Chess, Beauty, and the Martial Arts

Alison Berkowitz

December 16, 1996

 

Part 1: Using Chess for Studying and Applying the Martial Arts

 

As a black belt of Shaolin Kempo Karate, I have spent a great deal of time studying and practicing different martial arts techniques. As I learned about methods of analyzing chess strategy, I was struck by its applicability to the martial arts. First, for the sake of this paper, I will enumerate certain parameters through which the examination of the martial arts will be limited. It is taught for defense only. This does not indicate that aggressive strategies have no use. Instead, it means that the ultimate goal is to escape any situation unharmed, not to seek retribution or violence for another sake. Second, all discussion here will be limited to two-person confrontations for simplicity. Finally, in this paper, I will refer to formalized martial arts competitions, and not a regular street brawl. A win in such an organized competition is defined as a situation where one opponent incapacitates the other, or disables him from making a further attack.

Despite my eagerness to compare the martial arts to chess, there are two key features of chess that differ in the martial arts. First, while chess is a game of perfect information, a physical confrontation is not so. There is generally some ignorance about the opponent’s physical ability, or material parameters. While one might argue that a chess player does not know his opponent’s ability, this mental state is comparable to a fighter’s mental state. A fighter’s physical ability is analogous to the ability of the pieces on the chess board to move. Physical ability includes the material, a term for the prelearned routines that every artist acquires. Second, while in chess one cannot use an opponent’s captured piece against him, this limitation does not exist in the martial arts. Obtaining an opponent’s weapon may be key to a defeat. Although the martial arts diverges from chess in these two defining qualities, the analogy comparing different styles of play is still instructive.

There are two essential similarities between these forms of competition that make them extremely compatible for discussion. The first is the that they are both two-player zero-sum games. In a martial arts competition, the only possible outcomes are one player incapacitates the other, or there is a stalemate. There is no "win-win" solution. Second, the magnitude of alternatives available to both chess players and fighters is similar. In chess, the number of possible moves in a game is finite, but so large that it is functionally infinite. While the number of moves in a martial arts competition might possibly be finite or infinite, so many variations and combinations make it effectively infinite. Along the same line, both games have a clear goal (checkmate or incapacitating opponent), but many different ends that achieve that goal. This multitude, coupled with the huge total number of legal moves, makes it impossible to systematically link the end to the beginning. Even great chess computers cannot calculate fast enough to ever discover an optimal series of moves. People deal with our inability to link the end to the beginning by developing different styles of playing intended to maximize chances of winning while minimizing costs (like time, and required experience or brain power).

Reactive versus Selective Method

 

In chess, a player may choose between a reactive and selective style of play. The reactive style is akin to a reflex, or a rule of thumb. When certain conditions occur, the player will respond automatically according to set guidelines. There are several advantages to this style. Decisions are quick and simple, and they draw on examples of past success. This style is particularly useful to a novice who cannot yet apply more complex decision-making to the game, but even a master will use it in some situations like the opening. The drawbacks to this style need attention. Rules of thumb frequently conflict, and offer no mechanism for reconciling them. Additionally, there is no flexibility or way of adjusting to an opponent’s style or strengths. Finally, a rule of thumb is not necessarily linked to any particular end. It is useless to remember a certain move is advantageous, if one cannot recall what it will help achieve.

The reactive method plays a significant role in the martial arts. The nature of the competition requires a speedy response, one of the largest advantages to the reactive style. Therefore, a great deal of one’s early training in the martial arts involves acquiring a ken of heuristics, or reflexive responses called material. Paramount among the material taught is a genre called combinations. Combinations are a short series of defensive moves designed to counter to a particular attack. For example, when someone lunges and strikes overhead with a weapon in his left hand, a successful reaction of combination 1 will result in incapacitating the assaulter. Combinations are practiced incessantly precisely to make the responses reflexive. One of the qualities of a grand master of Shaolin Kempo is said to be a state of "No Mind," where there is no thought at all involved in certain responses. They are purely reactive.

The reactive method is the most simplified technique for dealing with the huge number choices available in these games. Rules of thumb are not developed by scanning and evaluating all alternatives, but by holding onto something that works. They will frequently overlook a better alternative. As in chess, the reactive method will not enable a martial artist to defeat someone with significant training. The selective method is required to surmount the limitations of the reactive method. This style can be subdivided into the combinational and the positional styles. In any game, the combinational style requires a narrowly defined material goal and a specific course of action to achieve it. In chess, this translates to planning an attack on one particular piece of the opponent’s. This style is favored because it is compatible with the majority of advanced players’ strategic ability to think only several moves ahead. In addition, in this style, the player focuses on a limited area of the board. The primary shortcoming of the combinational style is its failure to consider the overall position. While one player might take advantage of a combinational opportunity, his opponent could have intentionally sacrificed some material in exchange for improving his general position on the board. If the first player does not consider this, he could fall into a larger trap of his opponent. There is also a difficulty to the combinational approach. While the ultimate goal, to reach checkmate, is clear, choosing a short-term goal, or deciding which piece to attack is generally not obvious.

In Shaolin Kempo, the combinational style has some limited value. It is analogous to a technique called a "feign." A feign is a deceptive move intended to elicit a certain physical reaction, or state of mind from the opponent. It is combinational because a feign has the immediate goal of causing the opponent to do or think something particular. Though "material" in the martial arts is more nebulous than in chess, the immediate state of mind and physical state seem somewhat analogous to the pieces on a chess board. They are tools in the competition, but must be "manipulated" deliberately to defeat the opponent. In one example of a feign, a player will make one of his fists menacingly apparent to his opponent while shielding the other in some manner. While the opponent’s attention is fixed on the front fist, the player will attack with the hidden fist. The opponent’s reaction, being fooled, is to his disadvantage, but the first player’s ability to exploit this state is not included within this short-term strategy. In chess, this is similar to winning an opponent’s piece, and subsequently being unsure of what to make of your new advantage. Feeding an opponent misinformation with a feign is undoubtedly to the player’s advantage, but he is still left with the dilemma of how to proceed. The feign could not be considered a reactive strategy, though, because the move is not a response to a specific situation, but instead the player must select to make this move among many alternatives.

 

Subjectivity and the Positional Style

 

The style of play that takes into account both players’ overall situations is the positional style. In this style, a player considers how to improve his positional parameters. This may call for sacrificing some material, or making a move that has no apparent immediate value. The positional style, much more than the other two, depends very heavily on a player’s personal ability. Because the style considers not just the present moves, but the future too, a player must have confidence that in the future, he will be able to make clever moves, possibly a combination. In chess, the positional style involves considering the location of the pieces and one’s own ability to exploit it.

In Shaolin Kempo, the positional style is used both during a competition, and during pre-competition training. The Shaolin Kempo philosophy involves studying five animals: the snake, the leopard, the crane, the tiger, and the dragon. Each animal has different characteristics and strengths. One with supernatural powers would be able master all of the best qualities of each animal. However, due to people’s predispositions and physical limitations, each individual embodies a different combination of the animals according to his ability. This personal combination is called one’s own dragon. For example, as a small person, I use little tiger technique, which requires strength, and more snake technique, which takes advantage of wrapping around an opponent. A positional style in Shaolin Kempo means honing in on my optimal combination of the animals and exploiting my personal strengths. First, in a practice setting, this includes directing my study away from animals’ techniques that would be less beneficial to me, and concentrating on those I could successfully perform. In competition, it entails perceiving the opponent’s dragon and weaknesses to penetrate his position. For example, if I realize that my opponent is mostly a leopard, he will move on diagonals and attack my sides. I can turn my body to give him the smallest side target possible, thus improving my defensive position. Because I am mostly a snake, twisting my body is my strength and I am confident that I will be able to use this twisted position to my advantage later to incapacitate my opponent. A less experienced or differently proficient martial artist might lack the skill to take advantage of this position. The key to the relationship between the positional strategies of chess and the martial arts is the extreme subjectivity. In both disciplines, certain moves are only beneficial to one who is able to recognize opportunities for success from that position. This level of sensitivity requires both confidence and a realistic perspective of one’s own ability.

 

Extending the Analogy

 

Chess and the martial arts are nicely comparable because they are ancient, well-studied disciplines with room for a large disparity in playing abilities. However, the three styles of play discussed may instructively be applied to most forms of competition or conflict. The key that makes these approaches applicable is when a game is too extensive to be able to consider an moves. Each of these styles provides one way of handling enormity. The positional style is the most thorough, but it also requires the greatest amount of both thought and competence. It is no surprise that my martial arts instructor constantly reminded us:

 

The beginner is ten percent mental and ninety percent physical.

The black belt is ten percent physical and ninety percent mental.

 

 

Part 2: Analyzing Beauty in the Martial Arts

 

In the time that I have studied the martial arts, I have acquired certain a lingo that has never been rigidly defined, simply learned in context. For example, while sparring practice fighting, my peers and instructor have commented on "good moves," "clean fights," and "fair matches." Each of these ideas is well understood among martial artists, though perhaps not everyone has considered from where these implicit value judgments stem. Only after studying the elements of aesthetics did I realize that these terms were all a description of beauty in karate.

What is Beauty?

 

Though it is not at all obvious how a rainbow can be compared to a chess move or a sonata, this is only because their parameters are different, not because there is one kind of beauty in art and another kind in music or strategy. All objects and ideas can be analyzed according to two qualities: complexity and order. Understanding the parameters that comprise complexity and order, and how they are related to one another, may explain the aesthetic link between apples and the Brooklyn Bridge. When put together correctly, complexity and order can reveal an object’s inherent beauty, which is linked directly to its potential for development.

What precisely is included in order and complexity? Every object will have different particular parameters, but conceptually, they share common features. Complexity consists of the material parameters that compose the object. Material parameters include such qualities as physical composition and materials. Positional parameters deal more with relationships and the overall position, such as symmetry and stability. For example, in a painting, the material parameters would include the canvas and paint, as well as the subject portrayed in the painting. Positional parameters would include the space relations of the objects in the picture, the use of techniques like perspective and shading, and the relevance of the painting in its social context. Clearly, according to these criteria, beauty is dependent on individuals’ perceptions. This does not mean, however, that beauty is a purely conditional value. Order, and the qualities that compose it, are semiconditional because they consist of concrete, objective characteristics, but their value depends on an individuals’ subjective potential to appreciate it.

 

The Parameters in Karate

 

In order to understand beauty in the martial arts, we must first discern what are its parameters. The essential parameter that contributes to complexity is material. Material is a set of prelearned responses and heuristics that lays a foundation for the techniques that martial artists use. For example, a kata is a series of about 15 to 50 moves that details a defense to a preconceived scenario of being attacked. Though in an actual fight or competition, one never sees a complete kata, usually certain series of moves can be associated with a pattern learned from one or another set of material. Another parameter contributing to complexity is body size and type of the competitor and his opponent. Though karate teaches to maximize one’s own physical qualities, certain features like strength and flexibility will effect both players’ fighting styles and possibly the outcome of the competition. Material and body type contribute to the complexity aspect of karate because they add factors which can complicate or alter the outcome of a competition.

The attributes that contribute to the order in karate are those that synthesize the parameters of complexity. Degree of mastery of each player is key to the order of a competition. Mastery refers to the extent to which a player understands his material and can apply it in variations to real world situations. For example, someone can perform a pinion flawlessly, but lack conceptual appreciation. Although he would be said to "have the pinion" in his archive of material, he lacks the mastery to develop its potential in other situations. Grand masters of Shaolin Kempo Karate fight in a state of "No Mind," or complete mastery, where they can instantly draw upon a technique from any of their material without pausing to think. Such mastery creates order because it unifies all of the tools they have into one cohesive arsenal of potential.

Another crucial element of order in the Shaolin Kempo style of karate is called "knowing your dragon." The discipline involves studying the movements and techniques of five animals, each with different qualities and strengths. Every person has different physical characteristics and abilities, so must focus his studies on and actualize a different combination of the animals. "Knowing your dragon" refers to understanding which combination of the five animals you personally embody. Similar to mastery, "knowing you dragon" is a unifying quality that aggregates the material from another perspective. It is a completely subjective quality, depending on each individual, although it is generally based on the same parameters (i.e., physical ability, predispositions, etc.).

An additional parameter for order in the martial arts is the concept of fairness. Fairness is a condition that compares the circumstances of both opponents. Like mastery and "knowing your dragon," fairness is a unifying measure. However, fairness does not aggregate the parameters of complexity, but of order itself. It refers to the extent to which the players of equal training or ability, and the rules of competition are known and obeyed. A martial arts competition where one player uses a concealed weapon against the rules is unfair, no matter how important the weapon was to the defense of the cheater. Similarly, a situation where a trained expert tantalizes a novice is equally unfair. Fairness is an aesthetic state of equality and symmetry.

Each of the above mentioned qualities contributing to order can be considered positional parameters that indicate the individual’s or the situation’s potential for development.

 

Birkhoff’s Function

 

Simply defining features of complexity and order does not unlock the key to aesthetics. Complexity and order must be combined in a meaningful way in order to aggregate all of their values. George Birkhoff suggests one function:

 

Beauty = 0/C

 

His function divides total order by total complexity. Without even defining order or complexity, this function makes several comments about aesthetics. First, with all else equal, the more order the better. Similarly, if all else is equal, the less complexity the better. Birkhoff believes that complexity has a purely negative, or detrimental value to beauty. Taken to an extreme, this implies that a state with no complexity is ideal:

 

O/0 = infinity

 

In the martial arts, this equation would be a state where neither player has learned any material, i.e., they would not be martial artists. Such an illogical result could be averted if there were certain constraints on the values of complexity (for example C ¹ O).

However, Birkhoff’s function implies another troubling quality of beauty: aesthetics are purely relational, and have no cardinal value. In other words,

 

O/C º 20/2C

 

As discussed above, aesthetics represents potential for development. This equality neglects that simply having more elements of order and complexity can offer more opportunity for development.

 

 

 

An Alternate Function

 

Birkhoff’s function for beauty seems flawed. To redesign the function we should consider that material parameters, or complexity, can have positive value. In the case of the martial arts, material can be positive or negative, or both. One damaging element of material occurs when there is far more material than mastery, and the player cannot process the material successfully. In another case, one player may have far more material than the other, preventing a fair match. In other words, a state of "too much material" depends on other parameters.

Additionally, it seems that while both order and complexity may contribute positively to the function, added order would be more valuable than added positive complexity. Therefore, a new function should somehow take into account that the value of order rises at a faster rate than the value of complexity, or that beauty is more dependent on order than complexity. Such a function might look like this:

 

beauty = 02*C or 02+C

 

In the martial arts, these functions capture the relationship between order and complexity well. The value of the material (positive or negative) and physical situation can be summed up and then attached to total order squared. The order component is highly sensitive to changes in mastery, "knowing the dragon" and fairness. Consider a player with a high level of material and physical ability who does not know his own strengths and weaknesses. Surely the function should be more effected by some added understanding than by increased muscle power. It does not make sense to give complexity the same weight as order, because order already takes into account the elements of complexity and their relationship to the whole situation.

 

Example of Beauty in Karate

 

This study of aesthetics in karate leaves room for a wide range of beautiful displays. Two examples might illuminate this. One of the most handsome and gratifying events is to watch two grand masters compete. Their level of complexity, both with material and physical ability and training is high. Their order surpasses all martial artists. They have such command over their body that they scarcely show any motion to execute a move. They understand their opponent excellently, and show a fantastic level of "mental sparring" as they battle strategies and techniques. They employ only lawful tricks, such as feigns, but use no underhanded moves or external aids. Such a sight is a treat.

However, experts are not the only ones who can create beauty in the martial arts. In many ways, watching two novices fight offers similar charm. The competition is most fair, because neither person’s training has diverged from the basics. They each possess a limited amount of material in that they can only work with five or six moves each. Hence, such a competition is purely a test of mastery over these few moves. The aesthetic experience lies in watching the dance between the equality and asymmetry of these individuals.

 

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