhibitions of 8 STU may be reminders of the “Jupiter Number.”
Factorial Limits
For increasing values of factorials beyond 16! it is conjectured that Mayans were
able to handle any factorial, since their art and sculptures present the number
“1,512” (Fig.1, p.5, Part 1, above) equal to four sides of the “Quadrangle of Saturn”
of 378 STU. 1,512 can be a divisor for any number that is larger than 8-factorial.
It is possible that Mayans handled any desired prime. They could arrive at its value
by repeated additions.
Mayan dimensions illustrate the use of multipliers that identify significant primes
(e.g., 23, 29, 31, 37, 41, 43, 53, 59…) until 208 solar triple eclipses of 11,960 days are
recognized as the motif of the four-paneled patio of Teotihuacan’s Palace of Falcons
(“Quetzalpapalotl”?) whose product of 2,487,680 days = (4 x 52) x (23 x 520.) Divided
by 6! x 9 x 13 (which is 720 x 117, i.e., the Jupiter orbital multiplier and the preColumbian value of Mercury’s synodic orbit) we get 29.5308642:
29.5308642...
the moon’s synodic orbit, carved in stone at Palenque as 81 Moons are 6 Tun, 11
Uinal, 12 K’in = 2,160+220+12 = 2,392 days; 2,392 / 81 = 29.5308642… Registered in
the Dresden Codex; 405 moons are 11,960 days: 29.5308642 days per reappearance.
[edited 10-august-2006]
7
Harleston
Prime Numbers and Factorial Limits
TABULATION 3
Selected Prime Numbers in Teotihuacan Dimensions – STU, from the 1974 map
NORTH TO SOUTH
111
126
135
150
162
189
243
135
215
1125
=
=
=
=
=
=
=
=
=
=
3 X 37
3 X 42
3 X 45
3 X 50
3 X 54
3 X 63
3 X 81
5 X 27
5 X 21
5 X 225
NORTH TO SOUTH
343
504
66
396
693
195
936
207
87
558
=
=
=
=
=
=
=
=
=
=
7 X 49
7 X 72
11 X 6
11 X 36
11 X 63
13 X 15
13 X 72
23 X 9
29 X 3
31 X 18
NORTH TO SOUTH
111
148
222
1332
86
129
282
472
1314
801
=
=
=
=
=
=
=
=
=
=
37 X 3
37 X 4
37 X 6
37 X 36
43 X 2
43 X 3
47 X 6*
59 X 8**
73 X 18
89 X 9
NOTES: Spacing of three eastern platforms in the Citadel, each 22 sq. STU, from
N. to S. is 141—96--141 =378 STU. Average distance of earth orbit to the
sun is 141.4 millionKSTU, the square root of 2x100. Orbit diameter is the
square root of 8 = 282.8 million KSTU. 282 = 6x47 perhaps a coincidence
perhaps not. If earth orbit were 96 STU, then Mercury =36; Venus is 72;
Mars 144; Asteroids 288; Jupiter 520; Saturn 945; Uranus=1845; Neptune
is 2880; Pluto is 3780 (“Citadel” dimensions, plus N. to Cerro Gordo.)
[edited 10-august-2006]
**Note the eclipse multiplier times 8 is given by the centerline of the fourth
wall south of the Great Pyramid E/W centerline: 472 STU = 8 x 59.
Selected Prime Numbers in Teotihuacan Dimensions – South to North (1974)
396 = 11 x 36; 989 = (19 x 52) + 1; 207 = 23 x 9; 1184 = 37 x 32;
1332 = 37x36; 639 = 71x9; 774 = 43x18; 860 = 43x20; 531 = 59x9
Prime Numbers – East to West
48 = 3 x 16; 72 = 3 x 24; 108 = 3 x 36;
225 = 3 x 75; 225 = 5 x 45; 378 = 7 x 54;
231 = 11 x21; 222 = 37 x6; 333 = 37 x 9.
West to East (1974 map)
3 x 42 = 126; 3 x 54 = 162;
3 x 48 = 144; 3 x 63 = 189;
13 x 9 = 117; 23 x 9 = 207.
Reference Map is Fig.5-A, p.28A, A Mathematical Analysis of Teotihuacan, by Hugh
Harleston, Jr., Sept. 1974, presented at the XLI Congress of Americanists, Mexico
City. Deposited Library of Congress, Washington, D.C. and Fondren Library, Rice
University, Houston, Texas. Also see Harleston, H., Jr., The Keystone: A Search for
Understanding, Character Composition, Bellaire, TX, 1984, pp,123, deposited
Library of Congress, LOCCN 88-117575 and Fondren Library, Rice University.
8
Section V – Part 3
MAYAN DECIMALS?
A frontier research project rejects presuming to “know.”
If the universe were
known there would be no speculative research. We conjecture that some time in the
past at Teotihuacan there were several Balam, illuminated wise persons, on the
order of a Davinci, an Einstein, or a Newton (a DEN of jaguars,) personifying the
noble characteristic of innate valor, the courage to be that which it is, a human born
free of fear. We believe there also were X’Balam: intelligent evolved women.
Their inherited mathematical capacities could have been beyond belief. Such
savants could talk among themselves but not with others, not with beings whose
genetics, prejudices or preparation deny them access to the rarified atmosphere of
specialized numerical relationships.
Mayan formats suggest that the use of decimals could have been top secret
information. In the past it was customary to assume that the only rudimentary
mathematics that Mayans “must have known” was multiplications by the number
“20.” This image was generated by ignorant invaders of Mexico who, like Goebbels
under Hitler, bragged that the bigger the lie, the more the masses would believe it.
An example of modern belief is that the number 1,814,400 is seen as one million,
eight hundred fourteen thousand, four hundred. This has been created by pedagogical sophistry. 1,814,000 can also be written eighteen – one hundred forty-four –
zero zero: 18—144—00. A number like 362,880 (= 9!) can be expressed by first
one thousand Tuns of 360 days; i.e., 360,000. We add two thousand, and obtain
the sum: 362,000. Next we add 800, and finally 80. The total becomes 362,880.
There is no reason not to show 36—288—0; i.e., thirty-six, two eighty-eight zero.
There are STU dimensions that show us 36 & 288. There are 36-spoke wheels.
An intriguing correlation: the Platonic “Year” is 12 cycles of 2,160 years. But
which “year”? Was it a Mayan Haab, the count of 365 earth revolutions = “days?”
Astronomers call this a “vague” year. The product of 365 x 25,920 is 9,460,800
days. This can be 94—60—80—zero. Two-thirds of the cycle = 6,307,200 days =
17,280 vague years. A British cubic foot is 1,728 cubic inches, 12 cubed. The
day-count time period can be said to read 63—zero—72—zero zero.
Some ancient sources believed this was the time between planetary disasters. If that
were the case the last destruction or change of earth’s surface may have been 17,280
years before 2,137 A.D. The date becomes 15,143 BCE, a possible great flood. But
it could have been an evolutionary transformation, a planetary “uncovering” of
new psychic capacities of humanity. A “universal” flood may have been confined
to the “known” world of antiquity. The surprise is when we look at multiples:
[edited – 10-august – 2006]
9
Harleston
Mayan Decimals?
___17,280 “years”__
x (365) = 63 0 72 00
Multiples (days)___
x 2 = 126 144 00
x 3 = 189 216 00
x 4 = 252 288 00
x 5 = 315 360 00
x 6 = 378 432 00
Major parameters of STU dimensions at Teotihuacan are now visible. This tells us
that ancient memories could have been mythologized as time periods in code, and do
not necessarily refer to “planetary disasters”at all. Was this methodology to transmit mathematical relationships that could have other truths to express? Factors of
the Platonic “Year” can give us new “eyes” for the same landscape:
FACTORS OF 25,920
36 x 720
48 x 540
96 x 270
216 x 120
288 x 90 ___ (see drawing Parthenon Section III)
72 x 360
144 x 180
576 x 45 ___”Citadel” – platforms 24x24 STU
2160 x 12 ___“Tunnel” under Mexico’s Pyramid
2880 x 9 ___ Elevation atop Cerro Gordo in STU
4320 x 6 ___ Life of Brahma / Creation Number
6480 x 4 ___ (see drawing Parthenon Section III)
The first five are the basic design parameters compared with the Parthenon in
Section III (cf. Part 3, p.7 & pp.20-22.) To these dimensions add the number “6,”
the basic “creation number,” (as in “six days…”) The second set of three factors
are given, as well as the multipliers in the right-hand column, in the “Citadel.” The
last four numbers are Pythagorean Diatonic Units (Athens, p.22, Part 3, Section III.)
Question: “Did the Pythagoreans have access to secret mathematical information
independently transmitted to Mayans via differing routes of genetic inheritance?”
It is well known that a Pythagorean was sworn to secrecy on pain of death by
suicide if any coded secret knowledge were made public. Was this the case in, say,
630 B.C., probable date of the first (the “Moon”) pyramid, Long Count 6.6.0.0.0?
Other examples suggest the possibility that Mayan architects incorporated a
knowledge of decimals. Long Counts (7,200--144.000—1,872,000…) are multiples of
ten, 100, 1000. The format illustrated above (17,280 “years”) indicates a possible
code to handle sequenced decimal numbers in their monumental designs. Our
future research will be looking into this question.
[edited 10-august-2006]
10
Section V – Part 4
REDUNDANCY CUBED
In Section I, 2002 repeating dimensions were pointed out: 144, 162, 216 and the
major parameters: 378, 756 and 936 (see map, p.ii, above.) Section II, 2003 shows
that a basic key number 1,512 repeats as a factor 36 times as a count of universal
spheres in “numerical arks.” The repeating use of 3 and 9 as factors for planetary
synodic orbital counts also appears in Section I.
In 2004, Sect. III presents additional repeating dimensions: 231, 288, 312, 462 -- as
factors of factorials up to 16! There are only two platforms 18 by 18 STU as well
as two 20 by 20 STU.
Archaeologist S. Sugiyama excavated the first square
structure at the baseline level inside the “Moon” pyramid. It was 21 by 21 STU, the
Jupiter multiplier (21 x 19 = 399.)
Mayans had words that mean a triangular presentation. Others show a number
between “twin” numbers. See the “Citadel,” Fig.2, below, (also see Sect.III, Part 3,
p.10) A number between twin numbers is the sequence 108—162—108 = 378 STU,
the spacing of the four western platforms. 351 STU east of zero reference are three
platforms, each 22 STU square. The spacing between the centers of the platforms is
the sequence 141—96—141 = 378, marked in green to enhance those numbers.
At 228 STU east of the zero reference line, another twin number in the patio width
of 222 STU was marked: 81—60—81 = 222.
To illustrate a triangular presentation, on my 1984 drawing the inner patio of 222
STU has a staircase on its western wall that measures 30 STU. The sequence here is
96 –30 --96. The three eastern platforms mentioned above are separated by 96 STU.
A triangle is formed: 96—96—96 whose sum is 288. The “Citadel’s” north, south
and east walls are 72 STU, whose sum is 216.
These combinations were not seen when dimensions were mapped in the 1970’s
and 80’s. Triangular numbers were recognized Oct., 2005 when a search began
with dimensions recorded at locations other than the Citadel. On the “Sun” pyramid, there are three staircases: two on the 2nd body (height 15 STU) each with 49
steps, and one on the 5th body (height 9 STU) with also 49 steps.
When outer characteristics were damaged by reckless removal of material by
Leopoldo Batres in 1906 to 1909, the southern staircase was patched without today’s
archaeological restoration procedures. It appears that the southern staircase was
guesswork. By the time the fifth body was conserved, Batres retained its staircase
at 49 steps over the inclined face. The other, twin staircase is obviously guesswork.
[edited 10-august-2006.]
11
Harleston
Redundancy Cubed
The title for this part of Section V has been selected to show that triple combinations
repeat, but are not necessarily superfluous. Further triple combinations are at the
“Moon” pyramid. The main body has three heights combined: 11, 12 and 9 STU.
The first two total 23, the eclipse multiplier. Plus 9 = 32 STU, the number 2 multiplied by itself four times (two to the fifth power.) To the south, three additions are
each 8 STU in height, a triple number, 24 STU vertically, 8—8—8. We see 32
behind 24 behind 16, and a front staircase of 48 steps, each one-third STU (35.3 cm.)
The second addition is five bodies totaling 16 STU. It seems significant that there
are only two principal heights of 16 STU: the pyramid in the “Citadel” with six
bodies, and the add-on at the “Moon,” described here. If this information comes
from an ancient high technological civilization, then other correlations surface.
Oxygen can transmute to sulfur, at the atomic level. O2 is atomic weight 32, two
O-16’s. This splits to two atomic oxygens, that recombine at the nanocapillary level
in the human body to Sulfur-32. This is not alchemy. It is recent modern science
speaking to us, suggesting that we might be able to use non-verbal disciplines for
transcendental contact with beyond-the-speed-of-light consciousness.
There are overlapping numbers that add to the same sum. The 1984 drawing in
Section III, Part 3, p.11, is repeated below as Fig.2A, p.13A. At the “Moon”
pyramid’s vertical centerpoint, the distance from the north limit is 216 STU. This
is followed by 288 STU, formed by three demarcations of 96 (the same triple
number in the “Citadel,” mentioned above.) From there to the next demarcation is
also 216 STU. This overlapping design shows us 216 + 288 = 504, that repeats as
288 + 216 also equals 504. However, “504” times ten has nothing to do with “Plato’s
favorite number.” It has everything to do with 7! = 720 x 7.
720 STU is the spacing between the two largest pyramids, today named in Aztec as
“Moon” and “Sun.” Here is a double-overlapping design. The sum of 216 + 504 =
720; and from the north limit to the E/W centerline of the “Plaza of the Columns,”
is 432 + 288 = 720. Let’s look again and see that 288 STU defines the centerpoint of
the “Moon” pyramid to the E/W centerline of the “South Complex,” west of the
auditorium (now unused) for visitors to see a Light and Sound Show in times gone
by, surrounded by shops with tourist trinkets today.
The intricacy of the Mayan design is indeed stunning. There are other overlapping
configurations, but now let’s move on to other vertical correlations in Part 5.
13
Section V – Part 5
VERTICAL VISIONS
19thcenturyMexican professional painter Jose M. Velasco was internationally recognized for his painstaking realism. His paintings of plants were used for teaching
classes in botany. His landscape* of the Teotihuacan Valley, painted at age 38 in
1878, was to become a national treasure in Mexico’s Museum of Modern Art. It
clearly confirms that the grass-covered man-made “hill” was built with six stages.
20th century archaeological speculators tried to show that the Great Pyramid had
only four bodies. Let’s remember Benedetto Croce: the artist sees the landscape;
the rest of us surmise what the landscape ought to be. That fourth body has its own
history. Let’s go back to 1906-1910.
When Batres saw his error in trying to destroy a supposed covering on the first
three bodies (evidenced by remains of “buttresses” seven meters, three meters, and
on the third body a meter thick,) he mortared the fourth and fifth stages in place,
to make sure original stone overlay was conserved. Somebody later imagined that
the fourth stage “must have had” a giant “talud and tablero” built atop it. A
graduate thesis proved that the addition would have collapsed under its own weight.
Later opinions cited Velasco but it is clear today’s observations were subjective, not
what was there in 1878. Archaeologist Evelyn Rattray went into the tunnel on the
east side of the fifth body and turned south. She found inside the structure, on Teotihuacan north/south, an inclined wall that had the same angle as the exterior fourth
stage. At that time, it had not been established that Teotihuacan’s design was commemorating repeating mathematical relationships with Mayan dimensions.
Below is a photograph (Fig.3) of the first pyramid, “Moon,” possibly started 630
B.C., Mayan Saturn count six: 6.6.0.0.0, 12 Ahau, 18 Mol, tabulated Section I, p.16.
Five bodies are on the 1984 drawing, Fig.12, The Keystone. It is unmistakeable that
the fourth body is the same configuration as inside the 5th body, the Great Pyramid,
confirmed by Rattray’s work. Based on this, I predict (see Part 6, below) that a
similar structure could be found inside the “Moon.”
Mayan dimensions were neither haphazard nor irrational. A reexamination was
made of vertical measurements. First the “Sun” pyramid may have been dedicated to Jupiter and Hunab Ku. The zeroth level is under the structure at 2,160
STU above sea level, established by surveyors’ contour maps. The slightly inclined
floorline is at 2,288.4 meters. Above it, outside is an apparent base, at 2,166 STU,
and is not approximate. Excavation (1980’s) proved an original mortared floor
was eveled at 2,294.8 meters = 2,166 STU.
*Published in Nov./Dec. 2005 issue of Archaeology, under 100 Years of Excavation at Teotihuacan.
[edited 10-august-2006]
14
Harleston
Vertical Visions (contd)
The first body may be one-third underground and two-thirds above, total 18 STU.
Only 12 STU are visible. Three theoretical corners have not yet been explored.
The next body height is 15 STU if original material were replaced. The staircase has
69 steps, 3x23. The 3rd body is 12 STU, with two staircases, each with 49 steps. They
suggest that on ascending the north side, plus repeating the same count on the fifth
body, the total is 98, marking the days of Venus’ disappearance in front and behind
the Sun, a count Mayans used even though they knew that it has variations. As
Morning and Evening star Venus counts 486 days, a significant number: 6x81 (see
Sect.III, Part 6A, pp.23, footnote (4) re relation of this number to Egyptian design.)
On descending from above 49 steps are followed by 49 on the south staircase, this
time representing the years in three triple solar eclipses, counts also given by
dimensions in the “Citadel” (Part 2, p.6-7.) On the fifth body, 9 STU in height, 49
steps suggest: 9x49 = 441, which is 21 squared. “21” is the Jupiter/Saturn lag time,
7 times 3, two basic multipliers found in sacred texts worldwide.
The third body height of 12 STU generates: 12 x 49, equal to 588. This, too,
“contains” the Jupiter/Saturn key to orbital separations, as the product of 21 times
28 also equals 588. The number of falcon profiles on the columns of the
“Quetzalpapalotl” Palace are precisely 28, the days in a stellar constellation month.
13 constellations are a circle of 364 days, a Mayan stellar year, commemorated at
Chichen Itzá by four staircases having 91 steps per side on the pyramid.
At the fourth body, there is an apparent paradox. This stage is six STU high,
divided into 4 STU below and 2 STU above. The ascent, however, is 3 STU in
eleven steep steps, obliging us to turn and go up at an angle towards the south. As
we cross over the other 3 STU the staircase only has nine steps. They seem to be
easier, due to the lower ascent angle.
In reality, they are larger. Here mental habits can make us imagine that we are
using less energy. But my body, turning north to angle up the nine steps can sense
that there is a special message on these twenty steps. The message seems to be that
by being aware of the experience another dimension has been added to the
intellectual count being shared with myself as I ascend. The fourth body is a
reminder of the Mayan multidimensional multiplier: the number “20.” As
mentioned, the fifth stage is at a new angle, and has 49 steps = 7 x 7, seven squared.
In 1947 the 6th body was a formless mass, with grass growing over a semi-excavated
hole at its center. The material could have formed a platform 18 by 18 STU by 3
STU high. That would make it the third platform this size, with one in the
“Citadel” patio, a second to the south of the “Moon” pyramid, a ceremonial room
[edited 10-august-2006]
15
Harleston
Vertical Visions (contd.)
with nine altars (see Fig.3, below,) partly reconstructed in the 1960’s. Its roof was
supported by a statue 3 STU in height, called in Aztec a “Moon Water Goddess,”
whose head had sculpted rectangles, like bricks to support a ceiling. There was no
tenth altar, even though the archaeologists created one out of entirely new material.
But a building 19 meters across, over three meters high, requires a support in the
center or it falls down. That support was moved to the old museum by Batres.
Let’s follow the vertical sequence of the Great Pyramid’s bodies: 6 below, then
12—15—12, then 6—9—3 STU. I laid those verticals out in 1974, shown in detail in
The Keystone in 1984. Multiplications were intriguing:
180 times 12 = 2,160;
then, times 6 = 12,960 …
12 times 15 = 180;
a number seen in Egypt: around the world in Geographic Cubits = 129,600,000.
Next 6 x 9 = 54; 54 x 3 = 162; 12,960 x 9 = 116,640; 3 times 116,640 = 349,920.
And 349,920 = 108 x 108 x 30; = 144 x 30 x 81; = 162 x 216 x 10; = 405 x 864;
that is, a square 216 STU per side. Is this marked below the Great Pyramid?
Perhaps Mayans decided to leave underground in the mind of the observer.
Mayan logic lets us see that from the zero reference to the top of the sixth body is
3+6+9+12+15+18 = 63 STU. The top would have been at level 2,223 STU, and the
summit was said to have had a legendary building that might have been 9 STU, the
number of Hunab Ku. Total height would have been 9x8=72 STU at elevation 2,232
STU. The terrain drops by 9 STU, so at the Citadel the patio elevation is 2,151 STU
above sea level, and the No.3 pyramid’s rooftop would have been at 2,172 STU.
The overall vertical design would have been 81 STU: nine times nine:
9x9
Let’s now review the factors of 2,232 = 2,160 + 72, total elevation of the Great Pyramid: 2 x 2 x 558 = 4 x 18 x 31 = 72 x 31. We are convinced this was planned, not
chance. The prime number “31” appears elsewhere. But it is also connected to our
anatomy: there are 248 bones to support the body’s architecture, i.e., 8 x 31; there
are 31 double nerve connections at the central nervous system, i.e., 62, a Mayan dimensional factor on the Solar Way. If there had been a high civilizations on the
planet in the remote past, this type of information could have been transmitted
through genetics to any and all survivors of any and all planetary disasters.
What about the reconstructed “Moon” pyramid?” Original drawings of profiles
were given to me by Archaeologist Ponciano Salazar, who was in charge of the
1960’s restoration. Published in Mysteries of the Mexican Pyramids, 1976, p.246
they show that lines used by Salazar and Jorge Acosta followed stonework evidence.
16
Harleston
Vertical Visions (contd.)
Dimensions were close to actual field measurements in the files of I.N.A.H., Mexico
City. Logical correlations suggest that the 2nd adosado on the pyramid could be 49
STU wide (7x7) instead of 50, possibly due to the 1964 rebuild having an excess of
mortar across the staircase, almost 52 meters (49.1 STU) east to west.
Initial construction of the “Moon” is still undated. The five-body pyramid (Fig.3) is
at a base level of 2,181 STU above sea level, checked against the best maps. The
first body height, 11 STU (final construction,) was estimated by official archaeology
to be approximately 200 B.C. My Fig.5-Section I, Tabulation dates 7.7.0.0.0 – 9
Ahau, 8 Mac as July of 216 B.C.E.
The second stage, 12 STU, totals 23, the eclipse multiplier: 23 x 520 = 11,960 days,
three consecutive eclipses. The third stage was a vertical 9 STU, a total of 32 STU
at elevation 2,213 STU. Multiplication of 11 x 12 = 132, a number repeated at the
“Sun” and in the “Citadel,” to mark the vertical centerpoint of the No. 3 pyramid.
The next stage is the fourth body, a configuration that reappears on the “Sun”
pyramid. It is 6 STU in height, divided into 4 STU and then 2 STU. The angles of
the 2nd and 3rd stages (E to W) give the maximum elongation of the planet Venus: 47
degrees with respect to a sightline to the sun from our orbit. The angle whose
tangent is 1.05946, twelfth root of the number 2, is 46.65 degrees.
Above is the 5th stage, 4 STU high. The sequence is 11—12—9—6—4, ending at
elevation 2,219 STU. These total 42 STU, versus the Great Pyramid at 63. In the
“Citadel” the pyramid was 16+5 = 21 STU. The three largest structures express the
first triad of Jupiter/Saturn lag times: 21, 42, 63 days: with planned architecture.
Every combination is a dimension at Teotihuacan. Example: 9 x 11 = 99. There
are 99 moons during 8 earth vague years, or 5 Venus cycles of 584 days. Mayans
used this frequently. On the columns of the “Quetzalpapalotl” Palace are feathers
showing nines and elevens. Remember 9 and 11 steps on the 4th body of the “Sun?”
Additional planning: 12x11x9 = 1,188 = 11 x 108; then 1,188 x 6 = 7,128 = 33 x 216;
Every
then 4 x 7,128 = 28,512 = 32 x 891 = (8+8+8+8) x (9x99) or 16 x 2 x 11 x 81.
underlined number is an STU dimension, many repeating in four basic areas: the
“Moon,” “Sun”, “Citadel,” a “Street of the Dead” that perhaps was a “Solar Way.”
More Mayan logic. The summit of the “Moon” becomes elevation 2,223 STU to
match the “Sun” pyramid 414 years later (see p.15.) I propose there was a triple
building in three sections, rectangular, height 3 STU, bringing the elevation to 2,226
or six STU below a future Great Pyramid. The factors are: 6 x 7 x 53, a prime seen
[edited 10-august-2006]
17
Harleston
Vertical Visions (contd.)
elsewhere. 6 x 7 = 42 to reconfirm the five-body height, a multiple of the Jupiter/
/Saturn lag time of 21 days.
Topography and drawings of fallen stone pieces at the “Moon” plaza were carried
out by Geodecist Alfonso Rangel R., later forced to move from the high plateau of
Mexico to Durango, for reasons of heart problems that eventually ended his stay on
this planet. He informed me that original staircases up the “Moon” pyramid’s
south face were wider at the top, traced out by archaeological remains.
He tried to have the archaeologists use guide ropes and rebuild the staircases with
the original design. Perspective would have caused the lines to appear parallel as
the distance became greater. His request was ignored. Instead straight-line guide
strings were used. Superior Mayan engineering was obliterated. I hope later
(Section VI, 2006) to detail Rangel’s work at Tepeapulco.
He believed, as I do,
that Mayans knew how to calculate the azimuth angle for Venus at maximum
elongation, and placed stone field markers after calculating their locations.
Another subtlety: when standing on the 20 by 20 STU platform, 192 STU south of
the “Moon’s” center, I observed the southern face of the pyramid. I knew that the
staircase height is 16 STU. Behind it are three 8-STU bodies (Fig.3) for a
proportion 24 to 16, or three-halves. My eyes, however, and the illusion of
perspective, told me that the relationship of the triple-bodied first adosado to the 5bodied second adosado seemed to be a proportion of 5 to 4. Which should it be?
A strange feeling invaded my divided mental state. A different awareness of my
awareness answered: “Both answers are correct.” Did Mayans know this? I believe that they did.
A third checkpoint is No.3 pyramid in the “Citadel”. Foundation footprints on the
sixth body established the top building’s design. The elevation was 2,172 STU, lying
60 STU below the “Sun.” 60 STU, a logical number: one side of the pyramid itself.
The area of its base is 60 x 60 = 3600 square STU, 3,600 synodic orbits of Saturn
that, on the tabulation of the 400’s counts 1,360,800 days = 60 x 60 x 378, to mark
9.9.0.0.0—3 Ahau, 3 Dzootz, i.e., June 11, 613 A.D. Perhaps some day an engraved
stelae will be found at the Citadel with this inscription.
If not found, then researchers may find columns that have vertical designs from
below to above that count 9, then 9, then blank, blank, blank. Columns at the
“Quetzalpapalotl” Palace (Falcon Patio) have designs that count from bottom
upwards 7, then 7, then blank, blank, blank. That tells us: July of 216 B.C.E.
[edited 10-august-2006]
18
Figure 3
The misnamed “Moon Pyramid,” the first construction at Teotihuacan,
oriented NE to SW, possibly for observation of circumpolar stars. The
final structure had five principal bodies, an addition (1st “Adosado”)
with three stages each 8 STU in height, and a 2nd “Adosado” of five
bodies with total height 16 STU. The staircase has 48-steps, each 1/3rd
STU high. In front, the 9-altar building 18 by 18 STU was 3 STU high.
The main body was 144 STU– E/W, 128 STU- N/S = 2 to the 7th power.
Aerial photo by Cheryl Harleston
19
SECTION V – Part 6
CONCLUSIONS
(1.) The Mayan mathematical space and time baseline of the Great Pyramids of
Mexico at Teotihuacan could be “factorial nine”: 9! = 36 288 0 in Mayan format,
or 362,880 in modern display. 1 x 2 x 3… x 9 = 9! Mayan Long Count 9! is
2.10.8.0.0. There could be stelae bearing this or its multiples (see Predictions.)
Five times nine factorial is 18 144 00. Conventional display is 1,814,400; i.e., twelve
cycles of 400 Saturns (151,200 days,) registered as Long Count 1.1.0.0.0; namely,
one Baktun (Niktekatun) of 144,000 days multiplied by twelve; added to one Katun of
7,200 days multiplied by twelve; plus zero counts of 360 (one Tun,) zero counts of 20
(one Uinal,) zero K’in (one day.)
12 x 151,200 = 1,814,400 = 4800 x 378.
(2.) Modern units of length, time and angular rotation are limited. They were
apparently not selected as numerical values that can be used for both space and
time. Mayans, on the other hand, exhibited multidimensional concepts.
(3.) Structures at Teotihuacan are at precision elevations above mean sea level,
confirmed by modern maps. This could be Mayan knowhow, or inherited from a
previous civilization whose knowledge was conserved genetically or by tradition.
(4.) A scale model of earth reduced 100,000 to one has an averaged circumference of
378 STU = 6x7x9. A rotating earth deforms to an oblate spheroid of axial diameter
12 million STU. This is universal for any sphere assigned an axis of 12 million units.
(5.) Mayan measurements are defined by whole number factors of factorials beyond
16! A significant factor is four sides of the “Citadel,” each 378 STU, perimeter of
1,512. (See p.5, Part 1, “Plumed Shells” mural, which registers this key number.)
(6.) Multidimensional relationships require an intentionally inexact value of Pi :
= (9x7) / (5x4) = 63/20 = 3.15. The mathematical ratio Circumference / Diameter is
irrational and generates irrational products. Designs at Teotihuacan repeat 3.15.
(7.) Five repeating numbers in the Teotihuacan design are 288, 48, 216, 96, 36, all
divisible by “6”; hence, there are six basic numbers. The fact that natural logarithmic base e = 2.718281828… raised to the power 12th root of the number 2 =
1.059463094… produces the number 2.88482169636… leads to the conjecture that
Mayans could have known exponentials, and handled advanced mathematics.
(8.) Three universal geometric configurations encoded in the numerical/dimensional
design of Teotihuacan are:
20
Harleston
Conclusions (contd.)
(a) A sphere of diameter 6 and radius 3, with area and volume expressed by the
same rational number: 113.4 = 3x6x7x9 / 2x5 = 1134 /10.
(b) A cube with sides of 6. Square Area and Cubic Volume are 216.
(c) A regular tetrahedron of height 12 has sides the square root of 216, its apothem the square root of 162. Its vertex will be the square root of 8; and its
height = 2 x 6. The area and volume are 216 times the square root of 3.
All underlined numbers are dimensions displayed at Teotihuacan in STU.
(9.) 24 factors of 25,920 (p.10, Part 3) as well as 2, 7 & 25,920 itself, are factors of
factorial nine. Perhaps Pythagoreans and Plato knew more about factorials than
heretofore suspected. What was the source that proclaimed “25,920” as “Plato’s
Great Year,” a time-count of reverse rotation of the polar axis of earth, said to be
25,920 “years” (of ?? days?) Conjecture: it was 365 days, the vague year.
(10) Based on the significance at Teotihuacan of the twelfth root of the number two,
the dogmatic division of light into seven colors is questionable. The wave lengths
covered by human sight are approximately 3,600 (violet light) to 7,200 (red light)
Angstrom units; i.e., 36 to 72 millionths of a meter. This can be defined by six bands
(no indigo or dark purple is necessary) separated by the factor 1.0594(6) squared;
that is, 1.122(46)… A rainbow has six colors: red, orange, yellow, green, blue and
violet, equally spaced from invisible infra-red to invisible ultra-violet wave lengths.
Was “indigo” invented to match traditions of seven “virtues,” seven “sins,” seven
“heavens,” seven “pillars of wisdom,” seven “sisters,” ...and other mythologies?
(11) Section V studied Mayan concepts of twins (108-162-108), doubles (96–96),
(216-216,) triads (72–72–72), triples (8-8-8), overlapping numbers (720 = A+B =
B+A); repeats are in four zones. Add: mirror numbers (81–18, or 21–12, or 13–31),
and triplets (111, 222, 333,…) Mayan languages have synonyms to show their
breadth of thinking. An example is a mirror volume is the half-platform under the
Falcon Patio, which measures 3 by 6 STU by 1 STU high, against a wall, originally
mirror-surfaced with black obsidian. Reflection gives the complete volume and
numbers, shown by single and double oscillating circles (see Section II, Fig.20, p.28,
a reflecting telescope in a camara oscura.) Numbers include 4,536 (Jupiter/Saturn
conjunctions) and 45,360 (area of a spherical earth model reduced 100,000 times.)
(12) Part 5 demonstrates that vertical dimensions were selected by Mayans to show
multiples that repeat significant parameters.
These supplement the cubic
redundancy of Part 4. Magnificent interpenetration of highly complex concepts has
been woven by Mayan Halach, bearers of cosmic double truths.
21
SECTION V – Part 6
PREDICTIONS
1.) Internal overlays in the “Moon” pyramid should reveal a dating method to
define a beginning at 6.6.0.0.0 = July, 630 B.C.E. and completion of the third
overlay: July of 216 B.C.E., seventh cycle of 400 Saturns. If similar to designs in
“Quetzalpapalotl” Palace there can be columns that read from below upward: six
figures, six figures, zero, zero, zero. “Zero” can be horizontal strips of stone left
blank, as on existing columns: 7.7.zero, zero, zero.
2.) For a day-count of 9! of 362,880 days the Mayan Long Count is 2.10.8.0.0. Five
counts during the Oxlahkatun that began Sept.13, 3,114 B.C. could mark dates*:
2.10.8.0.0 (= 26 March-2,120 B.C.E.;) then 5.0.16.0.0 (= 07 October-1,127 B.C.E.;)
7.11.4.0.0 (= 19 April-133 B.C.E.;) 10.1.12.0.0 (= 31 October-861 A.D.;) and finally
12.12.0.0.0 (= 13 May-1855 A.D.,) marked with a secret ceremony by survivors.
Stelae should be found showing either 2.10.8.0.0 and/or the count of the dates in
question. These are: 5.0.16.0.0. = 725,760 days; 7.11.4.0.0. = 1,088,640 days;
10.1.12.0.0 = 1,451,520 days; and = 12.12.0.0.0, = 1,814,400 days, five counts of
factorial 9! The 9! count of 362,880 days is 993 solar years plus 195 days.
Conjecture: in the “Moon” pyramid there can be a legend or indication of 133 B.C.
The pyramid would have been finished for inauguration in 216 B.C.; 83 years later
a commemoration was held for the third anniversary of the factorial count. The
next Saturn ceremony would have been 8.8.0.0.0, June of 199 A.D., perhaps
inaugurating the Great Pyramid’s completion.
Excavations in the “Citadel” could reveal Mayan dating of a Saturn ceremony:
9.9.0.0.0, June, 613 A.D., a date registered at Palenque and Copan. Conjecture:
that Teotihuacan was still operating in the 7th century. Dates in southeast Mexico
indicate a strong wave of recognition of the mathematical prowess at stake. The
next 9! date was not until the 9th century: 861 A.D. Stelae should be found at
Edzna, Copan and perhaps Mayapan with 10.1.12.0.0. A Saturn ceremony, held at
Edzna in June, 1,027 A.D. (10.10.0.0.0) reinstated the use of the 13 Katun count of
93,600 days, and a stelae was erected. This was a well-known event.
Researchers are invited to test these conjectures, that new finds could confirm or
deny. Dates that might be found on older stelae would be for the earliest Saturn
commemorations; i.e., -2,700, -2,286, -1,872, -1,458, and -1,044 B.C.E. (see
tabulation in Section I, p.16, Fig.5.) Early material is scarce. This could take years.
[edited 10-august-2066]
*(chronological constant 584,314 by H.M.Calderon, replaces the erroneous MGT of 584,283 that was
appropriated from Martinez & Goodman by E.Thompson)
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Harleston
Predictions (contd.)
Prediction: there should be evidence that a special ceremonial celebration in
southeast Mexico commemorated the twelfth cycle of 400 Saturns. The approximate
date would have been May 11, 1,855 A.D., the day of zenital crossing near Latitude
17°North, with participation in locations that included Naranjo (Belice,) Lago Petén,
Yachilan and Piedras Negras, Guatemala. Also to be checked by historians are
Ocosingo and Tonina, Chiapas; Mitla and Monte Alban, Oaxaca; plus Juxtlahuaca,
Guerrero. The sacred ceremony was probably kept a secret, but the magnitude of
the event may have been given a publicly acceptable explanation by Mayans.
3.) Eventually there may be confirmation from Greece and Egypt that link the
correlations of Jupiter/Saturn conjunctions (every 7,182 days) as well as to tie the
information to architectural designs at Athens and Karnak. Recognition of
correlated data in India, China and other ancient sites could serve to stimulate more
research for whole-number relationships, instead of conventional attempts that use
rounding, decimal approximations, or speculative astronomical theories. The
numbers should be exactly the same and mathematically on sound footing.
FUTURE RESEARCH
Topics planned for investigation in Section VI – 2006:
1.) Mayan vocabulary shows triangular numbers and twin numbers, as well as
expressions that indicate that a revision by experts of the translations of the
Popol Vuh should confirm that encoded mathematical and astronomical data
suggest new interpretations of messages left by Halach.
2.) Detailed examination of the work of A.Rangel on alignments of marked
stones at Tepeapulco, and also his topography at Teotihuacan, explains why
the Great Avenue or Solar Way (now named “Street of the Dead”) was
oriented 15°-28’ East of astronomical North. The Great Pyramid and western streets are on 16°-34’/106°-34’, one more degree east. Rangel found
multiple marked alignments at Tepeapulco, a site for “measuring the year”
(Xihuingo in Nahuatl ) that fall on 47°, maximum elongation of Venus.
3.) Examples from squared columns of the Falcon Patio (“Quetzalpapalotl”) to
show dating was 7.7.0.0.0 = July, 216 B.C.E. Examples to be presented of
how geometrical designs are Jupiter counts.
4.) Details of calculations, with Mayan logic, of theoretical structures at the
baseline of the original “Moon” pyramid, and alternate stone overlay data.
Confirmation should appear as the internal excavations are made public.
[edited 10 – august – 2006]
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Harleston
Planned Future Research (contd.)
5.) Theoretical reconstruction of the buildings atop the summits of the three
major pyramids, using Mayan logic and data from Palenque and Chichen
Itza that could indicate the basis for architectural spacings.
6.) Conjecture: the hydrogen fines constant is a quantum ratio of 3700 / 27 =
137.037037037… based on dimensional presentations at Teotihuacan of
factors of 37 related to factors of 27, with many examples. Why does experimental physics not find this constant is a whole number value?
7.) A possible method of encoding decimals and long factorials into the design,
utilizing remainders of significant prime numbers given by Mayan
architecture. Mayans were proficient in decimals. Did they inherit
knowhow that was kept confidential? Multiple displays show ratios of 3.15
for Pi and 1.05 = Pi / 3; hence, other displays might be correlated.
8.) Identify Mayan formats for long factorials; e.g., 18!, 21!, 23!, 29!, 37!, 73!…
9.) Conjecture; relating m-v / m-o (particle mass at velocity v near the speed of
light as compared to rest mass m-o) shows a whole number increase to twice,
then 3 times, then jumps to 1,872 at near light speed. Mass values have been
found to be related to the sine of the vector angle of the velocity to the speed
of light. The basic Mayan design at Teotihuacan is 2 x 936 = 1,872. Was the
speed of m-v 99.9999857% of the speed of light, possibly confirmed by recent
RHIC high energy experiments with gold atoms? (see Riordan/Zajc, Sci.Am.,
Vol.294, No.5, May, 2006, pp.34A-41.)
Show calculations of August, 1976 were shared with three other researchers.
[edited 10 – august – 2006]
Hugh Harleston, Jr.
Tijuana, B.C., Mexico
May 5, 2006
24
Harleston
BEYOND THE SPEED OF LIGHT
…On the 100th anniversary of its publication in June 1905 by Einstein, a Columbia
University physics professor said “…when Einstein realized mass and energy were
convertible, getting the exact formula to relate them was a fairly basic exercise, requiring only high school algebra. His genius was not in the math; it was his ability to see
beyond centuries of misunderstanding and recognize that there was a connection
between mass and energy at all.”
Interrelated disciplines are the foundation needed to recognize that not only had
Mayans designed the 192-cityblock central zone of Teotihuacan, but also that they
knew more advanced mathematics than assumed previously. Mayans were dealing
with unknowns and unknowables, with words and concepts that moderns have long
ago forgotten to see as possibilities that humans will never be able to phrase with
sound nor calculate with a mysterious language of numbers.
Some of these relationships are described by Rumi, Rilke and Ramana Maharshi.
Others were taught by Gurdjieff and Krishnamurti. Myths were unraveled by Campbell and Santayana. Unanswerable questions were asked by Magueijo and Suarez,
provoking still more unanswerable interrogations.
Why do we believe that faster-than-the-speed-of-light does not exist today, yet has
been declared existent thirteen billion earth orbits in the past ? Are we unable to
accept that an unimaginable, not-of-this-world, multidimensional, tachyonic field is
another name for “consciousness”?
We cannot define in words and equations what Mayans call Hunab Ku: an unpronounceable, unknowable supreme being, giver of movement, measurement and love.
It is not forbidden to admit that we shall never be able to communicate this. Whoever has experienced contact with above-the-speed-of-light consciousness may recognize when another person has lived something similar, through whatever multipresent faculties that other person might possess.
Something is amiss with measuring units that have been certified for us to use. After
thousands of conversions of lengths measured in French meters, we can see that the
builders of Teotihuacan had their own “meter.” It became clear that measures of time,
that Mayans observed as blobs of light returning to a point in the sky, can, with appropriate corrections, permit predicting what will be seen in future skies. Mayans
followed celestial travelers with small corrections and high precision.
25
Harleston
BEYOND THE SPEED OF LIGHT
We found that when there is no reason that a circle having an arbitrary number of
divisions in Egypt is the way to go in Mexico, and that it’s possible to use an arbitrary
value for circles-to-diameters to show how the same numbers define space, time and
rotation. With this, we invite students who recognize hidden assumptions of moderns
to turn off their cell phone and turn on micro-cell intuition via organic threads
carrying messages inside the human body.
European invaders spent three centuries trying to sell the world that the peoples of
America were vicious, violent imbeciles, inferior to those fanatics who operated in a
context of false concepts with respect to unproved beliefs. One of the products of this
is the mindset of traditional authorities with respect to individuals who see contradictions in dogmatic proclamations.
Blind obedience is not obligatory with respect to a theory that is founded in confirmations of some of its tenets. A “Big Bang” produced from an infinitely small origin
could be visualized as “a tachyonic ‘point’… It becomes increasingly more difficult to
raise an objection to certified speculations, so we ask: how can we keep talking about
what happened 13 billion years ago, as if we were there?
In 2003 the sun was declared to be a liquid, not gaseous as previously assumed. This
is a radical change in perspective. In 2005 high energy physicists accepted a “soup of
gluons and quarks” as being a liquid and not a gas. It has been declared that the temperature of the universe is 3 degrees Kelvin. Do we really know this?
It was found that there is a mathematical relationship between the vector angle on
approaching the speed of light and the particle’s mass at the velocity being traveled.
It is possible that whole number values reach angular significance when the velocity
causes the rest mass to grow to 2 to 1, next 3 to 1, then to 1,872 to one, a highly significant dimension in Teotihuacan’s Ceremonial Zone. This conjecture is pending more
research to see if theory will be supported by evidence.
A tantalizing question: were Mayans cognizant of a multidimensional transmission of
beyond-the-speed-of-light energy? Beyond,… not “faster.” Could it be that conscience, outside our four-dimensional conventional universe, transferred itself to geniuses
freed from distortion by virtue of their dedication to disciplines of
self-awareness;…that is, to silent presence, to “dark energy”?
If frequent unanswerable questions are asked the effect on dormant parts of our neuronic systems might be that of leading us closer to objective answers.
26
Harleston
BEYOND THE SPEED OF LIGHT
A Zen master stopped after brush-painting a flat circle, triangle and square.
Mayan Halach expanded awareness of universal spheres, tetrahedrons and cubes,
then took us soaring skyward, beyond light, in a multidimensional, silent matrix:
A mirrored awareness.
Hugh Harleston, Jr. ©2006
Section V - Finis
27