Midnight Science (2014-2015), Volume 18, Paper 1
Author: Derek Cunningham
Paper Submitted: 24th March 2016, Published: 29th March 2016
In a study of three separate art types (stencilled handprints, linear geometrics and stones inscribed with “tally” marks) it is confirmed that the native aboriginal people of Australia described in a geometrical manner the data required to mathematically predict future eclipses. The method to encode the mathematical values involves the conversion of astronomical values to an angular array. The method is identical to the technique used in the upper Paleolithic era geometrics found in cave paintings at Lascaux, in France, and other ancient archaeological sites. In one sample of Australian artwork the encodement of astronomical data even appears to employ a three-dimensional geometrical trick to create a very basic optical illusion. Taken together the data suggests that it is now possible, for the first time, to scientifically compare dissimilar art types, and to use ancient art to investigate ancient migration paths.
After decades of argument1 it is generally accepted that numerous archaeological sites align with astronomical events, but it is also accepted by many that the evidence used by scientists to support the proposed astronomical links is still very weak. To understand why it is necessary to look at the logic employed in the earliest astronomical studies.
Ignoring simple and very general ideas, such as theories that simply stated that the stone circles were built as circles to reflect the shape of Earth, see Stonehenge, A Temple Restor’d to the British Druids, by William Stukeley2, the first genuine proto-archaeoastronomical studies were basic attempts to align archaic structures to specific celestial events. In turn any celestial markers observed in creating an alignment were linked, whenever possible, to local ancient festivals and lunar/solar calendars3,4.
Over time, these studies led to a concept that is best called “Linearisation”. First, Alfred Watkins proposed, very controversially, that ancient cultures created multiple short-distance linear alignments between neighbouring sites5. This, in turn, was followed by the detailed computational work of G. S. Hawkin6-8, and later Alexander Thom9-11, who, working separately, argued that linear sight lines were used to align Stone Circles, and other ancient structures, to celestial events. This theory has gained greater acceptance and one of their more far reaching conclusions was these structures were aligned to the appearance of specific stars to mark the change of seasons, an argument that has since influenced strongly the analysis of the Great pyramids of Egypt. Alexander Thom also argued that perhaps one of the key reasons for the complex nature of structures such as Stonehenge was the need to predict eclipses.
However, from a purely scientific standpoint, the reason why the evidence in favour of an archaeoastronomical link is considered to be quite weak is that despite many great strides there still exists too many gaps in current theories.
For example, many ancient structures are just too complicated to support the idea that they were built only to measure one single event, namely a simple solstice event, or even to track various astronomical, lunar and solar events. In fact, at this point in time too many alignments at Stonehenge produce no link to any recognised visible astronomical event; which gives rise to the very valid argument that a 95% failure rate in any other theoretical model would be considered clear evidence that the theory is flawed. However, because the solstice line is replicated at many ancient sites the inherent weaknesses in current astronomical theory is ignored.
Thus the hidden problem…if these structures were constructed only to view the solstices, it still leaves many wondering why these ancient structures are so complex, and why so much effort was made by the builders to make features with no obvious astronomical meaning.
To attempt to solve the over complexity in Stone Age art it is necessary to develop new testable theories. Theories that can move firmly away from the guesswork that has become prevalent in archaeology, and that instead try to attempt to understand the actual “intent” of the artists who created these geometric time pieces12-17.
One way to scientifically measure intent is to study the geometrical angles produced by various ancient structures. If a new theory is put forward that ancient people in their studies of astronomical events became aware of mathematics, it can be then argued that the geometric symbols seen in early geometric artwork just might be a form of early writing, where the mathematical values used to calculate time and predict eclipses (their mathematical magnitudes) were simply encoded as an angular array.
By drawing astronomical values as geometric lines it is possible to encode astronomical values in a number of different ways. The easiest approach is to visually convert mathematical terms to a linear drawing. For example, the 27.32 day sidereal month (which astronomers use to measure time) is in then simply drawn as a straight line at 27.32 degrees, and the 18.6 year lunar cycle as a line at 18.6 degrees. In this hypothesis, only the numerical value is considered important18-20.
In early tests of this theory it has been found that larger art pieces drawn on walls the angular offset used could be both to the horizontal and to the vertical, and for larger structures the offsets are either to due East/West or due North/South. Ancient art pieces thus often appear much more complicated than they need be because they often show a repetitive 90-degree rotational symmetry18,19.
In an attempt to see if this new theory could reliably be used to determine the “intent” contained in Stone Age art this study now looks at three Australian art pieces to see if all three artforms, despite substantial difference in artistic style, align to the same angular array. The data obtained from Australia is then compared to the geometric images found in distant Lascaux Cave.
For this study the three Australian art pieces must never have shown any prior known link to astronomy, or at best shown only an arguable, very questionable astronomical link.
This study also concentrates specifically on Australian artwork because of the continents known long-term isolation from the rest of the world.
In this new theory eight astronomical values are routinely used to predict solar and lunar eclipses18. These values are divided into two groups of four. The first four relate to the measurement of time, and are (1) the circa 1° sidereal motion of Earth as it travels around the sun; (2) the 27.32 day (degree) sidereal month, which is drawn in ancient art18 as; (3) its half value at 13.66 days (degrees); and (4) a value of 11, which equals the difference in days between the solar and lunar years. This is drawn as a line at 11 degrees.
The second group of four values link to the three orbital planes of the Earth, the Sun and the Moon and the time when they create nodes. These values are (1) the 6.511 draconic month period between eclipse periods; (2) the 5.14° angle of the moon’s orbital plane relative to Earth’s ecliptic; and (3 & 4) the 9.3/18.6 year lunar cycle, which relates to both the precession of the lunar nodal pattern, and the time between lunar standstills. Again these values are all drawn as angular values. Together these time and nodal values produce the eight Standard Values.
Naturally, some regional variations to the 8 standard values are seen when looking at data found worldwide. For example, in some cultures a line aligned to 33 days/degrees is more often used than the 11 days/degrees value; a value that represents the difference between the solar and lunar years. Here the 33-day value represents the three-year reset period, which is the earliest point in time that astronomers can reset the lunar and solar calendars, because each year there is an 11 day difference between the lunar and solar calendars. Also in some regions, Australia being one, a line at circa 23.6 degrees is sometimes found. This may relate to the angle of the Earth’s axial tilt. Finally another prominent regional value is a line drawn at either 3 degrees, or plausibly 3.14 degrees. These three angular values are termed Class 1 alignments.
Next are values that appear geometrical. These are line drawn at 0, 15, 30, 36, and 45 degrees. These are termed Class 2 alignments.
Finally the last category covers angular values that are unique to the art piece being studied, or are values that are seldom seen in astronomical art. This includes astronomical values relating to the Metonic Cycle, and values that create a continuation of a series. These are termed Class 3 values. This category also includes all values not listed above. Therefore, theoretically, there exists a greater probability that a line will randomly align to the Class 3 category. In addition if the drawn lines are tally marks it can be predicted that the lines should orientate randomly and not orientate to any specific astronomical value, or values.
Analysis of a Linear Pattern Drawn on an Australian Cylcon
The first art piece studied is an Australian cylcon discovered by shearing contractor Peter Manoel, at High Delalan, in New South Wales, Australia. The discovery was made in 1973, and the Cylcon is now held in the extensive collection of Martin Schøyen. Prior research carried out on cylcon stones has left no agreed use for these very unusual stones, and given the great variation in shape and design, it is probable that they were used for multiple, different purposes21-25. The term cylcon first came into use, in 1942, when Lindsey Black published a book in which the phrase cylcons was used25. No study of the method to make the lines was undertaken here, and the sample is studied as is26.
To remove bias, the first step was to analyse the most heavily inscribed face of the stone. This produced a fixed orientation for analysing the remaining faces. After the orientation of the first face was fixed, Martin Schøyen then provided access to images of the rear and one side of the cylcon (sides 2 and 3). These were analysed at the same angle defined by the first face. The fourth side is not analysed as part of this study, and will be analysed later, to create a double blind test.
On the first face 100 lines orientate to only 18 different angular values (offsets are measured to both the horizontal and the vertical18). 80.00% of the lines present on the front face) align to Standard values, with 66 lines (66.00%) of all the lines studied aligning to just four angles. These four angular values are 1.0° (15 times) 5.1° (19 times), 9.3° (17 times), and 13.66° (15 times). The 9.3°, and 13.66° alignments are half-values relating to two different orbital periods of the moon.
The remaining 20 angular values on side 1 belong to Class 1, 2, and 3. Within this group 14 lines belong to Class 1, and thus can be considered to be simple modifications of Standard Values. Thus, at the orientation selected, 94.00% of the lines align to astronomical values that are routinely seen in linear art found worldwide18. Only two lines belong to the Class 2 category, and just four belong to the Class 3 category, the largest category.
A study of the angular offset to the horizontal reveals that 9 lines belong to the Standard list; 2 lines to Class 1 alignments; 1 to Class 2; and 2 to Class 3. The same preference to Standard values is therefore seen irrespective of the orientation chosen.
The high degree of repetition in the results to a relatively small range of angular values has previously been seen by the author in other ancient art forms, but because the first face is aligned specifically to produce an “optimum alignment” the statistical significance is difficult to determine. It is thus of more interest to observe the results from the second and third faces, because the images were only provided to the author by Martin Schøyen the owner and curator of the Schøyen Collection after the first side had been set to its control angle. As their orientations of these two faces cannot now be changed it can be once more argued that the remaining sides should now show random orientations to the first side if current interpretation are correct that the lines are tally marks. If on the other hands they are a form of archaic text, with the angle perhaps defining the consonant, and the angle also reflecting astronomical features, the same angular array should appear on the other two sides.
Upon analysis of the remaining two sides it is found that all three sides produce surprisingly similar results.
On side 2, a total of 49 lines out of 56 (87.50% of the total) align to the Standard List. But perhaps more important is the observation that within this group of 49 lines, 35 lines (62.5% of the total) once more aligned to just three angular (astronomical) values; these being at 5.1°, 9.3°, and 13.66°. The same angular values seen most often on Side 2 thus replicate the angles seen most often on “Side 1”. Indicating the presence of 90-degree rotational symmetry, 7 out of the 9 lines that align to the horizontal also appear in the Standard Value list. Thus the Australian art piece exhibits the same 90 degree rotational symmetry first seen in the author’s prior study of the Orkney Venus.
For side 3, three lines at 5.1°, 9.3°, and 13.66° again dominate and match 17 out of the 31 lines studied, which equals 54.84% of the total, and 27 out of 31, (or 87.10%) again align to the Standard list. Only 12.90% (4 lines) align to Class 1 values. No Class 2 geometric-type, or Class 3 (unexplained, or rare angular values) could be observed on this face.
From this study, which looks at 187 lines, the repetition to 3 or 4 specific angular values clearly suggests that the lines drawn on this cylcon cannot be simple tally marks.
Within this sample there is a very clear constant repetition to lines etched at 1°, 5.1°, 9.3°, and 13.66°. This preference occurs in both a study of the actual angles drawn by the lines and very intriguingly even when the lines close to the edge of the observed image are changing their “apparent angle” because of the curvature of the stone (Table 1).
The important point to note here is that the lines close to the side of the stone appear to change their angle because the degree of curvature of the stone varies along the entire length of the Cylcon. Thus if this is indeed a form of archaic text based on angular values it would have taken incredible skill to create this specific piece due to the ever changing angles viewed as the stone is rotated around 360 degrees. To test if this is correct a secondary study was thus undertaken to study the effect of rotation of the stone on just one side of the stone.
In the more detailed study of Side 1, 16 images were taken, with the angle of the image changed sequentially to observe the effect of curvature on the observed “visual” angle drawn by each line. Looking at only the lines found directly under the camera lens there were in total 146 lines that could be analyzed to determine their true angular values.
From this reanalysis, the results if anything become even more intriguing. Looking now at the actual angle drawn by the various etched lines it was determined that 138 lines (94.52%) align to the Standard List and 90 lines (65.06%) align to just 4 values. These again are the angles of lines viewed directly under the camera lens, and thus are the correct angular values for the observed lines. Only 5.48% of the total align to Class 2 and Class 3 values. Thus once more there was found to be no substantial difference in the data obtained, and irrespective of the method used to study the stone – using an analysis of the actual angles drawn, or studying the optically-distorted values with the angles affected by the curvature of the stone, the same overall result was obtained. The cylcon is thus an extremely complex piece of art, and the results clearly suggests that the creator of this complex image understood perspective and understood basic three-dimensional optical illusions.
Analysis of Australian Handprint Art
At this point, attention now turns to the handprint and geometric art found at the Carnarvon Petroglyph site in Australia. Despite the extreme differences in the styles of art on display here the surprising result is the exact same astronomical data can be observed27-32.
It has to be said at the beginning that detailed studies of Australian art are very limited33-37, and the age of the images found at Carnarvon are unknown, but they are generally believed to be younger than other very similar images found worldwide38-41. Overall the various petroglyphs found at Carnarvon comprise mainly of a mix of handprints, simple geometrics grid-type images, and stylistic drawings that are described as boomerangs The various images are found on a single frieze, and thus can be directly compared to the horizon.
The first study here looks at the handprints (Fig. 2), which is found to exhibit a number of focal points that can be created by the fingers present in the handprints. These focal points can then be sequentially linked together, as shown in Figure 2, to create a number of lines offset to the horizon.
For this study 23 handprints were analyzed (Table 2). Contained within these 23 handprints are 86 measurable alignments that could be created using the fingers (Table 3). The angular distribution created is restricted by the observation that the lines are required to create a focal point. These 86 lines in turn created 21 discrete focal points that are located near the centre of each handprint. Two handprints, W located towards the lower right side of the pattern, and handprint “I”, which is a rare handprint that also contains an image of the persons arm, appear anomalous and fail to create well-defined focal points. As with a prior study of the Lascaux cave geometrics18, all alignments in this study are fixed to the horizon, or the vertical, and thus the image exhibits 90° rotational symmetry.
Looking at the image obtained it can be seen that two of the three anomalous lines that are linked to Class 3 alignments originate from handprint “I”. Within this group of 23 handprints “I” is the only analysed print that has the image of the arm attached. Handprint “I” also exhibits three distinct focal points, and an anomalous finger alignment that aligns to the Class 3 value of 42 degrees. Of the 89 fingers studied only 7 finger-alignments belonging to Class 3 “undefined and lesser used values”, and 3 out of the 7 belong to the two anomalous handprints, with two of the Class 3 values belonging to the handprint marked “W,” which likewise shows both a high percentage of Class 3 alignments, and no defined focal point. It is thus very plausible that these two specific handprints were not part of the original drawing.
Removing handprints “I” and “W” from the analysis and analysing the remaining 34 lines, it is found that 88.24% of the lines now align to either Standard, or Class 1 alignments, 8.82% align to the Class 2 alignments and only one single anomalous line, drawn at 38 degrees, belongs to class 3. In total 15 lines out of 34 (44.12%) align to 5.1, 13.66 and 18.6 degrees. These three values are again similar to the astronomical values that appear most often on the Delalan stone (5.1, 13.66 and 9.3 degrees). The last value simply being the half value of the hand print value (9.3 and 18.6). This suggests that the two art pieces were designed to the same astronomical theory.
Analysing the 82 finger alignments used to create the focal points, the highest percentage 68.29% (56 out of 82 alignments) are to the Standard list, 17 lines ((20.73%) align to Class 1 values (these are values that have undergone slight modification), 5 fingers (6.10%) align to possible geometric values and, only 4 alignments (4.88% of the total) are Class 3 alignments with all class 3 alignments drawn to an angle of 40°. The three angular values most frequently observed are lines aligned to 13.66, 18.6 and 27.32 degrees. These angular values are present in 34 lines (41.46%) of the total, and once more the 13.66/27.32 and 9.3/18.6 alignment-pairs generate two of the most common alignments. Thus the most prevalent alignments, seen here, once more appear to match the same astronomical logic employed in the cylcon stone.
Analysis of the Carnarvon Petroglyph Geometric Drawings
For the final study the Carnarvon site is again chosen. This time the study concentrates on the geometric grid-type artwork and several drawings that appear to represent boomerangs.
In total 27 out of the 27 lines studied (100%) align to clearly identifiable astronomical values. Within these 27 lines a total of 26 (96.3%) align to the standard list, and within this group the 18.6 year lunar cycle is the most frequently observed alignment with 9 out of 27 lines aligned to this specific value. Its half-value (9.3 years) appears 3 times. The next most frequently observed value is the 5.14° line, which represents the angle of Moon’s orbital plane relative to the Earth’s ecliptic plane. This appears 5 times, and equals 18.52% of the total number of analysed lines. Lines aligned to 9.3 and 27.32 degrees are both seen 3 times with each accounting for 11.11% of the total. Only 1 line (3.7% of the total) is from the Class 1 category. This is a line at circa 23.4 to 23.6 degrees, which appears to match the movement of the sun over the tropics. Overall the lines thus appear to concentrate on similar values seen on the Cyclon stone and the handprint images.
A small number of lines drawn by the boomerang motifs are not linear. There are several potential reasons for the presence of non-linear lines amongst linear artwork, such as the apparent difference in size of the moon at apogee and perigee. These are not analysed here. Of greater importance is that the distribution again matches very well the Delalan cylcon stone analysis.
Fig. 3. Alignment study of geometric grid art and lines produced by images in the shape of boomerangs at the Carnarvon Petroglyph Site. Similar to the analysis of the Delalan Cylcon, lines offset from the horizontal (±45°) are marked in yellow and lines offset from the vertical (±44.9°) are marked in white. Image provided courtesy of Don Hitchcock, donsmaps.com.
Comparison to other art found worldwide
It is now clear from this data that the Australian geometrical symbols are not drawn randomly. This is not surprising as the author’s previous studies have already proven that many ancient artefacts found worldwide are aligned to these specific astronomical values, but what is surprising about these results is the observation that the same preference to align to the same specific array of astronomical values is found worldwide.
Starting with the linear geometric found in the well-known Lascaux Cave, it is found that 49 out of 52 lines (94.23%) align to the Standard List, 2 lines (3.85%) align to Class 1 values, and just 1 line (1.92%) aligns to Class 3 values. Within the Standard list 6 lines align to 5.1 degrees, 17 lines to the 13.66/27.32 degree pair and 21 lines to the 9.3/18.6 degree pair – all angles are taken as offsets to the horizontal and vertical axes. These three astronomical terms account for 84.62% of all alignments seen in the Lascaux geometrics. The only difference is whereas Australian art emphasize the 13.66 half-sidereal month value, the Lascaux cave images shows a preference to the 27.32 degree/day full-sidereal month value. This is a very small difference, especially when one considers that the two art pieces are of approximately the same age and are located on the other side of the world – the latter value in the series is again a half value (13.66 and 27.32). Both values plot the sidereal month value.
Fig. 4. Examples of Lascaux Cave geometrics. Overall the alignment distribution shows a remarkable similarity to the angular values drawn by Australian geometric images.
Norris and Hamacher35 have previously noted that early Aboriginal cultures fully understood that eclipses were caused by the motion of the Sun and Moon37,42-44. However, no aboriginal stories are known that mention an ability to predict eclipses45. This suggests the astronomical data contained in these images must be very old, and in the case of the cylcon stone it is considered reasonable to estimate that this stone is circa 20,000 years old.
From this work there are thus three main results. The first is that the Australian art clearly show a geometric text that exhibits a 90 degree rotational symmetry, the second is that it is possible to test dissimilar art for common astronomical themes, and the third observation is that the Australian Aboriginal art has similar roots to the geometrical images found at Lascaux Cave. It appears that a key to unlocking the ancient past has indeed been uncovered.
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