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- Symonds Yat, the Wye
Valley and the Royal Forest of Dean
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Frequently Asked Questions
Symonds Yat West, Ross-on-Wye,
Herefordshire HR9 6DA, England
info@mazes.co.uk
Phone or fax +44(0)1600 890360
http://www.mazes.co.uk
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Maze Analogues
"Men forget where the way leads..."Heraclitus, Fragment V, 6th century BC
Maze Analogues were not known as mazes, but they have very similar symbolism. Strikingly, they are all based on some form of permutation, and there is often a single preferred solution. Like the unicursal labyrinth (which is also a combinatorial puzzle), Maze Analogues have an infinite number of solutions and it is not immediately apparent that they are chaotic.
- LITERARY MAZES & LATIN SQUARES:
- These were sentences which could be read in many ways - either through ambiguity, or a transposition of letters or words in a matrix - and there are many types. Although they were multicursal, they were used as a type of Magical Maze by Roman Christians. They have been around for at least 2,300 years, the earliest known examples being in the books of Daniel and Isaiah which were incorporated into the Old Testament of the Bible (the common scripture of Jews, Christians and Muslims) about 1,900 years ago.
- MAGIC SQUARES:
- These are arrangements of numbers in a grid, such that the sums of each row and column is a common number. They are set out systematically by a number of algorithms. In Qabbala mysticism, lines linking consecutive numbers form patterns which, by their similarity to signs of the zodiac, make them symbols of the planets. In Sufi mysticism, the numbers represent letters which further form literary mazes which are linked to the names of prophets. In Taoist mystic tradition, the numbers are represented in arrangements of an emblem called Ba Gua, and symbolise family members, the elements, and the land. In the Greater Vehicle of Buddhism they are the "universal Calculator" at the centre of the calendar and in Shinto they are used in astrological calculation.
- COMPUTI:
- These are tables and diagrams
used to calculate precession of the phases of the moon, outcasts in
dipping-games, or the dates of Movable Feasts. Logically, the
construction of these computi should involve difficult Modulo
Arithmetic, but in practice many Dipping Rhymes contain an encrypted
mnemonic for their solution. Skill at cheating in finding a solution
forms the basis of St. Peter's Game (a variant of the 2,000 year old
"Josephus' Problem"). Diagrams of the solutions of St. Peter's Game are
effectively linear representations of Mystic Roses.
Mystic Roses are stars which can be drawn by linking the corners of regular polygons without lifting the pencil from the paper. They include the Pentagram (a five-pointed star inside a pentagon), which can be drawn in 264 ways. One of these solutions was symbolic of health to Pythagorean "Mathematicians" - and it calculates the precession of heliacal risings of the planet Venus through the zodiac. The ancient Romans used the Mystic Rose of the heptagon to ensure dedication of the hours to the correct gods. In Taoism, the Mystic Roses of the octagon are represented in certain arrangements of Ba Gua. The Magic Square was used as a computus.
- POLYSKELIA:
- Versions include: the Hakenkreuz (hooked cross), Farmer's Fylfot, and Swastika (four-legged); Rgyan-'k'yil (three-legged); and Yin Yang (two-legged). The latter is the central figure of Ba Gua, and in the Magic Square configurations of Ba-Gua, the elemental symbols are arranged around it in pairs which form a swastika when they are joined by lines. Like the heptagon, it represents the number 5. The path of a Roman Maze is a path around the outside of a Polyskelion, usually a hakenkreuz.
- MEANDERS:
- These include the Greek Key-Pattern and Swastika-Meanders. They can be extended to form tesselations and "Celtic" Knot patterns (which are probably of Pictish origin), or deformed to make Classical Mazes or linked to make Roman Mazes. The Greek key-pattern was used to symbolise earth or the underworld.
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