Here we present selected parts of the very interesting paper titled “A Minoan eclipse calculator“, by M. Tsikritsis, E. Theodossiou, V.N. Manimanis, P. Mantarakis, D. Tsikritsis (Mediterranean Arhaeology and Archaeometry, Vol. 13, No 1, pp.265-275)
An observation by the British archaeologist Sir Αrthur Evans in his book The palace of Minos at knossos (Evans, 1935) led us to research the three figures he includes in the book of the Palaikastro plate.
According to Evans, these carvings were representations of the Moon and the Sun.
The first publication of this plate, including figures, was done by the archaeologist Stephanos Xanthoudides in the difficult-to-find journal Archeologiki Ephemeris (Xanthoudides, 1900). The article mentions that the findings were actually two plates, which were discovered together in the same field, 150 m NW of the village Palaikastro of the Siteia province in Crete in 1899. Today they are dated by archaeologists as originating in the 15th century BC.
Upon examination of the two plates, we concluded that only one of them has an astronomical significance.
The plate was probably used as a die for the production of possibly metallic (copper, silver or golden) copies of its depictions. The symbols and figures carved on the surface of this plate are described below.
The issue of dating is still open. However, in our opinion, the most probable dating is that of M. Nilsson (16th century B.C.) or the intermediate one of the 15th century BC.
Our team acquired high-definition photographs of the finding, provided by the Heraklion Archaeological Museum after issuing a permission to study, which could be studied at a magnification of about 5×. By examining the magnified photographs of the plate (Fig. 1c), our team observed that there were various depressions, notches and dots in number ratios that indicated a relationship to astronomical phenomena.
By studying the components of the die and correlating these with astronomical
phenomena, we were able to explain its intended use. The most obvious interpretation is that of an eclipse calculator, which could be produced by imprinting a copy of this die on a soft solid (e.g., malleable metal or even soft wood). In order to test this interpretation, we constructed a threedimensional model of the “ray-bearing” disc in its original dimensions: 8.5 cm × 8.5 cm.
We were able to carefully measure the dots that appear both on the disc itself and on the
triangular “rays” on its circumference, and arrived at the following results:
In the disc’s circumference appear 25 triangular “rays” or “teeth” (Δ). Each one of the 20 of them has 5 tiny dots (o) , while other 4 “rays” have three dots each and one ray has no dots at all, just one dash (-), denoting probably some starting point.
The total number of these dots is 112. Knowing that a saros cycle includes 223 lunar months, 112 seemed to be too close to half that number to be mere coincidence.
Until now, the earliest record of the saros cycle is by Babylonian astronomers from 750 BC to 1 BC. The saros is a period of 6585.3 days (approximately 18 years and 11 days) during which the relationship of the Sun, Earth and Moon will return to the same configuration as the starting eclipse.
Looking at the Palaikastro plate, we found that by moving six nodes every twelve
lunar months, then the triangular ray circle can cover one saros cycle. A different way
of expressing this is that if 112 is divided by 6, then the number (18.66) approximates
the number of years in a saros cycle.
Therefore, it seems logical that the nodes shift by 6 positions every 12 lunar months.
Inside the disc there are carved two circles, the outer one, which contains 58 small circular cavities (Ο), and the inner circle, which is a single depression that contains 59 carved short lines and is interrupted in four places by a cross. The two lines of the cross (diameters of the circle) bear dots in rows as follows: The vertical line bears 11 dots in its upper part and 10 dots in its lower part. The horizontal line bears two rows of dots, the upper row of its left-hand part having 10 dots and of its right-hand part having 7. The lower row has 11 dots in its left-hand part and 8 dots in its right-hand part (11 + 8 = 19). The horizontal diameter of the cross divides the disc into two semicircles, each of which has 28 dots.
It can be also observed that, if metallic imprints of this die are produced, then, in addition to the disc, there will be two pins, each 6 cm long, and a flexible tweez-ersshaped object that probably served as a compass (for drawing circles and measuring distances). Assuming that the disc and its carvings served the stated purpose, then these objects, which correspond to horizontal forms to the right of the ray-bearing disc on the die can be understood as tools for its proper functioning. The two pins could be cut into
three parts each, yielding six pins. Six pins are required for the proposed operation of
After our numerical results, it appears that the most probable use of the plate’s raybearing disc in combination with the pins and the pair of compasses pertains to
With the use of a pin placed at the center of the cross, its solar shadow on the disc’s
surface could lead to the determination of the following elements:
– The true solar time during daytime (use as a sun-dial)
– The geographical latitude
– The cardinal points on the horizon
– The first day of each of the year’s seasons
– The length of the tropical year
– The daily change of the declination of the Sun
The “ray-bearing” disc has 25 triangular “teeth”. If they are enumerated per 0.5-hour intervals and a pin is placed perpendicular to the central cavity, then the pin’s solar shadow indicates the point of the disc’s circumference that corresponds to the time of the observation when the central cross is aligned in the North-South direction. In this way, this simple device could be used as a portable sundial of 12.5 hours. Its “hour” corresponds to approximately 58 minutes, very close to the modern hour.
If the one pin and the pair of compasses are used, with the user marking every 14 or 15 days (half of a lunar month) the edge of the pin’s solar shadow at the moment of the
true noon (upper culmination of the Sun resulting in the shortest shadow), then in the course of one year an analemma would form, a figure similar to the digit 8. The shadow’s angle at the equinoxes is at the two edges of the cross at c, and it is equal with the geographical latitude, approximately 35°15′ N in the case of Knossos. If a user had drawn the analemma in the area of Knossos, after a year’s observations, and then travelled to a location to the North (e.g. latitude 51°), he would be able to find the latitude of the new
position within half a month without prior knowledge of the date of the year, by comparing the part of a new analemma he would draw with the old one. Using this
method, and marking the pin’s shadow (in 15-day intervals) while travelling back to the south, the user would know that he was at the same geographical latitude with Knossos once the shadow produced the same analemma as the initial one. It would be easy for him to then return to Crete by sailing east or west.
Α portable calculator for predicting lunar eclipses
It records every eclipse that occurs per lunar month and year whenever the Sun and the
Moon are in conjunction (i.e. either at the full moon or at the new moon phase) near a
node of the lunar orbit.
The inner circle is divided horizontally by the double row into two semicircles, the one with 29 carved dots (15 on the left and 14 on the right-hand side) and the other with 30 (16 on the left and 14 on the right-hand side), that is a total of 59 dots. These two inner rings, with the 29 and 30 dots, lead to the conclusion that they correspond to two successive lunar “orbits” — apparent orbits since their average is the number of days (29.5) in a lunar or synodic month, that is the average time between two successive full moons. The exact value is 29.53058866 days, a difference of only 44.05 minutes per month. To use the die as an eclipse calculator, six pins are required, corresponding to the following positions:
● One for the position of the Sun, which moves counterclockwise on the outer circumference with the 58 dots (small cavities on the imprint), one position per approximately 6 days. These dots are numbered in yellow (See Figure below).
● One for the position of the Moon, which revolves on the inner circumference with the 59 short carved lines. These lines are within the green dashed circle (See Figure below).
● Two for the nodes of the lunar orbit — the two points where the orbit of the Moon
around the Earth intersects the ecliptic (the plane of the Earth’s orbit around the
Sun), on the triangles or “rays” of the “ray-bearing” disc. These are the 112 dots
that run along the edges of the triangles (See Figure below).
● and two on the dots of the cross in order to follow the number of the lunar months and years that pass. The months are on the horizontal arm, and the 18 dots for the years are on the vertical arm. With such a device the astronomers of the Minoan period could predict with considerable accuracy and precision the lunar eclipses, as well as some of the solar ones (See Figure below).
Verifying the function of the device
The first step for testing the Palaikastro device is to verify whether it can predict future eclipses with a reasonable accuracy and precision.
We now use the device for the calculation of the lunar and solar eclipses of the next few years, starting (“initializing”) from the total lunar eclipse of December 21, 2010.
Fifteen days after the full moon, the date is January 4, 2011. On this date there is a new
moon and the Sun’s pin has been moved by 2 places towards the direction opposite to
the direction of the motion of the Moon’s pin; the nodes remain on the same dots. It is
observed that the Sun’s pin is in the area of the triangle of the node, therefore, since
there is a new moon, a partial solar eclipse takes place on January 4, 2011. Two lunar
months later, on February 23, 2011, the Moon will be in a full moon phase and the Sun’s pin will have been moved by 9 dots, while the nodes will have shifted one dot, On June 15, 2011, 176 days (or 6 lunar months) after the first lunar eclipse (December 2010), the position of the Moon corresponds to the full moon phase after it moved clockwise by one short line per day on the inner circle’s semicircles of 29 and 30 days. The Sun’s pin has been moved in the opposite direction and it is now on dot no. 28. The nodes have been moved clockwise by three positions during these six months.
On the left-hand side of the Figure above the node’s pin is on the dot (3), the Sun is within the opening of the triangle and the moon is full, a coincidence that denotes a total lunar
With this Minoan calculator one can further predict the total eclipse of December 10, 2011. This date comes 178 days or six more lunar months after the previous eclipse (178:29.5). Then the Moon’s pin will have completed three cycles of two lunar months each and will be on the same fullmoon line, while the Sun’s pin will have been moved by another 28 dots and it will be placed on dot no. 56 of the outer circle; the nodes in the triangles will have been moved by another three dots and will be at the point (6). The fact that one node is adjacent to the Sun and the moon is full testifies to the reliability of the device.
In order to avoid probable coincidence in the cases of the previous predictions, we
extended our testing to the future eclipses up to the year 2028 (one saros period), as
they are given in the NASA eclipse website(http://eclipse.gsfc.nasa.gov/OH/OH2010.html).
The Palaikastro device predicts, in addition to the lunar eclipses, the partial solar eclipse that will be visible from Greece on March 20, 2015. It should be noted that, in the case of a total eclipse, the positions of the nodes and the Sun are within the same region of the same triangle, while in the case of a partial or penumbral eclipse the position of the Sun is usually on the triangular region adjacent to the one where the node is.
As a conclusion it can be said that the device generated by the die of Palaikastro can be used as a competent lunar and solar eclipse calculator even to this day: In a total number of 33 eclipses only two are not predicted, giving a percentage of error of 6 percent, while 94 percent of the predictions are accurate in the course of one full saros period of 223 lunar (synodic) months.
However, a solar eclipse may well pass unnoticed for a civilization not possessing the proper equipment (partial or annular eclipse, or even no eclipse at all visible from the Mediterranean if the path is on the other hemisphere). Therefore, the device would
probably have been used primarily as a lunar eclipse predicting device in addition to its simpler uses as a sundial and a geographical latitude finder.
The Palaikastro die can be regarded as an integral part of the astronomical knowledge of the Minoans as it is evidenced by the astronomical orientations of palaces and peak sanctuaries that have been determined by archaeoastronomical research (Henriksson and Blomberg 2011, Shaw 1977).”
Research-Selection: Philaretus Homerides