sator rebus: An unsolved cryptogram?*, The

Cryptologia, Jul 2003 by Sheldon, Rose Mary

ABSTRACT: The sator square is one of the oldest, unsolved word puzzles in the world. Examples of the square and numerous variations on it, have been found in Europe, the Middle East, Africa, and the Americas. Examples date from first-century Rome to the nineteenth century. Many questions have plagued scholars: Who composed it? What do the words mean? How has it been used in magic, religion, medicine and superstition ever since? Does the solution lie with mathematicians, philologists or theologians? All these questions remain unsolved, but the number of attempts by scholars to answer them grows yearly.

KEYWORDS: Palindromes, cryptograms, rebus, sator-arepo, charms, Christian symbolism, acrostics, word games, magic squares, superstition, Latin word squares, Greekword squares.

These five words formed into a square, sometimes referred to as the Templar Magic Square, constitute one of the oldest unsolved word puzzles in the world.

The sator square has a history of at least two millennia and has appeared on all five continents. When written out as a sentence, the words form a palindrome.

As a square, the five words can be read consecutively either horizontally or perpendicularly. They appear in inscriptions in both of the versions; called the sator square (left) and the rotas square (right). The initial letter of each word spells the first word, the second letter of each word spells the second word, the third letter of each word spells the third word and so forth for the other two words. A translation of the Latin words themselves yields little. "The Sower Arepo (whatever that may mean) holds the wheels with care. "What does this message mean? Where did it come from? Is the square a cryptogram? And most importantly, can it be solved? After close to 150 years of scholarly commentary, no one has put forward a convincing solution. One scholar describes it as inhabiting the "mysterious region where religion, superstition, and magic meet, where words, number, and letters are believed, if properly combined, to exert power over the processes of nature... "1

Even recent books on the subject of magic squares only mention it briefly.2 It is my intention to place this enigma before the cryptographic community not only because of its historical interest, but also to assemble the ever-growing bibliography for easy reference in the hope that a solution may lie with the mathematically-minded rather than the philologists, ethnographers and pious theologians who have traditionally studied the problem. I have included bibliography in the text by topic rather than relegate it to footnotes in order to make it easier for the reader to reference the previously published solutions. Each entry is accompanied by a summary of the contents. A full bibliographical treatment by list in alphabetical order will appear in my forthcoming work.3

With the age of printed books, mention of the square became more widespread, and people began suggesting solutions for this ancient puzzle. Efforts to decipher the sator-formula date as far back as the fourteenth or fifteenth century. The Bibliotheque Nationale in Paris possesses a manuscript of Byzantine origin with an attempt at a translation. This is listed along with others in a comprehensive article by Dr. S. Seligman:

Dr. S. Seligman, "Die Satorformel," Hessische Blatter fur Volkskunde 13(1914), 154-183.

He has done an historical study of the sator rebus, and gives an interesting survey of the German examples of the formula. The majority of these are to be found on medals and plaques. He also discusses the various theories of origin. Here we will be examining them chronologically. Serious modern investigation of its origin and nature began in 1881 with an article by Reinhold Kohler: "Sator-Arepo-Formel," Zeitschrift fur Ethnologie 13 (1881), 301-306 and Kleine Schriften 3, 564. Since 1881, rarely has a year gone by when someone has not published a possible solution. The simplest approach was to translate the five words and then turn them into a meaningful sentence as we tried in the beginning of this article. The most frustrating aspect of this exercise, however, was that one of the words, Arepo, has no firmly established meaning. From the outset then, all constructions of the square that aimed at a direct rendering of all five words were open to question. This led some scholars to deny the possibility of producing an acceptable translation. Others advanced the idea that arepo is a nonsense word coined to provide letters needed for whatever anagram they had produced for the square, the most famous being the pater noster solution (see below). The various meanings of arepo are also discussed below in the summary of the articles in which they appear.

Another possibility suggested for the rendering of the words of the square was that it could be read boustrophedon (zigzag or literally in Greek "as the ox ploughs "), starting with the 'S' to give a complete sentence Sator opera tenet (arepo rotas). Many have proposed this approach and have construed its meaning either "as you sow, so you shall reap"or "the creator maintains his works."4