Magic squares in cultural history

Detailed history in progress

Magic matrices, with their almost impenetrable permutations, have a particularly symbol-laden history. The earliest magic square - the order three or Lo Shu (above left) - is enshrined in China as an integral component of many extant cultural practices (Hean-Tatt 1991), all united by the same long-established respect for mathematical precision and inquiry that inspired Leibniz in his development of the binary system that became a crucial component in the development of computing.

In the ninth century, Arabian astrologers used magic squares to interpret horoscopes, but the earliest recorded order four square is a Jaina inscription from between 1000-1100 CE within the remarkable temple complex at Khajuraho in Madhya Pradesh, central India.

The Indian vedic square (the multiplication table from 1x1 to 9x9 as a matrix of integers reduced to single numbers (or digital root) later became a cornerstone of Islamic art (Critchlow 1976) where the central cell of particular order five magic squares, occupied by the number 1, is left blank as the number of deity.

In the 15th century, Cornelius Agrippa associated the known planets of his time with squares of orders 3-9. The magic square had already been appropriated in some cultures as everyday magical talismans; and the varied glyphs formed by tracing the magic line (where each number from 1-n2 is joined in numerical sequence) have been the subject of complex ritual practices.

These rich threads of association first surfaced in western art sometime in 1514 behind the famous brooding angel's head in Albrecht Dürer's 'Melancholia I' (there is no known 'Melancholia 2'). Setting aside interpretation of the engraving's details, the scene itself is - significantly - said by Frances Yates (reinstating a neglected Renaissance view of melancholy as a portal to wisdom) to depict 'the melancholic inspiration of the artist-scientist' (Yates 1983).

A small photograph of Subirachs magic square, Sagrada Familia, Barcelona

In more recent times, on one façade of the Gaudí-designed Sagrada Familia Cathedral in Barcelona, the sculptor Subirachs placed an order four magic square.

References

Critchlow, Keith. (1976). Islamic Patterns: an Analytical and Cosmological Approach. Inner Traditions, Rochester, Vermont, 1999 (US Reprint).

Hean-Tatt, Ong. (1991). The Chinese Pakua: an Exposé. Pelanduk Publications, Selangor Darul Ehsan, Malaysia.

Yates, Frances A. (1979). The Occult Philosophy in the Elizabethan Age. Ark Paperbacks, London, 1983.