Mediterranean Archaeology and Archaeometry, Vol. 15, No.1 (2015) pp. 135-149 Copyright © 2015 MAA Open Access. Printed in Greece. All rights reserved. ASTRONOMICAL AND MATHEMATICAL KNOWLEDGE AND CALENDARS DURING THE EARLY HELLADIC ERA IN AEGEAN “FRYING PAN” VESSELS M. Tsikritsis1, X. Moussas1, D. Tsikritsis2 1 Department of Astrophysics, Astronomy and Mechanics, Faculty of Physics, School of Sci- ence, National and Kapodistrian University of Athens, Greece 2University of Edinburgh, Edinburgh, Scotland, United Kingdom Received: 18/08/2014 Corresponding author: X.Moussas ([email protected]) Accepted: 18/12/2014 ABSTRACT Analysis of the symbols engraved on prehistoric unknown use terracotae, the so called frying pan vessels (Teganoschema), reveal a symbolic writing that depicts astronomical phenomena, that are complex calendars based on the Sun and the Moon and all then known planets. The frying pan vessels are mainly found in Cyclades, and around the Ae- gean, Crete, Attica, and Thessaly. They are artifacts of the Cycladic civilization of the Ear- ly Helladic Era. They have been found mainly in graves and settlements. The first find- ings came to light during the late nineteenth century in the islands of Cyclades and their possible use is still causing strong scientific interest, as it is unknown. Until now, archae- ologists could not determine their use and the meaning of their representations. It was believed that these vessels were used in funeral rituals, therefore depicted patterns like the sun and the sea may be associated with beliefs about the afterlife. We have studied the morphology and the representations of the Cycladic frying pan vessels that are found in museums and in literature dating from the middle of the 4th millennium. In this paper we argue that the Cycladic frying pan contain calendars that are not only based on the periodicities of the Sun and Moon, but in a very advanced knowledge of the movements of the planets, their periodicities in relation to the Earth and the phases of Venus, which is used as calendar, as well as pregnancy and birth predictor calculator.. KEYWORDS: calendars, prehistoric astronomy, prehistoric mathematics, ancient astron- omy, ancient mathematics, frying pan vessels, pregnancy calculator, prehistoric Greece, prehistoric Europe, Aegean, Cyclades. 136 M. TSIKRITSIS et al 1. INTRODUCTION summations. The symbols vary with time The role of astronomy is crucial in all so- and region in the Greek seas. cieties from the dawn of humanity. Socie- Frequently terracotae that have the peri- ties from prehistoric times realize that their od of Venus have an eight rayed star like lives depend upon climate and seasons the Macedonian star, which naturally is which they realize change with the changes related with the eight year period of Venus, of the sunrise position on the horizon. while one of them has a five rayed star Gatherers relate collection of food, fruits which represents the 5 synodic periods of and hunters and fishermen organize fish- Venus in 8 solar years, which is one of the ing and hunting, with seasons and the symbols of Pythagoreans. Consequently phases of the Moon. Eventually they real- one can say that there was some sort of Py- ize that using astronomy and appropriate thagoreans four millennia before Pythago- mathematics enables humans to know ras. when to act properly in agriculture, to cul- tivate, to seed etc. Ancient civilizations 2. PERHISTORIC ASTRONOMY AND governed their lives influenced by natural FRYING PAN VESSELS phenomena, especially with the movement At this point some simple astronomical of the Moon (Liritzis and Kosmatos, 2005). knowledge is presented to understand bet- In this article new evidence based on the ter the astronomical finds on frying pan interpretation of marks and decorations on vessels. The Sun is the centre of the solar prehistoric terracotae (4400 to 2000 BCE) system and the planets move in ellipses named frying pan vessels (from their around the Sun. As humans observe the shape) indicates that during the Early Hel- sky every night they see the stars rotate ladic Era humans in the Aegean probably around the axis of the Earth, or axis of the record astronomical phenomena with the Cosmos, at a rate of 15 degrees per hour. aim to predict the position of the planets Observing the sky for long they realize that based on their periodicities. some astronomical bodies some of the The study indicates that humans at pre- brighter ones, move with respect to the historic times in Greece have knowledge of fixed stars. These are the planets, the wan- astronomy, they understand and use suc- derers, as their name implies, that move cessfully causality with accurate mathemat- with variable speeds, but with certain peri- ics that they have developed to describe odicities. and use the “laws of nature” they discover, On these terracotae the astronomical i.e. the periodicities and periods of planets phenomena are recorded with their peri- and probably the phases of the planet Ve- ods, the periods of the planets as seen from nus. the Earth, as a human living on Earth sees This study of the symbols on these terra- them, in the Geocentric system. These cotae indicates that they have developed numbers are very characteristic and unique some “advanced” mathematics that enable and every planet has a distinct number of them to use various symbols that enable days which give the identity of the celestial them to use large numbers (hundreds of body, the particular planet. days, expressed with symbols each repre- The most important periodicity of a senting a number, unity, the number 7 or planet (or the Moon) is the synodic period, 14 or 28, using multiples of them and more which is the time period the planet takes to rarely another number sometimes ex- reappear in the same position with respect pressed with the number of rays of star like to the Sun, as seen from Earth. central image that probably represents the It can be measured from syzygy, i.e. Sun. when the planet and Earth are approxi- The numbers and their multiples are ex- mately on the same line with the Sun to the pressed with symbols, multiplications and next syzygy. In particular we call the con- Mediterranean Archaeology and Archaeometry, 15, 1 (2015) 135-149 ASTRONOMY AND CALENDARS IN PREHISTORIC GREECE 137 junction for the outer planets (Mars, Jupi- days. This is the result of the very strong ter, Saturn) when the planet is behind the light of the Sun that makes planets invisi- Sun, when the Earth the Sun and the planet ble, when they are at a small angular dis- are in approximately the same line. We call tance from the Sun. opposition when the Earth is right in the All planets move around the Sun in the middle between the Sun and the planet, same sense, the direct or prograde motion. again in almost a straight line. For the inner The planets as seen from Earth that moves planets, Mecrury and Venus, we call inferi- too around the Sun perform a backward or conjunction when the planet is between motion for a period of time as seen from the Sun and the Earth and superior con- Earth. This backward motion is called ret- junction, when the planet is behind the rograde motion. Sun. For the inner planets we name largest Venus performs a retrograde motion for Eastern (or Western) elongation from the 20 to 21 days before and after the inferior Sun, the largest angular distance from the conjunction, and reaches the highest ap- Sun as seen in the morning or evening. parent brightness approximately 35 to 37 Inner planets are the planets with orbits days before the inferior conjunction as inside the orbit of the Earth, i.e. Venus and well. When the maximum apparent bright- Mercury, which some ancient Greek au- ness is reached, Venus is found on the east thors call solar planets. Superior planets, of the horizon at approximately 47 degrees. those having orbits larger than the Earth‟s, Afterwards until the inferior conjunction, can have only superior conjunctions with its brightness and height respectively to the the Sun. horizon is reduced. Synodic period is the time required for a After the inferior conjunction, Venus is celestial body within the solar system to observed in the West with increasing return to the same or approximately the brightness and within the following 35 same position in its orbit relative to the days reaches its maximum brightness, Earth and Sun. For example, it can be the while this angular distance from the Sun is time between two conjunctions, opposi- again the 47 degrees. For the following 228 tions, etc. In this paper we will use the term days, the brightness decreases while Venus synodic period for denoting the time inter- goes around the Sun. After these 228 days val between two successive conjunctions of (9 lunar months), Venus becomes invisible a planet with the Sun. due to its passage behind the Sun, and then Venus appears in the sky before the sun- reappears in the East. During moonless rise for 263 days and then after the sunset nights, when Venus has maximum bright- for 263 more days. The 263 days corre- ness (at 47 degrees from the Sun), its light spond to approximately nine lunar months creates soft shadows on the ground seen by (265 days). The fact that Venus orbits the good observers, as described by ancient Sun in 224.65 days and the Earth at 365.256 astronomers. days, it can be determined the synodic pe- From our analysis of the symbols on the riod from the following relationship: frying pan vessels, it is possible that some prehistoric people that probably already Synodic period= knew well the motions and the periodici- 1/(1/224 .65 - 1/365.25)=583.91days ties of the Sun and the Moon, all the plan- ets were a high interest too, based on our The synodic or conjunction period of interpretations of the records on frying pan Venus is a period of 584 days.