La aplicación de la Responsabilidad de Proteger a la población libia y siria

Games are one kind of play, just as acting is another. Almost any kind of play is based on make-belief, that is, the situation which defines it is contrived and does not of itself relate to the problems of day-to-day living. Almost by definition it is an escape from these problems, and if it has a social purpose, this is what best characterises it. The playing of children is pre-eminently of this kind: it is essentially that part of their life which they are free to live in their own way, to create their own world in opposition to that in which, by force of circumstance, they must grow up. This shows that play is defined also by context, which is almost certain to have both a spatial and a temporal dimension. The wood at the edge of the village, and the hour after school, provide the context for hide and seek,¹ and many other forms of play.

Context has also a social and cultural dimension. In terms of strategy (which is based essentially on arithmetical factors) there is not much to choose between the English bowls and the French boules, but the difference in the social and cultural contexts of the two games is obvious to almost any casual observer. The basic activity of a game may itself define two quite different and contrasting contexts in this sense. Golf, at a basic level, consists of hitting a golf ball with a golf club, with maximum effectiveness, but few in Japan would identify those who can afford to play on an actual golf course with the habituees of driving-ranges. Leaving aside the social niceties, and making the distinction in purely systemic terms, one could say that the former are actually playing the game of golf, while the latter are not.

The question then is, what makes playing into a game?² The line is difficult to draw. Hide and seek is also a game, and yet for any sort of numerical or even logical analysis, it must be excluded from the

140 The Japanese numbers game

category. For convenience, then, one must accept that a game is an institution defined by fixed rules. Playing the game means obeying the rules (Ahern 1981:59), and these rules, at least if they are to identify a winner in any instance of the game, must be logical, and their essential basis mathematical. At some stage the game must be reduced to the question, is x, greater than, equal to or less than y? This may simply be the end result of a numerical system of scoring, such as in the game of football. In other cases one must identify the winner and loser by means of a purely binary formula, so that, as in chess competitions, the winner scores 1, the loser, 0, and both players, 1/2, in the case of a drawn game.

Numbers, in the context of games, are a sort of Pandora’s box.³ Even the most elementary system of scoring allows for almost unlimited elaboration, as one can see from the grand-master points allocated to ranking chess-players. Sometimes such elaboration is built into the game itself: in Japan this is the case with go, but not with sh)gi, the Japanese version of chess. Judged in the light of the rules, scoring may be just one aspect of what makes a game, but it is still necessary to ask how it relates to the rules. To answer this question adequately requires establishing the taxonomy of rules at a deeper level.

There are essentially two cases to consider. The first is where without the rules, the game would not exist. A Japanese example is go,⁴ but this is but one of many. Rules in this sense are constitutive: in principle all that is needed to start playing the game is to read and understand the rules. The whole gamut of board games, such as Monopoly, satisfies this criterion.⁵ In many important cases, however, the rules are regulative, in that they make a game out of events which can exist apart from any rules.

This is what changes riding a horse into horse racing. The cultural transformation involved by this process is almost always quite radical, and tends to place the game in a comparative context, in which it can be related to other structurally similar events, in a way impossible at the level of pure play. In this way horse-racing and car-racing come to share common characteristics, not essentially tied to the enjoyment of horses or cars as a leisure activity. The key point is that the essential common denominator is something which can be expressed numerically, which in this instance is speed. With a game depending on regulative rules,⁶ their most essential function is to produce the numerical factors, x and y, which will determine the outcome.⁷ In a game defined by constitutive rules this result is automatic. The significant point is

that it follows in either case, something which may be better appreciated in Japan than in the west.

The distinction between the two types of games becomes critical in the field of strategy. This, in a constituted game, must be decided upon by the players on the basic of factors which are essentially numerical.⁸ The opposite is true of a regulated game.⁹ This distinction is largely effaced in any popular culture, particularly in relation to games, such as baseball or golf, where the rules impose an elaborate numerical framework.¹⁰ This is precisely the reason why, of all the games introduced into Japan from the west in the last hundred or so years, these two are among the most popular.¹¹

In classifying games the distinction is often made between skill and chance. This is the basis of a scale whose end-points are defined in terms of ‘agon’ and ‘alea’.¹² The Greek agon describes an open game, in which the factors determining strategy, at any stage, are apparent to both players. In Japan this is a characteristic of a very wide spectrum of games, ranging from go to golf. Alea, the Latin for

‘dice’, refers to the element of pure chance. Although it is possible for a game to be pure alea, it is then almost bound to be trivial in any competitive sense. Culturally, however, such a game can be exceedingly important, as the Japanese janken, which I consider in the following section, illustrates. The usefulness, however, of the present analysis is to be found in the very large number of games which combine both agon and alea. In these, alea is the factor which governs the arbitrary and uncertain element, such as the identity of the next tile to be drawn in mahjong. The critical point is that where both agon and alea are present, the former always wins over the latter, at least in the long run.

In a constitutive game, this means that the better mathematician is always the winner. This point, which may be counter-intuitive, is difficult to prove but easy enough to illustrate by means of an example.

A mahjong player, when his turn comes to draw a new tile, must also reject a tile already in his rack (which the other players cannot see). In deciding upon his choice, he has a fair amount of information at his disposal, which increases as the game progresses. He knows which tiles have been rejected by the other players, and what open sets they have already formed. This information, at every stage of the game, is always sufficient to determine the optimal strategy. The skill of the winning player consists in being more proficient than the other players in the mathematical processing of this material. The available information is the basis of the agon factor; the uncertain order of the tiles still to be drawn from the wall is that of the alea factor.

142 The Japanese numbers game

With a regulated game, the position is simpler, in that the skills required are not essentially numerical. Winning at golf is simply a question of being better than one’s competitors at hitting the ball so that it reaches a desired point. Even the 24-handicap player has mastered the mathematics of golf; his basic problem is that he cannot hit the ball straight. (This is where agon leads to agony.)

Strategy determines who wins the actual game, but this, in many important cases, is not the end to the matter. The result of a game, being numerical, can always play a part as a factor in a numerical operation, which in relation to that game is entirely abstract. Such operations serve a number of different purposes, of which three are particularly significant.

The first is to let the result of a single game determine the position of the players (whether individuals or teams) in a competition, a fortiori organised on the basis of constitutive rules, designed to produce a winner in the whole field in which the game is played. Although such competitions may be seen as having a distinctive form for each particular game, there is no essential connection between the two, and such forms as the knock-out can be completely general. The socio-economic importance of such competitions, in popular sports, cannot be gainsaid. In the anthropological literature, the classical case is the Balinese cockfight, in which, at the level of the game itself, the protagonists are not even human. But as Geertz points out, ‘it is only apparently that cocks are fighting. Actually it is men’ (Geertz 1973:417). At this level, gambling¹³ on the results—a sort of meta-game involving an almost unlimited category of participants—is much more significant than the game itself. For gambling, the game can be dispensed with: any chain of events, which produces numerical results, can be the basis of gambling,¹⁴ although it tends then to be called by another name, such as betting or speculation.

The second purpose served by the numerical results of a game is to rank the players on a recognised scale: in this way a hierarchy of merit is established. This, a notable characteristic of Japanese numerical culture, is considered further in the last section of this chapter.

The third purpose is to analyse the performance of participants, whether individuals or teams. This is almost obsessional with professional baseball commentators on Japanese television, who fill up every free moment with an endless stream of statistics and analysis relating to the players. The same amount of detail is to be found in the sporting pages of the daily newspapers (Whiting 1977:12), not to mention the magazines devoted to baseball.

These three purposes are clearly interrelated. Ranking is related to performance, and the two combine to create the popular image of the game, which, in turn, is the basis of popular involvement. This is the means by which the people themselves share, vicariously, in the fate of the protagonists (which is what being a fan involves), and gambling extends this commitment into the economic sphere.¹⁵

This section produces a taxonomy of games in three layers, relating successively to rules, strategy and sub-culture. The rules define the game, whether they do so by constituting it, or by regulating an established form of play. Strategy is essentially concerned with the process of winning. The sub-culture of a game defines not only its social context and the hierarchy among its players, but also the systemic means by which these are maintained. Every layer has a numerical base, whose importance varies according to each type of game. It may be tempting to build up a typology according to the degree of complexity in every layer, in which case sh)gi, the Japanese version of chess, would score highly, but a game need not be complex to be significant. The fact that a single game, known to almost all Japanese, is sufficient to make this point, provides the theme for the next section.

JANKEN

If janken, in its basic form a game for two players, is known far outside Japan, it is still entrenched in Japanese culture in a way unparalleled elsewhere. Viewed historically it is but one of many games known, generically, as ken, which simply means ‘fist’.¹⁶ The explanation is simple. All the different ken games depend on both players simultaneously making gestures, in one of a number of prescribed forms, with one or both hands.¹⁷ Janken uses only one hand, which can represent three positions, designated as ‘scissors’ (hasami) (index and middle finger apart), ‘stone’ (ishi) (clenched fist) and ‘paper’ (kami) (palm open). The winner is decided on the principle that stone blunts scissors, scissors cut paper, and paper wraps up stone. With two players there is always a result, unless both choose the same position. A drawn position in ken is known as aiko, but this is no more than a particular instance of the general sh)bunashi, meaning neither victory nor defeat. Janken is in fact but one version of the category known as sansukumi-ken, literally,

‘three-cowering ken’—so that the name is more or less self-explanatory.

The difference between different games in this category is in the three positions and what they represent. This difference is not important, so long as the rule of sansukumi is adhered to.

144 The Japanese numbers game

Before continuing with the case of janken it is useful to place the whole category of sansukumi in the general context of ken.

Historically the first occurrence of ken in Japan was with a numbers’

game known simply as honken, or ‘main ken’. The rules are simple.

The two players each shout a number from 0 to 10, at the same time displaying any number of fingers of the right hand. If A shouts ‘six’

and B, ‘eight’, while A shows two fingers, and B, four, then A is the winner of the round, for 2+4=6. B then has to pay the penalty of drinking a glass of sake (which of course makes it no great sacrifice to be the loser). Honken is also known as kazuken, or ‘numbers ken’, a name which clearly distinguishes it from all forms of sansukumiken. Honken was essentially a game for convivial social occasions, and as such had its own ritual, which included special, allegedly Chinese words, for the numbers from 0 to 10 (Daihyakka Jiten 1951:8; 387).¹⁸ Originally the different forms of sansukumiken occurred in a similar context, with t)hachiken¹⁹ being the most popular, but eventually all the different versions, with their social pretensions, fell into decline, leaving the field to janken.²⁰ This, although seen primarily as a children’s game by the Japanese, is played in a remarkable number of different contexts, even to a point of being a matter of life and death.²¹

The logical basis of janken is defined by a cyclical number-system containing three members. There is, however, an immediate practical obstacle to any purely logical analysis. In no single version of the game are these members designated by a purely abstract symbol, such as a written numeral or a letter of the alphabet. There are three immediate reasons for this defect. The first is quite simply that this sort of logical thinking is out of place in the popular cultural context in which janken is played. The second reason is that such abstract symbols lack the necessary metaphorical base which, cognitively speaking, gives the game its essential character. That is, if A, B and C are substituted for stone, scissors and paper, the metaphors based on blunting, cutting and wrapping up are immediately lost. There is no objection to adopting a different instrumentality, based on its own metaphors; this is what explains all the different versions of sansukumiken. What cannot be done is dispense with the metaphorical base altogether. Third, once the instrumentality has been decided upon, it operates, at the logical level, as a type of metonymy free from any ordered relationships inherent in any abstract symbolic system. The objection to any A, B, C system is that it contains the implicit relationship that A precedes B, and B, C, while this does not subsist between C and A. Mathematicians are used to

overcoming this sort of obstacle when dealing with cyclic groups (simply by ignoring the pre-existing order), but then very few of the players of janken have mathematical sophistication at this level.

The mathematics of janken, in the context of abstract algebra, is in any case elementary. Much more interesting are the implications of extending the game to more than two players. It is best to start with a simple example, observed on the long flight of steps leading up to the terrace in front of the tomb of the Meiji Emperor in the Kyoto suburb of Momoyama. Three children,²² starting at the bottom of the flight, are playing janken, to see who will first reach the top. In this case, there is only one chance out of three of a ‘no win’ round. The rest of the time, two children will present the same position, and the third, a different one. The winning child, or children, will then move up a step. If, in theory, one child could move far ahead, or lag far behind, so as to make the game unwieldy, in practice the distribution of winning and losing positions tends to keep the children all within a few steps of each other.

In any case, the race up the hundred or so steps will probably take about ten minutes.

In mathematical terms, the general case is defined in terms of an indefinite number of players, n. One can conceive of them standing in a circle, with each player making one of the three recognised gestures in every round. Where n>2, the possibility then exists that all three choices will be made, and as n increases, this becomes increasingly probable. The question is, how probable is an outcome, with n players, which divides them into two groups, one of winners, the other of losers.

This means that one of the three positions must not occur, nor must the positions of all the players be identical.

For the chance of this happening to be less than one in a hundred, there must be at least fifteen players. If this seems rather a large number, it can happen that janken is played on this scale, in certain situations. To take an actual case,²³ fourteen guests at a youth hostel must provide a detail of four to do the washing-up after the evening meal. Many of them are meeting for the first time, but all of them have grown up playing janken. Ages range from 15 to 50. The players stand in a circle and start off, making the familiar gestures with their right hands. At this stage the odds are marginally better than one in a hundred that a decisive position will occur. Taking a second as the time needed for a single round, there is then a better than even chance of such a position occurring in under a minute,²⁴ as one round follows another without any interruption.

So it is in this case. In just over half a minute, five players present

So it is in this case. In just over half a minute, five players present