Cliff, Victor, Karl sirs:
This is how I believe the Mayans would have viewed the results, so the precise accuracy of these >numbers is not particularly important at the end of the day, because of judiciously chosen rounding >effects within an integer based calendar. Like I said in a previous post, I am not so concerned with >precisely correcting the Gregorian calendar as I am in understanding simple calendric arithmetic >techniques used by the ancients, because that is the focus that Mesoamericans would have >adopted, without the benefit of a vigesimal fraction notation system for representing the >partitioning of the interval between zero and unity.I can imagine your concern for checking the results of Mayan culture and co-ordinate with present day research. You are right when you say, it would not matter - which lead to NEAR correct results and correctable (in long term useage). It is unfortunate that Mayan calendar and Harappan calendar that I believe to be contemporaries HAVE NEVER been linked, in the absense of *any specific literature - except the Mathematics of Vedic Ancients*, I have limited myself to the arithmatic of Harappan calendar - lunation of 29.5 days; and opted for the simplest approach of correcting the Gregorian Calendar with *minimal changes to be the World calendar for All Ages*. Since I have only selected studies, during my investigations, I hold my views on their arithmatics rather than historic interprettation 'unless they show better results'. I have placed my results at: http://www.brijvij.com/ ;http://www.the-light.com/cal/ and
http://homepage.ntlworld.com/calendar.creations/genesis.html My upgradings are placed at: http://www.brijvij.com/VGCalendr-fmt.docMy research, therefore, is pointing to a NEWER direction that can lead to A World Calendar for All Ages 'irrespective of cast, creed or culture'. Today is World Metric Day - 10th day of the Tenth month of Year 2006 - United States is celebrating this week as the Metric Week, some of whose seeds I planted in 1975 ( back in India). I join millions of YOUNG children desirous of learning the SI-Metric System of Units. I am aware, task ahead of me is great and I am positive my purpose of research is 'SI-ncere'; and after all EVERY WORK is initiated by a LONE RANGER. My early communications (1971.....) with BIPM & ISO headquarters only resulted in slow start, now taking some headway.
Brij Bhushan Vij(Sunday, Kali 5107-W26-00)/265+D-283 G.(WrldMetricDay, Tuesday, 2006 October 10H13:47(decimal) ET
Aa Nau Bhadra Kritvo Yantu Vishwatah -Rg Veda Jan:31; Feb:29; Mar:31; Apr:30; May:31; Jun:30 Jul:30; Aug:31; Sep:30; Oct:31; Nov:30; Dec:30 (365th day of Year is World Day) ******As per Kali V-GRhymeCalendaar***** "Koi bhi cheshtha vayarth nahin hoti, purshaarth karne mein hai" Contact # 001(201)675-8548
From: "vgray (gotsky)" <[EMAIL PROTECTED]>Reply-To: East Carolina University Calendar discussion List <[EMAIL PROTECTED]>To: [EMAIL PROTECTED] Subject: Re: AMTYear Re: Graph of Tzolkin Zenith Latitude Date: Sun, 8 Oct 2006 11:14:09 -0700 Dear Brij, Victor and othersI believe the missing leap day within the Gregorian calendar occurs in about 3,323y, although 3,320y is close enough for my purposes. The reason why I use a 3,328y approximation is that this is an integral multiple of 128y (i.e. 128*26=3328), and adopting this value does not introduce any significant error over the course of a 5,125y Mayan great cycle (since only integer days are representable as a calendar date anyway). I posit Mayans appreciated a 128y approximation for the missing leap day within a calendar that uses a 365.25d year, and hence understood that 132y is approximately 32 leap days (not 32*4y) and therefore 132/4 = 33y represents 8 leap days. Based on these arithmetical results I use 128*26= 3328y to represent the missing leap day within the Gregorian calendar, because the introduced error is acceptable within an integer based calendar, while the Mayans would have calculated that 128*40=5120y yielding approximately 40 missing leap days over a Mayan great cycle. Therefore a great cycle of ~5125y yields approximately 5120/4 - 40 + ~1 = ~1241 leap days. Or if you like 1241 = 146 mod(365). Using 128y is convenient and accurate enough for the purposes of understanding how Mesoamericans would have perceived these issues. Since the great cycle exhibits a 280d haab period residual (i.e. 1,872,000 = 280 mod(365)), then the above arithmetic immediately yields that 280 -146 = 134d, which is the tropical period residual of the great cycle. Period residual arithmetic is an adequate replacement for vigesimal fractions.The above arithmetic results also forms the foundations for the 68y interval I mentioned in prior posts, since 128/4 = 32y would be the subject of a 1/4d missing leap day, and hence 32*2y would be corrected to a 32*2 + 2 = 66y interval to accommodate this as a lower bound interval representing 16 leap days. Hence an approximate seasonal round within the TUN in 68y would be 16.5 haab leap days rounded to 17d, as an initial base equivalence between 360 tun leap days and 17 haab leap days. This 68y interval represents the Mesoamerican equivalent of defining the 365.25d calendar year resultant, as a subset of the 128y interval that represents a missing leap day, which is also conveniently an approximate TUN seasonal round interval in just over 68y. In other words it represents the longest interval that realistically could represent a purely Julian year calibration - rounded in an integer based calendar - without being impacted by the impending missing leap day at the end of 128y, and conveniently is also a universal calendric reference period as an approximate TUN round (also rounded down to 68y). Mesoamerican calendric arithmetic was all about using well chosen points for applying rounding results, that befits an integer based calendar.In like fashion the 29 calendar round interval of 1507y is upper bounded by 128*12=1536y, to gauge 12 missing leap days or 1536/4 - 12 = 372 leap days, and hence 1536 - (372-365)*4 = 1508y to gauge 365 actual leap days. Rounding this 1508y down to a conventional 29 calendar rounds or 1507y is then adopted as an approximation that befits an integer based calendar. In other words the small fractional leap day below 365d is simply rounded upwards to 365 leap days. Adopting a 1507y over the calculated 1508y for the haab seasonal round makes sense for the ease of calendric arithmetic that this offers, and the rounding error this introduces is not particularly significant for the purposes at hand.Such "inaccurate approaches" of course is what prompted you to ask why I use 3328y instead of 3320y to represent the Gregorian calendar's missing leap day interval. The bottom line is that judicious rounding in an integer based calendar simplifies the arithmetic, when one is limited in the arithmetic methodologies to be applied to the solving of calendric problems. I do not have the luxury of using decimal fractions as an arithmetical tool, but must be limited to using period remainders in a multiplicity of calendric base periods to represent fractions. I hope this answers your question of why I choose the particular values that I do.This is how I believe the Mayans would have viewed the results, so the precise accuracy of these numbers is not particularly important at the end of the day, because of judiciously chosen rounding effects within an integer based calendar. Like I said in a previous post, I am not so concerned with precisely correcting the Gregorian calendar as I am in understanding simple calendric arithmetic techniques used by the ancients, because that is the focus that Mesoamericans would have adopted, without the benefit of a vigesimal fraction notation system for representing the partitioning of the interval between zero and unity.The response to your question is a little long winded, but I believe the tone of my approach is perhaps not fully appreciated, and needs to be highlighted so that my chose of numbers is better understood. So 3,328y for a Gregorian calendar missing leap day interval, is then about 1.5d missing leap days over the course of the Mayan great cycle. Which I round down to 1d as a minimal estimate when using sunset to mark the ending of a day, or rounded upwards to 2d when using sunset as a beginning day point of reference.Cheers Cliff----- Original Message ----- From: "Brij Bhushan Vij" <[EMAIL PROTECTED]>To: <[EMAIL PROTECTED]> Sent: Saturday, October 07, 2006 4:53 PM Subject: AMTYear Re: Graph of Tzolkin Zenith LatitudeCliff & CC:.....What is relevant is the true tropical calendar, and by that I mean the actual tropical station >events.....During my discussions with Calendr-L, I observed that *Length of Tropical Year* varies and is dependent on the date of START of the calendar: such as Winter Solstice, Summer Solstice, Spring Equinox or Autumn Equinox. An average of 'four cardinal points' - Average Mean Tropical Year is often used by astronomers taken at: Y2000=365.242189669781 - 6.161870 x106) days.Is the figure right, since I worked this to be slightly less than 3320-years? Modern length of the year is (365.242189669781 - 6.161870 x106) days ─365d 5h 48m 45s.187469. With the Leap Day (February 29) Rule, Gregorian calendar still suffers a continued discrepancy of ONE day in 3320 years. This can be improved to get Mean Year value: (365+31/128) i.e. 365.2421875 days resorting to *modify Leap Day Rule from divide 4/skip 100th /account 400th years to divide four (4)/skip 128th years*. The Day, however, remain of 24-hour duration with the HOUR of 60 minutes & 60 seconds, additionally calibrated to 100 decimal minutes & each decimal minute into 100 decimal seconds. Thus, the second is 0.36% of SI-second and the day equivalence of 1440 minutes = 2400 decimal minutes. Nautical Kilometre, replaces the *concept of Nautical Mile* as: '1/100th of arc-Angle Pi/180 (1-degree)'. Please see:better alternative, other than a corrected Gregorian calendar with an additional leap year rule for handling a missing leap day every 3,328 years.You might not like the Gregorian calendar, but there is currently nohttp://www.brijvij.com/VGCalendr-fmt.docIn my opinion, any of the cardinal points can form the basis for START of the Year, practically in continuation with WINTER SOLSTICE, *but using the duartion of AMTYear which I reported to similar to 365.2421875 days.Brij Bhushan Vij(Thursday, Kali 5107-W25-04)/265+D-280 G.(Saturday, 2006 October 07H19:89(decimal) ETAa Nau Bhadra Kritvo Yantu Vishwatah -Rg Veda Jan:31; Feb:29; Mar:31; Apr:30; May:31; Jun:30 Jul:30; Aug:31; Sep:30; Oct:31; Nov:30; Dec:30 (365th day of Year is World Day) ******As per Kali V-GRhymeCalendaar***** "Koi bhi cheshtha vayarth nahin hoti, purshaarth karne mein hai" Contact # 001(201)675-8548From: "vgray (gotsky)" <[EMAIL PROTECTED]>Reply-To: East Carolina University Calendar discussion List <[EMAIL PROTECTED]>To: [EMAIL PROTECTED] Subject: Re: Graph of Tzolkin Zenith Latitude Date: Fri, 6 Oct 2006 19:40:07 -0700 Dear Victor and othersThe Gregorian and Julian calendars are irrelevant. What is relevant is the true tropical calendar, and by that I mean the actual tropical station events. The Gregorian dates are merely convenient date monikers referring to an idealized true tropical calendar, for lack of an alternative means of expressing solar dates within the TRUE tropical calendar. All the references are ACTUAL solar stations and some means of naming them is needed, and for convenience the Gregorian calendar (or a corrected version of it) I find the most appropriate. I never use the Julian calendar when naming tropical stations (a ludicrous practice used in some circles), so Aug 13th is a date within the corrected Gregorian calendar (i.e. an additional leap day dropped every 3200y), and all this means is a tropical station that is about 130d prior to winter solstice. If you like the date isn't really a Gregorian date, but merely a convenient date moniker, and let's leave it at that.Creating a new system of expressing tropical dates would only cause more confusion, and then you have to teach people how to use this new unfamiliar calendar. It is simply better to use the Gregorian calendar, and deal with its idiosyncrasies, with small trivial modifications applied to achieve a more accurate tropical calendar. It is possible to use a Mesoamerican based tropical calendar naming convention, but again it would be a new creation and suffer the disadvantages of being something totally unfamiliar. I could specify those tropical stations using Long Count nomenclature combined with leap day counts from various orbital calibration spans, but that would be less intelligible than using Gregorian tropical moniker dates.The Aug 13th vertical sun transit station stated as such within the Gregorian calendar is a practice that has been used for over 30 years by Mayanists, and published in various scholarly journals, and I do not see a readily available alternative to this practice.Rather than say "the date of summer solstice" it is more expressive to say Jun 22nd (CG) and explain what you mean by that, because often calendric arithmetic must be performed on dates. Every has a basic feeling about what Jun 22nd represents within the Gregorian calendar.The Long Count begins on Aug 13th, -3113 CE within the proleptic Gregorian calendar basis the '85-GMT, and is stated as such for about 100 years now (i.e. beginning with Goodman 1905), or expressed in a corrected Gregorian (CG) calendar of my own making it starts Aug 10th, -3113 CE (CG) basis the '83-GMT correlate (i.e. JDN 584283). I do not see how else you would express such calendric artifacts. The Julian calendar is hopeless in this regard when comparing dates. At least with Gregorian dates you can compare the tropical stations associated with groups of dates, and see the approximate tropical calendric structures portrayed by those date groupings.It is the use of Julian calendar dates as a practice that should be dropped when dealing with Mesoamerican dates. Now there is confusion if ever there was any, because it hides tropical calendric structures that are inherent in relative date relationships covering many centuries. I save a lot of calendric arithmetic effort by using a true tropical calendar, which the Julian calendar is not, and a corrected Gregorian calendar at least approximates. It is the Mesoamerican calendar I am trying to study and understand, not improve the Roman Christian calendar which are at best merely an annoyance.You might not like the Gregorian calendar, but there is currently no better alternative, other than a corrected Gregorian calendar with an additional leap year rule for handling a missing leap day every 3,328 years.How else would you express the over 180 vertical sun tropical stations (i.e. dates) within the tropics? Mark my words thousands of calculations in the Mayan calendar over 20 years, have proved to me that these are better expressed within the Gregorian calendar rather than the Julian calendar, when dealing with Long Count dates potentially spanning thousands of years. The only alternative I use is orbital calibration spans, but explaining the workings of these is far more complex than using mere Gregorian dates.So, Aug 13th (CG) is about 130d prior to winter solstice - broadly speaking, and this remains fairly constant over several thousand years. Of course there is jitter. But the important question is what calendric structures did Mesoamericans create based on their observations within a certain period of history.Venus sometimes suffers an 11d jitter from one cycle to the next, but this did not stop the Mayans from devising an AVERAGE state definition for Venus' orbital behavior. First they noticed the jitter is greatly reduced when dealing with 5 Venus cycles, and then an average state was defined relative to the 584d period based on this reduced jitter every 2,920d. Over 65 Venus cycles there are -5 Venus leap days every 104y relative to the average state progression of Venus' orbital rounds. That short term 11d jitter did not prevent a proper calendric analysis and implementation for the long term, and derive a realistic meaning for the Venus leap days over two Venus Rounds. Likewise tropical station jitter would be averaged and dealt with in some fashion as well.Cheers Cliff----- Original Message ----- From: "Engel,Victor" <[EMAIL PROTECTED]>To: <[EMAIL PROTECTED]> Sent: Friday, October 06, 2006 1:20 PM Subject: Re: Graph of Tzolkin Zenith Latitude Dear Cliff,Izapa is a large Early Formative Period site located in the far southeastern corner of the State of Chiapas, and once commanded a rich agricultural region called Soconusco which extended along the Pacific coastal plain from the area around present-day Tonalá, Mexico in the north to about San José, Guatemala in the south. The nearest modern city is Tapachula, some 6 miles to the west, and the geographic coordinates of the site are 14.8 º N. latitude and 92.2 º W longitude. The cone of Volcan Tajumulco (the highest mountain in Central America) marks the sunrise position of the Jun 22nd summer solstice on the north eastern horizon (as seen from the main pyramid).At one time I had all 33 Guatemalan volcanos memorized. It was required information at school. I was thinking Tacana was closer, but I guess it's Tajumulco. I just realized that Tajumulco is about midway between Zaculeuand Izapa. I doubt if there's any relevance, though, since the Cuchumatenesmountains block the view of Tajumulco from Zaculeu.It seems clear that not only was a specific 14.8 deg N. latitude chosen to yield the {Aug 13th, Apr 30th} vertical sun solar stations, but also an orientation that allowed the summer solstice rising sun to be seen perched above the mountain peak from the main pyramidal structure. Izapa's monuments are aligned to the Aug 13th rising sun, and 3000 years ago summer solstice occurred closer to Jun 22nd.I'm not sure what you mean by this and what relevance that statement has.The date of the June solstice has jitter to it in the Gregorian calendar. I think the date 3000 years ago would be in the range of the 23rd to the 25th.Now it's closer to the 20th to the 22nd, but so what? That just shows the Gregorian calendar does not track the June solstice.Izapa dates to as early as 1500 BCE. Interestingly, several dozen of the oldest and most important Mesoamerican sites are also solistially oriented to the highest mountain in view, including some Mayan sites like Tikal and Uaxactun. Izapa is the only major ANCIENT site (i.e. pre Mayan) at the correct latitude, where the 260d interval between the zenithal transits apply, and it is the orientation of the structures at Izapa which mark an Aug 13th solar station (rising or setting sun azimuth). I suspect the Olmec/Mayans centered the two intervals about the solstices conventionally. The haab is partitioned conventionally as {WS, 91, SE, 92, SS, 91, FE, 91, WS}, where WS/SE/SS/FE/ are the seasonal cardinals viewed as Dec 21st, Mar 22nd, Jun 22nd and Sep 21st. The extra day is placed between the spring equinox and summer solstice segment as 92 days.Whose convention is this?The Aug 13th and Apr 30th vertical sun transits are positioned 130d on either side of a Dec 21st winter solstice - CENTERED about the solstice. The complementary 105d interval between the zenithal transits appears 53d prior to Jun 22nd and 52 days after, where the slightly longer 53d interval also appears within the spring equinox to summer solstice segment of the haab. This is centered about summer solstice by convention.Again, whose convention?This 105d interval may also be viewed as two 52d segments on either side of summer solstice, separated by one day (the day of summer solstice). The segmentation model here is {WS, 130, Apr30, 53, SS, 52, Aug13, 130, WS}. The 52d interval between summer solstice and Aug 13th appears as an important interval in Mayan Long Count date structures. This centering of the intervals about the solstices is not greatly in error, and it is clear the "Olmecs" oriented their monuments to an Aug 13th solar station - 130d prior to winter solsticeClearly, they didn't use August 13th, since they didn't use the Juliancalendar, and the Gregorian calendar did not even exist. I suggest making aneffort to not use references to this calendar, since it is a potentialsource or confusion or error. I take it what you're really referring to hereis the date of the summer zenith. Victor
