- Category: Art
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This paper concerns itself with a unique fired clay disk found by Luigi Pernier in 1908 within the "palace" of Phaistos (aka Faistos) Called the Phaistos Disk, its purpose or meaning has been interpreted many times, largely seen as either (a) a double-sided textual momento in the repeated form of a spiral and outer circle written using an unknown pictographic language stamped in the clay or (b) as an astronomical device, a record or handy reference. We provide a calendric interpretation based on the simplest lunar calendars known to apply in Minoan times, finding the Disc to be (a) an elegant solution to predicting repeated eclipses within the Saros period and (b) an observation that the Metonic is just one lunar year longer, and true to the context of the Minoan culture of that period. [also as pdf]
Figure 1. The location of Phaistos Palace atop a commanding hill in the middle of the fertile Massara valley in southern Crete. The Phaistos Disk was discovered in 1908 in chamber 8 of the northeast wing of the "Old Palace" (pre 1700 BCE) as per above diagram inserted from Balistier, 2000, 5.
Scholarship does not see the Minoans maintaining a solar calendar. It was only by the end of the Archaic period that Greek cities might have developed a lunisolar calendar [Stern 2012, 49-52]. If it existed, this type of calendar would have been an adapted lunar year calendar based upon twelve named months, each a 'hollow' 29 days or a 'full' 30 days long. By this means and three 30 day intercalary months, later Greeks were able to re-synchronise their lunar year over eight solar years. An eight solar year calendar (octaetaris)*** produced an agricultural calendar, following the seasons of the solar year, by slighting the sacred lunar calendar. Some such synchronisation is typical within the fully-settled agrarian societies surrounding small cities, because ancient Greek populations still followed a sacred calendar based upon lunar months.
*** "This is the octennial cycle: 8 x 365.25 = (8 x 354) + (3 x 30). The intercalations (of 30 days) then fell at successive intervals of 3, 2, and 3 years - for example, in the third, fifth and eighth years. In the historical period we hear of four festivals celebrated in every ninth year…" [Thomson, George. 1943] Note that this system uses approximate lunar years of 354 days made up of months alternately 29 and 30 days long, the real lunar month being their average, 29.5 days whilst the true average lunar month is 29.53059 days long and the lunar year 354.367 days long.
A lunisolar calendar, through using these hollow, full and extra months, lost exact knowledge of the phase of the moon, for the first time since the stone age but could look at the moon in the sky. But the lunar calendar was drifting only to be reset after 99 lunar months and therefore month names became displaced, in the absolute sense, in order to suit the solar year. This would destroy the meaning of the Phaistos Disk's counting regime.
The modern calendar of Julius Caesar (January, 45 BCE) refined by Pope Gregory XIII (October 1582) totally lost track of the moon, requiring modern maths, published calendars or direct observation to catch up with the moon's phases. A reversal has taken place: a Minoan's knowledge of the solar year had been ad hoc, whereas modern knowledge only knows the phase of the moon "on demand", through calculation, publication of it or, again, through looking to the sky. The search for an ideal syntheses of these two luminaries has been an astronomical challenge since the Stone Age first quantified the month [Marshack, 1991].
The phase of the Moon in pre-1700 BCE Crete was a necessarily calendrical object; not least because it was emblematic of (a) women because of their menstrual cycle and the many beliefs surrounding that** and of (b) the goddesses forming at the heart of an inherently matrilineal or even matriarchal society based on pastoralism***. Their simple and direct counting of lunar months enabled the development of a sophisticated eclipse calendar, lost to the old world. The Phaistos Disc appears to have described and facilitated a reliable method of predicting eclipses through counting lunar months.
*** "Emanating as it did from the sexual life of women, moon-worship became involved with their social functions. It was their task to draw water [and] tend the plants, … The moon was accordingly regarded as the cause of growth in vegetation … The Egyptian moon-goddess Nit was the inventor of the loom, and in European folklaw the moon is still a spinner. These too are women's tasks …[as too] grinding corn, making pots or cooking." [Thomson, George. 1947. 212.]
Creating the Phaistos Disk made it easier to predict the repeat of a similar eclipse, 223 lunar months after an eclipse, a period now called the Saros. The alternative, of counting the years or days within the Saros (assuming one knew it was 18 solar years and 11 days or 6585 days) would have required a very large count and a corresponding numeracy to support that. The creators of the Phaistos Disk could avoid large numbers by counting lunar months and years, exploiting the fact that eclipses occur only at full or new moon in a repeat pattern. The lunar months of the Semitic lunar calendar, found anciently in the eastern Mediterranean and Near East, inherently provided the ideal unit of time with which to build an eclipse calendar and in turn, the Phaistos Disk represents a fulfilment of late Stone Age notations of the lunar month and year, then on bone and softer stones [Marshack, Alexander. 1972 & 1991].
Figure 2 The two sides of the Phaistos Disk
The same arrangement of textual elements is found on both sides of the Disk, an outer rim of twelve units and an inner spiral of eighteen units. The Disk was probably made in three parts, a blank sandwiched between two disks, pre-decorated on a single side, then fired to form a permanent object. [Balistier. 2000. 37-38.] The result is a slightly oblate biscuit of clay, impressed using stamps of pictograms held within scored rectangular boundaries.
Each side has,
- An anticlockwise spiral of eighteen groups of pictograms, expanding from the centre of the disk.
- Twelve groups around the rim
- Collocated gaps on either sides, punctuating the rims' groups of twelve, which corresponds with the end of the spiral groups of eighteen either side.
In a previous article [Heath, 2016] I offered a practical counting method adapting Reczko's insights into the Disk [Reczko, 2009]. There I interpreted the disk as counting the solar year as 12 1/3rd lunar months, eighteen times, to reach 222 lunar months (6 x 37), then one month short of the 223 month Saros period of near-identical eclipses. Such a count corresponded with other pieces of Neolithic art and monuments I have analysed** and interpreted. This scheme of counting (3 x 12.3333 = 37 x 6 = 222) is only one way of counting the Saros period in antiquity using lunar months. This article expresses a simpler process based on counting lunar months and lunar years, and this can answer to the repeated structural form on both sides of the Phaistos Disk.
** some of which are;
- Thornborough Henge as the Moon’s Maximum Standstill
- What stone L9 might teach us and
- Diagram of the Saros-Metonic Cycle
- Astronomical Rock Art at Stoupe Brow
Figure 3. Pernier's drawing of the Phaistos Disk
Numerical simplicity within lunar eclipse calendars
I will show how the disk could show, on its B side, the relationship of the Saros eclipse period to the nineteen year repetition called the Metonic period**, through a simple counting of the lunar year and its twelve months. This interpretation could explain why the Phaistos disk has two structurally similar sides: side A defining the Saros and side B relating the Saros to the Metonic.
** when any starting configuration of the sun, moon and stars is repeated.
If the Disk was a calendrical object of the Minoans, they were living in a mythic time world focussed upon lunar months and lunar years. Lunar months are highly visible and as we have said, they present an ideal unit of time for counting between eclipses: they are large enough to enable lunar counting between repeated eclipses using relatively small numbers; eclipses only involve exact full or new moons that occur due to the exact conjunctions of the sun, moon and earth at an eclipse. It would also seem likely that lunar eclipses were crucial to the Disk's development since (a) lunar eclipses are more frequent than solar eclipses and (b) they can be observed from half the surface of the Earth whilst solar eclipses are only locally visible and less frequent - making solar eclipses far less suitable for any ancient study of eclipse repeat patterns.
The rim of both sides of the Disk present twelve lunar months, which could be used to count the months of a lunar year calendar. After the 12th month of each counting cycle (a) a count of eighteen lunar years moves outwards in the spiral of eighteen, and (b) the lunar year count is reset to the 1st month. This allowed the spiral count to collect up to eighteen lunar years or 216 lunar months, just seven short of the Saros, of 223 months between similar eclipses**.
** the reader should be aware how astronomically short the duration of the Saros is: A similar eclipse occurs so early because in that time, a triple rotation of the lunar orbit's perigee nearly meets both the sun and the same lunar node after eighteen years, so forming a similar eclipse.
Side B presents the Lunar year of twelve months around its rim after an eclipse repeat, since the Metonic period ends exactly twelve months after a repeat eclipse. It is vital to re-state the obvious, that Saros periods are observable because eclipses are observable, and therefore, that the Metonic (an observation of an identical conjuction over a 19 year anniversary) is observationally obscure unless within the prior context in which repeated eclipses are being counted. Once the Meton was noticed, every full moon was seen to occur exactly 19 solar years after a previous one nineteen years before and hence, after an integer number of months equal to 235. This knowledge of the Metonic cycle subsequently became independent of the lunar calendar and, in reverse, became useful to solar calendars in harmonising the lunar to the solar calendar.
Side A: Counting the Saros
Side A functioned as a counter of the eighteen whole lunar years in the Saros of 223 months, the lunar year being defined as twelve lunar months. Once counting for repeat eclipses on side A had been grasped, the possibility of tracking multiple intertwined Saros eclipses emerged, of reusing side A via the use of an external notation referencing the disk. It is conceivable that Room 8 of the Old Palace was for recording and storing counts onto unfired tablets so that, only the disk survived intact. 'It lay at a slant. Tipped northward, in the midst of pottery chards and other rubble, approximately 50 centimeters (19.7 inches) above the stone floor. At the center of the disk was a symbol resembling a rosette.' [Balistier, 2000. 5.] covered over some 3600 years before.
Figure 4. A Diagram how Side A might have structured time to count 223 lunar months
In the first month after an eclipse, shown as 1 in figure 3, the central unit of side A (the flower or rosette) is marked as the current lunar year - both displaying the pictogram for a flower. The symbol for the eclipse would then be this famous flower, the first stamped mark observed when the disk was found in 1908. However, the disk was probably not like a board game, using markers to store the current state of the count***: both the current month and current year could be written down with ink on papyrus or using stamps on clay, thus employing the symbols given on the disk to record the count.
*** a marker can be disturbed and the count lost but making notating marks or pictograms in additional media is more reliable and generates persistent documentation that can be referred to.
Using modern numbers for convenience, one can notate the counting process as [year in the spiral)] / [month on the rim]. The spiral count would proceed as 1/1 to 1/12, then 2/1 to 2/12, etc. until 18:12 whereupon 216 lunar months would have been counted at the end of the 12th month of the 18th lunar year. The 19th spiral division, which touches the rim, is then counted 19:1 to 19:7, at the end of which month seven extra lunar months complete the count to 223 and the Saros eclipse repeated. At that point, the count has again reached the flower symbol on the outer rim.
An eclipse can occur within any month within a lunar year with named months. A Saros count dislocates the lunar year by eight months, implying that only the starting month name needs to be noted to locate a given Saros count. On this basis, it seems likely that the pictograms found within each lunar month division and each lunar year division are (a) identifiers transcribed to identify the state of the count, (b) notes on the counting process or (b) remarks on the significance of different time periods measured from the start.
To recap: side A proceeded from an eclipse that starts the Saros, the flower at the centre collocating with the flower at the start of the anti-clockwise rim count of months. Counting continued for eighteen lunar years and then a further seven months (the rim gap) to arrive at the end of the Saros (223 lunar months) as the flower of the first month.
Side B: Reaching the Metonic
Side B is a structural repeat in form but not in pictographic content. Another common feature is the flower appearing at the first month of the lunar year's rim count. The spiral again holds eighteen elements with a gap element next to that first month. A "walker" has been prefixed to the flower, which might mean "having counted to the Saros repeat", the counting of a lunar year of twelve around the rim will arrive at the Metonic repeat of 235 lunar months. Thus side B could repeat side A whilst presenting a further astronomical fact.
Figure 5. A diagram of Side B as showing twelve months separate the Saros and Metonic periods
This is, in my view, the conceptual beauty of the Phaistos Disk. It was arrived at because every eclipse event is the start of a Saros period, which period can be seen as the practical anchor also for the Metonic. Everything revolves around the lunar eclipse, and each eclipse triggers both the Saros of 19 eclipse years and the Metonic** of 19 solar years. And the first lunar year both starts a new Saros count and ends a completed Metonic count.
**19 solar year anniversary of sun-moon and stars is just over 20 eclipse years long
How the Numbers Work
We see that twelve months around the outside rim can be both a counting system for the eighteen lunar years in the spiral (side A) and the lunar year separating the Metonic from the Saros (side B). There are then 223 - (18 x 12) = 7 months before the Saros repetition of an eclipse and a further 12 months before the Metonic repetition. The sum is 7 + 12 = 19 and here one sees the numerical order emerging from counting using lunar months. There are 19 eclipse years in the Saros and 19 solar years in the Metonic.
After 19 lunar years, 19 x 12 = 228 + 7 = 235 lunar months of the Metonic period. And we know that the astronomical Megalithic Yard is 19/7 feet so, when counting using solar years as 12 (the lunar year) and 7/19th megalithic yards, excesses within a single solar year resolve metrologically as [Heath, Robin. 1998. 85.]:
- The excess of the solar over the lunar year is 7/19 lunar months which is 7/19 x 19/7 = 1, the English foot whilst
- the excess of the solar year over the eclipse year is 12/19 lunar months which is 12/19 x 19/7 = 1.7143 feet, the Royal cubit of 12/7 feet.
It is interesting that the spiral, and final twelve months are both initiated by a flower of side A and ended by the head ("scribe"), the person who has to recognise the end of such periods during month-counting.
The sun, moon and earth exhaust their ensemble of mutual aspects, relative to each other, within nineteen years and such ensembles are symmetrical, mirroring each other (***). This is what made the identical pattern of sides A and B a meaningful act, intuiting the inherent symmetry of the Saros and Metonic.
*** the Mirror Theorem developed by Roy and Ovenden [see Roy, 2005] that; "If n point masses are acted upon by their mutual gravitational forces only, and at a certain epoch each radius vector from the centre of mass of the system is perpendicular to every velocity vector, then the orbit of each mass after that epoch is a mirror image of its orbit prior to that epoch. Such a configuration of radius and velocity vectors is called a mirror configuration." [Celletti & Perozzi, 2007] These conditions being met for both the Saros and the Metonic and hence time-symmetric repeat cycles .
The Phaistos disk was and is a calendrical artefact whose purpose is easily overlooked in favour of a literary interpretation, epigraphy being a powerful and successful skill set in studying the ancient world. It is important to strengthen our understanding of the astronomical patterns relevant to pre-archaic Greek society before assuming the Disk is a literary device.
Minoan culture evolved out of the late stone age and the type of astronomy proposed here for the Phaistos Disk relates well to the megalithic monument building of the western European neolithic. Crete was too small to form a state on a par with Egypt or Old Babylonia and, being an island with limited scope for hunting or large scale agriculture, pastoralism was natural to Crete and matrilineal clans. Women rather than men give their names to children in matrilineage and men from other clans are the fathers, the norm until later invasions by patrilineal tribes. Minoan society instead grew economically, through trade with its colonies in the Aegean and Greek mainland, and with the near-eastern empires.
The general form of the disk, whilst a conceptually appropriate model of the Saros, was probably used as a codex for keeping astronomical records and enabling continuous eclipse prediction. Written notes referencing side A could save the counts for more than one Saros series, in parallel. If side B conceptualised the subsequent completion of the Metonic relative to the Saros, this was a permanent aide-memoir with the same structural form as the use of side A for counting, and the encoding and decoding of records based upon its pictographic codes.
This interpretation can be seen in the light of three related anachronisms:
- The Metonic period was memorialised in the myth of Apollo visiting his temple in Hyperboria once every nineteen years, a calendar synchronizing solar years with lunar months and eclipses. The myth could have been pointing towards Greek links to the megalithic astronomy of western Europe which had the methodology to count cyles such as the Saros and Metonic periods.
- We know that the Callippic cycle of four Metons and the alternation of 12, 12 and 13 (37) month years was used in the ancient Near East, and in western Christianity in calculating a date for Easter, Christianity's moveable feast.
- The key numbers of the Saros and Metonic (223 and 235) have been found within the mechanism bronze age "clock", the Antekythera Mechanism recovered from a 18 BC wreck of a Roman treasure boat just north of Crete. "On the back of the mechanism, there are five dials: the two large displays, the Metonic and the Saros, and three smaller indicators, the so-called Olympiad Dial, which has recently been renamed the Games dial as it did not track Olympiad years (the four-year cycle it tracks most closely is the Halieiad), the Callippic, and the Exeligmos." [Wikipedia 2]
Balistier, Thomas. The Phaistos Disk: An Account of its Unsolved Mystery. Trans. Monique Scheer. Edition Mahringen:Mahringen 2000.
Celletti & Perozzi. Celestial Mechanics: The Waltz of the Planets. Chichester: Springer-Praxis 2007.
Heath, Richard. Phaistos Disk as aide memoir for Saros Eclipse Period. www:academia.edu 2016.
Heath, Robin. Sun, Moon and Stonehenge. Cardigan: Bluestone 1998.
The Roots of Civilization: The Cognitive Beginnings of Man's First Art, Symbol and Notation. London: Weidenfeld and Nicolson. 1972
The Tai Plaque and Calendrical Notation in the Upper Palaeolithic. Cambridge Archaeological Journal 1. 1991: 25-61.
Reczko, Wolfgang. Analyzing and dating the structure of the Phaistos Disk.
Archaeol Anthropol Sci (2009) 1:241–245 DOI 10.1007/s12520-009-0015-2
Reczko's 2009 interpretation was similar in attributing the central spirals of eighteen as signifying years. He did not there comment on the twelve around the rim except to point to the lunar year of twelve lunar months was the most likely. Reczko then analysed the duplicates in the Minoan hoeroglyphics and deduces a specific pattern matching the eclipses in -1370s and -1360s Saros period, thus making his interpretation a specific observational record for a given Saros.
Roy and Ovenden. Orbital Motion 4th ed. Bristol: IoP 2005. Mirror Theorum 111.
Stern, Sasha. Calendars in Antiquity: Empires, States, & Societies. Oxford: UP 2012.
- Phaistos Disk. Global: wikipedia.org 2017.
- Antikythera_mechanism. wikipedia.org 2017.
- Category: Art
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I recently came across Rock Art and Ritual by Brian Smith and Alan Walker, (subtitled Interpreting the Prehistoric landscapes of the North York Moors. Stroud: History Press 2008. 38.). It tells the story: Following a wildfire, thought ecologically devastating, of many square miles of the North Yorkshire Moors, those interested in its few decorated stones headed out to see how these antiquities had fared.
Fire had revealed many more stones carrying rock art or in organised groups. An urgent archaeological effort would be required before the inevitable regrowth of vegetation.
Figure 1 Neolithic stone from Fylingdales Moor | Credit: Graham Lee, North York Moors National Park Authority. From <this site>
A photo of one stone in particular attracted my attention, at a site called Stoupe Brow (a.k.a. Brow Moor) near Fylingdales, North Yorkshire. The archaeology has been written up (in Proceedings of the Prehistoric Society. Volume 77. London: 2011. A New Context for Rock Art: a Late Neolithic and Early Bronze Age Ritual Monument at Stoupe Brow, Fylingdales, North Yorkshire. Vyner, Blaise.) The Prehistoric Society has a website detailing its publications including their proceedings, events, grants and membership. There is an online description of Stoupe Brow at ERA: England's Rock Art.
According to Blaise Vyner, this stone was originally upright, 90 degrees clockwise from its present position, and there is some weathering on its left side which perhaps led to this assertion. If so, this decorated stone is similar to those at Gavrinis (Carnac, Brittany) in that (a) it's engraved art is of a similar style and (b) had signs of having been outdoors at different locations/orientations prior to being incorporated in some sort of assemblage. At Gavrinis, engraved stones had been reused to build a chambered tomb whilst at Stoupe Brow. Parts of a probably egg-shaped stone circle was made using reused engraved and plain stones, surviving as a partial kerb integrated with at least one standing stone.
I have re-erected the stone photo according to Vyner and done some counting of elements so as to interpret the monument, not according to a possible anthropological ritual meaning, but from the standpoint of astronomy as practiced by the megalith builders.
Figure 3 (#10 of Vyner 2011) rotated into its likely original presentation, in negative and with extended calibration.
There are three main panels and two other related regions:
- A top panel made up of lozenges which in reverse are triangles whose bases touch the panel border. There are six such triangles on the bottom, then also touching the left and right panels.
- The left panel is a two by three rectangle, crossed by diagonals. The above triangle is scored by twelve vertical lines whilst the below triangle is scored by thirteen vertical lines. The left triangle is filled by a single chevron whilst the right triangle filled by a double chevron.
- The right panel has chevrons arranged loosely into a fish scale pattern containing twelve scales, leaving a thirteenth region of the panel empty.
- Between the left and right panel and below the top panel there is a strip terminated above but not below (hence not a panel), containing four whole lozenges, each with central dots. Alternatively, there are triangles running along the sides of the left and right panels. Between the fourth and fifth triangles of the top panel is a vertical line central to these vertical lozenges, perhaps indicating connection between the two rows of horizontal and vertical lozenges.
- The top panel also plays host on three of its sides to what appear to be thirty seven small holes/dots, terminating in the right panel.
These panels appear now to belong to an area of fine sandstone about one lunar month (of 29.53 day-inch counting, 75cm) wide and one megalithic yard high, in (native) megalithic units, if the 30 cm measuring rod in the photo is expanded to metre rods and applied to the photo.
One can see some kind of play between numbers twelve and thirteen within both the left and right hand panels, and the dots and repeated geometrical elements suggest a relationship to the counting of days and aggregation of such counts into larger units. These are significant astronomical numbers in units of lunar months, since twelve and thirteen months bracket the solar year. These two lunar year lengths are sometimes alternated to fit the Metonic cycle of 19 years equalling 235 lunar months. Wikipedia says:
- The solar year does not have a whole number of lunar months (it is about 12.37 lunations), so a lunisolar calendar must have a variable number of months in a year. Regular years have 12 months, but embolismic years insert a 13th "intercalary" or "embolismic" month every second or third year (see blue moon). Whether to insert an intercalary month in a given year may be determined using regular cycles such as the 19-year Metonic cycle (Hebrew calendar and in the determination of Easter)… <https://en.wikipedia.org/wiki/Intercalation_(timekeeping)>
If two years of 12 months are added to one of 13 months then the total "three year" period is 37 lunar months long, and this corresponds to the number of holes running around the top panel and into the right hand panel.
- The left hand panels usage of 12 and 13 scored lines is accompanied by two triangles containing chevrons, two on the right and one on the left, and this could have presented the formula of adding two twelve month lunar years to one thirteen month lunar year.
- The right hand panel contains thirteen areas, the twelve "fish scales" and a thirteenth "left over" area, and this could represent the twelve lunar months between the end of the Saros eclipse period of 223 months and of the Metonic 19-year period of 235 months, if counted from an eclipse. (Whilst the Saros is the strongest eclipse period known for similar eclipses to occur, the Metonic is also an eclipse cycle including just over 20 eclipse years to the Saros exact 19 eclipse years.)
These thoughts suggest an interpretation of the top panel, which links the left and right panels in an endeavour to count these two 18 and 19 year cycles and present how this is done on a flat-faced orthostat or standing stone, exactly as was done in the Carnac area with similar graphical elements. In this sense the attempt here, to interpret Stoupe Brow decorated stone 1, is to identify it as a teaching text for astronomical cycles, originally upright but then incorporated within a semi-circular kerb, on its side perhaps to store or conserve it.
The six triangular shapes within the top panel suggest that each triangle was an aggregate of 37 lunar months so that six of these equalled 222 lunar months, just one month short of the 223 whole months within the Saros period. In previous posts I have noted, at Carnac, engraved stones graphically presenting the counting of units of 37 lunar months in order to approach the Saros to within one lunar month. (We must remember that counting lunar months is especially appropriate since eclipses only occur at new and full moon).
Figure 4 Interpretation of Stoupe Brow Decorated Stone 1 as a counting left to right of periods 37 lunar months long, to arrive within one month of an exactly similar eclipse to one just occurred.
It appears likely that the Phaistos disk found on Crete, and due the Minoan civilization, counted 222 lunar months, but then using the 364-day year of the Mediterranean prior to the Late Bronze Age Collapse in 1200 BC, for reasons also visible on this decorated stone in the line between triangles four and five, which appear to "give rise to" the vertical column of lozenges/triangles. If we divide 37 lunar months of 29.53 days = by the lunar orbit of 27.32166 days the result is 39.99 lunar orbits within 37 lunar months. It is therefore the case that each unit of 37 months can equally be viewed as 40 orbits, and I believe that (by explanation at the time) it was useful to build in four vertical units that would equal the four horizontal time periods. But these are shown as smaller to bring out the fact that the lunar orbital period is smaller than the lunar month. In the Phaistos article I came to realise that the 12.368 lunar months of our solar year of 365.2422 days (being the earth's orbital period), was usefully shortened to the twelve and one third lunar months within the 364-day year so as to count three such years to give the 37 whole lunar month aggregate unit.
This 364 day year was called the Saturnian year and it had other calendrical benefits such as 13 months of 28 days (4 times 7) and exactly 52 seven day weeks, the Saturn synod having 54 seven day weeks. But here, the idea of mixing twelve and thirteen month units prefigures that scheme, perhaps without a 364-day week. However, in terms of the 364-day aggregate unit, four times 37 months equals 148 lunar months, 160 lunar orbits and twelve 364-day years. The interpretations above can now be viewed graphically:
This stone probably reveals to us that 37 lunar months was known to equate to 40 lunar orbits, so that the Moon's month of phases is 40/37 of its orbital period; and finding such new relationships through the rock art increases the likelihood that the stone's subject was astronomical.
- It is numerically obvious that the 223 lunar month period of the Saros is exactly one month longer than six periods of 37 months (or 40 orbits), thus being a perfectly normalized triangle, normalized by the lunar month. N = 222.
- The Saros and Metonic are also perfectly normalised by the twelve months between those two periods, that is they are normalized by the lunar year. N = 18.583, slightly less than 18.618 since the 223 to 235 relationship is not exact.
- Added to this the Eclipse and Solar year are normalised by the time taken for the lunar nodes to travel on DAY in angle, that is they are normalized by 18.618 days. N=18.617.
- The differential length of three solar years and three lunar years gave the megalithic their "yard" of 32.625 day-inches, a unit by which both periods were normalized by 32.625 days. N = 32.585, the length of the astronomical megalithic yard in inches.
This stone, decorated without having a unified mathematical culture exactly like ours, had knowledge that solar-lunar periods (counted in day-inches) tended towards being unified through their differential lengths, such as the megalithic yard. If so, their astronomy could predict eclipses and other cyclic events without modern calculation or observation of exact celestial positions within a system of coordinates. Instead, observable events could be "counted on" to arrive at future events.
- Category: Art
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In the Old Palace Period (2000-1700BC) of Minoan Crete, three locations were dominant: Knossos (near Heraklion), Malia (now a north coast resort) and Phaistos (central southern agricultural plain of Messara). Phaistos is especially known for a small clay disk retrieved.
The disk is about 15 cm (5.9 in) in diameter and covered on both sides with a spiral of stamped symbols. Its purpose and meaning, and even its original geographical place of manufacture, remain disputed, making it one of the most famous mysteries of archaeology. This unique object is now on display at the archaeological museum of Heraklion.
Wikipedia gives a helpful resume of theories considering what the spirals of grouped symbols might mean, of two types, linguistic and logographic. Linguistic theories look for a text and logographic look for meanings such as an astronomic meaning. I will provide the latter, as another demonstration of the utility of the number 222 as one less than 223, the number of lunar months making up the Saros period of 18 solar years and 11 days (after which an almost identical eclipse recurs). Of the few eclipse periods, the Saros is the definitive one, because similar eclipses belong to the recurrence of the same actual orbital conditions of sun and moon. The difficulty in predicting Saros events is a problem of counting numbers something simple (the lunar months) which is a natural integer and does not require too many to be counted, when numeracy might be a problem for ancient cultures.
In 2009, Wolfgang Reczko interpreted the disk.
The author suggests that the disk side A containing a petal in the center box shows astronomical eclipse information, which belong to a complete Saros cycle beginning −1377 and valid for the Phaistos Palace location only.
His summary of the disk is useful and he is also tying the disk to specific eclipse data. The outer disk on both faces has twelve groups of symbols with a small excess which could be remarking on the 0.368 (7/19ths) of a lunar month after twelve whole lunar months.
Rectzko then points to the spiral on both sides having eighteen blocks of symbols and these inner spirals with 18 divisions he interpreted as solar years so that the small boxes linking these to the rim are the 11 days excess over eighteen years of the Saros period.
I believe that, whilst the Saros is involved, it was not as 18 solar years but rather as 18 Saturnian years** (of 364 days) known to be associated with the matriarchal world documented in Greek myth. The 364 day year equals twelve and one third lunar months and this is shown on the rim as twelve boxes and a small box symbolising one third of a lunar month. Eighteen times twelve and one third lunar months equals 222 lunar months, one exact month before the Saros period completes (as already stated, to manifest an almost identical eclipse to the eclipse witnessed at the beginning).
** these years are called Saturnian because the Saturn synod divides by the seven day week, as 54 weeks whilst 364 days is 52 weeks. The Disk of Chronos makes this clearer, if you read my 2004 article.
Thus eighteen times around the circumference leaves just the small box of one lunar month before the eclipse, to reach the rim of the disk. Since eclipses occur when the sun, moon and earth are in alignment, a solar eclipse at new moon or a lunar eclipse at full moon, this made counting months the best time-keeping method and the prime number 223, of lunar months for the Saros period, could be reduced by factorising the number one less than 223; 222, itself the product of 6 and 37.
Thirty seven is the number of lunar months in three solar years, if and when the solar year is taken to be 364 days. I have found evidence at stone L9 in Gavrinis that the 37 lunar months in three solar years was used as a counter sometime around 4000-3500 BC. This early use of 37 lunar months has not previously been connected with the Saturnian year as being twelve and one third of a lunar month, one third of thirty seven.
A form of numeracy appears to be possible within the form of the Phaistos Disk, teaching its possessor a lesson in how to predict Saros eclipses. One merely needs six counters worth 37, three counters worth 12 and twelve counters worth one, lunar months. The process is
- count twelve months of the lunar year with markers worth one
- count lunar years with the markers worth twelve
- after three lunar years are counted, wait a further month
- count using a counter worth 37, and start again at step 1.
- count to six counters worth 37, wait a further month.
- The Saros Period has been counted, so start again at step 1 with no counters.
The Phaistos Disk is not a calendrical counting device but it probably defined the basis for a scribal procedure. If counts were to be kept then the above counting method would have to be replicated for each Saros eclipse series in which there was an interest.
However, the use of naming for both the peripheral and spiral sequences would enable counting to be notational using a type of positional arrangement similar to that seen in the long count or in Sumerian base-60 notation.
- The name of the current Saturnian year could be followed by
- the month name of the first month within the current lunar year followed by
- the current month name.
or some such means to maintain the state of the counting without using counters or a positional system like that of the Disk of Chronos.
It is interesting that the excess shown at the ends of both the spiral eight and peripheral twelve is approximately a triple square as if to signify the lunar month split into three parts, invoked as
- the difference between the lunar and 364 day years
- the situation of waiting an extra month at the end of 36 months or after 18 364-day years.
A new part of the Numbers menu item above is Calendars, where I hope to collect useful source materials to supplement pages like this. The first item in this is Robin Heath about the 364-day 'Saturnian' Year
- Category: Art
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One test of validity for any interpretation of a megalithic monument, as an astronomically inspired work, is whether the act of interpretation has revealed something true but unknown about astronomical time periods. The Gavrinis stone L9, now digitally scanned, indicates a way of counting the 18 year Saros period (within which almost identical eclipses re-occur) using triangular counters founded on the three solar year relationship of just over 37 lunar months, a major subject (around 4000 BC) of the Le Manio Quadrilateral, 4 Km west of Gavrinis. The Saros period is a whole number, 223, of lunar months because the moon must be in the same phase (full or new) as the earlier eclipse for an eclipse to be possible.
Handling the Saros Period
223 is a prime number not divisible by any lower number of lunar months, such as 12 in the lunar year. 18 lunar years equates to 216 lunar months, requiring seven further months to reach the Saros condition where not only is the lunar phase the same but also, the sun is sitting upon the same lunar node, after 19 eclipse years of 346.62 days.
However, astronomers at Carnac already had a number of 37 lunar months (just less than three solar years) in their minds and, it appears, they could apply this as a length 37 units long, as if each unit was a lunar month. We also know that the unit they used for counting lunar months was originally 29.53 inches (3/4 metre) or later, the megalithic yard. Visualising a rope of length 37 megalithic yards, the length can be multiplied by repeating the rope end-to-end. After six lengths, 222 or 6*37 lunar months were represented, one lunar month less than the 223 lunar months which define the Saros period.
This six fold use of the number 37 appears to be used within the graphic design of Gavrinis stone L9, as the triangular shape which has an apex angle of 14 degrees and which refers to the triangle formed at Le Manio between day-inch counts over three solar and three lunar years. It appears that this triangular shape was used to refer to the counting of solar years relative to a stone age lunar calendar (see 2nd register of stone R8) but it could also have the numerical meaning of 37 because three solar years contained 37 whole lunar months just as a single solar year contains 12 whole lunar months (the lunar year).
This triangle, symbolic of 37, often appear in pairs within stone L8 with their points adjacent so that they have one side also adjacent. The two triangles are found to be held accurately within the apex angle of another triangle, known to be in use at Carnac, the triangle with side lengths 5-12-13, with apex angle 22.6 degrees. These pairs would then effect the notion of addition so that each is valued at 37 + 37 = 74 lunar months.
All of the three pairs have this same apex angle, of the 5-12-13 triangle, chosen perhaps because 12+12+13 = 37 whilst the 14 degree triangle was known to be rationally held within it when the 12 side is seen as the lunar year of 12 months. The third side is then 3 lunar months long *** and forms an intermediate hypotenuse within the 5-12-13 triangle equal to 12.368 months, the solar year. Three solar years then appears to have been seen as composed of 12+12+13 which is exactly how Arab and medieval astronomers came to organise their intercalary months within the Callippic cycle of 4 Metonic periods (= 4 x19 years equalling 76 solar years).
The Saros period appears to have been indicated on stone L9, below these triangles, using the main feature of this stone, a near square Quadrilateral having one right angle. It has a rounded top, containing a wavy engraved design emanating from a central vertical, not unlike a menhir. The waves proceed upwards but then narrow to a vestigial extent after the 18th, which would be one way to symbolise the Saros period as 18 years and eleven days in duration. A different graphical allusion was used on stone R8, again showing lines as years but giving the 19th year as a shortened "hockey stick".
In Gavrinis stone L9, a primitive numerical symbolism appears to have expressed a useful computational fact: that the Saros period was one lunar month more than six periods of 37 lunar months. These three periods of 37 months were shown as blade shapes, each symbolising three solar years, but shown as pairs within three 5-12-13 triangles above a quadrilateral shape indicating 18 wavy lines plus a smallest period, this symbolising the 11 days over 18 years of the Saros Period, defined by 223 lunar months. This allowed 18 years to be seen as six periods of 37 lunar months, equal to 222, plus one lunar month.This enabled a pre-arithmetic culture to approach prime number 223 from a another large unit, repeated six times.
Many thanks to Laurent Lescop of Nantes University Architecture Dept, for providing the scan on which this work is based.
- Category: Art
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The last article looked at the second register up of engraved stone R8 (eighth on the right) in the corridor of Gavrinis cairn, 4Km east of Loqmariaquer, which appears to count the 19 years of the Metonic period and mark the 18th year which, plus a little bit, marks the ending of a given of the Saros eclipse period relative to a starting eclipse. Below this register, the first appears to show how the moon's orbit sits on top of the ecliptic (the sun's path within the year) so that every lunar orbit over 18.618 years sweeps out a different range of angles on the horizon at moon rise (or set in the west) according as to which part of the ecliptic it is curently sitting on: it can be above, below or on the ecliptic. When on the ecliptic, it can eclipse the sun or be eclipsed by the earth's shadow and the moon moves so quickly that when the sun is sitting at one of the two crossing points of the moon's orbit, these eclipses are highly likely (even if not visible).
It is therefore true that the Saros period, which is the dominant synchronicity regarding eclipses, is punctuated by actual eclipses which can only occur when the sun is sitting on a lunar node. But the cause of the eclipses, the nodes' locations (opposite each other) on the ecliptic, are forever on the move so as to "orbit" the earth in the 18.618 years of the Draconic period, travelling backwards relative to the planets and sun (i.e. retrograde). The first register of Gavrinis stone R8 appears to provide an explanation about how the moon's orbit sits upon the ecliptic in a variable way that leads to the 18 year saros period within which very similar eclipses recur, delineated in register two.
Register one of R8 is one of the most memorable images of Gavrinis, appearing to show three serpentine lines rising upwards, between lines that limit and demark them.
On the left is a common symbol for counting astronomical periods, a line or monolith with concentric bands. The arrow heads, sitting point down, are symbols of angles and it seems the custom at Carnac for such arrows to indicate specific multiple square geometries and their diagonals. Afour-square suggests, by its diagonal, the first arrowhead, this diagonal similarly angled to the median line of the central of three serpents, shown red as being the equinoctal mean of the sun's extremes in the year. If so then the serpent of the red line does not move except over thousands of years (due to precession).
The left hand serpent (with a blue median) is clearly an opposed sinusoidal-like wave, and the blue line is angled according to the triple square diagonal and left hand serpent median line. The right hand serpent has the opposite character, in phase with the solar serpent, and its vertical median line (coloured green like the triple square) probably borrows from the meaning of triple squares as time-factored structures. The base of a triple square is commonly associated with the eclipse year in length, relative to the (blue) diagonal which would then be the solar year in length.
This motif of serpents therefore appears to express in art
- the opposing nature of the lunar orbit and solar "orbit", causing the moon to peak where the sun's path is on the other side the celestial equator (the red median line).
- the additive nature of the lunar orbit and solar "orbit", causing the moon to peak where the sun's path is on the same side the celestial equator (the red median line).
Today one might introduce the Saros cycle by saying that the lunar nodes move causing eclipses to occur twice within a period less than a year until after 36 + 2 = 38, there have been 223 lunar months, just one lunar year of 12 months short of the Metonic period of 19 solar years. , R8 may have been viewed in the light of the fact that the lunar maxima occur at the extremes of the sun's path to north and south whilst instead the nodes are wherever the moon is known to be travelling on the ecliptic. The search for the mechanism of eclipses is a search for where the moon is not riding above or below the sun's path, but sitting exactly upon it, a circumstance of crossing the sun's path rather than exceeding it or not, on the horizon.
One has to learn to deduce the node's invisible location by studying the location of the moon relative to the ecliptic. Without any sky pointing technologies of measurement, the megalithic horizon event of the moons's rising or setting can indicate whether it is sitting on the ecliptic, if one knows
- which point of the ecliptic the moon should be sitting on (using a lunar simulator) and
- which point of the ecliptic is rising when the moon actually rises (using the circumpolar stars).
If the two points exactly correspond, then the moon is on one of its two nodes.
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