Project Gutenberg's A Primer of Mayan Hieroglyphics, by Daniel G. Brinton This eBook is for the use of anyone anywhere in the United States and most other parts of the world at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org. If you are not located in the United States, you'll have to check the laws of the country where you are located before using this ebook. Title: A Primer of Mayan Hieroglyphics Author: Daniel G. Brinton Release Date: July 19, 2018 [EBook #57540] Language: English Character set encoding: UTF-8 *** START OF THIS PROJECT GUTENBERG EBOOK A PRIMER OF MAYAN HIEROGLYPHICS *** Produced by Richard Tonsing, Julia Miller, and the Online Distributed Proofreading Team at http://www.pgdp.net (This file was produced from images generously made available by The Internet Archive/American Libraries.) 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 v 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 vi 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. 9 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). 10 11 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] 12 13 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] 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 14 15 16 17 Elements of the Mayan hieroglyphic writing. II. The Mathematical Elements. 18 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. 19