BOTVINNIK, M.M. (1970). Computers, Chess and Long-Range Planning. Springer-Verlag, New York/Heidelberg. LC 75-85203 - (1982). Meine neuen Ideen zur Schachprogrammierung (transl. Alfred Zimmermann). Springer Verlag, Berlin. ISBN 3-540-11094-1 --- Fig. 3 (p 12) - The decision-tree of a chess study by M. Botvinnik and S. Kaminer (white to play and win). The start position is given in the top left-hand corner. The black and white ‘knots’ – 145 in total - are the possible moves of the players (with restrictions). In: Visions of Four Notions - Marten Kuilman (2009; p. 11 - 14) It was only a mere brief item in a newspaper that attracted my attention some years ago because of its philosophical implications. The Russian ex-world-champion chess M.M. Botvinnik developed, around 1982, a chess-program that did not depend on the brute force of the computer, but highlighted the positional aspects of the game. The chess pieces were given, according to their position in relation to other pieces, certain values. A subsequent inventory led to a list of priorities and ultimately to the most favorable move. Botvinnik regarded the game of chess - with its different pieces, moves and rules within a given environment - as an inexact problem which had similarities with other complex organizations like the economy or in management-systems. Van der HERIK (1983) provided an early survey of the world of computer chess and artificial intelligence in his readable Ph.D.-thesis at the TH Delft. Life itself is, in many ways, also an inexact problem. The advancement of a game of chess into a theory of life is therefore less dramatic than it seems, in particular, with respect to its crude mechanisms and methods. It is possible, in chess as in life, to place the ‘subjective’ associative-positional aspect of the communication in juxtaposition to the ‘objective’ brute force of trial and error. A conscious decision depends just as much on our insight and experience, gathered mainly in the past, as from the courage to try something completely new in the future, just to widen our experience. There is no observation without an object. Subjectivity and objectivity are inextricably linked to each other. We have to come to terms with the reality that there is no searching without an assumption or understanding without an a-priori. Botvinnik’s book on chess programming is a daring attempt to describe the basic problems of transforming the game of chess into a digital model for the computer (BOTVINNIK, 1982). But it also encounters, in due course, some essential characteristics of communication-in-general. Botvinnik pointed out, that any system of decision taking should have three objectives: 1. The collection of information, 2. The valuation of the information and 3. The act of taking a decision. It will be clear in the end - or rather much earlier - that the act of decision making in any system is embedded in a sequence of minor decisions, which were made along the way. The final, visible choice is just an option from a long row of invisible, preceding choices. If we follow that sequence to its source, it will ultimately be the type of division, which sets the character for the rest of the communication. Botvinnik proposed a decision-tree (fig. 3) as the most appropriate mathematical tool to tackle the problems in relation to the three objectives given above. He regarded the game of chess as an inexact problem, which could be solved in two ways (as had been indicated by the American mathematician Claude Shannon in 1949). Firstly, there must be a search for all possible moves by the building of a decision-tree. This action is, in theory, of a relative simple nature, but leads, in practice, to unwanted consequences, which stands in the way of a solution. Decision-trees have the habit of growing into huge foliages, even into infinity. The possibilities increase exponentially ‘in depth’ and become a major stumbling block of finding a proper way out of the multitude. This leads directly to the second point. How should the number of alternatives be limited? Some restraints must be introduced to manage the size of the decision tree. The ‘pruning’ of the tree by excluding all useless possibilities seems a logical step. The so-called minimaxing method validates the individual possibilities one-by-one (in a dualistic way) and rejects certain continuations if a better solution is found elsewhere. The alpha-beta pruning aims at the computation of particular favorable continuations (values) without examining every imaginable possibility. The establishment of a horizon is crucial. If we are able to apply the minimaxing to the full depth of the decision tree (in other words: fix the limits of the horizon), then we continue to have an exact problem, which can give an exact solution. It all looks so wonderful objective: just apply a dualistic evaluation on a local level and an exact decision could be reached for the whole, pruned system. ‘Turning the machine into a good aide in the solution of inexact problems’, said Botvinnik (1970; p. 6), ‘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 mathematicians, by formalizing the solution.’ An objective algorithm might hold the golden key to success, but when it comes down to the nitty-gritty of (Shannon’s) valuation of pieces, there is obviously a case of subjectivism. The decision-tree is only the first step in the preparation of data for a binary computer. The selection and valuation of the possibilities are much more difficult and complicated, because the actual parameters for such an operation have to be stated in clear terms. Subjective history and experience enter the (seemingly) objective reality of the decision tree at the very start of the valuation process. The solution of an inexact problem is a stubborn entity: the introduction of pruning – in the early stage of collecting objective information – is also the introduction of the first subjective measures within the game of chess (or communication in a wider sense). It is better to face this fact right at the beginning of an interchange of information. There is no point in ‘forgetting’ our own choices during further investigations. European scientific research has been for too long dogged by the heritage of Cartesianism, which glorified the ‘objective’ approach to nature, in which the observer had no formal relation to the observed. Botvinnik pointed to accumulated experience and intuition as the driving forces behind the solution of inexact problems. Those two properties are also highly subjective in nature, born in a pluralistic environment of constant and repetitive attention (experience) and in the bright, daring setting of a unity (intuition). The use of experience, or subjectivity, is in many ways a much better guide for human decision making. Botvinnik distinguished four methods of how to make use of previous gained knowledge: 1. The ‘parrot’ method - following the established rules, without much thinking, because the valuation of the moves is more or less historically established. Certain moves have proven their worth in time to be the right ones in a given, known situation. The method has a mechanical nature. Often used at the opening of a game. 2. The information method - or the passive search for a similarity of positions in the memory of a player, based on experience. This pattern matching is the most productive method in the human approach to the game (of chess). Emanuel Lasker, the world champion of chess between 1894 and 1929, was asked one day how many moves he was thinking ahead. His answer was a tribute to pattern recognition: ‘Only one, but it is always the best one’. This method is particular useful in the endgame, but is also applicable to the openings game, when a transformation of moves takes place. 3. The deliberate method - The ambition to create a position in which the information method (2) can work to its full advantage. Now the art of pruning becomes vitally important. Validation turns out to be the name of the game. The method of biased searching is typical of the endgame and probably of the opening as well. 4. The associative method – or the search for ‘position-fragments’, which can be related to ‘library’-positions. This method demands some sort of subjective overview in connection with a body of favorable ‘historic’ positions, known from literature or own experience. This method of pattern matching is, due to its intensive and specific use of the past, the only one suitable for the middle game and complicated endgame. It is clearly Botvinnik’s pet method. These four approaches reflect, to a certain extent, the stages in a quadralectic communication. Intuition, pattern recognition, validation and quantitative matching are the very characteristics of the conceptual movements in the quadrants. The final aim of scientific research is - or should be - the ‘samanvaya’ of the Buddhists: the act of reconciling contradictory ideas by carrying them to a level of understanding at which it can be seen that they are not really in opposition. The gaining of this vision will be the ultimate goal in this book. The tool to reach this understanding consist of a widening of the initial fragmentation of a communication into a wider field. See also: visionsoffour.wordpress.com/