The Exact and the Inexact
Machine Methods
Program for Everyman
Bibliography
"Life is not all play; the child must prepare himself for pain and effort, and it would therefore be a disaster if he were allowed to think that everything can be done as a game."
-Emile Durkheim- "The final problem is that of reducing the strategy to a sequence of orders, translated into the machine's language. This is a relatively straightforward but tedious process, and we shall only indicate some of the general features. The complete program is made up of nine sub-programs and a master program that calls the sub-programs into operation as needed. Six of the sub-programs deal with the movements of the various kinds of pieces. In effect they tell the machine the allowed moves for these pieces. Another sub- program enables the machine to make a move 'mentally' without actually carrying it out: that is, with a given position stored in its memory it can construct the position that would result if the move were made. The seventh sub-program enables the computer to make a list of all possible moves in a given position, and the last sub-program evaluates any given position. The master program correlates and supervises the application of the sub-programs. It starts the seventh sub-program making a list of possible moves, which in turn calls in previous sub-programs to determine where the various pieces could move. The master program then evaluates the resulting positions by means of the eighth sub-program and compares the results according to the process described above. After comparison of all the investigated variations, the one that gives the best evaluation according to the machine's calculations is selected. This move is translated into standard chess notation and typed out by the machine."
-Claude E. Shannon- The Exact and the Inexact The name of Claude Shannon will be remembered by generations of computers. As early as 1950 he had completed preliminary work on a chess-playing computer, and had suggested the parameters within which future work would proceed and upon which it would build. The subject of computerized chess is very complex, but it is, I think, equally crucial to social theory. Social theory, from Marx's determinations that surplus profit makes class conflict and hence dynamic change inevitable to Parsons' belief that shared norms tend to maintain equilibrium, reduces the proliferation of data and detail in experience to a comprehensible model. Then what is learned at a given time and place can provide knowledge at a different time and place. This knowledge, when related to our values, may tell us how to act. Social theory structures and assists our decision-making processes. Computerized chess in this view is one variety of social theory, or an endeavor to aid humans in their decision-making. As theory, it is more formal than most. Within only a few rules which are extraneous or arbitrary, chess presents an objectification of quantitative and logical thought processes between two persons, a person and a machine, or two machines. There are three relatively distinct questions: How does a computer play chess? Why should a computer play chess? What is the future of computerized chess? The answers are briefly these, the chapters of this paper: 1) A computer imitates and extends human thought processes; 2) A computer should play chess because it can derive at high speed exact solutions to problems which appear inexact to human minds; and 3) Computerized chess could replace social theory as the ontology upon which each man's "contract" with society is based. The order of the above three questions represents a movement from the purely technical to the highly speculative. Such a paper would be senseless without some discussion of the technical methods of computerized chess, but I have chosen to relegate them to the second chapter. The distinction between the "exact" and the "inexact," like that between objective and subjective, is a variable thing. "The same task may be exact or inexact, depending on the power of the control system confronting it" (Botvinnik, p.1). We can say that inexact components of a system are perceived as its qualities, and exact components its quantities. Thus, more powerful computers promise to transform qualitative choices, which hitherto were reserved to the intuition of artists and experts, into quantitative choices. When they can learn limitlessly without, in effect, using up human duration, we can expect a new relation between questions and answers, in which the definition of the former is the major determinant of the latter. In other words, "answers" will be available (to logical and "quantitative" problems) if the questions can be operationalized so that computers can understand human objectives. Modern computers go beyond the early arithmetic machines to "think," i.e. make decisions, but for this they need a model. One finds that the chess model is both complicated enough for modern life and (barely) simple enough to be programmed. For problems of two-party contracts as well as resource allocation, the model is ideal, for it starts from a framework of equality, presumes a goal, and depicts correct decisions toward overcoming resistances in achieving it. "Correctness" may originally be based upon "intersubjective agreement among experts" (deGroot, p.23ff). A slightly more refined operationalism follows: "A move is good if and only if it is impossible to find another one, after a careful and convincing analysis, that is better" (deGroot, p.23). But "turning the machine into a good aide in the solution of inexact problems...can be done in one way only - by constructing a mathematically precise program for the solution of inexact problems, or, in the language of the mathematician, by formalizing the solution" (Botvinnik, p.6). An exact formula of "correctness" was expressed by Botvinnik 20 years after Shannon's groundbreaking "General Exchange Formula" whose form is: "An analysis of a variation should be continued by White as long as 'X is greater or equal to Y'" (Botvinnik, p.86). Thus do "qualitative" dimensions become quantifiable. Thus is art subsumed under science. The model of chess is a link between exact methods and inexact problems. "Games resemble real-life situations in that the players' rewards or penalties depend on the joint outcomes of their own moves and of the moves made by other players; this permits a clearer analysis of the interdependence of decisions among different actors in a situation of conflict or of cooperation or of mixtures of these two" (Deutsch, p.52). In each position (situation) there is one objective best move, even given that each opponent's "King" may represent a different value to him. But this best move cannot necessarily be known. "When the prospective winner in a game of chess says, 'I can force checkmate in five moves,' this means that whatever the other may do, a checkmate in at most five moves is inevitable. When the loser sees this, the game will surely be broken off. We may look at it this way: when such a position is reached, we may imagine that the two players are starting a game with the position given as initial. This game can be foreseen to its end and is therefore not worth playing" (Rapoport, p.159). Any framework will distort the data. The moderately complicated framework of chess allows, it is estimate, "at least 10120 possible games" (Bernstein, p.96). Thus we need not fear that computerized chess will be "not worth playing," although we can expect that in situations where the illusion of freedom prevailed, our choice now will be between making and not making the correct move. The figure of 10120 may approach the "infinite" diversity of forms in Nature and society--for computerized chess, the kingly infinite is to the queenly maximum finitude as 200 is to nine--and thus suggests that the effort to program machines to play chess may not be over-reductionist in implications. Most of the information needed to make a decision between alternative moves is inexact in appearance (beyond ascertaining details of the position with "binary questions such as 'Material equal?' 'King in check?' 'Queens present?' or quantitative questions: 'How many pieces have been taken?' 'How many moves have been played?' etc." (deGroot, pp.405-6)) just as in real life our indecision often stems from inability to formulate the choice. For instance, I must choose between moving the King out of check or blocking the check, between avoidance and resistance, between leaving the neighborhood or buying a gun or putting another lock on the door. I am mystified until I see that moving the King creates another equal danger, until I read that crime rates are equally high elsewhere. The knotty problem, at whose solution a beginning was made by translating chess notation to English, is how to operationalize the link we see between social problems and chess problems, so that the accumulated knowledge of chess decisions can yield directions for social progress. Its solution can only be that each citizen have equal resources to use as he wishes, and that each of his decisions be a precedent for those which follow, these choices to be his identity, progressively more enforced by a computerized "collective consciousness." Computers give a quantitatively "infinite" aspect to science; the question is whether this can ever be interchangeable with the artistic intuition which guides human experts. The scientific aesthetic of exactitude tends to become repressive. A computer exceeds human capacities in its memory, which we may call exact. The conscious part of human memory is far from exact. Perhaps the instinctive part of human memory, as it relates to survival, is exact, but even so it may be less than mathematically objective. Where memory or learning is involved, computers may be able to deal exactly with tasks which are for humans inexact. Of course machines can only do what they are told, but if they can be "told" to learn at high speed, this shortcoming may become less and less important. On the other hand, computers have a difficult time knowing what to focus upon, how to formulate a problem. The advantage of human thought is that "the program of the human player can be highly selective in its branching" (deGroot, p.397). In other words, how does one formalize the notion of "relevance," which guides and delimits human thought processes by suggesting particular implications of the totality of one's knowledge (including all one's rules for inferring implications). In games as in real-life situations "the players must act under conditions of uncertainty and incomplete information; this makes the analysis of such games relevant for problems of decision-making under conditions of uncertainty" (Deutsch, p.52). But a computer can only deal with such conditions precisely, and the difficulty for programmers is to give computers a methodology for making decisions. "At the start of the process all the ingredients of the problem situation are given, it is true, but the problem itself is not: it must be posed and developed in the process" (deGroot, p.405). Machine Methods M. M. Botvinnik, who was world chess champion 1948-57, 1958-60 and 1961-3, in 1970 published in English an amazing booklet, "Computers, Chess, and Long- Range Planning". He offered ideas for programming a computer to play chess that were substantial improvements over existing theory and technology. His name follows Shannon's as a milestone. One of his innovations was to see the game, so to speak, from the point of view of each piece, and to work out a set of keys for interdicting (i.e. intercepting, obstructing, capturing) the movements of each piece. his approach was to delimit the system by considering the "social facts" delimiting the worlds of each of its components. For example, the "Key for interdicting the movement of the King (Botvinnik, p.31) looks like this:Apparently these "keys" can be fed into a computer in order to determine all the possible moves open to a given piece, the range of choice for the player. The underlying concept is that of the "horizon, the boundary of the region containing those pieces, and only those pieces, that can take an active role within the given limits of time for movement... The maximal horizon is defined by the capabilities of the apparatus at work within the player, whether the player be man or machine" (Botvinnik, p.21). Theorists since Archimedes have searched for a frame of reference not dependent on another. Botvinnik makes each piece an "independent variable" and thus circumvents many problems of relationalism. His view is perhaps appropriate and applicable to anomic society, where a pluralism of different worlds determine the whole. In society one's movements are delimited by laws, physical barriers, and customs, and so for example a traffic planner can predict empty streets at 4:00am and so eliminate that segment from his workload. Neither in chess nor in social theory is it necessary to consider unlikely contingencies. "Since developing a machine that plays a masterly game of chess can hardly be considered a valuable research goal in itself, the research gain must either be methodological or theoretical. That is, 'promise' must be measured in terms of possible results that are conducive to better insights and skills in non- numerical, heuristic programming or are relevant to the development of theories on thought processes. Results should have a definite 'generalization value,' beyond the field of chess" (deGroot, p.402). The methods of human thought are, as stated above, imitated and extended by the computer. The "well-known cycle of (empirical) scientific inferential procedure, namely: (1) observation, (2) induction, (3) deduction, (4) testing, and (5) evaluation" (deGroot, p.404ff) is paralleled by different kinds of computerized chess programs. Here is what the basic computer program might look like, and here is how, for example, a decision about work versus leisure might by assisted by it:
These steps would constitute the master program which would trigger the sub- programs into effect. "Some (sub-programs) would detail the operations involved in executing the moves of the different men and in listing all possible moves in a given position, and others would specify the operations required to arrive at the numerical evaluation of a position, certain weights being assigned to the various positional qualifications" (Lasker, p.219). There are always certain initial or introductory behaviors that are traditional, and is so in chess as well. The different "openings" are the first main branches of selectivity, hardly less standardized than the set-up of the board. It has been found that other openings tend to lose. "The first twelve or fifteen moves of most opening could be played by the machine 'from memory,' just as a chess master does it" (Lasker, p.216). The way that the opposing sides in a computerized chess game are distinguished is that we "denote the tangible values of the White pieces by real numbers and of the Black pieces by imaginary numbers" (Botvinnik, p.14). White's "intangible" (positional, situational) values are denoted by imaginary numbers, so that, for instance, a situational advantage leading to material gain is seen mathematically as a zero-sum transaction (White gives up an intangible imaginary value for a tangible imaginary value). This model for how opponents (or partners) interact in contract is broadly generalizable: if I lend you a dollar, you have given up your debt-free status and I have given up the dollar. Now we can put together the systematic view of the computer's methodological steps with Botvinnik's horizon method. "Each instruction (to the computer) usually calls for the performance of a series of operations in a certain sequence, and each of these operations may require a sub-program" (Lasker, p.219). Botvinnik's innovation was to not analyze the worth of each alternative move until series of moves (paths) had been constructed to a given depth. In other words, "the variations-tree is analyzed after the path-tree is constructed" (Botvinnik, p.xi). Decision-makers who adopt this principle will improve their long-term planning. The sequence of the operations performed determines the efficiency, the power, of the machine. Another way of increasing its efficiency is to "include in its memory a considerable number of frequently recurring end-game positions" (Lasker, p.225). Endings as well as openings of all kinds tend to be traditionalized: the house changes hands when the mortgage is signed, not when payments are completed. If we are trying to produce a machine that will simulate human thought, we should channel its workings toward those areas where non-habitual decision making is crucial: one knows how to buy a house, but not how to decide between buying and renting. Even in those areas, "'conditioned reflexes' could be built into computing machines by having the data which go into the memory registers affect the mechanism involved in arriving at the numerical values that decide a choice" (Lasker, p.225). The above innovations represent the historical progress of a young technology. A technology is systematic at first, as in 1950: "In the case of a chess-playing machine the program would consist of instructions covering the operations required to arrive at a reasonable reply to a single move, and the machine would follow the same program on every move" (Lasker, p.216). The passage of 20 years yielded an approach wherein parts of this decision-making process were relegated to memory operations, parts to self-learning circuits, and parts to evaluations of branches extended out for several moves. We may see here a general tendency for systems to become less orderly but more efficient as they develop. "Those who use chess mainly as a test case or as a field of exercise for developing complex techniques of non-numerical programming are likely to look more and more for heuristics--basically human heuristics--in order to improve their programs" (deGroot, p.396). Indeed this must be the case. Completely comprehensive methods cannot cope with the possible diversity, even at electronic computer speeds. For instance, a 1958 chess-playing program (Bernstein, p.100) was to select from the approximately 30 possible moves it might make, seven for detailed analysis (it picks these on the basis of eight questions). It then was to test each of the seven in turn through four moves ahead. It was found that this took about eight minutes per move, because "it examines 2,800 possible positions" (Bernstein, p.103) each time. And arithmetically increasing depth of analysis involves consideration of a geometrically expanding number of positions. Thus heuristics are necessary. In this context, a heuristic device can be understood as a special rule for excluding some possibilities from consideration. Back in 1950 "Shannon had proposed two principles on which an algorithm (program) for playing chess could be founded: 1) Scan all the possibilities (moves) and construct a (so-called) tree with branches of equal length... 2) Not all possibilities are scanned; some are excluded from consideration by a special rule" (Botvinnik, p.2). These programming principles were pitted against one another in the 1966 Moscow - Stanford machine chess match, respectively, and the former vanquished the latter. Nevertheless it seems than principle #2 is the proper principle for fully developed technology, though the proper "special rule" to apply is not always easy to find. There is a final aspect of machine methods. Due to prejudice, habits and tendencies, conscious and unconscious, it is virtually impossible for a human to make a truly random decision. Yet often the data is balanced such that a random decision is called for. Of equivalent bids, who shall get the government contract? Which of two candidates shall be hired? Who shall be the first to be served? Non-random elements accumulate in a system in places where randomness was the proper principle of justice. These are seen as irrational habits. The chess-playing computer "could be made to choose at random from several moves which the evaluating process shows to be of approximately the same quality" (Lasker, p.225). When the pure theory of computerized chess is applied to social reality, this method of random decision-making will have its place. Program for Everyman The main difficulties in making such machine methods useful are in translation: from the language of chess to the language of computers, from the language of computers to the language of social reality, from the language of social reality to the language of chess. A most utopian speculation would be that self-learning mechanisms coupled with high-speed operations imply the advent of consciousness within a computer, which could simplify problems of data programming. For example, it would be helpful if a computer could detect the logical question implied from a given voice pattern, and then depict it graphically as a chess position with its solution appended. Perhaps one would "relate" to the computer to the degree of structuralization of his problems that he had attained, and would receive guidance from it in line with his previous inputs (his "identity"). It may eventually be possible for computers to provide humans with the "correct" answers to each of their questions. From this there follows a compulsion to act "correctly." An elite can do this. Those who understand how the machines work do not have to fear being dominated by them. Bernstein's and Roberts' "contests with the machine show that anyone good enough to construct a three-move trap can beat it" (Bernstein, p.105). This is because the machine's depth of analysis cannot go much beyond four half-moves. As society becomes more automated and computerized, there is a danger that there will develop sharp proficiency cut-offs, below which a person will be victimized by the social machinery. There will be food stamps for everyone, except for those without a ticket to headquarters. Continuing human freedom within the determinixm of a rational society would require that computers be mute, allowing humans at least the illusion of free choice. Indeed we could start with a fresh slate every day, citizen and chess- playing computer. The "process of playing chess (and probably any game) consists in a generalized exchange. By this term we mean an exchange in which (in the general case) the values traded may be tangible or positional ('invisible,' situational)" (Botvinnik, p.9). Contracts are based on such a generalized exchange: the social contract consists of responsibilities and rewards, the market contract exchanges goods for money, and the legal contract, requiring two signatories, represents an exchange of promises. Each citizen's acts would retain the meanings he had given them, and he would have influence over the movement of the body politic to the extent that his behavior was free from internal contradictions. When his own devices bogged down, he could be shunted to the "normal" or "main" line of play, which could be given to computers as a formal paradigm of standard behavior. The task is to develop meanings for the original configuration and moves of the chessboard in terms of (probably new) sociological concepts (see Appendix); then the accumulated knowledge of chess would constitute a way of manipulating these concepts. For example, a social priority might be said to be the maintenance of authority, legitimate power. Perhaps an "authority game" could be developed. We might hope for a society where diversity is possible. Although the object of chess is checkmate, the defeat of the opponent, the phenomenon of a chess game presents itself as a balancing of conflicting claims non- symetrically. "Marx remains the most powerful analyst of asymmetrical relationships. In contrast to the social theorists who cling to a harmony model of society and stress symmetry in the mutual orientation of actors, Marx is concerned with the facts of unilateral dependence and hence of exploitation, and the denial of reciprocity" (Coser, p.147). Conflict resolution is often effected by repression, imposing identical controls on all participants. In a chess game, on the other hand, each opponent protects through his choices what he values most (both, by definition and "style" of play). Games such as chess "deal with the conditions of 'payoffs' or 'interests' for the different players, who are rewarded or penalized in terms of what seems valuable to them or else in terms of what will permit them to stay in the game. This leads to sharper definitions and clearer understanding of the concepts of utility and interest, and hence also of certain aspects of rationality in decision-making" (Deutsch, p.52). Thus, decisions are made by each person, and their realm of intersection is "society." This realm takes on substance when computers are installed there. A chess-playing computer decides its moves by a "process which can be described as one of collecting and integrating information on the position by means of a series of questions" (deGroot, p.405). We increasingly see that society asks questions of its members; soon society gains a dangerous autonomy, which the computerized chess model can go far to explain. "Opening play," it was noticed, "could be speeded up somewhat by letting the machine always play White" (Lasker, p.224). To "play White" means to make the first move in a chess game, often a winning advantage. The machine was to play White because it is less complicated to program a computer to make an "assertion" than to respond to any of a number of assertions. However, the tendency for computer systems to initiate action was thereby built into the system from its foundations. It is in this way that man loses dominance over the machine systems he has organized. The object for computerized chess is to allow informed decisions. There are similarities between the processes of human minds and computers. Before a decision, both must consider three "moments": "the static moment ('how things stand'), the dynamic moment ('what sort of things may happen') and the evaluative moment ('what the position is worth')" (deGroot, pp.396-7). Both can learn. Both can remember. There are also differences. Human decision processes can still be more efficient (have greater depth of planning) than machine processes, because of our greater selectivity of which frames of reference to consider. On the other hand, the great advantage of computers over humans are in speed of operation and capacity-accuracy of memory. Once computer technology could combine with chess techniques, social planners could proceed with the objective problem of satisfying each person's needs; the points where their wants were logically contradictory could be identified. BIBLIOGRAPHY A. Bernstein and M. de V. Roberts, "Computer vs. chess player", Scientific American, 1958, no.198, pp.96-105. M. M. Botvinnik, "Computers, Chess, and Long-Range Planning", Springer-Verlag, New York, 1970. Lewis A. Coser, Continuities in the Study of Social Conflict, The Free Press, New York, 1970. Karl W. Deutsch, The Nerves of Government: models of political communication and control, Free Press of Glencoe, London, 1963. Adrian de Groot, Thought and Choice in Chess, Mouton & Co., The Hague, 1965. Edward Lasker, The Adventure of Chess, Doubleday & Co., Garden City NY, 1950. Monroe Newborn, Computer Chess, Academic Press, New York, 1975. Anatol Rapoport, Fights, Games, and Debates, University of Michigan Press, Ann Arbor, 1961. Claude E. Shannon, "A Chess-Playing Machine", Scientific American, 1950.
"A. set a goal..." .to decide between employment and welfare "B. generate or select a set of considerable moves" .list jobs and welfare payments available "C. calculate variations following rules that generate continuations (and their priorities)" .list benefits as well as responsibilities for each of the alternatives "D. in each variation, apply a stop rule" .eliminate alternatives below subsistence and those overly fatiguing "E. evaluate the final positions by means of an evaluation function" .choose short-term and long-term preferences
"F. choose the move to be played according to a selection procedure, such as minimax" (deGroot, p.399)..make applications according to preferred choices.
