Maya Numeration

The Maya numeration is a numeration of position of bases 20 (except for a irregularity).

The figures from 1 to 19 are written according to an additive system using horizontal features being worth 5 and of points being worth 1. The Maya system has moreover a notation for the zero positional one (the shape of shell - or the closed hand).

List figures

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Examples

Maya numeration writes the figures vertically, the units in bottom.

For the dates

Attention, the Maya system comprises only one irregularity (for the dates only!) : the third stage will not count a 400-groin but a 360-groin (20×18). This defers the stage following not to the 8000-groin but to the 7200-groin (20×18×20) and the fifth to the 144000-groin (20×18×20×20).

Form of the zero Maya cardinal

The form of the zero of the codices is not a shell. This lengthened sign represents a knife (in particular a knife of sacrifice) and probably derives from the sign of the polished obsidian mirror. The form shell rare, but is attested. On the monuments, the zero cardinal forever this form, but that of a half-flower with four petals, or that of a head characterized by the hand of the achievement, or of a corn flowering or obsidian mirror.

Graphic alternatives

The Maya scribes laid out, in addition to system of the figures not/bars above, of many written forms to represent the twenty figures necessary to the writing of their numbers (generally of the durations) or of the units of their system of units of time (the glyphes of period: kin, uinal, tun, katun, baktun, etc). The most famous system is certainly that of the figures céphalomorphes (each figure, from 0 to 19, is represented by a glyphe having the shape of a head).

Two zero Maya

The Maya scribes used a vigesimal numeration (at base twenty) and they laid out of two zero distinct, marked by different glyphes. In a general way, they always carefully distinguished the durations (of “cardinal” nature) and the dates (of “ordinal” nature), for example in the almanacs divinatoires, by writing the first in black and the seconds in red. In the same way, they carefully distinguished the constituent from figure (for example: two points “.” juxtaposed horizontally to form the figure or number 2) and the constituent of number (i.e. figures constituting a number in positional writing, for example two points “: ” juxtaposed vertically to form number 21, is “a-score one”). The first, which one can call zero cardinal , is one zero of position, like that of the decimal notation or of any other numeration of position. For example: 9.9.16.0 .0. (codex of Dresden p. 24) note duration 9 - baktun 9 - katun 16 - tun 0 - uinal 0 - kin , i.e. duration of 9 X.400 tun (year of 360 days account) + 9 X 20 tun + 16 tun + 0 uinal (20 days month) + 0 kin (day).

The ordinal second or zero was used to note first the 18 the twenty days months day or period complementary to five days which constitute the solar year (the ha' ab 365 days). For example, New Year's day was a 0 Pop .

The zero ordinal one is attested for the first time by pendeloque of jade (known under the name of plate of Leyde), and it dates from 9/17/320 (after J. - C.). On this pendeloque, same the glyphe also appears in a “literary” context where it notes the verb indicating the action to go up on the throne, the establishment of the king whose figure appears with the recto of the plate.

The zero cardinal appears for the first time on the steles 18 and 19 of Uaxactun, which count three occurrences of this sign in final position. One finds them in the expression (redundant, since, in this double example, all the units are expressed) of a date in long Compte (i.e. represented by the expressed duration of many days passed since the origin of the Maya chronology, are into 3113 before J. - C.): 8 - baktun 16 - katun 0 - tun 0 - uinal 0 - kin . The zero Maya cardinal is thus attested since the 2/2/357.

Spoken numeration (yucatèque, given of Beltran, XVIIIe century)

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Beginning of the yucatèque list of the names of numbers extracts from: Beltrán de Santa Rosa, Maya Arte LED idioma reducido has succintas regulated there semilexicon yucateco .

Suggestion . The component you ( tuy in front of vowel) is the contraction of the locative Ti “towards, in” and of the personal index of 3rd person U “its”, which is used to derive the ordinal one starting from the cardinal (like our suffix - ième who makes pass from 3 to 3rd). The locative can be implied, remains the personal index then (e.g. in 50). The whole amalgam, ti+u , can also be implied. For example, expression 35 data by Beltran is a shortened form of holhu you-Ca-KAL where one recognizes numeral the holhu “15” (makes the integrated compound of it (5,10)), the implied expression you prefixed with numeral the Ca “2” (that is to say towards 2nd) and the classifier measures KAL “twenty, score”. The form holhucakal is analyzed in ho.lahun ti+u-Ca-KAL and is translated element with element: “15 towards 2nd TWENTY”. These forms reveal the specificity of spoken Maya numerations précolombiennes, namely that the Mayas had an operation which we do not know in our arithmetic. An operation which gives result 35 when one makes it relate to arguments 15 and 40 (Ca-KAL is also the name of forty). The linguist Claude Hagège proposed to call this operation “operation of protraction”. André Cauty (1987) showed that yucatèque spoken numeration is of a special type which one can say the ordinal type in retrograde vision of anteriority. Indeed, if the expression of 35 known as something like “15 towards the 2nd TWENTY” or “15 towards 40”, its numerical value 35 can be obtained only while returning to the first TWENTY. To note that in the compounds of the second score (from 21 to 39), the yucatèques ones generally do not specify the “coefficient” of the TWENTY of which it is question (and who can be only the “first”, i.e. 2) as in the expression hun you KAL of 21, but not in that of 30 or 35 (where it is the relator you which is implied).

See too

Numbering system

Numbers in the Maya world
Calendar

External bonds

http://www.pbs.org/wgbh/nova/maya/glyp_wave.html. Interactive training in Shockwave.

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