Infinitum

Sator Square

The Sator Square is a word square containing a Latin palindrome featuring the words SATOR AREPO TENET OPERA ROTAS written in a square so that they may be read top-to-bottom, bottom-to-top, left-to-right, and right-to-left. The earliest known appearance of the square was found in the ruins of Herculaneum which was buried in the ash of Mt. Vesuvius in 79 AD. Therefore, its origins may well predate the Christian era.

The usual translation is as follows:

Sator

‘Sower’, ‘planter’

Arepo

Likely an invented proper name; its similarity with arrepo, from ad repo, ‘I creep towards’, is coincidental

Tenet

‘he holds’

Opera

‘works’, ‘(cares)’, ‘efforts’

Rotas

‘wheels’

Two possible translations of the phrase are ‘The sower Arepo holds the wheels with effort’ and ‘The sower Arepo leads with his hand (work) the plough (wheels).’ C. W. Ceram read the square boustrophedon (in alternating directions), with tenet repeated. This produces Sator opera tenet; tenet opera sator, translated: ‘The Great Sower holds in his hand all works; all works the Great Sower holds in his hand.’ (Ceram 1958, p. 30)

The word arepo is enigmatic, appearing nowhere else in Latin literature. Most of those who have studied the Sator Square agree that it is a proper name, either an adaptation of a non-Latin word or most likely a name invented specifically for this sentence. Jerome Carcopino thought that it came from a Celtic, specifically Gaulish, word for plough. David Daube argued that it represented a Hebrew or Aramaic rendition of the Greek Αλφα ω, or “Alpha-Omega” (cf. Revelation 1:8) by early Christians. J. Gwyn Griffiths contended that it came, via Alexandria, from the attested Egyptian name Ḥr-Ḥp, which he took to mean “the face of Apis“.

The oldest known representation of the Sator Square was found in the ruins of Herculaneum. Others were found in excavations at Corinium (modern Cirencester in England) and Dura-Europos (in modern Syria). It should be noted that the Corinium example is actually a Rotas Square; its inscription reads ROTAS OPERA TENET AREPO SATOR.

Other Sator Squares are on the wall of the Duomo of Siena and on a memorial, near the site where composer Anton Webern was shot in 1945.

An example of the Sator Square found in Manchester dating to the 2nd century is considered by some authorities to be one of the earliest pieces of evidence of Christianity in Britain. Like the Corinium square, the Manchester square reads ROTAS OPERA TENET AREPO SATOR.

Other authorities believe the Sator Square was Mithraic in origin.

An example is found inserted in a wall of the old district of Oppede, in France’s Luberon.

There is a Sator Square in the museum at Conimbriga (near Coimbra in Portugal), excavated on the site.

Magical uses

The Sator Square is a four-times palindrome, and some people have attributed magical properties to it, considering it one of the broadest magical formulas in the occident. An article on the square from The Saint Louis Medical and Surgical Journal vol. 76, reports that palindromes were viewed as being immune to tampering by the devil, who would become confused by the repetition of the letters, and hence their popularity in magical use.

The square has reportedly been used in folk magic for various purposes, including putting out fires, removing jinxes and fevers, to protect cattle from witchcraft and against fatigue when traveling. It is sometimes claimed it must be written upon a certain material, or else with a certain type of ink to achieve its magical effect.

Numerology

Using numerology, one can assign the value 1 to the letter A, 2 to the letter B, and so on, up to 26 for the letter Z. Then, adding the values assigned to the letters in the rows and columns of the Sator square yields the following:

       S A T O R  73
       A R E P O  55
       T E N E T  64
       O P E R A  55
       R O T A S  73

Each of these values digit sum to 10 and therefore also to 1, which some numerologists maintain gives the square “extraordinary powers”.

Tags: Magic, numerology, puzzle

The Knight’s Tour

The Knight’s Tour is a mathematical problem involving a knight on a chessboard. The knight is placed on the empty board and, moving according to the rules of chess, must visit each square exactly once.

There are a great many solutions to the problem, of which exactly 26,534,728,821,064 have the knight finishing on a square from which it attacks the starting square, on an 8 × 8 board. Such a tour is described as directed and closed. (A directed tour is a directed graph: the direction of the tour is specified. A closed tour is one that ends on the starting square.) The number of undirected closed tours is half this number, since every tour can be traced in reverse. Otherwise the tour is open (as in the first diagram). There are 9,862 undirected closed tours on a 6 × 6 board, and no such tours on smaller boards.

The pattern of a Knight’s Tour on a half-board has been presented in verse form (as a literary constraint) in the highly stylized Sanskrit poem Kavyalankara^[4] written by the 9th century Kashmiri poet Rudrata, which discusses the art of poetry, especially with relation to theater (Natyashastra). As was often the practice in ornate Sanskrit poetry, the syllabic patterns of this poem elucidate a completely different motif, in this case an open knight’s tour on a half-chessboard.

The first algorithm for completing the Knight’s Tour was Warnsdorff’s algorithm, first described in 1823 by H. C. Warnsdorff.

Tags: Knights, puzzle