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PUBLICATIONS OF THE UNIVERSITY OF PENNSYLVANIA
SERIES IN
Philology Literature and Archæology
VOL. III NO. 2
A PRIMER OF
MAYAN HIEROGLYPHICS
BY
DANIEL G. BRINTON, A.M., M.D., LL.D., Sc.D.
PROFESSOR OF AMERICAN ARCHÆOLOGY AND LINGUISTICS IN THE UNIVERSITY OF
PENNSYLVANIA, PRESIDENT OF THE AMERICAN ASSOCIATION FOR THE ADVANCEMENT
OF SCIENCE, ETC., ETC.
“Hieroglyphics old,
Which sages and keen-eyed astrologers,
Then living on the earth, with labouring thought,
Won from the gaze of many centuries.”
—KEATS
GINN & COMPANY
Agents for United States, Canada, and England
7–13 Tremont Place, Boston, U.S.A.
MAX NIEMEYER
Agent for the Continent of Europe
Halle, a S., Germany
------------------------------------------------------------------------
PREFACE.
In the following pages I have endeavored with the greatest brevity to
supply the learner with the elements necessary for a study of the native
hieroglyphic writing of Central America. The material is already so
ample that in many directions I have been obliged to refer to it, rather
than to summarize it. This will explain various omissions which may be
noted by advanced scholars; but they will not, I believe, diminish the
usefulness of the work as an elementary treatise.
In conclusion I would express my thanks to the officers of the Bureau of
American Ethnology, Washington, and of the Peabody Museum of Archæology,
Cambridge, for various facilities they have obligingly furnished me.
CONTENTS.
_I. Introductory._
PAGE
1. GENERAL CHARACTER OF MAYAN HIEROGLYPHICS, 9
2. THE MAYAN MANUSCRIPTS OR “CODICES,” 11
3. THEORIES OF INTERPRETATION. “ALPHABETS” AND “KEYS,” 13
_II. The Mathematical Elements._
1. THE CODICES AS TIME-COUNTS, 18
2. THE MAYAN NUMERAL SYSTEM, 19
3. NUMERICAL AND ALLIED SIGNS, 19
4. THE RHETORICAL AND SYMBOLIC USE OF NUMBERS, 24
5. THE MAYAN METHODS OF COUNTING TIME, 25
6. THE CALCULATIONS IN THE CODICES, 29
7. RULES FOR TRACING THE TONALAMATL, OR RITUAL CALENDAR, 31
8. THE CODICES AS ASTRONOMICAL TREATISES, 32
9. ASTRONOMICAL KNOWLEDGE OF THE ANCIENT MAYAS, 34
_III. The Pictorial Elements._
1. THE RELIGION OF THE ANCIENT MAYAS, 37
Itzamna—Cuculcan—Kin ich—Other Gods—The Cardinal
Points—The Good Gods—The Gods of Evil—The Conflict of
the Gods.
2. THE COSMOGONY OF THE MAYAS, 46
3. THE COSMICAL CONCEPTIONS OF THE MAYAS, 47
4. PICTORIAL REPRESENTATIONS OF DIVINITIES, 50
Representations of Itzamna—Of Cuculcan—Of Kin ich—Of
Xaman Ek, the Pole Star—Of the Planet Venus—Of Ghanan,
God of Growth—Of the Serpent Goddess—of Xmucane—Of Ah
puch, God of Death—Of the God of War—Of Ek-Ahau and
other Black Gods.
5. THE MAYA PRIESTHOOD, 68
6. FANCIFUL ANALOGIES, 69
7. TOTAL NUMBER OF REPRESENTATIONS, 70
8. FIGURES OF QUADRUPEDS, 71
9. FIGURES OF BIRDS, 72
10. FIGURES OF REPTILES, 74
11. OCCUPATIONS AND CEREMONIES, 76
_IV. The Graphic Elements._
1. THE DIRECTION IN WHICH THE GLYPHS ARE TO BE READ, 78
2. COMPOSITION OF THE GLYPHS, 81
3. THE PROPER METHOD OF STUDYING GLYPHS, 81
4. AN ANALYSIS OF VARIOUS GRAPHIC ELEMENTS, 82
The Hand—The Eye and Similar Figures—The “Spectacles”—The
Ear—Crescentic Signs—Sun and Moon Signs—Supposed
Variations of the Sun Sign—The Knife Signs—The “Fish
and Oyster” Sign—The Sacred Food Offerings—The _Ben ik_
and Other Signs—The Drum Signs—The Yax and Other
Feather Signs—The Cross-hatched Signs—Some Linear Signs
and Dots—Linear Prefixes—The “Cloud-balls” and the
“Cork-screw Curl”—Signs for Union—The “Tree of
Life”—The “Machete” and Similar Signs—Supposed Bird
Signs—The “Crotalean Curve”—Objects Held in the
Hand—The Aspersorium, the Atlatl and the Mimosa—The
“Constellation Band”—The Signs for the Cardinal
Points—The Directive Signs—The “Cuceb.”
5. THE HIEROGLYPHS OF THE DAYS, 109
6. THE HIEROGLYPHS OF THE MONTHS, 116
7. THE HIEROGLYPHS OF THE DEITIES, 121
_V. Specimens of Texts._
1. THE GOD OF TIME BRINGS IN THE DEAD YEAR. DRESDEN CODEX, 127
2. SACRIFICE AT THE CLOSE OF A YEAR. DRESDEN CODEX, 128
3. END OF ONE AND BEGINNING OF ANOTHER TIME PERIOD. CORTESIAN
CODEX, 129
4. THE GOD OF GROWTH AND THE GOD OF DEATH. CORTESIAN CODEX, 131
5. AUGURIES FROM THE NORTH STAR. CORTESIAN CODEX, 131
6. ITZAMNA, THE SERPENT GODDESS, AND KIN ICH. DRESDEN CODEX, 132
7. THE GODS OF DEATH, OF THE SUN, AND OF WAR. DRESDEN CODEX, 132
8. CUCULCAN MAKES NEW FIRE. CODEX TROANO, 133
9. THE GODS OF DEATH, OF GROWTH, AND OF THE NORTH STAR. DRESDEN
CODEX, 133
10. THE GOD OF GROWTH, OF THE SUN, AND OF THE EAST. DRESDEN CODEX, 134
11. AN INSCRIPTION FROM KABAH, 135
12. LINEAR INSCRIPTION FROM YUCATAN, 136
13. THE “INITIAL SERIES” FROM THE TABLET OF THE CROSS, PALENQUE, 137
14. INSCRIPTION ON THE “TAPIR TABLET,” CHIAPAS, 138
15. INSCRIPTION ON A TABLET FROM TONINÁ, CHIAPAS, 139
16. INSCRIPTION ON AN AMULET FROM OCOCINGO, CHIAPAS, 139
17. INSCRIPTION ON A VASE FROM A QUICHE TOMB, GUATEMALA, 140
A PRIMER OF
MAYAN HIEROGLYPHICS.
I. Introductory.
The explorations among the ruined cities of Central America undertaken
of late years by various individuals and institutions in the United
States and Europe, and the important collections of casts, tracings and
photographs from those sites now on view in many of the great museums of
the world, are sure to stimulate inquiry into the meaning of the
hieroglyphs which constitute so striking a feature on these monuments.
Within the last decade decided advances have been made toward an
interpretation of this curious writing; but the results of such studies
are widely scattered and not readily accessible to American students.
For these reasons I propose, in the present essay, to sum up briefly
what seem to me to be the most solid gains in this direction; and to add
from my own studies additional suggestions toward the decipherment of
these unique records of aboriginal American civilization.
1. _General Character of Mayan Hieroglyphs._
One and the same hieroglyphic system is found on remains from Yucatan,
Tabasco, Chiapas, Guatemala, and Western Honduras; in other words, in
all Central American regions occupied at the Conquest by tribes of the
Mayan linguistic stock.[1] It has not been shown to prevail among the
Huastecan branch of that stock, which occupied the valley of the river
Panuco, north of Vera Cruz; and, on the other hand, it has not been
discovered among the remains of any tribe not of Mayan affinities. The
Mexican manuscripts offer, indeed, a valuable ancillary study. They
present analogies and reveal the early form of many conventionalized
figures; but to take them as interpreters of Mayan graphography, as many
have done, is a fatal error of method. In general character and
appearance the Mayan is markedly different from the Mexican writing,
presenting a much more developed style and method.
Although the graphic elements preserved in the manuscripts and on the
monuments vary considerably among themselves, these divergencies are not
so great but that a primitive identity of elements is demonstrable in
them all. The characters engraved on stone or wood, or painted on paper
or pottery, differ only as we might expect from the variation in the
material or the period, and in the skill or fancy of the artist.
The simple elements of the writing are not exceedingly numerous. There
seems an endless variety in the glyphs or characters; but this is
because they are composite in formation, made up of a number of
radicals, variously arranged; as with the twenty-six letters of our
alphabet we form thousands of words of diverse significations. If we
positively knew the meaning or meanings (for, like words, they often
have several different meanings) of a hundred or so of these simple
elements, none of the inscriptions could conceal any longer from us the
general tenor of its contents.[2]
It will readily be understood that the composite characters may be
indefinitely numerous. Mr. Holden found that in all the monuments
portrayed in Stephen’s _Travels in Central America_ there are about
fifteen hundred;[3] and Mr. Maudslay has informed me that according to
his estimate there are in the Dresden Codex about seven hundred.
Each separate group of characters is called a “glyph,” or, by the French
writers, a “katun,” the latter a Maya word applied to objects arranged
in rows, as soldiers, letters, years, cycles, etc. As the glyphs often
have rounded outlines, like the cross-section of a pebble, the Mayan
script has been sometimes called “calculiform writing” (Latin,
_calculus_, a pebble).
2. _The Mayan Manuscripts or “Codices.”_
The hieroglyphic writing is preserved to us on two classes of
remains—painted on sheets of native paper, about ten inches wide and of
any desired length, which were inscribed on both sides and folded in the
manner of a screen; and engraved or painted on stone, wood, pottery, or
plaster.[4]
Of the former only four examples remain, none of them perfect. They have
all been published with great care, some of them in several editions.
They are usually spoken of as “codices” under the following names: the
_Codex Troanus_ and the _Codex Cortesianus_, probably parts of the same
book, the original of which is at Madrid; the _Codex Peresianus_, which
is in Paris; and the _Codex Dresdensis_, in Dresden. The two former and
the two latter resemble each other more closely than they do either
member of the other pair. There are reasons to believe that the two
first mentioned were written in central Yucatan, and the last two in or
near Tabasco.[5] This district and that of Chiapas, adjacent to it on
the south, was occupied at the time of the Conquest by the
Tzental-Zotzil branch of the Mayan stock, who spoke a dialect very close
to the pure Maya of Yucatan; they were the descendants of the builders
of the imposing cities of Palenque, Ococingo, Toniná and others, and we
know that their culture, mythology, and ritual were almost identical
with those of the Mayas. I shall treat of them, therefore, as
practically one people.
Although Lord Kingsborough had included the Dresden Codex in his huge
work on “_Mexican Antiquities_,” and the _Codex Troanus_ had been
published with close fidelity by the French government in 1869, it
cannot be said that the serious study of the Mayan hieroglyphs dates
earlier than the faithful edition of the Dresden Codex, issued in 1880
under the supervision of Dr. E. W. Förstemann, librarian-in-chief of the
Royal Library of Saxony.
The most important studies of the codices have been published in
Germany. Besides the excellent writings of Dr. Förstemann himself, those
by Dr. P. Schellhas and Dr. E. Seler, of Berlin, are of great utility
and will be frequently referred to in these pages. In France, Professor
Leon de Rosny, the competent editor of the _Codex Peresianus_, the Count
de Charencey, and M. A. Pousse, whose early death was a severe loss to
this branch of research, deserve especial mention. In England no one has
paid much attention to it but Mr. Alfred P. Maudslay, whose
investigations have yielded valuable results, forerunners of others of
the first importance. The earlier speculations of Bollaert are wholly
fanciful. In our own country, the mathematical portions of the essays of
Professor Cyrus Thomas are worthy of the highest praise; and useful
suggestions can be found in Charles Rau’s article on the inscriptions of
Palenque, and in Edward S. Holden’s paper on Central American
picture-writing.[6]
3. _Theories of Interpretation._
The theories which have been advanced as to the method of interpreting
the Mayan hieroglyphs may be divided into those which regard them as
ideographic, as phonetic, or as mixed. The German writers, Förstemann,
Schellhas, and Seler, have maintained that they are mainly or wholly
ideographic; the French school, headed by the Abbé Brasseur, de Rosny,
and de Charencey, have regarded them as largely phonetic, in which they
have been followed in the United States by Professor Cyrus Thomas, Dr.
Cresson, Dr. Le Plongeon, and others.
The intermediate position, which I have defended, is that while chiefly
ideographic, they are occasionally phonetic, in the same manner as are
confessedly the Aztec picture-writings. In these we constantly meet with
delineations of objects which are not to be understood as conveying the
idea of the object itself, but merely as representing the sound of its
name, either in whole or in part; just as in our familiar “rebus
writing,” or in the “chanting arms” of European heraldry. I have applied
to this the term “ikonomatic writing,” and have explained it so fully,
as it is found in the Mexican manuscripts, in my “_Essays of an
Americanist_,” that I need not enter upon it further in this connection,
but would refer the reader to what I have there written.[7]
The attempt to frame a real alphabet, by means of which the hieroglyphs
could be read phonetically, has been made by various writers.
The first is that preserved in the work of Bishop Landa. It has failed
to be of much use to modern investigators, but it has peculiar value as
evidence of two facts; first, that a native scribe was able to give a
written character for an unfamiliar sound, one without meaning, like
that of the letters of the Spanish alphabet; and, secondly, that the
characters he employed for this purpose were those used in the native
manuscripts. This is proof that some sort of phonetic writing was not
unknown.[8]
This alphabet was extended by the Abbé Brasseur, and especially by de
Rosny, who, in 1883, defined twenty-nine letters, with numerous variants
from the Codices and inscriptions.[9]
Two years later, Dr. A. Le Plongeon published an “Ancient Maya Hieratic
Alphabet according to Mural Inscriptions,” containing twenty-three
letters, with variants. This he applied to the translating of certain
inscriptions, but added nothing to corroborate the correctness of the
interpretations. Each sign, he believed, stood for a definite
letter.[10]
[Illustration: FIG. 1.—Landa’s Alphabet; after a photograph from the
original manuscript.]
Another student who devoted several years to an attempt to reduce the
hieroglyphs to an alphabetic form was the late Dr. Hilborne T. Cresson.
His theory was that the glyphs stood for the names of pictures worn down
to a single phonetic element, alphabetic or syllabic. This element he
conceived was consonantal, to be read with any vowel, either prefixed or
suffixed; and the consonant was permutable with any of its class, as a
lingual, palatal, etc. On this basis he submitted, shortly before his
death in 1894, to the American Association for the Advancement of
Science several translations from the Codex Troano. Previous to this, in
1892, he had announced his method in the journal “_Science_,” and
claimed that he had worked it out ten years before.[11]
An alphabet of twenty-seven characters, with variants, which the author
considered in every way complete, was published in 1888, by F. A. de la
Rochefoucauld.[12] By means of it he offered a volume of interlinear
translations from the inscriptions and codices! They are in the highest
degree fanciful, and can have little interest other than as a warning
against the intellectual aberrations to which students of these ancient
mysteries seem peculiarly prone.
In 1892 Professor Cyrus Thomas, of the Bureau of Ethnology, announced
with considerable emphasis that he had discovered the “key” to the Mayan
hieroglyphs; and in July, 1893, published a detailed description and
applications of it.[13] In theory, it is the same as Dr. Cresson’s, that
is, that the elements of the glyphs were employed as true phonetic
elements, or letters. In the article referred to he gives the characters
for the following letters of the Maya alphabet: _b_, _c_, _c’_, _dz_,
_ch_, _h_, _i_, _k_, _l_, _m_, _n_, _o_, _p_, _pp_, _t_, _th_, _tz_,
_x_, _v_, _z_; also for a large number of syllabic sounds which he
claimed to have recognized. With such an apparatus, if it had any value,
one would expect to reach prompt and important results; but, aside from
the doubtful character of many of his analyses, the fact that this “key”
has wholly failed to add any tangible, valuable addition to our
knowledge of the inscriptions is enough to show its uselessness; and the
same may be said of all the attempts mentioned.
* * * * *
A slight inspection of the Maya manuscripts and of almost any of the
inscriptions will satisfy the observer that they are made up of three
classes of objects or elements:—
1. Arithmetical signs, numerals, and numerical computations,
2. Pictures or figures of men, animals, or fantastic beings, of
ceremonies or transactions, and of objects of art or utility; and,
3. Simple or composite characters, plainly intended for graphic elements
according to some system for the preservation of knowledge.
I shall refer to these as, (1) the Mathematical Elements, (2) the
Pictorial Elements, and (3) the Graphic Elements of the Mayan
hieroglyphic writing.
-----
Footnote 1:
In accordance with usage in this study, I employ the adjective “Mayan”
when speaking of the whole stock, and confine “Maya,” in an adjectival
sense, to that branch of the stock resident in Yucatan.
Footnote 2:
This is also the opinion of Dr. Seler: “Es ist eine verhältnissmässig
geringe Zahl von Bildern und Grundelementen, die in diesen
Schriftzeichen wiederkehren.” _Verhand. Berliner Anthrop. Gesell._,
1887, S. 231.
Footnote 3:
“Studies in Central American Picture Writing,” in _First An. Rep. of
the Bureau of Ethnology_, p. 210.
Footnote 4:
Among those who have especially merited the thanks of archæologists in
collecting material for the study of the monuments are M. Désiré
Charnay, Mr. A. P. Maudslay, Prof. F. W. Putnam; and I shall hope to
add Dr. Le Plongeon, when he makes public his material.
Footnote 5:
The _Peresianus_ has been supposed by some to have been written in
Guatemala; by others, both it and the _Dresdensis_ have been
considered of Tzental origin. See Pousse, in _Arch. de la Soc. Amer._,
1885, p. 126, and Paul Perrin, “Les Annotations Européennes du Codex
Peresianus,” in the same, June, 1887, p. 87 sqq. Förstemann
(_Entziff._ III.) gives several cogent reasons for believing that the
Dresdensis was written in or near Palenque.
Footnote 6:
The four Codices can be obtained by placing an order with one of the
leading importers of foreign books in New York City. The four cost
about one hundred dollars. The study of the German writers is
indispensable. The contributions of Dr. Schellhas and Dr. Seler will
be found in the numbers of the Berlin _Zeitschrift für Ethnologie_,
1886 and later. Dr. Förstemann has likewise published in the
_Zeitschrift_, 1891, and also in the _Centralblatt für
Bibliothekwesen_, in which remote quarter some of his most thoughtful
contributions have appeared; and in the Proceedings of the
International Congress of Americanists. Four of his articles bear the
general title, “Zur Entzifferung der Mayahandschriften,” I, II, III,
IV. I refer to them by these numbers. The articles of Professor
Thomas, Professor Rau, and Mr. Holden are contained in the annual
reports of the Bureau of Ethnology, Washington, where they can be
readily consulted by American students.
Footnote 7:
The essays to which I particularly refer are: “The Phonetic Elements
in the Graphic Systems of the Mayas and Mexicans;” “The Ikonomatic
Method of Phonetic Writing;” “The Writing and Records of the Ancient
Mayas;” and “The Books of Chilan Balam.” All these are reprinted in my
_Essays of an Americanist_, published by Porter & Coates,
Philadelphia, 1890. As to how far this or any phonetic system is
consistent with the known differences of dialects in the Mayan stock,
is a question which space does not permit me to enter upon. I can only
say that the signification seems to me to have been fixed in the
Maya-Tzental district, and thence carried to the Chortis, Quiches,
etc.
Footnote 8:
The first copy of Landa’s alphabet published in the United States was
by myself in the _American Historical Magazine_, 1870. Twenty years
later, 1890, in my _Essays of an Americanist_, p. 242, I reproduced a
photographic fac-simile of it from the original MS. Though not without
considerable value in certain directions, I do not think it worth
while to dwell upon it here.
Bishop Landa’s important work, _Relacion de las Cosas de Yucatan_,
written about 1570, must be carefully read by every student on this
branch. It has been twice published, first by the Abbé Brasseur, at
Paris, 1864, and more fully at Madrid, under the competent editorship
of Juan de Dios de la Rada y Delgado, in 1884. On the relative merits
of the two editions, see my “Critical Remarks on the Editions of Diego
de Landa’s Writings,” in the _Proceedings_ of the American
Philosophical Society, 1887.
Footnote 9:
The Abbé Brasseur’s whimsical speculations are in his introduction to
the Codex Troano, published by the French government in 1869. The
chief work of de Rosny on the subject is his _Essai sur le
Déchiffrement de l’Ecriture Hiératique de l’Amérique Centrale_, folio,
Paris, 1876. He fully recognizes, however, that there are also
ideographic and pictorial characters as well as phonetic.
Footnote 10:
Dr. Le Plongeon’s “Alphabet” was published in the Supplement to the
_Scientific American_, New York, for January, 1885.
Footnote 11:
At the time of his unexpected death, Dr. Cresson had left with me a
full exposition of his theory. His enthusiasm was unbounded, and the
sacrifices he had made in the pursuit of archæological science merit
for his memory a kindly recognition among students of this subject.
Footnote 12:
_Palenqué et la Civilisation Maya_ (Paris, 1888). The “Alphabet
phonétique des anciens Mayas” is on pp. 10 sqq. The author was at one
time attached to the French legation in Guatemala.
Footnote 13:
In the _American Anthropologist_, Washington, D. C.
II. The Mathematical Elements.
1. _The Codices as Time-Counts._
In another work I have explained the numeral system in vogue among the
ancient Mayas, as well as the etymology of the terms they employed.[14]
It will be sufficient, therefore, to say here that their system was
vigesimal, proceeding by multiples of twenty up to very large sums. In
the same work I have quoted from original sources the information that
the fives up to fifteen were represented by single straight lines and
the intermediate numbers by dots. This has also been discovered
independently by several students of the manuscripts.
The frequency and prominence of these elementary numerals in nearly
every relic of Mayan writing, whether on paper, stone, or pottery,
constitute a striking feature of such remains, and forcibly suggest that
by far the majority of them have one and the same purpose, that is,
_counting_; and when we find with almost equal frequency the signs for
days and months associated with these numerals, we become certain that
in these records we have before us _time-counts_—some sort of
ephemerides or almanacs. This is true of all the Codices, and of nine
out of ten of the inscriptions. Here, therefore, is a first and most
important step gained toward the solution of the puzzle before us.
But did this incessant time-counting refer to the past or to the future?
Was it history or was it prophecy? Or, passing beyond this world, was it
astronomy? Was it mythology or ritual, the epochs and the eons of the
gods? Perhaps the disposition, sequence, and values of the numbers
themselves, once comprehended, will answer these vital questions.
2. _The Mayan Numeral System._
Unfortunately, the old writers, either Spanish or native, tell us little
about Maya mathematics. They say the computation ran thus:—
20 units = one _kal_, 20.
20 _kal_ = one _bak_, 400.
20 _bak_ = one _pic_, 8000.
20 _pic_ = one _calab_, 160,000.
20 _calab_ = one _kinchil_ or _tzotzceh_, 3,200,000.
20 _kinchil_ = one _alau_, 64,000,000.
The Tzental system was the same, though the terms differed somewhat: 20
units = one _tab_ (cord or net-ful); 20 _tabs_ = one _bac_; 20 _bacs_ =
one _bac-baquetic_ (bundle of bacs); 20 _bac-baquetics_ = one _mam_
(grandfather); 20 _mams_ = one _mechun_ (grandmother); 20 _mechuns_ =
one _mucul mam_ (great-grandfather), 64,000,000.[15]
No doubt in the numerical notation there were special signs for each of
these higher unities; but neither Bishop Landa nor the native writers
who composed the singular “Books of Chilan Balam” have handed them down.
Modern sagacity, however, has repaired ancient negligence, and we can,
almost to a certainty, restore the numerical notation of the aboriginal
arithmeticians.
The scholar who has worked most successfully in this field is Dr.
Förstemann, the editor of the Codex of Dresden, and I shall introduce a
condensed statement of his results, referring the student to his own
writings for their demonstration.
3. _Numerical and Allied Signs._
The first important discovery of Dr. Förstemann in this direction was
that of the sign for the naught or cipher, 0. It is given in Fig. 2.[16]
It has a number of variants, some ornamental in design. Next, he
discovered the system of notation of high numbers. This is not like
ours, but resembles that in use in the arithmetic of ancient Babylonia
and some parts of China. The numerals are arranged in columns, to be
read from below upward, the value of each unit of a given number being
that power of 20 which corresponds to the line on which it stands
counted from the bottom. This will be readily understood from the
following example:—
_Maya _Simple values._ _Composite
numerals._ values._
[Illustration] 8 (1 = 20^4, = 160,000; hence, 8 × 160,000) = 1,280,000
[Illustration] 11 (1 = 20^3, = 8,000; hence, 11 × 8,000) = 88,000
[Illustration] 8 (1 = 20^2, = 400; hence, 8 × 400) = 3,200
[Illustration] 7 (1 = 20, = 20; hence, 7 × 20) = 140
[Illustration] 0 (1 = 1, = 1; hence, 0 × 1) = 0
—————————
Total 1,377,340
FIG. 2.—Maya Notation.
This would be according to the regular system of the Maya numeration as
given above; but in applying it to the calculations of the native
astronomer who wrote the Dresden Manuscript, Dr. Förstemann discovered a
notable peculiarity which may extend over all that class of literature.
In the third line from the bottom, where in accordance with the above
rule the unit is valued at 20 × 20 = 400, its actual value is 20 × 18 =
360.
It immediately suggested itself to him that in time-counts this
irregular value was assigned in order that the series might be brought
into relation to the old solar year of 360 days, composed of 18 months
of 20 days each, in the native calendar.
This correction being made, the above table would read:—
8 (1 = 7200 × 20 = 144,000) = 1,152,000
11 (1 = 360 × 20 = 7,200) = 79,200
8 (1 = 20 × 18 = 360) = 2,880
7 (1 = 20) = 140
0 (1 = 1) = 0
—————————
1,234,220
[Illustration: FIG. 3.—Maya Numerals.]
An examination of the mural inscriptions showed that on them also the
same plan for the expression of high numbers had been employed, and Dr.
Förstemann was enabled to interpret with accuracy the computations on
the monuments from Copan, Quirigua, and Palenque; developing
incidentally the remarkable fact that the inscriptions of Copan contain
as a rule higher numbers and are therefore presumably of later date than
those of Palenque. The highest is that on “Stela N,” as catalogued by
Mr. Maudslay, which ascends to 1,414,800 days, or 3930 years of 360
days.[17]
The next step was the identification of the graphic signs for the higher
unities, 20, 360, and 7200,—corresponding to the native _kal_, _bak_,
and _pic_.
That generally used for 20 was identified by several students. It is
shown in Fig. 3, No. 3; another also employed under certain
circumstances for 20 is shown Fig. 3, No. 2. This was identified
independently, first by Pousse, later by Seler.[18] No. 4 is perhaps a
variant of it.
The signs for the _bak_, 360, and the _pic_, 7200, are not so certainly
established, but Dr. Förstemann has given cogent reasons for recognizing
them respectively in the two shown Fig. 4, Nos. 6 and 7.
Higher signs than these in the direct numerical scale have not yet been
ascertained; but such plausible reasons have been advanced by Dr.
Förstemann for assigning calendar values to certain other signs that
they should be added in this description of the numerals.
The first is that shown in Fig. 4, No. 8. It represents the katunic
cycle of 52 years of 365 days each, = 18,980 days. The second is No. 9.
This is taken to be the sign of the _ahau katun_, 24 years of 365 days,
= 8760 days. The third is No. 10. This corresponds to one-third of an
_ahau katun_, = 2920 days. The fourth, shown No. 11, is an old cycle of
20 years of 360 days, = 7200. No. 12 means an old katunic cycle of 52
years of 360 days, = 18,720 days, and No. 13 an old year of 360
days.[19]
[Illustration: FIG. 4.—Calendar Signs.]
There are also a series of other signs evidently connected with the
numerals, the precise value of which is yet undetermined. One of these
is a small right or oblique cross, or sometimes two arcs abutting
against each other, connected or not. It is usually by the side of a
single dot or unit, or between two such. In certain places, it seems to
be a multiplier with the value 20; in others, it would indicate a change
or alternation in the series presented of days or years. (See Fig. 5,
Nos. 1–4.)
[Illustration: FIG. 5.—Numeral Signs.]
[Illustration: FIG. 6.—The “Cosmic Sign” and its Combinations.]
Of somewhat similar value are the calendar signs [Illustration], Fig. 4,
Nos. 2, 3, 4, like an _S_ placed lengthwise. This is also understood to
be a sign of alternation or change of series of years or cycles.
Of an opposite sense is the sign No. 5, the spiral, and also the sign
No. 1, both of which are held to represent union.
This list exhausts the mathematical signs so far as they have been
ascertained with probability. Those for high numbers brought forward by
Brasseur,[20] have no evidence in their favor.
Mr. Maudslay has offered reasons for believing that the character in
Fig. 6, _a_, stands for the numeral 20 in a certain class of mural
inscriptions.[21] He further points out that the character _b_ is not
unfrequently united with _a_, and that it (_b_) almost alone of the
mural glyphs is found with a double set of numerals attached to it as in
_c_. One or both these sets of numerals are at times replaced by the
sign _a_, giving the composites _d_, _e_, and _f_. It is thus evident
that _a_ has some numerical or calendar meaning. As a character itself,
it is the “cosmic sign,” conveying the idea of the world or universe as
a whole, as is seen by the examples to which Mr. Maudslay refers, from
various Codices. The cross-hatching upon it means, as I shall show
later, “strong, mighty,” and is merely a superlative. It may very well
mean 20, as that is the number conveying completeness or perfection in
this mythology.[22] That it appears on what Mr. Maudslay calls the
“Initial Series” of glyphs (which I consider terminals), is explained by
the nature of the computations they preserve. Another combination,
belonging most likely to a similar class, is the following
[Illustration] where the “cosmic sign” is united as a superfix to the
_pax_ and the flint. It has usually been explained as a “phallic
emblem,” and by Thomas as “tortillas.”[23]
4. _The Rhetorical and Symbolic Use of Numbers._
In the old Maya language we find that certain numbers were used in a
rhetorical sense, and this explains their appearance in some
non-mathematical portions of the Codices and inscriptions. The two most
commonly employed were 9 and 13. These conveyed the ideas of indefinite
greatness, of superlative excellence, of infinity, etc. A very lucky man
was a “nine-souled man;” that which had existed forever was “thirteen
generations old,” etc. The “demon with thirteen powers” was still
prominent in Tzental mythology in the time of Nuñez de la Vega. Other
numerals occasionally employed in a symbolic sense were 3, 4, and 7.[24]
All these occur in the Codices as prefixes in relations where they are
not to be construed in their arithmetical values, but in those assigned
them by the usages of the language or the customs of religious
symbolism. Thus, “twenty,” owing to the vigesimal method of numeration,
conveyed the associated ideas of completeness and perfection; and as the
month of 20 days was divided into four equal parts of 5 days each, by
which markets, etc., were assigned, these numbers also stood
independently for other concepts than those of computation.
5. _The Mayan Methods of Counting Time._
Having ascertained the characters for the numerals, and having learned
that these records are mainly time-counts, the next question which
arises is: How did the Mayas count time?
About this we have considerable information from the works of the
Spanish writers, Landa, Aguilar, Cogolludo, Pio Perez, etc., which has
been supplemented by the researches of modern authors.
The Maya system was a complicated one, based on several originally
distinct methods, which it was the duty and the aim of the
astronomer-priests to bring into unison,—and the effort to accomplish
this will chiefly explain their elaborate computations.
Undoubtedly their earliest time-count was that common to primitive
tribes everywhere—a measurement of the solar year by lunations or
“moons.” The exact lunar month is 29 days, 12 hours, 44 minutes, 3
seconds; but primitive peoples usually estimate it at 28 days, and allow
13 months to the solar year, as do yet many North Asiatic peoples, and
as probably did the early Aryans;[25] or, they estimate the “moon” at 30
days, and allow 12 moons to the year. There are good grounds for
believing that the Mayan tribes were at one time divided in custom about
this, some using one, some the other method. At the time of the Conquest
they had undoubtedly reached a knowledge of the length of the year as
365 days; and there is considerable probability that some of them at
least made the correction arranged for in our bissextile or leap
year.[26]
This is all familiar enough and would create no difficulty in
deciphering these aboriginal almanacs; but a disturbing element enters.
The real time-count by which they adjusted the important events of their
lives, and which is most prominent in their records, had nothing to do
with the motions of the sun, or the moon, or any other natural
phenomenon. It was based on purely mythical relations supposed to exist
between man and nature. As the number 20 (fingers and toes) completes
the man, and as all the directions, that is, potencies, of the visible
and invisible worlds were held to be 13, these two numbers, 13 and 20,
formed the basis of an astrological and ritual calendar, by which
auspicious and inauspicious days were assigned, future events foretold,
the major feasts and festivals of religious worship dictated, and the
like.
This singular time-count of 20 × 13 = 260 days was adopted with slight
variations by every semi-civilized nation of Mexico and Central America,
and even the names of the 20 days are practically of the same meaning in
all these languages.[27] It constituted the _tonalamatl_ of the Nahuas,
the “Book of Days,” used in divination.
This sacred period was subdivided into four equal parts of 65 days each,
each of which was assigned to the rule of a special planet or star, and
to a particular cardinal point with attendant divinities; and each was
marked with a color of its own, white, black, red, or blue.
Each “month” of 20 days was subdivided into four periods of five days
each, again each having its own divinity, assignment, etc.
But the importance to us of the _tonalamatl_ is that its computations
underlay the measurement of long periods of time, the less and greater
cycles. These were estimated by the methods of the sacred year, in
groups of 13, 20, 24, 52, 104, 260 years, etc. These irregular numbers
had to be brought into unison with the lunar and solar years, with the
vigesimal system of counting by 20 and its multiples, and with the
observed motions of the planets, who were divinities controlling the
ritual divisions of time.
To devise a mathematical method of equalities and differences by which
these conflicting numbers could be placed in harmonious relations,
subsumed under common measures, and the ceremonies and forecasts which
they controlled assigned by uniform laws—this is the arithmetical
problem which fills the pages of the Mayan Codices, and in parts or at
length is spread over the surface of the inscribed monuments and painted
vases. We need not search for the facts of history, the names of mighty
kings, or the dates of conquests. We shall not find them. Chronometry we
shall find, but not chronicles; astronomy with astrological aims;
rituals, but no records. Pre-Columbian history will not be reconstructed
from them. This will be a disappointment to many; but it is the
conclusion toward which tend all the soundest investigations of recent
years.
Let us recapitulate the numbers which the Maya mathematician had to deal
with and adjust under some scheme of uniformity:—
1. The “week” of 13 days, 13.
2. The “month” of 20 days, 20.
3. Its division into four parts (called _tzuc_), each, 5.
4. The complete _tonalamatl_, 13 × 20 days, 260.
5. Its divisions into four parts, each, 65.
6. The solar year, counted as 18 months of 20 days each, 360.
7. The solar year, counted as 12 months of 30 days each, 360.
8. The solar year, counted as 13 lunar months of 28 days each, 364.
9. The solar year, counted as 28 weeks of 13 days each, 364.
10. The true solar year, days, 365.
11. The bissextile year (?), 366.
12. The apparent revolution of Venus (_Noh-ek_, the Great Star),
days, 584.
13. The apparent revolution of Mercury (?), days, 115.
14. The apparent revolution of Mars (?), days, 780.
15. The _kin katun_, or day-cycle of years, 13.
16. The older cycle of years, 20.
17. The newer cycle of years, 24.
18. The _katun_ cycle of years, 52.
19. The double cycle of years, 104.
20. The great cycle of years, 260.
6. _The Calculations in the Codices._
The Codices contain numerous calculations intended to bring these
various quantities into definite relations as aliquot parts of some
arithmetical whole, which might be taken as a general unit. The scribes
appear to have begun by establishing a period of 14,040 days. This
equals 39 years of 360 days each, and also 54 years of 260 days each,
together, of course, with the divisors of these numbers, 13, 18, 20, 65,
etc. Then followed the determination of the period of 18,980 days, = 73
_tonalamatl_, = 52 solar years, so prominent in the calendar and ritual
of the Nahuas.
This number, however, could not be adjusted to the cycle of the _ahau
katun_, which was 24 years of 365 days each;[28] nor to the ceremonially
prominent revolution of “the Great Star,” Venus, which coincides with
the Earth’s revolutions in 2920 days, or eight solar years. To bring
these into accord with the _tonalamatl_ required a period of 104 solar
years, or 37,960 days; and to adjust under one number the _katuns_, the
_ahau katuns_, the revolutions of Venus, the solar year, and the
_tonalamatl_, three times that number of days are required, that is,
113,880, = 312 years.
This period had still to be brought into relation to the old year of 360
days, and this requires the estimation of a term covering 1,366,560
days, or 3744 years; and this extended era we find expressed in the
Dresden Codex, page 24, in the following simple notation, the
interpretation of which into our system of calculation, according to the
method above explained, I add to the right.
This long period allowed all their important time-measures to be dealt
with as aliquot parts of one whole, and would seem to be sufficient for
the purposes they had in view. The credit of establishing it from their
ancient writings is exclusively due to Dr. Förstemann, whose
demonstrations of it appear to be conclusive.[29]
[Illustration] 9 (unit = 144,000) = 1,296,000
[Illustration] 9 (unit = 7,200) = 64,800
[Illustration] 16 (unit = 360) = 5,760
[Illustration] 0 (unit = 20) = 0
[Illustration] 0 (unit = 1) = 0
—————————
Total, 1,366,560
This acute observer has, however, discovered some reasons to suppose
that the native priests occasionally contemplated a much more extended
era; some of their calculations seem to require an era which embraced
12,299,040 days, that is, 33,696 years![30]
No doubt each of these periods of time had its appropriate name in the
technical language of the Maya astronomers, and also its corresponding
sign or character in their writing. None of them has been recorded by
the Spanish writers; but from the analogy of the Nahuatl script and
language, and from certain indications in the Maya writings, we may
surmise that some of these technical terms were from one of the radicals
meaning “to tie, or fasten together,” and that the corresponding signs
would either directly, that is, pictorially; or ikonomatically, that is,
by similarity of sound, express this idea.
Proceeding on the first of these suppositions, Dr. Förstemann has
suggested that the character, Fig. 4, No. 8, signifies the period of 52
years, the Nahuatl _xiuhmolpilli_, “the tying together of the years,”
represented in the Aztec pictographs by a bundle of faggots tied with
cords. The Maya figure is explained as the day-sign _imix_, representing
the first day of the calendar, and, by a kind of synecdoche, the whole
calendar, with a superfix.
7. _Rules for Tracing the Tonalamatl, or Ritual Calendar._
That the computations of the _tonalamatl_ underlie most of the numerals
in the Codices is shown by the rules for reading them, formulated by
Pousse with reference to the red and black numerical signs. These rules
are as follows:—[31]
1. If to a red number be added the black number immediately following
it, the total less 13 (or its multiples, when the total is above 13)
equals the next following red number.
2. When the red and black numbers are written alternately on the same
line, they are to be read from left to right; when written one above the
other, they are to be read from below upward; when in two vertical
columns, they are to be read passing from one column to the other,
beginning with the first black number on the left, passing to the first
black number on the right, returning to the second black number on the
left, and so on.
Sequences of this kind are governed by the following rules:—
1. In any of the above systems the beginning is always marked by one or
more columns of days surmounted by a number.
2. This number is always the same as that which ends the series, and
both are written in red.
3. The sum of the numbers written in black, multiplied by the number of
days with different names represented by the hieroglyphs attached,
always equals 260, that is, the number of days in the _tonalamatl_.
The above rules enable the student to recognize the relations of the
different parts of the Codices. They prove, for instance, that the pages
are not to be read from top to bottom, but that the separate parts or
chapters are to be read in many instances from left to right in the
section of the page in which they begin, without respect to the folds of
the MSS.; and that evidently in reading these “books” they were unfolded
and spread out. A good example of this is in Cod. Dresden, pages 4–10,
on which one chapter covers all the upper thirds of the seven pages.
8. _The Codices as Astronomical Treatises._
A careful examination of Dr. Förstemann’s remarkable studies, as well as
a number of other considerations drawn from the Codices themselves, have
persuaded me that the general purpose of the Codices and the greater
inscriptions, as those of Palenque, have been misunderstood and
underrated by most writers. In one of his latest papers[32] Professor
Cyrus Thomas says of the Codices: “These records are to a large extent
only religious calendars;” and Dr. Seler has expressed his distrust in
Dr. Förstemann’s opinions as to their astronomic contents. My own
conviction is that they will prove to be much more astronomical than
even the latter believes; that they are primarily and essentially
records of the motions of the heavenly bodies; and that both figures and
characters are to be interpreted as referring in the first instance to
the sun and moon, the planets, and those constellations which are most
prominent in the nightly sky in the latitude of Yucatan.
This conclusion is entirely in accordance with the results of the most
recent research in neighboring fields of American culture. The profound
studies of the Mexican Calendar undertaken by Mrs. Zelia Nuttall have
vindicated for it a truly surprising accuracy which could have come only
from prolonged and accurately registered observations of the relative
apparent motions of the celestial bodies.[33] We may be sure that the
Mayas were not behind the Nahuas in this; and in the grotesque figures
and strange groupings which illustrate the pages of their books we
should look for pictorial representations of astronomic events.
Of course, as everywhere else, with this serious astronomic lore were
associated notions of astrology, dates for fixing rites and ceremonies,
mythical narratives, cosmogonical traditions and liturgies, incantations
and prescriptions for religious functions. But through this maze of
superstition I believe we can thread our way if we hold on to the clue
which astronomy can furnish us. In the present work, however, I do not
pretend to more than prepare the soil for such a labor.
A proof of the correctness of this opinion and also an admirable example
of the success with which Dr. Förstemann has prosecuted his analysis of
the astronomical meaning of the Codices is offered by his explanation of
the 24th page of the Dresden Codex, laid before the International
Congress of Americanists, in 1894.
He showed that it was intended to bring the time covered in five
revolutions of Venus into relation to the solar years and the ceremonial
years, or _tonalamatl_, of 260 days; also to set forth the relations
between the revolutions of the Moon and of Mercury; further, to divide
the year of Venus into four unequal parts, assigned respectively to the
four cardinal points and to four divinities; and, finally, to designate
to which divinities each of the five Venus-years under consideration
should be dedicated.
This illustrates at once the great advance his method has made in the
interpretation of the Codices, and the intimate relations we find in
them between astronomy and mythology.
Such a theory of the Mayan books which we have at hand is world-wide
distant from that of Thomas and Seler. Take, for example, the series of
figures, Cod. Cort., pp. 14^a, 15^a, 16^a.[34] Förstemann and myself
would consider them to represent the position of certain celestial
bodies before the summer solstice (indicated by the turtle on p. 7);
while Thomas says of them, “It may safely be assumed that these figures
refer to the Maya process of making bread!!”[35]
9. _Astronomical Knowledge of the Ancient Mayas._
Our information from European sources as to the astronomical knowledge
possessed by the Mayas is slight.
That they looked with especial reverence to the planet Venus is evident
from the various names they applied to it. These were: _Noh Ek_, “the
Great Star” or “the Right-hand Star;” _Chac Ek_, “the Strong Star” (or
“the Red Star”); _Zaztal Ek_, “the Brilliant Star;” _Ah-Zahcab_, “the
Controller or Companion of the Dawn;”[36] and _Xux Ek_, “the Bee or Wasp
Star,” for reasons which will be considered later. In the Tzental
dialect it was called _Canan Chulchan_, “the Guardian of the Sky,” and
_Mucul Canan_, “the Great Guardian.”
The North Star was well known as _Xaman Ek_ (_xaman_, north, _ek_,
star), and also as _Chimal Ek_, “the Shield Star,” or “Star on the
Shield.”[37] It was spoken of as “the Guide of the Merchants” (_Dicc. de
Motul_), and therefore was probably one of their special divinities.