Our Four Elements and Why We Have Introduced Them

In this book we are going to consider four basic elements:

1. Paradox   2. Depth   3. Geometry   and 4. Flow.  

These terms will be defined more fully (with many examples) when we come to the individual chapters dedicated to each of them; but for the present, the following should help you to understand what we mean by them.

1. Paradox

Surprise, outrageousness. An immediate confrontational tension is created. The response to a paradoxical move might be 'How can this be possible?' or 'That simply cannot work!'.
An example would be the move 2 Qf2!! in the solution to the Gurvich study (see the first example in the book) or the underpromotion 6 c8R!! in the Saavedra position.
To win by such means is a heroic form of achievement, and, other things being equal, the more paradox in the play, the better.

2. Depth

Subtlety, complexity. A deep move is one which is not obvious (though not necessarily paradoxical) and for which the point is well hidden. Initially one does not understand it, and later the response is 'Ah, so that was the point!'.
In the study by Ratner given earlier, the move 1 Be2! would qualify as being deep. In the Richter position 1 Kb7!! is both paradoxical (moving away from the action) and deep. Depth relates to the complexity of what is being achieved. Again, other things being equal, the deeper the moves the stronger the aesthetic effect. A game with no deep moves at all might be enjoyable the first time you see it, and maybe even a second time if it is good for other reasons; but some degree of depth is required to generate sufficient tension to count as a true masterpiece that can be played over many times with pleasure.

3. Geometry

Patterns , repetitions, echoes, mutual interferences between a rook and a bishop... The response might be 'Oh, what a pretty pattern!'.
An example of mainly geometrical play would be the Nissl position (see the end of the brief history section). Here the bishop jockeys with the rook (in what could be described as a geometrical duel) before completing a diamond- shaped 'rundlauf' (Bg5-h4-g3-f4-g5).
In the Sam Loyd Organ Pipes mate in two, the mutual interference on lines and diagonals would also be called geometrical. As explained earlier, the brain is good at spotting such patterns and the prettier the pattern that is involved in achieving something, the better (the tension is resolved in a pleasing, aesthetic fashion).

In our extended meaning of 'geometry', any striking pattern or special feature could be included. For example, if during the solution to a problem one side promotes pawns to each of the four possible pieces (Q, N, R, B known as 'Allumwandlung') this would be a 'pattern' or feature that the brain might easily recognize. Many tasks and special effects achieved by composers fall into this broader 'geometry' which is not restricted entirely to its spatial sense.

4. Flow

Smoothness of movement. It relates to the length of the sequence of moves for which the tension is dynamically maintained. For example in the Rinck position (see history section), the play flows across the board as the king chases the bishop for a whole series of moves.
The degree of tension (or 'area' of tension) could be seen in terms of length x depth. The response to flow might be something like: 'Whoosh! I'm being carried along!', and again, the more flow the stronger the aesthetic effect. Often, in top class studies, an elegant flow is abruptly halted by a paradoxical finish.

These four factors are relatively independent of one another and have come about after a sort of 'instinctive factor analysis' of our experience of beautiful chess ideas.

What is the point of this categorisation? Basically to help us communicate about tension and the aesthetic effect in chess and chess composition.
Games, studies and problems exist regardless of how we try to describe them. There is nothing 'real' about our categories, they are just words and one should not expect too much from them. As with any descriptive theory, if the categories prove helpful in communication, they will be useful and will survive. If not, they will die and we would have failed in our task. Certainly your co-authors find the categories useful. With surprising consistency and clarity we agree as to which of the four elements (one, two, three or all four of them) are present in a piece of chess action. The categories help us identify and pinpoint the tension- creating features of the play and thus to talk more usefully about aesthetic issues (and it is never that easy to talk about such abstract matters).

Extract from Secrets of Spectacular Chess (J.Levitt,128 pages,Batsford,1997,12.99 ISBN 0 7134 8049 1)
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