HISTORICAL CHESS
Chessays

 

Mystical Numerology in Egypt and Mesopotamia
Chapter 2: Mystical numerology in Egypt and Mesopotamia
by Dr. Ricardo Calvo

"Senet" is the best known and most widely popularized board game from ancient Egypt. Based upon a 3x10 board of 30 squares, it consisted of a race game played with knucklebones that could be engaged between two players or, as some temple drawings suggest, by a single player. Connected with mystical numerology, variants of the game consitently demonstrate that square 15 symbolized the "House of Rebirth" and square 26 "The Beautiful House", while case 27, a water hazard, was one to be avoided. The game itself symbolized the path of the dead through the underworld. "I must enter the Hall of the Thirty and I become God at the 31" says one papyros. An extensive analysis can be found in Wolfgang Decker's "Sports and Games of Ancient Egypt" 1992, Yale University.pp 124 ff,

Underscoring their fixation with numbers in general, patterns emerge which clearly indicate that the numbers 15 (5x3), 26 (13x2) and 31 contained symbolic content that must have been well known among the Egyptians themselves. As but one example among many, Senet echos the established Egyptian tradition of placing coded numerological statements within the semantic body of various sacred texts, art and artifact - an outstanding factor that is pervasively comemmorated in the architecture of the Pyramids.

Through convergences of structural similarlity, evidence exists that the Egyptian system of three sacred numbers was assimilated into the Hebrew kabbala. The 15 was a subject of reverence because it represents the sum of the first two letters IH (Jod=10, He=5) attributable to the sacred tetragrammation IHVH, which, of itself, equals 26. Additionally, 31 is the kabbalistic reverse of 13, known also as "the Crown of Jahveh", whereas the Pythagoreans adopted most of the connections with the "sacred five".

Most of the knowledge linked with board exercises seems to have been restricted to the initiated. Although Jewish participation within the conventions of chess is not clearly documented, given the general cultural frame fo reference, the Hebrew role as a bridge between several ancient civilizations deserves more thorough examination. Thomas Hyde, Moritz Steinschneider and recently, Victor Keats, have collected pertinent chess references among Jewish authors which give rise to some positive hopes in this area, despite that no clear picture has thus far emerged regarding the question of Hebrew involvement in the main points of chess evolution.

Recent scholarship is closing in on establishing connections which demonstrate that Hebrew culture acquired their alphabet and numerological co-relations from Egypt. An impresive update by Nessod and Roger Sabbah "Les secrets de l. Exode: L'origine égyptienne des Hébreux". Godefroy. Paris 2000 seems a turning point in this question. Whereas a more detailed view of an enormous field of study is relevant to the history of culture, religion and monotheism, cross-disciplinary relationships may also impact upon inquiry into the origins of protochess.

The concise appelation of the deity which the Old Testament refers to as Jehovah or Yahweh, derives from the Hebrew name of four letters, "IHVH". The true pronunciation of it is known to very few. I myself am aware of some scores of different mystical pronunciations, although it is generally assumed that the exact and original pronunciation remains shrouded in absolute, unapproachable secrecy. "He who can rightly pronounce it, causeth heaven and earth to tremble, for it is the name which rusheth through the universe." Therefore, when a devout Jew comes upon it in scriptural passages, he either does not attempt to pronounce it, inserting a short pause instead, or else substituting the name Adonai, "ADNI", or Lord, wherever it appears in the text. The radical meaning of the word is "to be," and it is thus, like "AHIH", or Eheieh, that it gains significance as a glyph or an affirmative pronouncment of existence. Capable of twelve transpositions, all of which convey the meaning of "to be"; it is the only word that will bear so many permutations without altering its essential meaning. Also known as the "twelve banners of the mighty name," they are said by some to rule the twelve signs of the Zodiac. They are, as follow: --- IHVH, IHHV, IVHH, HVHI, HVIH, HHIV, VHHI, VIHH, VHIH, HIHV, HIVH, HHVI.

The German orientalist Oskar Fischer considered the number 13 as being what he called "the constant of Yahweh" hidden in many biblical words related to divinity. The value of the sacred tetragrammation JHWH is Jod (10), He (5), Waw (6), He (5), which, through numerological evaluation, composes 26=2x13. (Oskar Fischer. "Der Ursprung des Judentums im Lichte alttestamentarischer Zahlensymbolik". Leipzig 1917.p. 67-69. You may refer also to his book "Orientalische und Griechische Zahlensymbolik". Leipzig 1918.).

Thus, the number 26 represents a sacred figure indicative of the Holy Name. This should be borne in mind when considering the reasons for the Gnostic success of the 8x8 board and its magic constant of 260 as well as the bearing it has upon several board game exercises, including chess.

Jahveh - or Yahweh - transmitted at the Sinai (SJNJ = Samek (60), Yod (10), Nun (50), Yod (10) =130 =10x13). Additionally, the Torah (TWRH = Tau (400), Waw (6), Resch (200), He (5) = 611 = 47x13)..

The numerical value of names has therefore been one of the most predilected subjects for Jewish gnostics. Fischer indicates that when Yahweh decides to intervene directly in the destiny of a man, this may result in a change of name in some cases. The specific example of Abraham is given in Genesis, 17,5 :

"You shall no longer be called Abram but your name shall be Abraham; for I will make you the father (Ab-Hamon) of a multitude of nations"

The "gematría" of the new name is as follows: Ab-Hamon (aB-HMWN):Aleph (1), Bet (2), He (5), Mem (40), Waw(6), Nun (50) =104 = 8x13

Later (Genesis 18, 17-19), when Abraham was already "99 years old" (i.e. near the maximum life expectancy) he laughs at the anouncement that his wife Sara, also in her ninties, shall become pregnant. The son, Isaac ("the one who shall laugh") is also destined to became father of nations. His gematria is: Isaac (JZCQ): Yod (10), Zade (90), Chet (8), Qoph (100) = 208 =16x13

Jacob changes his name after wrestling against the angel of (Genesis 32,29) " He said: You shall no longer be called Jacob, but Israel, because you have contended with God Elohim) and men, and have triumphed".

Israel, means "God's fighter" or, "God fights". The ending El (value 31) means God. Jisra, with a final "h", means "fight" and its value amounts to the sum of 515. Therefore, Israel absorbs the divine factor of 13. (Total sum 546 = 42x13)

Jacob (JAQB): Yod (10), Ayin (70), Qoph (100), Bet( 2) = 182 =14x13 Israel (JShRHaL): Yod (10), Shin (300), Resc (200), He (5), Aleph (1), Lamed (30) = 546 = 42x13

In the case of Joseph: Joseph (JWSP): Yod (10), Waw (6), Samek (60), Pe (80) =156 =12x13 Fischer gives many other examples: Selah, which according to some scholars is the most mysterious word in the Bible, appearing first at the end of Ps. 33 and then repeatedly, on 71 subsequent occasions, in other Psalms. There is no explanation for its meaning although the gematric value of Selah is 2x13x13.

There are other patriarchs with a factor of 13:

Enos (27x13), Henoch (6x13), Caleb((4x13), Hosea ben Nun (41x13) may be included among them. A nephew of Aaron, named Pinehas, (16x13) received the priesthood due to his devotion, Jair (17x13), Ibzan (11x13), Abdon ben Hillel (3x7x13) and Elon (7x13) also bear the same constant.

The factor of 13 applies among the holy places as well: The country of Canaan (37x13), the mountains of Sinaí (130=10x13) and Gilead (2x12x13), Jebus (6x13), the city Salem (50x13) and Hebron (in defective writting 20x13) find inclusion. In Genesis 35:27 Kiriath ha Arba ( 76x13) is the place were Jacob went to join his father. The terebinth of More (Genesis 12:6) sums 2x13x13, Kiriath-Yearim (80x13). Genesis, chapter 14, mentions: En Mispat (43x13), Hazezon Tamar (68x13), Jabes (2x12x13), Jerico (18x13). Bethel and Beth Awen in defective spelling, also contain the respective values of 34x13 and 36x13. The constant of Yaweh is furthermore apparent in Amos, 5,5.

Divine atributes such as sovereignity (2x13) or supreme sanctity ("Godesch Godaschim" 66x13), tabernacles ("ohel moed" 12x13), the holy house (35x13), the oracle bag (64x13) and the four precious stones inside it also fall within the constant Of the stones, (I 5x13x13, II+III 109x13, IV 150x13. Altogether, these create the sum of 12x27x13.

Majesty is sometimes expressed by allegoric concepts, which apply words like "lion" to evoke the appropriate imagery. (Schajal, 2x13x13 (or ?) Schobal 2x13x13) or cedar (Erez, 16x13). Words of particular importance such as Heaven ("jamayim" 390 = 30x13), Son ("ben" 52 = 4x13), Father (13), Oil (30x13), Bread, Salt (6x13), Strong (10x13), Cave (16x13), Angel (Òmaleach 91 = 7x13), Ephod ("God's image" 91 = 7x13), Temple ("hejal" 65 = 5x13), Law ("Tor" 47x13), Right (33x13). Agar (with "H" initial), the servant in Isaac's house and Ismael's mother sum 208 =16x13, which is the same figure as Haak, who dwelled and prayed at salvation's fountain (Gen. 16:14, 24:62 or also 25:11). Memuchan (12x13) in Esther 116 ff.

Professor Fischer's overall theory is not easy to refute. It opens suggestive topics for further speculations due to the fact that the choice of the 8x8 board in chess and its magical sum of 260 (13x2x10), as well as particular numerical sequences encompassing the movements of the pieces themselves may have been related to such Gnostic considerations.

Oskar Fischer's ideas had precedents in the Christian kabbala of the Renaissance. For instance, in Italy, I have found evidence of a certain Rafael Aquilino, about whom little is known. In 1571 he published a "Trattato pio nel quale si contengono cinque articoli pertinenti alla fede christiana contra l'hebraica ostinatione, estratti dalle sacrosante antiche Scritture". The book was reprinted ten years later with several additions. Aquilino used a big kabbalistic library and states "All these mysterious things are however unclear, and most of Hebrew passages end with "Vehamschil iabin" ("The wise man shall be the one who understands") In the 1581 edition of his "Trattato" dedicated in flattering style to Pope Gregor XIII , Aquilino makes reference to 13 benedictions.

"In the Holy Language it is imposible to say "Ahebah" (love) without finding the numerical value of 13. The same happens with "Agudda", the mysterious union of God's love with the synagogue built by 13 tribes though a union similar to that of Jacob's alliance with the 12, or to Jesus' affiliation with the 12 apostles. And today, your Sanctity is named, not without mystery, Gregor XIII".

Similarly, each of t he words AChD, Achad, Unity, One, and AHBH, Ahebah, love, equal 13; for A =1, Ch = 8, D = 4, total = 13; and A = 1, H = 5, B = 2, H = 5, total = 13. Other numerological coincidences, though weaker, are perhaps worth mentioning. For instance, the number of chess pieces is 32, whereas in the first great treatise on Kabbala, the "Sefer Yezira" or "The Book of Creation", a compelling reference to the 32 paths of wisdom (10 Sephirot plus 22 Hebrew letters) appears.

72 is also a number persistently linked to mystical references of many kinds. Pico della Mirandola, in his conclusion 56, states that a wise man can deduce the magic figure of 72 from sacred tetragrammation. He explains the method in his "De arte kabbalistica": Yod = 10, Yod He = 15, Yod He Waw = 21, Yod He Waw He = 26. 10+15+21+26 = 72. (See F. Secret "La kabbala cristiana del Renacimiento". Taurus. Madrid 1979, p.85)

The reverse, or the mirrored expression of 13 is 31. Both numbers identify themseves when writing from right to left, as in the Semitic languages, or also in Indo-European writing, from left to right. The number 31 seems to be a linguistic representation of the "originary root", (ed, note: "original" root?) as Professor Fischer put it. The word "El", which means God in Semitic languages (hence the Arabic Allah), amount to the exact sum of 31. Therefore, all words ending with "El" bear the same divine factors. After the Babylonian exile, the redactors of the Bible seem to have recovered the mystical association linked with the number 31 and to have reversed it in its mirror 13 as well.

"Sesac" is a name appearing in Jeremiah which bears a hidden reference, to Babel or Babylon. In Hebrew, Sesac is written as "SSC", with the letters Shin-Shin-Caph. The clue is a kabbalistic code (one of many) classified as "at-bash", where the alphabet letters are interchanged as follows:

The first one is replaced by the last one, the second for the penultimate, the third for the fore-fore last, etc..(?) Shin is the penultimate letter (of 22) and Caph the 12th beginnig from the end. When we replace them with the second and the 12th from the beginning we obtain "Beth-Beth-Lamed", or Babel. The reason for the secret code is to protect the identity of the writer, who forwards dangerous political warnings. In the case of Jeremiah, the prophecy refers to the conquest by the Babylonian King Nabuchodonosor of every kingdom in the area, including Judah's. But the moment will arrive when:

"...and after them the king of Sesac shall drink,"(Jeremiah 25:26)

The clue is deciphered by Jeremiah himself a few chapters later:

"How has she been seized, made captive, the glory of the whole world, Sesac! What a horror has Babylon become among nations!" (Jeremiah 51:41)

The sum of the Sesac letters is 300+300+20 = 620 = 20x31. Therefore, the factor of "31" seems to bear a numerological symbolism which points toward Mesopotamia. Also in reference to the rivers, Fischer reinforces this interpretation with other examples:

Sinear, the soil of Babylonia, also supplies the same Gematrical result: 620 = 20x31. The word "hannanar" means "the flow" and delineates the river Euphrates. Its value is 310 =10x31. An identical sum occurs with "hajjarden", the Jordan river.

Previous reference to Sesac appears in anterior passages referring to Egypt (Isaac Asimov. Guía de la Biblia". Plaza y Janés. 1988. I, pp 303-305, 375) In this case, Sesac is an Egyptian general (not a Pharaoh) who offered refuge to Jeroboam, a rebel revolting against Salomo. Sesac is the first Egyptian king named by the Bible and is accredited with founding the XXII Dynasty and correspondingly, controlling the Nile delta.

2. 3 Magic squares

A Magic Square is an arrangement of the numbers from 1 to n^2 (n-squared) in an "n x n" matrix, with each number occurring exactly once, and such that the sum of the entries of any row, any column, or any main diagonal is the same. The simplest magic square is the 1x1 magic square, of which, the only entry possible is the number 1. The next simplest is the 3x3 magic square and those derived from it by symmetries of the square. This 3x3 square is definitely "mathemagical" insofar as it satisfies the definition given above. As stated by Thomas Hyde, the origin of Magic Squares points toward Egypt::

"Sciendum est, quod Orientales multum delectentur Combinatione numerorum in Tabellae quadratae Areolis inter se convenientium ad quamcunque plagam numeraveris: et ille qui ejusmodi Combinationes eleganter componere novit, multum aestimatur, et pro ingenioso habetur. Tale Schema vocatur “Wephk”, et Ars illud componendi seu conficiendi vocatur "Scientia Concordantie seu Convenientiae", et inter doctrinas seu Eruditiones Aegyptiorum haec non est minima: nam in talibus Schematis Voces Litteraeque exprimuntur Numeris magna mysteria continentibus; quae, eisdem Numeris rursus in Voces resolutis, evertendo eliciuntur. Et hoc quidem modo res sua natura planae, operte et mysteriose exprimuntur; et obscuritate involvuntur; quod laudabile et pro elegantia nunc (ut et olim) in Aegypto habitum."

There follow the astrological correlations of Magic Squares "Hujusmodi Tabellae a se invicem diversae ab Astrologis conduntur pro singulis Planetis: viz. Convenientia 3 in 3 pro Saturno, 4 in 4 pro Jove, 5 in 5 pro Marte, 6 in 6 pro Sole, 7 in 7 pro Venere, 8 in 8 pro Mercurio, 9 in 9 pro Luna."

Since ancient times, Magic Squares have been related to the different planets or luminaries of the Ptolemaic system. The board of 8x8 was adscribed to Mercury. 3x3 is Saturn, 4x4 Jupiter, 5x5 Mars, 6x6 the Sun, 7x7 Venus and 9x9 the Moon. The most conservative estimate shows that they were employed as talismans during hellenistic times. As early as the first Century C.E., The Neo-Pythogorean, Apolonius of Tiana, concentrated upon the esoteric derivations of the Saturn board. Arabic literature also bears scattered reference to numerology, and later, the same will be done by kabbalists and Jewish alchemists. Such relationships appear again in other works of the so-called Christian Kabbala of the Renaissance and were assimilated into the esoterical work of Agrippa von Nettesheim: "De occulta Philosophia" (1533). Moreover, the mathematician and occultist Girolamo Cardano" deals with the subject in his "Practica arithmetica generalis" (1539),

With regard to the relationship of Magic Squares on the 8x8 board, see a full review of the publications on the subject in Pavle Bidev: "Geschichte der Entdeckung des Schachs im magischen Quadrat und des magischen Quadrat im Schach" . Schachwissentschaftliche Forschungen nr 5. January 1975. I shall comment upon it later on, because it involves clues regarding the invention of chess movements or, as Bidev put it, "the genetic code of chess",

2. 4 Gnostic boards

There are several other boards engraved in the Egyptian temple of Kurna, besides the "chess" board (see Figure ). Board A from Kurna ("three man morris") appears as late as 1283 in the "Libro del Acedrex, de los dados e de las tablas" of king Alfonso X el Sabio under the name of "Alquerque de tres" which also inserts a comment upon the game having been derived from "saberes antigos" (ancient knowledge) : "et assi fueron descendiendo fasta en una casa:que partieron en ocho partes. E todo esto fizieron por grandes semeianzas segunt los saberes antigos que usuan los sabios".

Etymology explains that "alquerque" was an Arabic term having the root "qirq, qirqa", which comes from the Latin "circus" (field or playing area). In the "Kittab al agani" (ca. 967) we find references to an inhabitant of Mecca who kept boards for chess, nard and qirq (Murray, BG p.37) at his disposal. The Arabs draw such boards on sand or dust when stating something with solemnity (Doughty."Arabia deserta" 1988. i, 267. Cit. by Murray. p.614)

The actual name for such games, according to the orientalist Dozy is "Dris" or "Idris", which is also the Arabic name of the Biblical patriarch Enoch, the patron of occult sciences in Semitic mystical tradition. Murray, p.613, doesn't identify Dris with Idris, but the internal evidence seems convincing enough. Enoch appears in the list of patriarchs who lived an extraordinarily long amount of years. The number for Enoch is 365, as recorded in Genesis V, 23-24:

"The whole lifetime of Enoch was three hundred and sixty five years. Enoch walked with God, and he was seen no more because God took him".

The exact figure of the year cycle points toward the incrustation of an Egyptian (or Babylonian) myth. (Isaac Asimov. "Guía de la Biblia". Plaza y Janés, 1988. I, p.34. The so-called "Books of Enoch" are one of the earliest sources dealing with the subject of Jewish gnosis ( Gershom Sholem."Die jüdische Mystik in ihrer Hauptstömungen". Suhrkamp, Frankfurt, 1980). Some of its elements appear connected with protochess. Rumour of the gnostic "Books of Enoch" appear in the New Testament, and can be referenced in the Epistle of Jude 1,14:

"Now of these also Enoch, the seventh from Adam, prophesied..."

Board E is the "alquerque de seis", popular during medieval times and it appears, at least untill the 17th century, depicted or engraved in the under face side of usuak chess boards (Carrera P. "Il Giuoco degli Scacchi " 1617). Board D is the famous Pentalfa ("Five alfas" - which can be seen in its figure). This star can be traced continuously with a pencil without leaving the paper. It appears expressed with the Sumerian sign UB in pre-cuneiform inscriptions in Mesopotamia, some 3000 years B.C.E. A symbol of the goddess Ishtar (or Isis in Egypt), it was also used by Pythagorean schools throughout the Hellenistic period. In the 3rd century BC it appears on a coin with 5 letters reading "PITAN". A game using this board is still being played in Crete, Malta and other Mediterranean points. On the other hand, it embodies not only mystical or religious inferences, but also many interwoven mathematical properties commonly attributed to "sacred geometry".

HINTS IN THE EGYPTIAN AND HELLENISTIC GNOSIS

Figure 1 shows several boards engraved in the Egyptian temple of Kurna, among them a "chess" board consisting of an 8x8 square configuration. This temple, situated upon the western shore of the Nile, was built by Ramses I (1400-1366 BC) and finished by Seti I (1366-1333 BC). (Murray "Board games" pp. 18-19). The presence of a chess board among the others is interesting enough, because many additonal chess-like scenes are profusely depicted in ancient Egyptian iconography. The union of mathematical genius and mysticism is common enough, and the history of mathematics is full of examples. The most venerable is perhaps Pythagoras of Samos (fl. 530 BCE), who must have been one of the world's greatest men, but he wrote nothing, and it is hard to say how much of the doctrine known as Pythagorean (and sometimes Neo-Platonism or Gnosticism) is due to the founder of the society and how much is of a later development. It seems plausible however that most of it was borrowed from very ancient sources, and in fact, Pythagoras travelled for years through the Middle East and Egypt. In the last period of his life, he founded at Kroton (in southern Italy), a society which was at once a religious community and a scientific school. Such a body was bound to excite jealousy and mistrust, and we hear of many struggles. Pythagoras himself had to flee from Kroton to Metapontion, where he died.

Hardly any school ever professed such reverence for its founder's authority as the Pythagoreans. On the other hand, few schools have shown so much capacity for progress and for adapting themselves to new conditions. A central point of the doctrine is the famous watchword: "Everything is ruled by the Number" or, "Number is the essence of all things". The Pentalfa was seen by the Pythagoreans as an emblem of cosmic beauty and harmony in nature, as in the five petals of the flowers. Even many centuries later, the Pentagram represented the microcosmos which we find depicted among the famous engravings by Cornelius Agrippa von Nettesheim in Lib. IV of his "De Occulta Philosophia". Its esoterical meaning was kept with great secrecy among Pythagorean circles (It is said that a certain Hipasos of Metapontion was expelled from the brotherhood because he had revealed part of it).

The five "Platonic Solids" or regular (poliedres) (polarities?) are a tri-dimensional amplification of the Pentagram. The Five Platonic solids (Tetrahedron, Cube or (Hexahedron), Octahedron, Dodecahedron & Icosahedron) are ideal, primal models of crystal patterns that occur throughout the world of minerals in countless variations. These are the only five regular polyhedra, that is, the only five solids made from the same equilateral, equiangular polygons. To the Greeks, these solids symbolized fire, earth, air, spirit (or ether) and water respectively. The cube and octahedron are duals, meaning that one can be created by connecting the midpoints of the faces of the other. The icosahedron and dodecahedron are also duals of each other, and three mutually perpendicular, mutually bisecting golden rectangles can be drawn connecting their vertices and midpoints, respectively.

The tetrahedron is a dual unto itself. Pythagoreans went so far as to adopt it as a sign of mutual recognition (Iamblicus, Vita Pyth. XXIII). Its Greek name was "Hugeia", with the meaning of "health" (The same root as in the word "Hygiene". The goddess Higeia , daughter of Asklepios or Esculapius, was named Salus” among the Romans, a blessing and protective divinity) "Hugeia" is also a very frequent inscription in the talismans of the Classical period. Pythagoreans used as a greeting the word "Hugiaine!", in the sense of health, blessing, plenitude (Aristofanes "The Clouds" 609, Lucian "Pro lapsu" 5). On the contrary, the reversed Pentalfa was named "The Druid's Foot" in Medieval folklore, and seen as a devilish symbol by occultist circles. (A fallen star, like Satan, who in the Book of Revelation is described as a two-horned beast emerging from the Earth).

The 3/4/5, 5/12/13 and 7/24/25 triangles are examples of right triangles whose sides are whole numbers. The 3/4/5 triangle is contained within the so-called "King's Chamber" of the Great Pyramid, along with the 2/3/root5 and 5/root5/2root5 triangles, utilizing the various diagonals and sides. There are 13 Archimedean solids, each of which are composed of two or more different regular polygons. Interestingly, 5 (Platonic) and 13 (Archimedean) are both Fibonacci numbers, and 5, 12 and 13 form a perfect right angle triangle.

The axis of mystical numerology in Pythagorean thinking was the sacred five. Its derivations are described for instance in Matila Ghyka. ("El número de Oro". Ed.Poseidon. Barcelona 1978.) or in Ernest Bindel ("Die geistigen Grundlagen der Zahl". pp.39-102.) The Five was considered as an abstract archetype of generation. Pythagoreans named it "the generator" (gamos), because it was formed by the first even number ("female") and the first odd male number (2+3), being its Goddess Aphrodite (Venus). The first decade of numbers circles around the five. So, medieval kabbalists named the five a "circular number, because it turns around itself, and its products finish either in 0 or in 5 " Ben Esra indicates that the 5 is the end of the first class of numbers in the decade. Centuries later, the ideas of circular five were retaken by the so-called Christian Kabbala of the Renaissance. Pico della Mirandola commented in his conclusion 63 of the second part of his treatise the spheric nature of the five. "Lets draw a circle. Put 5 diameters numbered from 1 to 9, 2 to 8, 3 to 7, 4 to 6 and 5 to 5.(...) If we subtract from the biggest number the quantity with which it surpases 5 and we add it to the lesser number, we will always obtain 5. So it is a spheric number".

Round boards in Kurna may have been related to similar exercises. Such Gnostic properties of the number "five" diffused by various means and were incorporated into other religions. Hebrew kabbala related it with the letter He and with the idea of Health. In Tarot, 5 is The Great Priest, which signifies salvation, help and health. In Islam, the 5 is a pivotal element in allegoric numerology, inclusive of the five pillars, five daily prayers, as well as the five ethical categories and their fuinction in Islamic law. In their Gnostc encyclopedia (see later), a mystical group named "the Brothers of Purity" established some occultist correlations of the five. During its earliest developmental stages, Christianity poured "new wine in old recipients", whereas, 5 appears in old Christian anagrams depicting the name of Jesus, amid its allegory of fish (Ictis in Greek) or in the famous magic square of SATOR . (P. Jérôme Carcopino "Le Christianisme secret du Carré Magique" Études d'Histoire Chrétienne. n. 54/3080. Ed. Albin Michel. Paris 1953. P. de Jerphanion "La formule magique SATOR. AREPO, vieilles théories et faits nouveaux". Recherches de Science Religieuse. 25, (1935) pp 188-225)

Part 2 THE INVENTION OF CHESS MOVEMENTS

2. 1 The Safadi Board

Here is the starting point of my research. It shows an important intellectual achievement which may explain several obscure aspects of the origins of chess. This numerological arrangement on the chess board appears in the Arabic manuscript MS Berlin 7663-1, written by a certain Al Safadi, and according to Wieber "is the only magic square in the form of a chess board present in Arab manuscripts". (Wieber.op.cit.p.119. The Manuscript Berlin 7663, 1: 40a-48 shows the Safadi board, without further explanation, on fol 43b.) Its origin must certainly be much older than chess, as we will see, although Safadi, a disciple of the famous Ibn Khallikan, lived towards the end of the 14th century, (v.d Linde I, S 5 Bibl: John Wallis. Opera Mathematica. Oxonii 1699. Bd. I. S. 159-64 ) References to magic chess boards are older:

Another clue appears in an Arab manuscript from 975 which puzzled Van der Linde. The anonymous author speaks about magic squares of 3x3, 8x8 and 9x9. The Arabic author writes about a numerological construction in which there are the "house of the Knight" "the march of the Pawn", "the moves of the Visir " and refers to the usefulness of it as a talisman. A chess piece with a rectilinear movement it would obtain the same sum of 260 after eight moves in any column or in any line of the Safadi board, as we shall call it from this point onward.

THE SAFADI BOARD
A chess piece moving step by step along the two great diagonals which can be plotted on the surface of the board obtains the "magic" result of 260. So far there is however nothing absolutely extraordinary, because many other "magic squares" can be constructed on any board of any size fulfilling the same property. In the chess board more than 200 million of such "magic Squares" are possible. In exact terms these number 207,852,480 different possibilities, according to the French mathematician Lucien Gérardin. "Les carrés magiques". Dangles. Paris 1986. p. 20 But marvels in this chess board appear when we start thinking in terms of the movement of the chess pieces.

Step by step, the diagonal movement portrays the "farzin", or what refers directly to the old arabic "queen". In addition, the rectilinear, stepwise movement may be ascribed to the King. Consequently, an alternative diagonal jump in two adjacent lines or columns (which can be done by either of these two pieces) also provides the identical constant sum of 260. For instance 53-63-11-4-13-6-50-57= 260. This third property is already something exceptional.

A further surprise comes with the arabic "bishop", named the "al-fil" or elephant. This piece moved diagonally to a third square, no matter if the intermediate was free or not. Its movement was identical to the capturing move in the game of draughts. Correspondngly, an al-fil of arabic chess had only 8 squares available to it on the whole board throughout the entire course of play. Thus, when we place the al-fil in any case of this chess board, we invariably obtain the magic sum of 260 after 8 jumps. For example: 3-17-30-16-44-58-39-53 = 260. Or 64-46-5-23-28-33-51-10 = 260.

A further shock arises as we proceed with our examination of the movements of chess pieces. A pawn (and to some extent, also the king), could be kinetically characterized by a vertical movement followed by a diagonal step. It produces the same sum: 5-12-45-36-28-21-52-61 = 260. The initial placement is irrelevant: 57-50-23-32-40-47-10-1 = 260. The same happens if we repeat the procedure in horizontal sense, as would be proper for the King and not for the Pawn: 17-55-11-45-44-14-50-24 = 260. It doesn't matter whether the first movement is diagonal or not, providing the alternation is maintained.

It is difficult to describe the serious complications which evolve as we attempt to calculate what the anonymous arabic author of 975 C.E. called "The House of the Knight". The Knight also retains a great variety of routes from which it might obtain the constant sum. For instance: 64-11-17-38-33-22-16-59 = 260. Most often, after 4 jumps we gain half of the sum, 130, which can serve as a guide when testing out one of the many possible paths.

Increasingly, through mathematecal investigation, it would appear as though the rules of chess are somehow miraculously present in this numerological arrangement. Even today, this ancient board makes a tremendous intellectual impact because all movements of the pieces are directly engraved upon it. Therefore, the logical conclusion is to connect it with the invention of chess, as several scholars have already done during the past century. (See a full review of the publications on the subject in Pavle Bidev. "Geschichte der Entdeckung des Schachs im magischen Quadrat und des magischen Quadrat im Schach" . Schachwissentschaftliche Forschungen nr 5. January 1975)

It would be preposterous to think that chess movements were invented arbitrarly and that afterwards a magic square should appear containing all of them. As a consequence, the inventor or inventors of chess must have used this pre-existent numerological arrangement (the "genetic code of chess", as prof. Bidev put it) before deciding how to institute the various moves of the different chess pieces upon the board.

THE HIDDEN CLUE IN FIRDAWSI

To reinforce this conclusion, there is a decisive passage in Firdawsi's legendary story about the invention of chess which seems to have been neglected so far in its obvious meaning. The relevant chapter of Firdawsi's "Book of Kings" can be seen, for instance, in Antonius van der Linde "Geschichte und Literatur des Schachspiels". Berlin 1874. (reedited by Olms, Zürich 1981), II, p. 245 ff. About the sources from Firdawsi, I, p.4. V. der Linde uses the French translation of Jules Mohl, which differs in at least one very important point from the copy used by Murray, as we shall comment later.

Abu al Quasim Mansur, also named Firdawsi (932/42-1020/25) is the most reliable source for pre-Islamic chess in Persia. (Antonius van der Linde. "Geschichte und Literatur des Schachspiels". Berlin 1874. Ed Olms, Zürich 1981. II, pp 245 ss) In his "Book of Kings", Firdawsi describes chess as an Indian invention from the country of "Hind" brought to Persia during the brilliant period of Cosroes I the Great (531-579) also named Nushirwan or Anushirawan. Firdawsi ("the paradisian") does not describe the movement of the pieces, but all of the actual chessmen are mentioned, and its initial placement includes the central position of the king and his counsellor flanked by elephants, riders and rukhs, with foot soldiers in front of them.

The story stresses a rather bizarre point: The Indian ambassadors who brought chess to the Persian court outlined as a condition that, upon pain of the forfeit of further tributes, the wise men of Persia had to discover not only the placement of the pieces, but also its rules of movement. This task was given to them to be accomplished without the aid of any previous documentaion. "Give the order to those more used to Science to put before them the chess board and discuss among themselves the way to ascertain the rules of this noble game, to recognize by its name every piece, to fix their movement and their cases, to study the pawns, the elephants and the rest of this army, the rooks and the knights, and the movement of the vizir and the king".

No wise man in the world, even a legendary one, could ascertain the rules of movement of the chess pieces under these conditions unless they were not the result of a caprice but pre-determined by some kind of code implicit in the chess board. This code must necessarly be the numerological arrangement in the Safadi board shown above. Buzurdjmir, the legendary wise man in Firdawsi's story, discovered the secret after one day and one night, and told the Persian king: "O King of victorious fortune! I have studied these black figures and this chess board, and, thanks to the mighty Ruler of the World, I have realized completely the laws of the game".

Firdawsi's legend may or may not have a solid historical basis, although, according to Murray, his sources have the highest degree of reliability. The important fact to remember, however, is that it gives further proof that the rules of chess rules are not arbitrary. An underlying code was necessary if this legend is to make sense. Though Firdawsi writes more than 400 years following the assumed introduction of chess in Persia, his sources have been traced back towards the middle of the 6th century (C.E) as a continuous and solid chronological chain: (Van der Linde. Geschichte. I, pp 3-4. quotes Adolf Friedrich von Schack."Heldensage von Firdusi. In deutscher Nachbildung nebst einer Anleitung über das iranische Epos". Berlin, Wilhem Hertz, 1865)

King Cosroes I, an illustrious monarch, (he was responsible for translating the Hindu Panchatantram into the Pahlavi fables of Bidpay and Pilpay, later known ín arabic as "Kalila wa Dimna") ordered a compillation of any old Persian documents connected with the history of the Sassanid dynasty. (Van der Linde ("Geschichte... I, pp 3-4, n.2) Further attestation may be derived though the following sources: Albrecht Weber. " Academische Vorlesungen über indische Literaturgeschichte. Berlin. Ferd. Dümmler. 1852, pp. 196. A. Weber," Indische Skizzen", 1857, pp. 107-108. Th. Benfey. "Pantschatantra, fünf Bücher indischer Fabeln, Märchen und Erzählungen". Leipzig, F.A. Brockhaus, 1859, I, pp.64 ff). This material, coming from all provinces of his empire, was completed in 641 by a certain Danishwer under the tittle "Chodai-Nameh" (Book of the King) in Pahlavi. Towards the end of the 8th century Jaqub ben Leis, the founder of the Muslim dynasty of the Soffarids, ordered its translation into Parsi, and the inclusion of further material in the chronological gaps. During the years 961-976 a Zoroastrian named Dakiki was in charge of putting it in verse, but he managed to complete only one thousand verses. Under Mahmud I (997-1030) the task was retaken by Firdawsi, who employed 12 years (999-1011) in writting the 60.000 verses of the Epos "Shah-Nameh" (Book of Kings)

Even if the whole context is more legendary than historical, a historical conclusion can be drawn out of it. The same happens, by the way, in many mythological stories.

To quote only a few examples: Cain and Abel reflect the fight between nomad shepherds and stable land owners. Enoch, the biblical patriarch of occult knowledge, lived exactly 365 years, which signifies the inclusion of the solar cicle as part of a legendary formulation. In keeping with the ways and means through which legend continues to play a significant role in the accumulation of verifiable historical fact, the Trojan war was long held to be a literary fiction until the archaeologist Schliemann discovered the actual ruins of the old city.

Legends often bear a scientifical message expressed in allegorical language. This seems also to be the case with the invention of chess and the pretension implicit in FirdawsiÕs tale that chess rules can be rediscovered.

THE NATURAL SQUARE OF THE 8: REDISCOVERING A REDISCOVERY

The Natural Square of the 8

The wise Buzurdjmir in Firdausi's legend required one day and one night in rediscovering the laws of the earliest form of chess simply by examining or meditating over the board. His mental process can be followed regardless of whether one legendary man or many succesive groups of men took hundreds of years to achieve these results. Furthermore, Chess evolution from a mathematical exercise into a war game can be rediscovered anew by a procedure of logical thinking, which may be called "Buzurdjmir's method".

First of all, imagine that we are Buzurdjmir, and that we must determine the rules of chess and the movement of 6 different classes of pieces with no other help save direct observation of the board itself. A first step is to numerate from 1 to 64 every square of the board as follows This is the so called "natural square of the 8". and through it the first question which arises is: "How many grains of corn, or stones ("calculi" in Latin), or coins do we need to represent the figures". The so-called Indian-Arabic numerals were not yet discovered, and the usual procedure of calculation involved the employ of "calculi" upon a board, most frequently the chess board. In modern terms:

What is the sum of the arithmetical progression from 1 to 64? During his schoolboy years, the German mathematician Carl Friedrich Gauss solved the following problem: "How much is the sum of the first 100 numbers?". Instead of proceeding like all his school comrades by adding up 1+2=3, 3+3=6, 4+ 6=10 etc. he realized that the first and the last number (1+100) sum 101, like the second and the fore-last (2+99=101), and the third and the fore-fore last (3+98=101) and so on. Indeed, the problem can be rapidly solved by considering 50 pairs of numbers adding up to 101. Accordingly, 50x101= 5050. The same idea must have ocurred to Buzurdmir or to other people centuries before. To calculate the arithmetical progression upon the chess board, he considered 32 pairs of numbers adding up to 65 (1+64 = 65, 2+63 = 65, 3+62 = 65 etc). So 32x65 = 2080 stones, coins or grains of corn. The corresponding pairs of numbers can be represented graphicaly as the next figure shows. A geometrical expression of rare beauty with all lines and pairs of numbers joining at its vertex, or emanating from it is thereby produced. In an allegorical sense, the secret number of the chess board is not 64, but 65, because all other numbers are related to it.

This "polargram" on the chess board expresses the visual correspondence between each pair of numbers of the "Natural Square of the 8 " adding up to 65. The Apex 65 reflects two of the sacred numbers of God, 13x5. (It is interesting to notice that the same correspondence is kept in the Safadi board and in the so-called "Magic Square" of Mercury which we shall see later). Bidev compared it to the "Rose of the winds". Gnostic or childish eyes could look at it as a pyramid seen from above or seen from below, wherepon it is easy to see how pyramids are the Gnostic emblem "par excellence".

From the central point 65, the apex of the Pyramid, 64 lines of emanation go to the square basis, showing 8 on each side. Symbologists interpret the Pyramid in a Gnostic context: The quadrate basis represents the Earth with the apex signifying both the starting point and the end goal. This is the symbolic factor of the point. What unites the base with the point is the triangular face, symbol of fire ("Pyros", in Greek), of divine manifestation (Moses in Sinai) and of creative forces. "So, a Pyramid represents the whole Creation" (Juan Eduardo Cirlot. "Diccionario de Símbolos". Barcelona 1979. p. 365.- quoting Marc Saunier. "La Légende des Symboles". Paris 1911)

The mental procedure involved in the method is the same as in the kabbalistic language known as "atbash". In this code, each of the 22 letters of the Hebrew alphabet is replaced for another. The first is substitued by the last, the second is replaced by the penultimate and so on. The best known example is Babel, written in Hebrew BBL. Beth, the second letter, is replaced by Shin, the 21th. Lamed, the 12th letter, is substitued by Caph, the 12 letter counting from the end. So, Babel appears as Sesac, as in Jeremiah 51:41.

THE MERCURY BOARD

A third step in the Buzurdjmir procedure. The two great diagonals in the natural square of the 8 are exclusively formed by 4 pairs of numbers adding up to 65, so both diagonals produce the same constant sum of 260. Buzurdmir would certainly like to obtain also the same sum in lines and columns. In other words, to produce a "Magic Square". Since in the first line the numbers are too small and in the last line the numbers are too big, a sensible method is to interchange the placement of 4 pairs of numbers in each line and in each column. The result is the so-called "Mercury board" shown below.

In the 16th century, Hyeronimus Cardanus and Cornrlius Agrippa von Nettesheim rediscovered the method, which is probably very ancient, dating back to Egypt. The proof that this is the method is given in a later mathematical manuscript of the 14th. century written by the Byzantine Moschopoulos and kept at the Bibliothèque Nationale in Paris ) (Grec MS n. 652.) (Manuel Moschopoulos, born in Crete in 1394, dedicated his treatise on mathematics to his teacher Nicholas of Smyrna. Part of his work was printed in Europe in 1540, but the manuscripts on Magic Squares remained unknown untill 1886, when the historian Paul Tannery published them. (Lucien Gérardin."Les carrés magiques". Dangles. 1986. p. 30)

The Mercury board appeared in the Arab compilation of the Gnostic society known as the "Brothers of Purity". It is also shown in a kabbalistic book on alchemy. An area which is so far unexplored is the connection between the magic squares of protochess with alchemy. The basic source is a treatise from the 16th century in Hebrew or Aramaeic with the tittle Esh Mosaref ("The refiner's fire") The data resides in Rafael Patai. "The Jewish Alchemists". (Princeton University Press 1994. Cap. 36, p. 322.) The original book is lost, but Christian Knorr von Rosenroth (1636-1689) found an Italian version and included it in his three volumes on Latin writtings: "Kabbala denudata seu doctrina Hebraeorum transcendentalis et metaphysica atque theologica", printed in 1677, 1678 and 1684 in Sulzbach byr Abraham Lichtenthaler. Kabbalistic references to alchemy appear especially in the first volume.

Each magic square is dedicated to a given metal. The Mercury board was used for "me-zahav" (water of gold). What are the connections between the Mercury board and chess? Several exist, for as in any Magic Square, the movements of two chess pieces, step by step, vertically, horizontally or diagonally, are represented by reaching the constant sum of 260. Most important of all is the fact that the "jumping rukh" which accesses a third square vertically or horizontally, as depicted in the theory of Kohtz appears here in an astonishing manner despite starting from any square. After 8 jumps, the result is 260. After 4 jumps, half of it, or 130. This result is obtained with two alternative paths. In one of these are the numbers producing the pair 63+67=130. For instance (57-6)+(43-24)+(38-25)+(62-1) = 260. The numbers 63 and 67 are equidistant in 3 units to the mystical point 65.

In another example, the configuration of the "jumping rukh" makes even more sense when choosing the combinations leading to the pairs 49+81=130. For example (57-24)+(43-6)+(61-20)+(47-2) = 260. The number 49 and 81 are equidistant from 65 in16 units. Moreover, 49 is the square of 7 and 81 the square of 9. So, like 7 and 9 these are the "shoulders" of the 8. Its squares 49 and 81 can be seen in mystical considerations as companions of the pyramidal diffusion of 65. Starting from any point, after 8 jumps the magical sum of 260 is constantly obtained. Moreover, half of the sum (130) is obtained after 4 jumps,and precisely with continuous partials sums of 49 and 81. 49 is the square of 7. 81 the square of 9. Both are equidistant in 16 units to the emanation of the square of the 8, the allegoric number 65. So, a jumping "rook" (or "elephant" if you prefer) not only existed in protochess, but is even older than other chess movements like the diagonal jump of the arabic Alfil.

Such mathematical exercises must be very old, und signify the first drafts for the future game of chess, no matter if the stones performing the paths of 360 were animals or, probably much later, elements of the army. By the way, the Mercury board offers a clue for solving another mystery concerning the marked squares on the Ashtapada board. Fig. 7, taken from Murray, shows a historical and geographical evolution of the markings. So far, there is no satisfactory explanation of its meaning. Hyde, (Thomas Hyde. "De Ludis Orientalibus". Oxford 1698. II. pp. 74 ff) and Murray after him, supposed that in the race game of Ashtapada, played with dice, the marking indicated a safe case where a piece could be placed without being captured, but this speculative explanation is far from convincing. At least, it is questionable, since we need only to add in the oldest form of the board given by Hyde a further marking in 4 blocks of 4 numbers each, to obtain all the squares of the Mercury board where the original natural series of numbers from 1 to 64 remain unchanged.

There is a good case in favour of another interpretation: The marked squares could serve, in my opinion, as a reminder of the procedure of building a Mercury board, persisting even today in a progresively mutilated form, despite that its initial arithmetical meaning has been forgotten.

CONSTRUCTION OF THE SAFADI BOARD

Up to a certain stage, poor Buzurdjmir has re-discovered many things which amount to only the movement of 3 chess pieces on the Mercury board. However this is not yet enough, since according to the task proposed to him, he has to ascertain the movement of six different kinds of pieces. There is another possibility, based on the same idea, to be tried when building up a magic square. Instead of interchanging pairs of numbers: 2-63, 3-62, 6-59 and 7-58, etc., we can interchange the more central ones: 3-62, 4-61, 5-60 and 6-59. Repeating this procedure in all the borders and in the next lines and columns, allows us to obtain a Magic Square, but this time no more and no less than the Safadi Board which was shown above.

Buzurdjmir was inspired. He tried, from the Natural Square of the 8, to interchange numbers situated in more central points than those given in the Mercury procedure. This astonishingly simple method produces the tremendous result already commented. The procedure seems to have been re-discovered several times. Agrippa von Nettesheim makes a mention of it in his "De occulta Philosophia (1533). A certain Molleweide made about it a dissertation in Leipzig 1816. (P. Bidev. "Der Panmagische Torus 8x8 und die Panmagische Ebene 8x8. Igalo 1981. S. 3 .Typoscript)

The Safadi board contains in itself all movements of all chess pieces, and even more.

The enlarged Knight's jump (for instance, from a8 to d7, and from d7 to a6 etc) is characteristic of other pieces in other chess varieties, such as the chess in a 12x12 board described by Alfonso the Wise in 1283, and referred also as having been invented in India. The enlarged jump also produces the constant sum of 260 after 8 jumps. So, Buzurdjmir obtained a model more than adequate to define 6 different types of movement. The second part of the task is easier. To ascertain the placement of the pieces brought together with the board is a matter for more generalized considerations.

The most important, the King, must be placed in a central square whereby its rectilinear and diagonal movement, may cover all 64 cases. To his side, the adviser or "farzin", which covers 32 cases of only one colour is placed. With the three jumping pieces are grouped together, one thing is clear, which is that the knight must remain between the other two, because its movement is also intermediate between a rectilinear and a diagonal jump.

Historically, there seems to have been some initial confusion with regard to the respective placement of rook and al-fil, and most likely the rook stood in the more central position, as in the Indian four-handed chess described by al-Adli. The al-fil in the corner obtains more harmonic numbers after his obligatory first jump (57+43 =100, 8+22 =30, 64+46 =110, 1+19 = 20. The first jump of all four al-fils sum 260, the magical constant.) than if it were placed upon its actual squares. The 8 small pieces belong logically to the second rank. In any case, a solid and very important conclusion can be drawn from all this: The movements of the pieces are based in mathematical considerations that are older than the game of chess itself.

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(ed note - Illustrated content copyright Donald McLean - 2003)
(additional edits to text - Donald McLean 2007)