The Double Quincunx

One important feature of the 3x3 magic square is the quincuncial relationship of even and odd numbers around the center number. A quincunx is defined as an arrangement of five things with one at each corner and one at the center of a square. The even numbers of the first nine numbers will occupy the corners (or four quadrants) and represent earth, the odd numbers will form a cruciform with the number five at the center and represent heaven; this is known as a double quincunx. To the early Chinese, this model of numerology represented heaven and earth in microcosm, the four cardinal directions and the "cosmic center" or the meeting of heaven and earth. This model also represented time and space as well as establishing universal order by the application of mathematics. In summary, this is what makes this motif a cosmo-magical design that was used by many cultures throughout history.

All magic squares in the Luo Shu format will have a cross of odd numbers that run through the vertical and horizontal axis. The odd and even numbers pivot around the center, or axis mundi, the point at which heaven and earth coincide—hence the reference to the “cosmic center.” 

Examples of Iznik tiles adorning the Rustem Pasha Mosque, c. 1560, Istanbul, Turkey.

Turkish carpet, c. 18th century, Turkish and Islamic Arts Museum, Istanbul, Turkey.

Morosque tile, c. 15th century, from the Countess of Lebrija Museum, Seville, Spain

Morosque textile, c. 1350 from the Lazaro Galdiano Museum, Madrid, Spain.

Roman mosaic from Caligula's ship, 1st century. Museum of Roman Ships, Nemi, Italy. 
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Illuminated manuscript, Lindau Gospels, c. 9th century, Morgan Library, NY, USA. First known western usage of the Chinese Magic Square. 

All these images originate from different cultures and have incorporated the model of the Chinese Magic Square which generates the artistic geometry that became a common motif for the last two thousand years. The oriental influence on art and architecture can now be further explained by examining the numerology of the Chinese Magic Square of Three also known as the Luo Shu.

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effective date of registration: January 30, 2025
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Author: Robert Dickter

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