From: owner-ane@ (ANE Digest) To: ane-digest Subject: ANE Digest V2001 #329 Reply-To: Sender: owner-ane@ Errors-To: owner-ane@ Precedence: bulk ANE Digest Sunday, December 16 2001 Volume 2001 : Number 329 ane Xochicalco datable texts! ---------------------------------------------------------------------- Date: Sat, 15 Dec 2001 15:02:28 EST From: ECOLING@aol.com Subject: ane Xochicalco datable texts! Folks: Here is a proposal for exact dating of the Xochicalco stelas. Most plausible seems from 595 (first date on Stela 3) to 729 (last date on Stela 2). A second alternative would be 104 years earlier, 491 to 625. Please regard this as a copyright draft. Copyright (c) 2001 Ecological Linguistics. A more formal document is in preparation. Lloyd *** There are some dates on Xochicalco stelas 1 to 3 which plausibly have pairs of day names, one used as year name, the other as day-within-the-year. That interpretation was arrived at before any of the following calculations were attempted, based on the large number of day-name glyphs in the three stelas, and the lack of any strong indications that many of these should be interpreted as personal names rather than actual dates, other than the three at the top of side A of each stela. Of the pairs which are candidates for Yearname + Dayname status, the lower member of the pair is always a year-bearer day in the set Flint, House, Rabbit, Reed, while the upper member of the pair is sometimes outside that set (6 Movement, 2 Death). Dates in human lives can of course happen anytime, but dates in a structured calendar may show regular patterns. So we can attempt to analyze those which do not appear to be events of a human nature. Three of the dates which are candidates for Yearname + Dayname, both of the two on Stela 3 column B, and one of the two on Stela 1 column B, have the same abstract glyph with them, I am assuming a verb. The glyph has a cross shape contained within it. Before doing the calendrical analysis, I wondered whether this verb might conceivably refer to the four cardinal directions, conceivably even to a place-of-origin like the Maya turtle shell with K'an-cross inside, which the glyph slightly resembles. The intervals between these days are quite interesting. At a minimum, they must span a bit more than 17 years out of one 52-year cycle, but they could span more if they are separated by any additional number of 52-year cycles. Year 9 House day 12 Reed (10 days before year-bearer, or 250 days later) Year 10 Rabbit Year 11 Reed Year 12 Flint Year 13 House Year 1 Rabbit Year 2 Reed day 2 Reed (the year-bearer day itself) Year 3 Flint Year 4 House Year 5 Rabbit Year 6 Reed Year 7 Flint Year 8 House Year 9 Rabbit Year 10 Reed Year 11 Flint Year 12 house Year 13 Rabbit day 5 Reed (5 days after the year-bearer, or 255 days earlier) A first notable property of these three dates is that they are all very close to the year-bearer of the year, in one of the three the day date is that year-bearer itself. This is true because of the structure of the 260-day cycle, so this conclusion remains valid whether the year-bearer day is the 1st day of the year, the 360th day of the year, or the 365th. This property does not hold for a fourth date, the remaining one of the two on Stela 1 column B, which uses a different verb (which I suspect is related to the trapeze-and-ray military headdress). Year 9 House day 6 Movement falls114 days after or 146 days before the year-bearer. A second notable property is that the intervals between these dates are all multiples of 20. From 9 House 12 Reed to 2 Reed 2 Reed is 6 x 365 + 10 = 2200 = 6 x 360 + 40. From 2 Reed 2 Reed to 13 Rabbit 5 Reed is 11 x 365 + 5 = 4020 = 11 x 360 + 60. And as a consequence of those two, not an independent fact, From 9 House 12 Reed to 13 Rabbit 5 Reed is 17 x 365 + 15 = 6220 = 17 x 360 + 100 It does not matter if we take any of the three dates to be a full calendar round earlier or later, since 52 x 365 is also divisible by 20. There is no obvious reason why this should be true. But if this verb had a calendric significance, and were somehow restricted to seatings of 20-day Uinals, then we might expect such a pattern. Note here that we really must mean Uinals, not Months. The months are displaced by the 5 nameless days every year, But Uinals count continuously by 20's. So I conclude tentatively that the inhabitants of Xochicalco who were recording this event (on these stelas) may have been keeping a continuous count of Uinals, wich may imply a long count of the general type of the Maya. They were however recording the dates on the stelas in a Central Mexican type of calendar. So it might be concluded that they were an outside elite. *** Whatever the event is, it cannot, if the days are close together in a single 52-year cycle, by multiples of Tuns (360 days) or K'atuns (7200 days). What if we displace one of these dates by a 52-year calendar round? 52 x 365 = 18980. 52 x 360 = 18720. The difference is 260 days, 52 x 5 = 260. Adding 260 to the 100 days excess noted in the third interval above, we do reach an even multiple of Tuns. 17 x 360 + 100 52 x 360 + 260 69 x 360 + 360 = 70 x 360. So it is quite possible that this verb actually refers to the celebration of Mayan-type period endings on at least a 10-Tun basis. Or it could refer to even-tun anniversaries of some earlier event. If the date 9 House 12 Reed precedes the date 13 Rabbit 5 Reed by a full calendar round plus the 17 years and 15 days, the interval is exactly 70 Tuns, or 3 K'atuns and 10 Tuns. Is it just chance that it is a multiple of 10? Perhaps not. This is worth investigating, at least. On the assumption that the three Xochicalco stelas, so similar in style, were commissioned close to each other in time, and that they record life spans of single rulers, the interpretation I most favored was in fact the following: Year 9 House Day 12 Reed Ruler of Stela 3 first noted as celebrating this ceremony Interval of 46 years Year 3 Reed Ruler of Stela 3 defeated and cremated? Interval of 23 years Year 13 Rabbit Day 5 Reed Ruler of Stela 1 first celebrates this ceremony The total in years is 69 x 365 = 25,185 days. Adding the 15 days because 12 Reed precedes 9 House by 10 days and 5 Reed follows 13 Rabbit by 5 days, we have 25,200 days, or exactly 70 Tuns. These lines of reasoning confirm each other, and were conducted independently of each other. Tentatively, I conclude again that those who commissioned these stelas at Xochicalco were using a calendar which counted continuous Uinals and Tuns (units of 20 and of 360 days), and probably laid special significance on multiples of 10 Tuns at least. Contrary to my initial expectation, further analysis was probably not consistent with these dates themselves being the seatings of Uinals, but only with their being multi-Tun anniversaries in the case of the two whose interval is 70 Tuns. *** This section explores alternatives which I think do not work. If you wish, skip to the next "***". Placing the dates in the other order would not work the same way, as 52 years subtracting 17 years 15 days yields this: From Year 13 Rabbit Day 5 Reed To Year 9 House Day 12 Reed 52 x 360 + 260 17 x 360 + 100 subtracting 35 x 360 + 160 not an even multiple of 360. It is not easy to get back to an even multiple of Tuns this way: If we add successive 52-year cycles to this, we have 160 + 260 = 420 = 60 more than an even 360 60 + 260 = 320 320 + 260 = 580 = 220 more than an even 360 220 + 260 = 480 = 120 more than an even 360 120+ 260 = 380 = 20 more than an even 360 20 + 260 = 280 280 + 260 = 540 = 180 more than an even 360 180 + 260 = 440 = 80 more than an even 360 80 + 260 = 340 340 + 260 = 600 = 240 more than an even 360 240 + 260 = 500 = 140 more than an even 360 140 + 260 = 400 = 40 more than an even 360 40 + 260 = 300 300 + 260 = 560 = 200 more than an even 360 200 + 260 = 460 = 100 more than an even 360 100 + 260 = 360 So after 16 calendar rounds, we finally reach an even Tun interval. Very unlikely to be what is recorded here. * What about the third date recorded with this verb? This is much more difficult, and I have no satisfactory solution to propose. Taking first the interval between the two dates with this same verb on Stela 3, we have this: 6 x 360 +40 We would have to add 4 Calendar Rounds, 208 years, to reach an even Tun interval. More difficult. Or in the other order: 52 x 360 + 260 6 x 360 + 40 subtracting 46 x 360 +220 We would have to add 13 Calendar Rounds, 676 years, to reach an even Tun interval. Completely excluded. Taking now intervals between the 2 Reed 2 Reed date and the 13 Rabbit 5 Reed date: 11 x 360 +60 We would have to add 15 Calendar Rounds, 780 years, to reach an even tun interval. Completely excluded. 52 x 360 + 260 11 x 360 + 60 subtracting 41 x 360 + 200 We only need to add 2 Calendar Rounds, 104 years, to reach an even Tun interval. Quite possible, though not as good as the one we had before. If this interval also was intended as an even number of Tuns, it was From Year 13 Rabbit Day 5 Reed To Year 2 Reed Day 2 Reed 41 tuns + 200 days 52 Tuns + 260 days 52 Tuns + 260 days 145 Tuns + 720 days = 147 Tuns even. This is not a multiple of 10 or even of 5 Tuns. If all three of these represented even numbers of Tuns, we would have: From Year 9 House Day 12 Reed To Year 13 Rabbit Day 5 Reed Interval 70 Tuns. From Year 13 Rabbit Day 5 Reed To Year 2 Reed Day 2 Reed Interval 147 Tuns The two dates on Stela 3 column B would then be separated by 217 Tuns, impossible within the lifespan of a single individual. So I reject this interpretation. And I am left with no account of the date Year 2 Reed Day 2 Reed within the calendric analysis pursued here. *** How about astronomy? This is a bit difficult given that we do not know what calendar was being used in Xochicalco. But if we can believe that those who commissioned the stelas were using a calendar with Uinals and Tuns, like the Maya, then perhaps we can also consider that in translating to a Central Mexican system they were using Mayan years. One way of calculating these things is to assume the year bearer day was day 360 of the 365-day year, as is traditional for studies of Central Mexico (and if the calendar was being translated for the stelae, it would be people familiar with Central Mexico who would be doing it). Under this assumption, I checked the four dates from Stelas 3 and 1 column B for the time span 450 to 1000 C.E.. In this time period two events stood out astronomically more than any others, and reinforced the suggestion that the verb might refer to a "place of origins" K'an glyph. The two are not within the intervals from each other which the precediing analysis suggests for the stelas, but one of them might possibly be regarded as an anniversary of an earlier date, and the other one could be contemporary. As to the astronomical analogies noted below, please keep in mind that the Mayan date for the beginning of this world age, "4 Ajaw 8 Cumk'u" in 3114 BCE is calculated to have the properties that Mercury and Venus were in conjunction, almost fallen into the Sun, and Saturn also almost fallen into the Sun. * The first of the dates which emerged as having significant astronomy is the Xochicalco Year 9 House Day 12 Reed. The Year 491 C.E. Mayan 9.2.16.2.3 is a day 9 Ak'bal 1 Uayeb, with a day 12 Ben 10 days earlier. Mayan "Ak'bal" and "Ben" equate to Central Mexican "House" and "Reed". This is Julian 3 April of the year 491, using correlation constant 584285, but I am not trying to be precise with that as opposed to 584283. I use the Tuckerman Tables for the day 23 March, the 12 Ben day, interpolating. On this date there was a stark separation of the planets. The Sun was at 3.97 degrees Mercury was at 22.59 degrees. Venus was at 1.37 degrees, in conjunction with the Sun.. Mars was at 307.28 degrees. Jupiter was at 309.58 degrees. Saturn was at 309.49 degrees. This could easily be interpreted as one of the conjunctions of Jupiter and Saturn which recur about every 20 years, special this time because Mars was also there, and a time of origination because one of the "first fathers", Venus, was being reborn in conjunction with the Sun (perhaps here the second generation of the Twins, since Mercury was perhaps visible). But it is more special than that. It is not merely a Jupiter-Saturn conjunction, it is one of the very rare ones of those, in which the two planets stay together for a very long time. In fact, from mid-March when they come within a degree of each other, to mid-November of that year, the two planets are never more than about 5 degrees apart, and they come within two degrees again from approximately 10 September to 15 October. It is not technically a "triple conjunction", unlike the famous Palenque record of 2 Cib 14 Mol, Mayan 9.12.18.5.16, July 20 in the year 690. But it is special like that Palenque one in that Mars is in conjunction with the other two outer planets in 491 just at the time of their first approach (conjunction). The astronomy is therefore remarkable enough that we can assume Mayans at least paid great attention to it. If the date on the stela is indeed in relation to this astronomy, it could be either that it refers to a date in the year 491, in which case the stelas are early, or that it refers to a later commemoration of that early date. Between Mayan 9.0.0.0.0 and 10.7.0.0.0, there was no other date with anything at all close to such remarkable astronomy matching the criteria for 9 Ak'bal 1 Uayeb. (For 9.18.12.8.3, January 15 of 803, 10 days earlier, approximately 2 January, has Mercury and Venus simultaneously in conjunction with the Sun.) * The second date whose astronomy sticks out as special might match the Xochicalco Year 13 Rabbit Day 5 Reed. Year 664. Mayan 9.11.11.9.8 is a day 13 Lamat 1 Uayeb (with day 5 Ben 5 days later), Mayan "Lamat" and "Ben" equate to Central Mexican "Rabbit" and "Reed". This is Julian 19 February of the year 664. The Sun was at 335.43 degrees. Venus was at 357.01 degrees, rising as evening star. Mercury was at 350.29 degrees, invisible. The outer planets Mars and Saturn were about 10 degrees apart, interpolating for February 21st: Mars at 280.69 degrees Saturn at 269.16 degrees on But this time Jupiter was not so close, at 156.64 degrees. This is not a re-enactment of the astronomy of 491 March 23, but it is close in several respects. Between Mayan 9.2.0.0.0 and 10.8.0.0.0, there was no other date with anything at all close to such remarkable astronomy matching the criteria for 13 Lamat 1 Uayeb. * For the criteria 2 Reed (Ben) 1 Uayeb, there is nothing astronomically as striking between Mayan 9.2.0.0.0 and 10.7.0.0.0 except possibley 9.5.14.16.13, March 19 of the year 549. The outer planets were close together, and Venus was rising as evening star. * For one other date, 6 Flint (Etz'nab) 1 Uayeb, which was recorded with what may be a descending-Venus verb on Xochicalco Stela 2 column B upper clause, there is nothing astronomically striking in the same way between Mayan 9.2.0.0.0 and 10.8.0.0.0. That is actually good for our hypothesis, because if it were the same verb, we might want to see similar astronomy. But the date 9.11.17.19.8, February 17 of the year 670 may warrant some attention. It is more or less the opposite of the two dates discussed in detail above. There had been a conjunction of Jupiter and Saturn a few days earlier, and they were now fallen into the Sun. Mars was already there, not yet emerged from the Sun. Mercury was near its maximum as evening star, and Venus was descending as morning star. So this time, the inner planets were visible, and the outer planets were in conjunction with the Sun. *** I have not yet explored the possibility of treating the year bearers at Xochicalco as the first days of the year, using criteria 1 Pop instead of 1 Uayeb to locate the dates. But without yet doing that, here are the best solutions given what has been explored. Either take the stelas as early, the year 491 as contemporaneous, or take them as middle classic, the year 664 as contemporaneous. I offer the second one here, perhaps more probable given the archaeology of Xochicalco? Specialists can advise on this. (If the other alternative is chosen, the results seem not as good, and the history sketched below would be pushed back 104 years.) * If year 664 is contemporary, then: Year 595, Mayan 9.8.1.10.3 Year 9 House (Day 12 Reed is 9.8.1.9.13) Ruler "4 Movement" of Stela 3 first celebrates the "place of emergence" ceremony, perhaps in commemoration of the astronomy of the same date in the year 491, exactly one Venus cycle of 104 years earlier. On the actual date in 595, Mercury and Venus were invisible in the Sun, Venus was in exact conjunction 5 days earlier. They both became visible around 15-20 days later. Although the rest of the astronomy was not remarkable enough to choose this date on its own, the reasoning suggests this date by back-calculation from 664. The positions of Venus and Mercury suggest it was probably also a celebration of the event of 595, not merely a commemoration of an earlier event. [46 years interval since 595] Year 641 Year 3 Reed (Day 9 Monkey? or other?) Ruler "4 Movement" of Stela 3 was defeated and cremated? Year 647, 9 House, perhaps a military event by Ruler "7 ReptileEye" of Stela 1. [23 years interval since 641] Year 664, 19 February Mayan 9.11.11.9.8 Year 13 Rabbit (Day 5 Reed is Mayan 9.11.11.9.13) Ruler "7 ReptileEye" of Stela 1 first celebrates the "place of emergence" ceremony. The total in years is 69 x 365 = 25,185 days. Adding the 15 days because 12 Reed precedes 9 House by 10 days and 5 Reed follows 13 Rabbit by 5 days, we have 25,200 days, or 70 Tuns. The Mayan interval 3.10.0.0 is from 9. 8. 1. 9.13 to 9.11.11. 9.13. Year 684, 7 Rabbit Ruler "7 ReptileEye" of Stela 1 is cremated. Year 686, 9 Flint Ruler "7 Rain" of Stela 2 conducts war event? Year 722, 6 Flint, Day 2 Death (48 days after the yearbearer) I found this only after establishing the chronology within which this discussion occurs. Stela 2 has what looks like a standard Venus sign descending, with an adjacent day 2 Death which I took as the date. On this day, Mercury is in conjunction with the sun, having descended as evening star. Venus is just in process of becoming invisible, also as evening star, and for some time had been descending parallel to Mercury. That day is 24 March in 722, Mayan 9.14.10.8.6. On 23 March, Venus was 16.60 degrees from the Sun. On 2 April, Venus was 1.35 degress from the Sun, so it became invisible somewhere near 27 or 28 March. I count this as strong confirmation. Year 729, 13 Reed Ruler "7 Rain" of Stela 2 is cremated. ------------------------------ End of ANE Digest V2001 #329 **************************** Back issues are available on the Oriental Institute World-Wide Web (WWW) site at: http://oi.uchicago.edu/OI/ANE/OI_ANE.html