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From the back cover:
In this compact book, a Soviet Grandmaster and former World Chess
Champion has analysed, and advanced a hypothesis about, the intuitive thought processes of master chess players and translated
these thought processes into mathematical form.
On one level this formalization of thought processes provides a basis for a computer program
that seems likely to succeed in playing chess.
On a second level, Botvinnik's concepts of the inexact problem, the variable horizon and
the setting of goals are all close to the core of the problem of how to plan. They are a significant and fundamental contribution
to the art and science of long-range planning.
Review by Hoa H
I first read the book in 1985. The topic is interesting, the
book title is impressive. After the first two chapters, the rest looked like Greek to me. The next three chapters are the
"meat" of the book. Finally last week, after 18 years of "soul-searching", it begins to make sense to me. Between then and
now, I revisited the book at least 5-6 more times. Difficult book! There are two reasons that this book threw me off. Dr.
Botvinnik used lots of Greek letters to represent his formulas: alpha, beta, psi, theta, sigma, tau, rho, phi, delta, pi,
sigma, etc. (See what I meant.) If that was not enough, he added in the "complex number representation" as a "bonus." That
was the first reason. The second was the way he wrote those expressions, I thought they were "well-known continuous functions"
in math or science. Most of them are NOT. They are binary functions, either have values of 1 or 0; which now can be represented
as Boolean math in standard programming language.
The main way to use his evaluation expressions is with the assumption there is always an "attack" provided an material
exchange. This was applicable for tactical chess; while for state-of-the-art program, the positional evaluation is more involved.
The first is about the historical match between the USA-USSR programs, which resulted in favor of the USSR's. The
second, a lot of theories and background which are useful in chess-playing technique, computer programming, management decision-making,
human-reasoning, etc. Chapter 3 has: the confusing math expressions with those beautiful Greek letters. Chapter 4: using bit-map
to represent attack-defense paths that the decisions and evaluations in chapter 3 will compute. Chapter 5: using the his famous
win over Capablanca as experiment to illustrate his math expression. Chapter 6: a useless one; he spent 7 pages to list some
of his own games as exercise. (Why? If we want examples, Alekhine's, Capa's, Lasker's, Tal's or Fischer's are more typical.)
In addition, many diagrams are so large, while the whole book is only about 90 pages. More than 10% of the pages goes wasted,
killing at least 3 trees. Chapter 7: the future of computer chess. There are four chapters for the Appendices.
In summary, it is good book at the time, too confusing (at least to a literacy-challenged reader like me), and some
minuses mentioned above. Four stars for your book, GM and many-time world chess champion Botvinnik!!!! (****)
p.xi An Algorithm [JLJ - The title of the Russian version of this
book is An Algorithm for Chess] is a hypothesis about the intuitive thought process of a chess master. Like any hypothesis,
An Algorithm needs to be tested by experiment; in this case, an experimental test means writing a program and running
it on a machine. This task has been taken on... by a young mathematician and first-class chess player, V. Butenko.
p.xii As a chess player I see no way to solve the problem of choosing
a move in a chess game but via the path sketched out in An Algorithm [JLJ - once again, An
Algorithm is the Russian title of this book]. I hope that this edition of An Algorithm will give new impetus
to the testing of this hypothesis and will hasten the accomplishment of the tasks laid down by Shannon in 1950.
p.2-3 If the rule for excluding weak moves is well founded, the processing of the information is more fruitful
and the scan of alternatives is deeper... At the outset, we must acknowledge our debt to Shannon's insight. All computer programs
for playing chess published by mathematicians in recent years are basically no different from those established in principle
by Shannon... The use of the given weighting function to evaluate a position is also a doubtful procedure.
Shannon proposed the inclusion of numerical "weights" for the material relation of forces, open lines, mobility of the pieces,
advanced and doubled pawns, control of the center, and so on, which are listed in every manual for beginners. We should note,
as the authors of the textbooks usually do, that it is far from necessary to take account of all these factors at
all times and that their calculation yields only a sketchy estimate of the position. To sum up, the mathematical
goal of a game of chess, according to Shannon, is a number - the value of the weighting function.
p.5 The machine may play chess badly, like a beginning amateur, but the machine is not guilty. Man
is guilty. He has not yet succeeded in teaching the machine, in transferring his experience to it... To write a finished
program, one must master both chess and the art of programming.
p.7 Man solves inexact problems by relying on his accumulated experience and on intuition. The following
method for creating an exact program for the solution of inexact tasks therefore suggests itself: the program
must be modeled on human thought processes... It seems to me the only real way.
p.9 In my opinion, 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). The goal of a generalized exchange is a relative gain of these tangible or positional (situational) values.
There are not and cannot be other goals. In the end, this generalized exchange process in chess must lead to the winning of
infinitely great tangible value (i.e., to mate).
p.9 The tangible value of the pieces in chess is well known to all beginning chess players. But
what of the invisible, conjuctural (positional) value of the pieces? This value depends on the position of the piece and on
the role of the piece in the general combat then taking place on the board. The positional value of a piece is subject
to sharp changes
p.10 We shall assume, moreover, that the algorithm imitates the mode of play of the human, that is, it defines
a scan and an evaluation of the available moves. The scan, however, is controlled... What must the algorithm now envisage?
As a minimum, it must envisage a solution to the following three problems: 1. How to limit the number of alternatives...
2. When to stop computing a variation... 3. What move to make if the analysis of variations gives no clear answer...
The solution of these three problems is essential, even though we may later find that it is not sufficient.
p.13 An attacking piece has an intangible value or values in addition to its tangible value;
its total value is the sum of the tangible and intangible values. The intangible value of an attacking piece
reflects its ability to annihilate an enemy piece.
p.14 The Path of a Piece: An attack must have real features. There must be an object of attack and
a path, made up of actual squares, over which the attack is to be carried out. These squares are of two types: 1)
squares where the pieces come to rest, which we shall denote alpha, and 2) squares over which the pieces pass, denotes by
beta. There must always be alpha-squares; there need not be beta-squares. When the King, the Knight or the Pawn makes a move
(except for castling and the initial two-square move of the Pawn) there are no beta-squares. Similarly, there are none when
the Queen, Rook or Bishop moves to an adjacent square.
p.22 If the attack path is unsafe (closed) the master... looks about him: can he bring other pieces
into the game, to better the attack paths (the functions) against the enemy pieces and lessen the attacks against his own
pieces? This is what "positional" play amounts to. I believe that this part of the theory (on positional warfare)
is radically different from what has been presented up to now.
p.23 Play directed at changing a path [of a piece towards its objective] has the same character,
and proceeds by the same formulae, as play for annihilation, with the distinction that now the object of
attack is not an enemy piece itself, but a change in the attack-functions.
p.23 One possibility for improvement [Botvinnik is in the middle of explaining his algorithm] that comes
to mind is the use of modern mathematical methods to define moves most likely to lead to success. Then to every "positional"
move there would correspond a weighting function (a number) which would allow the definition of the most useful move, by a
more perfect method than the chess master now uses.
p.24 Positional play consists in converting Type IV values [pieces not in the line of sight of enemy
pieces] to Type III [pieces within the realistic future mobility "horizon" of enemy pieces] (and the reverse).
p.26 The reader is now familiar with the principles involved in constructing and analyzing a mathematical
map of a chess position. I believe that the chess algorithm presented in this book and based on these principles represents
the thought process of a chess master during a game
p.61 Why was Wiener not a good chess player? Why could he not foresee moves by his opponent that were obvious?
Shannon put these questions to me in 1965, and I could only shrug my shoulders. How could I know? The question is extremely
serious. No one can doubt the intelligence of Norbert Wiener, a very great scientist. Nor can one doubt the intelligence of
Alekhine, a very great chess player. Why was Wiener helpless at chess and Alekhine at mathematics?
I think we can now form a hypothesis as to the reasons for Wiener's errors at the chessboard... To
the scientist these qualities of the chess warrior [extraordinary development and an exceptional training of that portion
of the brain which is dedicated to operational memory and to calculation] are probably not necessary, since the scientist
has the right to solve his problems without haste... Above all, he must have the ability to do research. And what is that?
It seems likely that it is the ability to solve a variety of problems.
p.63 Perhaps chess itself will prove to be a sharp tool that will carve out new paths for investigation.
At the present time a young mathematician, V.I. Butenko, is translating the algorithm discussed in this book into the language
of the M-220 computer. For the time being he is programming the standard and very important part of the algorithm. He is "teaching"
the machine to determine the attack paths on a board filled with pieces, within a given horizon. He has had some successes:
for instance, the determination of all shortest paths of the King from the square a4 to the square h4 (and there are 393 such
paths) is made by the machine in something like a tenth of a second. The determination of all the attack paths (the assertions)
in a three-half-move horizon for the position discussed previously, from Botvinnik-Capablanca game (Fig. 22), required only
5 seconds.
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