## Introduction – Age of Tiwanaku

Posnansky calculated the age of Tiwanaku in the following manner,

“it has been noted that when the observer stands at the center of the west wall of Kalasasaya of the Second Period, the north and south pillars of the east wall are so located that the **sun would rise at the solstices on the outer corners of these pillars.** Also approximately at the center of the building, let us say at the middle of the monumental perron, the** sun appears on the morning of the equinoxes.**

Now then: if, at the solstices, one observes the sunrise without the aid of instruments, it will be noted that it does indeed still come up on the corners of these pillars. However,** if we examine this phenomenon with precision instruments, we note a difference of approximately eighteen angular minutes**, which represents the change in the obliquity of the ecliptic between that of the period in which Kalasasaya was built and that which it has today. **This difference has served as the basis for the calculation of the age of Tihuanacu.** From what has been discussed in previous chapters, there is not the least doubt that **this building was indeed built on the astronomic meridian and its angles were the points marked exactly by the amplitude of the sun between the solstices.** These few introductory words will explain to the reader in a summary fashion how the basis for calculating the probable age of Tihuanacu was obtained. However, in practice, the question is not as simple as the foregoing lines might indicate.

The aforementioned difference of eighteen angular minutes noted in Kalasasaya is the basis for our calculations and this coefficient was applied to a curve constituted on the basis of the formula of extrapolation recommended by the Ephemeris Conference of Paris in the year 1911 and which is as follows:

eps (t) = 23° 27′ 8.26″ – 468.44″ t – 0.60″ t2 + 1.83″ t3

If this curve should vary with future studies and trials in the coming centuries of exact astronomy, then the calculation in regard to the age of Tihuanacu would also vary. However, in any event, even leaving aside the calculation by astronomical methods,** the age of Tihuanacu, a figure somewhere beyond ten thousand years** (the age of the Second and Third periods) will always be, on the basis of geology, paleontology and anthropology, very great — no matter by what method or standard it is judged.”

*A satellite photo of Kalasasaya compound with superimposed sight lines showing the positions for calculating the solstice sight lines described by Posnansky.*

Source: http://www.atlantisbolivia.org/tiwanaku.htm

Thus it is that looking today from the observation point toward the northeast corner of **Kalasasaya**, there is an elevation of 2° 47′ and toward the southeast corner one of 0° 16′. In the long space which separates us from the construction of the Second Period of Tihuanacu, which is presumed to be, as will be shown later, from ten to fourteen thousand years, there were, in our opinion, definite tectonic movements and alluvial accumulations which undoubtedly could have changed the topography of the high plateau. On the subject of tectonic changes, we presented a paper in 1931 before the Twenty-third International Congress of Americanists meeting in New York City entitled *“La remoción del cíngulo climatérico como factor del despueble del Altiplano y la decadencia de su alta cultura”*.

On the basis of the explanations set down in that work, we presume that when they planned to construct Kalasasaya, there was perhaps an almost free horizon to the east. But in the case that the present hills extended toward the east at the time of the Second Period, they still could have constructed the temple in the same place in an exact mathematical manner, in the following way. With a sight similar to the one described above — in a temporary observatory near Tihuanacu — (for example the already mentioned one of Lukurmata or one on an island in the lake where to the east there would have existed an apparently free horizon) they would make note of the solar amplitude and mark the angle on the metallic plate underneath the sight.

Later, on the spot where they wished to construct the “east wall”, they would determine the line of the meridian and from the middle of this line they would strike a perpendicular. At the distance that they believed fitting for the size of the building they would set on the perpendicular line the observation point, and on it the sight with the angle of amplitude brought from the temporary observatory, and they would prolong the sides of the angle until they struck the line of the meridian. Of course, previously they would have divided the angle of solar amplitude in the middle and then would proceed in the manner described above for the plan of **Kalasasaya**.

Carrying out this operation, as without doubt they must have done, the people of Tihuanacu were the first to observe the obliquity of the ecliptic. Thus, without question, Kalasasaya must have been constructed, using one or the other of the systems which we have studied and described. Kalasasaya being divided longitudinally into equal parts and, of course, also the angle of solar amplitude, they believed likewise that they had divided the year into four equal parts. This belief proved to be erroneous and later they had to rectify it, as we shall see subsequently when we consider the great monolithic perron which, in the east wall, gives access to the Temple of the Sun.

After various careful triangulations carried out in the interior of the great enclosure of Kalasasaya, we discovered that the angles of its four corners were not completely right at the present time. Those of the southeast and northwest are somewhat acute while those of the northeast and southwest are slightly obtuse. We transcribe herewith the measurements of these angles made by Professor **Arnold Kohlschütter**, Dr. **Rolf Müller** and the author.

**Angles of the Corners of Kalasasaya**

Southwest |
Southeast |
Northeast |
Northwest |
Observer |

90° 19′ | ——- | ——- | ——- | Müller |

90° 29′ | 89° 29′ | 90° 27′ | 89° 36′ | Kohlschütter |

90° 19′ | 89° 37′ 13″ | 90° 20′ 41″ | 89° 43′ 5″ | Posnansky |

The lack of rectitude in these angles causes the east wall not to be orientated on the meridian at the present time and gives it a deviation of 1° 1′ 30″; that of the west shows a deviation of 1° 6′ 30″. The north and south walls, instead of being orientated mathematically in a north-south direction, show deviations. The north wall shows a deviation of 40′ and the south 42′. The verification of the German Mission is as follows:

South Wall |
West Wall |
North Wall |
East Wall |
Observer |

89° 24′ | 358° 55′ | 89° 20′ | 358° 53′ | Kohlschütter-Becker |

89° 12′ | 358° 52′ | ——- | 359° 4′ | Müller-Posnansky |

89° 18′ | 358° 53′ 30″ | 89° 20′ | 358° 58′ 30″ | AVERAGE |

**Dr. Müller** believes that this small deviation with the resultant lack of absolute rectitude in the angles was intentional and he gives the basis for his opinion in his aforementioned work (*Baesler-Archiv*).

As far as we are concerned,** we believe that Kalasasaya in its time was correctly and mathematically orientated, not only with relation to the meridian but in the angles of the corners of the building and that it is not a question of any error on the part of those conscientious, prehistoric architects and astronomers.** — Source: http://www.bibliotecapleyades.net/arqueologia/tiahuanaco/posnansky5.htm

Read more about **extremely old age of the Tiwanacu and Puma Punku >>**

## Pre-Columbian Calendar of South America

**The Gate of the Sun from ancient Tiwanacu and Cracking the Muisca Calendar**

*by Jim Allen*

*Copyright Jim Allen, Presented with permission of the author.*

### Muisca Calendar – Background

*Gate of the Sun as it appeared to George Squier, 1877.*

The **Muisca were a pre-Columbian people** who lived in the territory now known as Columbia in South America.

In 1795, Dr **Jose Domingo Duquesne**, a priest of the church of Gachancipa in Columbia published a paper detailing the **Muisca calendar**, which information he claimed to have received from the Indians themselves. His paper was later ridiculed as being nothing but an invention of his.

Yet the figures given by Duquesne do in fact relate to** a lunar calendar** although Duquesne himself may not have fully understood the workings of it since it seems possible that** the calendar was more sophisticated than might appear at first glance**, and **two types of lunar month** may have been used, the Sidereal Lunar Month when the moon returns to the same position relative to the stars (27.32 days) and the Synodic Month which is the period between full moon and full moon (29.53 days).

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At **Tiwanaku** we found how the **solar year was divided into 20 months of 18 days and also interlocked with the Inca calendar of 12 sidereal lunar months of 27.32 days** (making 328 days) so that 3 x solar years also equalled 40 sidereal lunar months and the **two calendars came together every 18 solar years which equalled 20 Inca years** when the cycle started all over again (also known as the Saros Cycle).

**Jose Domingo Duquesne**

At first difficult to read and understand, Duquesne’s *(shortcut to Wikipedia info about Duquesne)* paper begins with a background about the Americas and the Egyptians and how the Muiscas counted by their fingers with names for each number up to ten, and then on to twenty. He then relates their calendar to harvesting and sowing and begins:

*El año constaba de veinte lunas, y el siglo de veinte años* (the year consisted of twenty moons, and the century of twenty years) then goes on to relate this to lunar phases and harvests.

The first thought on reading this, was that as at Tiwanaku, they might have **divided the Solar Year into twenty for their months**, but the text implies that** 20 lunar months made the year and it also implies that Synodic or phase months were intended.** This year of twenty months he tells us was called a** “Zocam” year.** Now a period of 20 x 20 months which Duquesne mentions might seem worthy of fitting into an Aztec or Mayan calendar since 20 x 20 gives 400, but further down the text, if we read closely, Duquesne says that

*“Twenty moons, then, made the year. When these were finished, they counted another twenty, and thus successively, continuing in a continuous circle until concluding twenty times twenty. The inclusion of one moon, which it is necessary to make after the thirty-sixth, so that the lunar year corresponded to the solar year, and thus they conserved the regularity of the seasons, which they did with consumate ease.”*

Now, here is a question, not of translation, but of meaning. Because a little further along, Duquesne explains how the year of 37 months was a period of 36 months plus a “deaf” month so that the year adjusts to the solar year. This year of 37 months is called an “**Acrotom” year.** He also tells us that **20 x 37 of these months corresponds to 60 of our years, divided into four parts so that each part was ten Muisca years which equalled fifteen of ours.**

From this we can easily work out that **60 of our solar years divided by 20 x 37 gives a month of 29.61 days suggesting that here, the synodic or phase month from full moon to full moon was intended** since the synodic month has an average of **29.53 days.**

*Above, the Synodic month is based upon the time taken from full moon to full moon.*

But returning to the earlier statement

*“Twenty moons, then, made the year. When these were finished, they counted another twenty, and thus succesively, continuing in a continuous circle until concluding twenty times twenty. The inclusion of one moon, which it is necessary to make after the thirty-sixth, so that the lunar year corresponded to the solar year, and thus they conserved the regularity of the seasons, which they did with consumate ease”.*

What I think is meant here, is that **they counted in twenty times twenty then added an extra month in the same manner as they added an extra month to 36 months to make 37, so the real figure here is not 20 x 20 = 400 but 20 x 20 + 1 = 401.**

There is also another difference.

I think** they were running two calendars in parallel with each other**, so the 37 month calendar was in Synodic Months of 29.53 days while the 20 month and 401 month calendar was in **Sidereal Lunar Months of 27.32 days**, although at the same time Duquesne counts the 37 month year as being 20 months + 17 months (because the counting system was based on twenties) making 37 months when the solar and lunar calender synchronised, in this instance these 20 would be synodic months the same as the 17 months and he also explains this another way, as the extra month being inserted at the end of every three lunar years so they counted two x lunar years of 12 months then one of 13 months, the thirteenth month being the “sordo” (deaf) or extra month. So after 1 x Muisca year of 37 synodic months (3 solar years), sowing would begin again on the same day in January, while the intervening two years had a system of counting the months on the fingers as Duquesne puts it…

But returning to the calendar of 20 months running continuously as 20 x 20 months with an extra month inserted to give 401 months, we can check the figure of 401 Sidereal Lunar Months to see if it relates to a solar year and 401 x 27.32 days comes to a great period of 30 Solar Years, which in turn equals 10 Muisca Acrotom years of 37 x synodic months of 29.53 days….

Every three solar years equals the Muisca “Acrotom” year of 37 Synodic Months of 29.53 days and at the same time corresponds to 40 Sidereal Lunar Months of 27.32 days, and every one and a half solar years corresponds to a “sidereal lunar year” of 20 Sidereal Lunar Months which is the true “Zocam” year of the Muiscas.

So to sum up so far,

1 x Tiwankau Solar year = 20 “months” of 18 days (using a rounded-off 360 day year divided by 20).

1 x Tiwanaku Lunar year = 12 sidereal lunar months of 27.32 days (328 days) – also used by Incas.

1 x Muisca Zocam year = 20 sidereal lunar months of 27.32 days = 1½ solar years

2 x Muisca Zocam years of 20 sidereal months of 27.32 days = 1 Muisca Acrotom year of 37 synodic months

1 x Muisca Acrotom year = 37 x synodic months of 29.53 days

1 x Muisca Acrotom year = 3 x solar years = 40 x sidereal lunar months of 27.32 days = 2 x Muisca Zocam years

½ Muisca Acrotom year = 1½ solar years = 20 x sidereal lunar months of 27.32 days = 1 x Muisca Zocam year

18 solar years = 20 Inca years = 6 x Muisca years of 37 x 29.61 days = the Saros Cycle

10 Muisca Acrotom years = 30 solar years = 401 sidereal lunar months of 27.32 days = 20 Zocam years.

20 Muisca Acrotom years = 60 solar years = 2 x 401 sidereal lunar months of 27.32 days = 40 Zocam years.

It might appear that Duquesne made an error when stating that “the ‘century’ of the Muiscas consisted of 20 intercalcated years of 37 months each, which corresponded to 60 of our years, which comprised four revolutions counted in fives, each one of which equalled ten Muisca years, and fifteen of ours until completing the twenty….”

Since 1 x Muisca year of 37 months equals 3 solar years, then 10 x Muisca years should be 30 solar years as per the table above, and since Duquesne was talking about how they counted up to twenty in periods of fives which corresponded to five fingers, what he should have said here was that each of the five was five Muisca years of 37 months equalling fifteeen of ours. But in fact he is correct except it is 10 x Sidereal lunar month years of 20 x 27.32 days which equal the fifteen solar years…..

5 Muisca Acrotom years of 37 synodic months of 29.53 days would be 15 solar years

10 Muisca Zocam years of 20 sidereal months of 27.32 days would be 15 solar years

I suspect therefore, and it is fairly clear, that the 20 month year which Duquesne called the “Zocam” year was actually the sidereal year of 20 sidereal months but the name may have mis-understood by Duquesne as a period of 20 synodic months if Duquesne were unaware of a different type of lunar month in use, otherwise there would have been little point in having years of 20 synodic months running continuously when they were actually grouped in 37 month years and by contrast 2 x 20 sidereal months mesh both with the Acrotom year and solar year at 3 year intervals and over longer periods.

To see how they compare at three year intervals,

37 synodic months of 29.53 days would be 1092.61 days

40 sidereal months of 27.32 days would be 1092.8 days

3 solar years of 365.2524 days would be 1095.72 days

Because of the small discrepancy, over long periods of time some adjustments would probably be necessary such as the extra month inserted after 400 sidereal months on the Zocam calendar making

401 sidereal months of 27.32 days = 10955.32 days

10 Muisca Acrotom years = 370 synodic months of 29.53 days = 10926 days

but if they added another month that would bring them to 10955.5 days and back into line with the Zocam sidereal lunar calendar and closer to the 30 solar years of 365.24 days = 10957.26 days

The Muisca “Acrotom” 37 month synodic month calendar with the phases of the moon was probably a more “user friendly” calendar for the man in the field, whereas the “Zocam” 20 month sidereal lunar calendar was probably of more interest to the time keeping priesthood and for bringing the other calendar into alignment periodically.

Duquesne also tell us that the Muisca “week” was a period of three days, and at face value, this would appear to have no relationship to the Muisca calendar whether using sidereal or synodic months, but then the calendar itself, in spite of Duquesne’s explanation as a usage for agriculture does not seem really practical for agriculture or at least not as practical as the Tiwanaku one but perhaps having the advantage that no construction of pillars or standing stones was required.

The calendar which is practical for agriculture is the one found at Tiwanaku where the solar year is divided by twenty and determined by the setting of the sun over a pillar, so it would be fairly easy to note the same pillar where the sun would return to each year, and this is the calendar which is easily divided into periods of three days, and period of nine days were also known to have been worked in that region.

So perhaps the Muisca also ran a solar calendar, undiscovered but in the same style as Tiwanaku, or perhaps their customs were left over from some forgotten era, based on the same mathematicas as Tiwanaku with it’s interlocking sidereal lunar calendar and counting in twenties.

* Note to advanced visitors: * Click here for the scientific dissertation

*(4 MB, PDF – slow loading)*by Manuel Arturo Izquierdo Pena:

*“The Muisca Calendar: An approximation to the timekeeping system of the ancient native people of the northeastern Andes of Colombia”.***Appendix A.1**contains (in Spanish) “

**dedicada al s. d. d. Jose Celestino de Mutis, director general de la expedicion botanica por s. m.por el d. d.**

*Disertacion sobre el Calendario de los Muyscas, Indios naturales de este nuevo reino de Granada.***Jose Domingo Duquesne de la Madrid**, cura de la iglesia de gachancipa de los mismos indios. Ano de

**1795**.

**Calendario de los Muyscas, Indios naturales del Nuevo Reino de Granada.****Return to Tiwanaku**

The Muisca calendar then, is another important piece in the jigsaw of the lost knowledge of the Andes.

If the origins of the Muisca calendar were to be found at Tiwanaku, then perhaps they were also built into the Gate of the Sun which gives the clues to the workings of the Tiwanaku calendar.

Many people have studied the icons on the Gate of the Sun at Tiwanaku and tried to relate them to a calendar. The icons are called “chasquis” or Messengers of the Gods and because there are fifteen of them on each side, some people have thought that they represented a thirty day month in a solar year of twelve months. But as explained earlier, this calendar at Tiwanku is not based upon a divison of the solar year into twelve, but into twenty, and this is represented by the eleven smaller icons forming the freize at the bottom which represents the eleven pillars on the west side of the Kalasasayo which is the actual calendar. So if you count from the central icon or pillar out to the right hand end, then back past the central icon to the left hand end, then back to the centre, you will have effectively counted in twenty divisons and followed the path of the sun over a year.

So if the chasquis do not relate to the days in whichever number of days we choose for the months of the year, could it be that the chasquis represent the years themselves?

*Top part of the “Gate of the Sun” at Tiwanaku, Bolivia*

*Above, detail of the “Gate of the Sun” at Tiwanaku, Bolivia showing the principal grouping of thirty “chasqui” figures with beneath them the freize showing eleven icons and forty condors heads arranged in two rows of twenty heads.*

If each chasqui were to represent a solar year, then each column of three chasquis would represent three revolutions of the sun around the eleven pillar calendar wall and three solar years are equivalent to 1 x Muisca Acrotom year of 37 synodic months of 29.53 days and also equivalent to 2 x Muisca Zocam years of 20 sidereal months of 27.32 days.

*Above, each Chasqui represents a Solar Year and counting in threes, then three Chasquis or years make* *1 x Acrotom year of 37 synodic lunar months or 2 x Zocam years of 20 x sidereal lunar months.*

*The freize beneath the Chasquis shows forty condor heads in two rows of twenty representing two x zocam years of 20 sidereal months and also indicating that the calendar is based upon divisions of twenty.*

There are fifteen chasquis on each side of the central figure and each block of 15 chasquis would represent fifteen solar years which would be

5 Muisca Acrotom years of 37 synodic months of 29.53 days or

10 Muisca Zocam years of 20 sidereal months of 27.32 days

*Above, the 15 Chasquis represent 15 solar years, equal to one quarter of the Muisca “Great Century” and respectively* *5 x Zocam years or 10 x Acrotom years.*

The total number of chasquis is thirty chasquis representing thirty solar years which would be

10 Muisca Acrotom years of 37 synodic months of 29.53 days or

20 Muisca Zocam years of 20 sidereal months of 27.32 days

The choice of thirty chasquis as thirty solar years is no random figure, because after thirty solar years have gone by, it becomes necessary to add one sidereal lunar month to the Muisca Zocam calendar making it 20 x 20 + 1 = 401 sidereal lunar months to bring it back into line with the solar year.

At the same time of adding one sidereal month to the Zocam sidereal calendar, it also becomes necessary to add one synodic lunar month to the Muisca Acrotom calendar making it 10 x 37 + 1 synodic lunar months to also bring it into line with both the sidereal lunar calendar and the actual solar year.

Each of the sections with fifteen chasquis corresponds to the period of fifteen solar years which Duquesne tells us was one quarter of the great “century” of the Muiscas so to sum up, each block of fifteen chasquis represents fifteen solar years which is 10 Muisca Zocam years or 5 Muisca Acrotom years, the two blocks together make 30 chasquis representing 30 solar years which is 20 Muisca Zocam years or 10 Muisca Acrotom years and 2 x the 30 chasquis gives 60 chasquis representing 60 solar years completing the great “century” of the Muiscas which was therefore, 40 Muisca Zocam years or 20 Muisca Acrotom years.

*Above, detail of the “Gate of the Sun” at Tiwanaku, Bolivia, the 30 Chasquis represent 30 Solar years,* *equal to 20 Zocam years of 20 sidereal lunar months or 10 Acrotom years of 37 synodic lunar months.* *At the end of this period, 1 x lunar month had to be added to the lunar calendars* *to bring them back into phase with the solar year..*

*Above, the “Gate of the Sun” at Tiwanaku, Bolivia, the 30 Chasquis represent 30 Solar years,* *equal to 20 Zocam years of 20 sidereal lunar months or 10 Acrotom years of 37 synodic lunar months.* *At the end of this period, 1 x lunar month had to be added to the lunar calendars* *to bring them back into phase with the solar year.* *Beneath the chasquis can be seen the freize with 11 smaller chasqui heads* *representing the 11 pillars on the calendar wall which in turn divide the solar year into* *20 months of 18 days, and the 40 condor heads represent the 40 sidereal months which mesh* *with the solar calendar every three years.*

*Above, when the sun reached the end of the pillars, it appeared to “stand still” before beginning its journey back in the opposite direction.*

**Click on the link below to view :
Tiwanaku 3 years Animated Calendar**

*Copyright Jim Allen, Presented with permission of the author.*

**More articles by Jim Allen:**

- http://www.atlantisbolivia.org/lostcalendarandes.htm
**Tiwanaku – a city lost in time****Books by Jim Allen**

Note: The above post is part of our larger article** Ancient Timekeepers, Part 4: Calendars **

## Related Links and Resources

- http://www.math.nus.edu.sg/aslaksen/teaching/heavenly.html#Calendars
- http://www.math.nus.edu.sg/aslaksen/calendar/links.html
- http://www.atlantisbolivia.org/lostcalendarandes.htm

**Archaeoastronomy: Astronomical Alignments of Ancient Structures:**

http://www.world-mysteries.com/alignments/index.htm- http://blog.world-mysteries.com/science/ancient-time-keepers-archaeoastronomy/
- http://www.world-mysteries.com/achronology.htm
- http://www.math.nus.edu.sg/aslaksen/teaching/heavenly.html
- Lost Civilizations of the Andes [ http://davidpratt.info/andes2.htm ]
- http://gigapan.org/gigapans/28209/
- When Time Began
**Very Early Calendars**- The Lunar Cycle Calendar & Moon Phases

## PS1 A critique of the analysis of the Gate of the Sun by J.M. Allen

*by Keith M. Hunter*

*Copyright 2014*

*Keith M. Hunter**Presented with permission of the author*

### PART 1

In the beginning of his evaluation Allen discusses the work of Dr Jose Domingo Duquesne from 1795, about the calendar system information passed to him from the natives. The cycles noted by Duquesne are those that Allen evaluates. And admittedly, is it difficult to reconstruct what Duquesne is saying. However, be that as it may, Allen does tie-in the solar year, sidereal month, and synodic month, in terms of their harmony, or re-synchronisation after a certain time has passed.

His first approximation, appearing to relate to the writings of Duquesne, indicates that all 3 cycles re-synchronise after about 1092.61 to 1095.72 days. Reproduced from his article, I present Allen’s connections as follows:

- 37 synodic months of 29.53 days would be 1092.61 days
- 40 sidereal months of 27.32 days would be 1092.8 days
- 3 solar years of 365.2524 days would be 1095.72 days

Now, Allen further goes on to suggest that over longer periods of time “some adjustments would probably be necessary…” This led him to propose the following, indicating greater accuracy in re-synchronisation, close to 10955.26 days:

- 401 sidereal months of 27.32 days = 10955.32 days
- 371 synodic months of 29.53 days = 10955.5 days
- 30 solar years of 365.24 days = 10957.26 days

Now let me reproduce again the above two analyses, this time using very accurate values for the solar year, sidereal month, and synodic month. The citations are as follows:

The Astronomical Almanac 2003.

Nautical Almanac Office, United States Naval Observatory, and H. M. Nautical Almanac Office, Rutherford Appleton Laboratory. (2001)

Page D2: **29.5305891 **Synodic Moon Month

Explanatory Supplement to the Astronomical Almanac.

University Science Books. (1992)

Page 701: **365.2421897** Earth Tropical Year

From this:

(365.2421897 / ((365.2421897 / 29.5305891) + 1)) =** 27.32158245 **sidereal month.

**Allen’s first analysis: **

- 37 synodic months of 29.5305891 days would be 1092.6317967 days
- 40 sidereal months of 27.32158245 days would be 1092.863298 days
- 3 solar years of 365.2421897 days would be 1095.7265691 days

Discrepancy – greatest range = 1095.7265691 – 1092.6317967 = **3.0947724 days**

**Allen’s second analysis: **

- 371 synodic months of 29.5305891 days would be 10955.8485561 days
- 401 sidereal months of 27.32158245 days would be 10955.95456245 days
- 30 solar years of 365.2421897 days would be 10957.265691 days

Discrepancy – greatest range = 10957.265691 – 10955.8485561 = **1.4171349 days**

The second analysis is far better than the first. But I think we can go further and achieve an even greater level of accuracy far beyond what Allen presented. Consider this:

- 4366 synodic months of 29.5305891 days would be 128930.5520106 days
- 4719 sidereal months of 27.32158245 days would be 128930.54758155 days
- 353 solar years of 365.2421897 days would be 128930.4929641 days

Discrepancy – greatest range = 128930.5520106 – 128930.4929641 = **0.0590465 days**

The question is,** did the natives know of this more advanced synchronisation?**

### PART 2

### Gate of the Sun Evaluation

In examining Allen’s evaluation of the Gate of the Sun, I personally believe that the iconography has nothing to do with the above calendar cycles, especially Allen’s first set. I view the Gate of the Sun very differently. Consider first though what Allen says of it:

Focusing upon the central detail, Allen gives a caption below this picture of it:

*Top part of the “Gate of the Sun” at Tiwanaku, Bolivia*

*Above, detail of the “Gate of the Sun” at Tiwanaku, Bolivia showing the principal grouping of thirty “chasqui” figures with beneath them the freize showing eleven icons and forty condors heads arranged in two rows of twenty heads.*

Allen suggests that the 15 *“ chasqui” figures* on one side of the main icon, and 15 on the other, each represent a solar year. I believe this is in error. Also, he notes 11 further icons on the bottom. I do not believe this is quite right either in terms of a true total.

*My Own Explanation** *

Consider the 11 icons on the bottom, with their ‘faces’. You will note that they alternate, between being ‘sat’ directly on the lower edge, and ‘sat’ on a raised platform. What does this mean? I suggest that they represent the 2 types of successive conjunctions of a moon synodic month.

Essentially, from a top down view of the solar system, starting with the moon aligned with the sun and earth, the moon initially being in the middle of these 2 bodies, about 15 days later (half a synodic month) the moon will conjunct again with the earth. This time with the earth in the middle of the arrangement. *The alternating icons – ‘lower or higher’ along the bottom – are the alternating types of moon conjunctions every 15 days or so. *

This of course leads me to point out that the 15 chasqui figures on either side of the main large Icon are most likely the 15 days between the different types of conjunctions. The total of 30 represents 30 days: a rounded up figure for the synodic moon month of 29.5305891 days.

Now I do realise this differs from what Allen says:

*” But as explained earlier, this calendar at Tiwanku is not based upon a division of the solar year into twelve, but into twenty, and this is represented by the eleven smaller icons forming the freize at the bottom which represents the eleven pillars on the west side of the Kalasasayo which is the actual calendar. So if you count from the central icon or pillar out to the right hand end, then back past the central icon to the left hand end, then back to the centre, you will have effectively counted in twenty divisions and followed the path of the sun over a year.”*

I understand where he gets 20 intervals from i.e. 11 icons bound 10 intervals, which is doubled. However, if I am right about the icons representing the 2 types of moon conjunctions, then surely, the 15 chasqui figures on either side of the main large Icon must represent 15 days between these conjunctions. And not be representative of solar years.

Also, consider that there are NOT 11 icons. There are 12. Critically, the main central icon is a big ‘blow-up’ of one of the 11. The number 12 is a factor here. Indeed, if we multiply 12 x 15, we get 180 days. This is an ‘ideal half year’. 360 days is a full ideal year.

In the little animation Allen produces he shows 11 posts in the ground with the sun changing position over a 6 month period. This is half of 1 year. Note that the central pole looks bigger than all the others. It is simultaneously the 12th (big) icon as well as being one of the other 11.

In summary, in my opinion, the Gate of the Sun has nothing to do with the cycles noted by Duquesne.

*by Keith M. Hunter*

*Copyright 2014*

*Keith M. Hunter**Presented with permission of the author*

**Official Websites of the author**

### Book by Keith M. Hunter:

*The Lost Age of High Knowledge*

The Lost Age of High Knowledge Review

Keith Hunter has written a fascinating book, based on the work of Bruce Cathie, that relates the earth, the moon, the sun, and the planets, using knowledge from the ancient Sumerian culture. It is Hunter’s contention that the celestial bodies in the solar system, including the earth and the moon, are in fact based upon completely harmonious relationships, and that over the eons these relationships have gone subtly wrong. Not only does Hunter explain the ideal relationships between planetary orbits, equatorial circumference, and the length of the year — and their importance to a more harmonious existence — but he also explains how these relationships have changed, and why our so-called “modern” civilization has devolved from this ideal state into conflict and war.

Readers familiar with Cathie’s work will find “The Lost Age of High Knowledge” much more accessible. Having read most of Cathie’s books, which are very dense analyses, I found this book to be much more readable. Hunter, in this book, has clarified much of what I had read (and found confusing) in Cathie’s works.

Mr. Hunter has the ability to explain this somewhat esoteric knowledge using clear, modern language, and avoiding confusing jargon. Using simple arithmetic and diagrams, Mr. Hunter explains the knowledge of the ancients; knowledge based upon mathematical harmony. Mr. Hunter shows that if this ancient knowledge were well understood today, our societies would be happy and productive, instead of being riddled with conflict, poverty, disease, and injustice.

This is an important work for those who want to understand why the human race cannot “get its act together.” If more people understood the ancient knowledge of harmony, we would be well on our way to a positive and harmonious transformation of our planetary societies.

Kenneth MacLean, author of:– A Geometric Analysis of the Platonic Solids and other Semi-Regular Polyhedra

– The Vibrational Universe

– Miracles Can Happen

Website of Kenneth MacLean: The Big Picture

## PS2 The Astronomical Science of Tihuanacu. How Kalasasaya was Built to be Used as a Stone Almanac

Now we shall consider another point of great importance with respect to **Kalasasaya**: that of the massive *perron* which gives access to this significant and useful monument of American man.

This staircase is not in the center of the east wall of the building as would be demanded by symmetry and all architectonic standards. Not the slightest architectural consideration caused the massive staircase to be 1m. 116 mm. to the north.

Interested for a long time in this problem, the author advanced various vague opinions and hypotheses in former publications, which of course are superseded by the present publication. Discussing this knotty problem on various occasions with **Dr. Müller**, the opinion of the author of the present work was always that expressed by Dr. Müller on p. 8 of his study *“El Concepto Astronomico”*, or in other words that the perron had to mark a main calendarian point for the time of the equinoxes. Already at that time the author pointed out that the deviation of the staircase from the intermediate line of the building of Kalasasaya must have some relation with the perihelion and the aphelion of the terrestrial orbit. And thus is the case.

The sun not being in the center of the orbit but in a center of the eclipse in which the earth turns about the sun (*see above*) the earth needs a greater length of time to go from the autumnal equinox to the winter solstice and return to the vernal equinox than to go from the vernal equinox to the summer solstice and return to the autumnal equinox.^{ }That is to say, that for the moving of the earth from the twenty-first of March (autumnal equinox) to the twenty-third of September (vernal equinox) it needs 186 days, 11 hours (winter) while to travel from the vernal equinox to the autumnal equinox it needs only 178 days, 19* *hours (summer). Thus there is a difference of 7 days and 16 hours between the winter and summer semesters. This is the crux of the problem as to why *the perron of Tihuanacu* is not in the center of Kalasasaya but is located 1 m. 116 mm. to the north. Let us explain this in simpler form.

After the priest-astronomers of Tihuanacu had established — we may presume with the system of the “topo” sight — the northeast and southeast corners (the solstices) of Kalasasaya, and after having logically divided the angle in half, they thought that they had also divided the year into four parts. However, in practice they noted the aforementioned fact that the sun needed more time to go from the north to the center of the building than from the south to the same place.

Thus, since they wished to divide the year into four equal parts, they made further observations in order to determine where the sun would rise at the exact middle of the year, on the twenty-fourth of March and the twenty-first of September, and they then noted — surely with no little surprise — that the sun did not rise in the center of the temple *but 1 m. 116 mm. to the north. *With this observation they were perhaps the first men in the world to note the perihelion and the aphelion, or the eccentricity of the terrestrial orbit. This difference corresponds for the 21st of September to 1° 0′ 56.3″ toward the north and for the 24th of March to 1° 6′ 45.3″ toward the south.

This is the way in which they established the point which marked the rising of the sun at the exact middle of the year as the center of the massive perron. This, the principal access to the palace, was at the same time a calendarian point for the determination of the great solar festivals: in Aymara probably Kjapak-Tokori and in Quechua, Citua-Raymi (for them the twenty-first of September) (according to Felipe Guaman Poma de Ayala: Koya-Raymi).

The twenty-first of September was the beginning of spring for them, the beginning of the year, and six months later came the “Willka-Tokori” (in Aymara) or the Inti-Raymi (in Quechua), the beginning of the autumn, the festival of the harvest (according to*Guaman Porna: Inca-Raymi*; making a mistake of a few days he designates it as “April”).

The solstices, the “Willka-kuti”^{ }were festivals of prayer in which the sun was implored not to go farther away but to return and favor man with its light and benign heat. These principal agricultural periods and astronomical seasons gave rise to great festivals and the determination of their dates was the motive for the construction of the great Temple of the Sun in the Andes.

Other important dates connected with agriculture or the raising of cattle were certainly determined by the rising of the sun over this or that column and were accompanied by their respective celebrations. Thus, there is almost no doubt that the rising of the sun in the center of each pillar of the east wall, and later the setting of the sun on the pillars of the balcony wall to the west, signified important dates in the life of man of that time.

The west balcony wall which belonged to the SECOND PERIOD, is not in existence at the present time and we have found only remains of the short corner wall of the south side. On June 18, 1939, we discovered remains of the north side.

At the present time, these connect the west wall with the balcony wall of the Third Period, or they may be the structural prolongations which connect it with the northwest and southwest pillars of the wall of the Second Period. As we shall see farther on, only the balcony wall was completely replaced in the Third Period. Its principal object was to guard the tabernacle of solar observation and its mysteries from profane eyes.

At about two meters from the center of the west wall of the Second Period and on the dividing line of the temple a great slab 2 m. 5 cm. wide, 2 m. 75 cm. long and 25 cm. thick (Fig. 20) was found. In our opinion this slab has no connection at all with the observation point or with its base; it belongs to the Third Period and later on we shall consider its object. Some 8 m. from the slab and also on the dividing line of the temple, in the course of the excavations in 1903, the piece which we have called the “observation pedestal”, was found. In Fig. 20 it can be seen at the moment of the excavation, still in its original place, of in the fifth test pit counting from the great slab.

On the basis of the material and the technique, it belongs without question to the Third Period. At the time of the construction of the modern church of **Tihuanacu**, it was covered with earth. It was therefore saved from destruction and only similar blocks of red sandstone found on the surface and supposedly from the Second Period were used. At the present time they are enchased in the balustrade of the atrium of the church, (Vol. I, Plate IV a and Plate XIV a). We judge that these pedestals may have served a purpose similar to that indicated by the drawing of the sight.

The north and south cardinal walls of **Kalasasaya**, as can be seen in the illustrations of Vol. I, Plate XVII a and b, are of red sandstone and at the present time consist only of a few pilasters — today showing a very rustic appearance owing to erosion — and remains of the same.

Their object at the time of the construction of the temple was to support the intermediary walls, as can still be seen perfectly on the south corner of the west wall of the Third Period (Plate XV a) and on the walls of the temple of the First Period (Vol. I, Pls. VI and VII) as well as in the remains of the west wall of the Second Period which were recently excavated. This technique, which we have called “Kalasasaya”, is still in use in rural constructions, especially in fences, throughout Bolivia and Peru. It is not unusual to see this very old system in all parts.

The columns today have the appearance of crude stones planted in the ground. However, in their time they were not only carefully aligned and carved but on the sides facing the interior of the building were magnificent symbolical inscriptions as can be seen on a piece that has fallen from one of them and on which a part of these drawings has been miraculously saved, (Figs. 21 and 21a). Because of the enormous age of these great pilasters which were the support of the walls, some of them have fallen down and others are so thin in certain parts that they threaten to fall over from one moment to the next.

At the present time nothing is being done to preserve this precious monument which still serves, as it has for centuries, as a quarry for the inhabitants of the region. Possibly they were also enchased with carved human heads, as in the walls of the temple of the First Period, (Cf. aforementioned figures). This idea is supported by the discovery — from the Third Period — of intermediary blocks which show such carved heads and in the most perfect technique of that period, (Fig. 22).