Tiwanaku soli lunar calendar

by Jim Allen
author
Atlantis: the Andes Solution
The Atlantis Trail
Atlantis: Lost Kingdom of the Andes
Atlantis and the Perisan Empire
Tiwanaku: A City Lost in Time

Background

In the year 2,000, I found myself in Tiwanaku with the Discovery Channel filming for “Atlantis in the Andes” and in the company of Oscar Corvison, a Bolivian Archeoastronomer who was keen to explain his interpretation of the vigesimal (base 20) system of the Tiwanaku calendar.

             Oscar explained that it was not the Sun Gate which was the Tiwanaku calendar, but a wall which today is to one side of the Sun Gate, inside a courtyard called the “Kalasasaya”. He was particularly upset because he said, in the reconstruction of the western wall of the Kalasaya, one of the large stones which had originally been part of the calendar had not been restored, but left laying in a field a couple of hundred metres to the west of the wall.

Tiwanaku soli lunar calendar    Tiwanaku soli lunar calendar
Above, left, The Gate of the Sun with the calendar wall behind. The position of the missing pillar is arrowed. Above, right, Oscar Corvison shows us the missing pillar in the field behind.

          Oscar gave me a self-produced booklet which explained how the wall functioned, and it seemed simple enough to understand that the year had been divided into 20 parts as he claimed, so I thought no more of it until the end of December 2008, when it became necessary to give some book references to my editor who was going over the draft of my “Atlantis: Lost Kingdom of the Andes” for publishing on 21 May 2009 by Floris Boooks.

       The reference in question referred to a statement I had made regarding a unit of measurement said to be found at Tiwanaku by Arthur Posnansky and called a ‘loka’, so I looked up Posnansky's book on the Internet and additionally found his major work, “Tihuanacu; the Cradle of American Man.” In this large work, I discovered his explanation of the unit he called the ‘loka’ as well as his measurement of a wall of eleven pillars which I recalled was the wall Oscar Corvison had shown me as the Calendar of Tiwanaku.

Since my own fascination is for ancient measurements rather than calendars, I began to study Posnansky's measurement of the wall, and discovered the wall was not simply a solar calendar as had been previously thought, but incorporated a sophisticated calendar based on sidereal lunar months.
The rest of this essay and the discovery of the sidereal lunar calendar follows on from Oscar Corvison's pioneering discovery of the base 20 system in the Tiwanaku calendar.

The Measurements

When I had visited the Akapana pyramid in Tiwanaku with Freddy Arce of the Tiwanaku Institute, Freddy had told me the dimensions of the pyramid which is in fact a sort of ‘T’ shape. One side, he said was 210 metres (688.9 ft). I pulled out my pocket calculator as that number sounded familiar. A quick analysis showed that 210 metres was 400 Egyptian Royal Cubits of 525 mm (20.67 inches) or one Egyptian Royal Stadium. The other side was 194.4 metres (637.8 ft). A quick calculation again revealed that 194.4 metres was 432 Egyptian Geographic Cubits of 450 mm (17.7 inches).

            The Akapana is not alone in being constructed using ‘Egyptian’ royal cubits. The writings of Arthur Posnansky tell of a building similar to the Kalasasaya (the semi-sunken temple in Tiwanaku) which he records as existing on the island of Similake in the entrance to the Desaguadero River (Posnansky 1937). According to Posnansky, this structure has sides measuring 30 ‘loka’ of 175 cm (68.9 inches). This would make the overall length 52.5 metres (172.24 ft) which is 100 Egyptian royal cubits of 525mm (20.67 inches).

            The relation between the geographic cubit and the royal cubit was that the geographic cubit consisted of 6 palms of 75 mm (3 inches) and the royal cubit had an extra palm of 75 mm making 7 palms to the cubit. This was the metric equivalent (derived from the Earth's circumference) of the ‘pure’ cubit of 21 inches (derived from the Earth's diameter) comprising 7 palms of 3 inches and the ‘pure’ geographic cubit comprising 6 palms of 3 inches.

            The 21 inch cubit also served as the diameter of a wheel used for measuring distances, rolling out a Sumerian double yard of 66 inches, which is 100 Sumerian shusi. 120 revolutions would measure the Sumerian furlong of 660 English feet or 600 Sumerian feet.

If the Andean measurement unit was a ‘loka’ of 175 cm as suggested by Posnansky then its correct interpretation and significance may have escaped previous investigators. Put simply, three ‘loka’ of 175 cm are equal to 10 Egyptian Royal Cubits of 525 mm. Arthur Posnansky began studying Tiwanaku in 1904 and in 1945 published his monumental work "Tihuanacu, the Cradle of American Man." He thought Tiwanaku had been constructed in three distinct stages or periods and in note 73 of Vol II, Chapter II section E gives the value of a ‘loka’. But his figures seem to be inconsistent since he begins ‘The loka of the first period of Tihuanacu was 174 cm as can be seen clearly in the preglacial building on the island of Similake in the Desaguadero River (Cf. Posnansky Antropologia y sociologia andina, 1937)’. Then he states ‘each loka of the First Period measures 175 cm. The building of Similake has thirty ‘loka’ of the First Period. In the Second Period … it seems that the ‘loka’ had the same size of 175 cm as in the First Period. With regard to the ‘loka’ of the Third Period of Tihuanaku, it is only 161.51 cm.’

Posnansky thought that the change of length in the ‘loka’ which he considered to have an ‘anthropoligical origin’ was due to the length of an arm span of one of the local inhabitants from fingertip to fingertip and the reduced size to be due to the reduced stature of the inhabitants of the Third Period. 

An alternative explanation might be that the orginal units were lost over time and different units used by different builders in different phases of construction, not all of whom may have had an interest in using an accurate system of measurement, but when some distances turn out to be in round numbers such as 100, 360, 400 or 432 of units found in the “Old World”, it does suggest that a scientific method of planning was used instead of the oft quoted arm’s length derisorily promoted by some researchers.

As there seems to be some inconsistencies in Posnansky’s figures and his attempts to establish the ‘loka’, we can look at them again.

His reduced size for the value of the ‘loka’ seems to be based on a measurement of a row of 11 pillars in the Kalasasaya which is assumed to be an ancient calendar of Tiwanaku. Posnansky measured from the centre of the first pillar, pillar ‘A’ to the centre of the last pillar, pillar ‘K’ and found the distance to be quote, ‘48 m 45 cm 7.5mm which divided by thirty normal measurements would give the figure of 161.51 which would be the true average of the meter of Tihuanacu of the Third Period’.

It immediately leaps out at you, why did he measure from the centres of the pillars at each end, and not from the ends of the pillars at each end? Is that why his Third Period ‘loka’ is so small? Fortunately he gives the measurements for each pillar, so we can add in 442.5 mm for the half width of pillar ‘A’ and 400 mm for the halfwidth of pillar ‘K’. This makes the overall length of the row of pillars as 49,300 mm.  In fact, Posnansky did measure from the end of pillar ‘A’ to the end of pillar ‘K’ and found it to be 49 m 30 cm. But he then took the figure from the centre to the centre of the end pillars to use in his calculations instead!

Tiwanaku pillars measurement
Posnansk's measurements for the row of pillars.

Instead of dividing by 30 as Posnansky did on the assumption they represented periods of 30 days on a Solar calendar, we can divide them by Egyptian Royal Cubits to see if there is any consistencey with Egyptian Royal Cubits found previously at the Akapana pyramid. So 49,300 mm divided by 525 mm Egyptian Royal Cubit comes to 93.9 cubits, almost 94 cubits.

But the Egyptians had other variations in the length of the Royal Cubit, the cubit in which the Great Pyramid of Egypt is built has a length of 20.62" (523.74 mm) or sometimes quoted as 20.625" (523.87 mm) (see Berryman’s Historical Metrology, page 71 and page 72). This was the cubit used for land surveying and was derived from a ‘remen’ which originated as a 1/5,000 part of the mean figure for a minute of latitude or geographic mile where the remen formed the side of a square and the royal cubit was the diagonal of the square. Dividing the length of the pillars (49,300 mm) by 94 gives a cubit of 524.468 mm which is 20.64" so it seems an ‘Egyptian’ Royal Cubit could after all have been intended. Berriman noted that when the King’s Chamber of the Great Pyramid in Egypt was measured as accurately as possible by four different surveyors over a period of time, they each found a different length for the Royal cubit ranging from 20.5 to 20.66 inches (showing how difficult it is to obtain a truly accurate measurement).

A further confirmation of the use of the Royal Cubits in Tiwanaku may be found in Posnansky’s figure for the length of the terraces used to support the walls of the Kalasasaya which he measured as being 41 m. 90 cm which would be 80 Egyptian Royal Cubits of 20.62 inches.

Posnansky seems to have considered the row of pillars as representing a calendar based upon 30 days and states that the solar year of twelve months was used with the sun showing through the gap between the pillars each month. But there’s a flaw with that. With eleven pillars, there are only 10 gaps or spaces, not 12 … Posnansky would have done better to pay attention to one of his own quotes, in section E, note 78 where he quotes a sixteenth century Peruvian historian as saying ‘They divided the year into twelve months by the moons. Already each moon or month had its marker or pillar around Cuzco, where the sun arrived that month.’ (Ondegarda 1571)


the sun gate and the calendar wall.


Posnansky's interpretation of the Sun Gate calendar is wrongly based upon an assumption that the year was divided into 12 months of thirty days (based upon the Inca calendar). He has counted the central icon twice and arranged the months so that in some instances they pass from pillar to pillar and in other instances they leapfrog over the pillars in order to make it fit his interpretation.

By the time of the Inca empire, a calendar of 12 months of 30 days had been introduced, not to be confused with the original calendar of Tiwanaku and the Sun Gate. The Inca calendar is reported by Acosta and also Guaman Poma to have begun with the festival of Ccapac Raime in December, whereas the Aymara calendar is today still celebrated in Tiwanaku at the beginning of the Aymara New Year on 21st June.


Above, describing the Inca calendar in "Peruvian Antiquities", (1858),
the writer tells us sometimes the year was calculated from the summer solstice in June
other times from the December solstice...


Confusion in the interpretation of the Inca calendar may also occur when comparing it to European calendars, Acosta for example writes that "the first month was called Rayme and answereth to our month of December," but that could also mean that it was comparable to the Spanish December on account of the seasons being reversed in the southern hemisphere.


Above, the writer from Peruvian Antiquities appears to make the same mistake since he says the year began with the festival of Inti Raimi at the winter solstice, but the winter solstice in Peru is in June, not December.

gate of sun
Above, Acosta describes 12 solar towers.

calendar 12 towers
Above, viewing the sunrise through 12 pillars would divide the year into 20, not 12.

Acosta writing in the year 1600, tells us that 12 towers were set up which divided the year by the sunrise and sunset into 12 months. But Acosta was not familiar with how the system worked, and thinking in European terms, assumed because Europeans used a calendar of 12 months, then each of the towers represented a month on a calendar of 12 months. But that's not how it works. The towers are used to track the position of the sun either rising or setting along the horizon throughout the year. So if there were 12 towers in a line, the sun rising or setting upon each tower would divide the year into 22 divisions or "months" - not consistent with any known measurement system of the years. There again, if we viewed the sun in the space in between the towers, that would mean 11 spaces which would divide the year into 20 divisions or "months". But the sun cannot both rise and set upon the same pillar, it rises in the east and sets in the west. So if the 12 pillars were arranged 6 to the east, and 6 to the west of Cuzco, that would mean the year was divided decimally into 10 months.

calendar 12 towers
Above, with 6 pillars, the year would be divided into 10 with the sun rising or setting on the top of each pillar as it progresses throughout the year along the horizon from solstice to solstice and back again. It is not the number of pillars which represents the number of months, but the number of time intervals as the sun moves either from pillar to pillar, or from space to space between the pillars

calendar 12 towers
Above, when the sun reaches the end pillars at the solstices, it appears to stand still.

The Inca Empire which spanned the length of the Andes was effectively brought to an end by the capture of their leader, Atahualpa by the Spanish conquistador, Francisco Pizarro at Cajamarca in 1532. The first conquistador to visit the site of Tiwanaku and write an account was Pedro Cieza de Leon who describes it in his "Chronica del Peru" of 1549.

Cieza de Leon records that the city was already long abandoned in the time of the first Inca, it had not been built by the Incas and the locals had no idea who had built it. He also recorded that the people of that region, that is to say, the Aymara, used a year of 10 months.


The first recorded description of the Collao (region around Lake Titcaca)
by Cieza de Leon in 1549 describes a year of 10 months. This is consistent with an early Inca calendar of 10 months using 6 towers to the east and 6 towers to the west of Cuzco.

It is also the same as the Tiwanaku calendar since a year of 10 months of 36 days is also
20 "half months" of 18 days or
40 "weeks" of 9 days.

gate of sun
Above, Acosta tells us the Inca calendar was reformed by Pachacutec....
Perhaps it was at this time the Inca calendar was changed from the ancient 10 or 20 month division to the 12 month division which is more commonly spoken of, although at the same time the Inca also used a lunar calendar of 12 sidereal months.....

gate of sun
Above, Garcilaso tells us that at Cuzco, eight towers were set up to the east and eight towers to the west of the city, to calculate the year which was divided into 12 months.

gate of sun
With eight towers, the sun is observed through the spaces between the towers
resulting in a division of 12 months.

gate of sun
Above, at Chankillo in Peru, there still exists a row of thirteen solar towers - these would divide the year into 24 parts viewed when the sun set or rose over the towers, making each division a half-month and every two towers a month of 30 days in a 12 month year.

gate of sun
Above, in Tiwanaku, the 11 pillars divided the year into 20 "half-months" of 18 days
or 10 "months" of 36 days.

tiwanaku calendar 1 year animation
animation of 1 year of the calendar, counting 40 weeks of 9 days, 20 half-months of 18 days, 10 months of 36 days: sidereal lunar months, zocam years of 20 sidereal months, acrotom years of 40 sidereal months or 3 solar years, the Saros cycles of 18 solar years = 20 Inca years of 12 sidereal months. click here for 3 years animation

tiwanaku calendar 30 year animation
The chasquis on the calendar count 30 solar years when an extra month has to be added to the lunar calendars.

Above, the chasqui icons are arranged vertically in threes - every three solar years was equal to 40 sidereal lunar months, marked by the 40 condor's heads on the freize, there are 30 chasquis because every thirty years an extra sidereal lunar month was added to synchronise the solar and lunar calendar.

the calendar counts:
30 solar years of 10 months solar
20 zocam years of 20 months lunar
10 acrotom years of 40 months lunar

In Ecuador, according to the calendar of the Muiscas, 20 sidereal months was known as a "Zocam" year while the period of 40 sidereal months was known as an "Acrotom" year which was also equal to 37 ordinary lunar months or 3 solar years. This corresponds perfectly well with the numbers recorded on the Gate of the Sun showing the advanced mathematical and astronomical knowledge of the ancient Tiwanakotan peoples.

 
Above, left, winter solstice ceremony, 21 June 2010 at Tiwanaku.
above right, summer solstice ceremony 21 June 2010 at Stonehenge.
winter in the southern hemisphere is summer in the northern hemisphere.

 kalasasaya stones The stone gateway which is today in the Kalasasaya is baptised ‘the gate of the sun’ and ‘Kalasasaya’ according to Posnansky simply means ‘standing stones’. When he investigated Tiwanaku the stone pillars had more of the appearance of a 'Stonehenge', there was no wall there as there is today, (most of the wall was assumed to have been carried off so in the 1960’s as part of a reconstruction the spaces between the pillars were filled in to form a wall) and only 10 of the giant pillars remained. The 11th missing pillar may be found laying face down in a field some 229 metres to the west. According to Oscar Corvison, a Bolivian archeo-astronomer who studied the site, the eleven pillars represented the division of the year into periods of 20 (Corvison 1996). This seems more logical, since if you count from the central pillar (representing the equinox) out to the end pillar on the left (representing the south solstice), then back past the centre to the far right pillar (representing the north solstice), then back to the centre again, you arrive at a division of 20.

The Inca were sometimes said to be people of the sun, whereas the Aymara were sometimes said to be people of the moon, so I wondered whether in fact the pillars may also have been a soli-lunar calendar since what is called the ‘Saros’ cycle of lunar eclipses repeats itself every 20 ‘Inca’ years and 20 ‘Inca years’ of 12 months of 27.32 days is very close to 18 solar years of 365.24 days (Allen 1998 and Aveni 1990) and the people who built Tiwanaku were a race long before the Inca and possibly even before the Aymara. On the other hand, if used for agricultural purposes, it may simply have marked the winter and summer solstices with the appropriate pillar or space between the pillars marking the return of the sun to a suitable time for plantings crops, which is what Posnansky thought the purpose of the calendar was in the first place.

This is how it works. In the centre of the Kalasasaya 30 ‘loka’ (100 royal cubits) from the centre pillar there is a large block of stone which is said to represent the original observation point. From here the sun could be watched setting on the horizon over the pillars each night. When the sun set over the central pillar, the day would be the 22nd September and Spring would begin. When the sun set over the next pillar to the left, one twentieth of a year would have passed and so on until reaching the pillar at the far left a quarter of a year later on the 21st December marking the Summer Solstice. (Seasons reversed in southern hemisphere).

tiwanaku calendar animation
The calendar counting in twenties

The sun would now begin to move back towards the centre, reaching here another quarter of a year later on March 22, marking the Autumn equinox, then it would continue to the right, reaching the end pillar on June 21st marking the winter solstice and the beginning of the Aymara New Year (the great festival of Inti Raymi) and returning back over the centre pillar one year later on the following 22nd September to mark the beginning of another Spring. (Explanation thanks to Oscar Corvison).

Kalasasaya outside wall
View from the field showing the reconstructed wall, the position of the missing pillar can be easily seen, just behind where the person appears to be running.

Although Corvison was correct in identifying the use of a solar calendar based on divisions of 20, (and this should not be a surprise since both the Aztec and Maya civilisations used a base 20 calendar) he does not seem to have considered the possibility it could also have been a lunar calendar.

However, on the above basis, when the sun reached the first pillar it would have travelled a 1/20th of a solar year which is 18.26 days. By the time it reached midway to the next pillar, it would have travelled half as much again, which when added to the first figure means 27.39 days would haved passed — virtually a sidereal lunar month —  every one and a half pillars would add another sidereal month and continuing the process would take us back to the central pillar after 13 and a third such sidereal lunar months (or divisions) had passed, completing a year and making it a dual purpose, soli-lunar calendar.

Tiwanaku Calendar

Now I wondered if this in some way tied in with the Saros cycle and since it takes thirteen and a third sidereal lunar months to circle round the calendar stones in order to complete one 'lap' and come back to a full year, how many ‘laps’ would it take to fulfil the Saros cycle?

Well, three ‘laps’ round the pillars would make the sun once more over the central pillar and represent 40 sidereal lunar months and since each lap around the pillars is a solar year, a total of 18 ‘laps’ round the pillars would complete the Saros cycle, the sun would be back again over the central pillar and the cycle would all begin all over again!

Maybe that’s why the Amautas (mathematicians) of the Aymara thought they had discovered the most perfect calendar in the world. Could this be the calendar of Atlantis? Some people thought so (Corvison 1996), but they failed to realise the Altiplano was Atlantis.

          When Posnansky measured from centre to centre of the end pillars he was in one respect correct ­– that this could represent the year ­–­– since in addition to the lunar year the calendar also represents a year of 360 days as well as a year of 365.24 days. How it could do that may be something like this. From the centre to the centre of the end pillars is taken as 360 days (counting from one end to the other end then back again) then the distance from the outside to the outside of the opposite pillar (and back again) would represent 365.24 days. In this way, the calendar could mesh the Solar calendar with the Lunar calendar, the extra four and a quarter days being ‘lost’ (to view) when the sun reaches the end pillars ready to return in the opposite direction. Each division from pillar to pillar would be 18 days, which could be arranged either in groups of 3 x 6 days or 2 x 9 days. The pillars would therefore be Posnansky’s figure of 48.4577 metres divided by 10 making 4.84577 metres from centre to centre which is virtually 16 feet representing 18 days. The half space between pillars would be 8 feet so the one and a half pillars space would be 24 feet marking the sidereal lunar month intervals, while returning to the 16 feet interval between pillars, a different unit would be necessary to divide this space into three for the three weeks of 6 days. Fortunately we already have a unit to hand, because the Babylonians or Sumerians used a unit which is called a ‘barleycorn’ and was a third of an inch, with two barleycorns making the ‘shusi’, and 30 shusi making the Sumerian cubit, usually counted as 19.8" and sometimes as 20”.

            The space between the pillars as a solar calendar would be 16 feet or 288 shusi, and each week would be one third of that which is 96 shusi and each day of the six day week would be 16 shusi or 32 barleycorns. It seems that in the Andes, a work period of six weeks of nine days was also used, which would therefore correspond to three divisions of the pillar calendar and be two sidereal lunar months. Counting in Sumerian cubits, the pillars would be 96 cubits from the centre of one end to the centre of the other end and using cubits of 20" the distance would be 160 feet (48.768 m) or using cubits of 19.8" it would be 158.4 feet (48.280 m), which compare to Posnansky’s measurment of 158.98 feet (48.457 metres).

           I have set out the principles behind the calendar which being built of rough blocks of stone, may not have been set to a particularly high degree of accuracy to begin with.

The key to the calendar was said to be built into the Gate of the Sun, today found near the Kalasasaya pillar wall and put there when the Kalasasaya was restored. It consists of a giant block of stone with a gate cut into its lower half and an elaborate decoration on the upper part. In the centre of the decoration there is a representation of the ‘weeping’ god — presumably Viracocha and in his hands he carries two staffs, which look like measuring or mathematical staffs since although the rest of the monument is symmetrical, the staffs are different, the one in his right hand has two sets of three circles and the one in his left hand has two vertical lines over three circles. But who can read the monument today?

gate of sun icons
The upper part of the Gate of the Sun shows the key to using the calendar

On the upper level, on each side there are three rows of iconic figures called ‘chasquis’ — messengers of the gods, each row has eight chasquis, but they are arranged to look like a block of five with five on the inner and three on the outer side, it can also be noted that 32 of the chasquis have condor faces looking forwards and 16 of the chasquis have condor heads looking upwards. 

gate of sun freize
The freize with eleven icons represents the eleven pillars of the wall.

Beneath these chasquis there is a continuous row of smaller icons arranged so that eleven of them stand apart from the rest. We can assume that these eleven represent the pillars of the calendar. Now it has usually been wrongly assumed that because the upper chasquis in horizontal rows total fifteen on each side (not counting the outer ones) that the total of thirty chasquis represent 30 days since a solar year of 360 days divided by 12 months would give a 30 day month. But as explained above, the actual calendar is divided by 20, which would make solar divisions of 18 days. These in turn could be divided either as 3 weeks of 6 days or 2 weeks of 9 days and it seems that work periods of 6 weeks of 9 days were used in the Andes thus corresponding to two sidereal lunar months.

                     The reason why people can’t see the correct number of chasquis on the lower freize of the Sun Gate is because the eleven chasquis in a row represent a circular or elliptical orbit, so the two end chasquis represent the solstices when the sun reaches the ends of the orbit, but the remaining nine chasquis conceal another chasqui behind them so to speak (if viewing the orbit in plan view) so the total is two end chasquis plus eighteen ‘double’ chasquis making 20 all told.

Tiwanaku orbit
Apart from the end chasquis, each chasqui conceals a twin behind it representing the same position on the other side of the orbit

        This is clearly shown on the freize itself where there is like a route marked round the chasquis telling you to go round the calendar in an orbit, then there are 20 condor head symbols in pairs on the upper part of the freize, and 20 condor head symbols on the lower part of the freize in pairs, telling you to count in twenties and forties. Additionally, each chasqui has a slightly different form, some seem to include symbols so that the upper row adds up to 20 and the lower row adds up to 18 – indicating the 20:18 ratio of the Saros cycle of the calendar.

gate of sun freize orbit
The freize tells you to follow the orbit of the sun around the pillars, counting like this, in twenties

gate of sun freize
The pillars seen in plan view.

Many people have mistakenly thought that the Gate of the Sun was the calendar, but it isn’t. The pillar stones built into the west wall are the calendar and it could be instead, that the chasquis are telling you how to operate the calendar.

Instead of reading horizontally, if we read vertically, they seem to be saying, ‘count in blocks of three.’ But blocks of three what? When we studied the operation of the stones on the wall, we found that every one and a half pillars represented one sidereal lunar month. Therefore every half division between the pillars represented one forthieth of the year or a third of a sidereal lunar month, the month itself being the prime unit. Now on the Gate of the Sun there are a total of 48 Chasqui icons which therefore represent 48 sidereal lunar months. Tahuantinsuyo, the empire of the Incas was ‘the land of the four quarters, or four divisions’ so dividing the 48 Chasquis by 4 results in 12 Chasquis — meaning 12 sidereal lunar months — which was the Inca lunar year of 328 days. In turn 328 days divided by 4 gave the 82 day (three month) period at the end of which the moon would be visible against the same group of stars etc and that I believe, is the message of the Chasquis — how to operate the calendar.

kalasasaya
This satellite image shows the Kalasasaya courtyard with the calendar wall to the west and the observation stone marked

chankillo towers A row of thirteen towers has recently been found in Peru, which according to the system above would represent the division of the year into 24 and correspond to 12 solar months, suggesting the ancient calendar was later reformed into 12 months of 30 days which may have misled some scholars in their attempts to understand the original Andean calendar. (See http://news.bbc.co.uk/2/hi/science/nature/6408231.stm )

I have expanded quite a bit on the ancient measurement systems in the hope that it may be useful for future investigators and encourage them to look at the measurements of Andean monuments and cities in a new light.

Posnansky also measured an inner temple he calls the ‘Sanctissimum’ in the centre of the Kalasasaya complex and found it to measure 63.80 by 71.80 metres. Had he measured it in sacred cubits of 25", he might have defined the same measurements as 100 by 113 sacred cubits.

  In the ‘Old World’ the confusion of so many different measuring units led to the introduction of the metre, which was intended by the French Academy of Sciences in 1790 to be a new decimal system based upon a division of the Earth’s quadrant circumference – the distance form the North Pole to the Equator – into 10,000,000 parts. The originators of the modern metre were completely unaware that a ‘metric’ unit already existed in ancient Egypt where the royal cubit of 525 mm was then divided into 28 digits, while 24 digits gave the cubit of 450mm, and 16 digits gave the ‘metric’ foot of 300 mm. (Thompkins 1978).

Amongst the other values of Egyptian cubit, the cubit used for land surveying of 20.625 inches (523.87 mm), was also related mathematically to the Sumerian cubit of 19.8 inches (30 shusi) in the ratio of 24/25. It also explains why both units could be found in the temple of the Kalasaya and it is no surprise that the ‘Sumerian ‘yard’ of 33.0 inches has also been found in Peru. So when we say the sides of the Akapana pyramid have a measurement in Egyptian Royal Cubits we could also put it the alternative way round, as John Villegas pointed out: ‘Or is it that the Egyptian pyramids are built in “Bolivian cubits”!’

At the same time though, we cannot discount the fact that different cultures could arrive at the same value for their cubits because they both used as a starting point the dimensions of the Earth subdivided according to their own mathematical preferences.

Tiwanaku soli lunar calendar

Appendix A

We can consider further the use of Sumerian cubits at Tiwanaku. The Sumerian cubit of 19.8" (502.92 mm) was related to the Egyptian cubit of 20.625" (523.875 mm) in the ratio of 24/25. I suspect this may have some relationship to the fact that the earth day is 24 hours but the moon takes 25 hours to orbit the Earth. Or it could also have practical uses in land surveying since with an allotment of 10 x 10 stades such as Plato described, we might wish to divided the allotment decimally, or we might wish to divide it by halves, quarters and eights, or by thirds. If the allotment is of 165 feet by 165 feet, it would be 100 x 100 Sumerian cubits of 19.8". If we divide this stade of 165 feet which is actually 150 Sumerian feet by 1/3rd, we would have a distance of 55 English feet which is 50 Sumerian feet and also 32 Egyptian cubits of 20.625". So the Egyptian cubit has a practical use in relation to the Sumerina cubit depending on whether we wish to divide by 24 or 25, or by 5 or by 6.

We should also note that a wheel which has a diameter of 21" will have a circumference of 66" which is two Sumerian yards of 50 "shusi" making 100 shusi for this unit.
Evidence of the Sumerian cubit has already been found on the Altiplano where a system of ancient parallel canals appears to be set out in multiples of "Sumerian" cubits of 19.8". Each cubit of 19.8" was 30 Sumerian"shusi" of 0.66". The Sumerian foot was 13.2" which was 20 shusi and there also existed "links" of 7.92" which was 12 shusi.
Returning now to the dimensions of the stone pillars we can look to see if the Sumerian cubit might have been used. This is because each division between the pillars represented 18 days on the ground, and it would be convenient in theory, if each day corresponded to a known distance on the ground, i.e. on the calendar.

The overall length of the pillars is 49.300 metres (161.74 ft) and the distance from centre to centre of the end pillars is 48.4575 metres (158.98 ft) so the row of pillars is virtually 160 feet long if we were using English feet.
If we assume the distance between pillars A and K (48.4575 metres) were intended to be 96 cubits, then each cubit would have a length of 48.4575 metres divided by 96 = 504.76562 mm = 19.872" .
Each division between the pillars represents 18 days since the calendar is a year divided into 20 and from A to K represents half the year, so each division between the pillars would be 48.4575 metres divided by 10 = 4.84575 metres per 18 days and each day would be 269.20833mm = 10.59" = 16.0587 shusi..

To work the equation backwards in order to get an exact measurement of 16 shusi per day, the length between the pillars would need to be 16.0 shusi = 10.56" =268.224 mm x 18 = 4.828032 metres between the pillars which gives distance of 48.28032 metres for the row of pillars, which is exactly 96 Sumerian cubits of 19.8 ".

The difference between the exact number of Sumerian cubits (48.28032 metres) and the measurement by Posnansky (48.4575 metres) is 177 mm or 88.6 mm at each end (3.5") at each end and considering the calendar is made of giant stones may not have been constructed to this degree of accuracy in the first place.

And also visit www.atlantisbolivia.org bookstore for link to paperback edition "Decoding the Tiwanaku Calendar"

Tiwanaku
click here Tiwanaku

Tiwanaku cubits
click here Tiwanaku cubits

Atlantis Stade
Click here Atlantis Stade

webpage compiled 4 Jan 2009, updated 16 January 2012 with new animation
J.M. Allen
webatlantis@hotmail.com


"Atlantis: Lost Kingdom of the Andes" - the discovery
new edition out by Floris Books,
21st May 2009


atlantisbolivia.org