Chess - A Mathematical Model of the Cosmos

by Pavle Bidev

From an article appearing in British Chess Magazine, 1979 - originally published in Mail Chess, Beograd, December - vol. 1951 and January - vol. 1952 under another title: "New Investigations about Chess Origins".

Author's introductory comments on this article:
It has been read by H.J.R. Murray (1) who rejected my explanation of the elemental symbolism of the chess pieces with the following phrases: "Having an adequate reason of Indian evidence / Bana / I am not disposed to propound an alternative factor, bearing in mind Occam's razor."

The last has said: "Essentia non sunt multilicanda praeter necessitate". Having the military symbolism of Bana / Chaturanga on Ashtapada, my cosmic symbolism is accordingly superfluous. Both are in fact two visions of the same and one thing. Both are mathematically founded on the base of Magic Squares. The three aspects of Hindu chess do not exclude another. See my three articles in FIDE review since 1952, my book, "Chess a Symbol of the Cosmos" (1972) and the articles in ROCHADE.

Graphic Appendix

The Sanskrit terms for the Indian primeval chess and its pieces have been well-known. The chess was called "chaturanga". What is the meaning of this word? Murray says (pp 42-43) "The meaning of this name is perfectly plain. It is an adjective, compounded from the two words CHATUR, four, and ANGA, member, limb, with literal meaning having four limbs, four-membered, quadripartite. In this original sense it appears in the Rig Veda, X, xcii, 11 in reference to the four limbed human body and in the Satapatha Brahmana (XII, iii, 2, 2). It also occurs repeatedly in the Mahabharata (which existed in its present form by 500 A.D.), in Ramayana (which goes back in its oldest form to the 5th century B.C.), in Kamandaki's Nitisara (dating from the beginning of the Christian era), and in the Atharva Veda - Parisistas (which are not any earlier than 250 A.D.) either in agreement with the word bala, army, or used absolutely as a feminine or neuter substantive in the sense of army generally. It is clear that the word "chaturanga" became the regular epic name for the army at an early date in Sanskrit.

What was meant by the four members of the Indian army is perfectly plain from the repeated connection of the word "chaturanga" with chariots, elephants, cavalry and infantry? In Ramayana (I. ixxiv. 4) the army is expressly called hasty-ashwa-ratha-padatam, the total or aggregate of elephants, horses, chariots and foot soldiers." A little further, Murray says (top 44-45) "The same four elements - chariot, horse, elephants, foot-soldiers - appear as four out of the six different types of force in the board game chaturanga. The remaining types prefigure individuals, not types of military force. The presence of the King needs no justification. The addition of the Minister or Vizier is in complete agreement with Oriental custom, and the Code of Manu (VII, 65) lays stress on the dependence of the army on him. The self contingency of the nomenclature and the exactness with it reproduces the composition of the Indian army afford the strongest grounds for regarding chess as a conscious and deliberate attempt to represent Indian warfare in a game. That chess is a war game is a commonplace of Indian, Muslim and Chinese writers.

Murray, as well as all the other historians of chess before and after him takes literally the meaning of the Sanskrit terms mentioned. It has not occurred to anyone to ask whether these expressions have some other hidden and figurative meaning in an allegorical sense. Starting from the well-known fact that "India is a classical country of symbols" (Paul Deussen), I have taken the task to consider the Sanskrit terms for chess and its pieces in the light of Indian ideas of religious and philosophical symbolism. The way was unpaved, difficult and full of wrong ways, but after long wandering, it has brought me at last to the aim desired. As a final result of such a method of work, I have got the next translations or symbolic meanings of the Sanskrit terms: chaturanga = four elements of material (fire, air, water and earth), ratha (chariot) = earth (prthivi), ashwa (horse) = water (apas) hastin (elephant) = wind or air (vayu), mantrin (wise man) = fire (agni), rajan (king) = ether (akasha). Murray as very close to a right solution of the chess puzzle, translating the term "chaturanga" as "four elements", but unfortunately he understood by it only four elements of the Indian army,and not the elements of material. Moreover, my translation has seemed correct to me from another point of view, viz. according to the analogous terms in the classical culture of the Greeks and Romans.

The great Roman polyhistor M. Terentius Varro (116-27 B.C.) has for the elements the term "quattor partes". The famous philosopher-poet, Lucretius calls them "maxima mundi membra ae partes" (De rerum natura, V. 244-5), which when translated means, "the big parts and libs of the world". The propagandist of the four elements theory by the Greeks, Empedocles (6th Century A.D.) calls the elements by the name "tetrada" = fourfoldness. Some other terms of the classical era have also been known to me. Plutarch states that the square was a Pythagorean symbol for the four elements. By the religious sect. Mithraist's quadriga with four horses had symbolized the four elements. Plutarch states, op. cit. cap. 63, that the Egyptian priests had considered four chords of the sacred instrument sistrum as symbols of the four elements. Bearing all that in mind, I began to search for the corrresponding terms in Indian culture.

With regard to the holiness of the number four, the Indians have many different terms in mythology, religion and philosophy with chatur: chaturveda (4 Vedas), chaturyuga (world seasons), chturvarna (4 castes), etc. However, I have come upon only one, but significant example which is in connection with the elements. By the name "chaturmaharajikas" (means 4 great kings) the Buddhists call the gods of fire, water and earth who dwell in the North, South, East and West, with their suites upon the horses in four different colours. With the term chaturmaharajikas I have immediately brought in connection the term "chaturangi" (means four kings) as one calls in India the four-handed chess. For that chess, two names exists, chaturanja and chaturanji. It used to be played by four players with pieces in four colours. The arrangement of pieces is shown in Diagram No 1. The white and black are the allies against the yellow and green. In that game, even the kings could be captured as common pieces. To me it has been clear at once that the term "four kings" is in connection with the elements. The pieces are arranged in the North, South, East and West, each group being coloured differently - just the same case as with the elementary gods - with the Kings and their suites. While v.d. Linde believes that the common chess has developed from the chess of four Kinds (Geshichtem I, B. 4), Murray (p.46) considers the two handed chess probably older than the former. How close Murray was to the correct solution of the problem shows (in) the next example. On pp. 348-49 of his work he mentions a kind of chess which has been described in the manuscript of the Spanish King Alphonso X of Castile (1251-84). Murray writes: IV, (18) Four-handed chess. Ajedrez de los quattros tiempos (f.87a). The four playes symbolized the struggle between the following groups of four:

SEASONS ELEMENTS COLOURS HUMOURS
Spring Air Green Blood
Summer Fire Red Choler
Autumn Earth Black Melancholy
Winter Water White Phlegma

The ordinary chessboard was used for this game, but the two major diagonals were drawn across the center group of 16 squares. The reasons given for this is that it divided the players and showed which directions the Pawns were to be moved. I give a diagram of the arrangement of the board (see Diagram No. 2). It will be noted that each player has K, R, Kt, B and 4 Ps as in the four-handed Indian dice chess, but they face along the edges of the board and on reaching the opposite edge become Alferzas (Qs) at once. And now I shall try to show how the whole structure of primeval chess is in all its details in accordance with the old Indian theory of elements. If we start with the boarder towards the center, we come upon the piece which is called nowadays: Turm, Castle, ... etc. Its Sanskrit name is Ratha and means chariot. In my investigations this piece represents symbolically the earth in several ways: 1) by the place where it stands 2) by the way in which it used to be moved 3) by its name 4) by the fact that it consists of eight parts i.e. four pieces and four pawns.

The starting position of pieces in chaturanga corresponds to the present state of affairs and consequently the chariots once stood in four corners of the boards as they do nowadays. The geometrical position of the earth in the Indian philosophy of nature (the literature of Tantra and Yoga-Tattvaupanishad) is a square. This ancient conception is to be found also among the Chinese, Jews and some primitive nations. The starting position of the chariots gives staticaly a pure picture of a square, but dynamically too - the way in which they used to be moved in the same way as in modern chess. It is evident that in this way they touch one another dynamically even in the starting position, so forming the picture of a square. Murray and Kohtz oppose v.d. Linde, claiming that the chariots in the primeval chess had limited moves in the straight direction, and that in a spring on the third square off. I accept their conception as right, and starting from it, we are able to see still clearer that the chariots really form the picture of a square.

It may be seen that when a chariot crosses all the squares on which it may stand, springing on the third square off in a straight line. Diagram No 1 shows that one chariot has (at) its disposal 16 squares in total and these, when tied up by straight lines, form nine squares. The diagram shows also that each chariot has it own zone of moving in the form of a square. All that shows that the square is really a geometric picture of the corner piece moving. This is a geometric proof that the chariot represents a symbol of the earth element. There is also an arithmetic proof based upon the mixed theory of elements. Indian scientists had elaborated the teaching that every element in nature consists of eight eights, four of which are formed of the element itself, and the other four eights are composed of other elements. It means that no element appears as a pure one, but always mixed with some others. So, for instance, the earth is composed of 4/8 pure earth, 1/8 of fire, 1/8 of water, 1/8 of air, 1/8 of ether. It is shown clearly enough on the chessboard. The Pawns are, in fact, embryonic forms of elements because they contain in an embryo the movements of great pieces. They are the elements in development, and therefore they move only forward and become pieces of elements only on the eight rank. There are some old rules by which a Pawn could become a Knight only if it appears at b1 g1 respectively, b8 and g8; similarly, it could become an elephant at c1, f1: c9 and f8, and so in turn for other pieces. The promotion was dependent on the nature of the square. The Pawn, consequently, was once a potential piece of each element and it is the same at (the) present time.

The chariots represent the earth by their fundamental position on the chessboard, too. In the old pictures of the world, the earth is the most universal celestial body, and that carries inside and outside itself the other elements. At last, by its name as well, the chariot represents the earth symbolically. Among the Indians, the chariot is a traditional symbol of the earthly body of man. Three of the greatest philosophical schools teach that the human body is made only of earth, and the comparison of body with chariot is a common Indian, widespread and popular one. Now we turn to the piece of Knight (or Horse, as it is called on the Continent), which stands next to the chariot and represents the fluid element of nature - the water. To mythologists it is well-known that the horse is an ancient symbol of water among the Aryan nations.

It is almost impossible to number all those cases in which the horse appears in connection with water. Various sea, well, lake and river divinities, ghosts or demons appear in the form of a horse or with a horses head. Indian myths look even for the very origin of the horse in water. Bachofen (Urreligion und antike Symbole, II Leipzig 1926, S. 171) indicated that the very words horse and water, equus and aqua, are etymologically identical. The English and the Italian still call the sea waves - horses (mares): white horses, resp. caballoni. The horse has always stood on the chessboard on its known place and has been moved in its original manner. In two springs it can draw a half moon, the Indian symbol of water. The Brahmanic symbol of water is a half-moon, and the Buddhist one is a circle. The Horse is able to describe the both pictures. In eight springs it can describe a closed circle line around the King. If we let four horses move side by side along a longer chessboard, we shall get nice transversal waves on water. Someone may note that the moves of the knight are straight and not curved lines. The followers of Einstein's theory of relativity give right to me, and a voice of defense in my benefit has been heard even from the Middle Ages. The famous Jewish writer Abraham Ibn Ezra, in his poem, "On Chess" writes about the movement of the Knight (v.d. Linde I. 165):

"Des Rosses Fuss, sehr leicht ist er im Streite,
Er gehet auf gekrummtem Wege;
Verkurummt sind seine Wege, nicht gerade."

In the case of the Knight too, there is an arithmetical proof that it is the symbol of water. On the base of mixed theory of elements, the water consists of eight parts, i.e. 8/8, 4/8 of which is pure water. 1/8 fire, 1/8 ether, 1/8 air and 1/8 earth. The mixed theory of elements is given by Paul Deussen in "Die Philosophie der Upanishads" , 1919 Leipzig S. 174; Die nachvedischse Philosphie der Inder, Leipzig, 1920, S. 446, 494, 598, 629, 652.

{Interlined note presumably from the desk of Dr. Ricardo Calvo - The elemental symbolism of chess pieces is confirmed by a Chinese document of 569 A.D. concerning the primeval astrological protochess of emperor Wu Di. His protochess handbook is lost, but it is conserved in the foreward by his chancellor Wang Bao. The elemental symbolism in question has been found by three authors: Israel Regardee in Golden Dawn - before 1940, by Bidev at the same time and by Nicolai Rudin in Moscow 1968. His discovery was made, in fact in 1917, according (to) his letter addressed to me before many years.}

The second animal in the primeval chess is the gigantic elephant (nowadays Laufer, Fou, Bishop, etc.) whose name is still kept in Russian chess. The appearance of the elephant symbolizes the third element of material - the air, or, as it is called by the Indians, the wind (vayu): 1) by its name; 2) by the way in which it used to move in the primeval chess; 3) by the place it stands on, and 4) by the number of pieces and pawns (8/8).

As the horse represents an ancient symbol of water, so the elephant, the religious animal of the Indians, is the attribute of the atmospheric god Indra, the king of all ghosts in the airy space. Indra in the atmosphere possesses lots of elephants (a poetic picture for dark clouds) and his favourite elephant on whose back he gladly rides is called Airavata. Some India elephants are represented also with the wings flying through the airy space.

I accept as correct the opinion of two older Indologists that Indra etymologically means "the blue air" (Christian Lassen, Indsche Altertumkunde I, 2. Aufil, Leipzig, 1867, S. 893, A. 3.). In that way there would be a symbolic connection between the air and the elephant. Even nowadays the elephant is, in the eyes of the Indians, the symbol of a dark cloud in the atmosphere. The god of wind, storm and thunderstroke, Indra on the back of an elephant is beyond any doubt, the mythologic picture of a cloud out of which it lightens.

Not only by its name, but also by the way in which it moves in the primeval chess, the elephant symbolizes the air. The geometric picture of the air in the Indian philosophy of nature is a six-pointed star - i.e. two intercrossed triangles. It may be seen most clearly if from two corners the moves of the elephants are projected along the central diagonals (see Diagram No. 1)

The shorter moving, too, along the diagonal, however, leads principally to the formation of triangular pictures. The historians of chess think that the elephant of Chaturanga used to spring obliquely on the third square off itself. I accept that opinion as correct. If we project the springs of the elephant from their primary position in the frame of the square of chariots, we shall obtain six triangles that partially cross one another in the centre. (see Diagram No. 2).

In Chaturanga the elephant could spring only upon eight squares. In that way it divides nine squares of the neighbouring chariots into eighteen triangles, as the picture below shows (see Diagram No. 3). So we have a geometric proof that the picture of elephant moving is a triangle.

The connection among the elephant, six-pointed star, and airy space exist in the well-known myth about the conception of Buddha. The six pointed star is the geometric emblem of Ganesha, the god with the elephant head. That emblem consists in fact of three six pointed stars. on put into the other (H. Zimmer Kunstform und Yoga im indischen Kultbild, Berlin, 1928, S. 114). Ganesha, as the donor of wisdom, wealth and as the remover of obstacles, is the most popular deity of the Indians. Only in the holy town of Benares he has about 200 temples.

Arithmetically, the star also consists of eight eighths, as a matter of fact the same case as with all the other elements. The elephants represent 4/8 of pure air, and the pawns in front of them 4/8 of the other elements. (See Diagram No.4)

Now we turn to the central pieces, the King and the Wise Man (rajan and mantrin). They symbolically represent the first and the main elements of the world, ether and fire - takasha and agnu. Therefore, they are represented with the human appearance. C. Capeller gives the following translation of the word mantrin (A Sanskrit-English Dictionary, Strassburg, 1891): mantrin a. wise, clever, m. enchanter, conjurer; a king's minister or counsellor. Mantrin is in fact the man who knows mantras, the prayers and magic sayings, consequently a priest - wise man. His procession was inherently connected with the cult of holy fires. That element is the symbol of the Brahmanic caste and their knowledge and wisdom. Agni is the priest - wise man among the gods, and his representatives on the earth are the Brahmans. The name mantrin directly symbolizes fire, as fire, vice versa, symbolizes the Brahmanic caste. In French, "les lumieres" means knowledge, science, education, at any rate a remembrance of the ancient cult of fire.

The symbol of fire is a common triangle. Nowadays the Queen goes everywhere obliquely and straight, but formerly the piece "mantrin" could step only obliquely along the diagonals and that only upon one square far from itself, i.e. half shorter than the elephant. Maybe because the picture of fire is a common triangle and the picture of air a double triangle. The mantrin could draw the picture of its element from the primary position in three moves. (See Diagram No. 5)

Here is an appropriate occasion to compare the moves of the chariot, horse and mantrin. The picture of the Earth, a quadrate, is composed of four lines: the chariot draws it in four moves. The picture of water, the half-moon, consists of two lines: the horse draws it in two moves (See Diagrams No. 6 and 7). The picture of fire, a triangle. consists of three lines. The mantrin draws it in three moves. The picture of air, a six-pointed star, and the picture of ether, a circle, cannot adequately be presented on the square space, but approximately only.

"The king goes to all the squares round about...", says an Indian author from the 18th Century in the work Charturangavinoda (Murray, p.66). By this description he throws light to the question why the fathers of chess had given the King the known way of moving. It seems that they could not otherwise express more economically the idea of a circle on a square space (See Diagram No. 8 ).

With Aristotle, ether is a divine celestial element and as a perfect one has its moving in a circle. Fire and air, light by their nature move in the direction upwards and water and earth, heavy by their nature, move downwards. That is what Aristotle tells us in his physics.

The King even by his name symbolically indicates ether. That is the first and chief element finer than fire and air, while in the language of symbols, the King means that which is first and chief. That is why chess is called a royal game, because it, like a King, stands above all other games and not because the principle pieces in it are the Kings. So ether, is a royal element too.

In the case of the King and mantrin, it is not possible to draw the arithmetical proof that each of them consists of 8/8. I suppose therefore, that in the center only, fire was prefigured first and only later on a difference was brought out between the mantrin and the King - i.e. between fire and ether. Even the name of chess, chaturanga = 4 elements shows that the state of affairs in the primeval chess was perhaps like that.

Of ether itself, different conceptions exist in Indian philosophical schools. While some (Shankhya and Yoga) indicate it as an element, the others (Vedanta) simply identify it to space. Maybe the first element (akasha) was originally represented by the area of the chessboard. In that case, the square form of the board would not correspond to the circular figure of ether.

By this, in a few words, in the shortest lines, is exposed the argumentation that the pieces of chess are the symbols of material elements of nature. It still remains to explain why there are white and black pieces, as well as the reason why nature (The Universe) is represented in chess in the form of a game.

The Indian philosophy of nature teaches that three fundamental factors (trugunas) determine the life of material in the whole universe. These are sattvam, rajas and tamas - or, in translation, light, moving and darkness. This translation is the simplest and the best (see the excellent article about gunas by Richard Garbe, the best judge of that question in Hasting's Encyclopedia of Religion and Ethics, Vol VI, p.454).

It is clear without further explanation that the factor light (sattvam) is symbolized by the white pieces, the factor "tamas" or darkness, by the black ones and the middle factor moving (rajas) is potentially between the white and the black pieces. i.e. - between light and darkness.

The Indian conception of the world of the Universe is a game, undertaken by a supreme deity (Brahma, Vishnu or Shiva) 1) The dualists, (the School Samkhya) consider this game performed by the primeval material (prakrti) without any participation of the gods. They differ the static and dynamic stadium of the Universe. In the former there are three factors, light motion and darkness, entirely drawn within their limits, completely quantitatively balanced, so that neither is more or less than the other. (R. Garbe, Die Sampkhya-Philosophie, Leipzig, 1917, S 283-284).

In the dynamic stadium, the middle factor motion (rajas) starts its activity and in that way causes the game of the world's development. The material from the state of repose passes into the state of activity, the three factors begin the struggle for supremacy, the result of which is the evolution of material and all the rest of the Universe. For tat dynamic stadium of material, the Indians have a technical term - lil + game. Chess is apparently a small but excellent illustration of this Indian theory. Either stadium of material is nicely shown symbolically (See Diagrams No 9 and 10).

In the Indian conception of the world prevails the opinion that the world is a flat disc (in Sanskrit: jagad-vimbam). The world's game develops in the plane of two dimensions, consequently out chess is two dimensional. In error are all those reformers of chess who want to change the square of the chessboard to a cube or something like that, in order to make chess, in their opinion, a true picture of nature. They do not take into account the specific characteristics of the Indian conception of the world. The same may be said also of the Englishman Charles Bettie, who proposes his model of "total chess" to us now. By the way, I mention that our solar system is a flat plate because the moving in a circle of the planets, satellites, planetoids and comets takes place in two dimensional space.

One look at chess shows that its structure is built on the basis of the number 8. That is the sacred number of the Brahmanic caste, but its role in the Indian view of life, in mythology, religion, philosophy, in natural and spiritual sciences, cult and ceremonies is in fact infinite. Therefore without any exaggeration, one may say the=at the number 8 represents the national emblem of Indian culture. A similar case is also with the numbers 4 - 8 - 16 - 32 - and 64.

From the static and dynamic point of view, the structure of chess is based evidently on purpose on the progression of the numbers 1 - 2 - 4 - 8 -16 - 32 - 64 which plays a great part in the Indian view of life, especially in cosmographic theories of the Indians (cf. v. d. Linde, 1, 2, 3; Murray, 210). The pieces in chaturanga had the eight squares on their disposal differently:

8 --- elephant

16--- chariot

32--- mantrin

64--- King and horse

They are statically divided into two halves, grouped in four ranks, each of them having eight stones, each half having 16 of them - 32 in total. The board is a visible picture of the number 4 (square), whose side is 8. the perimeter and surface of one board quadrant = 16. the perimeter of the whole quadrate = 32, the surface = 64. In all its details, the chess game is and exact mirror of the Indian conception of the world.

To me, it was a great inner pleasure when I learned that the great American investigator of games, Stuart Culin, defended the standpoint of chess similar to mine, In his great works Culin searched into pastime and ceremony games of the peoples of white, red, black, and yellow race, and he came to an important knowledge that, as emphasized by Murray (op. cit. p.50), deserves full attention. Culin thinks that pastime games trace their origin to magical processes of long ago, and that the present games of ours represent their survived remainders. Culin's conception of the origin and meaning of chess games I expose here according to Murray (op. cit. p 49-50);

" Another story of the ancestry of chess has been put forward by Mr., Culin in his Chess and Playing Cards (Washington, 1898). He sees in our present games the survivals of magical processes adapted to classify according to the four directions, objects and events which did not of themselves reveal their proper classification. Dice of some popular agent represent one of the implements of magic employed for the purpose. According to his theory, chess is a game derived from a game of the race type, and the steps of the ascent are: 1) two-handed chess; 2) fourhanded dice chess (chaturanji); 3) Pachisi, a fourhanded race game; 4) a two-handed race game. It is therefore a development of the Cox-Forbes theory which aims at carrying the pedigree still further back. Culin's argument is thus stated, (op. cit. 858). The relation of the game of Chaturanga (i.e. the four-handed dice chess) to the game of Pachisi is very evident. The board is the square of the arm of the Pachisi Cross, and even the castles of the latter appear to be perpetuated in the camps, similarly marked with diagonals on the Chinese chessboard. The arrangement of the men at the corners of the board survives in the Burmese game of chess. The four-sided die is similar to that used in Chausar (i.e. Chaupar). The pieces of the men are of the same colours as in Pachisi,and consist of the four sets of men or pawns of the Pachisi game, with the addition of the four distinctive chess pieces, the origin and significance which remain to be accounted for. By analogy it may be assumed that the boards, if not indeed all boards upon which games are played. stands for the world and its four quarters (or the year and its four seasons) and that the game was itself divinitory".

Very important is Culin's conclusion that the games are "based upon certain fundamental conceptions of the Universe" (Culin, Korean Games; Murray op. cit. p.31). That can be fully applied to chess. I am sorry, but the space does not allow me to describe other games as well, with the astronomic and cosmological themes and to show that chess is not a solitary phenomena in the kingdom of games. Right is Culin's opinion that the board in chess represents the world. And what are the pieces? Having rejected the military interpretation of chess as a martial game, he only put the question, not being able to find a proper answer. By that, Culin has come only half way in looking for the scientific truth. The pieces are the elements of the world, its material components: the earth, water, fire, air and ether divided into the forces of light and darkness. Such ought to be the second part of the truth. In the history of man, the elements played a great part in all parts of the world and among all races. The theory of elements plays a dominant part in the science and philosophy of the Ancient and Middle Ages in the East as well as the West. Under the powerful authority of Aristotle, the learning of the four elements and of ether as quinta essentia lived in the West over two thousand years, up to the beginning of the 18th Century. At the end of the 17th Century, the English chemist Robert Boyle founded the experimental methods for detecting the chemical elements, and so gave the first big blow to the theory of the four elements. The water, air and earth were separatedinto their component elements, and when later on the flogistonic theory of fire was also destroyed, finally came the end of the classical theory of elements. As to the role of the culture of the Indians, it is almost inestimable. Mythology, religion, philosophy, medicine, magics, all the branches of science and life practice. all of them are in one or another way attached to the elements.

Goethe was right when he called the Indians "die Verehrer des Feuers und der Elements" (in Westostchlicher Divan", Berlin, 1872, p. 245; according to v.d. Linde, Geschicte, II, 335), because in their religious conception of life and world, and especially in the occurrences of cult and ritual, the elements are alpha and omega of the world. The Indologist Rienhold F.G. Muller emphasizes that the elements(he calls them Gross-Wesen) make the main base of the old Indian natural science ("...die Gross-Wesen bilden eine hauptsachlichen Grundlage der altindichen Naturewissenschaft", Sinneslehre altindischer Medizin, Haalle, 1944, S. 31 (7) Anm. 16).

It is very difficult to answer the question who might be the creator of chess. i.e. to which philosophical school or religious sect he could eventually belong. When one takes in consideration the rationalistic spirit of chess, (a) game where logic and reasonable reckoning play a considerable part, it would be logical to conclude that the philosophical school Sankhya is the ideal crib of our game. In it, the Indian rationalism reached its top. But at that school, nobody mentions the geometric symbols of elements, so that RIchard Garbe does not speak about that at all in his excellent monography, "Die Samkhya-Philosophie". I should point to the school of Yoga as to the spiritual mother of chess, having several reasons for doing so.

Firstly, Yoga has included in its system all the theories of Sankhya-philosophiy; secondly, in the learning of Yoga, he geometrical figures of the elements play an important part, e.g. in Yoga-tattva-upanishad; thirdly, Yoga ha developed meditations about the elements and the methods how to subdue them in a magic way. Why has the Indian created in chess a small model of the Universe? To that question I dare answer only in coordination with Stuart Culin. I think his theory is on firm ground when he states that games had been developed from from magical processes, because for that statement he offers a good deal of facts. Starting from his standpoint, I hold that chess had been derived from that part of Yoga learning which deals with natural magic. The ruling over the natural phenomena, over the elements by means of magics, that is the fantastic aim of royal Yoga. The adept (of Royal Yoga) tends to be the unlimited master over the whole Universe. How can he achieve it? The magician makes a model of that on which he wishes to influence. If he wants to captivate a woman, he makes her a small figure of wax, fancies that it is identical to the original, speaks the formulas of entreaty, piercing her heart with a needle. The creator of chess had a similar aim. He wanted the magical play of natural matter to learn and overcome in an original way. He made for himself a small model of the Universe in strict correspondence with his conception of the world. He divided in harmony three factors of the matter, light, darkness and motion; he set the elements on their proper places and regulated their moving according to their geometrical figures, all that in concordance with the sacred mystic of numbers, according to the progression 1 - 2 - 4 - 8 - 16 - 32 and 64, as the divine evolution runs. Having created his own small world, he believed it was identical to the big one, the macrocosmos and that by help of the former, he could affect the latter. And as the whole device had to remain a holy secret comprehensible only to the dedicated to the secret science of Yoga-philosophy, he had chosen the names for his device and its pieces such that only bespoke the entity of the device, that told only half that they referred to, and that only for the adepts of the secret science.

For the outside world the device had to be a nice martial game and nothing else. In that, the creator of chess had entirely succeeded. In the course of 1,500 years he achieved to lead the whole world by the nose, from children and simple people up to the highest representatives of science. Indologists remained fascinated by the Sanskrit names which literally meant the army and its parts. They have forgotten that Indian gods do not like what is said directly, but only what is wrapped in a secret, which is only intimated. I cite from the work of Dr. M. Witernitz "Geshichte der Indischen Literatur", I., 2, Ausg., Leipzig, without the year, S. 161: "Die Gotter lieben das angedeutete, das Geheimnisvoll", ist ein in den Brahmanas oft weiderkehrender Satz. Brhadaranuaka-Upanishad IV, 2, 2:, "Die Gotter lieben das versteckt Angedeutete und hassen das direkt Gesagte". Chess has two faces; the egsoteric one, which is available only to the outside world and profane science, and the esoteric one, which can be understood by those dedicated to the secret science of the Indians.

There are two possible interpretations of the chess game: the first one is the traditional and popular explanation that chess is a nice martial game and nothing else; it has become the communis opinio of the whole human race and the highest representatives of science. Goethe once said that the greatest enemies of new truths were the old errors. It is difficult to correct the errors. I am now in the position of the man who with a granule of sand hits at a gigantic rock. Nevertheless , I think that the truth is on my side and the moment of triumph shall come. The new interpretation that I give is the true face of (the) chess game, the clue of its secret of many centuries. The boyish tale that chess is a martial game represents but the false face of chess, its backside.

At the end of this brief review of my unpublished book I should like to touch the question of the scientific worth of the the interpretation of chess as a martial game that is so resolutely defended by v.d. Linde, Murray, Kohtz and the Indologist Albrecht Weber. The reader keeps in mind from the first part of this article the arguments by which Murray defends his standpoint. I put forth against him and the others the following contra-arguments.

1) The formation of fighting forces on the chess board does not correspond to the arrangement of the Indian army in the battle field. This formation was not taken in consideration even as a theoretical possibility in the work of Kamandaki "Nitisara", which is cited by Murray and v. d. Linde. The elephants should stand in the first battle file in front of the pawns, because in the ancient wars they used to play (the) part of our present tanks.

2) It is quite understandable why the horse and elephant spring in primeval chess, because they are animals. But that a chariot springs over the pieces and pawns, that is really a little strange. The four chariots may eternally circulate in chaturanga without meeting one another anywhere; the same is with the elephants and mantrins. This does not correspond to the state of affairs on the battlefield.

3) The moving of the pawns only forward cannot be understood from the point of view of military interpretation of chess. The explanation that the pawns represent the symbols of elements in developing is more natural. Their metamorphosis on the eighth square is a small but magnificent illustration of the dialectic law of the passing of quantity to quality.

4) Militarism is no characteristic of the Indian people. As nicely emphasized by the well-known Inologist H Oldenberg (Aus den alten Indien, Berlin, 1910, S. 53), "the Indians have nerves, not muscles". The Indians have caused the world's admiration by their religious and philosophical doctrines, not by their military conquests. From that point of view chess cannot in principle have a military mark. Chess is a product of Indian scientific and philosophical thought, not of their warfare skill. The old legends of the ancestry of chess unanimously claim that the creator of chess comes from the Brahmanic caste in whose domain goes everything but military skill and making war. That was the concern of the caste Kshatri, the professional warriors. Legends do not mention them at all as the inventors of chess.

5) The invention of chess belongs approximately to the sixth century of our era, maybe a little earlier or later. That era represents the end of the golden age of Indian history, when under the rule of the Gupta dynasty, Indian culture was living to see its zenith. That is a long-lasting epoch of peace that was disturbed by only one big war. If we look at the origin of chess in frame of the surrounding, race and time factor by which Hippolite Taine explained the birth of the great works of art, then we can see the whole worthlessness of these theses of militaristically disposed historians of chess. The social surrounding is the Brahmanic caste, whose subjects are engaged on science and philosophy. Their national inclination towards religious meditation and philosophical contemplation is very well known. The historical moment was not convenient for creating of cultural works with a militaristic mark. That ear represents the middle of the Indian Middle Ages, when mysticism of every kind was flourishing. In such a climate, on such a soil, the exotic plant, whose name is chess has grown up. What can it have in common with war and militaristic spirit?

6) From that point of view, it is not possible to explain either the arrangement of the pieces on the board or their movements. Why does the chariot spring orthogonically, the elephant diagonally, the horse tortuously, the King on squares around, and the mantrin obliquely on one square? V. d. Linde, like Murray and Kohtz come to a tragi-comical situation when they try to find a reasonable explanation. True science requires exact proofs and detailed explanations for every thesis. Who defends the theory that chess is a martial game must give precise arguments in favour of that conception. In that case they act formally and nominally when Murray and others claim that chess is a martial game only because the names of the pieces mean the parts of the Indian army. In that way they stay at mere names, and do not go further into deepness or wideness. Games have been relatively little explored and thanks to the great works of Stewart Culin, we are able now to know a little better the factors which played an important part in the beginning of games.

It seems that dramatic and amusing games have the same parents: cult, ceremonies and magical practices. About that speaks also the latest book of the English scientist Lewis Spence "Myth and Ritual in Dance, Game, and Rhyme", which in 1947 lived to see its two editions in London. Further investigations will certainly develop in that direction, and that will be of great use also for the history of chess.

As accredited by the author:

(1) "A History of Chess" a monumental work by Harold Murray, has been considered the last word in the science of chess origins. It was published in 1913 by the University of Oxford just in the town where, in 1694, the first history of chess from the pen of the scientist Thomas Hyde, "Mandragorias... saw the world. Even the first historian of our game made a correct hypothesis that India was the cradle of chess and that was later magnificently confirmed by the investigations of Indeologists and...historians of chess. Since I cannot expose the course and development of these works within the limits of this article, I direct the curious readers to a short but excellent review of that subject in the article of Alan C. White's "History of Chess" in the British Encyclopedia, Vol 5, p. 430.