[The following was transcribed directly from the published pammplet, regardless of existing typographical errors.] CHESS--CURIOUSER AND CURIOUSER by V. R. Parton DEDICATED TO BLIND PLAYERS OF CHESS ------- The author sincerely thanks Professor J Boyer (Paris), Miss G. M. King, and his brother, Mr. C T. Parton, for their very kind help concerning this little book on "Alician Themes" in Chess and related ideas. In certain cases, the letter H is used for "Horseman" as the equivalent of "Knight." In two chapters, the modern notation is used: the files are lettered, from left to right in relation to White; and the ranks are numbered, from White's back rank towards Black's side of the chess board. ----------------------------------------------------------------------------------------------------- [page 1] SCACETIC "You seem very clever at explaining words, Sir," said Alice to Humpty Dumpty. "Would you kindly tell me the meaning of the poem Jabberwocky?" "Let's hear it," said Humpty Dumpty. I can explain all the poems that ever were invented, and a good many that haven't been invented yet......" ".......well, slithy means lithe and slimy; lithe is the same as active. You see it's a portmanteau; there are two meanings packed up into one word." "Alice through the Looking-glass." Some players who, in their schooldays, were taught Latin grammar, perhaps succeeded, under the painful lashes of their master's whipping tongue, in reaching the level in Latin of slow, clumsy translation of the opening section in the first book of Caius Julius Caesar's war memoirs: De Bello Gallico. (If he had foreseen to what scholastic uses his book would be put in the future, would Caesar have really wished to fight that Gallic war?) Such players may, since their schooldays, have come across unusual applications of the celebrated fact, stated in Caesar's book: "Gaul is divided into three parts." My abstraction, the Scacetic country with which the medley of matters and ideas described in this small book is concerned, can also be divided into three parts, like Caesar's own Gaul. The three elements which are involved in any kind of Scacetic philosophy are: Boards, Men or Pieces, Purposes or Aims, for which such boards and men can be rationally used. The medieval Latin word "scacus"(plural: scaci) has the meaning: man or piece used in playing Chess, without distinction between pawns and pieces proper. My special word Scacetic is to be regarded as in the nature of Humpty Dumpty's portmanteau words, for it packs up at least the meanings of "scaci" and "synthetic" into one word. Scacetic philosophy includes the attempt to blend different (more or less antagonistic) speculative systems about "scaci" into one unified metaphysic, a universal system, a logicial integration. My portmanteau packs up into itself also the meaning "syncretic" among others. Unless a player is a little smeared with the natural attribute of a "sceptic," he can hardly understand the Scacetic philosophy which I seek to give in this "Alician Tale." Scacetic art does deal with the Roses, Orchids and other lovely flowers in Queen Caissa's gardens. More obvious, it also concerns this Queen's spiny Cacti! The animals of the Queen's world are various, the Horse and the Elephant have long been known. In the future, one may even find the "Ceti" Queen Caissa's own Whales! And as its final ingredient is "acetic," my Scacetic Soup may taste a little acid and sour to an orthodox sweet-tooth. THE FIRST LESSSON IN CHESS (According to the Red Queen's Idea) "When our youngest Pawns are first taught the game," the Red Queen said to Alice, "their very first lesson is, how to play the game of Chess on a straight line." "That seems a strange way to begin, Your Red Majesty," said Alice. "It is the proper way," snapped the Red Queen. "If you have never learned how to play the game on just one straight line, you could not play it on sixteen straight lines together." Her Majesty paused, frowned and muttered to herself, "that cannot be the right number." Alice then saw the Red Queen take a small chessboard out of her crown and begin counting the lines on it. (From the "Alice" unwritten.) Some readers may have scoffed at the Red Queen's dictum. To such scornful minds a double challenge is here made. First, they must commence by reading the following brief account of the Scacetic features of a straight line. ----------------------------------------------------------------------------------------------------- [page 2] Theoretically, a "Linear Board" consists of a definite group of fixed positions, all of which lie in the same straight line. These positions may be considered as points at which pieces may stand, or else as "playing spaces" generally termed "cells" which pieces may occupy. The chief Scacetic idea regarding pieces is that which derives from the idea of "Adjacency"(whether point or cells) to some other positions of its board. The idea of movement on a board from some position to a new position adjacent to it is the most natural, being the simplest among Scacetic moves of which one can think for that board. A piece able to move itself from its cell or point to one adjacent, but having no other sort of move, is the type of piece which I call a "Stepper." The second important Scacetic principle concerning pieces is that deriving naturally from the idea of cells in a straight row, or points, lying in the same straight line on this board. it extends a specific stepping move into a movement on the board which continues in the same direction or line in which the initial step itself has been made. The "generalized linear moving piece" can, of course, go from its position to another in the same straight line, even if it passes over occupied cells in its path. Such a general type, which I call a "Flier," has hardly attracted the spirit of inovation, no doubt because this piece is too powerful. On the Linear Board, it is obviously an impossible idea, as it cannot be defended against. The following types of pieces(under the names which I have chosen for them) are based on the second principle. A Hopper moves across an adjacent cell, whether this be vacant or occupied, into the next cell beyond in the same direction. A Runner can change its position by "running," as it were, through a number of empty cells in a straight line, but it can never jump over any position. The Jumper, on the other hand, can change its position in a straight line only by jumping over a piece in its path. It may jump over only one piece, which may be friend or foe, and which is not disturbed by being jumped over. Another important Scacetic principle concerns the matter of capture. A piece shows its mastery over a foe by the simple direct method of actually occupying the position of that foe, which is therefore removed from the board as a vanquished enemy. The scornful reader is now further challenged to take some clean cardboard, a pair of scissors, and red(or green) and blue(or black) inks or pencils. He cuts out some round pieces of cardboard over an inch in diameter. To indicate a particular chessman he can mark it in the required colour with the capital letter S for Stepper; R for Runner; H for Hopper; J for Jumper; K for King. For elementary play, the Linear Board should have 21 cells marked on it, but they need not be in actual straight row, for this 21 cell line can be marked out in the shape of U or S for compactness and convenience. The odd number of cells prevents the first player from gaining an immediate advantage in territory over the other. A player has two S, two H, one R, one J and his K, seven pieces in all. The initial arrangement which is probably the best here is: S S H H R J; K at the rear. Pieces may only advance in actual play, but for problems there is no special reason to bar pieces moving backwards also, along the row of cells. ----------------------------------------------------------------------------------------------------- [page 3] With a Linear Board of 25 or 27 cells, a second Jumper and second Runner can be suitably added to the player's force already described. This seems to be the "natural form" of Linear Chess, but the game may, of course, be played on larger(longer) boards and with more pieces than those which have been mentioned so far. "Cordia" ought to be the Scacetic name for this special domain in Queen Caissa's vast empire, for it is really the "Heart" of that empire. Though not the historical first stage in the general idea of Chess, the game of Linear Chess is the first stage logically in this idea. DUNCE'S CHESS IN THREE GRADES On which the wretched Hatter trembled so, that he shook both his shoes off. "Give your evidence," the King of Hearts repeated angrily, "or I'll have you executed, whether you're nervous or not." "I'm a poor man, your Majesty," the Hatter began in a trembling voice, "and I hadn't begun my tea ...... not above a week or so ...... and what with the bread-and-butter getting so thin ...... and the twinkling of the tea ......" "The twinkling of the what?" said the King. "It began with the tea," the Hatter replied. "Of course, twinkling begins with a T," said the King sharply. "Do you take me for a Dunce?" "Alice in Wonderland." Grade 1.--For Absolute and Perfect Dunces. A player has besides his King the two Bishops and the two Knights, which are placed in their normal positions on the board. Pieces can only advance, and consequently, their taking and checking operate only in forward directions. The player wins who can force the enemy King into a position of either checkmate or stalemate. Grade 2.--For Half Dunces. A player has the same pieces as in Grade 1, but added to them is the normal row of eight pawns. Pieces may still only advance, and are still strictly limited to forward takes and checks. It is obvious that pawns have no power to promote. (If the reader cannot see why this is so, he should return to Grade 1.) Grade 3.--For Quarter Dunces. The player has all his sixteen ordinary pieces. Moving, taking and checking are still restricted to forward directions. This grade of Dunce's Chess is my original idea of this game, to which I gave the name pf "Advancing Chess." ----------------------------------------------------------------------------------------------------- [page 4] "IMPERIAL FIDDLESTICKS" Here something began squeaking on the table and made Alice turn her head just in time to see one of the white pawns roll over and begin kicking. She watched it with great curiousity to see what would happen next. "It is the voice of my child!" the White Queen cried out, as she rushed past the King so violently that she knocked him over among the cinders. "My precious Lily! My imperial kitten!" and she began scrambling wildly up the side of the fender. "Imperial fiddlesticks!" said the White King, rubbing his nose which had been hurt by the fall. He had a right to be a little annoyed, for he was covered with ashes from head to foot. "Alice through the Looking-glass." For the game described in this short chapter, the pieces can be arranged on the board in their usual formation. (Irregular arrangements are quite as suitable for the game.) Because his Majesty the White King so unkindly made a sort of denunciation on the very humble little pawns, I have as a sort of just retribution or retaliation for that, deprived all Kings of their royal dignity for the time being. All the pawns, which ought now to be called by their new name of "Fiddlesticks," are granted that invisible status of "Imperial" dignity which the White King in his bad temper bestowed, rather unwisely, on these Fiddlesticks at the same time as he so named them. Kings retain their ordinary move, of course, but they are now humiliated as it were, by being treated on the same level as the rest of the chessmen. In this game a King can suffer the indignity of being captured and lifted off the board and dropped into the chessbox, just as the White King was unceremoniously lifted up by Alice in her story. The elements of check and checkmate have no place in "Imperial Fiddlesticks." The real objective in play is now not the enemy KIng, but the eight enemy Fiddlesticks. The winner will, in consequence, be the player who can first capture all Imperial Fiddlesticks in his opponent's army, regardless of what other sorts of pieces he may take. The player can scarcely expect to conquer if he is too reluctant to sacrifice his Rooks or Queen in order to seize enemy Fiddlesticks. While he could feel "sane" in giving up a Knight or Bishop for one hostile Fiddlestick, and even if he would throw his King to the winds for one, he may hesitate long over losing such a strong piece as a Rook for one. A major problem which can confront the player is: would he be foolish to let his Queen go if he could capture two Imperial Fiddlesticks in exchange? One special situation may arise which requires a ruling. If any Fiddlestick should reach the enemy rear rank, it is converted into a King! At the same time, it loses its initial imperiality and is thus regarded as an ordinary piece. Moreover, on being forced to convert into a King his very last Fiddlesticks, a player will lose the game. The idea contains some interesting problems in tactics. The balance between rushing to capture Fiddlesticks quickly and fear of becoming defenceless thereby, (loss of major pieces) seems to be subtle and delicate. Probably more lively but less subtle in character are the following two variations of my idea. The Marseilles form of "Imperail Fiddlesticks" gives the player of course, two moves at each of his turns of play. The rule which I use for this purpose is the following: At his turn a player must move two of his chessmen, one of which must be a pawn, but he may move two pawns if he chooses, or even the same pawn twice. The Scottish(or Progressive) variation increases the number of moves which are made at each turn of play. White on his first turn moves only one of his pieces, but Black in reply must move two; at his next turn White make three moves and Black four in reply. And so on until one of the players has no Fiddlesticks left. ----------------------------------------------------------------------------------------------------- [page 5] THE QUEEN'S RELATIONS The Red Queen was talking to Alice about crowns, teacups and dust, when a strange-looking chessman passed haughtily by. At first glance, Alice thought he must be a Rook which had been badly shaped by some lazy wood-carver. "Please, Your Red Majesty, that Rook seems out of shape." "That is not a Rook; she is the Biok," said the Red Queen with much annoyance. "She is very conceited, for she now regards herself as my sister, but she is really--" the Queen whispered to Alice, "only my half-sister. She behaves awkwardly like the other half-sister." "Alice unwritten." The particular feature to which I here call the reader's attention is this Scacetic idea: a chessman takes in the same manner as he moves. This feature in the general character of pieces is important, because it obviously simplifies the player's thinking while he plays a game. Many readers will be impatient here to interrupt with the remark that, like all rules, this Scacetic idea has its special exception in the pawns. When taking the pawn advances one square diagonally, but straightforward in its file when not capturing. It can be pointed out, however, that in Japanese Chess a pawn takes as it moves. An enemy piece on the square immediately in front of the Japanese pawn, does not obstruct its advance because this pawn can seize the foe there. In the Chinese game, also, the pawn take in the same manner as it moves, which includes a lateral step. The concept of the "ordinary pawn" provides a very mild example of a new type in Scacetic variety. this piece has a duality in its moves; it is rigidly restricted to one sort for capturing and to the other sort for mere change in its position. The Queen is often regarded as the compound of Rook and Bishop, but for all that one could scarcely think of either piece as being a "Half-Queen." In theory, an alternate compounding for the queen exists, which give two Half-Queens. When non-taking moves are completely seperated from the taking moves, then the Queen has really four components. It is now possible to combine the diagonal (Bishop) non-taking move of the Queen, with her orthogonal (Rook) taking move into one piece, and the orthogonal non-taking move with the diagonal capturing move into the second piece. The "half-sisters," as these may be considered of the Queen, are consequently the "Biok" who moves like the Bishop but captures like the Rook, and the "Roshop" who behaves reversely. Together, these two Half-Queens compound into the Queen proper. Other interesting relatives to the Queen of similar nature are the "Quight" and the "Kneen." The Quight moves like the Queen but captures like the Knight; and her companion the Kneen moves like the Knight but takes like the Queen. The four pieces described can have interest even in the played game. One may "go the Scacetic hog," and treat the Bishops as Bioks and the Rooks as Roshops; the Queen as the Quight and the Knights as Kneens. No doubt their awkward behaviour on the board will twist up the player's planning. As the Red Queen said to Alice, "a straight bit of thought that cannot be bent is a bad one; but if it cannot be made straight it is even worse." ----------------------------------------------------------------------------------------------------- [page 6] THE DODO'S CHESS "What I was going to say," the Dodo said in an offended tone, "was that the best thing to get us dry would be a Caucus race." "Alice in Wonderland." Alice felt no surprise at all, even when she came across the Dodo "through the Looking-glass." She recorded this second meeting in her memorandum book. That extinct bird was, on the occasion Alice saw it once again, trying to explain to the White and Red Kings how they ought to play chess according to its special rules. The Dodo earnestly and with many tears in its eyes begged Alice to write down the rules, in order that Dodo Chess, quite unlike the poor bird Dodo itself, should never, never, never, become extinct! The game which is explained in this short chapter, the reader may regard merely as a novelty. Even though it was created just as Scacetic amusement, the idea on which it is based is at least original enough in Scacetic art. The chief peculiarity of Dodo Chess is, that the purpose of play is a sort of racing. (Such an idea was naturally to be expected from the Dodo). The form of the game, as it has already been described in a Chess review, is played as follows:-- The player has his eight pieces proper K, Q, R, B, H. but no pawns. The white and black pieces are arranged on the same side of the board as shown in the diagram. All the chessmen have their usual moves, and they can be captured, Kings excepted. There is no checkmating in the Dodo's game, but nevertheless the element of checking plays a role indirectly in the game through the operation of these two rules:-- (a) A player cannot expose his own King to check. (b) Pieces are strictly forbidden to make moves checking the enemy King in any manner. It will thus be seen that Dodo Chess is a game "without checks," but in the negative sense, that it is really the idea of check which determines which moves cannot be made. In this game, a player has the racing aim, to attempt to advance his THE DODO'S CHESS King across the board to some square [ ][ ][ ][ ][ ][ ][ ][ ] in the farthest rank before the opponent [ ][ ][ ][ ][ ][ ][ ][ ] can do so with his King. As the [ ][ ][ ][ ][ ][ ][ ][ ] two monarchs are moving across the [ ][ ][ ][ ][ ][ ][ ][ ] board in the same direction and to the [ ][ ][ ][ ][ ][ ][ ][ ] same goal, the opposite rear rank, they [ ][ ][ ][ ][ ][ ][ ][ ] are (just as the Dodo intended) "racing" [K][R][B][H][H][B][R][K] against one another. The King first [Q][R][B][H][H][B][R][B] reaching the eighth rank is the victor in The black pieces are on the left, their contest. The initial arrangement of the white on the right. the pieces may be modified, and the race of the Kings can be extended to a "double course." to go to the eighth rank and then return to the first for victory. ----------------------------------------------------------------------------------------------------- [page 7] RETTAH Alice found the Hatter gazing into the Looking-glass; he was admiring the reflection of the hat on his head. "That's a beautiful hat," he said to Alice, "it is worth any crown, gold or tin." He then added very proudly, as he raised himself on tiptoe, "It makes me every inch a King!" From the "Alice" unwritten. The idea described in this chapter was the first that I ever thought of in the field of Chess. The game "Rettah" was the creation with which I first dared to leave the orthodox parochial corner and step over the official boundary into those forbidden realms of Queen Caissa's vast empire. My terrible heresy lay in the fact that, under my new idea, his Majesty the King himself was most violently seized and transformed into a Monster! The idea of Rettah arose from my dislike of the weak Kings in the ordinary game. Such a monarch at that time offended my own belief on what is "the ideal" for the game. The King ought to be strong, not feeble, by aesthetic standards: he is the centre around which turns the whole game itself. In consequence, my Rettah monarch is the most powerful of all pieces. Whichever enemy piece attacks (checks) the great Rettah, then if needs be, this monarch himself must be able to capture his checking foe. This new sort of King has the moves and taking powers of the three basic pieces, Rook, Bishop and Knight. A simple way of playing Rettah is as follows: The initial position of the chessmen is modified by placing the pawns on the third rank and omitting the King's Rook. At its first move a pawn may advance only one square. The special "rule of check" applied in Rettah is that an enemy piece checking the Rettah monarch must be taken at once. If no other fellow piece is available just then to capture that foe checking Rettah, then the foe must be taken by the Rettah King himself. Should two hostile pieces be checking the King at the same time, the King can take either, but he must take one of them. The player who captures the hostile Rettah monarch is, of course, the victor in this game. The following position will illustrate "checking" as it concerns the Rettah Kings. White: King on KB1, Rook on KR4, first Knight on K KT4, second Knight on KR2. Black: King in Q Kt 5, Queen on K B3, Bishop on QR 6. Here the move belongs to White whose King is attacked (checked) by the Black Queen. White must capture that enemy Queen at once, and can do so in two ways. (1) If White plays K x Q, then Black plays B - Q Kt7 with check again. White is now forced to capture with K x B and then Black promptly wins with K x K. (2) If White plays Kt x Q, then the Black Rettah monarch becomes checked by the unmasked white Rook. Black must play K x R, to which White replies Kt - KB 3 check. After this follow K x Kt by Black, and White wins with K x K. ----------------------------------------------------------------------------------------------------- [page 8] "SIMPLETONRY' "I never heard of Uglification," Alice ventured to say. "What is it?" The Gryphon lifted up its front paws in surprise. "What, never heard of uglifying! You know what to beautify is, I suppose." "Yes," said Alice doubtfully, "it means ..... to make anything ..... prettier." "Well then," the Gryphon said, "ifyou don't know what to uglify is, you must be a simpleton!" "Alice in Wonderland." If the opinions of certain players be accepted as the right standard by which one should measure what is "sane thinking," then the reader of this book must be a Simpleton! Even, if a Chess student knows clearly all the moves of the chessmen and the laws of ordinary Chess, it is no reason for him to expect that when he plays games, his level of Chess thinking will be above that of a six-year-old player! Though a learner may not be stupid enough to move a chessman incorrectly, he mostly does not know where to move it in a reasonable scheme. The true objection to a learner's Chess is that he has far too wide a choice of moves for the larger part of a game: he has a banquet instead of a simple meal to digest. In order to prevent the novice's mental sickness through over-rich food or over-eating, I am reducing Chess to a simple meal by the idea given in this chapter. The idea of "Simpletonry" removes from Chess most of the student's confusion by severely limiting what he may do in the game to a "simple diet" of permitted moves. The sorts which the players may use now, are restricted in three ways as follow:-- The first condition imposed on a player is that if one of his chessmen can make a check on the enemy King, then the player must make that check. (Between two ways of checking, however, the player has a choice.) The second condition: If one of the player's pieces can take an enemy piece, that take must be made, but the player has a choice between two ways of capturing which occur at the same time. The third condition: If the player can make neither a check nor a take with any of his chessmen, he may play only some pawn of his army. Should both a check and a take (not involving a check) be possible at the same time, the checking move must be made. For example, the opening P - K4, P - Q4; in which case White must now play B - Q Kt5 check, and not the take P x P. The preceding restrictions are, of course, not applied when a player is obliged to parry checks on his King. ALICIAN (Dedicated to "Queen Alice".) Certain philosophers may perhaps be skilful enough to apply their art of word analysis successfully to the logicalities and illogicalities of Lewis Carrol's two stories about the young maiden Alice. Others may be successful in their endeavours to reveal the profundity of the metaphusic which the symbolism of these two stories so well disguises from the dull-mind adult who reads them to a child in boredom maybe. In case the reader has forgotten or is ignorant, then he or she is reminded that in the second story "Through the Looking-glass" (one modern little girl commented that only the vulgar people say "looking-glass" for "mirror") Alice enters into the world of chessmen and thus becomes involved in very strange game. ----------------------------------------------------------------------------------------------------- [page 9] The fantasy "inspired" me to the creation of a curious form of Chess to which the name Alician Chess, or Alice Chess, has therefore been given. Just as Alice encounters strange situations by passing through that looking-glass from reality to its reflection, so for Alician Chess a strange game is created by playing it on two seperate boards! One board being as a looking-glass to the other, the resulting play is a game which has a character as fantastic perhaps as Alice's own game in "Through the Looking-glass." What a great loss it has been that Lewis Carroll never left his stamp on some idea for Chess! Whether he would approve of my using Alice's own name of the present game is an unsolvable problem. The chessboards used in Alician Chess are placed side by side between the players. At the start of play the pieces of both players are arranged in the normal manner on one of the two chessboards, termed Board A, the other Board B being of course, unoccupied. The basic rule of the Alician game is this: After a player has moved one of his pieces, whether it is a simple move or take, this piece played cannot remain on that board where it has just been moved, but at once must be transferred to the corresponding square on the other board. Any piece moved in Alician Chess thus vanishes strangely off its board to appear suddenly on the other board, magically out of thin air! For this special move to be "legal" the corresponding square to which the piece is transferred on the other board must be vacant. If that corresponding square is occupied, even by an enemy, then the whole movement is forbidden, as the transfer of the piece played is compulsory. Naturally, the piece must make a legal move or take on its own board before it is transferred to the other board. For example, the King may never move to a checked square on his board, even though the transfer to the other board immediately afterwards might actually move the King to a safe square. The ordinary notation requires no alteration for this Alician Chess. For instance, the move P - K4 simply implies that the K pawn make the proper advance to square K4 on his own board and immediately transfers to the corresponding square K4 on the other board. The regular opening of (1) P - K4, P - K4, will, for example, leave the two Kings facing one another in open file on their board, as their pawns are now on the other Board B, the one initially empty of pieces. A piece attacks or checks only squares of the board on which it is actually standing. It does not attack and check their corresponding squares on the other board. This particular point follows from the rule that any piece should be transferred only to the corresponding squares on the other board if these are not occupied at the time. A brief examination of what happens when the popular opening in ordinary Chess of (1) P - Q4, P - Q4 is played for the Alician, may indicate a little of the strangeness of my idea. After the opening, White plays Q x Q! It will be noted that the White Queen cannot be captured by the Black King, as she has been transferred to the square Q8 on Board B after she captured the Black Queen. Moreover, the White Queen on Q8 of Board B does not check the Black King, though in one sense they are on adjacent squares! Another brief example (1) P - KR4 Kt - KB3, (2) R x P but Black retorts with Kt x R. Obviously, the ordinary notation does not require the further mention of the particular board on which a piece is standing, because one in a pair of corresponding squares must at least be unoccupied. Naturally, a piece which has moved an even number of times in play is on board A (its original board) and a piece which has moved an odd number of times is on Board B. The checkmate of the enemy King is orthodox as far as possible, but the rules of the Alician idea can bring certain unpleasant surprises for the player whose King is hard pressed. Though a King checked may be able safely to move out of that check in his own board, he may nevertheless find his escape route barred on the other board; either the corresponding square on that board is already occupied, or else it is under attack from an enemy piece on that board. ----------------------------------------------------------------------------------------------------- [page 10] The player will frequently find an illusion due to his customary interpretation of a Chess position on a single board. He may think quite unconsciously that one of his pieces is protected by another on the same baord--just from habit! In the Alician it is not the actual square on which a piece stands that needs guarding, but the corresponding square on the other board, for an enemy will, after seizing that piece, transfer to this corresponding square. The opening (1) P - KR4, P - K4. (2) R x P, will illustrate the illusion of the Black King's Rook guarding the pawn before him. The Black Rook cannot take the White Rook in reta;iation; they are now on opposite boards. However, in the opening (1) P - KR4, Kt - KB3, the Black Knight guards the square corresponding to that on which the threatened pawn stands, and consequently, if White plays R x P, it is sharply answered by Kt x R. When a player wishes to interpose a piece between his King checked and the enemy checking, he may forget that his pieces on the same board ashis Kings are useless for such a purpose. For this intervention he must find a piece on the other board able to move there legally and then transfer to a position between the King and the checking enemy. The Alician game is really a pair of complementary positions. It resembles the task of a painter who has a pair of uncompleted paintings on which he is working, simultaneously. When the artist has decided to paint a certain detail on one of the pair of pictures, he is obliged by his task to paint that detail exactly as it ought to be, not on that picture, but in the same spot exactly on the other picture. To simplify the Alician game a little by playing it on a smaller scale, one can easily regard the ordinary chessboard as seperated into two rectangular boards 4 x 8 by the central vertical line. A player has twelve pieces, four pawns being omitted from his normal force. The twelve chessmen are initially arranged on the lefthand rectangle (Board A) in the manner shown in the diagram. A piece of red cord can be placed round the board to mark the central vertical dividing line; but the players must remember, of course, that the two "half boards" are completely independent with no communication whatever by rank or diagonal. Alician Chess can also be played on three boards of identical size. In this case the player has now a choice between two corresponding squares to which the piece that he plays may be transferred, though of course one these may sometimes happen to be occupied, thus allowing no choice. The Alician game has a character which is really intermediate between a game played in a plane (on the flat) and a game in space, where the vertical dimension is also involved. Fools Mate in Alician style. (1)P - K4, P - Q4, (2)B - K2,PxP, (3)B - Q Kt5 and the black monarch is checkmated. Here it will be seen that the move Q - Q2 (as well as B - Q2) fails to intervene as the Q (or B) would be transferred to the other board, still leaving their King in check to the White Bishop. Naturally, the move K - Q2 is forbidden, because the King would break the Alician rule that he must make a legal orthodox move before being transferred. (This quick mate was given by Mr. C. H. O. Alexander on radio.) Players will find Alician fascinating as a game, to get their minds into maddening diffuculties! ----------------------------------------------------------------------------------------------------- [page 11] ALICIAN | [R][Q][K][R]|[ ][ ][ ][ ] [H][B][B][H]|[ ][ ][ ][ ] [P][P][P][P]|[ ][ ][ ][ ] The two "halves are regarded as [ ][ ][ ][ ]|[ ][ ][ ][ ] completely seperate boards, each [ ][ ][ ][ ]|[ ][ ][ ][ ] being 4 x 8 in size. [P][P][P][P]|[ ][ ][ ][ ] [H][B][B][H]|[ ][ ][ ][ ] [R][Q][K][R]|[ ][ ][ ][ ] Board A | Board B THE BLACK KING'S COMPLAINT Alice heard someone weeping behind the chessbox, and there she found the Black King shedding bitter tears into a bucket. "What is the trouble, Your Majesty?" asked Alice with sympathy. "They are most unkind. Why am I always the one chosen to be checkmated in problems? They are not fair to my royal dignity. It is really time that old White King took his turn." Suddenly the Black King stopped weeping as a crooked thought came into his wooden mind. A broad smile slowly spread over his face. "I know now what I must do. I will disappear; then they will really have to find something else to checkmate." Alice saw the Black King thereupon change himself completely into hot tears and splash into the bucket, where he boiled rapidly away from sight! From the "Alice" unwritten. Between the ordinary game and the indignant Black King's idea, which is described in his short chapter, there is certainly one basic difference, whatever may be the minor dissimilarities. Quite unlike the White force, the opposing Black has no King at all, because that Black monarch has truly boiled himself away into teporary nonexistence for his game! The white pieces are initially arranged in their formation; so are the black, but the absent black monarch is now replaced by a second black Queen, who occupies his square. (If the reader wishes to object about such a substitution as unfair, the Black King himself "ordered" that rule.) ----------------------------------------------------------------------------------------------------- [page 12] The aim of the black side is naturally to attack and finally checkmate the white monarch; but if they obviously cannot do so within a reasonable number of moves, then the white will be the victorious side, of course, in this rather unusual sort of struggle between them. Scacetic variations (like the Black King's idea) in which one player has a King but not the other, belong to the variety which I term "Unirexal." In the ordinary types the combat takes place between equal forces, each of which has the same purpose or aim in play; but for the Unirexal the absence of the King in one of the forces, creates a radical distinction between the character and aim of the King's force and its enemy the "kingless" force. The latter is the real attacking party, and the former the real defending party in their struggle. In the Black King's idea of Unirexal Chess, the "boiled away" monarch has been replaced by a second Queen, but a Rook, Bishop, Knight or even a pawn, may replace him, should the player consider the balance between the two sides is made more reasonable an just thereby. For some Unirexal games, the black pieces may all be of a single type, for example, Knights as shown in the diagram. Here the black force of twenty Knights must try to checkmate the White King within, say, 50 moves, or lose. THE BLACK KING'S COMPLAINT. Black [H][H][H][H][H][H][H][H] [H][H][H][H][H][H][H][H] [H][ ][ ][ ][ ][ ][ ][H] [ ][ ][ ][ ][ ][ ][ ][ ] [ ][ ][ ][ ][ ][ ][ ][ ] [ ][ ][ ][ ][ ][ ][ ][ ] [P][P][P][P][P][P][P][P] [R][H][B][Q][K][B][H][R] White ----------------------------------------------------------------------------------------------------- [page 13] TWEEDLEDEE AND TWEEDLEDUM When Alice came back to the Queen of Heart's croquet lawn, she found the place in confusion, and the creatures there rather like a buzzing swarm of bees. The ten flat oblong soldiers carrying clubs were marching Tweedledee and Tweedledum as prisoner to the King of Hearts. The Knave of Hearts stood calmly by, holding in one hand a large plate of tarts, which he leisurely ate one by one. When first Alice had met Dee and Dum, these two little fat men looked exactly like a couple of great schoolboys. On this occasion, however, each of them had on his head, not a school cap but an oversized king's crown! Alice thought them more comical than ever. The soldiers said: "These two villians were found in the royal treasury stealing crowns, Your Majesty." "That is very serious," cried the King angrily, "but they have dared to put on my crowns, and that is low treason." "High," said Alice. "If they had dared to put on your Majesty's shoes, it would be low treason." From the "Alice" unwritten. Perhaps this chapter ought not to be included in my book! As the reader is probably still thinking the illusion that the book deals only with "Irrational and Absurd Chess" (so he may name my ideas) the present chapter could therefore be excluded on the grounds that its subject is actually "Orthodoxy" itself. The idea to be explained here is the idea of pure, perfect or complete Orthodoxy in Chess, or the only reasonable fashion of playing Orthodox Chess among experts and in world championships! One can first ask: to what extent the present form of "Orthodox Chess" has developed the basis of this game to its full logical completeness. When the medieval game changed about 1500 A.D. into the modern, the Firzan (Counsellor) became the Queen and the two Fils (Elephants) the two Bishops. That medieval game was not logically and fully developed in one element at least; the diagonal directions of the board were not used to their maximum extent in contrast with the horizontal and vertical directions. The basis of "Orthodoxy" gives each player a pair of Rooks, a pair of Bishops and a pair of Knights. One Rook is thus matched and balanced by the other Rook; and the same for Bishops and Knights. Symmetry and balance are logical as well as aesthetically ideal from the view point of structure or design. Even a pawn is symmetrically balanced by some other pawn of its own colour. When a player thus has "pairs" of Rooks, etc., why in the very names of Caissa, Reason and Imagination has he only one Queen in his force? The natural completion and logical perfection of Orthodoxy requires that the player must have a pair of Queens as well as his other pairs. The second Queen in his force will add enormous scope for possible combinations, and will much multiply the power of attacks generally. The "fluid" nature of positions will naturally increase through the great mobility contributed by the second Queen on each side. These four Queens together must create play of very vigorous character. The further natural development of this essential principle of "Pairs" of pieces leads to what some readers may find startling in my idea of the "pure form" of Orthodox Chess. This is, that in the player's force the King himself must likewise be balanced and matched by his own Twin King. The fact of having two vital points at which a player can strike in the enemy camp, will doubly sharpen the dangers inherent in attacks. The defences of both the Kings in the player's force are equally vital and essential because the player is defeated immediately one of his twin monarchs is properly checkmated by the enemy pieces. ----------------------------------------------------------------------------------------------------- [page 14] Sudden switching of attack from one enemy King to the other can deeply complicate difficulties for the protection which the opponent must provide for both of his Kings. Moreover, there is the terrible menace of check being made simultaneously on both monarchs by a single hostile piece, and the check against each must be destroyed simultaneously by the defender if he is to save his game. The initial arrangement of a player's pieces is symmetrical, for his Kings (one on each wing) must be identically situated and protected at the commencement of play. Logical perfection itself demands that the offensive and defensive aspects of the positions should begin with complete equality for all the four monarchs engaged in the struggle. It is only play itself which can justly create serious inequality later between one King's position and his Twin's. The initial symmetry gives the opponent no advantage nor reason to attack one Twin King rather than the other in the early stages. As the situations round his Kings get dissimilar, a player may soon find guarding one King becoming more difficult than guarding the other. The initial arrangement of the chessmen for "Twin Chess," as I have named this game, is shown in the diagram. The row of pawns is situated at the third rank; two extra pawns are, however, added to support the centre. Such is my own idea for developing the basis of Orthodoxy to its natural and logical completion. While his pair of Queens will provide the player's main hopes for victory, his twin monarchs King Tweedledee and King Tweedledum jointly provide his sequence of headaches! Twin Chess is also played on the 10 x 10 board. TWEEDLEDEE AND TWEEDLEDUM Black [H][K][B][Q][Q][B][K][H] [R][ ][ ][P][P][ ][ ][R] [P][P][P][P][P][P][P][P] [ ][ ][ ][ ][ ][ ][ ][ ] [ ][ ][ ][ ][ ][ ][ ][ ] [P][P][P][P][P][P][P][P] [R][ ][ ][P][P][ ][ ][R] [H][K][B][Q][Q][B][K][H] White ----------------------------------------------------------------------------------------------------- [page 15] MOCK TURTLE'S PSEUDOMORPHY "Once (said the Mock Turtle with a deep sigh to Alice) I was a real turtle." "Alice in Wonderland" When the White King saw Alice and the Mock Turtle, he commanded them to come and bow. He smile at Alice but looked at the Mock Turtle in disbelief. "What are you, strange thing?" the White King asked. "I'm the Mock Turtle, your White Majesty." "I felt at once in my whiskers, you must be something not real," said the King. "To be unreal is silly." "I'm a real Mock Turtle," answered the Mock Turtle, very annoyed at the King's doubt on its reality. "Royal stuff and nonsense! You'll be telling me and Alice next there are real mock chessmen." Then he added scornfully, "I suppose you wish us also to believe they can even play games of real Mock Chess!" "Yes, there are," the Mock Turtle shouted back very angrily, "and they can as well." From the "Alice" unwritten. My game of Scacia is a real Mock Turtle! It is a proper pseudomorph to Chess, for it has no elements of check and mate whatever in its basis. Kings are now merely treated like any other chessman. Though a King keeps his usual move, he can be placed deliberately in danger or taken just as a Queen or pawn may be. The aim of play in Scacia is not an attack on a specific enemy chessman (the King) but is a general attack on the whole force of hostile men. If all the enemy pieces can be captured, then the player has defeated them and wins. The special rules for Scacia are: When a player can capture an enemy piece, he is obliged to make that take. If the player should at the same turn have two or more ways of taking, however, he has complete freedom to choose the capture which seems best for his chances of victory in the long run. Only one enemy piece may be captured at a time. On the ordinary board, this game is best played with three rows of pieces. The pawns are initially placed on the third rank, and the second is occupied by a complete duplication of the pieces in the rear rank. DAMIFICATION A Scacetic Metamorphosis. The baby grunted again, and Alice looked very anxiously into its face. There could be no doubt that it had a very turn-up nose, much more like a snout than a real nose; also its eyes were getting extremely small for a baby. "If you're going to turn into a pig," said Alice, "I'll have nothing more to do with you. Mind now!" ......When it grunted again, so violently, she looked down into its face in some alarm. This time there could be no mistake about it; it was neither more or less than a pig! "Alice in Wonderland." The word which has been chosen for the title of this particular chapter has not been given, as the reader may at first think, in error for the word "damnification." It is even possible that the latter word may express the inward comment of certain heresiophiles themselves when they have read through the description presented here of my idea of damification, and find it also involving a game outside the strict game of Chess. The resulting game will very probably look to many as illegitimate, even as heresy! ----------------------------------------------------------------------------------------------------- [page 16] The general idea of Damification is more or less the introduction and application to the game of Chess of the principal elements characteristic of its sister game, that of Draughts. Such an idea may appear as most shocking to some players of either game; let heresies at least be orthodox and not unorthodox in themselves! The etymology of this term "damification" is quite clear, for the international name of Draughts is virtually "dama," which is the actual name of Draughts in Spanish and Italian. The words Damenspiel and Damspel are its names respectively in German and Dutch. The Russian players use the word "damka" as the term for the crowned draughtsman. In brief, my scacodamistic idea is the application of the essential features of the Draughts game to chessmen in general. For such process of damification the elements which have been taken from Draughts are five in number, and their natural adapting to chessmen is explained in the five following sections A-E, each being concerned with one of those elements. (A) Not only the pawns but also all the other chessmen are at first limited entirely to advancing movements across the board into the enemy camp, just as are ordinary draughtsmen restricted. (B) If a piece reaches a square in the opponent's rear rank, this piece is promoted in status; it is granted at once the full powers of movement which it has in ordinary Chess. Such promotion is naturally the feature which corresponds to the operation of crowning in Draughts. The distinction between "promoted and crowned" Chessmen, those which have gained their complete normal Chess movements by reason of their successful arrival in the opposite rear rank, and "unpromoted and uncrowned" chessmen, those which are restricted to their advancing movements, is made by using chessmen of a small size to represent the latter sort, and pieces of a larger size to denote the "promoted or crowned" chessmen. (C) In my scacodamistic idea, a chesman takes in a manner similar to the mode of capture used in Draughts and not as it takes in ordinary Chess. In this new idea a chessman will capture an enemy piece by leaping over it (in proper fashion, of course) instead of capturing that foe by the simple occupation of its square. Captures made by a scacodamistic Bishop are, of course, made only in the diagonal directions, but those made by a scacodamistic Rook are vertical and horizontal "capturing leaps." A Rook or a Bishop can capture an isolated enemy in its path even when several vacant squares separate this Rook or Bishop from its foe. The capturing Rook or Bishop can leap to any vacant square on the opposite side of its captive. For example, a Rook on square a1 can take an isolated enemy on square a4 by leaping over it to a5, a6, a7, or a8 beyond. Similarly, a Bishop on square a1 can take an isolated enemy on d4 by leaping over it to square e5, f6, g7 or h8 beyond. If the square immediately beyond the enemy is occupied, then there is no take existing in that direction. In the preceding example, the Rook on a1 could not capture its foe on a4, if the very next square (a5) should be occupied. Neither could the Bishop capture (from a1) the enemy on d4 if the next square e5 should be occupied. Naturally, a scacodamistic Queen will use the leaping takes of both the Rook and Bishop. A pawn captures exactly like an ordinary draughtsmen; it takes an isolated enemy on an adjacent square diagonally before it by the "short hop or leap" which is used by draughtsmen. For example, a white pawn on square a2 can capture a black piece on the adjacent square b3 in in front by making the short hop over it to square c4 if this is vacant. ----------------------------------------------------------------------------------------------------- [page 17] A scacodamistic King can capture an enemy piece on a neighboring square simply by leaping over it into the first square on the opposite side. In other words, a King takes like the crowned pieces in Draughts, but can do so even in vertical and horizontal directions, as well as diagonal. The take by a Knight naturally follows the usual "skew" movement. The Chessman captures an enemy on a square adjacent to it by making a "short skew hop" over its captive. It will be seen that the Knight has usually a choice of two squares into which it can go when taking its adjacent foe. For example, a Knight on square c3 can capture an enemy of d4 by hopping (crookedly) over it to either square d5 or e4. It is understood, of course, that chessmen while unpromoted may capture only in a forward direction. (D) Taking is compulsory in the scacodamistic idea, just as it is in the game of Draughts. (E) One striking contrast between Chess and its siter game is the fact that in certain positions a draughtsmen may take several enemy pieces at one and the same turn. Similarly, in this new idea, a chessman may be able sometimes to make a multiple take, destroying its victims in a succession of "leaping takes." After leaping over square from which it can "leap-take" another enemy. Whenever several ways of taking occur at the same time, it is compulsory to capture the greatest number possible of the hostile pieces. Should an unpromoted chessman reach the opponent's rear rank by a capturing move, then it must remain there for at least one turm in order to become promoted to full powers of movement. The reader may wonder what pawns should become on their arrival at the enemy's rear row. Such pawns are promoted to any pieces proper which the player wishes. The scacodamistic games may commence with the normal set of chessmen arranged initially in the usual manner on the board. One may, however, add another row of pawns (on the third rank) to the ordinary arrangement. That extra row can even be formed of eight draughtsmen! (It is obvious that the crowned pieces of ordinary Draughts, are just the scaco- damistic version of the Firzan, which piece in Shatranj or the medieval form of Chess, moves one square in diagonal directions, and the "unpromoted Firzan" is the ordinary "man" in Draughts.) The scacodamistic idea may be played with one of three aims as the proper purpose for victory. First, the game can be treated as Chess proper: the player who succeeds in capturing the enemy King is the winner. Secondly, it can be treated as Scacia, in which the player capturing all the chessmen of his opponent will be the victor. Thirdly, it may be played as Schlagschach (the inverse idea of Scacia) the player who loses all his chessmen being the actual winner in this case. Not all readers may know that two of the pieces in my scacodamistic idea have their existence already in Draughts itself. In the Spanish form of the game the crowned pieces, termed "dama" move diagonally like the Bishop; and in the Turkish-Arab form the crowned pieces move vertically and horizontally like the Rook. The principle of damification, which results in this new "genus" of pieces, is a logical part of Scacetic philosophy. My scacodamistic idea is at root the natural development and generalization of that link already existing between Chess and Draughts. ----------------------------------------------------------------------------------------------------- [page 18] "A NEW PUDDING" Scaci Partonici. "Now the cleverest thing that I ever did," said the White Knight, " was inventing a new pudding during the meat-course." "In time to have it cooked for the next course?" said Alice, "well, that was quick work certainly." "Well, not the next course," the Knight said in a slow thoughtful tone, "no-- certainly not the next course." "Then it would be next day. I suppose you wouldn't have two pudding courses in one dinner." "Well, not the next day," the Knight repeated as before, "not the next day. In fact," he went on, holding his head down, and his voice getting lower and lower. "I don't believe that pudding ever will be cooked! And yet it was a very clever pudding to invent." "Alice through the Looking-glass." The reader who feels puzzled by the association of this word "pudding" with a Scacetic matter, may here be reminded of a rule in making puddings. The ingredients in many of these must be well mixed, and I think that "mixing the chessmen together" does really have some literal sense in the actual play of this special idea. The special character of Scaci Partonici arises from the unusual modes of capture which are used instead of the ordinary Chess takes, in which, of course, the captor occupies the square of its capture. The simple form of partonic take is made as follows:-- A player moves one of his pieces to a vacant square adjacent to an enemy piece, by which foe there is already another of his chessmen standing adjacent, so that the foe now becomes situated between both of his pieces. The three pieces must lie in a straight line, but its direction can be horizontal, vertical or diagonal. The piece so "gripped" as it were between its two enemies is a captive (by this partonic take) and it is therefore removed form the board. 1st Position. White. Rook on KR2, Bishop on Q Kt5, Knight on QB3, Pawn on KB5. Black. Queen on QB4, Pawn on K Kt3. In the first diagram, if the White Knight on QB3 goes to square q5, the Black Queen will then be between the White Bishop (at Q Kt5) and this Knight himself. The Black Queen is thus captured by a simple partonic. The White Rook on KR2 by moving to KR7 would trap (diagonally) the Black Pawn between himself and the White Pawn on KB5. (2) Contrapartonic take. The contrary idea of the simple partonic produces the mode which I term contrapartonic taking. In this variety the idea is quite reversed. It is not the piece between its two enemies which is captured, but those two enemies between which it is moved that fall victims in the contrapartonic capture. 2nd Position. White. King on K Kt5, Queen on Q R4, Knight on Q B2. Black. Rook on K B2, Bishop on Q B5, Knight on K5, Pawn on K R4. In the second diagram, the White Knight by moving to square Q4 can capture at the same time both the Black Bishop and Black Knight between which he is moved. Also, the White King can, as it were, contrapartonic the Black Rook and Pawn by moving to square K Kt6 between those pieces. Black could here capture the White Knight and Queen by playing the Black Bishop between them. In this mode of capture, two enemies are taken and consequently the threat of a contrapartonic is generally sharper than the simple partonic. ----------------------------------------------------------------------------------------------------- [page 19] (3) Line partonic. For this mode the partonic idea is extended so that a straight line of two or more enemy pieces become capturable at a single turn. Instead of only one enemy between two of the player's own chessmen, two or more enemies now lie in a straight row between his two pieces when the line partonic is created. 3rd Position. White. King on KB5, Queen on K7, Knight on Q Kt1. Black. Queen on Q Kt5, Rook on Q3, Knight on QB4, Pawns on Q6 and QB7. In the third diagram, the White Knight by moving to square QR3, can make a line partonic take. Here the three black pieces Queen, Knight and Rook are "gripped" in a straight row between the White Queen on K7 and this Knight. The three black chessmen are thus taken with a line partonic and so are removed together from the board. (4) Line contrapartonic. Naturally the line partonic just described has its contrary form as the simple partonic has its contrary. In the case of the line contrapartonic the player attempts to create a straight line in which two or more of his chessmen will be situated between two foes. By this contrapartonic the player will therefore capture those two enemies. In the third diagram, the Black Knight can make a line contrapartonic take by joining the two black pawns to form a line between the White King and Knight, which two pieces are therefore captured. The character of partonic taking makes a strong contrast with that of the ordinary Chess captures. In the latter mode, a chessman can challenge any individual hostile piece. Though the play of the men is naturally interlocked, the idea of "single combat" between a chessman in the player's own force and one in the enemy force is not quite fiction. It is the absence of direct conflict between two hostile chessmen which is so strange in Scaci Partonici. Taking, in my idea, depends on three pieces at least being brought into a special sort of position. In consequence, chances of obtaining such positions are less probable than are chances of capturing in cases where only two men are involved. The four varieties of partonic together form a logical unity, and provide a proper system for dealing with the various formations which the enemy chessmen can take up on the board when under attack. The reader may realize that the venom of chessmen is gone, under this partonic game. No longer can a Queen or Rook bully with their aggressive powers of capture, an enemy pawn, or terrify the enemy King when they come into his lines. Capturing is truly positional and co-operational: play in Scaci Partonici is rather like weaving a spider's net to entangle enemy chessmen. The usual method of playing this game is as follows:-- The ordinary set of chessmen are arranged on the board with the pawns in the rear rank and the pieces proper in front. A restriction is imposed on the movement of pieces; every piece must move only forward. Consequently, Rooks, Queens and Kings have even no lateral movement along their ranks. Whenever any chessmen reaches the rear rank in the enemy camp, it must just remain there. This method of playing Scaci Partonic has certain advantages. It creates a very straightforward game for "duffers." It eliminates opportunities for time wasting and repetitions of the same positions. It streamlines the pieces into proper combat, and so leads to a definite result within a reasonable number of moves. Naturally, in this game a player will lose if his King should finally be forced into a situation where the opponent can seize that monarch in some partonic capture. By carefully advancing his King, a player may succeed in getting him safely through the enemy force. (If both players should do so, the game is drawn.) ----------------------------------------------------------------------------------------------------- [page 20] Another method of playing Scaci Partonici requires the 10 x 10 board. The previous restriction imposed on the movements of pieces is now removed, but the "men" used for play are arranged in a special manner on this larger board. A player's King and Queen with his two Bishops are placed in the central four squares of his rear rank. Opposing them there is on the fourth rank a complete row of ten enemy pieces arranged as follows:--R - Kt - 6P - Kt - R, Such enemy line beseiges as it were the King's camp and in general cuts off escape from there. Pawns are promoted on arrival at the enemy rear rank. As these now have only three squares to advance for that purpose, they give a player chances to gain rapidly some material strength over his opponent. (Pawns may be allowed to advance daigonally as well as straightforward.) The idea of separating a player's force into two parts by and intervening row of hostile pieces is a practical means of coping with the normal moves of Rooks, etc., in a game based on partonic modes of capture. It helps to "mix" the pieces of the two forces together in a suitable manner. To use a botanical metaphor, I consider that most variants of Chess are really different "species" in the same "genus," but the idea of Scaci Partonici is a new Scacetic "genus" in the particular "order" to which the first "genus" belongs. In the "genus" of ordinary chessmen is the radical feature that such a piece can, by its own power, take enemy pieces. In the contrary, a "partonic piece" has not inherent power to take. Partonic takes spring from three pieces being together in a very special postion; and lines takes from even more. PODOSPHERISM "What are those chessmen doing on my best cardboard croquet lawn?" cried the Queen of Hearts angrily, rushing to the palace window that overlooked the lawn. Alice and the sharp-chinned Duchess followed quickly after her to see what was happening. The Knave of Hearts followed them more leisurely, still munching a jam tart. Alice saw a number of white and red chessmen rushing wildly about the croquet lawn, and shouting loudly at the same time. With several other chessmen the White Queen, whose hair and shawl were as untidy as ever, was chasing after a red Bishop who was (very undignified it seemed to Alice) rolling an egg-shaped wooden ball along with his feet. "Why do they keep shouting Fowl?" asked the Queen of Hearts. "I can't see any fowls there." She repeated her first question, "What are those chessmen doing?" Just then Alice saw that the White Knight on his Horse, challenged the red Bishop and took the egg-like ball from him. The Knight's gallant steed then gave the ball a great blow with both rear hoofs, and thereupon the ball came sailing with a wobble through the window and knocked the unfortunate Knave of Heart's jam tart out of his fingers. "Goal," shouted the white chessmen in glee. From the "Alice" unwritten. To what strange and absurd limits, the very stern orthodox player will protest, is the heretic's fancy going to stretch the Scacetic art? Perhaps the strangest theme has been the idea of bringing into the Scacetic field even something of the spirit of the football game! J. Boyer has really been the originator of this very unusual idea of "podospherism," which is the Scacetic introduction of "footbal teams" among the chessmen. ----------------------------------------------------------------------------------------------------- [page 21] The idea of podospherism has been used in the J. Boyer game in the following manner:-- This game is played on a board of 9 x 9 squares, and each player has the eight pieces proper but no pawns, to act as his team of podospherists. The centre squares in the back ranks, squares E1 and E9, represent the "goals" for the two teams. An extra piece, which represents the Scacetic football, is palced on the central square (E5) of the board at the commencement of play. The chessmen have their usual moves, but there is, of course, no checking and no taking. (Kings behave as ordinary pieces.) A chessman may not move on to any occupied square, and never on to a "goal" square. A piece can as it were "kick" the football when it is on a square adjacent to that ball. The movement which the ball must make on being kicked has to be a move like those made by the piece which has just given the kick. For example, if a Bishop makes the kick, the football must therefore move diagonally, not orthogonally. Should a King make the kick, naturally the ball must move only one square in accordance with that King's limited move itself. When any Knight kicks the ball, this will, of course, make a Knight move; but the new square of the ball must not be adjacent to the kicking Knight. For example, with the ball on square d4 and the Knight on c3, then the latter's kick can send the ball to square b5, b6, e6, e5, f3, or e2, but not to square b3 or c2, as these are, of course, adjacent to the kicking Knight. Unlike the Knight, who can often kick in several directions (just as explained) there is only one definite line along which, under the J. Boyer rules, a King, Queen, Bishop or Rook can kick the ball. The direction in which the ball is kicked by that K, Q, B or R, is the very line wherein the ball and kicking chessman stand at the time. Moreover, the movement of the ball must be away from the kicker. For example, if the Queen is on square a2 and the ball on b2, she can kick the ball only to a vacant square (c2, d2, etc.) in the same rank where she and the ball are just then. In the case of a King on square a2 and the ball on b2, the monarch's kick can send the ball only to c2, not further. The rules of the game forbid a Rook to kick if he is diagonally adjacent to the ball. For example, a Rook on square a1 and the ball on b2: here the Rook cannot kick the ball because the direction of kicking would be diagonal. Similarly, the Bishop cannot kick if he is orthogonally adjacent to the ball. The player who succeeds in getting the football into the "goal" square of his opponent wins the game. The J. Boyer form of podospherism involves also the "principle of passing the ball" from one chessman to another. When a chessman kicks the ball on to a square adjacent to some other piece of the same team, the latter can in that same turn kick the ball still further if the position permits. Several such passes may be made during the same turn. For example, Rook on a1, Bishop on c5, King on g7, and the ball on d2. The Rook moves to d1, and then kicks the ball to d6, where the Bishop on c5 kicks it further to f8, and finally the King on g7 sends the ball into the goal square e9. The player's eight footballers initially occupy the rear rank, the goal square not being occupied. ----------------------------------------------------------------------------------------------------- [page 22] CONTRAMATIC "I can't explain myself, I'm afraid sir," said Alice to the Caterpillar (a large blue one that was sitting on top of the large mushroom and smoking a long hookah) "because I'm not myself, you see." "I don't see," said the Caterpillar. "I'm afraid I can't put it more clearly," said Alice very politely, "for I can't understand it myself to begin with, and being so many sizes in a day is very confusing." "It isn't," said the Caterpillar. "......said Alice, "three inches is such a wretched height to be." "It is a very good height inded!" said the Caterpillar angrily, rearing itself upright as it spoke. It was exactly three inches high. "Alice in Wonderland." From the memorandum books of both Alice and the White King, it is learned that this Caterpillar did, by some magic, get its three inches of "blue Caterpillarness" completely through the same fairy-tale Looking-glass as Alice herself. There this creature's contradiction was even more frequent and more scornful than its contradiction when Alice first met in Wonderland. Neither the majestic presence of the Kings, nor the graceful presence of the Queens could stop the flow of its contradicting remarks. The aggravating insect despised the very idea of Orthodox Chess! It gave some explanation of its own special Scacetic idea, which fortunately both Alice and the White King noted down in their memorandum books. A poem written by Caterpillar Esquire is:-- Scacian Fairy, Quite contrary, How do your chessmen go? Silly Kings, Risking things, Rash before the foe. That bit of jingle is to introduce the Blue Caterpillar's own bit of corresponding "Contrary" into the game of Chess. The new idea explained in this chapter is best approached by first asking the question: What are the essential features in the basic idea of orthodox checkmate? By the Blue Caterpillar's analysis on the subject there are three such principles involved, which are:-- (A) A player is forbidden to make any move which would expose his King to check. (B) When his King is in check a player is obliged to make some legal move or take whereby this King will no longer be in any sort of check. (C) When a player makes a move checking the enemy King, this move must not expose his own King to any kind of check at the same time. The idea of the Blue Caterpillar's game, which I now present as the "crowning irony and paradox" of my book on Scacetic philosophy, involves principles which are quite contrary to those rules just stated. As the character of my "Blue Caterpillar" idea is truly the logical contrary of orthodox checkmate, my name of "Contramatic" is obviously the right name to give this Antipodean idea. (The Blue Caterpillar fully contradicted the principles of "official checkmate" as neither logical not ideal!) The three fundamental laws for Contramatic are: (A) A player is forbidden to make any move or take which would expose the enemy King to check. (B) When the enemy King is in check, a player is obliged to make a move or take whereby that enemy King would no longer be in check. ----------------------------------------------------------------------------------------------------- [page 23] (C) If a player makes a move putting his own King in check, this move must never expose the enemy King to any kind of check at the same time. (Each of these rule is, of course, the logical contradiction of the corresponding rule in the first group.) Shocking though the idea may be, this idea of Contramatic naturally means that the player tries to put his own King into check, just as the very words in that bit of jingle "Silly Kings, risking things, rash before the foe" are intended (metaphorically) to imply as the aim of play in the Contramatic game. On the other hand, the player must not check the hostile monarch, which idea is quite contrary to the player's aim in ordinary Chess. When a player is reduced in Contramatic to the position where he must play a move that would put or leave the enemy King in check, then he has, of course, lost the game to his opponent. In ordinary Chess, a player is concerned with guarding his vital King behind a shielding group of static pawns, or interposing some piece between his King when checked, and the foe giving such check. In the Contramatic game, a player now finds that his King can gaily move among the enemy and seek these out in order to get himself checked! In the ordinary game, the player usually thinks of the King as what is "hunted or chased." Whereas formerly the enemy pieces attacked the miserable monarch, here now he is attacking and chasing them instead. Very probably, the most "chased and hunted" by this special King will be the hostile Queen, as she check in eight directions at full range. From the Contramatic King's point of view, hostile Rooks and Bishops are only about half as useful to hims as the enemy Queen, because they can check only in four directions at full range. One special point ought to be clarified: the two Contramatic Kings must not stand on adjacent squares because that would break the Contramatic Rule C. The spirit of Contramatic requires both mobile pieces and space for their manoeuvre, in order that the character and possibilities of the idea may be properly developed. Pieces that can check at long range are really the right types for playing the game; pawns generally should be avoided. Because of its rather limited space, the ordinary chessboard is not very satisfactory for Contramatic games. For another reason, it has a "geometrical defect" with regard to this idea: the really suitable board must have a true central square. The board of 9 x 9 squares is required for Contramatic, but the board of 11 x 11 squares is probably the ideal for this game. A player should have in his force two Queens, two or more Rooks, four Bishops and one Knight, besides his Contramatic King. The actual composition of a player's force is rather a matter of the size of the board and also of whether players wish for short or long games to result. The game is begun in the following manner: White places his King on the central square in his rear rank, but he can place his other pieces where he chooses in his own part of the board. Black then does likewise with his chessmen. White opens the game proper by moving one of his men, and play proceeds in the usual manner. Each player attempts to get his King into check. If a player is checking the hostile monarch, he must, of cours, eliminate such check at once. If he fails to annul that check on the enemy King, it means that he has lost the Contramatic game. It will be seen that, in order to win, the Contramatic King must get himself into a situation where two or three enemy pieces are checking him at the same time. The two peculiar features in Contramatic play are: (a) that the King moves far more frequently than any other piece; (b) that an enemy piece is very rarely captured. The reason for the latter is obvious; to take an enemy is to reduce one's chances of getting the King into check! ----------------------------------------------------------------------------------------------------- [page 24] THE RULES ACCORDING TO THE MARCH HARE "Two days wrong!" sighed the Hatter about his watch. "I told you butter wouldn't suit the works," he added, looking angrily at the March Hare. "It was the best butter," the March Hare meekly replied. "Yes, but some crumbs must have got in as well," the Hatter grumbled, "you shouldn't have put it in with the bread-knife." The March Hare took the watch and looked at it gloomily; then he dipped it in his cup of tea and looked at it again, but he could think of nothing better to say than his first remark "It was the best butter." Alice's Note.--While dodging out of the way of the Red Queen, the White King chanced to meet the March Hare who was very sadly studying a grandfather clock. Having just then once again forgotten the Official Rules of Chess (something he often did) the King begged the March Hare to recite for him the nursery rhymes about the rules. The curious set of "very wrong rules" which the March Hare actually recited to him, the White King wrote down in his enormous memorandum book. Alice later copied this into her own book. "Alice in Wonderland." The characteristic of "March Hare Chess" is this: A player has at each of his turns to make, not just one move, but two. For the first of his two moves he simply plays one of his own pieces, but for his second he must "meddle" with his opponent's men on the chessboard. This means, of course, that for the second move of his turn he must actually play one of his enemy pieces! (1) If the player for the first of his two moves should play a pawn in his force, he can play for the second any one of the hostile men, including even the enemy King! (2) If he moves Q, R, B or Kt in his force, he must move only an enemy pawn. (3) If he moves his own King, he can play any hostile piece but the enemy King. When a player's King stands in check, he must nullify that check immediately with a legal move of one of his own pieces; if he cannot do so he loses the game. "KNIGHTMARES" This is, of course, the White Knight's own idea, of which he sang:-- "Creatures of distorted thought are they! Sirens to lead the Chess Mind astray, These monsters must I chase away--away!" Alice saw the White Knight come galloping on his Horse, and his lance set as if he charged at something dangerous in his path. Then the Horse stopped suddenly and the White Knight came tumbling off amid much noisy clatter of his armour. Alice went to help the unfortunate Knight to rise, and to gather the pieces of armour which had been flung off by his fall. "I have missed them again. This lance must be blunt," the White Knight complained bitterly, "for they are always getting away from me." Alice looked carefully all round and she even peered up into the Looking-glass sky. "I cannot see anything,"said Alice very puzzled. "That is just the trouble with my Knightmares, for they are never here," explained the White Knight. "You must think a Knightmare," and he added sadly, "I am not very good at thinking them, though I do try so hard." From the "Alice" unwritten. The player whose credo is the full Code of Laws and Regulations of Official Chess, from its capital letters down to its full stops, will recite official and private anathemata on the work of "nonconformers" like myself. Unlike George Orwell, that player may use the half dictum "All such are equally mad." Let me restate his dictum thus "All players of Chess are equally mad, but some are more equal than others in Chess madness." ----------------------------------------------------------------------------------------------------- [page 25] It is not unreasonable to suggest that the "mad" should decide the actual point at which he, the "mad" consider himself to be at his own "maddest." I myself will select that point where I believe myself to be at the zenith of Scacetic madness. The idea which I wish to explain in this chapter is my "Knightmare," my maddest, my own confession to the touch of Midsummer Night lunacy! Thr idea of Knightmares is the idea of "mad chessmen" which are truly devilish "Nightmares" for the players to control and move about in play with a quiet and calm mind and in full sanity. Whether the reader will still be "sane" after attempting to solve the problem at the end of this chapter is doubtful, so I advise him not to try! This lot of Scacetic nightmares are chessmen of double character, for each is a kind of "two pieces in one." A Knightmare is not only the union of two chessmen quite different in movement and take, but these two pieces must also be different in color! In consequence, both players can make a move or take with such a piece, though its character will be different for each of them. In the eyes of the most rigid orthodox player, the very idea of uniting a white Knight and the enemy black King together into a Knightmare will be something crazy, shocking and distasteful. Very paralyzing on a player's mind would be the absurd sight of his King leaping like a Knight at the hands of his opponent into a position of check. Naturally, this name of Knightmares seems to mean a piece in which one of the two enemy components is a Knight. Even in that restricted sense, Knightmares are perhaps the dominant group among such double-charactered pieces. Whatever value a Knightmare may have as a piece, I am, of course, deliberatly intending that piece to be a disagreeable chessman for both players. The seperate characters of the two hostile pieces associated in some particular Knightmare are, in themselves, not quite what determines the merit or interest of their joint result as a Knightmare. It is really sharp contrast, not similarity between the two components, which gives their union its merit and annoying power, to the resulting Knightmare. Though a white Rook and a black Rook together can form an "improper" type of Knightmare, such would scarcely be regarded as one in spirit of my idea. The resulting "Double Rook" would allow too easily the opponent chances of at once restoring the old position, which consequence would not be satisfactory from the practical point of view. Moreover, in the capture of such a "Double Rook," each player would merely lose an equal amount of power, which would not be so very exciting for the play itself. The principle in the formation of ideal Knightmares is clearly the following rule:-- the moves and takes of the two enemy components ought to have nothing in common. The union of a white Rook and a black Bishop gives a proper Knightmare, because the diagonal move of the black element is sharply contrasted with the orthogonal move of the white companion. The idea Queen-Rook is "improper" for the Queen movement includes the Rook moves. Also, the idea Queen-Bishop is "improper," though here the contrast between the powers of Q and B is a little sharper than in the case of Q-R. Players bold enough to swallow a bowl of very diluted "Soup a la Knightmare" may try this very mild version: The pieces are arranged in the usual manner on the board; all are orthodox pieces except the Kings, who are the only "Knightmares" used. A player can move the enemy King as a piece in his own force; he treats that piece as a Knight and can even capture foes with it! The restriction on moving the enemy King is that a player may not move that enemy Monarch twice in succession, nor at his first two moves. ----------------------------------------------------------------------------------------------------- [page 26] GRYPHON'S FANCY AND FUN The Gryphon sat up and rubbed its eyes; then it watched the Queen of Hearts till she was out of sight; then it chuckled. "What fun!" said the Gryphon half to itself, half to Alice. "What is the fun?" said Alice. "Why she," said the Gryphon. "It's all her fancy; they never executes nobody. Come on." They had not gone far before they saw the Mock Turtle in the distance sitting sad and lonely on a little ledge of rock; and as they came nearer Alice could hear him sighing as if his heart would break. She pitied him deeply. "What is his sorrow?" she asked the Gryphon. "It's all his fancy that; he hasn't got no sorrow." "Alice in Wonderland." "Just to be ordinary piece is something I know I would dislike very much," said the Gryphon to Alice, "except perhaps a pawn, for that does sometimes change." (Alice had come across the Mock Turtle and the Gryphon trying to dance the Reflection figure in the new-fangled Lobster Quadrille with some red pawns for mock-lobsters.) After a pause it went on: "An ordinary piece must have a very dull existence for it is always the same thing. Now look at me, am I not two things all at the same time?" Alice, looking at the Gryphon with its eagle's head and wings, but with its lion's body, thought to herself: "It isn't really two things at the same time, but only parts of these two things." She saw a grin slowly spreading about the creatures beak as a thought spread through its mind. Then it chuckled and said, half to itself and half to Alice: "What un-fun!" "What is the un-fun?" asked Alice with curiosuty. "Ordinary pieces," replied the Gryphon. "It's all their un-fancy, of course; they hasn't got no metamorphosis. Indeed, the plain unvarnished truth of this fancy is that the pieces does change, and they does be complicacious." It repeated the word "complicacious" as if it found this word a tasty morsel to have in its beak. Even to the reader with the normal mind, it will be obvious that the theme of this chapter is the idea of the Gryphon's fancy and fun, the game of "Complicacious Chess." The pieces are arranged on the board in their usual formation, but the Kings are omitted. When a piece moves, it not only changes its squares, but also its very nature at the same time, because it is "complicacious." If a player advances one of his pawns, on its new square it becomes a completely new sort of piece, namely a Knight! Should he move one of his Knights, this piece becomes one the new square a Bishop. In like fashion a "complicacious" Bishop changes into a Rook and a "complicacious" Rook into a Queen. Finally, on moving to a new square, the player's Queen changes her gender and becomes this player's King! Briefly, the rule of promotion or change in "complicacious" pieces is: P - Kt - B - R - Q - K, the order of change being the ranking of the importance of the pieces themselves. It will be seen at once that a complicacious pawn reaches the status of kingship in five moves, whereas a complicacious Rook does so in two moves. When having at last attained kinship, a complicacious piece remains a King till the end of the game. In consequence, a player might find himself in time the proud possessor of several Kings. If one of those Kings is checkmated, the game is lost, of coutse, to their player. The aim of play is to attempt to force the opponent to be the first to promote a Queen to kingship. Naturally, a player will not capture the enemy Queen! Neither will he desire to move his own Queen, to provide the necessary target for his opponent to win by. ----------------------------------------------------------------------------------------------------- [page 27] Perhaps the player of "Complicacious Chess" may follow rigidly this "theory of openings": to play only pawns until they all become Knights; next to play only Knights until these are all changed into Bishops; etc. One result might thus be that each player might have 15 Queens on the board, but nothing else! The reader may complain that several extra boxes of chessmen will be needed for Complicacious Chess in practice. To keep the spirit of the idea is the true purpose here; hence a limitation on the number of pieces of the same sort actually on the board can be imposed on a player's force. If not more than four Rooks, Bishops or Knights in play are permitted to the player, then only one extra box of pieces will be required for this game. Naturally, interest in this "Complicacious" variation arises from the deliberate scheming by each player to remain in his "kingless" state up to the very last move if possible. The aggressive player will, however, see no real excuse for delaying the entry of Kings into play, and will demand their presence on the board from the start. In the second variation of Complicacious Chess, his wish is granted! The pieces, including the Kings, are arranged in their usual formation. In this new form of the idea, a Queen on moving does not change into a King, but into a pawn. The complicacious pieces are now "circular" in character; a piece may thus change twice (or even more times) through the change order Q-P-Kt-B-R-Q-P. The player's King is always the orthodox piece, of course, in this variation. (The restriction that a player cannot have more than 4 R, 4B or 4Kt may be imposed also in this case.) A simplified form of "Coplicacious" is played as follows:-- A player has only his King and eight pawns. These pawns change through the regular complicacious order and terminate in kingship. _____________________________________ ----------------------------------------------------------------------------------------------------- [page 28] THE REALM OF CIRCUM MORUS The Scacetic Explanation of the Jabberwocky. "You've begun wrong," cried Tweedledum. "The first thing in a visit is to say How d'ye do, and shake hands." Here the two brothers gave each other a hug and then they held out the two hands that were free to shake hands with Alice. She did not like shaking hands with either of them first for fear of hurting the other one's feelings, so as the best way out of the difficulty she took hold of both hands at once. The next moment they were dancing round in a ring. She was not even surprised to hear music playing; it seemed to come from the tree under which they were dancing. "But it certainly was funny," Alice said afterwards to her sister, "to find myself singing, Here we go round the mulberry bush." "Alice through the Looking-glass." The player who knows some Latin will quickly spot that the new name "Circum Morum" is merely a bad Latin translation of the phrase "round the mulberry bush." The basis of the Circum Morus chessboard is a system of concentric circles which are crossed by a set of diameters through the common centre. The positions at which chessmen may stand on this board are the points where the circles are intersected by the diameters, with the central point (as that of the common intersection of the diameters) also included as such a position. A board formed of five concentric circles crossed by a set of six diameters gives a board of 61 playing points or positions, which seems to be a satisfactory size for a Circum Morus chessboard. For a notation the circles can be lettered a-e (outwards) and points numbered 1-12. The central point is marked 0, the zero point. When the Scacetic character of the Circum Morus board is considered, it is seen that two distinct sorts of chessmen (Steppers, Hoppers, etc.) spring from the pattern of this board. A point of intersection can naturally be regarded in two ways: it is a particular point on one of the circles and at the same time a point on one of the radial lines. The radial Stepper moves from its position to one adjacent in the same radial line, whereas the circumferential Stepper moves from its position to one adjacent in the same circle. A radial Stepper can operate over all positions of the board, but can, of course, change its radial line only by getting to the "mulberry bush," as the central point may be called. Kings will step both radially and circumferentially if the analogy with the ordinary monarch's move is followed. Humpty Dumpty boasted to Alice that he could explain all the poems ever invented! Concerning the mysterious poem of Jabberwocky, a bit of his "ordinary" explanation has been given, of course, in one "Alice" story; but what has not been properly revealed so far is H.D.'s true Scacetic explanation of that poem. Alice did fortunately record it in her memorandum book very carefully. One line in the poem is "So rest he by the Tum Tum tree," and according to H.D. that tree name is the secret name for the "mulberry bush," the centre of the Circum Morus chessboard. The curious creature called the Tove (something zoologically between a badger, a lizard and a corkscrew) likes to "gyre," and according to H.D. that word means to run round and round. It is obvious that in its scacetic sense, this Tove is the circumferential Runner, for it could continue to run round and round the same circle if no position on this circle should happen to be occupied, so obstructing such a Runner. (Ideally, at least, a player ought perhaps to have one Tove to operate on each circle of the board.) ----------------------------------------------------------------------------------------------------- [page 29] The bird called the Jubjub in the poem is, as a chessman, naturally a "Flier," it moves radially, and being a Flier can pass across occupied positions in its path. The Borogroves, those shabby-looking bids with feathers sticking out all round like a live mop, are the circumferential variety of Fliers. The Bandersnatch, the poem describes as "frumious," that is, furious and fuming by nature. The White King, when Alice asked him to be good enough to "stop a minute," remarked to her, "A minute goes by so fearfully quick; you might as well try to stop a Bandersnatch." A little later the White King said with regard to the Queen, "she runs so fearfully quick, you might as well try to catch a Bandersnatch." This queer creature is clearly the Scacetic equivalent on the Circum Morus board, to the Queen on the ordinary chessboard. They are the "general Runners" of their respective types of board. The Bandersnatch can, therefore, move any number of positions (points) not occupied, of course, in either a radial or circumferential direction. The great riddle is: what is the Jabberwocky "with eyes of flame," about which the hero in the poem is gravely warned to beware "the jaws that bite, the claws that catch." This monster must be the terrible Dragon (of all Chessboards) the "general Flier," whose path nothing can obstruct. The Circum Morus type of chessboard (concentric Circles crossed by a set of diameters) has a simple pattern, and so is easy to mark out in rough form, especially as no colouring of spaces is involved. Like the Linear Chess, I consider this Circum Morus realm to be an interesting idea where the reader can, in a mood of lightheartedness or seriousness, find much to explore if he has some Scacetic curiosity, and also is not too lazy to make such an attempt! Perhaps the reader may consider that, because the very familiar name of Rook and Bishop are used for the two basic Runners of the ordinary board, it is commonsense as well as convenient to use them also for the Basic Runners of the Circum Morus boards. He will see, however, that the terms "diagonal, orthogonal" have no natural or direct relation whatever with the new terms "radial, circuferential." The choice between Bishop and Rook for "radial Runner" may thus seem to be a mere question of whims only. Nevertheless, the Radial Runner can operate over the whole Circum Morus board, not so the circumferential Runner. For that reason, Rook is more suitable as the commonplace name for a radial Runner than is the other term. The Rook of the Circum Morus idea can move across any number of point (positions) not occupied, of course, in a radial direction, whereas the Bishop does so in a circumferential direction. The King (as the general Stepper) and the Queen (as the general Runner) have already been dealt with as Circum Morus equivalents to the ordinary chessmen. The idea of the Horse or Knight may be taken as the piece that moves one step radially and then one step circumferentially, the intermediate point being, of course, passed over whether it is occupied or not. This rule gives a Circum Morus equivalent for the "skew hop," the Knight's move on the ordinary board. The games of Scacia and Schlagschach can easily be played on this new sort of board. Each player arranges his pieces as he wishes on his own side of the board. The diameter formed of the radial lines 3 and 9 is the neutral row of points separating the two camps. A player's force contains 12-18 pieces, and its composition is agreed on by the players beforehand. For these two game pawns may be used as "circum Hoppers," pieces which move always two points along their circle. Naturally, the Lewis Carroll nature of the Circum Morus comes from the two fantastica- tions (a) the "mulberry bush" or central point, the only position a Rook can change its radial line; (b) the circular movements which idea permits one to introduce even the "narrow- minded Bishop" who will, with all dignity, run clockwise, but refuse to run counterclockwise! ----------------------------------------------------------------------------------------------------- [page 30] THE CATERPILLAR'S IDEA OF C.C.C. "I shall contradict you," said the Caterpillar with much contempt, to the very angry Red Queen, "even if I have to contradict myself to do so; but it wont be a proper contradiction of what I may say. It will only be an improper contradiction." From the "Alice" unwritten. This chapter is really the sequel to the earlier chapter where the attentive reader will have carefully studied the Caterpillar's idea of Contramatic. In the prologue of that chapter, the reader was told that this very contradictious Caterpillar had afterwards begun to even contradict its own idea. The logical reader will understand that a "proper" contradiction of the contradiction of some particular thing is merely this same thing again. It is obvious that even such a contrary- natured creature as this large blue Caterpillar would scarcely be so stupid as to contradict itself in a circle, wide or narrow! Fairness to the irritating creature demanded therefore a second survey of what Alice and the White King had both written down in their memorandum books concerning the Caterpillar's supposed contradiction of Contramatic. The new examination of its remarks as there recorded, makes it clear that the creature was in this case speaking only of "improper" contradiction of itself. The present chapter deals with the "improper Contrary" which the Caterpillar had been speaking of. The abbreviation of C.C.C. stands for the Caterpillar's name of "Complete Contramatic Chess." The idea of Contramatic which has already been described in the earlier chapter may be regarded as the "narrow or simple" meaning of the term. Nevertheless, as the Caterpillar pointed out to the Red Rook (on the Queen side) it is logical to believe that the Contramatic idea is complementary--it is curious that Alice and the White King both misspelt that word with an "eye"--as well as contrary to the idea of orthodox checkmate. Cannot there be for that reason a "complete form" of Chess (asked the Caterpillar of the Red Rook) where both the orthodox mate and the contramatic are together in one and the same game? In such a variation, the possibilities of mate proper and contramate must co-exist in the very same Chess position on the board. Naturally, in order that both sides of this synthesis can come together, in a player's force there must be present both the orthodox King and the special King of the Contramatic idea. Consequently, the play in the Caterpillar's game of Complete Contramatic Chess involves not two but four Kings; and the complex nature arises from the basis that now Orthodoxy and Contramatic are here running in double harness. A player is thus able to win the game either by normal checkmate or by contramatic. The synthesis of these two contrary aims may cause the sceptical reader to doubt seriously whether C.C.C. is really playable on a board even though problems in this mode of Chess can be composed. Players can commence the game in the same way as is explained for the simple Contramatic game, which is to place the chessmen gradually on the board while play goes on. Here the chief question is, perhaps: which ought to be the particular turn at which the player should place his orthodox King on the board. Probably the best for general interest is this rule: the player's orthodox King to be the last of his pieces which he places in the combat going on. The general questions concerning the size of chessboard, and the number of chessmen and their type suitable for a player's force in C.C.C. are partly answered by what has been stated about Contramatic itself. Naturally, the introduction of normal checkmate as an element into Contramatic, increases the difficulty of finding the "ideal balance" among the elements. ----------------------------------------------------------------------------------------------------- [page 31] Before ending this chapter on my favourite idea, I should now refer to certain matters in order to help clear this idea of possuble ambiguity and vagueness. As the new form of Contramatic involves two sort of monarch, then it will help to avoid confusion over names if the letter K is used definitely to denote the familiar (orthodox) King in Chess, and the letter C the special (Contramatic) kind of monarch. Certain special situations concerning the K and C are coverd by the following rules. The C can move to a square adjacent to the enemy K both to check that for and to get itself checked by that same foe, which is a case of the C checking and "contrachecking" that K. On the other hand, the K may not move to a square adjacent to the enemy C, because this would break the rule in Contramatic that in no circumstances must the enemy C be attacked. It would also break the orthodox rule that the K must move into check. If a player's K is adjacent to the enemy C, he has only one remedy, namely, to move his K away from that foe. Under the Contramatic idea, the C must never move to any square adjacent to the enemy C. (This is, of course, the only exception to the general rule about the C, that the C can move freely into danger and be exposed to attacks.) Though in C.C.C. either checkmate or contramatic alone can win, both these can be entangled together in a win. ____________________________________