Sunday, March 9, 2008

Magic Square: Worlds in Space-Time

For milleniums, all these multi-pattern squares have served as boardgames and temple decoration all around the world.

Tic-Tac-Toe or three-in-a-row is one of the most famous square used as a boardgame.

One needs to make three in a row orthogonally or diagonally and block their opponent from completing three in a row. Considering winning combinations, there are 255,168 possible games and 362,880 ways of placing your pieces and your opponent's pieces on the board. Regarding the boards previously showed, all strategical rules are all the same: blocking your opponent from making a row (a chain), and making your own. A similar process of blocking a cell from making a chain of proteins.

This square was found in Lascaux and dated back to 15,000-12,000 BC. A rare abstractive figure for that time. Actually, once can notice the 9 squares (3x3) of the magic square.

Symetrical figures are created when numbers are linked orderely.

Lo Shu (it means book of the river) is part of the legacy of the most ancient Chinese mathematical and divinatory tradition (over 5000 years old). The odd and even numbers alternate in the periphery of the Lo Shu pattern, the 4 even numbers are at the four corners, and the 5 odd numbers(outnumbering the even numbers by one) form a cross in the center of the square. The sums in each of the 3 rows, in each of the 3 columns, and in both diagonals, are all 15 (fifteen is the number of days in each of the 24 cycles of the Chinese solar year). Since 5 is in the center cell, the sum of any two other cells that are directly through the 5 from each other is 10.

The magic square based on a binary system

According to Wim van Binsbergen : In the most archaic Sumerian writing (ca. 3000 BCE) the agricultural field was simply represented by a rectangle divided by vertical lines: the image of a field divided by irrigation ditches...which ultimately led to the standard character.

In Chinese (Hân Yîng Cídian 1988; cf. Wieger 1965: 316f) the character for field is (t'ien):

This representation of ‘field’ is already attested in the most archaic Chinese writing on seals and oracle bones (2nd mill. BCE), as:

In Ancient Egyptian hieroglyphic, again, the oblong grid: has the cognate meaning of ‘district’, "administered land area" (Faulkner 1962: 54, 178 and passim) — which was rendered in Greek as nomós, and is generally¸considered to represent a (manually) irrigated field.

This board was often found associated with a game called the "Alquerque". The word alquerque might come from the Arabic word "El-Quirkat" meaning "the mill".

Alquerque is known to date back at least as far as 1400BC, since boards have been found cut into the roofing slabs of the temple at Kurna in Egypt. A game called Quirkat is mentioned in an Arabic work of the 10th Century AD.

Alquerque in the wall of a medieval mill in "Arroyo de los Molinos", Andalucia, Spain.

From the "Catedral de Ourense" (Orense), in Galicia, Spain.

Nine Men's Morris or Merels board

Supposedly, the first carved board ever discovered was found 3500 years ago at the temple of Kurna, Egypt. However, in 2006, archeologists have found a Men's Morris engraved stone dated back to the last Ice Age. The last Ice Age started about 50,000 years ago and ended around 8,000 BC.

This engraved rock is thought to be an early games board (Nen Men's Morris). Photo Creswell Heritage Trust. Creswell Crags, England is a Scheduled Ancient Monument and Site of Special Scientific Interest and could also become a World Heritage Site.

Even, Earth and Underworld

The science of trinity...

According to Bengt Hemtun, " This is the Gateway to Underworld made of clay to manifest the concept..."

"To that we can add this golden plate from a Stonehenge grave. The groves show the three steps to Underworld."

1 comment:

Nikita said...

this is really amazing stuff!! shows us that people had a knowledge not only of maths but the power,logic and magic in maths a long time before the Pythagoreans.