Magic Squares

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Magic square of the planet Jupiter, from J. Weirus in Opera Omnia, 1660. Courtesy Fortean Picture Library.

Magic Squares

(religion, spiritualism, and occult)

An arrangement of numbers in the form of a square so that every row and column, plus both diagonals, will add up to the same number. This number is called the constant. Each number may only appear once in the square. Magic squares have been known and used from ancient times, engraved on metal talismans and drawn on parchment ones. Used in ancient India and China, they were introduced into Europe early in the Christian era and have been found in many of the grimoires of Ceremonial Magic.

Heinrich Cornelius Agrippa von Nettesheim (1486-1535), best known simply as Cornelius Agrippa, founded several secret magical societies and wrote a number of books on magic. His best known work was De Occulta Philosophia (1531). He constructed seven different magic squares that he aligned with the seven planets: Saturn, Jupiter, Mars, Sun, Venus, Mercury, and Moon. These have become standards in ritual magic. The Saturn square is probably one of the oldest, being found in the Chinese I-Ching. Its constant is 15.

Francis Barrett in his The Magus (1801), Eliphas Levi in Transcendental Magic (1896), and others followed the lead of Agrippa, employing magic squares for a variety of purposes from protection in childbirth to making a man powerful. In 1932, S. L. MacGregor-Mathers published a translation of The Book of Sacred Magic of Abra-Melin, the Mage, purported to be the manuscript of a fifteenth-century grimoire. Much of the book is made up of magic squares for many different purposes, but the majority are comprised of letters rather than numbers. These are arranged so that the words read the same from the left, right, downward, and upward. One of these, known as the Sator formula, from the first word across the top of the square, was discovered engraved on old drinking vessels and on fragments from a Roman villa near Cirencester, England. It was believed that a witch could not stay in the same room as a talisman engraved with the Sator square.

Great care had to be exercised when constructing magic squares. When drawn on parchment, the squares should be marked in black ink with the numbers or letters in red ink. All should be drawn with the parchment set up so that the maker's shadow does not fall on the parchment. The red lines should not touch the black anywhere. As with all magical items, it should be appropriately consecrated before use.

References in periodicals archive ?
One of the most important extensions of magic squares began with a paper of the great mathematician Leonhard Euler published in 1776, which was then refined in the 19[sup.
Next, ask them to step back a little and make up a 2 x 2 magic square.
Indeed, it would seem at first glance that the method of construction for this type of magic square was not properly understood by the author of this amulet; for even though errors in magic squares are not uncommon, (5) we here find the same number (261) repeated twice.
Now following is the magic square in the form of Smarandache functions.
Since then the popularity of magic squares has spread to the rest of the world.
The "magic" will always refer to a magic square and our idea starts with the famous 3x3 LoShu square of ancient China.
Note that the game is a draw if the players succeed in making a Magic Square which totals fifteen.
These magic squares may have applications m tournament schedules.
Magic counting A physicist established that Benjamin Franklin's remarkable magic squares are just three of more than a million possibilities (scieneenews.
Moreover, he found that there are even "translation" relationships among them: either two primary magic squares could share the same secondary logorithmic magic square, or one primary magic square could be alphamagical in more than one language.
Even today some people think that these magic squares can bring good luck and ward off evil spirits.