The Ritual Temporal Symbolism of the Ajaw Station of the 260-day Calendar
I put forward the hypothesis that linear Long Count calendar time was symbolically governed by the cyclical 260-day calendar. This is manifested by a ritually celebration of the station Ajaw of the 260-day calendar intimately combined with zero dates of specific time periods, so-called “period-endings”, of the Long Count calendar in classic Maya temporal philosophy.
First we must consider the Mesoamerican mathematical and philosophical concept of zero (Lat. Ne ullus, “nothing”) in the calendar system. The concept of zero may have had religious symbolic importance in the Mesoamerican temporal and vigesimal (base twenty) numerical positional system. The concept and positional value of zero, recorded at the beginning of the first centuries in India, came to 12th century Europe through the Hindu-Arabic numeral and positional system.  A mathematical system consisting of the concept of zero was invented in Middle America (aka Mesoamerica) independent of India. The Mesoamerican mathematical and philosophical concept of zero is recorded in the classic Maya inscriptions as mih with the meaning “nothing”. The meaning and symbol for the digit zero as placeholder in a place values system was possibly conceived by the earlier Olmec civilisation (Grube and Nahm 1990; Justeson 2010: 49-5o).i6i Zero is a symbol for nothingness or the absence of existence but also completion. The position shift is made at twenty and not at ten, which we know from the European decimal system (base ten). This is illustrated by the 365-day calendar. The 365-day calendar was organised as a cycle incorporating a last (4 Wayhaab) and first (1 K’anjalaw) day of the 365-day year. The Maya started the new veintena with a day, a zero day, before the first day of the new veintena. The coefficients are therefore 0-19, in every of the 18 winik, e.g. K’anjalaw-Ohl and 0-4 in Wayhaab. The first day of the year was thus “seating of K’anjalaw” the second day was 1 K’anjalaw etc. The last day of the 365-day year was 4 Wayhaab. The “installing of K’anjalaw” (chum/cum) and “the end of Wayhaab” (ti’) alludes to the same day. A new veintena was installed or seated when the new veintena’s first day and last day of the previous veintena overlapped.    Chum of the cyclic 365-cay calendar do not, however, represent zero or twenty but the transition between the 19th of the preceding time period and the first day of the succeeding time unit (Blume 2011: 65-66).^ A notion of a beginning or an end did consequently not exist. This system follows a cyclic and not a linear logic where the days of the veintena were counted in terms of elapsed time and not present time. The day only received a coefficient when it had been completed. K’anjalaw replaced i K’anjalaw as the “seating” of K’anjalaw or the first day of the New Year (Wichmann 2000: 49; Bricker and Miram 2002: 39-40). It is intriguing that the endings of stations within the cyclic 365-day calendar, by the word chum or “seating” in the inscriptions, has the sense of both a beginning and a termination, which indicates a horror vacui philosophy of time. The verb chum had a special significance because it alludes to the seating of both the old and new time unit. It is, in this connection, striking that the world or time of the contemporary world age or time era was said to have been created, not on the date 0.0.0.0.0, but on the last day of the previous Long Count calendar, 220.127.116.11.0 4 Ajaw 8 Ohl (Kumk’u).
It is indeed fascinating that ritual practice of time could as noted only be celebrated on the day-sign Ajaw, which is the twentieth sign of the 260- day calendar, and only when one of the interval time units were at zero position of the Long Count calendar. But had zero a symbolic significance in celebrating the rituals of time of this linear calendar?^ Zero, represented by one of several signs (Stuart 2012c), as aforementioned is read as mih with the meaning “nothing” (Grube and Nahm 1990)165 but Justeson hypothesis this word to be an adjectival predication signifying “lacking” or “no”, which indicates a non-existence of certain time periods within the Long Count notation (Kaufman with Justeson 2003: 1553; Justeson 2010: 49-50). Mih in a non-calendrical context is recorded on the Hieroglyphic
Stairway, Copan in the collocations: “mi-'temple, mi-‘altar, mi-kab’-ch’e’n”?, which can be translated as “no pyramid, no altar, no earth/cave” (Hull 2003: 464). Mih outlines moreover absence of tribute according to an inscription on a vase (Grube and Nahm 1994: 699). Interestingly, mih of the vigesimal numerical notation system only appears with calendar and astronomical mathematics and not with trade and tribute in the extant inscriptions. The place notation system of the Long Count calendar was restricted to time reckoning, and never applied to the purely vigesimal counting structure reflected in Mayan languages (Blume 2011: 61; Stuart 2012c). As noted, Mih may in a calendar context refer symbolically not only nothingness but also completion. A calligraphic variant at Xultun and Pomona Panel 7 might be associated with the concept pet, “totality” suggesting zero as a number position that has reached its “totality”” according to Stuart (Stuart 2012c).
As I shall argue in the concluding section of the book, the 260-day calendar is the principal Mesoamerican calendar. This calendar exercise influence upon other Mesoamerican calendars: the 365-day calendar, the 52-year calendar and the Long Count calendar. The 260-day calendar was associated not only with other calendars but also with personal names and world ages in various cultures of Mesoamerica. The mathematical composition of the 260-day calendar—i.e. 20 days multiplied with 13 numbers = 260—reflect the numerical organisation of the previous Long Count calendar, which vigesimal units ended with the number 13. 20 k'in constitute 1 winal, 20 tun make 1 winikhaab, 20 winikhaab compose 1 pik. The exception to this symbolic mathematical principle is that 18 winal represent 1 tun (360 days), which exhibit 360 days of the Mesoamerican 365-day calendar. Furthermore, we recollect that a multitude of Long Counts or time ages (world eras) had existed before the present time era. Stelae 1, 3 and 5 of Coba record the beginning of the contemporary Long Count era, 18.104.22.168.0 4 Ajaw 8 Ohl, in relation with twenty Long Counts set at 13. It is probably not coincident that the coefficients 13 x 20 equal the components of the 260-day calendar.
The later postclassic Short Count calendar consists of 13 k’atun (winikhaab) or 13 x 7200 (vigesimal) or c. 256, 43 years because there can only be 13 Ajaw days from the 260-day calendar. The cyclical Short Count calendar make history repeats itself as prophecies at 13 possible period- endings after the important day-name Ajaw of the 260-day calendar. The Long Count calendar and the Short Count calendar are accordingly arithmetically founded upon the coefficients 13 and 20, which together compose the 260-day calendar.
That every “period-ending date” of the Long Count calendar is identified with the twentieth day of the 260-day calendar Ajaw is hardly a coincidence. On the other hand, the first day of the time units within the Long Count calendar is always Imix (Taube 1988: 204-206). Imix do not seem, however, to have enjoyed a similar symbolic prominence in the ritual inscriptions. Incontestably, it is symbolically significant that Ajaw, “lord”, was a title of the regent of the classic Maya city or city-state.
In Mesoamerica only the Maya 260-day calendars, like the classic Maya and Yucatec, contain a word for “ruler” or “lord” (ajaw). The apparently last day-name of the Mixtec 260-day calendar is according to special day-sign vocabulary in the dictionary of Alvarado huaco, “flower” (Dahlgren 1954: 367; Smith 1973: 24-25). The Zapotec culture employ Lao, Loo, “face” (Cordova  1987: 204-212; Caso 1967: 84)  , the Otomf apply andoeni, “flower” (Caso 1967), the Mixe has jugwin or “bee”, “fontanelle”, “point”, “eye” (Caso 1967; Lipp 1991: 63) whereas the Aztec use xochitl or “flower” as the apparent last day-name of the 260-day calendar (Caso 1967).^ In some Maya 260-day calendars, however, the day Ajaw is replaced byjunajpub’ or junajpu ((hun)ahpu) (cf. Thompson 1978: 68; 87-88). The literal translation ofJunajpub’ or Junajpu is “One Man Blow-gunner.”i69
The classic Maya celebrate the day-name Ajaw at “period-endings” in ritual practices of time at many different intervals of the Long Count calendar (according to local traditions). As we saw from various inscriptions there were no established synchronisation with the date of creation (22.214.171.124.0 4 Ajaw 8 Ohl) but a commemoration with identical Ajaw dates of not only the contemporary Long Count but as well with previous Long
Counts in “Deep Time” or “Great Time”. “Like-in-kind connections” between past, contemporary and future “period-ending dates” with equivalent Ajaw positions were recorded. This principle of pattern history, where identical Ajaw stations are symmetrically repeated or commemorated, related to the pivotal ritual practice of time, is surely no coincidence but has strong religious symbolic and temporal significance. Consequently, the anniversaries of identical Ajaw dates suggest the importance of the cyclical 260-day calendar as related to the linear Long Count calendar.  Moreover, inscriptions on numbered stones and discs with Ajaw notations, “X Ajaw Tuun”, were seated or erected represented “period-ending stations” and time intervals of the Long Count calendar and the Short Count calendar respectively. This is also much later recorded in the The Books of the Chilam Balam from the early colonial period.
Another indication of the ritual-symbolic importance of the day-station Ajaw of the 260-day calendar is that this day-sign consistently appear in the so-called “Cord-taking”, rituals (cf. Stuart 2000). These were connected to events 2.9.0 (i.e. 900 days) after the ending of a winikhaab. In the Stucco inscription from Temple XIX at Palenque there is a numerological pattern that link three Ajaw dates in chronological order:
- 126.96.36.199.0 3 Ajaw 3 Yaxk’in
- 188.8.131.52.0 6 Ajaw 13 Muwan
- 184.108.40.206.0 9 Ajaw 18 Kasew (Stuart 2000: 1).
There are several indications that the inscription outline a retrospective pre-accession ritual which involve the prospective ajaw (Stuart 2000: 5-6).171 It is hardly no coincidence that the three associated ceremonies, which were all separated by the same time period, are related to the day- sign Ajaw of the 260-day calendar.
Schele and Looper have worked out the dates of the complicated inscription on Stela J, Copan where the day-station Ajaw of the 260-day calendar plays a significant role. The first date is 220.127.116.11.0 1 Ajaw 3 Mol (September 5, 453 ad). Then 1 Ajaw is projected 14 pik back into the previous Long Count to the date 18.104.22.168.0 2 Ajaw 18 Ik’at. The inscription continues to a completion of 13 pik and to the date 22.214.171.124.0 1 Ajaw 8 Chaksihom of the past Long Count which correspond to the historical date of the contemporary Long Count (Schele and Looper 1996: 104). Moreover, the north and south side of Stela J records “period-ending” expressions of from 126.96.36.199.0 1 Ajaw 3 Mol into the future (Schele and Mathews 1998: 138; Newsome 2001: 78; 8790). Haab or tun counts were known from many sources in the postclassic and colonial period where they had a historical content with a relation to prophecy and to predicting omens. The inscription on Stela J display that also the classic Maya recorded a haab series, which were recorded as a prophecy (Love 1994: 36-38). Love argues that:
Marking the passage of tuns was important, but the function of such counts in Maya society remains elusive. Numbered tuns very likely had their own omens which coloured predictions and prognostication for upcoming events (Love 1994: 38).
Personal names from the 260-day calendar were not common among the classic Maya according to the extant inscriptions. But the previously noted inscription from Palenque state that the lord K’an Joy Chitam [II] carry the title huk ajaw tan-lam, “the half-diminisher of 7 Ajaw” in celebrating the completion of a half-period containg the date 7 Ajaw of the 260-day calendar. The tan-lam (”to diminish in the middle”) formula in various inscriptions suggests that it is the Ajaw position of the 260-day calendar, not the ritual specialist, which possesses the linear time of the Long Count calendar.
We saw that in his analysis of the “half-period hieroglyph” or tan-lam, Wichmann has detected that time units held possessive relations (Wich- mann 2004: 637-638, note 6). The -il suffix imply that it is a close connection between the possessed object and the possessor of the object. Such an inalienable connection is only relevant between a half-period and a full time period: “The middle-diminish of pik and winikhaab”. Various inscrip?tions contain a grammatical pattern where the possessor is, not the ritual performer, but another calendar time computation like for instance:
u-lam-il 6 Ajaw, “It is the diminishing of the middle of 6 Ajaw”. Stucco Relief,
(pC1-pD1), Tonina (Houston, Robertson and Stuart 2001: 30, Table 7).
We see here that the time period of the Long Count calendar is marked by the Ajaw position of the 260-day calendar. I hypothesise that the grammatical pattern cited above highlights the importance of the Ajaw position of the 260-day calendar. It is this cyclic position, which owns linear time. For instance, the ritual scattering (u chok) is outlined executed on 10 Ajaw of the 260-day calendar (188.8.131.52.0 and 184.108.40.206.0) according to the inscription on Stela I, Quirigua (A9). This ritual formula conveys the importance of the Ajaw station of the ritual practice of time of the Long Count calendar. We have previously seen that there was a ritual emulation of incidents and ceremonies, of both former Long Counts and of the present Long Count, on the exact same Ajaw date of the 260-calendar, i.e. “pattern dates”. As noted it is compelling that this central position of the 260-day calendar, which mathematically was the ending date of “period-endings” within the Long Count calendar, had the same name as the title of the classic Maya political-military sovereign and religious ritual specialist. An intimately symbolic religious-political connection, expressed by the concept “Ajaw”, between the ritual practice of time and of government is therefore conceivable. Stuart claims that Stela 11, Piedras Negras represent the winikhaab (k’atun) when the accession of the depicted lord took place. The seated ruler is portrayed with an object containing the date 4 Ajaw, which refer to the “period-ending date” 220.127.116.11.0 (Taube et al. 2010: 69). This demonstrates the intimate relation between the lord (ajaw), the 260-day calendar and the Long Count calendar. It is no coincidence that Ajaw constitute the title of the ruler or rulers of the classic Maya city-states. The ruling lord is generally the religious specialist who executes the crucial rituals of time. We have seen that in some cases both the stone marking the “period-ending period” and the celebrating lord share the same “X Ajaw Tun” title. Furthermore, the expression ajaw-yan, “becoming a lord”, convey the notion of a new winikhaab in Palenque. Time notations with Ajaw dates are known to be inscribed (tattoed) on the body/face of various lords. There are also iconographic identification between the day sign Ajaw and portraits of lords in day cartouches displaying a common identity. As aforementioned accession to office ritual of the ajaw has the same verbal formulas of inauguration as “period-endings” (chum, “seating” and k’al, “binding”).
The collection of written sources exhibit a principle symbolic temporal importance of the twentieth day (Ajaw) of the classic Maya 260-calendar, in combination with various “period-endings” marked by zero/twenty of the Long Count calendar, which was required to be ritually observed.
Figure 1: Map of Mesoamerica with cultures of the analysis.
Figure 2: T153-T217 & T220 & MZP-b’a from Stela C, Quirigua (East side) (B6). Autograph by Matthew G. Looper (Looper 2003: 159, fig. 5.1).
Figure 3: Vase of the Seven Gods, K2796. Photograph by Justin Kerr, 2001 (Kerr 2001: http:// famsi.famsi.org:950o/dataSpark/MayaVase.©
Figure 4: Full-figure signs of pik (bak’tun), winikhaab (k’atun) and haab (tun). Autograph by Miss Kisa Noguchi (Thompson 1950: fig. 28).
Figure 5: Full-figure signs of winal/winik, k’in and Lunar Series. Autograph by Miss Kisa Noguchi (Thompson 1950: fig. 29).
Figure 6: Female figure as Ajaw day sign. Autograph by David Stuart (Stuart 1996: 169, fig.20).
-  Bourbaki, Nicolas. Elements of the History of Mathematics. Berlin, Heidelberg, andNew York: Springer-Verlag 1994: 45-46; “algebra.” Encyclopedia Britannica. EncyclopediaBritannica Online Academic Edition. Encyclopsdia Britannica Inc. , 2012. Web. 27 Oct. 2012.
-  We remember that the Epi-Olmec culture (c. 300 bc - c. 250 ad) in the central regionof Veracruz of Mexico was a successor to the Olmec civilisation (c. 1200 bc to c. 400 bc) inthe Gulf coast region of southern Mexico. The Olmec are probably the predecessor of thepresent day Mixe and Zoque cultures of Oaxaca and Chiapas, Mexico.
-  This phenomenon was designed in the classic Maya inscriptions as “the end of’ (ft':“mouth”, “edge” and haabf year”; ti’haab’: “the limit of the year”) (Wichmann 2000: 49).
-  Cf. also k’aab’ or “end of’, which only occurs in the number position of the 365-daycalendar count of the Calendar Round.
-  For works about numerology and zero in other cultures cf. for instance Christoma-lis 2010; Bag and Sarma 2003; Ifrah 2000; Seife 2000; Urton 1997; Rotman 1993.
-  165 Blume (2011) has written a research history of the zero signs in the Maya logosyllabicsystem.
-  The pik and higher units do not exceed the number 13 according to the inscriptionsfrom stelae 1, 3 and 5 from Coba. It is interesting that the previous higher units of the Cobastelae have 13 as its highest number and that there are 20 different units with this coefficient.13 x 20 = 260-day calendar (Stuart 2011: 236).
-  Cf. Urcid for a reconstruction in the writing system of the Zapotec 260-day calendar(2001: 79-278).
-  Alfredo Caso has collected lists of day-names of the 260-day calendar from variouscultures of Mesoamerica (Caso 1967: Table IX).
-  The verb ‘pubaj’ means to “blowgun” that is to say hunt with a blowgun. )/un’ means‘One.’ A person who uses a blowgun is an AjPub’ or AjPu: a blow-gunning man. The name,Junajpu or Junajpub,’ is found in the Popol Wuj as one of the hero twins who both haveblowgunners (Vincent Stanzione p.c. 2011).
-  The La Corona Panel 1 sharing the same pattern date of 4 Kan of the 260-day calendar display that other time stations, than Ajaw of the 260-day calendar, were emphasisedby the classic Maya. Cf. also Stuart about the symbolic pattern of the day 9 Ik’ of the 260-daycalendar in the history of Palenque (Stuart 2006b: 183-185).
-  These ceremonial actions, including an obscure involvement of the deity GII, tookabout 5 years. The rituals are delineated by the not deciphered “Heron sign”. This sign is“related conceptually to the water bird costume worn by the protagonist, “Upakal K’ihnich”.The bird-man and cord taking sign can both have outlined a ritual that found place every900 days or at a 1/8th of a winikhaab-period. Celebration of a commemoration of the 1/8thof a winikhaab-period is identified, they are of the self-evident kind, in a variety of inscriptions from Tonina and Palenque. The inscription of Stela J, Copan encloses a list of individual tuns within the winikhaab period. The tun has each their own “designation”. “Threeof these terms describe actions or rituals involving the word ch’am or k’am, “take, receive,”perhaps strengthening the notion that “cord taking” event is a similar sort of term used todesignate or describe a set period or sub-division of the K’atun” (Stuart 2000: 5-6).
-  Cf. Houston, Robertson and Stuart (2001: 26-32).
-  u-tan-lam-il 2 Ajaw (18.104.22.168.0) (Stela 22, B3, Waxaktun); VERB t-u-tan-lam-il8 Ajaw(22.214.171.124.0) (Stela 6, Copan); VERB t-u-tan-lam-il 8 Ajaw (126.96.36.199.0) (Stela 1, TUL) (Wichmann2004: 637).