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Dossier Rongorongo Tablet Keiti: a discussion

Lunar calendar in rongorongo texts and rock art of Easter Island

Paul Horley
p. 17-38

Résumés

L’analyse le calendrier lunaire Mamari, à partir de données paléographiques, astronomiques et ethnologiques, confirme que les deux derniers croissants de ce calendrier correspondent à des nuits sans lune. Deux petits croissants (précédemment interprétés comme une insertion de nuits intercalaires) ont une explication paléographique claire. Ainsi, le calendrier lunaire Mamari comporte trente nuits, en accord avec l'astronomie et les calendriers des autres îles polynésiennes. L’observation à l’œil nu d'une lunaison complète et l’étude des pétroglyphes de Rapa Nui permettent de proposer une interprétation alternative des groupes délimiteurs, en référence à des observations de lune effectuées au lever ou au coucher du soleil. S'appuyant sur le fait que la pleine lune est représentée dans le texte Mamari par le signe pictographique 152, il est proposé que le reste des glyphes explicatifs nocturnes représentent des caractéristiques de surface de la lune permettant d'identifier la phase lunaire correspondante. La comparaison avec les calendriers lunaires polynésiens prouve clairement que le calendrier de l’île de Pâques a des racines polynésiennes. Cela suggère que le peuplement de l'île de Pâques s’est produit en un seul événement, après quoi il n'y avait aucune possibilité de concilier ce calendrier avec ceux des autres sociétés polynésiennes.

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1Humans have always been concerned about proper timing of activities to ensure their successful outcome – the crops should be planted at a correct moment to produce the most abundant harvest, hunting will be more efficient during the seasonal appearance of the hunted animals, the construction tasks are easier in a season offering favorable weather conditions, and so on. Apart from purely practical applications, time reckoning was extremely important for religious and cultural events, marking the dates for ceremonies, holidays and festivals.

2As seasonal change is caused by the motion of the Earth in space, it is natural to solve time-tracking problem basing on astronomical observations. The agricultural activities are related to the solar tropical year of 365.242 days (Borkowski, 1991: 127), which can be observed through annual variation of sunrise/sunset azimuth. Easter Islanders had a good knowledge about the motion of the sun, as they constructed ceremonial structures oriented to sunrise/sunset points at equinoxes and solstices, including Ahu Huri A Urenga, Vinapu, Heki’i and Tongariki (Liller, 1993: 11-16).

3At the same time, the changes of the moon phases offer efficient time-tracking that do not require marking of a specific point on the horizon. The complete cycle of lunar phases – synodic month or lunation – averages to 29.53 days (Grego, 2005: 52). As lunation does not contain an integer number of days, the lunar calendars usually present a sequence of a “full” month of 30 days followed by a “hollow” month of 29 days, totaling in a bimester of 59 days. The error of this approximation will make up for 24 hours in over 983 days, which can be easily corrected by re-adjusting the calendar by observation. A more complicated problem arises from the fact that the synodic month does not have an integer multiple to make a tropical year, with the latter containing 365.24/29.53 = 12.368 lunar months. In a three-year course, the remainder will accumulate into 13th lunar month and three extra days, which would require additional corrections to the calendar. One particular solution to the problem was obtained in Ancient Greece, yielding the Metonic cycle of 19 years that will correspond to 235 lunations (Long 1998: 19) with an error of 0.01 days, making a complete day in 1900 years.

4There is no information (to the best of my knowledge) on how the ancient Rapanui synchronized lunar and solar cycles. However, it is known for sure that they used lunar calendar and were very keen about the things related to time-accounting, as witnessed by the first missionary to Easter Island, Eugène Eyraud (1866: 124-125):

“Their measure of time is a lunar year. But these memories are fading, so they [islanders] couldn’t come to an agreement about the number of the moons [lunar nights]. A remarkable fact! These savages show an extreme interest for everything related to these questions. When I was talking about the months, the sunrise, etc., everybody were coming closer, even the old people, were coming to take their place among the students.”

5Further confirmation about the importance of the moon in the ancient culture of Easter Island comes from the “lunar calendar” of rongorongo tablet Mamari (Barthel, 1958: 242-243; Guy, 1990) and petroglyph panel carved with a sequence of 28 crescents (Lee, 1992: 180). Despite a large number of publications on the subject, the question about lunar observations of Easter Islanders still leave a considerable room for discussion. This paper is devoted to a partial solution of this problem, analyzing the available epigraphic, ethnographic and astronomical data, aiming to reconstruct the ancient Rapa Nui calendar.

6The paper uses Barthel’s notation for rongorongo artifacts and individual signs; glyph tracings are made by the author after the published photographs (Heyerdahl, 1975; van Hoorebeeck, 1979; Ramírez and Huber, 2000; Orliac and Orliac, 1995, 2008).

Ethnographical record of Rapanui calendar

7The first ethnographical data on Rapanui lunar calendar was published by Thomson (1891: 546):

“The month is divided into two equal portions, the first beginning with the new moon, and the second with the full moon. The calendar at the time of our visit ran about as follows, the new moon being full on November 26.” (Table 1)

Table 1. – Thomson’s moon calendar

Kokore tahi

Nov 27

Kokore toru

Dec 13

Kokore rua

Nov 28

Kokore hâ

Dec 14

Kokore toru

Nov 29

Kokore rima

Dec 15

Kokore hâ

Nov 30

Tapume

Dec 16

Kokore rima

Dec  1

Matua

Dec 17

Kokore ono

Dec  2

Orongo (LQ)

Dec 18

Maharu (FQ)

Dec  3

Orongo taane

Dec 19

Ohua

Dec  4

Mauri nui

Dec 20

Otua

Dec  5

Mauri Kero

Dec 21

Ohotu

Dec  6

Omutu

Dec 22

Maure

Dec  7

Tueo

Dec 23

Ina-ira

Dec  8

Oata

Dec 24

Ra Kau

Dec  9

Oari (NM)

Dec 25

Omotohi (FM)

Dec 10

Kokore tahi

Dec 26

Kokore tahi

Dec 11

Etc.

Kokore rua

Dec 12

Etc.

8The abbreviations FQ, FM, LQ and NM stands for the first quarter, full moon, last quarter and new moon, respectively. Apart from being the first documentation of lunar nights of Easter Island, Thomson’s calendar is considered to have a special value because “it appears to have been collected day by day during his stay on Easter Island in 1886” (Guy, 1990: 135). The latter statement is slightly misleading for several reasons. First, the Mohican expedition stayed at the island from December 18 till “the evening of the last day of the year” (Thomson, 1891: 476), so they could not observe the moon together with the natives on a day-by-day basis for the whole period listed in Table 1. Moreover, the schedule of the expedition was extremely tight – in less than two weeks they performed excavations at Vinapu and Orongo, surveyed the whole circumference of the island measuring and recording 112 ceremonial platforms, gathered a significant ethnographic collection, managed to purchase two rongorongo tablets and spent several evenings in a considerable effort to localize and interview Ure Va’e Iko, “one of the patriarchs of the island […] [who] […] have been under instructions in the art of hieroglyphic reading” (ibid.: 514). Under these circumstances it seems doubtful that the expedition team had a dedicated time for daily moon observations. Most possibly, the question about the calendar surfaced just once during thenights “devoted to making notes of the native traditions as translated by Mr. Salmon” (ibid.: 477), and the islanders narrated the complete list of the nights with explanations which name correspond to which phase of the moon.

9It is instructive to note that Thomson’s calendar starts on November 27, when USS Mohican was still on her course to Rapa Nui, while for the exact observation diary one would expect the calendar to start on December 18 or 19. It can be objected that Thomson wanted to start the list with a new moon – but the calendar does not begin with a new moon proper, illustrating terminological confusion about the “new moon” term. In the modern astronomy language, the moon is called new when it is in conjunction with the sun and is not visible. However, in many cultures – including Polynesian (e.g., Best 1922a: 29) – the term “new moon” can be used for the first appearance of lunar crescent after the sunset. Most possibly Thomson was told about this, because he treated the “new moon” Ari in a modern sense (no moon is visible), starting his calendar with what he thought would be the first crescent – the night kokore tahi.

10Thomson reports that the new moon occurred on December 25 (when the Mohican was anchored at Easter Island) – which would be the day to start the calendar in want to present the whole month starting with the new moon. Despite the expedition left five full days after the last date given in the calendar, the corresponding nights are marked as “etc.” offering an additional evidence that lunar observations were not carried out after December 26. Therefore, the author is inclined to think that Thomson asked Easter Islanders about their calendar within a week from his arrival, when the new moon did not occurred yet – and that is why he was more disposed to “map” the lunar nights to the preceding month rather then to shift the bulk of the calendar to January. Thus, while it was remarked that “Thomson’s record of the phases of the moon is not based on a nautical almanac, but on direct observation. This is important, for it means that Thomson’s must be a naïve, first-hand account […] to be taken at face value” (Guy,1990: 139), the question of accuracy of Thomson’s calendar remains open, especially because his 1891 report has many other misprints (Horley, 2009b).

11The corrected Thomson’s calendar was re-published by Métraux (1940: 50)

“revised in spelling and sequence by Dr. P.H. Buck so as to correspond with other Polynesian systems. […] The prefix “o” was undoubtedly added before some nights by the Tahitian, Salmon. […] Thomson’s list ends with Tueo (misspelling for Tiero [sic, Tireo]), Oata and Oari, which in other parts of Polynesia are names for the first nights of the moon. […] By transposing the names Tiero [sic], Ari, and Ata, and inserting Hiro, the Easter Island list is brought into conformity with those of New Zealand, Tahiti, Cook Islands, and Tongareva, and the number of named nights is brought up to 30 as required by the lunar month which has 29.5 days.”

12Englert’s version of the moon calendar (1948: 311-312) includes Hiro as a new moon, confirms that Motohi corresponds to the full moon and says that Hua is the first quarter. Englert’s list lacks the Hotu and treats Ari asan alternative name for Hiro, ending up with 28 nights. It was suggested that the unusual shortness of Englert’s calendar owes to the fact that “his informant gave him the basic, 28-day month without its intercalary nights” (Guy, 1990: 139). The supporting evidence for this conclusion seems to appear in the rongorongo inscription Mamari, discussed in the next section. As Englert mentions both Thomson and Métraux on calendar pages of his book, it seems that his night list was not collected independently but rather based on their publications, which possibly implies that omission of night Hotu could have been accidental.

13Another native document related to the observations of the moon surfaced during the Norwegian Archaeological Expedition, 1955-56. One page of the manuscript belonging to Esteban Atan (Fig. 1) bears an inscription “He po rae o te mahina he tahi kokore he maro 1936” – “The first night of the moon is the first kokore, June of 1936” – and presents the list of the nights accompanied with schematic drawings of the lunar phases. This list was studied in by Kondratov (1965: 409, 416). The most striking feature of this lunar calendar is significant divergence from the other published versions and overall “shuffling” of night names. While the other sources give the new moon as Hiro or Ari, Atan’s list starts with the first crescent moon in Kokore series expanded to seven nights. The names preceding Rakau were forgotten and replaced with invented series of four Popo nights. The full moon Motohi is followed by Maure (which precedes it by two nights in Thomson’s calendar) and Hiro, heralding a new series of seven [Te o] Hiro nights replacing the set of five Kokore listed by Thomson, Métraux and Englert.

Figure 1. – Moon calendar from Esteban Atan manuscript

Figure 1. – Moon calendar from Esteban Atan manuscript

(image courtesy of the Kon-Tiki Museum)

14As the Esteban Atan’s manuscript was created before the publication of Métraux’s monograph in 1940, it may have happened that the detailed knowledge of the moon calendar was already lost, keeping only the “key” nights such as Motohi and Kokore series. This situation might have improved when Métraux’s book reached the island, so that the correct night names were put to use again.

15It is important that despite of all its irregularities, Atan’s manuscript lists 30 nights in complete accordance with astronomical requirements to accommodate both “full” and “hollow” months. Thus, while the names of many nights were forgotten, the number of nights was remembered correctly. The confirmation of this fact can be found in Juan Haoa manuscript, mentioning that months Maro and Anakena had 29 days, while month Hora iti had 30 (Kondratov, 1965: 410; Guy, 1992: 121). These results cast additional doubts on Englert’s calendar of 28 nights.

Moon calendar of tablet Mamari

16The repetitive patterns carved on tablet Mamari (Fig. 2) were mentioned by Butinov and Knorozov (1957: 10, Table 3.1), but it was Barthel who suggested that left- and right-facing crescents in lines Ca6-9 have different meaning, correctly identifying 30-night moon calendar (1958: 242-243):

“in the passage Ca6-9 […] a stereotypic expression divides the text into eight sections. Each of these has a number of moon signs, surely including special forms 143 and 152, totaling to 30 occurrences […] a characteristic number of nights in the synodic period.”

17Barthel properly assigned two sets of kokore nights, identified glyph 152 with full moon Motohi and suggested that two last crescents of the calendar starting line Ca9 correspond to “dark moon”, where our natural satellite is invisible being in conjunction with the sun (ibid.: 246).

18Figure 2. – Photograph of tablet Mamari from Alphonse Pinart’s archives

Lunar calendar is written in lines Ca6-9.

(image courtesy of Bancroft Library, University of California, Berkeley).

Figure 3. – Lunar calendar of tablet Mamari.

Figure 3. – Lunar calendar of tablet Mamari.

The Roman numerals correspond to the “night groups”.
The calendar ends with two crescent signs in line Ca9;
the following phrase starting with signs 520-70 also appears in Cb13-14 and Bv2.

19The moon calendar as identified by Barthel is illustrated in Fig. 3. Each lunar night is assigned a number 1-30 starting from the nights corresponding to the first crescent. The delimiter groups marking the division of the calendar into eight parts are denoted with Roman numerals I–VIII. While it is widely accepted that the calendar starts with the first delimiter group, it is far from obvious where it actually ends. Barthel (1958: 244, 246) and Guy (1990: 136) agree that the calendar ends with two crescents (Fig. 3, marked 29 and 30), though the authors interpret these crescents differently. Rjabchikov (1989: 123-124) and the Berthins (2006: 94-95) suggest that two more glyphs 520-70 should be included into the calendar. The author is inclined to think that Barthel’s opinion (1958: 246, footnote 6) was correct, because signs 520-70 enters to the parallel passages shared by the different tablets (Fig. 3, Ca9, Cb14 and Bv2).

20Basing on Barthel’s readings of rongorongo signs, Krupa made “an attempt […] to interpret [the lunar list of Mamari] as a coherent poetical text” (1971: 8-9). Krupa’s interpretation was criticized by Guy as:

“not compatible with the calendars gathered by Englert, Thomson, andMétraux, and not compatible with a lunar calendar in general, at least, a functional one.” (1990: 146)

21Guy contributed a fundamental paper dedicated to Mamari calendar, comparing it with the moon phases during the anchorage of USS Mohican at Easter Island, and suggested tentative phonetic values for the glyphs associated with individual nights such as Hua, Atua, Maure, and Rongo Tane (Guy, 1990: 143-144). Studying the delimiter groups from tracings published by Barthel, Guy proposed that up/down fish sign 711 in ligature 8.78.711 may be meaningful:

“all three occurrences of [upward] glyph 711 precede the full moon, all four occurrences of [downward] glyph 711x follow it. […] I see there very strong evidence that 711, either on its own or perhaps only in combination with the two glyphs to which it is attached […] expresses the notion of waxing and [vertically flipped] glyph 711x that of waning” (Guy, 1990: 140-141)

22Further analysis of delimiter groups IV and VI resulted in another conclusion:

“glyph 41h, a small version of [crescent] glyph 41, could well refer to the observation that […] the moon is near its apogee […] to signal when the apparent diameter of the moon was to be observed (or measured) in order to decide whether intercalary nights were to be use” (ibid.: 140)

23This hypothesis offers exciting perspectives to “upgrade” Mamari inscription from a simple list of lunar nights into an astronomical canon governing insertion of intercalary nights into the calendar. In this way, one seemingly can explain three peculiarities:

  1. Englert’s calendar of 28 nights, which can be treated as a “basic” form of lunar month without intercalary nights;

  2. two separately carved crescents in line Ca9, serving as a “repository” of intercalary nights; and

  3. two superscript crescents 41h in the delimiter groups IV and VI, presumably related to observation of the apogee moon with its smaller visible diameter.

24Fischer’s documentation of the original tablet Mamari revealed an unexpected detail:

“It has to be noted that the composite glyph, perhaps v631By.78, has been incised on the tablet edge that begins line RR2a7 [Ca7] in other words, within the ‘calendar’s’ text. Since it is on the edge of the artefact, this glyph appears neither in any photographs of the tablet nor in Barthel’s transcription.” (1997: 418)

25The existence of these additional signs was successfully confirmed by study of the original tablet at the Exhibition of 60 objects from Easter Island in Galerie Louise Leiris, Paris, June 3 - July 31, 2008 (Horley, 2009a: 254). The “edge glyphs” perfectly fit the inscription, completing the delimiter group II to the form seen in other delimiters of the calendar. The signs were obviously omitted by a mistake and had to be incised on the edge of the tablet. The evidence for scribal corrections (ibid.: 251-255) proves that rongorongo menpaid a serious attention to the accuracy of the texts they produced.

Figure 4. – Close-up to Fig. 2 showing superscript crescents 41h in lines: a) Ca7 and b) Ca8 (image courtesy of Bancroft Library, Berkeley).

Figure 4. – Close-up to Fig. 2 showing superscript crescents 41h in lines: a) Ca7 and b) Ca8 (image courtesy of Bancroft Library, Berkeley).

The tracings published by Barthel are given below.

  • 1  The line written above glyph heads is a preceding line, limiting even more the space available to (...)

26The study of the original artifact revealed that superscript crescents 41h in the delimiter groups IV and VI could be completely explained from a paleographic point of view (Horley, 2009a: 255). The impression is that these crescents were intentionally carved small despite there was enough space to depict them in full size stems from the tracings published by Barthel, in which the mutual position of the signs was slightly modified to improve the general presentation. The photograph (Fig. 4) clearly shows that these mini-crescents were inscribed into narrow spaces between the signs1, classifying as omitted and re-inserted glyphs. Moreover, the corresponding crescent sign in the intermediate delimiter group V features abandoned hairline contour of a bird 670, which was re-carved properly nearby (ibid.: 253; Fig. 4.b, upside-down contour right above the small crescent in line Ca8). This means that the crescent in delimiter group V was also omitted but, because there was no place to fit it even as a superscript glyph, there was no other option but to discard pre-incised bird and write the sign 41 in full size. Therefore, three delimiter groups in a row – from IV to VI – had one crescent sign omitted and re-inserted, while the remaining groups I-III, VII and VIII feature full-size crescent without any hints about corrections.

27Paleographic explanation of small crescents in groups IV and VI influences the hypothesis that tablet Mamari contains an astronomical canon for insertion of intercalary nights based on observation of the apogee moon. Wanting to save this hypothesis, one may resort to a possible supporting suggestion that treats the hole in the tablet as a kind of sighting device to measure visible diameter of the moon (Horley, 2009a: 256-257).

28From an astronomical point of view, the 28-night lunar month is considerably questionable. While the average length of synodic period is 29.53 days (29d 12h 44m), the shortest/largest duration of a complete lunation is 29.27 (29d 6h 35m) and 29.83 days (29d 19h 55m), respectively (Grego 2005: 52), so that even the shortest synodic month exceeds 29 days. The sideral period (the time required for the moon to return in the same position with respect of the stars) is 27d 7h 43m long (ibid.: 43), but it is much less straightforward to observe. Only anomalistic month averaging to 27d 13h 19m approaches 28 day period (containing 27.55455 days, Steves, 1998: 551). But detection of this period corresponding to the time between two consecutive perigees or apogees of the moon will need careful measurements of its visible diameter on a regular basis. However, these variations are not that pronounced if observed out of full moon phase; please see the difference in size w of Mare Crisium observed for 3rd and 15th lunar nights, separated approximately by a half of anomalistic month (Fig. 8).

29Therefore, synodic month of 29.53 night is the most favorable for observation, requiring 30 lunar nights to compose a month. On the other hand, if Rapa Nui calendar had a basic lunar cycle of 28 days, one should insert intercalary night each month, which poses a question whether that night can be actually called “intercalary”. On the basis of this evidence, I am inclined to think that omission of the night Hotu from Englert’s night list was just an occasional mistake, unrelated to any “basic” 28-night month.

30Moon-related motifs in Rapa Nui rock art

31Among the numerous petroglyphs of Easter Island, there is a lava panel (site 31-44) located in the vicinity of Ahu Ra’ai and featuring “turtles and lines [that] may have some connection with a lunar count; both lines and cupules add up to 28” (Lee, 1992: 180). More details are as follows:

“one great panel has a series of curved lines and cupules in association with three turtle motifs. There are 28 lines, including the edge of the turtle, which gives us a possible hint of an astronomical association” (Lee, 2000: 50)

and

“[a panel] near Ahu Ra’ai, was called Papa Mahina, or ‘moon rock’. According to Georgia Lee, exactly which one is debatable since several papa are scattered around the area and modern Rapanui guides are not always in agreement […] Perhaps Papa Mahina was named after the moon because of its round shape; maybe it was a star map showing where the moon moved.” (Liller 1993: 36)

32It is important to stress that a similarity between the number of the crescents and the number of nights in synodic month gives us a reason to believe that this panel represents a complete composition with all its details (crescents and turtles) carved within a narrow time window, permitting to analyze this design as a whole. The panel (Fig. 5) should have a preferred viewing direction, possibly with a beholder staying on/behind the turtle tagged “observer” (Fig. 5a). In this case, the crescents of the carving will appear facing left, similar to the crescents denoting lunar nights in tablet Mamari (Fig. 2, 3). Importantly, two crescents in the end of the cycle are set within the carapace of the turtle, while two last crescents in Mamari calendar appear after the sign group 280-385y-385 (Fig. 3), the first of which also supposedly depicts a turtle. The similar separate depiction of two last moons of the month both in rock art and rongorongo is remarkable, strengthening Barthel’s suggestion that these crescents correspond to the “moonless” nights (1958: 246).

Figure 5. – Turtle petroglyph site 31-44 near Ahu Ra’ai:

Figure 5. – Turtle petroglyph site 31-44 near Ahu Ra’ai:

a) tracings (image courtesy of G. Lee). The numbers designate lunar nights; the turtles “embracing” the crescents can be related to the sun: the first crescent follows the setting sun and the old moon gets “caught up” by the rising sun. The two crescents inside the “sunrise turtle” for the nights when the moon is invisible being in conjunction with the sun;

b) general view of the panel with “observer turtle” (image courtesy of K. Merritt);

c) “sunset turtle” (image courtesy of C. Stevenson);

d) “sunrise turtle” (image courtesy of C. Stevenson). Letters H, F and C marks head, front fins and carapace outline; the arrows inside the carapaces mark directions in which head and fins are oriented. The curved arrow follows the general “flow” of the crescents.

33Analysis of the general composition of the panel 31-44 indicates that two turtles “embracing” the crescents can be tentatively related to the sun. The leftmost crescent is carved behind the “sunset turtle” that swims away; the first moon also appears at just after the sunset. At the right side of the panel, the crescents are being followed by swimming in “sunrise turtle”, which correspond to last crescents disappearing at dawn. The moon of night 28 can be difficult to spot (Fig. 7b), so it is carved coinciding with the outlines of the carapace (i.e., “touching the sun”, Fig. 5a). Two crescents carved within its carapace (“inside the sun”) suggest that the ancient Rapanui knew that the absence of the moon is caused by its conjunction with the sun. Maori lore explains this phenomenon in the following way:

“at certain time the moon approaches its elder brother, the sun, and the two move for a period. The moon belittles itself in the presence of its more important elder; its importance (brightness) is lost in the superior magnificence of the sun. After a time the moon leaves the sun behind; then it is said by man ‘The moon is again seen’.” (Best, 1922b: 20)

34The Polynesian tradition of re-appearance of the first crescent also involves the sun:

“The popular Maori myth […] is that the stricken moon hides to the waiora Tane, or life-giving waters of Tane […] She bathes in that fountain of youth, and returns to earth again young and beautiful. This quaint fancy is known as far away as Hawaiian Isles, where the clearest proof exists that Tane is the personified form of the sun.” (Best, 1922b: 22)

35Fedorova (1978: 18) continues:

“For many Polynesians Tane is the god of light and life; on Hawaiian islands […] the houses were facing the East in honor of god Tane; on Mangareva he was the symbol of solar heat and fire.”

36At first glance, it is tempting to speculate that the turtles of panel 31-44 with their round “sun-disc” carapaces may represent Tane. However, one will rather expect that sea creatures should personify Tangaroa (Fedorova, 1978: 19). This problem can be solved by suggesting that turtles might have been considered as “carriers” of the sun across the sky. The “transporting” role of turtles is known from the legend “Uho and the turtle” (Métraux, 1940: 372-373). A young girl Uho followed the turtle to arrive to the foreign land, where she married a man called Mahuna-te-raa. Curiously, mahuna translates as the “seed” (Fedorova, 1988: 145) and ra’a means “sun” (ibid.: 168). Nostalgic about her home, Uho sings the song “This country of yours is dark, o Mahuna-te-raa my husband, it is not like our country on the bright side” (Métraux, 1940: 373), as if hinting that the land she came might be the Underworld where the “seed of the sun” dwells waiting for the dawn. Namely at dawn the turtle carries Uho back to her homeland (ibid.). Another legend narrates:

“at Omohe […] large turtles are said to figure in a still-remembered legend concerning a man who left and then returned to the island on the back of a turtle. This man really was a god Makemake in disguise” (Lee, 1992: 82)

37According to Métraux (1940: 314) “Makemake [can be considered] the local Easter Island name for the old god Tane”, seemingly corroborating the hypothesis that the sun (as personification of Tane, or Makemake of Rapa Nui) could have been carried by a turtle.

38More petroglyphs are possibly related to the sun and the moon. Two turtles with round carapaces carved inland from Ra’ai (Fig. 6a) follow each other nose-to-tail in East-West direction (Lee 2000: 48, Fig. 9). Curiously, the leading turtle is associated with a fish hook, which is also the case of “sunset turtle” on panel 31-44 (Fig. 5a). The designs from Ava o Kiri (Fig. 6b) shows the sun (bottom right) situated below wavy lines (the horizon?) with two crescent shapes above. The crescents are carved “horns upward", just as the young moon is seen from Rapa Nui (Fig. 8a). It is tempting to suggest that the right moon represents the first crescent, while the left one (which is thicker and is depicted at larger distance from the sun) would be the second lunar night.

Figure 6. – Petroglyphs possibly related to the sun and the moon

Figure 6. – Petroglyphs possibly related to the sun and the moon

a) two turtles from “paenga factory” inland from Ra’ai, oriented East-West;

(images courtesy of G. Lee)

b) the moon and the sun from Ava o Kiri.

Figure 7. – Course of the moon in the skies above Easter Island for 30-day lunar month of August 2008:

Figure 7. – Course of the moon in the skies above Easter Island for 30-day lunar month of August 2008:

first crescent (night 1) – August 2; full moon (night 15) – August 16. Dark moons (nights 29, 30) for August 31 and September 1 are shown as black circles in bottom right corner. The figures represent a composite computer-generated image visualized with Stellarium. The celestial dome is shown in stereographic projection, in which zenithal moon appears smaller than that close to the horizon. The visible diameter of the moon is increased for the clarity of presentation. Moon observations are intended to be performed at a fixed hour a) after the sunset; b) before the sunrise.

39Resuming the analysis of the panel 31-44, one should address the question of night count. As we have seen, it is quite improbable that the lunar calendar includes only 28 nights; moreover, a remarkable coincidence of this petroglyph panel with Mamari inscription (orientation of the crescents and a separate depiction of two last nights inside the turtle) makes one think that both monuments should have the same night count of thirty. It is worth noting that the “observer turtle” faces the middle of the moon series (Fig. 5a), which coincides with a promontory of the panel (Fig. 5b, d). The crescents of waxing moon become pronouncedly rounded for the nights 13 and 14, but for the month of 30 nights the full moon should occur on the 15th night. However, one should note that there is a curved line in front of the “observer turtle”, slightly raised above the other crescents. It is quite probable that this highlighted night should correspond to the full moon (Fig. 5a, 15). This suggestion is seemingly confirmed by the orientation of the panel, with the “observer turtle” facing approximately to the east, towards Poike peninsula (Fig. 5b). As Moon is full when being in opposition to the sun, it will be rising at sunset (Fig. 7a, 15). Thus, if the turtles of the panel 31-44 are related to the sun, the “observer turtle” looking towards the mark for the 15th lunar night can be interpreted as a depiction of the setting sun “facing” the rise of Motohi moon.

40Counting back from the crescents carved inside the “sunrise turtle” (nights 29 and 30), one will find that the crescent standing to the right from the full moon mark represents night 17, with no crescent for 16th night documented. However, considerable erosion of panel 31-44 (Fig. 5b and c) and suspiciously wide space between the marks for the 15th and 17th nights (Fig. 5a) makes one think that the crescent for 16th lunar night may be there, escaping documentation due to the bad condition of rock surface.

Observations of the moon

41To understand lunar calendar better, it was decided to observe and photograph the moon during a complete lunation (Fig. 8). The extremely favorable meteorological conditions in Lisbon (Portugal) with July and August almost devoid of clouds made these observations possible, resulting in photographic documentation of 25 out of 28 visible lunar phases. The missing phases, low dusk and dawn crescents, were very hard to spot due to the obstructed horizon in urban multi-store environment. The missing phases and images of the new moon were visualized with Stellarium (www.stellarium.org).

42The naked-eye observations of the moon were extremely beneficial. It became immediately clear why the majority (eight out of eleven) of “explanatory glyphs” associated to lunar nights in Mamari calendar accompany the waxing moon – that is, when the moon is most easily observable in the evening sky. Two of the remaining “explanatory glyphs” are given for the 8th and 9th nights after the Motohi phase, when the waning moon appears high in the sky at the sunrise. In other words, the “explanatory glyphs” stand by the moon phases that are comfortably observable under normal life activities and time dedicated to sleeping.

43Moreover, twilight observation is beneficial due to a mild visual contrast of the moon. This detail becomes essential closer to the full moon phase, when later at night the moon shine is strong and irritates the eye aimed to study the main lunar features. Twilight moon gazing reveals another useful property – the lunation can be easily divided in half by observing the moon right after the sunset or right before the sunrise. The full moon will emerge just as the sun disappears below the horizon. As Moon moves daily for about 13o (Grego 2005: 52), each night it will rise later, with a retardation from dozens of minutes to about an hour depending on the angle at which the ecliptic intersects the local horizon (ibid., 54). Therefore, one night after the full moon, the moonrise will be delayed in relation to the sunset. This detail will spare the observer from meticulous verification if the moon is still round enough to be called Motohi.

Figure 8. – Photographic record of the moon during the 30-day lunation of August 2008 (images are taken by the author in Lisbon)

Figure 8. – Photographic record of the moon during the 30-day lunation of August 2008 (images are taken by the author in Lisbon)

The orientation of the moon corresponds to that seen from Easter Island, according to Stellarium. The numbers in the bottom right corner correspond to the moon age; the numbers in upper left corner are dates, prefixed with “A” for August and “S” for September. The images for the nights 1, 27-30 are generated by Stellarium. The Roman numbers I-VIII in the bands refer to Mamari calendar groups. The diagram below illustrates the conversion between the days of 00-24 hours and moon nights: moon rising just before the midnight “joins” two neighboring days (i.e., the moon of August 17 is the same as that of August 16, hence August 17 should be skipped); moon setting before the sunrise is distinct from the moon appearing in the same evening (so that September 1 should be counted twice, as new moon before the sunrise and as first crescent after the sunset). The effect of librations is shown in the bottom right corner, comparing distance d of Mare Crisium from the edge of the moon. The change in width w of this formation is due to apogee/perigee moon, observed on nights 3 and 15 separated by about a half of anomalistic month.

Figure 9. – Main seas and craters visible to a naked eye (top panel)

Figure 9. – Main seas and craters visible to a naked eye (top panel)

Below: tentative identification of the moon features with the “explanatory glyphs” of Mamari calendar.

44Therefore, the first half of the lunation can be conveniently viewed at the dusk (Fig. 7a). In a similar way, starting from the night after the full moon, the rest of the lunation is easy to observe at dawn (Fig. 7b). These observations agree well with Thomson’s comment (1891: 546) that Rapa Nui lunar calendar was bipartite. The delimiters of Mamari calendar have two scribal variants of a characteristic group 8.78.711 (Fig. 3), with final fish facing up (with the only exception of the edge glyph of group II) when the moon is waxing and facing down when it is waning (Guy, 1990: 141). In the light of twilight moon gazing hypothesis, one can suggest an alternative interpretation of the ligature 8.78.711, which may mean that the moon rises/sets after the sun, or, perhaps, that the moon follows/precedes it. At the first glance, possible inclusion of the sun into this ligature seems favorable, because sign 8 was read as “sun” by Metoro (see Jaussen list, Robinson, 2002: 228). However, one should take an extra caution with Metoro’s readings (Guy, 1999). On the other hand, if rongorongo represent syllabic script, the ligature 8.78.711 could constitute a word related to the motion, with its final fish element possibly adding a visual hint for up/down direction.

45It is essential to emphasize that the glyph corresponding to the full moon is purely pictographic, showing woman-in-the-moon (Guy, 1990: 136). This lunar pareidolia is common to the South Seas, with the correct orientation of the picture for moonrise observation (Fig. 9.15). One may ask whether the other “explanatory” glyphs for individual nights may also contain pictographic hints to some characteristic lunar features. Outside of the calendar, these glyphs are expected to behave normally (i.e., to represent syllables if rongorongo is syllabic or words if it is logographic).

46The idea about “identification tags” for the key phases is attractive. As any astronomic observation, moon watching is heavily dependent on weather. With several cloudy days, it is easy to loose the track of calendar if it is not recorded on a day-by-day basis – for example, moving a stone over an array of cupules. However, such records are vulnerable to vandals, heavy rainfall, etc., so that it would be highly relevant to reconcile the day count at the first possible observation of the moon.

47It is worth noting that the division of the month in half is indicative that first crescent and full moon were the most important nights. The apparent lack of interest for the intermediate key phases (such as the first and last quarters, which help to divide a lunation into weeks) was perhaps due to variability of the related periods:

“More confounding […] is the fluctuation of […] time between any two successive [key] phases, full moon to last quarter, for example. […] If these periods were equal, each would span 7.38 days, or one quarter of synodic month. But instead, they vary by […] plus or minus 19 hours […] [so that the time between the aforementioned phases changes] from six to nine calendar days, although most periods are not this extreme.”(Long, 1998: 19)

48Therefore, one may hypothesize that the main task of moon-based time-keeping was to know (or to be able to predict) how many nights are left or passed since the full moon. The similar calendar re-synchronization by means of full moon observations was used in the astronomical practices of Maori:

“the fifteenth night is an Ohua [full moon in New Zealand], but in certain months it is the sixteenth night, and sometimes it is the seventeenth night – that is, were the condition of full moon is attained. If the moon does not become full until the seventeenth night, then the fifteenth, sixteenth, and seventeenth nights are all termed Ohua, and then the last three nights of the moon, Orongonui, Maurea, and Mutu, are omitted, because a new moon has appeared.” (Best, 1922b: 30)

49The sighting of the first crescent was an important event, which naturally explains the presence of the “explanatory glyphs” associated with two initial lunar nights. For some days since then, there was no need to worry about the full moon, so that the whole Kokore series of six nights don’t have any additional glyphs associated. However, as the moon passed the first quarter, the task of phase identification seemingly gained more weight that explains the presence of six “explanatory glyphs” for seven nights including Motohi. After that, the astronomer could rest till the last quarter (around which two more “explanatory glyphs” are placed), perhaps implying that at this time the calendar could have been adjusted again upon necessity in preparation for the forthcoming new moon. The final “explanatory glyphs” mark the group of two moonless nights, closing the lunar month.

50Figure 9 presents names of lunar seas, mountains and craters; below, we illustrate each night with its descriptive glyph. It is important to comment that libration (slight “rocking” of the moon around its vertical axis due to interplay between its changing orbital and constant rotation speed) may shift the terminator (the boundary between illuminated and dark parts of the lunar surface) for the different lunations. The effect of libration can be seen as variation of the distance d of Mare Crisium from the border of the moon (Fig. 8, lower right corner, nights 3 and 15). Thus, one should have in mind that, for a given lunation, a phase with the best match of moon features to that of “explanatory glyph” may be shifted for about a day either forward or backward due to the librations.

51The descriptive glyph 40.10 for the first night Ata perhaps only conveys the notion that the moon is born. The second night Ari is associated with feathered glyph 30. While the presence of barbs on the line could have been intended to denote that moon grew thicker this night, it may be also plausible to associate the shape of glyph 30 with a crescent displaying Mare Crisium, which will resemble a characteristic “ear” of the sign. For the observed lunation, this feature becomes visible on the 3rd night (Fig. 9.3). However, due to librations it may appear on the 2nd night as well. The 10th night Hua is associated with glyph 74f; it is expected that the similar shape should appear on the left-hand side of the moon, which may be a light oval to the left of Mare Frigoris (Fig. 9.10). However, this identification is uncertain. On the other hand, one can also maintain that glyph 74f is hinting on the night’s name as “ideogram for ‘hua’ meaning ‘fruit, to fructify’” (Guy, 1990: 143-144).

52The 11th night Atua is associated with a “feathered hook” sign 59f standing to the left of the crescent. Similarly, one can see a “hook” on the left side of the moon disc formed by Apennine, Caucasus and Jura mountains contrasting with darker Ocean Procellarum. The bottom right appendage (foot?) of the sign will correspond to Kepler crater (visible due to its light-colored halo) appearing partially at the terminator (Fig. 9.11). The crescent sign for the night Atua has an irregular appendage to the right; one may tentatively relate it to the characteristic “pointed” look of the right-hand side of the moon, filled by the bright lines spreading from the crater Tycho.

  • 2  Guy (1990: 135) suggests that “glyph transcribed 44 by Barthel has been transcribed here as 78 … [ (...)

53On 12th night crater Kepler appears away from the terminator; it looks like an isolated object now, dispelling the illusion of being a “leg” of the “hook”. For this night, Maure, the crescent in tablet Mamari is appended with a wavy object, identified with Barthel’s sign 44. It may serve as a hint for the night name as “a visual pun: a crescent (40A) with a penis (78)2,‘ma ure’” (Guy, 1990: 144). However, on this night Mare Frigoris with a very similar shape is seen on left side of the moon. One night before it seemed isolated, but on 12th night it looks connected with Ocean Procellarum, just as it is carved in ligature 44.40 (Fig. 9.12). The 14th night Rakau is depicted as a crescent “embracing” the oval, glyph 143. It may express the notion that the bottom “coast” of Ocean Procellarum is not seen yet, so that the moon misses this “closing curve” to be complete. The full moon Motohi is associated with a unique sign 152 depicting an oval described around a woman-in-the-moon formed by Mare Tranquilitatis/MareSerenitatis (body), Mare Fecunditatis (head), Mare Nectaris (arm) and Mare Vaporum/Sinus Medii (foot). The crossed pointed contours at the bottom of the glyph 152 represent Mare Imbrium and Mare Nubium/Mare Humorum, with the latter two looking considerably pointed (Fig. 9.15).

54The 23rd night is associated with a ligature 3.40. Remarkably, there is a line of light-colored formations in Ocean Procellarum (craters Bulliadus, Kepler and Aristarchus), superficially resembling the “feathered garland” glyph 3 (Fig. 9. 23). The 24th night is preceded with a bird sign 600, which may be “a frigate bird (‘taha’ in Pascuan) […] [functioning] as a phonogram for the first syllable of Tane [in Rongo Tane]” (Guy, 1990: 143). As an alternative explanation, one can suggest that the bright/dark areas on the moon may make a semblance of an avian head with Mare Humorum being an eye and crater Grimaldi – a nostril (Fig. 9.24). The remaining “explanatory glyphs” 280-385-385 prefixing two last crescents of the calendar are associated with “dark moon”, and hence, cannot be related to any lunar features.

55Thus, in addition to Guy’s interpretation (1990: 143-144) of the “explanatory glyphs” in Mamari calendar, it is possible to propose another hypothesis treating these glyphs as pictographs of characteristic lunar features that helps to identify the current phase of the moon.

Lunar calendars throughout Polynesia

56Voicing the concerns about the accuracy of the Thomson’s calendar, it is important to compare it (together with the corrected version published by Métraux) against the inscription of the Mamari tablet. Associating Kokore series with the groups of six and five crescents following the delimiter groups II and V, one will find the following controversy: Thomson’s list gives eight nights between Kokore series, while the calendar of Mamari contains only seven of these (Fig. 3, nights 9-15). Treating Mamari’s version as correct genuine Rapanui inscription, one reaches the conclusion that Thomson’s list contains a misplaced night. The most suspicious name in this group is Ina-ira, which “is a form without equivalent in Polynesia and may be a misprint” (Métraux, 1940: 51). Curiously, “ina ira” translates as “not there” (Englert, 1948: 455), suggesting that Thomson’s informants may have mentioned a wrong night; to correct the situation, they said that the night was “ina ira” – not there – and thus has to be removed. Instead, Ina-ira was recorded as a legitimate name.

57Further comments by Métraux (1940: 51) say that “Thomson’s list omits Hiro (2nd night) which was given to me as the name for a new crescent moon […] Tapume and Matua [also] have no parallel elsewhere”. With these comments, one can compare a corrected Rapa Nui calendar (with Mamari night groups marked in Roman numerals) with lunar calendars collected from the other Polynesian islands (Table 2). The columns in the table are arranged in accordance with geographical location, listing the places by their approximate increasing distance from Easter Island (Fig. 10).

Figure 10. – Map of Polynesia (background image courtesy of Natural Earth, naturalearthdata.com) showing the islands with analyzed lunar calendars, Table 2

Figure 10. – Map of Polynesia (background image courtesy of Natural Earth, naturalearthdata.com) showing the islands with analyzed lunar calendars, Table 2

58It is important that the other calendars include 30 nights (with exception of Moriori that lists 31 of these), confirming that Mamari inscription contains a complete lunation. Easter Island version of lunar calendar can be successfully aligned with those from the other islands. However, the full moon at Rapa Nui is Motohi, which belongs to Rakau-Motohi series that follow Hotu-Maure-Marangi series including full moon on the other islands. Thus, Easter Island calendar appears shifted by about 3 nights relatively to pan-Polynesian version. Of course, one can observe “shuffling” of night order in other calendars as well, but the shifts of the characteristic groups (such as Kokore or Tangaroa) are far less prominent. I am inclined to explain the observed calendar shift by the isolation of Easter Island. The first settlers most probably had a pan-Polynesian lunar calendar, which became eventually “dephased” during its on-island evolution. The absence of further contacts with the outside world excluded the chances to re-synchronize the calendar with other sources.

59Due to the shift, the nights Tireo and Hiro close the lunation at Easter Island, when on the other islands (Tahiti, Moriori, New Zealand) they open it together with the night Ata. The Rapa Nui night Ari seems to be out of place, as in other calendars it belongs to Huna-Ari group preceding Maharu-Hua-Atua. The variations of Kokore series are curious: the only other calendar in Table 2 featuring just Kokore (Ole) series is that from Hawai’i. However, even in this case there are vestiges of some other series, reduced to numbers (Kukahi, Kulua, Kukoru, Kupau). The geographically closest calendar from Mangareva in addition to Kokore (Korekore) has Maema group, which is also present for Marquesas, Tahiti and Mangaia as Maheama, Hamiama and Amiama, respectively. Tahitian calendar makes a “bridge” introducing Tamatea night, which expands to a full group in Mangaia, Moriori and New Zealand (Table 2).

60The grouping of the nights in Mamari text highlights an important detail about the structure of the calendar. The nights Maharu, Hua and Atua (group III) appear clustered in all calendars studied despite being “shuffled”. As Ina-ira had to be omitted to agree Thomson’s list with night count of Mamari, the resulting calendar became one night short. The “missing” night can only appear in the groups VI-VIII and I, because night groups II-V are perfectly adjusted.

  • 3  There is a slim chance that the 21st night of Easter Island, Tapume,could be an erroneous re-spell (...)

61Group VI corresponds to Tangaroa nights showing up with regional variations (Takao, Taaroa, Kaloa, Tangaro) in all calendars studied except for Mangareva and Rapa Nui3. Tangaroa group usually has three nights (perfectly agreeing with three crescents in Mamari’s group VI). On Marquesas, there are two Takao nights, soon followed by Vehi night, which on Mangareva makes a group of four nights replacing Tangaroa. It is worth noting that both Mangareva and Easter Island with “forgotten” Tangaroa nights are located it the same corner of the Polynesian triangle (Fig. 10). The night Rongo of Easter Island is paired with night Rongo Tane, which, in turn, belongs to Tane-Rongonui-Mauri group on other islands, usually consisting of three nights except for Mangareva and Marquesas (2 nights) and Rapa Nui (4 nights). As one can see from Table 2, usually there are Rongo Nui and Mauri; on Easter Island, Mauri splits into Mauri nui and Mauri kero. The lunar group VII has five crescents, as if suggesting that these should stand for two Rongo and two Mauri nights plus the night Mutu, which appears in the calendars from Tahiti to New Zealand. On the basis of this evidence, one can suggest that the missing night, perhaps called in unusual way such as Vaka or Vehi of Marquesas, should have been inserted to the VI lunar group of Mamari calendar, (Table 3, Reconstruction A; the detailed night-by-night list is given in Table 2).

Table 3. – Tentative reconstruction of Easter Island calendar

Reconstruction A

Reconstruction B

1 Ata

1 Ari

2 Ari

2 Huna

3-8 Kokore tahi – ono

3-8 Kokore tahi – ono

9-11 Maharu – Atua

9-11 Maharu – Atua

12-15 Hotu – Motohi

12-15 Hotu – Motohi

16-20 Kokore tahi–rima

16-20 Kokore tahi–rima

21 Tapume

21-23 Tapume – Rongo

22 Matua

24-27Rongo Tane-Mutu

23???

28 Tireo

24-28Rongo – Mutu

29 Hiro

29-30 Tireo – Hiro

30 Ata

Night groups are highlighted as in Mamari text.

62A less structurally coherent but possible reconstruction consists in inclusion of night Huna (appearing in every remaining calendar, Table 2) to form Huna-Ari group in the beginning of the month (Table 3, Reconstruction B). Ari was set before Huna to mimic calendars of Mangareva, Marqueses and Mangaia, while for Tahiti, Moriori and New Zealand this order is reversed. The rest of the calendar proceeds much the same with Tireo, Hiro and Ata being three closing nights, which fits the three-night “shift” of Easter Island calendar. However, in this way the lunar groups of Mamari inscription will separate the night Rongo from Rongo-Mauri series (group VII), also joining Tireo night there. The latter issue may be not so crucial, as it also happens in Mangaia calendar ending with Omutu, Otireo and beginning with Iro and Oata.

63Therefore, Rapa Nui lunar calendar shows strong parallels with other Polynesian calendars, with the main night series clearly marked by the delimiter groups of Mamari calendarinscription. The most remarkable structural similarity can be seen between Easter Island and Mangareva calendars (the same sequence of nights from Maharu to Motohi with only the inserted night Oturu, large Kokore series exceeding three nights, “forgotten” Tangaroa series and unusual Orongo-Mauri series that do not have three nights as it is the case elsewhere).

Crescentarrangements in rongorongo texts

64If there is a lunar calendar in tablet Mamari, could it be that the other rongorongo texts also feature more astronomic contents? And, as far as the moon is concerned, could the combinations of crescent signs appearing elsewhere encode parts of lunar calendar or individual nights? These questions are really difficult to answer as long as rongorongo remains an undeciphered script.

Figure 11. – Crescent arrangements and other examples of sign symmetry from different rongorongo texts

Figure 11. – Crescent arrangements and other examples of sign symmetry from different rongorongo texts

65In his paper Wieczorek (2011) addresses the question of a possible astronomical content on tablet Keiti, discussing delimiter groups with two crescents and anthropomorphic signs (Fig. 11, Er1-Er6) following the structural analysis performed by Melka (2008: 161-164) . As some of these crescents face to the right and some to the left (as glyphs 40 and 41 in Mamari calendar), one can consider this orientation meaningful and potentially containing some information about lunar cycles.

66However, the delimiter groups of Er1-Er6 feature a considerable number of minor variations, such as inclusion/exclusion of anthropomorphic signs (that are connected in different ways to the crescents), replacement of closing glyph 24 with round upper part with glyph 28 that have notched upper part in the same line Er1, and pronounced “flipping” of the crescents between left/right orientation. These changes are surprising because nine out of ten occurrences of this glyphic group fall into the neighboring lines Er1-3, so that the carver could have easily consulted the completed passages to ensure textual uniformity. Studying the photographs of the tablet (Horley 2010: 46), one will find that the complete forms of this delimiter group appear in the first half of the line (Fig. 11, Er11-2, Er21-2, Er41), while the abbreviated forms with omitted anthropomorphic glyphs are carved close to the end of the line (Fig. 11, Er13, Er23, Er61) or belong to the wedged line Er3. These details suggest that the carver abbreviated delimiter group upon approaching the end of the line for space-saving purposes.

67On the contrary, all delimiter groups of Mamari calendar, also occupying neighboring lines, are always written in full with careful correction of the omitted glyphs, using even the edge of the tablet when it was necessary (Fig. 3). Therefore, it seems that the topic of Mamari inscription allowed less liberty to the scribe than that of Keiti – or the scribe of Keiti was less caring for the details. Also, it is worth noting that orientation of the crescents in Mamari calendar serves to distinguish crescents of delimiter groups (sign 41) from those of the calendar text (sign 40). In delimiters of Keiti, both glyphs are either mixed (Fig. 11, Er11, Er21 and Er31) or seemingly harmlessly replaced for only left/right facing crescents.

68According to Barthel’s glyph occurrence tables (1958: 99), sign 40 is considerably more frequent than glyph 41. Scanning the corpus for sign 41 and taking into account parallel passages, it is possible to show that crescent glyph orientation is not always preserved (Fig. 3, Ca9 and Cb13-14; Fig. 11, Pv2 and Qv3, Pr5 and Aa1). The orientation of the clustered crescents (Fig. 11, Bv2, Hv10, Pv11 and Cb13) can be flipped on the whim of the scribe to get the desired symmetric pattern, which may also apply to the delimiter groups of Keiti.

69Actually, the question about right/left sign orientation is deeper, overlapping with concerns voiced by the Pozdniakovs (2007: 4) for the “instances when anthropomorphic glyphs are rotated [i.e. facing] to the left”. A preliminary study on this topic was made by Barthel (1958: 159, note 2) for the sign 53, which for different artifacts may predominantly face to the right, to the left, or feature a “mixed” orientation. The orientation of this sign is not always preserved in parallel passages (Fig. 11, Pv2 and Qv3).

70Analyzing various sign groups, one becomes inclined to think that symmetric glyph arrangement was considerably appreciated and employed by the rongorongo men to improve the visual appearance of their texts. For example, signs 66 in the parallel passages Bv3 and Hv10 (Fig. 11) alternate their sides in a seemingly free manner, which most probably should not influence the reading of the passage. However, the symmetric arrangement of two glyphs “embracing” head-down sign 95x in line Bv3 or its analogue 559 in line Hv10 improves text composition. Moreover, it could be said that inside “branch” orientation of the sign 66 in the former text allowed to save space (note: glyphs in Fig. 11 are set apart to improve the clarity of the presentation), while the same scheme could not be applied for the line Hv10 because the inner glyph 559 is wider and leave no space to carve the branches looking inside the group. Both glyphs 66 appearing further on in line Hv10 form ligatures 66.61, so that their branches turned left to simplify the carving. Several signs to the right, both signs 66 “embracing” glyph 22f have their branches to the right, which may be caused by preceding sign 207/307 whose hand does not leave much space for left-facing branch of the first glyph 66 in this group (Fig. 11, Hv10, Bv3). The similar side-flipping of sign 66 can be seen in another copy of the same passage appearing in line Bv9.

71Another good example illustrating a considerable variation of sign 66 (with its side branches to the right, to the left, to the both sides, or without branches at all) is a structured sequence written in lines Aa1, Hr5, Pr5, Qr5 (Butinov and Knorozov, 1957: 14). Guy made the following conclusion regarding the use of signs 66 in this sequence: “only right [facing] variants of form [with] 1 [branch] occur on tablet P, only left variants on tablet Q. There seems to be no conditioning factor as to when form [with] 1 or 2 [branches] is used” (1985: 382), suggesting that sign orientation here most probably does not have any meaningful role.

  • 4 Despite the tracings published by Barthel (1958) and Fischer (1997: 503) depict here sign 99 with n (...)

72Glyph 522 also makes a nice example of asymmetric sign that can be carved with its “proboscis” looking to the right (in the majority of the cases) or to the left. The stable glyphic group 4-522-700-600-59f appearing in seven texts (Bv12, Ev6, Gr2/Kr3, Ma2, Hv12, Ra5) provides a good illustration for interchangeability of left-proboscis (Bv12, Ev6, Ma24, Hv12) and right-proboscis (Gr2, Kr3, Ra5) versions of this glyph (Fig. 11, Ev6 and Ra5). The Large Washington tablet contains the evidence on seemingly non-meaningful side-flipping of proboscis-bearing glyph 520 entering into group 1.520-4.64 repeated twice (Fig. 11, Sa31). Further on, one can see symmetric arrangement of glyphs 522 (Fig. 11, Sa32). However, not every occurrence of quasi-neighboring signs 522 on this tablet is symmetric (e.g., Fig. 11, Sa6).

73Other glyphs also display the similar side-flipping: compare the orientation of glyph 4 in the passages Ev6, Ra5 and its symmetric reduplication 4.3-4.3 in line Cb8 (Fig. 11). The double-head signs 308, 409/410, 609, 770, as well as duplicated glyphs 420, usually have their heads arranged with mirror symmetry (Fig. 11, Aa6).  Even highly standardized sign 7, presumably depicting reimiro, can be written “back-to-back” (Fig. 11, Da1).

74Therefore, it seems plausible to conclude that horizontal flipping of rongorongo glyphs most probably does not influence their reading/meaning, though, in certain cases, as in Mamari calendar, right and left orientation of the crescents helps to avoid visual confusion between the signs belonging to the delimiter group and to the list of the nights proper. With this evidence, the probability that orientation of the crescents appearing in delimiter groups of tablet Keiti (Fig. 11, Er1-Er6) is meaningful seems to be quite slim.

75Searching more calendar-related contents in the inscriptions, it could be productive to look for the ligatures related to the “explanatory glyphs” of the lunar nights, which points out to the similarly-looking compounds 41.74f (Fig. 11, Hv11 and Gv4) and 40.3 (Fig. 11, Gv3). However, the corresponding “explanatory glyphs” for the nights 10 and 23 (Fig. 9) feature the inverse element order (with the crescent being the second). Moreover, as the same compound appears written as a vertical ligature in the both cases involving Barthel’s glyph 42 for a rotated crescent (Fig. 11, Hv11 and Gv3), it becomes doubtful to conclude that these ligatures can be associated with the lunar nights.

76Therefore, while it is completely reasonable to expect that Easter Island tablets may contain references to individual lunar nights/month names, it seems that the crescent series appearing in lines Ca6-9 of tablet Mamari form the only complete lunar calendar in the survived rongorongo corpus.

Conclusions

77The study of authentic Easter Island documents connected with moon observations (tablet Mamari, petroglyph panel 31-44 and Manuscript A) proved that the ancient lunar calendar of Rapa Nui should have consisted of 30 nights, perfectly agreeing with astronomy and other Polynesian calendars. Two last nights of the month correspond to the new moon in conjunction with the sun; these nights are carved separately on tablet Mamari and placed within a carapace of the turtle (which can be related to the rising sun) in panel 31-44. One of the turtles in the panel is oriented eastwards, facing the mark that can be interpreted as a full moon. Observations of a complete lunation suggested an alternative interpretation for the “explanatory glyphs” of Mamari calendar, which may have helped to identify the phase of the moon. The comparative analysis of Easter Island calendar confirmed its undeniable Polynesian origin, highlighting peculiarities indicative for isolated development.

In the first place, I would like to express my gratitude to Isabelle Leblic for her kind invitation to write this paper. Many special thanks to Susan Snyder (Bancroft Library, University of California, Berkeley) and Reidar Solsvik (Kon-Tiki Museum, Oslo) for their generous permission to publish the images of tablet Mamari and lunar calendar page from Rapa Nui Manuscript A. This research would have been impossible without the great help of Christopher Stevenson (Virginia Department of Historic Resources) and Kathleen Merritt (Easter Island Foundation), to whom I am grateful for their wonderful photographs of petroglyph panel 31-44. I am also cordially thankful to Georgia Lee (Easter Island Foundation) for her kind permission to reproduce her magnificent tracings of Rapa Nui petroglyphs. My most sincere thanks to Catherine and Michel Orliac, Konstantin Pozdniakov, Steven Fischer, Jacques Guy, Ilse Jung, Martyn Harris, Albert Davletshin, Tomas Melka, Rafal Wieczorek, Jenya Korovina and Scott Nicolay for their great help with the literature and information about rongorongo artifacts, helpful advices and numerous stimulating discussions.

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Notes

*  Yuri Fedkovych Chernivtsi National University, Chernivtsi, Ukraine, paulmn@operamail.com

1  The line written above glyph heads is a preceding line, limiting even more the space available to the scribe.

2  Guy (1990: 135) suggests that “glyph transcribed 44 by Barthel has been transcribed here as 78 … [that] resembles it far more than glyph 44”. However, the real shape of this glyph is quite different from both signs 44 and 78 (compare the photo with tracings published by Barthel, Fig. 4.a).

3  There is a slim chance that the 21st night of Easter Island, Tapume,could be an erroneous re-spelling of a quick hand­writing for Ta[n]garoa.

4 Despite the tracings published by Barthel (1958) and Fischer (1997: 503) depict here sign 99 with no proboscis, the digital photography from the Museum für Völkerkunde reveals that actually it is glyph 522 (which perfectly agrees with other parallel passages), with its proboscis turned to the left.

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Table des illustrations

Titre Figure 1. – Moon calendar from Esteban Atan manuscript
Crédits (image courtesy of the Kon-Tiki Museum)
URL http://jso.revues.org/docannexe/image/6314/img-1.png
Fichier image/png, 73k
Légende Lunar calendar is written in lines Ca6-9.
Crédits (image courtesy of Bancroft Library, University of California, Berkeley).
URL http://jso.revues.org/docannexe/image/6314/img-2.png
Fichier image/png, 585k
Titre Figure 3. – Lunar calendar of tablet Mamari.
Légende The Roman numerals correspond to the “night groups”. The calendar ends with two crescent signs in line Ca9; the following phrase starting with signs 520-70 also appears in Cb13-14 and Bv2.
URL http://jso.revues.org/docannexe/image/6314/img-3.png
Fichier image/png, 160k
Titre Figure 4. – Close-up to Fig. 2 showing superscript crescents 41h in lines: a) Ca7 and b) Ca8 (image courtesy of Bancroft Library, Berkeley).
Légende The tracings published by Barthel are given below.
URL http://jso.revues.org/docannexe/image/6314/img-4.png
Fichier image/png, 111k
Titre Figure 5. – Turtle petroglyph site 31-44 near Ahu Ra’ai:
Légende a) tracings (image courtesy of G. Lee). The numbers designate lunar nights; the turtles “embracing” the crescents can be related to the sun: the first crescent follows the setting sun and the old moon gets “caught up” by the rising sun. The two crescents inside the “sunrise turtle” for the nights when the moon is invisible being in conjunction with the sun;
URL http://jso.revues.org/docannexe/image/6314/img-5.jpg
Fichier image/jpeg, 124k
Titre Figure 6. – Petroglyphs possibly related to the sun and the moon
Légende a) two turtles from “paenga factory” inland from Ra’ai, oriented East-West;
Crédits (images courtesy of G. Lee)
URL http://jso.revues.org/docannexe/image/6314/img-6.png
Fichier image/png, 11k
Titre Figure 7. – Course of the moon in the skies above Easter Island for 30-day lunar month of August 2008:
Légende first crescent (night 1) – August 2; full moon (night 15) – August 16. Dark moons (nights 29, 30) for August 31 and September 1 are shown as black circles in bottom right corner. The figures represent a composite computer-generated image visualized with Stellarium. The celestial dome is shown in stereographic projection, in which zenithal moon appears smaller than that close to the horizon. The visible diameter of the moon is increased for the clarity of presentation. Moon observations are intended to be performed at a fixed hour a) after the sunset; b) before the sunrise.
URL http://jso.revues.org/docannexe/image/6314/img-7.png
Fichier image/png, 206k
Titre Figure 8. – Photographic record of the moon during the 30-day lunation of August 2008 (images are taken by the author in Lisbon)
Légende The orientation of the moon corresponds to that seen from Easter Island, according to Stellarium. The numbers in the bottom right corner correspond to the moon age; the numbers in upper left corner are dates, prefixed with “A” for August and “S” for September. The images for the nights 1, 27-30 are generated by Stellarium. The Roman numbers I-VIII in the bands refer to Mamari calendar groups. The diagram below illustrates the conversion between the days of 00-24 hours and moon nights: moon rising just before the midnight “joins” two neighboring days (i.e., the moon of August 17 is the same as that of August 16, hence August 17 should be skipped); moon setting before the sunrise is distinct from the moon appearing in the same evening (so that September 1 should be counted twice, as new moon before the sunrise and as first crescent after the sunset). The effect of librations is shown in the bottom right corner, comparing distance d of Mare Crisium from the edge of the moon. The change in width w of this formation is due to apogee/perigee moon, observed on nights 3 and 15 separated by about a half of anomalistic month.
URL http://jso.revues.org/docannexe/image/6314/img-8.png
Fichier image/png, 207k
Titre Figure 9. – Main seas and craters visible to a naked eye (top panel)
Légende Below: tentative identification of the moon features with the “explanatory glyphs” of Mamari calendar.
URL http://jso.revues.org/docannexe/image/6314/img-9.png
Fichier image/png, 267k
Titre Figure 10. – Map of Polynesia (background image courtesy of Natural Earth, naturalearthdata.com) showing the islands with analyzed lunar calendars, Table 2
URL http://jso.revues.org/docannexe/image/6314/img-10.png
Fichier image/png, 66k
Titre Table 2. – Comparison of Easter Island lunar calendar with those of other Polynesian islands
URL http://jso.revues.org/docannexe/image/6314/img-11.png
Fichier image/png, 189k
URL http://jso.revues.org/docannexe/image/6314/img-12.png
Fichier image/png, 197k
Titre Figure 11. – Crescent arrangements and other examples of sign symmetry from different rongorongo texts
URL http://jso.revues.org/docannexe/image/6314/img-13.png
Fichier image/png, 144k
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Paul Horley, « Lunar calendar in rongorongo texts and rock art of Easter Island », Le Journal de la Société des Océanistes, 132 | 2011, 17-38.

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Paul Horley, « Lunar calendar in rongorongo texts and rock art of Easter Island », Le Journal de la Société des Océanistes [En ligne], 132 | 1er semestre 2011, mis en ligne le 30 juin 2014, consulté le 18 novembre 2017. URL : http://jso.revues.org/6314 ; DOI : 10.4000/jso.6314

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