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A Bundle of Information about Calendars

Our Calendar:

The Julian Dates and the Gregorian Calendar

The Julian calendar was introduced in 46 B.C. by Gaius Julius Caesar, the pontifex maximus (it is called Julian after the second Caesar’s name; the calendar could have been changed only by a high priest – pontifex maximus, which Caesar was). This so called Julian reform was based on the fact that with immediate effect every fourth year was classed as a leap one with 366 days in the year.
Since after several centuries this calendar showed an error which kept increasing and shifted the calendar in comparison to such steady points as a solstice and equinox, the pope Gregory XIII introduced a new calendar in 1582 (our current calendar is called “Gregorian” after him) by omitting ten days between 5 and 14 October 1582 from the calendar (4 October was followed immediately by 15 October) and since then the years in a whole century which cannot be divided by 400 have not been leap ones (i.e. only the year that can be divided by 400 has been a leap one).
This new calendar caused new problems in counting of time and time periods and made it rather confusing. Therefore a French astronomer, Joseph Justus Scaliger (1540 – 1609), proposed the chronology to be counted not according to years, the length of which is irregular, but according to individual days. He set the beginning of dating to be 1 January 4713 BC, i.e. 1 January of a year minus 4712. He called the system of dating Julian (according to the author of the Julian calendar Gaius Julius Caesar) which resulted in the number of the Julian day, which is the serial number of the subject day in the calendar from the hypothetic beginning of the calendar of 1 January 4713 BC. This finding moved him very close to the system of the Mayan date setting, which in, at the time, in almost unknown Central America worked faultlessly for more than two thousand years.
However, soon it was discovered that when counting the time round about the year when Christ was born or over the year, the result will be wrong, since in the decimal system, in which our chronological data is recorded nowadays, the year of zero is missing. These problems were first addressed by astronomers and it was Cassini, the Director of Paris Observatory’s, (at present in 2004 “Cassini” probe is operating near Saturn!) whose incentive in 1740 instigated a decision that the year preceding the “first year after Christ”, will be marked as year zero, and both in astronomical and historic time counting years “before Christ” will be marked with the minus sign and that one unit will be subtracted from the year before Christ; for instance year 256 BC is year -255.
From the above information we can conclude that our calendar was being created to achieve its current form for over two thousand years. If the Mayas had worked on their calendar for the same period of time, which is more than likely, they must have been seriously involved in calendar setting at about 2500BC; at that time they must have had a mathematical system developed: their vigesimal system, adjusted to follow the time with respect to the length of a sun year.

The System of Recording Numbers Used in Europe

Under the influence of Roman culture numbers were recorded in Roman signs in Europe (basically a confusing system of recording using letters I=1, V=5, XIV=14, XVIII= 18, XIX=19 , IL=49), whilst the concept of 0 (zero) and a position numeration were not known. Roman digits cannot be written in the positional recording system, therefore zero and the position recording are absent in European mathematics until middle ages. For us usual years with zero at the end were at that time written in letters: year 10 was equal to year X in Roman digits, year 50 = L, year 100 = C, year 500 = D, year 1000 = M. You should try to add, subtract, multiply and divide in Roman letters.
The oldest reference to Arabic figures comes from 976 AD in the Codex of Vigilanus. In 1275 a manuscript was published in France which popularised a pamphlet by Leonardo of Pisa on algebra. This pamphlet is based on the work of an Arabic scientist Abú Abdulláh Muhammad ibn Músá al-Chwarízmí who lived between 780 – 850 AD.
Only the knowledge of the concept of 0 (zero) together with Arabic figures and the positional recording in the decimal system, which Christian Europe acquired from the Islamic Culture as late as after 1300 AD, allowed a development of mathematical and other sciences connected to mathematics such as astronomy and astrology.

The Beginning of Our Calendar

The beginning of our calendar was set by a Roman monk of a Scythian origin, Dionysius Exiguus, as late as 525 AD. When calculating Easter tables he realized that it was necessary to grasp a steady point. Therefore he attempted to anchor our calendar from the year of Christ’s reincarnation – “. . . ab incarnatione Domini nostri Jesu Christi” – i.e. from his resurrection when Jesus Christ was 33 years old. The years “after Christ’s birth” were inferred from that date. These calculations and chronological relations are very complex; however the fact is that the year 1 after Christ’s birth is the first year after the year when Christ should have been born. This corresponds to the astronomical calculations of time when, in fact, the year of Christ’s birth equals year 0 (zero). Christ could not have been born a year before he was born (i.e. in year 1 BC), although since being part of God, he could have done even that. Also, Dionysius Exiguus of course could not set the beginning of the calendar with a zero, because the system of Roman figures did not allow that. Or was Christ born in a year which did not exist? Would this be in the year after Christ’s birth that does not exist? Could Jesus Christ really exist when the year in which he was born does not exist? He could have done so if he was part of God.

This is the place where I have to disagree with the statement by Mrs. Marie Bláhová in the below mentioned publication, page 331. The first Millenium was expected as a great change of everything in the year CMXCVIIII or CMXCIX, as the year 999 was written at that time, not only a change in date for the new and unfamiliar M. This was a major change in life for people, the other change from M to MI was already irrelevant. Even hundred years ago people celebrated a turn of the century when the century really turned which means the moment when the new century 1900 started, which was on 1 January 1900. This is the way we were taught at school and also our parents were thinking that way. Surely, there are newspaper articles about the turn of the century from the end of year 1899 and beginning of 1900, but there is non on this theme on the turn of 1900 and 1901!
And now we can watch the Americans who in year 2000 came with an advertising campaign for another turn of the century and millennium! Suddenly the so far valid truths are not valid any more (because we live in a post-modern times!) and they are replaced by different ones! Let’s celebrate our entry into the new millennium once more! On 1 January 2001! It will be a great business! This, however, means that not only myself but also Jesus is a year older than both of us should be! And the 20th century lasted 101 years!

A Brief Comparison of the Principles of Faith

A brief comparison of the principles of faith from the position of an Extra-Terrestrial observer who watches it from the bird’s - eye view, and knows nearly the same of each of them:

He will rule pagans with an iron sceptre;
he will dash them to pieces like pottery
just as I have received authority from my Father
(Holly Bible, Revelation of St. John 2:27)

I am writing here about “being part of God” because Christianity is said to be faith with one God. However, this one and only God is in fact three figures and at the same time a virgin who must have been inseminated to give birth to her son, and hundreds of saints and the blessed ones. A few pagan gods must have been wiped out through killing millions of “pagans” so that the cult of one god, involving many more gods than the enslaved pagans believed in, could be established.
Christians worship one god who is the God, the Holly Spirit and Jesus Christ (by worshipping whom they invoke a murder), The Virgin Mary, and hundreds of saints and amongst them also St. Jacob. The original inhabitants of both Americas were almost totally eradicated in the name of the two latter mentioned part of the Christian God. Killing in the name of “the Mother with a Baby in her arms” must have been so difficult to understand for Central American Indians in the 16th century as for an ExtraTerrestrial and maybe also for a normal person of the 21st century. Moors (Muslims) were murdered in the name of St. Jacob of Compostela. One can say that this is not so surprising when Christ’s murder on a cross is a Christian symbol. Christians should not forget that it was a mere coincidence that their symbol is a cross, and not gallows, a block with an axe, a guillotine, a garrotte, an electric chair or Christ’s head blown in two with a rifle. It was a mere coincidence due to the local habit of executing people those days that determined which kind of murder would become a symbol of Christianity.
Let’s admit that Mel Gibson’s film “Crucifixion of Jesus Christ” is so popular thanks to drastic scenes and not for any mystic transcendental features or for a better explanation of why one should believe in the Christian God presented this way instead of another one.
Therefore Christianity is so appealing nowadays: blood is still oozing from Christ’s wounds. Amen.

(And if a Christian, when attempting to discuss faith and as an answer to a question about the roots and principles of his faith, does not know another answer but “Hallelujah, Jesus loves you”, then he should not be surprised if the answer he will hear is for instance “Allah akbar” (God is Great) accompanied by a blow with a kinjal in the head, despite the fact that both participants in the discussion might have wished to discuss the same topic, i.e. faith and God. But – in our 20th century world faith has been replaced by fanaticism which reduced itself into several sentences or sayings, which we have experienced enough of in Bohemia: First of all it was “Heil Hitler” and “Sieg Heil” and later “Honour to Work” and “Long Life to the Communist Part of Czechoslovakia”.
I added this paragraph under the influence of a very aggressive Christian campaign (Jesus Loves You) held at Budìjovické Square in Praha (Prague) with such blaring loudspeakers that I, although living in Kaèerov, got agitated by the Fascist-Bolshevik yelling so much that I followed the sound to find its source at Budìjovické Square. The campaign was held on 24 June 2004 between approximately 4 – 5 pm. There I learned how merciful God is – all this through a truly terrorist Christian yelling through megaphones. I am lucky that since being a pagan, a disbeliever, I have nothing to do with this kind of mercy.)

Note for English speaking people:

I have to use hooks (¡) and prolongings (´) because they identifies the meaning of written word. E.g. “KACEROV” means nothing in Czech. “KAÈEROV” means “The Place of Male Ducks”, perhaps of Donald family, whilst “KACÉØOV” is “The Place where Heretics held their Congregations”. Please do respect our hooks and prolongings.

And fight on the God’s path against those who fight you,
Don’t cause injustice, because Allah does no love those who commit injustice.
(Koran, Sura 2, The Cow, 186/190)

Islam, which is also a single God religion, knows only one God – Allah. It also knows Satan, which is depicted as an American. It also knows angels, for instance Gibril (Gabriel), and prophets, such as Jesus. Yes - Islam, recognises Jesus as a prophet. Primarily, Islam was a bearer of culture, top quality sciences and religious tolerance. Islam of course conquered new territories but was quite tolerant towards other religions in Spain and the Ottoman Empire for a rather long period of time. To prevent the present out-flow of its believers and to stop secularisation it opened flood-gate of blood due to its fundamentalism and terrorism. Islam women in black habits call for more hectolitres of blood “in the name of merciful and pitiful god” (bismi llhárí r’rahmání r’rahímí). Alláh akbar.

The blossoming death descended here,
It followed us to Earth,
They cause death there in Tlalpallan
Our nearest prepare it for us
Those who live with us and come here.
Ohuaya ca yancayo
(extract from Axayacatl song)

Also the religion of Central American Indians in the times prior to Columbus could be characterized as a single-god one. They believed in “a single god in plural”, in Mayan “HUNAB KU” (HUN = numeral one, -AB = ending denoting plural, KU = god). They saw God in everything that was around them because everything that was up in Heaven, the Earthly world and in the Underworld was divine, all that was one god. All god’s names known to us were only a metamorphosis and personification of the fundamental deity and a proof of its omnipresence. What is characteristic for the religion of Central American Indians is the notion of the principle of duality. Nothing is just black or just white. Polarity is present everywhere in togetherness: both black and white, both good and evil, a sword (war) and a flower (poetry), eating and excretion, light and darkness, heat and cold, love and hatred, a man and a woman, life and death – always together and penetrating each other. Also these contrasts are in agreement with the concept of a single god, and it is the necessary co-existence of such extremes that confirms the Mayan concept and understanding of divine omnipresence in its uniqueness and singularity.
Even here they had to seal their faith with blood. There is no need to describe in detail pulling out hearts whilst the victims were alive, throwing bleeding bodies on pyramid walls or into wells.

The Mayan Calendar

The Mayan calendar consists of three independent cycles:
1) the so called Long Count
2) the Tzolkin or the divine cycle
3) the Haab or the cycle of the Sun

1) the Long Count

First of all it is necessary to state that the Mayas used a mathematical system different from ours, i.e. the vigesimal system, the system of twenty units. (This was based on the fact that they had altogether twenty fingers and toes, ten on hands and ten on feet).
They used their regular vigesimal system everywhere except to count time, e.g. they use it in business and trade, to count their measures of length, capacity, in surveying their buildings and towns. Mayas should use this regular vigesimal system in their geometry of which we know nothing now, but they left a demonstration of such knowledge for us: equal slope of pyramide walls, knowledge of right angle, ability of astronomical measurements and building locations after results of such recognitions, and last but least, orientation afer stars.
A pretty example of Maya mathematics is their practice in milpa surveying. Milpa is a maize field, formed of mecates , which is a square measure of 400 m2 (at about 20x20 meters). Mecates was surveyed in squares by „mecate rope“, the length of which was about 21,5 meters instead of regular 20,0! The Maya said „a mecate“ should be a bit larger because of the birds eat up.
They used zero and the positional recording when digits of individual orders were written above one another. They recorded numeral one as a big full stop, numeral five as a thick line, zero as a horizontal shell shape, almost like our zero written horizontally. In manuscripts zero was often written in red (you can see the Mayan numeration in the picture on the introductory page to calendars, it is a facsimile of a Dresden manuscript – Codex Dresdensis).
This vigesimal mathematical system was known to the Olmecs and the Mayas and was used by them at least a thousand years BC.

To count time, they adjusted their vigesimal system of twenties to the, at present so called, Long Count (details below).
The Long Count is in fact a number of days elapsed from the beginning of the Mayan calendar recorded in the adjusted vigesimal system. The number (400) of units of the second order of regular vigesimal system has been reduced to (360) units of Long Count by changing the number of units for the first order from 20 to 18. By this arrangement the Tun of Long Count approaches the length of the Sun year (365) to five days.
This error, that will be shown mainly in the shift of the same date of the Haab to another season of the year only after several tens of years, is virtually worthless when calculating the age of one human life. A person o 52 years of age according to the Haab, the Sun year, is at the same time 52 tuns (years of 360 days) according to the Long Count. There will be a difference in one Tzolkin only, i.e. 260 days – and what difference do 260 days make in the age of 52?

52 years, i.e. 18,980 days, was another important time cycle. It is a multiple of 260 times 365 and its is called the Calendar Round . This is in fact one human life. Only after this time elapsed, the same combination of the Tzolkin and the Haab could have appeared in the Mayan calendar, such as 4 Ahau 8 Cumhu; but this information is a bit premature.

The adjusted Mayan vigeseimal system of twenties to count time in the so called Long Count is as follows:

1 kin 1 day
1 uinal20 kins20 days
1 tun18 uinals360 days
1 katun20 tuns7 200 days
1 baktun20 katuns or 400 tuns (years) 144 000 days
1 piktun20 baktuns or 8 000 tuns2 880 000 days
1 calabtun20 piktuns or 160 000 tuns57 600 000 days
1 kinchiltun20 calabtuns or 3 200 000 tuns115 2000 000 days
1 alautun20 kinchiltuns or 64 000 000 tuns23 040 000 000 days

12.19.11.0.15  3 Men 3 Kayab 12.19.11.0.15  3 Men 3 Kayab

A date recorded in the Long Count then looks as follows: “12.19.11.0.15” (12 baktuns, 19 katuns, 11 tuns, no uinals, 15 kins) or 1, 868,775 Mayan days. To record the Mayan system of twenties in our decimal system, a full stop is used to separate individual lines.
Our calendar does not have an equivalent to the Mayan count, which in its zero order states the exact number of past days and in the second order shows how many tuns or years of 360 days have elapsed. If we look back at the Long Count table, we will find out that if we omit the first two orders of the Mayan Calendar system (the zero kin - day, and the first uinal – month), we will get a date in tuns (years of 360 days): “12.19.11.”, which we could understand as year “2004” in our chronological system. We must not forget that the Mayas date is in the adjusted vigesimal system with the adjusted beginning of the calendar somewhere round 3113 B.C. and our calendar is in the decimal system with the beginning of the calendar in the first year after Christ was born.
The Long Count can be compared to our number of the Julian date; the number of the Julian day does not tell us anything about the number of elapsed years.
The picture on the left shows a complete date, i.e. the information in the Long Count “12.19.11.0.15” complemented with the information in the Tzolkin “3 Men” and in the Haab “3 Kayab” in the so called “handwritten” form of the Mayan letters. The picture on the right shows the same date in the “print” of the Mayan alphabet.

2) The Tzolkin

This is a cycle of 260 days, sometimes called maternal because its length is close to the length of development of a human foetus from conception to birth. It is a combination of numbers from 1 to 13 and names of twenty days, i.e. altogether 260 days. The recording of the day in the Tzolkin could have looked like this: “3 Men”. In a very remote way the Tzolkin could remind us of days of week with the names of saints in our calendar, for instance “Tuesday, St. Mathew’s Day”.

3) The Haab

This is a year with 365 days and it consists of 18 months (the months have their names but not numbers) with 20 days, numbered from 0 to 19, and so called 5 “surplus days” of the month of Uayeb, “nemontemi “ in Aztecs, numbered from 0 to 4. The recording of the day in the Haab could look like this: “3 Kayab”. Because we also use a similar system, with approximately 30 days in a months instead of 20 Mayan days, the equivalent of the Mayan date in the Haab could be “24 February” in our calendar.

Complementary data, so called Secondary Series and Supplementary Series, sometimes given on plaques with church scripts or in manuscripts.

The Mayas complemented their calendar data with other information, for instance information on the position of the day in a mystic nine day long cycle of the underworld (bolontiku), information on the Moon phase and other positions in ritual cycles, for instance the position and the phase of Venus and Mercury.
The so called Ring Number was important. This was a number written in a kind of a loop with a bow, written in manuscripts in red colour. This number indicated the correct position of the day in a year. As we can conclude from the above information, the Haab with its constant number of 365 days could not maintain a position of a day, for instance the “New Year” 0 Pop in the same season, because it was behind by almost a day in every four years. The Ring Number was used to identify the exact position of a date in a year. A comparison of the Mayan dates containing a ring number for various periods recorded on plaques on temple scripts, on altars and preserved manuscripts showed a surprising finding: the Mayas had a more accurate calendar as early as in the first half of the first millennium AD than we have nowadays.

The Beginning of the Mayan Calendar

The Mayas had a firmly set beginning of their calendar. It was the date of 0.0.0.0.0 4 Ahau 8 Cumhu, which was also found in the form of 13.0.0.0.0.4 Ahau 8 Cumhu. Because this date is placed in 3114, long before Christ, scientists reckon that the Mayas set the date hypothetically and retrospectively since the calendar with its complexity was composed much later.

How the Mayas Recorded their Data

The Mayas recorded their data in hieroglyphic script in wood, stone (we can place records in pottery, jadeite and stone jewellery, etc. here) and finally in their books.
The Mayan writing can be characterised by two different forms in which it has been recorded since its beginning, both of them used also by us: the handwriting and the print .
The so called print was used to record writing with chiselling in stone or carving in wood (wooden temple plaques, wooden altars or wooden beams above thresholds zapote), while handwriting was used to record data in books; this was written with a brush or spiky wooden stick or reed dipped in various colours. These Mayan scripts really differ like our handwriting and print do. To transfer our date into the Mayan one, I used handwriting on my page because it is easier and clearer than the print form using various shapes of a face from the profile and complex hieroglyphs to represent digits and mathematical lines (baktun, katun, tun, etc).

The original inhabitants of current Central America made their books from bark of ficus cotonifolia L., which they processed to make paper and then impregnated it with lime. The result resembled of something like a cross between canvas and chalk paper. This material was then folded and glued together to make a book on the pages of which various data and events were written on both sides. Topics of these books varied. There were mathematical and calendar notes, astronomical data like the tables of the eclipse of the Sun and the Moon, tables of the times when Venus rises and sets, phases of Mars and Mercury. Some books contained genealogies of various forms of gods together with the history of ruling families, book-keeping records of paying fees and taxes, others dealt with philosophy, politics, ethics or poetry.
Bishop Diego de Landa says: “In their towns I had those devil’s books piled up in heaps as high as their pyramids and I had all of them burnt to ash.” However, later he had to put a lot of effort in compiling data on the country which he had previously burnt down, destroyed and almost slaughtered for his Spanish king. In this way he created a monopoly for writing the only detailed book on the conquered country: “Relación de Las Cosas de Yucatán”. (He and other Catholic priests caused a bigger disaster to the Central American Indians than Hernán Cortés, the Conquerer.)

Only three books have been preserved out of the vast number of the Mayan pre-Columbus books to recent times:

1) Codex Tro-Cortesianus, or the Madrid Codex (56 sheets)
Was found in the 60s of the 19th century in Madrid, divided in two parts. The bigger part was owned by Senor Juan de Tro y Ortolano, the smaller part by Senor José Ignacio Miró who called it the Codex Cortesianus. Nowadays, the Codex is kept in the Museum of Archeology and History in Madrid.
2) Codex Peresianus or the Parisian Codex (12 sheets)
Was found in the Bibliothéque Nationale de Paris in 1860 in a dust-bin, wrapped up in paper with the word PEREZ written on. The Codex is still in the Bibliothéque Nationale in Paris.
3) Codex Dresdensis or the Dresden Codex (39 sheets)
Was found in 1739 in Vienna where it was given as a gift to a librarian of the Royal Library in Dresden who happened to be passing through Vienna at that time. The Codex is still kept in the Land Library in Dresden. This is the best preserved, the most extensive and probably also the most detailed book from the pre-Columbus period. Its facsimile was published in a limited edition in Berlin in 1962 (see below). The pictures on the pages of the Bunch of Calendars come from the Dresden Codex.

Correlation of the Mayan Date Setting

A correlation is a formula or a number showing a relation between our and the Mayan Calendar. It is a number defining a relation between a number of the Julian day and the number of the Mayan day according to the Long Count.
Historic novels could be written on the topic of setting the correlation. Unfortunately those, both the Spanish and the Indians, who lived at the time of the clash of two cultures, let’s call them the culture of native America and the invading European culture, did not leave behind enough detailed and clear evidence which could be compared without any doubts.
Several correlations have been calculated; the last disputes that took place were between Spinden-Makemson’s (489,138) and Goodman – Martinez – Thompson’s (584,285) correlations. The correlation by Spinden – Makemson compared to that of GMT shifts the whole Mayan history by approximately 260 years earlier. Nowadays, the GMT correlation is usually more widely accepted; some scientists still use an adjustment of two days. It is necessary to point out that Spinden – Makemson’s correlation is chronologically supported by C14 test results. W.F. Libby used this test to analyse for instance dated wooden altar friezes in Palenque, wooden beams above thresholds in Yaxchilán or Tikál. Results of the test contradict the GMT correlation and completely rule out correlations with the later number of 600,000 and higher. Therefore these correlations, for instance Böhm’s (622,261) are not included in date conversion tables.
The so called “C14 method” is a method of how to establish a half-life period of radioactive carbon C14 isotope in organic substances. This method helps to establish the time elapsed from the time when the life of an object ended (a tree having been cut down or an animal’s death) to date. Willard Frank Libby was awarded Nobel Prize in 1960 for the discovery of the method.

The whole Mayan date “12.19.11.0.15 3 Men 3 Kayab” could, in the GMT correlation, represent our date of “Tuesday of St. Mathew’s, 24th February 2004 AD”.

The Transfer and Relation of Time and the UTC

A Julian day starts at noon of the world time, which means that the number of the Julian day turns at 12 o’clock (noon not midnight!). Therefore the number of the Julian day is for instance 2000000,46 before midnight and 2000000,56 after midnight.
A day in a week is then connected to the Julian day from – 0.5 to +0.5. This means that Thursday is for instance from 2000000,5 to 2000001.4999999.

Even this time must have its steady point. Now we are not concerned with the beginning of a calendar but with the so called “invoking of noon”. The time of day can be counted in relation to the Sun or in relation to a remote star. The procedure is complex and the results can differ, of course. Therefore the Universal Time Co-ordinate was established which, apart from for us insignificant and almost unnoticeable differences is seconds, is almost identical to GMT, not meaning the correlation by Goodman-Martinez-Thompson but Greenwich Mean Time.
What we have to bear in mind is that due to our Eastern longitude in Prague we are one hour ahead and when adding summer time (DST) to that we are already two hours ahead. Therefore the right day of a week will start in winter at 1 o’clock at night and in summer even at 2 o’clock at night.

More about the Topic

- Bláhová, Marie, Historická chronologie, Libri, Praha, 2001.
- Tozzer, Alfred M., Landas´s Relación De Las Cosas De Yucatán, Peabody Museum, Harvard University, Cambridge, Mass., 1941.
- Willson, Robert W., Astronomical Notes On The Maya Codices, Papers Of The Peabody Museum, Cambridge, Mass., 1924.
- Makemson, Maud W., The Maya Correlation Problem, Vassar College Observatory, Poughkeepsie, N.Y., 1946.
- Makemson, Maud W., The Miscellaneous Dates Of The Dresden Codex, Vassar College Observatory, Poughkeepsie, N.Y., 1957.
- Thompson, J. Eric S., Maya Hierogylyphic Writing, University Of Oklahoma Press - Norman, 1962.
- Codex Dresdensis, Maya Handschrift Der Sächsischen Landesbibliothek Dresden, Akademie-Verlag.Berlin, 1962.
- Schlenther, Ursula, Die Geistige Welt Der Maya, Deutscher Verlag Der Wissenschaften, Berlin, 1965.
- Schele, Linda, and Freidel, David, A Forest Of Kings - The Untold Story Of The Ancient Maya, W. Morrow and Co., Inc., N.Y., 1990.

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