The 3×3 magic square is believed to provide much wisdom to those who study it. Since it houses the numbers one through nine in an arrangement considered magical, it is of no wonder why. From its first appearance, this grid of nine cells has captured the fascination of many with its numeric relationships portrayed inside its border.
The squares are considered magical if the numbers contained within the rows, columns, and diagonals sum to the same amount. A 3×3 magic square’s constant is number fifteen. Although there are numerical tables of larger size which are believed to display powerful, influential qualities, the smaller 2×2 square cannot be found magical. Some feel the four numbers relate to the four elements (fire, earth, air, and water) and this lack of ability to be balanced, resulted from man’s original sin. The smallest square, holding only the numeral one, has been considered by Agrippa to be God’s magic square and represents His eternal perfection.
Geber, one of the first practicing alchemists, associated important characteristics and values to the 3×3 magic square. The number seventeen, produced by adding the four, bottom left, corner cells of the numbers, one, three, five and eight was seen especially significant. This, in turn, left the gnomon (the remaining five numbers) to value twenty-eight.
Both these numbers of 17 and 28 were powerful to Geber and are also found connected to the Egyptian god of Osiris. Plutarch, in his work entitled Moralia, writes how it was believed the 17th of Athyr was the date on which Osiris (Egyptian god of the underworld) was killed. In some accounts, Osiris had lived for 28 years. In others, it was he reigned for 28 years. Either way, the numbers of 17 and 28 are noticed in association to the life and death Osiris. The total sum of 45 in the 3×3 magical square, divided in this way, could be seen to represent this aspect of Osiris.
According to the myth of Osiris, he was murdered by his brother Set and was later resurrected by Isis, his wife. Because of the violent act which happened upon the 17th date, Plutarch shares Pythagoreans felt seventeen was a detested number. They also considered it to be ‘the barrier.’ Seventeen was realized to separate the only two numbers where the perimeter values of their rectangular shape encloses the same area as their own perimeters. The perimeter of a square of 16 (4+4+4+4=16) equals its area (4×4=16). The same appears for the number 18. The perimeter of a rectangle of 18 (3+6+3+6=18) is the same as the area, 3×6=18.
The number 17 was realized to stand between these two numbers in another way, as well. In the following answer to the problem; “what is the number, where the 1/8 of a number added to its self, equals 18?”, seventeen is again seen to separate a relationship between the two numbers of 16 and 18. (If one takes an eighth of number 16 (which is 2), and adds it to 16, the answer is 18).
Interesting correlations remain. The life of Osiris of twenty-eight years connects with the gnomon of the 3×3 magical square. The whole square can be seen broken by the number 17, his date of death. But, as the definition for the word gnomon is ‘that which knows’, one may wonder if a deeper and secret understanding isn’t to be found between these two numbers of 17 and 28.
Plutarch, Moralia, reviewed December 2012
Pickover, Clifford, The Zen of Magic Squares, Circles and Stars, Princeton University Press, 2002