The "dn" Numbers of the Maya and the 819 Dilemma

In 1998, Floyd Lounsbury decided he had to create series of coefficients for the
Maya glyphs. As he atempted to make the MOD units. He decided that the 819
number was the lowest common denominator by combining six “dn” units  
[n0, n1,, n2,, n3,, n4, n5] ALL of which are divisable by Five.

    There was an odd reason for that. He created that 819 number by combining:

n1 - Uinal = 01-day

n2 - Veintana = 20-days

n3 - Sacred Almanac = 260-days

N4 - Nine days = 19-days

and n5 - Calendar Year = 365-days of 52-years or 18,980-days

   Other grouped units that could be used were 9-days, 819-days, 4 x

819-days, and the moon which has 29 or 30 nights.

Now if anyone could get through the 819 calculation by assuming that all
of the above unit numbers, which the author claimed are divisible by 5,
then one could run five of those numbers together to reach the 819 figure
which would then become the coefficient for each one. Lounsbury made
a disclaimer, just in case.

“It is not known whether this was the Maya  way; it probably was not.”

In other words, he made up the process in order to create another math  problem
that might solve the Maya Calendar computations. On the other hand, I must
assume that the Maya had a specific way of counting number’s: like a bar
(=5) + a dot (=1) = 6. They also had a set of names for very large numbers: from"

kin = 1-day;

uinal = 20-days;  

tun - 360-days;

katun = 7200-days;.

baktun - 144,000-days.  

Added were more titles: pictun, calabtun, and kinchiltun, eetc.which seem to have

come through those people who research dates of the Maya.  This set of three
seemed appropriate for Maya numbers, but there is no information that the Maya
ever used those names themselves.

Lounsbury also obtained the Yucatec names used for 1 to 20 numbers.

He probably took them from the Maya calendar maker in Merida, who was also

attempted to find the names for higher groups of Yucatec/Maya numbers.

The worst of the inferences was when it was the n0  dn numbers were used to find the month names as far back as the BC centuries. Even though the Maya recorded over and over again:

“the month names were created by Rome in 1583 for the year 1584
Month Name became 0-POP. “   [Edmonson, Munro, ( , 78, 81,
86-87, 89, 90, 93, etc )  The Book of the Year]

In other words, Rome sent out new month names which they had created.
The new names would be used  to make Maya dates comparable with the
European calendars.

We must not forget the distance numbers, marked in Lounsbury’s Calculus
formula as “dn.” There is also a Maya commentary on them which has also
been ignored by the scholars.

Native Maya Calendar Makers, after much discussion, decided that
although Rome’s dates would be used in the post-conquest monuments,
they would continue to use the dn numbers as the true Maya calendar
of 360-day, the same as those used in China for their 60-year sequence.

“Let us permit our calendar to gain on the true year; as fast as it will. We will
allow our calendar to function without change, but when we erect a monument,
we will engrave upon it, IN ADDITION TO  THE OFFICIAL CALENDAR DATE OF ITS
DEDICATION DATE, A CALDENDAR CORRECTION FOR THAT PARTICULAR DATE.In this
way, no matter WHAT DATE OUR CALENDAR MAY REGISTER, WE WILL ALWAYS KNOW,
whenever, we erect a monument, the POSITION OF ITS CCRRESPONDING DATE IN
THE TRUE YEAR.”   

The above gives us the definition of the “dn” numbers. They are nothing more
than the Maya date method of IK being the first day of a 360-day year. That would
be the very same date that is in Rome’s approved calendar beginning with IMIX
[from February 8] as the first day of Rome’s version of the month of 0-POP [from July 26.]

Wouldn’t it be wonderful to have Maya teachers who could teach us
their math in simple Maya terms instead of Rome’s convoluted dating system.
The Maya actually gave the correct Maya math for Rome’s version of their calendar.
So to begin with we have had a very good lesson from the Maya about the “dn” numbers after the glyphic version of dates on monuments of stone. But as usual, no one cared enough to listen to the Maya. The researchers as youngsters just on their first archaeological dig, usually could not communicate in Maya, and not very well in Spanish.

So the Math that they learned was that 52-weeks are 52-years in Calculus.
At the end of those 52-years: a great First Fire would be celebrated, and
everything used in the homes would be destroyed. All new items during the
First Fire celebration would be bought to replace pots, ollas, cups, plates,
baskets, digging sticks, rebozos, skirts, shirts, sandals, . . .everything NEW
to be used for the following 52-years.

It would be akward to have burned food in the bottoms of pots and ollas,
which could not be removed. . . . since clay is porous to begin with. Germs
could produce diarhea and other disturbances of the intestines. These might
be a grave problem if pots and ollas are constantly used for 52 years.

As it was, Floyd Lounsbury’s paper,  was an experiment with enough clues throughout the 28 pages, that it was just a paper about that which he wanted to
accomplish; however, his theories were never specifically fixed into a usable formula.

On page 804. After comparing sun and moon eclipses during the time that

his inferred formula would not work well:  So he tried again:

10.   7. 4.    3. 5. = 3 Chicchan, 13 Yaxkin  and subtracting

-- 8. 11    7, 13, 5.    = 3 Chicchan, 8 Kankin

______________

   1. 15. 16.     8. 0. = 2 x  (17.13.4.0)         

                                  = 2 x (128,960 days)

By the time he reached the end of the very long paragraph, he had decided
the math was still wrong.

10.   7. 4.   3. 5. = 3 Chicchan, 13 Yaxkin  and substracting

                        -4 = Interval conj. to crescent moon.

______________

10.   7. 4.   3. 1.  = 12 Imix , 9 Yaxkin (conj.)              

        1. 7. 8. 13      = 335 lunations

 _______________

   10.  5. 16. 12.   8 . = 12 Lamat 11Tzec  (epoch)

--    9. 16.   4. 10. 8.     = 12 Lamat 1 Muan  (epoch)

  _______________

         9. 12. 2.  0. = Interval between epochs

 --      8. 6.  2. 0. = 5 full eclipse cycles

     _______________

           1 6. 0. 0.     = one short cycle = 9,360 days or 36 almanacs

The preceding computation was Lounsbury’s solution to the eclipse problem.  
Therefore,

10.   7. 4.    3. 5. = 3 Chicchan, 13 Yaxkin  and substracting

-- 9. 17.   8, 8, 5.    = 3 Chicchan, 18 Xul

_______________

         9. 15. 13. 0.     = 5 x (1.13.4.0) +    1.9.11.0.

                                  = 5 x (11,960) + 10,660 days

Still between page 804 to 818, he had not worked out the solution. In this way, the  

best possible date for the 3 Chicchan, 13 Yaxkin, would probably be between 1210 and

1536 AD.   On page 766, Lounsbury indicated that his count was far distant from the

Neither assumption was helpful to understanding his own calculations.  

The last statement Lounsbury made as his proposed conclusion for all his
efforts was:

“It is perhaps superfluous to such that this {paper] should be

taken as no more than one person’s attempt at a chronology

of the developments in Maya calendrics and astronomy,

that it is incomplete in many respects and thaft the dates

rashly ventured here are held subject to revisions.”

[Lounsbury, F. (1998, 759-818) Maya Numeration,

       Computation, and Calendrical   Astronomy]

As far as I know, Carlos Barrera Alueste is still working with the 819
created by Floyd Lounsbury. He is trying to fit it into the Venus Tables of the Dresden Codex.  

The exception to the Venus Tables in the Dresden, is the about birth of
the “venus” glyph on D-47b, which shown by the Skeletal ruler of the
western Land of the Dead and the single shaft of a lance with two obsidian
spearheads. Two comets with one body. One of the Night and the other
named for the day, who eclipsed the sun and the moon on the same day,
and left a “mirror” at high noon, so it could return to its [sun] home in
the east.{Tedlock, D. (1996)]

Therefore, it has nothing to do with the Planet Venus which as the
Morning star goes behind our sun and emerges eight days later
as the Evening star in the west.

                                        

         Fig. 01: The God of the Land of the Dead in the West.

Counting the Maya Nbrs the Easy Way

A very long time ago, in 1975, I had attended a class with a professor who was trying to study
Maya glyphs. The year previous, I had attended a class with Professor E, for whom I had done
a short comparasion between the Hittite glyphs and the Maya glyphs. Apparently, the other
unnamed professor knew that I had done it and he wanted to speed up my knowledge base.

In his class, I told him that I did not know enough about the Maya glyphs and could not write
anything worthhile about them. He threatened me by saying that he would not give me a grade
for his class, unless I took a class the next semester with him.

So, I took the other class. At the end of the class, I understood that I still could not decipher
anything in Maya because I could not understand any of it even after looking through the glyphs
again for him. When I got my two grades, I found that I had gotten two “F’s.”  Wow. well, that was
a hard lesson to learn, even more difficult than the Maya glyphs.

Then, I discovered in 1978, Linda Schele was going to teach Maya glyphs. Was that what I was
waiting for? Maybe. In Llinda’s class, I was given a choice: Draw out all the glyphs, or do a paper on
any of them. I spoke to Linda about drawing them out, but she knew I would not be doing it correctly.
She was right. I had drawn them out in pencil, not careully in ink, in a small hardback covered book.

I had done all of the gluphs that she had taught that semester. Taking each glyph apart by its prefixes
and suffixes, and any sub or superfixes. With its translation as I thought I had learned it. But, when
I spoke with Linda, she told me that she preferred that I write a paper.

Instead of going through the ones I had drawn out, I chose a monument investigated by Professor
Benson of the Benson Library at the University of Texas’ at Austin. The monument illustrated a woman
standing erect, with a shield over one arm and a lance in the other hand. Beside her head there was
a set of glyphs that gave her Title. The first glyph was “ma-bacc-el” H.m.m.m.m. That looked like a glyph
that Linda  had translated as “Mother of Child.” Since I cannot find even Tom Jones lessons that had it
printed clearly, I cannot even remember how it was spelled.

As it was, I was also trying to memorize Greek. Browsing in the little Greek library on Speedway,  
I happened upon a Turkish dictionary. Since I was always trying to match words around the world,
I pulled out the book and on pge 252, I discovered “mübeccel.”  But it was the translation that
fascinated me most: “Honoured, Reverenced.”

It fit the Warrior Woman much better than “Mother of Child.” And that was the way I wrote it up
for Linda Shele with proper cross-referencing from Sarah Blaffer‘s book, not the Turkish Dictionary,  
The Black-man of Zinacantan and her references to “Bats and Rulers.” The main glyph of “Mother
of Child” was a Bat with an upturned nose. The prefix was a “Ma-” similar to two seashells connected
by a curved line, standing erect on the bottom shell.

Linda Schele asked me one question: “What did I say about that glyph?”  And my dumb answer was
“I don’t know.” Because it was so out-of-place for a warrior, man or woman, I ignored it completelu. As
a result, I acquired another “F.”  My research was supposed to include my teacher’s view of the glyph
FIRST and FORMOST. The next decision I had to make was: “Do I quit getting “egg-on-my-face?” or
do I forge ahead and find what I can find anyway. That was not a hard choice to make at all.  It was Full Speed ahead!

My History lesson, a page of a series of history books. I was to take two books of my choice and write a short
paper about each. The first I commented on was Thomas More’s Utopia. I claimed that he had helped to destroy the
Maya Empire. Thomas More actually sent a ship called the [Ste] Barbara filled with colonists, but the crew when
they reached Ireland, the all mutineyed. . . . .

The second book was The Confessions of Nat Turner. I was informed the writer of this particular book about
a slave during the Civil War, was a black author, I claimed he was white. As for the black author, he appeared on
campus a month or so later, but had changed into a white man. My reference for that statements was the Reader’s
Digest. The Digest had short entries about a great variety of events. One was of a church group who printed up
bibles for an island of black church goers. They wanted to be accurate about what the people believed, so printed
the bible with black angels doing God’s work on earth. The church group blew it. The islanders said they knew
without a doubt that they, after death would be pure angels of light, no longer being black but white.

A Greek professor who told me, my attempts to translate the book about the Desert Fathers  was an utter failure.
He advised me to quit the class, but said I could stay to audit it. The Lesson? It was about Christian monks in Egypt
in the third century AD.

Since my efforts were useless as a translator, I located the English version at the HRC.
My suggestion was that the book was post-Inquisition or about the 14th century AD.. He told
me to prove it, and I did. It contained the strappado [water] torture, putting one’s arms or legs
into a cauldron of hot oil,  to get a confession; and also a monk’s idea of earning heaven was to
have his arms tied on a crossbar withfood in each hand. All typical of the 14th century Inquisition.  
This professor was more interested in how fast it was for me to get the information from my
computer. I lied, I had written my notes on index cards. However I did tell him in only took a few
seconds [to shift the cards] so I could choose what I thought was relevant. Later, the notes were
properly entered into my database.

My research went everywhere but I managed to graduate in 1979 and I made no move to get
an MA, or a Ph.D.  I felt that those titles only put me into a solid frame of agreeing with my
peers and would keep me from poking into corners of the world; especially my eclectic kind.
Many scholars would find something that was different, but because a certain path of learning
had to be followed, their conclusions missed its substance or complicated the circumstances
that produced the find. Which brings this page to its purpose:

COUNTING MAYA NUMBERS THE EASY WAY.

This Chart of a Vertical Trecena is slightly over-loaded with extra numbers: the number ONE
was written three times within the Vertical Trecena matrix in order to mAke a continuous sequence
of a Horizontal Trecena in what computer geeks call a “repeating loop” of 52-week work schedule
of a week of only four days.The other two days (our Saturday and Sunday) which  the farmer can
choose to be a volunteer in his community or he can choose to help a neighbor to build a house.

The Geeks do not care at all if a number has a name or not. They learned 440000 equals
a ”black” color [for letters and numbers in any program and they went from there. Al diablo
con palabras!

Their creations went from simple ”find” searches to more complex Excel calculations. They
were pleasantly surprised that the PI 3.14159 for the constant, a radius of a circle could be carried
over to 20 or more Zero’s, and many more if they were needed for a calculus measurement.

Writing about Calculus brings to mind a strange number 819, that the Maya never used on
their monuments or their history sessions.  Exoerts have created chart after chart and explanation
after explanation. Nevertheless, they failed to give any valid information about such a count.

There was an odd reason for that. The person who created that 819 number, did it by
combining n0, n1, n2, n3, n4, and n5 as his base. He decided that all these subscripts were
divisable by five. Really?

n0  -  uinal = 1-day

n1 -  Trecena = 13-days

n2 - Veintana = 20-days

n3 - Sacred Almanac = 260-days

n4- Nine days = 19-days

and n5 - Calendar Year = 365-days of 52-years or 18,980-days.
Other number groups were 9-days, 819-days and 4 x 819-days,

the moon days of 29 or 30 days.

Now if anyone could get through the 819 calculation by assuming that all of the above
number are divisible by 5, then one could run five of those numbers together to reach
the 819 figure which would become the coefficient for each one. The scholar made
a disclaimer, just in case.  

"It is not known whether this was the Maya  way; it probably was not.”

I assumed that the Maya had a way of counting numbers:  like bar(5) + dot(1) = 6.
They also had a set of names for very large numbers, from

kin = 1-day; uinal = 20-days;   tun = 360-days; katun = 7200 - days;. baktun = 144,000-days.  

And pictun, calabtun, and kinchiltun, which seem to have become through those who research
dates of the May.  This set of three seem appropriate for Maya numbers, but there is no
information that the Maya ever used them.  
The worst of the pretensions was when someone thought they knew it all and began
to use the n0  numbers to find the month names as far back as the BC centuries. Even
though the Maya recorded over and over again:

"the month names were created by Rome in 1583 for the year 1584
beginning with the first day of the month being IMIX and the first
Month Name became 0-POP. “

In other words, Rome sent out the month names which they had created and made a rule  the
new names would be used to make Maya dates comparable with the European calendars. And yet,

we should not forget the distance numbers, marked in the calculations as dn. There is also a Maya
commentary on them which has also been ignored by the gringo scholars,

Native Maya Calendar Makers, after much discussion, decided:

“Let us permit our calendar to gain on the true year; as fast as it will. We will

allow our calendar to function without change, but when we erect a monument,

we will engrave upon it, in addition to the official calendar, date of its dedication,

a calendar correction for that particular date. In this way, no matter what date

our calendar may register, we will always know, whenever we erect a monument,

the position of its corresponding date in the true year.”

Would it not be wonderful to have teachers who could teach us   the mathematics in such
a simple Maya terms. Terms that do not say 52-weeks belong to 52-years and at the end of
those 52-years there would be a great First Fire, where everything used in the homes would
not be destroyed and all new items would NOT have to be bought to replace pots, ollas, cups,
plates, baskets, digging sticks, rebozos, skirts, shirts, sandals, . . .everything NEW that should
last to be used for another 52-years.

A Conclusion of Sorts

Can you imagine a child being born shortly after the First Fire and having
diapers to wear baby clothing for 52-years. Would it not sound silly to any grown person? Would not
a person laugh at such a life? Do such numbers really exist in real life?

The Aztec Sun Stone

In order to clarify and not confuse the count of the Trecena I have only placed a quarter
section of the Sun stone as an example because, under the fire glyphs of the serpent, there are
three units of four bound by a star-glyph that I believe indicates the actual count of the Vertical
I have gone as far back as the Madrid Codex to emphasis the comparisons between various
translators and their beliefs about the date and story changes that turn up when they rely on
current documents for their theories.

************************************

A decision was made by Rome, after the Friars, who accompanied the soldiers to
Mesoamerica, reported the natives counted on their fingers and maybe even used their
toes. They then inferred there was no way the natives could have known what a 360-day
year was or when a 365-day/year evolved.

Only the glorious ancient Roman ruler, Julius Caesar, was supposedly capable of
re-adjusting the agricultural stars by mandating a longer year of 445-days in the first century,
so the seasons would realign with European farming methods. This was a strange belief
since the comet that changed the calendars had never appeared in Caesar’s 100 +/- BC era.

There was another Julius Caesar in the 15th century who could have created such a calendar.
But was this JC too late in years to do anything about an ancient calendar system? Was the whole
of both Americas only inhabited by primitive natives? The Trecena was shown on the three sections
directly under three fire glyphs of one of the two serpents on the stone. The large star under the four
circles probably was meant to be a knot on the cords of a single year.

So the 52-year cycle was a decision made for the strange stone with four Ages of the Sun, each
determined to be 676-years.The number 676 multiplied by 4 equals 2704 which is the square
of 52. But if the numbers of the Sun Stone are only 3 X 676, then what? The answer only
equals 2028. Would that mean that the 52-year cycle is only a 39-year cycle?

Diego de Landa (1566, 59) edited by William Gates (1937 & 1978, 59 note*)
Yucatan Before and After the Conquest, [Dover Editon]. Although the 52-year cycle
is mentioned in his book, it is only in Wm, Gates’s Footnote* on pages 59-60. Gates, there stated ]
that the Maya "never used a 30i-day month."
[My Note: Does anyone in modern offices, used a 30 or 31 day month to schedule their office hours?
Or do they just use the Monday thru Friday part of the week]: It was not until de Landa died in
1579, that Rome readjusted the Mesoamerican calendars to include month names for the year
1584, [See Jose Castillo-Torre (1955) for how those dates came to be.] The Madrid Codex might
give more information.

Madrid Codex

a. Cortesiano (1867, M-12 to M-19) It contains the Horizontal Serpent Trecena pages in proper
English reading order (i.e. left to right) IMIX was the first column, introduced by Rome in 1583-4.
It is necessary to understand why two KIMI’s were in columns 45-46. A KIMI or Death glyph was
an indication that the ending at 52 weeks would not mesh with the Vertical Trecena, the second
unit of a 4-day week, nor the third unit of a 4-day week. Yet, the Serpent pages one can also read
about the myth of the Sovereign Serpent found in the Popol Vuh] by reading the figures associated
with the Madrid Serpent Calendar. They are to be read Right to Left. [M-18 to M-12]

b. Troano 1866 is the original Madrid Codex starting from M-112 reading the Heavenly Bees
in their homes marked with sky bands. They represented Tlaloc’s “Burning Ash of Resin or of
Turpentine” for 52 X 7 [= 364-years] on the Sun Stone to the carving of the Wooden Manikins
[M-101] and Chalchuitlique’s “Water” of 52 X 6 [= 312-years] The two Ages of the Sun when
added together; the 364 plus the 312 equals 676].

These two versions of mathematics are found below in the History. Page 157 detailed the
same 1 to 13 numeration (see chart below for error] used within the Tonalpohualli with a different
set of 159-weeks which are not connected to the 532/13 coefficient pattern.. The 52-year cycle is
now established [mathematically]. Has it become incised in stone forever? Even so, page 154
agreed with the Horizontal Trecena version for the 1 - 13-day cycle.

Each week rotated separately but only using the 4-day names found in each week. This error of
number 13 throws any Horizontal Trecena calculation out of sequence. The previous Chart for The
Trecena in four different Languages; sing the NUMBERS ONLY creates a minor problem of one extra
day at the end of three Vertical years.1870-1878-1883 and J. Hemry Phillips (1945, 8) The History of
the Mexicans as Told by Their Paintings. contain segments of the Codex Ramirez. It is on page 8 that v
erifies the above calculations: [52 X 7 and 52 X 6] which indicated that 52 is a coefficient of 676, as
is 6 + 7 which combined gives the other coefficient as 13.

Because it is an Aztec manuscript and not a Maya one, where the names of all participants in Part I and
Part II of the Popol Vuh were not an Aztec myth, the Maya story and calendars have become separate
and distinct versions and are seldom connected to the Aztec/Olmec/Toltec stories.

George C. Vaillant, (1941, 1962, 75, n,1, 244; 154, 164. 165) Aztecs of Mexico, Page 75 emphasized
the 52-year cycle had used the Planet Venus cycle as its confirmation. Page 154 also accommodated
the 1-13 numbers without names against the 20-day names as a continuous rotating sequence over
the years. Vaillant also mentioned the Calendar Stone on pages 82-3; 133-4; 139; and 188; with two
versions of the Sun Stone placement: i.e the round disk and a disk above an abbreviated temple
staircase. None of his pages follow the Maya Popol Vuh sequence.

However, the storyline is still the same. The First and Last Ages of the Sun with the four 676 numbers
are still stated contrary to the Popol Vuh version of the proper sequence..

José Castillo-Torre (1955, 98) Por La Seňal de Hunab Ku. On Page 98 in his book illustrated how the

Trecena was set-up in the first set of these four names as the Vertical Trecena countdown: Ik, MANIK,

EB, CABAN. The Horizontal set of the four names tell us which would start the first column of each of

the 20-day units for the total of 20-day names,

Each would be combined to add up to a 52-week sequence of the Vertical Trecena within the
Horizontal version. It is then laid out on page 100, to show the true use of the number 13.----that
of a “pre-computerized loop” [Noted in the above chart} so that three milpas can be rotated every
three years to ensure nutrients can be restored to the previous milpas in proper order so each can
have a good harvest for the fourth year of planting.

Oscar Rueda, (1976 ) “El Secreto de la Piedra del Sol” Even though the Sun Stone was moved
into the Museo Nacional de Arquoelogia E Historia in 1885, it remained only an image to be admired.
In the year 1976, Oscar Rueda decided to do a complex study of all the possible measurements
that could be obtained.

In his heart he knew there had to be something special about the monumental Sun Stone, he could
not quite put his finger on the underlying story of the Stone. He completed more than 18 diagrams
of different vector combinations, but still did not understand what exactly the Sun Stone
was inferring by its silent glyphs. The glyphs seemed to point to specific details, but, the
details were not stated in any particular order.

Editor: Micheal P. Closs, (1986, 213-259) Native American Mathematics. By this time, the 52-year
cycle called the “Sacred Bundle,” was found on page 222, as a firmly established numbered cycle
that sequence was to be used in Mesoamerican mathematics.

Munro S. Edmonson, (1988, 20) The Book of the Year: Middle American Calendrical Systems.
This author started out referring to his early sources for verifying his premises. Two statements on
page 20 explained his rationale. The first: “It is not always possible to reconstruct the ‘reasons for
a date that does not fit. . . “

And the second date that begins the explanation for the inferred year 679 BC:
“If Caso and Bernard (1965, 871) are right about the dating of Cuicuilco and if the inhabitants
of that site used dot numerals instead of the digits of Oaxaca and Chiapas, and if this figure is
read as an Olmec year, then this is the earliest calendar-round date known.”

The date was found on an earspool now at the Museo de Cuicuiloco. It reads:

“679 BC, I2 IX J, or 6.3.10. 9.0 or 2 Ahau 3 CEH T (2 Lord, 19 F, Olmec.

The next inferred year of 667 BC claimed that the Olmecs used the Type V Year Bearers
which are determined by using the 1-13 down a list of days as a repeating loop through
eternity. From these few pages, all the way to 1584 on page 83, every date had the year,
month and the 1-13 day count applied to each year the author identified. The European
calendar scholars had created coefficients and other calculus features. Even though the earliest
AD/BC years that had no month names until 1583-4.

Thereafter, from the above pages to the 1584 date to page 83, there are various reasons why
the dates do not agree with the computations known to present scholars. The excuses run from

"transcription errors" to dates "calculated to 23 years earlier" OR "one that was 27 years later;"

OR "native scribal errors."

A statement on page 211 gave a statement that might have explained the Mixtec reason:

“month names remain linguistically undocumented.”

Conculsion

The Horizontal Trecena count is a little different. It only counts five weeks of four working
days for each name of the Trecena: IK, MANIK, EB, and CABAN. Or as Rome insisted in

1584 IMIX, CIMI, CHUEN, AHAW.  It is only the IK MANIK sequence that will mesh perfectly

with the Vertical Trecena group, whereas each of the 52 weeks of the Horizontal Trecena

must rotate IK by putting it under the CABAN until IK rises to first place at the end of the

20-day period.

( The best way to understand the weekly changes is to go to the Serpent calendar pages in the Madrid and follow the correct sequence for all but the last section.  There, one will find a CIMI in the correct place but the next column will show another CIMI in the MANIK slot. The two so close together was basically to tell the reader that the IMIX at the beginning will not adjust to fit into the Vertical Trecena.

And writting about the word “slot,” Remember that the “One-armed bandits” of the gambling halls use the same technique to keep their gamblers on edge as the lemon, cherries, [and whatever] roll to a stop, each of the four figures must be the same to win. It seldom does, because each column runs on its own individual wheel, probably each also has a different speed differential.

Welcome to the world of CALCULUS Mathematics. Thank heavens, it is not the Maya method of counting, except when mathematicians decide they want a newer faster system to find the months,
days, years, and distance numbers in Maya.)