A27.Inglish BCEnc. Blauwe Kaas Encyclopedie, Duaal Hermeneuties Kollegium.

Inglish Site.27.
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TO THE THRISE HO-
NOVRABLE AND EVER LY-
VING VERTVES OF SYR PHILLIP
SYDNEY KNIGHT, SYR JAMES JESUS SINGLETON, SYR CANARIS, SYR LAVRENTI BERIA ; AND TO THE
RIGHT HONORABLE AND OTHERS WHAT-
SOEVER, WHO LIVING LOVED THEM,
AND BEING DEAD GIVE THEM
THEIRE DVE.
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In the beginning there is darkness. The screen erupts in blue, then a cascade of thick, white hexadecimal numbers and cracked language, ?UnusedStk? and ?AllocMem.? Black screen cedes to blue to white and a pair of scales appear, crossed by a sword, both images drawn in the jagged, bitmapped graphics of Windows 1.0-era clip-art?light grey and yellow on a background of light cyan. Blue text proclaims, ?God on tap!?
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Introduction.
Yes i am getting a little Mobi-Literate(ML) by experimenting literary on my Mobile Phone. Peoplecall it Typographical Laziness(TL).
The first accidental entries for the this part of this encyclopedia.
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This is TempleOS V2.17, the welcome screen explains, a ?Public Domain Operating System? produced by Trivial Solutions of Las Vegas, Nevada. It greets the user with a riot of 16-color, scrolling, blinking text; depending on your frame of reference, it might recall ?DESQview, the ?Commodore 64, or a host of early DOS-based graphical user interfaces. In style if not in specifics, it evokes a particular era, a time when the then-new concept of ?personal computing? necessarily meant programming and tinkering and breaking things.
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Index.
107.Enochian/Rosicrucian chess.
108.String Theory.
109.Sufism.
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107.Enochian/Rosicrucian chess.
Enochian chess is a four-player chess variant, similar to Chaturanga, associated with the Hermetic Order of the Golden Dawn. The name comes from the Enochian system of magic of Dr. John Dee (magus and astrologer to Queen Elizabeth I), which was later adapted by Victorian members of the Golden Dawn into "a complete system of training and initiation."
Enochian Chess was created by William Wynn Westcott, one of the three founders of the Golden Dawn, but the rules of the game were probably never completed by him. The game was finished by S. L. MacGregor Mathers, who put its rules into final form. The game was four-handed because each set of pieces corresponded to one of the four classical elements and their several watchtowers, and the game was used for divination as well as competition. The four sets of pieces were variously colored, and identified with Egyptian deities or "god-forms". The main identifications of the pieces were:
1.Osiris, represented by the king;
2.Isis, the queen;
3.Horus, the knight;
4.Aroueris, the bishop; and
5.Nephthys, the rook or castle.
The chess board itself was also varicolored, and divided into four sub-boards in which each of one of the four elemental colors predominated. The rules of the game were partially derived from shatranj and other historical forms of chess; the queen is played like a fers, with a two square diagonal leaping move. The four players would form pairs of two, with each player having a partner. MacGregor Mathers, who finalised the game's rules, was known to play with an invisible partner he claimed was as spirit. Joseph Hone, biographer of William Butler Yeats, claimed, "Mathers would shade his eyes with his hands and gaze at the empty chair at the opposite corner of the board before moving his partner's piece."
The game, while complex, was in actual use; Georgie Yeats, wife of poet William Butler Yeats, relates actually playing the game as a part of her occult training in Golden Dawn circles. Her husband took part in some of these games, as did MacGregor Mathers.
Enochian Chess introduction.
Chess variants are sometimes created and played in a particular subculture outside the chess community itself. Notable examples of such an origin include Tridimensional Chess, hailing from the world of Star Trek, and Gary Gygax's Dragonchess, an offspring of the Dungeons & Dragons role-playing phenomenon. Enochian chess, an interesting variation on Chaturanga for Four Players, also has its origins in a particular subculture, in this case the world of Victorian occultists.
Enochian chess first appears to have been played by members of the Order of the Golden Dawn, who used their boards and pieces for divination as well as gameplay. Documentary evidence for the existence of the game (in the form of a Golden Dawn paper dating from no later than 1897) has come to light, but no historical documents discovered so far have given the complete rules for game play. Nobel Prize-winning poet and Golden Dawn member William Butler Yeats (1865-1939) records in his memoirs that in 1894 he played "a curious form of chess at which there should be four players" with two other members of the Golden Dawn. One of the other players was MacGregor Mathers (1854-1918), a founding father of the order. In his book The Golden Dawn noted occultist Israel Regardie (1907-1985) provides a description of the boards and the pieces used in Enochian chess. He also gives two arrays and the occult methodology whereby the others may be derived. Regardie attributes part of the information he provides, including the movement of the pieces, to an "Official Ritual" written by Mathers.
The Golden Dawn considered Enochian chess to be a secret teaching. At least partially because of this veil of secrecy, authorship of this variant is unclear. Golden Dawn founder Dr. Wynn Westcott (1848-1925) has been suggested as the inventor of this particular variant, but some (including Westcott himself) have claimed that the documents describing Enochian chess were among those supplied to him from an older occult group operating in Germany. The complete rules presented here are based upon a modern reconstruction by Golden Dawn student Chris Zalewski.
The magical practices of the Golden Dawn are of no concern to the chess variant community, so this essay will focus on Enochian chess as a game. Information of an occult nature will be omitted or glossed-over wherever possible.
Board.
Enochian chess can be played on the 8x8 board of FIDE chess. (Golden Dawn members did not use orthodox boards. For more information on the traditional equipment used to play this variant, see Appendix I.) However, play is facilitated by making the corner spaces of the board at least twice as large as the other squares. After some experimentation the author of this essay found the following board to be particularly suitable:
Figure 1: Board
The four corner spaces (a1, a8, h1, h8) are the throne squares and have special properties involving the four kings that will be explained below.
Setup.
Each of the four players begins with a king, a queen, a rook, a knight, a bishop and four special pawns. Enochian Chess allows for eight different initial arrangements of these pieces, each designated by reference to a combination of the classical 4 elements (fire, earth, water & air). One such array, "Air of Air & Water", is given below. For the others see Appendix II.
Figure 2: One Possible Setup
YELLOWking & bishop, a8
queen, b8
knight, c8
rook, d8pawn of bishop, a7
pawn of queen, b7
pawn of knight, c7
pawn of rook, d7
BLUEking & bishop, h8
queen, h7
knight, h6
rook, h5pawn of bishop, g8
pawn of queen, g7
pawn of knight, g6
pawn of rook, g5
REDking & bishop, h1
queen, g1
knight, f1
rook, e1pawn of bishop, h2
pawn of queen, g2
pawn of knight, f2
pawn of rook, e2
BLACKking & bishop, a1
queen, a2
knight, a3
rook, a4pawn of bishop, b1
pawn of queen, b2
pawn of knight, b3
pawn of rook, b4
In all eight initial arrangements each throne square is occupied by two pieces, a king and another piece (in the above case a bishop). This double occupancy is only allowed at the beginning of the game. Once either the king or the other piece moves off of the throne square then for the remainder of the game only one piece may sit on that particular throne square at any one time. Both pieces are captured if an enemy piece moves into a throne square while it is still occupied by the both original pieces.
Pieces.
The king moves one step in any direction as in FIDE chess. More information concerning the king may be found in the Rules section.
The queen moves by leaping two squares in any direction, as would an alibaba. The movement of a queen is illustrated in Figure 3. The queen has a special form of capture only allowed against other queens. For more information on this special case, see Rules.
Figure 3: Queen's Leap
The rook moves orthogonally as in FIDE chess. Castling is not allowed in Enochian chess.
The bishop moves diagonally as in FIDE chess, except that like the queen it has a special form of capture only allowed against other bishops. More information on this can be found in the Rules section.
The knight behaves exactly as it does in FIDE chess.
The four classes of pawn (pawn of queen, pawn of rook, pawn of bishop, and pawn of knight) behave much like FIDE pawns, moving one space forward or capturing one space in the forward diagonal. For yellow, "forward" constitutes movement towards row 1. For blue, forward movement is in the direction of column A. Red pawns move towards row 8 amd black pawns toward column H. Upon reaching the far rank/file, pawns can promote as in FIDE chess, except that promotion of pawns only occurs after a player has lost at least one pawn. Promotion must be delayed if all four of a player's pawn are uncaptured. Also, a pawn may only promote to its type. (A pawn of rook promotes to a rook, a pawn of knight promote to a knight, etc.) Furthermore, pawns are not allowed an initial double step.
Notes.
Neither the original Golden Dawn material nor Zalewski's reconstruction use the "pawn of ..." terminology. Both simply refer to these pieces as pawns. The nomenclature has been adapted from Tamerlane chess in an attempt to clarify the promotion rules.
Although Zalewski's reconstruction of the rules for Enochian chess may be sound, the author of this article cannot help but wonder if in an earlier version perhaps the queen and bishop moved more like their Chaturanga counterparts, i.e. the queen as a ferz (one square diagonally)and the bishop as an alfil (leaping 2 squares diagonally). Such a suggestion is merely speculation on the part of this essayist. Regardie and through him Mathers both support Zalewski's descriptions of the queen and bishop.
Rules.
Summary.
Enochian chess is a four player chess variant in which two teams (always blue & black versus red & yellow) strive to capture both kings of the opposing team.
Before Play Begins.
Prior to the start of a game the players should choose which of the eight arrays they will use. The players will also need to determine what color each will play (thereby determining who will be on which team) and what color will go first. (The Golden Dawn had a special procedure for making these determinations that had no substantive impact on play. For a description of this procedure, see Appendix IV.) Once these issues are settled play may proceed, going clockwise around the board.
Team Play.
There is no individual winner in Enochian chess. For example, if the blue army is eliminated from play and the black army goes on to the capture the red and yellow kings, then the team of blue and black have won the game.
Team members are normally forbidden from capturing each other's pieces, unless otherwise noted. Pieces belonging to armies on the same team do not threaten each other. (E.g. The blue and black kings can be adjacent without giving each other check.)
Capture of the King.
Kings are not mated in Enochian chess, though players must warn their opponents that the king is threatend by declaring "check" as in FIDE chess. A king in check MUST be moved, even if that means putting the king in check again. The player with the king in check may move another piece only if the king is blocked by friendly pieces so that it cannot be moved out of check.
When a king is captured all the pieces of that color become frozen. They remain on the board, but are unable to move, do not threaten other pieces, nor can they be captured. They simply sit on the board acting as blocking terrain.
Seizing the Throne.
Moving the king onto the throne square of a friendly player transfers control of the friendly army. The two armies still take separate turns, but are under the control of one player. Frozen pieces may be reactivated by this method. The player retains control of both armies even if the king that seized control is moved off of the throne square. If the usurping king is captured, control of the friendly army reverts to the original player, assuming that the army still has a king to lead it. Otherwise both armies are kingless and those players have lost the game.
Exchange of Prisoners.
Two opposing players who have both captured enemy kings may agree to an exchange of prisoners. The exchange can only be made if both players with captured kings agree and neither have lost their own king. The kings are placed upon their own throne squares, or if a throne square is occupied, the nearest empty square. Zalewski does not indicate how to place a king if the thrones square is occupied and multiple alternative squares are equidistant from the throne square.
Frozen pieces revert to normal pieces when their king is brought back into play in this manner.
Priviledged Pawn.
If a player is reduced to a king, a queen, and a pawn; a king, a bishop, and a pawn or a king and a pawn, then the pawn is considered to be priviledged. Upon reaching its normal promotion zone a priviledged pawn may be promoted to a queen, rook, bishop, or knight as the player chooses. In effect, the pawn becomes a normal FIDE pawn. However, if a priviledged pawn is promoted to a piece still in play, the original piece is demoted to the pawn of its type. This effect is illustrated by Figures 4 and 5.
Figure 4: Before Using Pawn Privilege
Black has a pawn of bishop ready to promote and sees an opportunity to fork red's king and rook. Since the pawn of bishop is priviledged, black chooses promotes to a queen. Black already has a queen on the board, which is demoted to a pawn of queen.
Figure 5: After Using Pawn Privilege
What would happen if the above scenario were to involve a pawn of queen instead of a pawn of rook? Zalewski is unclear on this point, but it could be guessed that the original queen can avoid demotion, allowing two black queens on the board. Otherwise the player would be penalized for having priviledge.
Concourse of Bishoping.
A perusal of the eight possible arrays reveals that opposing bishops are bound on opposite colors. The special case known as the concourse of bishoping allows bishops to capture enemy bishops. The concourse of bishoping is similar to the triumph of the boat found in Chaturanga for Four Players. By completing a 2x2 square formation involving all four bishops, the moving bishop takes all three other bishops. A concourse is a special case in which capturing a teammate's piece is legal.
Figure 6: Concourse of Bishoping
In Figure 6 above if the black bishop were to move to e4 it would complete the concourse, capturing all three of the other bishops. Unlike the triumph of the boat, the concourse maneuver is legal in only five positions on the board. A concourse can happen either at c4, c5, d4, & d5 as illustrated above and at the sets (b2, b3, c2, c3) or (b6, b7, c6, c7) or (f6, f7, g6, g7) or (f2, f3, g2, g3). The other four concourse locations are illustrated by Figure 7.
Figure 7: The Other Four Concourses
Concourse of Queens.
Opposing queens are also bound on opposite colors. A concourse of queens occurs under exactly the same circumstances as a concourse of bishoping. Bishops and queens may not be combined in a single concourse capture. All pieces involved must be either bishops OR queens.
Bare King.
When two players on the same team are both reduced to bare kings the game is a draw.
Withdrawing.
A player may withdraw from the game at any time, leaving their pieces in command of their teammate. If the withdrawing player has only a bare king, the remaining teammate is allowed to move either the bare king or their own pieces on BOTH colors' turns. If any other pieces remain in the army of the withdrawing player, then each color army may only be moved on its own turn.
Stalemate.
If a player has no move available except such that would put their unchecked king into check, that player is stalemated. Play continues, but the player is not allowed to take a turn until such time as a move by another player alleviates the stalemate condition. The game is drawn if a player is stalemated and their teammate is also currently out of the game (teammate also stalemated, teammate's king captured, teammate withdrawn or the stalemated king has seized a friendly throne).
Two or Three Player Games Enochian chess may be played with fewer than four players by having one or both players command two armies. Each color still receives its own turn and pieces cannot be played out of turn. (E.g. If one player is playing both red and yellow, no red pieces may be moved during the yellow turn unless the yellow army has taken control of the red army.) A player operating both armies may not withdraw as described above.
Bibliography.
Howe, Ellic. The Magicians of the Golden Dawn. London: Routledge & Kegan Paul, 1972.
Regardie, Israel. The Golden Dawn. St. Paul: Llewellyn Publications, 1989.
Yeats, W(illiam) B(utler). Memoirs trans. and edited by Denis Donoghue. New York: Macmillan Publishing, 1973.
Zalewski, Chris. Enochian Chess of the Golden Dawn. St. Paul: Llewellyn Publications, 1994.
(Please note that off the four texts listed above, only Regardie and Zalewski will be of any possible use to the chess variantist. The others are cited only to help establish the historical pedigree for Enochian chess.)
Appendix I: Traditional Enochian Chess Equipment.
Figure 8: The Air BoardEnochian chess was traditionally played on one of four specially constructed boards. Each board represented on of the classical elements. Each square of each board was divided into 4 triangles, which were painted one of four different colors. These triangles were not game spaces themselves, merely components of the larger square cells used to play the game. Although confusing to the eye, an Enochian chessboard is functionally identical to a FIDE 8x8 board.
The pieces used in Enochian chess were generally stiff paper stand-ups much like the paper dolls and paper toy soldiers of the era. Each major piece had a unique name and design taken from Egyptian mythology and all the pieces were painted in four-color paint schemes. Figure 9 depicts the front of an example piece. Each piece was mounted upright on a base colored red, yellow, blue, or black to show its affiliation. The back of the pieces were each painted a solid color depending on piece type: Kings were painted white on the reverse. Knights were red. Queens were painted blue. Bishops were yellow and rooks were black.
Figure 9: Horus, the black knight
Appendix II: Alternate Arrays
The setup described in the main body of this essay is one of eight provided by Zalewski. The seven other possible set-ups are given below. All eight are equally valid arrays, with no preference given between them. Regardie indicates that there are 16 possible arrays, but Zalewski concludes that there are only eight arrays because there are eight pairs of arrays that are functionally identical. For example, the arrays "Air of Fire" and "Air of Earth" have the exact same piece arrangement. Therefore these two arrays are listed below under a single category, "Air of Fire & Earth".
Figure 10: Air of Fire & Earth
YELLOWking & bishop, a8
rook, b8
knight, c8
queen, d8pawn of bishop, a7
pawn of rook, b7
pawn of knight, c7
pawn of queen, d7
BLUEking & bishop, h8
rook, h7
knight, h6
queen, h5pawn of bishop, g8
pawn of rook, g7
pawn of knight, g6
pawn of queen, g5
REDking & bishop, h1
rook, g1
knight, f1
queen, e1pawn of bishop, h2
pawn of rook, g2
pawn of knight, f2
pawn of queen, e2
BLACKking & bishop, a1
rook, a2
knight, a3
queen, a4pawn of bishop, b1
pawn of rook, b2
pawn of knight, b3
pawn of queen, b4
Figure 11: Fire of Air & Water
YELLOWking & knight, a8
rook, b8
bishop, c8
queen, d8pawn of knight, a7
pawn of rook, b7
pawn of bishop, c7
pawn of queen, d7
BLUEking & knight, h8
rook, h7
bishop, h6
queen, h5pawn of knight, g8
pawn of rook, g7
pawn of bishop, g6
pawn of queen, g5
REDking & knight, h1
rook, g1
bishop, f1
queen, e1pawn of knight, h2
pawn of rook, g2
pawn of bishop, f2
pawn of queen, e2
BLACKking & knight, a1
rook, a2
bishop, a3
queen, a4pawn of knight, b1
pawn of rook, b2
pawn of bishop, b3
pawn of queen, b4
Figure 12: Water of Air & Water
YELLOWking & queen, a8
bishop, b8
rook, c8
knight, d8pawn of queen, a7
pawn of bishop, b7
pawn of rook, c7
pawn of knight, d7
BLUEking & queen, h8
bishop, h7
rook, h6
knight, h5pawn of queen, g8
pawn of bishop, g7
pawn of rook, g6
pawn of knight, g5
REDking & queen, h1
bishop, g1
rook, f1
knight, e1pawn of queen, h2
pawn of bishop, g2
pawn of rook, f2
pawn of knight, e2
BLACKking & queen, a1
bishop, a2
rook, a3
knight, a4pawn of queen, b1
pawn of bishop, b2
pawn of rook, b3
pawn of knight, b4
Figure 13: Earth of Fire & Earth
YELLOWking & rook, a8
bishop, b8
queen, c8
knight, d8pawn of rook, a7
pawn of bishop, b7
pawn of queen, c7
pawn of knight, d7
BLUEking & rook, h8
bishop, h7
queen, h6
knight, h5pawn of rook, g8
pawn of bishop, g7
pawn of queen, g6
pawn of knight, g5
REDking & rook, h1
bishop, g1
queen, f1
knight, e1pawn of rook, h2
pawn of bishop, g2
pawn of queen, f2
pawn of knight, e2
BLACKking & rook, a1
bishop, a2
queen, a3
knight, a4pawn of rook, b1
pawn of bishop, b2
pawn of queen, b3
pawn of knight, b4
Figure 14: Earth of Air & Water
YELLOWking & rook, a8
knight, b8
queen, c8
bishop, d8pawn of rook, a7
pawn of knight, b7
pawn of queen, c7
pawn of bishop, d7
BLUEking & rook, h8
knight, h7
queen, h6
bishop, h5pawn of rook, g8
pawn of knight, g7
pawn of queen, g6
pawn of bishop, g5
REDking & rook, h1
knight, g1
queen, f1
bishop, e1pawn of rook, h2
pawn of knight, g2
pawn of queen, f2
pawn of bishop, e2
BLACKking & rook, a1
knight, a2
queen, a3
bishop, a4pawn of rook, b1
pawn of knight, b2
pawn of queen, b3
pawn of bishop, b4
Figure 15: Fire of Fire & Earth
YELLOWking & knight, a8
queen, b8
bishop, c8
rook, d8pawn of knight, a7
pawn of queen, b7
pawn of bishop, c7
pawn of rook, d7
BLUEking & knight, h8
queen, h7
bishop, h6
rook, h5pawn of knight, g8
pawn of queen, g7
pawn of bishop, g6
pawn of rook, g5
REDking & knight, h1
queen, g1
bishop, f1
rook, e1pawn of knight, h2
pawn of queen, g2
pawn of bishop, f2
pawn of rook, e2
BLACKking & knight, a1
queen, a2
bishop, a3
rook, a4pawn of knight, b1
pawn of queen, b2
pawn of bishop, b3
pawn of rook, b4
Figure 16: Water of Fire & Earth
YELLOWking & queen, a8
knight, b8
rook, c8
bishop, d8pawn of queen, a7
pawn of knight, b7
pawn of rook, c7
pawn of bishop, d7
BLUEking & queen, h8
knight, h7
rook, h6
bishop, h5pawn of queen, g8
pawn of knight, g7
pawn of rook, g6
pawn of bishop, g5
REDking & queen, h1
knight, g1
rook, f1
bishop, e1pawn of queen, h2
pawn of knight, g2
pawn of rook, f2
pawn of bishop, e2
BLACKking & queen, a1
knight, a2
rook, a3.......
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108.Sufism.
Sufism (Arabic: ???????? al-??fiyya; Persian: ????? ta?awwuf ) is a concept in Islam, defined by scholars as the inner, mystical dimension of Islam; others contend that it is a perennial philosophy of existence that pre-dates religion, the expression of which flowered within the Islamic religion. Some academics have argued that Sufism has been heavily influenced by Neoplatonism. Traditional Sufis, throughout history (i.e. Bayazid Bastami, Jalaluddin Rumi, Haji Bektash Veli, Junaid Baghdadi, Al-Ghazali etc.) and presently, however, have maintained Sufism to be purely based on the tenets of Islam and the teachings of Muhammad. There are some who hold the notion that its essence has also been expressed via other religions and metareligious phenomena, while others believe Sufism to be totally unique to Islam.
A practitioner of this tradition is generally known as a Sufi, (??f?) (/?su?fi/; ???????). Sufis belong to different ?uruq or "orders"?congregations formed around a master?which meet for spiritual sessions (majalis), in meeting places known as zawiyahs, khanqahs, or tekke. e.g. Khanqah Khairiyyah.
All Sufi orders (turuq) trace many of their original precepts from the Islamic prophet Muhammad through his cousin and son-in-law Ali ibn Abi Talib, with the notable exception of the Sunni Naqshbandi order who claim to trace their origins through the first sunni Caliph, Abu Bakr. However, Alevi, Bektashi and Shia Muslims claim that every Sufi order traces its spiritual lineage (silsilah or Silsila) back to one of the Twelve Imams (even the Naqshbandi silsilah leads to the sixth imam Ja'far al-Sadiq and Salman the Persian, a renowned follower of the first imam Ali ibn Abi Talib), the spiritual heads of Islam who were foretold in the Hadith of the Twelve Successors and were all descendants of Muhammad through his daughter Fatima and Ali. Because of this Ali ibn Abi Talib is also called the "father of Sufism".
Prominent orders include Alevi, Bektashi, Burhaniya, Mevlevi, Ba 'Alawiyya, Chishti, Rifa'i, Khalwati, Naqshbandi, Nimatullahi, Oveyssi, Qadiria Boutshishia, Qadiriyyah, Qalandariyya, Sarwari Qadiri, Shadhiliyya and Suhrawardiyya.
Sufis believe that they are practicing ihsan (perfection of worship) as revealed by Gabriel to Muhammad: "Worship and serve Allah as you are seeing Him and while you see Him not yet truly He sees you". Sufis consider themselves to be the original true proponents of this pure original form of Islam. Sufism is opposed by Wahhabi and Salafist Muslims.
Classical Sufi scholars have defined Sufism as "a science whose objective is the reparation of the heart and turning it away from all else but God". Alternatively, in the words of the Darqawi Sufi teacher Ahmad ibn Ajiba, "a science through which one can know how to travel into the presence of the Divine, purify one's inner self from filth, and beautify it with a variety of praiseworthy traits".
Muslims and mainstream scholars of Islam define Sufism as simply the name for the inner or esoteric dimension of Islam which is supported and complemented by outward or exoteric practices of Islam, such as Islamic law. In this view, "it is absolutely necessary to be a Muslim" to be a true Sufi, because Sufism's "methods are inoperative without" Muslim "affiliation". In contrast, author Idries Shah states Sufi philosophy is universal in nature, its roots predating the rise of Islam and Christianity. Some schools of Sufism in Western countries allow non-Muslims to receive "instructions on following the Sufi path". Some Muslim opponents of Sufism also consider it outside the sphere of Islam.
Classical Sufis were characterised by their attachment to dhikr, (a practice of repeating the names of God, often performed after prayers) and asceticism. Sufism gained adherents among a number of Muslims as a reaction against the worldliness of the early Umayyad Caliphate (661?750 CE). Sufis have spanned several continents and cultures over a millennium, originally expressing their beliefs in Arabic, before spreading into Persian, Turkish, and Urdu among dozens of other languages.
Two origins of the word sufi have been suggested. Commonly, the lexical root of the word is traced to ?af? (????), which in Arabic means "purity". Another origin is ??f (????), "wool" in Arabic, referring to the simple cloaks the early Muslim ascetics wore. The two were combined by the Sufi al-Rudhabari who said, "The Sufi is the one who wears wool on top of purity".
Others have suggested that the word comes from the term ahl a?-?uffah ("the people of the bench"), who were a group of impoverished companions of Muhammad who held regular gatherings of dhikr. These men and women who sat at Al-Masjid al-Nabawi are considered by some to be the first Sufites in existence. Abd al-Kar?m ibn Haw?zin Qushayri and Ibn Khaldun both rejected all possibilities other than ??f on linguistic grounds.
According to the medieval scholar Ab? Ray??n al-B?r?n?, the word sufi is derived from the Greek word sofia (?????), meaning wisdom.
While all Muslims believe that they are on the pathway to God and hope to become close to God in Paradise?after death and after the "Final Judgment"?Sufis also believe that it is possible to draw closer to God and to more fully embrace the Divine Presence in this life. The chief aim of all Sufis is to seek the pleasing of God by working to restore within themselves the primordial state of fitra, described in the Qur'an. In this state nothing one does defies God, and all is undertaken with the single motivation of love of Allah.
To Sufis, Sufism involves the study and ritual purification of traits deemed reprehensible while adding praiseworthy traits. This is independent of whether or not this process of religious cleansing and purifying leads to esoteric knowledge of God. This can be conceived in terms of two basic types of law (fiqh), an outer law concerned with actions, and an inner law concerned with one's own actions and qualities. The outer law consists of rules pertaining to worship, transactions, marriage, judicial rulings, and criminal law?what is often referred to, broadly, as qanun. The inner law of Sufism consists of rules about repentance from sin, the purging of contemptible qualities and evil traits of character, and adornment with virtues and good character.
The typical early Sufi lived in a cell of a mosque and taught a small band of disciples. The extent to which Sufism was influenced by Buddhist and Hindu mysticism, and by the example of Christian hermits and monks, is disputed, but self-discipline and concentration on God quickly led to the belief that by quelling the self and through loving ardor for God it is possible to maintain a union with the divine in which the human self melts away.
Teaching.
Entrance of Sidi Boumediene mosque in Tlemcen, Algeria, built to honor 12th century Sufi master Abu Madyan
A Sufi student enters the faith by seeking a teacher. Sufism emphasises a strong relationship between the seeker and the teacher. To be considered legitimate by the Sufi community, the teacher must have received the authorization to teach (ijazah) from another Master of the Way, in an unbroken succession (silsilah) leading back to Muhammad.[dubious ][citation needed] To the Sufi, it is the transmission of divine light from the teacher's heart to the heart of the student, rather than worldly knowledge, that allows the adept to progress. They further believe that the teacher should attempt to inerrantly follow the Divine Law.
According to Moojan Momen "one of the most important doctrines of Sufism is the concept of the "Perfect Man" (al-Insan al-Kamil). This doctrine states that there will always exist upon the earth a "Qutb" (Pole or Axis, of the Universe)?a man who is the perfect channel of grace from God to man and in a state of wilaya (sanctity, being under the protection of God). The concept of the Sufi Qutb is similar to that of the Shi'i Imam. However, this belief puts Sufism in "direct conflict" with Shi'ism, since both the Qutb (who for most Sufi orders is the head of the order) and the Imam fulfill the role of "the purveyor of spiritual guidance and of God's grace to mankind". The vow of obedience to the Shaykh or Qutb which is taken by Sufis is considered incompatible with devotion to the Imam".
As a further example, the prospective adherent of the Mevlevi Order would have been ordered to serve in the kitchens of a hospice for the poor for 1,001 days prior to being accepted for spiritual instruction, and a further 1,001 days in solitary retreat as a precondition of completing that instruction.
Some teachers, especially when addressing more general audiences, or mixed groups of Muslims and non-Muslims, make extensive use of parable, allegory, and metaphor. Although approaches to teaching vary among different Sufi orders, Sufism as a whole is primarily concerned with direct personal experience, and as such has sometimes been compared to other, non-Islamic forms of mysticism (e.g., as in the books of Hossein Nasr).
Many Sufi believe that to reach the highest levels of success in Sufism typically requires that the disciple live with and serve the teacher for a large period of time. An example is the folk story about Baha-ud-Din Naqshband Bukhari, who gave his name to the Naqshbandi Order. He is believed to have served his first teacher, Sayyid Muhammad Baba As-Samasi, for 20 years, until as-Samasi died. He is said to then have served several other teachers for lengthy periods of time. He is said to have helped the poorer members of the community for many years and after this concluded his teacher directed him to care for animals cleaning their wounds, and assisting them.
Eminent Sufis such as Ali Hujwiri claim that the tradition first began with Ali ibn Abi Talib. Furthermore, Junayd of Baghdad regarded Ali as the Sheikh of the principals and practices of Sufism.
Practitioners of Sufism hold that in its early stages of development Sufism effectively referred to nothing more than the internalization of Islam. According to one perspective, it is directly from the Qur'an, constantly recited, meditated, and experienced, that Sufism proceeded, in its origin and its development. Others have held that Sufism is the strict emulation of the way of Muhammad, through which the heart's connection to the Divine is strengthened.
According to Marshall Hodgson, the Muslim conquests had brought large numbers of Christian monks and hermits, especially in Syria and Egypt, under the rule of Muslims. They retained a vigorous spiritual life for centuries after the conquests, and many of the especially pious Muslims who founded Sufism were influenced by their techniques and methods. However, others disagree with this view by asserting Sufism to be unique within the confines of the Islamic religion and contend that Sufism developed from devout followers of Islam, like Bayazid Bastami who in his utmost reverence to the Sunnah refused to eat a watermelon as he did not find any proof that the prophet Muhammad ever ate it. According to late Medieval mystic Jami, Abd-Allah ibn Muhammad ibn al-Hanafiyyah was the first person to be called a "Sufi".
Important contributions in writing are attributed to Uwais al-Qarni, Harrm bin Hian, Hasan Basri and Sayid ibn al-Mussib. Ruwaym, from the second generation of Sufis in Baghdad, was also an influential early figure, as was Junayd of Baghdad; a number of early practitioners of Sufism were disciples of one of the two.
Sufism had a long history already before the subsequent institutionalization of Sufi teachings into devotional orders (tarîqât) in the early Middle Ages. The Naqshbandi order is a notable exception to general rule of orders tracing their spiritual lineage through Muhammad's grandsons, as it traces the origin of its teachings from Muhammad to the first Islamic Caliph, Abu Bakr.
Formalization of doctrine.
Towards the end of the first millennium CE, a number of manuals began to be written summarizing the doctrines of Sufism and describing some typical Sufi practices. Two of the most famous of these are now available in English translation: the Kashf al-Mahjûb of Hujwiri, and the Risâla of Qushayri. Two of Imam Al Ghazali's greatest treatises, the "Revival of Religious Sciences" and the "Alchemy of Happiness", argued that Sufism originated from the Qur'an and thus was compatible with mainstream Islamic thought, and did not in any way contradict Islamic Law?being instead necessary to its complete fulfillment. This became the mainstream position among Islamic scholars for centuries, challenged only recently on the basis of selective use of a limited body of texts.[example needed] Ongoing efforts by both traditionally trained Muslim scholars and Western academics are making Imam Al-Ghazali's works available in English translation for the first time, allowing English-speaking readers to judge for themselves the compatibility of Islamic Law and Sufi doctrine. Several sections of the Revival of Religious Sciences have been published in translation by the Islamic Texts Society. The Alchemy of Happiness has been published in a complete translation by Claud Field (ISBN 978-0935782288), and presents the argument of the much larger Revival of Religious Sciences in summary form.
Growth of influence.
The tomb of Khoja Af?q, near Kashgar, China.
The rise of Islamic civilization coincides strongly with the spread of Sufi philosophy in Islam. The spread of Sufism has been considered a definitive factor in the spread of Islam, and in the creation of integrally Islamic cultures, especially in Africa and Asia. The Senussi tribes of Libya and Sudan are one of the strongest adherents of Sufism. Sufi poets and philosophers such as Khoja Akhmet Yassawi, Rumi and Attar of Nishapur (c. 1145 ? c. 1221) greatly enhanced the spread of Islamic culture in Anatolia, Central Asia, and South Asia. Sufism also played a role in creating and propagating the culture of the Ottoman world, and in resisting European imperialism in North Africa and South Asia.
Between the 13th and 16th centuries CE, Sufism produced a flourishing intellectual culture throughout the Islamic world, a "Golden Age" whose physical artifacts survive. In many places a pious foundation would endow a lodge (known variously as a zaouia, khanqah, or tekke) in perpetuity (waqf) to provide a gathering place for Sufi adepts, as well as lodging for itinerant seekers of knowledge. The same system of endowments could also pay for a complex of buildings, such as that surrounding the Süleymaniye Mosque in Istanbul, including a lodge for Sufi seekers, a hospice with kitchens where these seekers could serve the poor and/or complete a period of initiation, a library, and other structures. No important domain in the civilization of Islam remained unaffected by Sufism in this period.
Present.
Mawl?n? Rumi's tomb, Konya, Turkey
Current Sufi orders include Azeemia, Alians, Bektashi Order, Mevlevi Order, Ba 'Alawiyya, Chishti, Jerrahi, Naqshbandi, Nimatullahi, Qadiriyyah, Qalandariyya, Sarwari Qadiri, Shadhiliyya, Suhrawardiyya, Ashrafia, Saifiah (Naqshbandiah) and Uwaisi (Oveyssi). The relationship of Sufi orders to modern societies is usually defined by their relationship to governments.
Turkey and Persia together have been a center for many Sufi lineages and orders. The Bektashi was closely affiliated with the Ottoman Janissary and is the heart of Turkey's large and mostly liberal Alevi population. It has been spread westwards to Cyprus, Greece, Albania, Bulgaria, Macedonia, Bosnia, Kosovo and more recently to the USA (via Albania). Most Sufi Orders have influences from pre-Islamic traditions such as Pythagoreanism, but the Turkic Sufi traditions (including Alians, Bektashi and Mevlevi) also have traces of the ancient Tengrism shamanism.
Sufism is popular in such African countries as Tunisia, Algeria, Morocco and Senegal, where it is seen as a mystical expression of Islam. Sufism is traditional in Morocco but has seen a growing revival with the renewal of Sufism around contemporary spiritual teachers such as Sidi Hamza al Qadiri al Boutshishi. Mbacke suggests that one reason Sufism has taken hold in Senegal is because it can accommodate local beliefs and customs, which tend toward the mystical.
The life of the Algerian Sufi master Emir Abd al-Qadir is instructive in this regard. Notable as well are the lives of Amadou Bamba and Hajj Umar Tall in sub-Saharan Africa, and Sheikh Mansur Ushurma and Imam Shamil in the Caucasus region. In the twentieth century some more modernist Muslims have called Sufism a superstitious religion that holds back Islamic achievement in the fields of science and technology.
A number of Westerners have embarked with varying degrees of success on the path of Sufism. One of the first to return to Europe as an official representative of a Sufi order, and with the specific purpose to spread Sufism in Western Europe, was the Swedish-born wandering Sufi Abd al-Hadi Aqhili (also known as Ivan Aguéli). René Guénon, the French scholar, became a Sufi in the early twentieth century and was known as Sheikh Abdul Wahid Yahya. His manifold writings defined the practice of Sufism as the essence of Islam but also pointed to the universality of its message. Other spiritualists, such as G. I. Gurdjieff, may or may not conform to the tenets of Sufism as understood by orthodox Muslims.
Traditional Islamic scholars have recognized two major branches within the practice of Sufism, and use this as one key to differentiating among the approaches of different masters and devotional lineages.
On the one hand there is the order from the signs to the Signifier (or from the arts to the Artisan). In this branch, the seeker begins by purifying the lower self of every corrupting influence that stands in the way of recognizing all of creation as the work of God, as God's active Self-disclosure or theophany. This is the way of Imam Al-Ghazali and of the majority of the Sufi orders.
On the other hand there is the order from the Signifier to His signs, from the Artisan to His works. In this branch the seeker experiences divine attraction (jadhba), and is able to enter the order with a glimpse of its endpoint, of direct apprehension of the Divine Presence towards which all spiritual striving is directed. This does not replace the striving to purify the heart, as in the other branch; it simply stems from a different point of entry into the path. This is the way primarily of the masters of the Naqshbandi and Shadhili orders.
Contemporary scholars may also recognize a third branch, attributed to the late Ottoman scholar Said Nursi and explicated in his vast Qur'an commentary called the Risale-i Nur. This approach entails strict adherence to the way of Muhammad, in the understanding that this wont, or sunnah, proposes a complete devotional spirituality adequate to those without access to a master of the Sufi way.
Contributions to other domains of scholarship.
Sufism has contributed significantly to the elaboration of theoretical perspectives in many domains of intellectual endeavor. For instance, the doctrine of "subtle centers" or centers of subtle cognition (known as Lataif-e-sitta) addresses the matter of the awakening of spiritual intuition in ways that some consider similar to certain models of chakra in Hinduism. In general, these subtle centers or latâ'if are thought of as faculties that are to be purified sequentially in order to bring the seeker's wayfaring to completion. A concise and useful summary of this system from a living exponent of this tradition has been published by Muhammad Emin Er.
Sufi psychology has influenced many areas of thinking both within and outside of Islam, drawing primarily upon three concepts. Ja'far al-Sadiq (both an imam in the Shia tradition and a respected scholar and link in chains of Sufi transmission in all Islamic sects) held that human beings are dominated by a lower self called the nafs, a faculty of spiritual intuition called the qalb or spiritual heart, and a spirit or soul called ruh. These interact in various ways, producing the spiritual types of the tyrant (dominated by nafs), the person of faith and moderation (dominated by the spiritual heart), and the person lost in love for God (dominated by the ruh).
Of note with regard to the spread of Sufi psychology in the West is Robert Frager, a Sufi teacher authorized in the Khalwati Jerrahi order. Frager was a trained psychologist, born in the United States, who converted to Islam in the course of his practice of Sufism and wrote extensively on Sufism and psychology.
Sufi cosmology and Sufi metaphysics are also noteworthy areas of intellectual accomplishment.
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109.String Theory.
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory aims to explain all types of observed elementary particles using quantum states of these strings. In addition to the particles postulated by the standard model of particle physics, string theory naturally incorporates gravity and so is a candidate for a theory of everything, a self-contained mathematical model that describes all fundamental forces and forms of matter. Besides this potential role, string theory is now widely used as a theoretical tool and has shed light on many aspects of quantum field theory and quantum gravity.
The earliest version of string theory, bosonic string theory, incorporated only the class of particles known as bosons. It was then developed into superstring theory, which posits that a connection ? a "supersymmetry" ? exists between bosons and the class of particles called fermions. String theory requires the existence of extra spatial dimensions for its mathematical consistency. In realistic physical models constructed from string theory, these extra dimensions are typically compactified to extremely small scales.
String theory was first studied in the late 1960s as a theory of the strong nuclear force before being abandoned in favor of the theory of quantum chromodynamics. Subsequently, it was realized that the very properties that made string theory unsuitable as a theory of nuclear physics made it a promising candidate for a quantum theory of gravity. Five consistent versions of string theory were developed until it was realized in the mid-1990s that they were different limits of a conjectured single 11-dimensional theory now known as M-theory.
Many theoretical physicists, including Stephen Hawking, Edward Witten and Juan Maldacena, believe that string theory is a step towards the correct fundamental description of nature: it accommodates a consistent combination of quantum field theory and general relativity, agrees with insights in quantum gravity (such as the holographic principle and black hole thermodynamics) and has passed many non-trivial checks of its internal consistency. According to Hawking, "M-theory is the only candidate for a complete theory of the universe." Other physicists, such as Richard Feynman, Roger Penrose and Sheldon Lee Glashow, have criticized string theory for not providing novel experimental predictions at accessible energy scales.
The starting point for string theory is the idea that the point-like particles of elementary particle physics can also be modeled as one-dimensional objects called strings. According to string theory, strings can oscillate in many ways. On distance scales larger than the string radius, each oscillation mode gives rise to a different species of particle, with its mass, charge, and other properties determined by the string's dynamics. Splitting and recombination of strings correspond to particle emission and absorption, giving rise to the interactions between particles. An analogy for strings' modes of vibration is a guitar string's production of multiple distinct musical notes. In this analogy, different notes correspond to different particles.
In string theory, one of the modes of oscillation of the string corresponds to a massless, spin-2 particle. Such a particle is called a graviton since it mediates a force which has the properties of gravity. Since string theory is believed to be a mathematically consistent quantum mechanical theory, the existence of this graviton state implies that string theory is a theory of quantum gravity.
String theory includes both open strings, which have two distinct endpoints, and closed strings, which form a complete loop. The two types of string behave in slightly different ways, yielding different particle types. For example, all string theories have closed string graviton modes, but only open strings can correspond to the particles known as photons. Because the two ends of an open string can always meet and connect, forming a closed string, all string theories contain closed strings.
The earliest string model, the bosonic string, incorporated only the class of particles known as bosons. This model describes, at low enough energies, a quantum gravity theory, which also includes (if open strings are incorporated as well) gauge bosons such as the photon. However, this model has problems. What is most significant is that the theory has a fundamental instability, believed to result in the decay (at least partially) of spacetime itself. In addition, as the name implies, the spectrum of particles contains only bosons, particles which, like the photon, obey particular rules of behavior. Roughly speaking, bosons are the constituents of radiation, but not of matter, which is made of fermions. Investigating how a string theory may include fermions led to the invention of supersymmetry, a mathematical relation between bosons and fermions. String theories that include fermionic vibrations are now known as superstring theories; several kinds have been described, but all are now thought to be different limits of a theory called M-theory.
Since string theory incorporates all of the fundamental interactions, including gravity, many physicists hope that it fully describes our universe, making it a theory of everything. One of the goals of current research in string theory is to find a solution of the theory that is quantitatively identical with the standard model, with a small cosmological constant, containing dark matter and a plausible mechanism for cosmic inflation. It is not yet known whether string theory has such a solution, nor is it known how much freedom the theory allows to choose the details.
One of the challenges of string theory is that the full theory does not yet have a satisfactory definition in all circumstances. The scattering of strings is most straightforwardly defined using the techniques of perturbation theory, but it is not known in general how to define string theory nonperturbatively. It is also not clear as to whether there is any principle by which string theory selects its vacuum state, the spacetime configuration that determines the properties of our universe (see string theory landscape).
Strings.
The motion of a point-like particle can be described by drawing a graph of its position with respect to time. The resulting picture depicts the worldline of the particle in spacetime. In an analogous way, one can draw a graph depicting the progress of a string as time passes. The string, which looks like a small line by itself, will sweep out a two-dimensional surface known as the worldsheet. The different string modes (giving rise to different particles, such as the photon or graviton) appear as waves on this surface.
A closed string looks like a small loop, so its worldsheet will look like a pipe. An open string looks like a segment with two endpoints, so its worldsheet will look like a strip. In a more mathematical language, these are both Riemann surfaces, the strip having a boundary and the pipe none.
Interaction in the subatomic world: world lines of point-like particles in the Standard Model or a world sheet swept up by closed strings in string theory
Strings can join and split. This is reflected by the form of their worldsheet, or more precisely, by its topology. For example, if a closed string splits, its worldsheet will look like a single pipe splitting into two pipes. This topology is often referred to as a pair of pants (see drawing at right). If a closed string splits and its two parts later reconnect, its worldsheet will look like a single pipe splitting to two and then reconnecting, which also looks like a torus connected to two pipes (one representing the incoming string, and the other representing the outgoing one). An open string doing the same thing will have a worldsheet that looks like an annulus connected to two strips.
In quantum mechanics, one computes the probability for a point particle to propagate from one point to another by summing certain quantities called probability amplitudes. Each amplitude is associated with a different worldline of the particle. This process of summing amplitudes over all possible worldlines is called path integration. In string theory, one computes probabilities in a similar way, by summing quantities associated with the worldsheets joining an initial string configuration to a final configuration. It is in this sense that string theory extends quantum field theory, replacing point particles by strings. As in quantum field theory, the classical behavior of fields is determined by an action functional, which in string theory can be either the Nambu?Goto action or the Polyakov action.
Branes.
In string theory and related theories such as supergravity theories, a brane is a physical object that generalizes the notion of a point particle to higher dimensions. For example, a point particle can be viewed as a brane of dimension zero, while a string can be viewed as a brane of dimension one. It is also possible to consider higher-dimensional branes. In dimension p, these are called p-branes. The word brane comes from the word "membrane" which refers to a two-dimensional brane.
Branes are dynamical objects which can propagate through spacetime according to the rules of quantum mechanics. They have mass and can have other attributes such as charge. A p-brane sweeps out a (p+1)-dimensional volume in spacetime called its worldvolume. Physicists often study fields analogous to the electromagnetic field which live on the worldvolume of a brane.
In string theory, D-branes are an important class of branes that arise when one considers open strings. As an open string propagates through spacetime, its endpoints are required to lie on a D-brane. The letter "D" in D-brane refers to the fact that we impose a certain mathematical condition on the system known as the Dirichlet boundary condition. The study of D-branes in string theory has led to important results such as the AdS/CFT correspondence, which has shed light on many problems in quantum field theory.
Branes are also frequently studied from a purely mathematical point of view since they are related to subjects such as homological mirror symmetry and noncommutative geometry. Mathematically, branes may be represented as objects of certain categories, such as the derived category of coherent sheaves on a Calabi?Yau manifold, or the Fukaya category.
Dualities.
In physics, the term duality refers to a situation where two seemingly different physical systems turn out to be equivalent in a nontrivial way. If two theories are related by a duality, it means that one theory can be transformed in some way so that it ends up looking just like the other theory. The two theories are then said to be dual to one another under the transformation. Put differently, the two theories are mathematically different descriptions of the same phenomena.
In addition to providing a candidate for a theory of everything, string theory provides many examples of dualities between different physical theories and can therefore be used as a tool for understanding the relationships between these theories.
S-, T-, and U-duality.
These are dualities between string theories which relate seemingly different quantities. Large and small distance scales, as well as strong and weak coupling strengths, are quantities that have always marked very distinct limits of behavior of a physical system in both classical and quantum physics. But strings can obscure the difference between large and small, strong and weak, and this is how these five very different theories end up being related. T-duality relates the large and small distance scales between string theories, whereas S-duality relates strong and weak coupling strengths between string theories. U-duality links T-duality and S-duality.
M-theory.
Before the 1990s, string theorists believed there were five distinct superstring theories: type I, type IIA, type IIB, and the two flavors of heterotic string theory (SO(32) and E8×E8). The thinking was that out of these five candidate theories, only one was the actual correct theory of everything, and that theory was the one whose low energy limit, with ten spacetime dimensions compactified down to four, matched the physics observed in our world today. It is now believed that this picture was incorrect and that the five superstring theories are related to one another by the dualities described above. The existence of these dualities suggests that the five string theories are in fact special cases of a more fundamental theory called M-theory.
String theory details by type and number of spacetime dimensions.
TypeSpacetime dimensionsDetails
Bosonic26Only bosons, no fermions, meaning only forces, no matter, with both open and closed strings; major flaw: a particle with imaginary mass, called the tachyon, representing an instability in the theory.
I10Supersymmetry between forces and matter, with both open and closed strings; no tachyon; gauge group is SO(32)
IIA10Supersymmetry between forces and matter, with only closed strings; no tachyon; massless fermions are non-chiral
IIB10Supersymmetry between forces and matter, with only closed strings; no tachyon; massless fermions are chiral
HO10Supersymmetry between forces and matter, with closed strings only; no tachyon; heterotic, meaning right moving and left moving strings differ; gauge group is SO(32)
HE10Supersymmetry between forces and matter, with closed strings only; no tachyon; heterotic; gauge group is E8×E8
Extra dimensions.
Number of dimensions.
An intriguing feature of string theory is that it predicts extra dimensions. In classical string theory the number of dimensions is not fixed by any consistency criterion. However, to make a consistent quantum theory, string theory is required to live in a spacetime of the so-called "critical dimension": we must have 26 spacetime dimensions for the bosonic string and 10 for the superstring. This is necessary to ensure the vanishing of the conformal anomaly of the worldsheet conformal field theory. Modern understanding indicates that there exist less trivial ways of satisfying this criterion. Cosmological solutions exist in a wider variety of dimensionalities, and these different dimensions are related by dynamical transitions. The dimensions are more precisely different values of the "effective central charge", a count of degrees of freedom that reduces to dimensionality in weakly curved regimes.
One such theory is the 11-dimensional M-theory, which requires spacetime to have eleven dimensions, as opposed to the usual three spatial dimensions and the fourth dimension of time. The original string theories from the 1980s describe special cases of M-theory where the eleventh dimension is a very small circle or a line, and if these formulations are considered as fundamental, then string theory requires ten dimensions. But the theory also describes universes like ours, with four observable spacetime dimensions, as well as universes with up to 10 flat space dimensions, and also cases where the position in some of the dimensions is described by a complex number rather than a real number. The notion of spacetime dimension is not fixed in string theory: it is best thought of as different in different circumstances.
Nothing in Maxwell's theory of electromagnetism or Einstein's theory of relativity makes this kind of prediction; these theories require physicists to insert the number of dimensions manually and arbitrarily, and this number is fixed and independent of potential energy. String theory allows one to relate the number of dimensions to scalar potential energy. In technical terms, this happens because a gauge anomaly exists for every separate number of predicted dimensions, and the gauge anomaly can be counteracted by including nontrivial potential energy into equations to solve motion. Furthermore, the absence of potential energy in the "critical dimension" explains why flat spacetime solutions are possible.
This can be better understood by noting that a photon included in a consistent theory (technically, a particle carrying a force related to an unbroken gauge symmetry) must be massless. The mass of the photon that is predicted by string theory depends on the energy of the string mode that represents the photon. This energy includes a contribution from the Casimir effect, namely from quantum fluctuations in the string. The size of this contribution depends on the number of dimensions, since for a larger number of dimensions there are more possible fluctuations in the string position. Therefore, the photon in flat spacetime will be massless?and the theory consistent?only for a particular number of dimensions. When the calculation is done, the critical dimensionality is not four as one may expect (three axes of space and one of time). The subset of X is equal to the relation of photon fluctuations in a linear dimension. Flat space string theories are 26-dimensional in the bosonic case, while superstring and M-theories turn out to involve 10 or 11 dimensions for flat solutions. In bosonic string theories, the 26 dimensions come from the Polyakov equation. Starting from any dimension greater than four, it is necessary to consider how these are reduced to four-dimensional spacetime.
Compact dimensions.
Calabi?Yau manifold (3D projection)
Two ways have been proposed to resolve this apparent contradiction. The first is to compactify the extra dimensions; i.e., the 6 or 7 extra dimensions are so small as to be undetectable by present-day experiments.
To retain a high degree of supersymmetry, these compactification spaces must be very special, as reflected in their holonomy. A 6-dimensional manifold must have SU(3) structure, a particular case (torsionless) of this being SU(3) holonomy, making it a Calabi?Yau space, and a 7-dimensional manifold must have G2 structure, with G2 holonomy again being a specific, simple, case. Such spaces have been studied in attempts to relate string theory to the 4-dimensional Standard Model, in part due to the computational simplicity afforded by the assumption of supersymmetry. More recently, progress has been made constructing more realistic compactifications without the degree of symmetry of Calabi?Yau or G2 manifolds.
A standard analogy for this is to consider multidimensional space as a garden hose. If the hose is viewed from sufficient distance, it appears to have only one dimension, its length. Indeed, think of a ball just small enough to enter the hose. Throwing such a ball inside the hose, the ball would move more or less in one dimension; in any experiment we make by throwing such balls in the hose, the only important movement will be one-dimensional, that is, along the hose. However, as one approaches the hose, one discovers that it contains a second dimension, its circumference. Thus, an ant crawling inside it would move in two dimensions (and a fly flying in it would move in three dimensions). This "extra dimension" is only visible within a relatively close range to the hose, or if one "throws in" small enough objects. Similarly, the extra compact dimensions are only "visible" at extremely small distances, or by experimenting with particles with extremely small wavelengths (of the order of the compact dimension's radius), which in quantum mechanics means very high energies (see wave?particle duality).
Brane-world scenario.
Another possibility is that we are "stuck" in a 3+1 dimensional (three spatial dimensions plus one time dimension) subspace of the full universe. Properly localized matter and Yang?Mills gauge fields will typically exist if the sub-spacetime is an exceptional set of the larger universe. These "exceptional sets" are ubiquitous in Calabi?Yau n-folds and may be described as subspaces without local deformations, akin to a crease in a sheet of paper or a crack in a crystal, the neighborhood of which is markedly different from the exceptional subspace itself. However, until the work of Randall and Sundrum, it was not known that gravity can be properly localized to a sub-spacetime. In addition, spacetime may be stratified, containing strata of various dimensions, allowing us to inhabit the 3+1-dimensional stratum?such geometries occur naturally in Calabi?Yau compactifications. Such sub-spacetimes are D-branes, hence such models are known as brane-world scenarios.
Effect of the hidden dimensions.
In either case, gravity acting in the hidden dimensions affects other non-gravitational forces such as electromagnetism. In fact, Kaluza's early work demonstrated that general relativity in five dimensions actually predicts the existence of electromagnetism. However, because of the nature of Calabi?Yau manifolds, no new forces appear from the small dimensions, but their shape has a profound effect on how the forces between the strings appear in our four-dimensional universe. In principle, therefore, it is possible to deduce the nature of those extra dimensions by requiring consistency with the standard model, but this is not yet a practical possibility. It is also possible to extract information regarding the hidden dimensions by precision tests of gravity, but so far these have only put upper limitations on the size of such hidden dimensions.
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