NUMBER SYSTEMS AND CALENDARS OF THE BERBER POPULATIONS OF GRAND CANARY AND TENERIFE
by Jose Barrios Garca

In the 14-15th centuries Grand Canary and Tenerife were inhabited by Berber populations, called Canarians and Guanches. They presumably came from the nearby continent on different occasions between the first millennium BC and the first millennium AD. These populations remained relatively isolated until the European rediscovery of the Islands in late 13th century. At this time the population of each Island was about 40-60,000 inhabitants, sustaining a developed agricultural (barley, wheat) and stock raising (goats, sheep, pigs) economy.

Written sources from c. 1300 AD on certify the arithmetical and calendrical activities of these groups. On this basis, I started the research on the mathematical and astronomical practices of these people that crystallized into my doctoral dissertation (editors note: congratulations to Jose for his recent defense of thesis at the University of La Laguna, Tenerife). For each Island the study considered: 1) the economical, social, political and religious organization of the Island 2) the written and archaeological evidence regarding numerical and calendrical activities 3) the economic and cultural context of the number systems and the calendars.

Both Islands used a pure 10-based system, deeply related to both proto-Berber and ancient Egyptian numeral systems, without discarding the possibly concurrent use of a 12-based system related with calendrical counts. Drawing evidence from ethnographic written sources I establish the existence of systematic records of lunar, solar and sidereal counts for both Islands.

The research for Grand Canary is complemented with an archaeoastronomical study of the mountain of Cuatro Puertas, usually considered of great religious importance. From the evidence collected I infer that at its top there is a summer solstice marker which works by mean of the shadow a certain rock casts at sunrise upon a great sign carefully carved on the opposite wall.

Archaeological, ethnohistorical and linguistic evidences led me to propose that the Canarians systematically recorded numerical, astronomical and calendrical data by mean of geometrical figures (squares, triangles, circles, etc.) painted in white, red and black on wood planks and on the walls of certain caves. Evidence from the decoration of the Painted Cave of Galdar (the main preserved painted cave of the Island), led me to propose they use a chessboard of 3 (vertical) x 4 (horizontal) squares, named acano, to represent 12 moons. On this base, I proceed to study the acano as a lunar calendar, showing how the vertical numeration of its squares force the solstitial, equinoctial and eclipse moons to move across the board with very simple and stable patterns. These patterns provide a safe and clear mnemonic guide for performing on the acano an easy arithmetical calculus of seasonal and eclipse moons over extended periods of time.

The proposed calculus establishes the octaeteris and the 135-moon eclipse cycle as basic periods of the acano. The Canarians certainly observed the summer solstice and had important festivals on the crescent moon that followed. I present two accounts from ancient sources supporting the idea that they measured one and half eclipse years as 520 days. The proposed calculus on the acano would reveal an unsuspected high level of Canarian mathematical astronomy and pose the question of the origin of this set of techniques.

My main thesis with respect to the Guanche calendar, is the fundamental role played played by the phases of the star Canopus. Its heliacal rise about middle August fixed the first moon of the Guanche lunar calendar, while its heliacal set on late April and its acronical rise on late January fixed the two other well documented feasts of the Island. The Guanche cult to this star was later transferred to what have been by far the main Catholic cult of the Island after the conquest: the Virgin of Candelaria. Additional evidence drawn from continental Berbers supports the antiquity and widespread of a Canopus cosmological system in Northwest Africa.

On the Guanche record keeping, written sources point out the use of tally woods and, very specially, small clay beads joined with a string to form a sort of necklaces, commonly found in funerary caves. Nevertheless, the absence of well preserved examples in a reliable archaeological context impede testing these accounts. My Thesis ends with an Appendix, listing c. 140 manuscripts, copies or editions of the 31 written ethnographic sources supporting the research, and ranging from 14th to 17th centuries.