Skyscript: The Moon and Ancient Calendars, by Robin Heathl`"y3
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Since the early part of the twentieth century, information about the prehistoric sites of Britain has been amassing to the point where it is now possible to discover, not only the underlying system by which sites were placed, but also the measures used in the process. Robin Heath is a leading researcher in this field and his recently released title The Measure of Albion (co-authored by John Michell), demonstrates that the Earth's dimensions were accurately known prior to 3000 BC and that a system of surveyance and measure based on simple numerical and geometrical rules existed. This article, extracted from his ground-breaking work, reveals how the cycles between the Sun, Moon and Earth, acted as the basis for imperial units of measurement. 


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The relationship the orbital period of the earth holds to the lunation cycle - the moon's phases, is a complex one, and the sun and the moon are not easily married. There are intrinsic difficulties and compromises which exist in the design of any calendar, and only one calendar-structure, our Gregorian 'Roman' calendar, is ever discussed in our schools. This is regrettable, because the different calendars used by various cultures throughout history provide a fascinating and instructive view of human cultural and social development. 

Anthropologists have suggested that human culture began with the structuring of time and ritual, this was followed, much later, by regulation of weights and measures. The calendar preceded the measures, and we should not be surprised to find that the word mensuration is still in force to describe accurate measurement of quantity - length, areas, volume. From these are derived the weights. The root of this word, mens, relates directly to the moon, and we might inquire why this should be so. The modern sophisticated lifestyle, enjoyed within what has been described as a 'solar culture', latterly neglects the moon and is largely abstracted from any actual observations of the sky. As a consequence our technological culture finds difficulty in appreciating the role of an ancient skywatcher, even more so when it comes to reckon how their observations might have been recorded and subsequently analysed. But we must answer a basic question: how is measurement linked with the moon? 

It must be an obvious first fact that initially, for any calendar type, a set of observations had to be wrestled from the skies. These observations, we shall discover, had to be stretched over many years. In ancient times, even in preliterate times, they must have been recorded in some form or another. Whenever this important practical detail has been addressed by researchers, it has often been assumed that the ability to write down numerical values was possible by whichever culture was undertaking the observations. Linguistic or numerical listing was employed and the storage media were clay tablets, papyrus codices, leather scrolls or hieroglyphics. 

Whilst this may have been true for the 'classical' cultures of antiquity - Egyptian, Sumerian, Hindu-Greek and Graeco-Roman - it is supposed not to have been true for the megalithic culture of northwestern Europe, thought to be pre-literate. Here, some archaeologists suppose that, in the absence of any other hardware, the mythical astronomer-priest remembered it all, a view expressed by the late Professor Richard Atkinson, who said of megalithic astronomers, 


"...supposing that the Astronomical Ephemeris is not published, but is transmitted by word of mouth to its users in the form of epic verse which must be strictly memorised and reproduced." 


The result is a vague and largely unsubstantiated theory concerning oral tradition, involving the transmission of all those observations by word of mouth from some able-memoried yet chimaeric 'astronomer-priest'. Every full and new moon and every sunrise and sunset position is somehow remembered by an alleged process of memory and passed down through the generations - a process for which not one shred of hard evidence exists. 

Thus the evidence for advanced ancient astronomy in megalithic Europe - and there is a considerable amount of it - lies wholly at odds with the lack of any known storage medium other than the sites themselves. Unfortunately, in the European climate, then or today, we cannot expect artefacts such as tally sticks or knotted rope to have survived. To the orthodoxy, only two things are thought to have survived the passage of time - and ironically these are committed to memory by our present students through the somewhat disparaging nick-name given to that section of an archeology department which studies neolithic and bronze age culture - 'stones and bones'. 

The geometry and astronomy of ancient sites is not currently seen as a useful artefact in providing evidence about the culture which built them. This is hardly scientific and it is far from satisfactory to leave this situation unchallenged. In this article I suggest that mnemonics were used to aid the process of passing valuable astronomical information down through perhaps 100 generations of neolithic astronomers. These mnemonics are inherent within the geometry used to implement the actual designs of stone rings. The shapes store the astronomical information. 

We may begin with a tantalizing piece of evidence which suggests that the neolithic and Bronze Age astronomers could count in the sense that we would understand the term, and to quite high numbers. This evidence is hidden, somewhat obscurely yet characteristically within the difficult texts of professor Alexander Thom. During the surveys of many alignments to the key stations of the solar year, Thom found that the equinoctial markers were not aligned truly east-west, as one might have expected them to have been. Consistently, equinoctial markers and alignments were made to an declination well over half a degree to the north. Thom figured, and it is hard not to agreed with his reasoning here, that the builders of stone calendars were attempting the efficient task of making one set of markers record the dates for both summer and winter halves of the year. Now, the summer half is longer than the winter half, and to make one set of stones 'do' for a calendar throughout the year is an obvious labour-saving piece of practical engineering. Thom equated the misalignment from east-west to the difference between winter and summer halves of the year and concluded that the observers had divided the solar year into two in order to arrive at the correct declination. His conclusions remain unchallenged to this writer's knowledge. 

The site plans for megalithic sites indicate a sophisticated use of geometry involving the right triangle and accurate surveying. The practical skills involving the construction of Avebury and Stonehenge would (and do) tax even our eminent specialists today. It remains obvious that tallying the number of days in the year or month was eminently feasible, and several mesolithic fragments of bone seem to confirm this fact amongst early humans. Even amongst tribal communities today, wooden tally sticks and knotted ropes are used for the same purposes of recording days and lunations, this further substantiating a belief that counting by notches or knots would reasonably have been de rigeur in neolithic times. 

To attempt to shed light on this largely misunderstood area of our past it is necessary for researchers to place themselves within the mindset of ancient astronomers by repeating the measurements and experiencing the more practical ways to record astronomical events. The writer has spent the past ten years emulating as far as is realistically possible the horizon observations of neolithic people. This has been undertaken at a variety of sites in Britain and France, and within the present climatic conditions of much greater cloud cover than occured five millenia ago. Memorising solar and lunar positions was seen as an unnecessary imposition from the start - and less arduous methods quickly become obvious when faced with such a herculean task. 

Sunrises and sunsets swing annually along an arc of the horizon whose angle is determined, given flat terrain, wholly by the latitude of the observations. Because this angle changes quite rapidly over the latitude limits of the megalithic culture, sites confirm the astronomic intention of their builders because of their unique angular relationship to the local horizon, which aligns the site to the local extreme solar azimuths. In southern Britain, the angle is about eighty degrees, whilst in northern Scotland it widens to ninety degrees. Many examples of neolithic sites which monitor solstice and equinox positions of solar rise or set, or the extreme lunar standstill positions, may be found catalogued within the works of Thom, Somerville, Lockyer and others. It is not proposed to detail these here, but as an example, the Station Stone rectangle at Stonehenge appears to have been built around the fact that, uniquely at the latitude of Stonehenge, the extreme sun and opposite extreme moon rises and sets occur at right angles to each other, indicating both that the monument was intelligently sited to take advantage of this fact, and that the builders were aware of the astronomic and geometric implications of the station stones, aligning them to indicate these major solsticial and lunsticial points against the horizon. If Stonehenge had been constructed at either Southampton or Oxford, this relationship would break down and the Station Stone rectangle would become a parallellogram, impossible to then place around the perimeter of the Aubrey circle. 


The ObservationstR0
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In marking off days and lunations on lengths of dowel, the eleven day disparity between the solar year and the lunar year is found directly. In performing this simple task it is seen how important this disparity must have been to ancient man. It is the vital data from which the calendrical relationships between sun and moon cycles may be understood - and therefore the most important piece of numerical data after the number of days in a lunar month and the length of the solar year. 

The lunar year, that is twelve lunations, takes 354 days to complete, whilst the solar year over-runs by about a further 11 days to give 365 days. These are approximate figures and do not include the fractional parts of days. They are the raw figures that an amateur observer, with keen eyes and persistence, could be expected to return using a solar horizon marker and noting the lunar phase cycle of about 29 or 30 days days. Counting days does not even require that the sun be visible, although its rising on an equinoctial marker must be observed to complete the count at 'year-end'. 

With a twentieth century mathematical education, one counts or tallies 365 days from an initial tally and discerns that the new moon occurs between every twenty-nine and thirty days. Even without the benefit of modern mathematics, tally rods show clearly and unequivocally a mismatch of about a third of a lunation between the end of 12 lunations (the lunar year) and the end of the solar year. If Christmas Day enjoys a full Moon, then in three year's time, there will be another full Moon at Christmas. There are about twelve and a third lunations in the tropical (seasonal) year. 

In a culture which we assume not to have understood fractions, the only way to understand synchronous events between two different periodicies is to await a 'return' - a repeat cycle when the fractional component disappears within a whole number multiple of itself. As a very basic example, to serve an apple pie to three people involves recognising that three thirds equals a whole. Get the angle wrong and someone gets a small piece! For the cycles of the sun and the moon, the phase of the moon at the end of each solar year 'fixes' the angles in a three-solar-year pie, so that, if we wish to fit 36 lunations in three lunar years (3 x 12) - then all is equal and there are no fights. But if we wished to fit 36 lunations into three solar years, the third slice of the 'lunation' pie is larger, containing an additional lunation (plus a bit more) - and the pieces in time order are 12, 12, 13 lunations, totalling 37 in three years. No mathematics beyond the tally marks and no fractions are needed - after three years, the phase of the moon is almost the same as it was at the first observation - there will have been observed 37 lunations plus a small addition. 

This observation is the most basic repeat cycle calendar that is possible. As such it is the first soli-lunar calendar possible, and the traditional Muslim calendar is based on the above observations. Every month, the first crescent of the new moon is observed, defining the beginning of the new month, whilst each year Ramadan commences 11 days earlier. To synchronize solar to lunar cycles, after 36 lunations (1063 days), an extra or intercalary month (lunation) brings the tally to 1092.63 days, whereas three solar tropical years take 1095.72 days to complete. The differential error in three years is 3.09484 days, which is 0.1048 lunations, and to account for this, a final extra lunar month is added every 30 years. 


Cultural Implications#
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The threefold nature of the lunar cycle is already familiar to us. Culturally, the folklore of the three stages of womanhood - maiden, mother and crone (wise-woman) is now reinforced astronomically, and it is the final year which invokes the thirteenth month, the number of the wise-woman or crone. The trefoil motif of much Celtic art, such as the Manx symbol, is suggested here. In constrast, the solar year presents a four-fold structure annually to any observer, through the two solstices and two equinoxes, and today we still resolutely identify four seasons. Solar emblems, icons and talismans from ancient cultures are almost invariably four or eight-fold structures and we may cite the swastika and the wheel of Shiva as popular examples in modern use. The pagan calendar 'quarter day' festivals of Imbolc, Beltane, Lugnasagh and Samhain are further confirmation that solar calendars invoke division of the year into four or eight, however much neo-pagans convince themselves that the quarter days are 'lunar' and therefore related to the Goddess. 


Calendar Structures[Yf
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The assumption that ancient neolithic astronomers were familiar with this three year synchronous cycle is greatly reinforced beyond comparing it with Bronze Age art and Celtic designs, when one investigates other (closer) synchronicities between elapsed years and lunations. At some time in the distant past each of the examples below appears to have been used to fabricate a useable calendar. 


The Five year 'Coligny' Calendar 
After five years, there are 61.84 lunations, an undershoot of just 0.16 lunations (4.7 days) from 62 moons. Despite carrying the largest error in the group, the famed Coligny calendar, a Roman-Celtic artefact from the fifth century BCE, is based on five solar years and is of 62 lunations in length. 


The Eight year 'Mithraic' Calendar 
After eight solar years, another and very close synchronicity delivers 99 lunations (98.945 lunations, an undershoot of 0.055 lunations or 1.59 days). Because of the numerical structure of the Great Henge at Avebury (99 stones) and the two inner circles (27 and 29 stones), I have suggested elsewhere that Avebury was built in order to monitor this 8 year soli-lunar cycle. It is interesting to note that Venus is also closely synchronized to this 8 year period, completing five synodic periods of 584 days. The link between Cretan practices and their mythology is mentioned by Frazer in The Golden Bough, and suggests that this soli-lunar calendar was in general use before 1500 BCE. 

8 solar years  = 2921.937592 days 
99 lunations  = 2923.52841 days 
5 Venus synodic cycles 
(584 days) = 2920 days 

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The Nineteen year 'Metonic' Calendar 
The most accurate synchronous cycle of the sun and moon known to the ancient world (although not presently identified with the neolithic astronomers of Europe) now emerges automatically from the three and eight year cycles identified here. The cycle attributed to Meton and named after this fourth century B.C.E. Greek mathematician-astronomer takes nineteen solar years and synchronises with 235 lunations, to within just two hours. The astonishing accuracy may be better understood when we consider the errors of the three year cycle (+3.09 days) with those of the eight year cycle (-1.59 days). Nineteen is twice eight plus three, and twice -1.59 plus 3.09 gives a combined error of better than 0.01 day (about two hours). It's one hell of a coincidence. 

At Stonehenge we find nineteen slender dressed bluestones within the sarsen circle of (originally) thirty upright stones. Many stone circles contain 19 stones in their perimeters, particularly in the south-west of England. These examples indicate that the builders may have been familiar with, and may even have originated knowledge of, the Metonic cycle. It is hard to believe that Meton discovered the cycle when the Jewish calendar based on its numerical sequences pre-dates the 4th century BC. 
These calendars, and therefore the relationship between solar and lunar cycles, are likely to have naturally evolved from initial observations of the three-year soli-lunar cycle, if only because here the solar-lunar synchronicity is first noticed. So far, I have neither produced evidence nor any cultural artefact which might suggest that the three-year cycle was a calendar structure understood by neolithic culture, an omission which must now be rectified. 

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Measuring Astronomical Periodicities with Length98
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We first demonstrate that there is a presumption amounting to a certainty that a definite unit was used in setting out these rings. It is proposed to call this the Megalithic yard. it will appear that the Megalithic yard is 2.72 ft. 


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Professor Alexander Thom published the survey plans of over 300 megalithic circles and worked with Piggott and Atkinson to provide the most accurate survey plans ever undertaken of both Avebury and Stonehenge. His discovery of the Megalithic yard met with derision in many quarters and it is not proposed to pick through the spent conflicts of the past here; Thom's suggested length for the Megalithic yard was accurately delivered from his data and subsequent statistical analysis: 2.72 feet plus or minus 0.003 feet. 

For anyone who wishes to begin to understand the relationship between the sun and the moon as seen from earth, the single most important numerical data is the 'over-plus' of the solar year over the lunar year. It is 10.875 days, interestingly ten and seven-eighths days. In three years this accrues to 32.625 days, thirty-two and five eighths days. For a culture without the tool-box of modern mathematics, this would be observed as a three-year cycle of synchronicity - 37 lunations plus a three day overshoot of the moon's position. Thirty-six lunations take 1063.1 days to complete, leaving 32.625 days to the end of the third solar year. Using modern decimals, in three years there are 37.10480 lunations and to obtain such a string of decimal points requires repeated observations over many three year periods. 

Another way to arrive at the same figure is to note that the 36 lunations (three lunar years of 12 lunations each) fall short of three solar years, and 1.104812 additional lunations must then elapse before the completion of the third solar year. Now, 1.104812 lunations is 32.625 days, a figure which in inches is also 2.7188 feet, and placed well within Thom's tolerance figure for the Megalithic yard. Therefore, if one inch is assumed to equal one day, the Megalithic yard corresponds exactly to the three year mismatch between sun and moon cycles - the 'error' in days. To be so exact implies a level of astronomical observation and mathematical procedure far beyond the currently held beliefs concerning this culture. This begs a question - do we now enlarge our perception about megalithic culture or attribute the above numerical relationship as a strange coincidence? 

Perhaps additional information will assist the reader in answering this question. In a single 'average' year there are 12.3682659 lunations. At the risk of repetition, the reader will appreciate that to obtain such an accurate figure requires that many year's observations be recorded, summed and averaged, as the following table demonstrates. 

In 3 years there are 37 lunations:  37/3 = 12.333 
In 5 years there are 62 lunations: 62/5 = 12.400 
In 8 years there are 99 lunations:  99/8 = 12.375 
In 19 years, there are 235 lunations: 235/19 = 12.36842 


The annual lunation figure approaches (but does not equal) the actual value only after 19 years's worth of observations have been tallied. If we now assume that the Megalithic yard represents one lunation period, then 0.3682659 x 32.625 inches yields 12.01 inches, or almost exactly an Imperial foot (error 0.12%). In other words, if one is using the Megalithic yard as a length (of time) which represents the lunation period then the annual discrepancy between solar and lunar cycles becomes a foot. In three years, this discrepancy becomes, of course, the Imperial Yard. 

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ConclusionseNq
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It must be seen as very curious that, in the same countries where neolithic people were constructing their stone monuments using the Megalithic yard, and were observing solar and lunar cycles assiduously, the units of length which arose from their astronomy uses those same units which, until very recently indeed, remained the preferred units of measurement of these same countries. Indeed, it is only because the writer is well grounded in the use of Imperial units that the above correlations were noticed; the metric system of units completely obfuscates the connections here shown. Fortunately, it is still possible to visit a stationers and purchase a foot ruler subdivided into inches, whilst a builder's merchants will happily supply a yard-rule, marked up in feet and inches. 

So curious is this accurate connection between units of length and the astronomy of the sun and moon that I suggest, from the evidence presented here, that the origin of these units dates from at least four millenia ago in neolithic Europe. The earliest accurate observational astronomy presently known to us was based on the inch and the foot, whilst the Megalithic yard itself 'stored' the astronomical constants needed to marry the sun and moon into a useable calendar.