Beyond Magic Squares
Yahya Fiuzi, architect
Iran, January 29, 2004


In 1974, during a journey to the dessert and finally to the city of Yazd, in an antique store, a torn, folded piece of fabric attracted me. This delicate fabric displayed a graphic order of 10,000 numbers. A square divided into 10,000 smaller squares, 100 on each side. These 10,000 numbers in red and black were placed in a special ordered relationship. I was not familiar with the work or the meaning of these numbers. But what I did understand is that if one adds up the numbers along any vertical or horizontal line, one finds that the sums are equal in numeric value. I also learned that the agreed name for this type of work was the magic square.

The first recorded discovery of magic squares can be traced back to the Chinese culture. The Chinese were fascinated by patterns. The simplest magic square consisting of numbers from 1 to 9, is as old as 2000 years. It is a 3x3 graph with the sum of each row and column arriving at the numeric value of 15. Creating a magic square by utilizing conventional mathematics, probability or even computer science is very difficult. For example, in the 4x4 order which has only 16 numbers, one will have to create a total number of charts equal to 1x2x3x...x16>2x1013 in order to find the one that will qualify as a true magic square.

Only one chart from this large number will have the qualities of a magic square. If we presuppose that for each row 1/1000 of a second is necessary, it will take eight months to sift through all possible variations of numerical order to find the one that works. It is therefore necessary to have a certain level of wisdom in addition to specialized talent in mathematics, geometric methods, layering patterns and interrelationships in order to work with and truly grasp the essence of the magic square system.

The 4x4 magic square was created hundreds of years later in the 5th century of the Islamic calendar and sprouted in Islamic countries. This square was named after the planet Jupiter–Bergis or Keivan. Iranians expanded the 4x4 magic square with unbelievable genius. This development used a linear method and incorporated an unlimited amount of numbers. The only weakness of this graphic order is that it does not incorporate a center and it is therefore more like a puzzle or mosaic.

The first Islamic Empire which lasted from 650-750 AD was a very unique period in history which witnessed incredible scientific and intellectual achievements. During this period, mathematical research was suspended in Europe and the center of science and mathematical discoveries was relocated to the Darolhekmeh or House of Wisdom in Baghdad. Books of Greek philosophy, science and geometry were translated and new books on mathematics and astronomy were written. In addition, descriptive mathematic and astronomical graphs were created and slowly established in societies.

Government officials asked scientists to build a calendar system using numbers related to words and the meanings of words. These projects explored the mysteries of the rotation of the earth, the moon, the sun and the stars. As a result, astronomical events were predicted and used in relation to the activities on earth. These predictions instilled a new belief system in society, which explained the relationships between the length of days and nights, the four seasons, the lunar and solar calendars and concrete historical events and facts of earthly life in terms of the mystery inherent in numbers. Good numbers cast in good charts, bearing Qoranic verses and prayers were integrated and painted on telesmanic shirts to protect human life against disastrous events.

By using a numeric base as well as the Arabic or Abjad alphabet (whereby selected letters substituted for numbers), one thousand names of God became numeric value. The science of arithmomancy was established and various charts of arithmomancy were prepared. These numbers indicated good and bad days and when the charts displaying the same mysterious magic squares combined with sound science and astronomy, the idea to map the sky, the placement of stars, their orbits and constellate order became a powerful tool. Interpretations of numbers indicating the distance between the stars were established, imaginary squares were predicted in the plan of the sky. But there were no methods, proofs or reasons to explain that these charts and numbers were in fact related to the placement of the stars, galaxy, or order of space.

The Mayan civilization which goes back 3000 years, had a sacred calendar that had 260 days which is divisible by the numbers 13 and 20. The 8x8 chart of the mysterious magic squares which Benjamin Franklin discovered, in all vertical and horizontal rows have a sum of 260. From this perspective, one can see that similarities between the sacred Mayan calendar, magic squares, the I Ching codes, the art of Raml and Astrolabe exists.

As an architect, it occurred to me that the magic square could be the base for designing patterns, introduce harmony in weight, wave length, colors and/or distance. I began my work with the smallest and simplest square, and converted numbers to colors. For converting numbers to colors, I began with a base of 3 and eventually higher bases inherent in Calcule Resonable, which I utilized in my method. Hundreds of art work were created which were harmonic from the point of view of color, rhythm and relationships which followed different sequences between numbers and fractions. In addition, by expanding the charts to the third dimension, I discovered elliptical forms with numerous centers. This discovery was unprecedented. The many centers found in the elliptical form indicated the movement and orbit of the planets in the constellate order of space.

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