Davies takes four stabs at solving this most vexing peculiarity:
Four possible explanations suggest themselves. Firstly, Red might move the White pieces by mistake. Under Law IX White could insist that the moves stand. Secondly, according to Law XIV, if White were moving out of turn Red could insist that the moves stand. Neither of these contingencies is very likely in view of the number of consecutive moves made by White. Thirdly, the game might be played at odds. Both Walker and Staunton devote much space to various methods of giving odds to a weaker player. But the order of the moves—one Red, eight White, one Red, three White, one Red, two White—would imply an impossibly difficult mathematical basis for the giving of odds.
There remains a fourth possibility. Book V of Staunton’s Companion is entitled “On Odds.” Staunton begins with a discussion of the origins of chess and remarks that at first the giving and receiving of odds was unnecessary because the game was not one of pure skill. At the remote period of its birth in India it belonged to the widespread family of human games based on chance and “the moves were governed by the casts of dice”. These significant words occur in the very first sentence of the treatise Staunton wrote and Lewis Carroll bought. They provide a key that turns easily in the lock of the door to Alice’s secret garden. White has more moves than Red because White wins on the throw of the dice more often than Red!
“They don’t keep this room so tidy as the other,” thought Alice to herself when she arrived behind the looking-glass and discovered a world beyond the care of providence or the decrees of fate. How disturbing if Carroll is suggesting that this ‘other world’ is, after all, the real one and that it is ruled by the principle of uncertainty! A pawn’s progress towards the eighth rank is hazardous in the hands of a skilled chess player. In looking-glass chess its survival depends on the casting of unseen dice by an invisible master. No wonder Alice cried as she threw herself down on the last square, “Oh, how glad I am to get here!”
None of these four suggestions resolves anything about the moves because none explains either the character or implications of the game itself. Only the fourth suggests a real solution—the game is controlled by “an invisible master” and “is ruled by the principle of uncertainty!” Gardner more narrowly implies the same: “Carroll may be suggesting… that the knights, like Punch and Judy, are merely puppets moved by the hands of the invisible players of the game” (295). Richard Kelly can assess the same evidence and come to the complementary conclusion that “in the Looking-Glass world life is completely determined and without choice.”5
These men come to different conclusions about the character of the game either because they are either examining different objects, or the same object from differing points of view. Actually, they are doing both. Davies and Gardner view Carroll’s chess puzzle as a game, using a player’s point-of-view totally beyond the game and finding the game symbolizes the uncertainty of human existence. Kelly sees the puzzle as a chess problem and takes the point-of-view of the pieces. Kelly finds this world narrow, limited, and totally determined.
What is our puzzle—problem or game? Alice calls it a “huge game of chess that’s being played—all over the world—if this is the world, you know” (207-8). However, Carroll has already called it a “chess-problem” in his “Preface” (172).
If we look at our puzzle carefully, we will find that it is both game and problem, and that this paradox is the solution to the highly symbolic narrative plot.
In his fine book The Enjoyment of Chess Problems, Kenneth S. Howard makes an essential distinction between the chess problem and the chess ending:
There is an essential distinction between a chess problem and a composed endgame. In an endgame the solver has to demonstrate a win or draw for white against a superior, or at least an equal, force, and is allowed an indefinite number of moves in which to do so. The point of the endgame is based on the difference in the apparent relative material strength of white and black. In a problem it is not a question of relative strength but of the possibility of showing a mate against any defense in a limited number of moves. In an endgame the solver is fighting against material odds; in a problem he is fighting against time.
The modern chess problem is an illustration of some particular powers of the chess men in their interaction with one another. The chess problem is not primarily merely a puzzle.6
However, in neither the problem nor the ending is the solver actually playing against another mind. He is acting within the rules of the problem situation, and for the most efficient win or mate in the game-like ending. If a problem mate can be escaped or solved in fewer moves than required, the problem is said to be “cooked.” In the ending, the situation must be a win or draw for the appointed side or it too is ruined. For both problem and ending, one’s opponents are the pieces, rules, and the situation set forth on the board. The game of chess pits two minds against each other, the board situation remaining at their mercy.
Carroll’s Looking-Glass problem is “cooked”: it has overlooked early mates (3, Q-K3 mate), captures avoided by Red, and no plot reference to the White Rook at KB1. As Edmund Miller notes, “This chess problem is completely arbitrary and so does a wonderful job of organizing everything else in the nonsense book.”7 If the puzzle-plot is considered as problem, the reader is confined to the limited perspective of the chess pieces which only know what they must do and little or nothing of the complete plot/solution. Alice (as Pawn) and the other chessmen see only some of the play; the Queens know the rules, but the other pieces do not speak of them. As Taylor points out, Alice never grasps the purpose of the game; at the eighth square she asks if the game is over.8 It is not over, of course, until later when she herself captures the Red Queen.
Martin Gardner is correct: “the mad quality of the chess game conforms to the mad logic of the looking-glass world” (172). The moves of the game (Gardner will call it a “chess problem” on p. 336) are correct and meaningful if seen within Alices’ limits on the board—the logic is that of the moves laid out in Carroll’s diagram; that is, the narrative plot and the chess problem are identical. As problem, only the placement of pieces and their “character” (narrative and chessic) determine its moves and thus limit our view to their own; the moves therefore do not matter as chess. The logic of the puzzle and of each piece makes the actual chess moves unobservable from within the problem, and the plot-moves seem both logical and real.
If we view our puzzle as absolute outsiders, as a chess game, the absurdity of the moves are apparent. Who is really playing the game is unknown, even to Alice; the Red King “was part of my dream, of course—but then I was part of his dream, too!” (344). Whoever the unseen player may be—Carroll, God, Alice, the Red King—from his view mistakes, errors, blunders, lost chances, and illegal moves are obvious. In a chess game, rules are never to be violated willfully, foolishly, or made part of the puzzle.9
We have resolved the chess paradox: one puzzle is both game and problem, for we see it from both points-of-view at once—as player/reader, and as Alice/chessman. The puzzle has also resolved itself as a symbol of human existence. If Carroll had totally ignored the rules of chess, his allegory would then suggest human existence is blind, directionless, and meaningless, like a child moving chessman without purpose. But purpose is accomplished—the Red King is mated, though Alice is unaware until she is awake and outside the game (until, in human terms, she is wise and mature enough to see) and changes her point-of-view.
On the other hand, if Carroll had presented perfectly straightforward chess (game or problem), he would imply human existence lacks freedom, spontaneity, and charm. As a Church of England clergyman and as teacher of math and logic at Christ Church, Oxford, the Reverend Dodgson could not believe in blind chance or transcendental puppetry as descriptive of the nature of human life. He believed in God, logic, and science; and these beliefs he translated into a charming literary puzzle.
Carroll’s story provides the same problems and resolution for the nature of human existence as Emmanuel Kant had done in his Critique of Practical Reason: man lives in two realms at once—the realm of Nature in which all facets of his existence are completely determined and explained by mechanical causation (the chess problem); and the transcendental realm of freedom in which he is a free, unconditioned cause acting on the world, bringing novelty and uncertainty into being (the chess game). For Lewis Carroll, the game of human existence presents a deep problem which he resolved in a happy ending in Through the Looking-Glass.