PRINCIPIA SCACCHORUM, Part 6: Chess Axioms

As you know from the previous post, we set out to lay down the chess axioms. The main purpose of it is for us to ultimately come up with new 21st-century methods of teaching and learning chess following Nimzovich's idea from almost ninety years ago. These modern methods will focus on how mind would acquire the most basic mental models at the core of all chess knowledge construction, not tons of useless information.*

What you will read here may look too simple, even trivial at the first glance. But looking at it we realize a simple truth that all chess is about the use of force. The movement of pieces, that we pay most attention to at Square One, in fact, only serves force and facilitates its more effective use. This indicates that we should redesign early teaching methods to start with the power that pieces exert, not their moves.

It is not accidental at all that Nimzovich starts teaching with attacking contact between two pieces (2a below), not individual moves that lack the reason for making them (Dr. Lasker). The basics of everything is mindset.

It is time to get started.

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There are three aspects around any system. They are about members, their relationships and purpose of the system.

Let us see how everything applies to chess.

(1) Members and their abilities

Members do a finite number of things to serve a system. Chessmen can only do three things: a), b) and c) below.

a) They are power agents. The concept of force assumes there is a power dwelling in chess pieces. We can picture in the mind's eye that there are invisible lines of force propagating from pieces through the 8x8 chess space (this is reminiscence of the ancient armies using bows and spears). This space, as well as other objects (friendly and enemy pieces found in it), all feel the effects of the "charge" that chessmen have. We can call this control, or attacking effect.

b) They block lines of force of other pieces. A chess piece cuts off the lines of force of other pieces from propagating further through space. This we may call body effect.

This corporal effect affects the movement of pieces (1c) as well. A chess piece impedes the passage of other pieces through the square it occupies.

c) They are mobile. Chessmen can move along the very lines of fire spreading from them into the surrounding space as far as the body effect of other pieces permits. The mere fact that the lines of force and the lines of movement coincide makes any arguments that we must start learning with the moves baseless and untenable.

Every move changes power distribution on the board. It is important to note that movement is subordinate to and always serves power. For example, we deploy our forces for effective action. We also (by chasing, or even offering sacrifice) direct the movement of enemy forces into inconvenient positions, so they can be attacked (2a) with greater effect.

The two-fold effect of (a) and (b), plus mobility, is a measure of how active pieces are. Activity is the main principle in chess: one wants to increase activity of their own forces while suppressing that of the opposing army (=Dr. Lasker's universal principle of Struggle).

There is is an important addition to (a, b, c), namely:

d) Pawns can queen. Promotion drastically changes the balance of power on the board. This feature distinguishes Western chess from other variants, like Chinese chess, giving it its unique identity.

En-passant, or castling, both comparatively newer additions to the rules, are not relevant here as they really don't change the basic character of the game.

(2) Members' interaction and relationships

A complex system of any kind can never be understood just from the properties of its members though. The true nature of a system and its raison d'être can only be revealed by understanding how the members connect during the life of the system to form a network, or structure. "Hell is a place where nothing connects to nothing." (Dante)

The interaction of pieces has two facets.

a) Pieces attack enemy pieces. This happens between two hostile pieces when one stands in the line of fire of an attacking enemy piece. This is the basic element of power structure in chess. This particular (2a) concept, together with (1a), is at the very core of chess. All chess operations relate to it all the time.

There are two special cases coming from (a).

a1) Threat of attack. There is no attacking contact between two enemy pieces as of yet, but it is possible and could be established in one move.

a2) Multi-attack. This is any combination of attacks and/or threats. Double attack is most common. One piece may attack two enemy pieces, or two pieces attack two enemy pieces (as in discovered attack), or two pieces attack one enemy piece.

According to Averbakh, chess pieces develop only four distinct relationships during chess battles, attack, restriction, protection, and cover (pin). Any position on the board is a structure that is made up of these four. Attack is the generic one, while the remaining three contacts that Averbakh defines can all be deduced from it (we will see how later on).

b) Pieces can eliminate (capture) enemy pieces. This instantly removes all power influence the captured piece has had on the battlefield.

And that is it: 1a-c and 2a-b are the basic building blocks of chess life. These chess axioms lay a foundation for study of all chess.

Even though chess players may be totally unaware of them, as FM Prof. Saariluoma acknowledged above, we can immediately recognize them in the protocols of thought process of Masters as the first thing that pops up in their mind when they study a position, before more and more complex mental construction begins to unfold. This can be clearly seen in Adriaan de Groot's seminal Thought and Choice in Chess, from the interviews he conducted with such preeminent chess players as Alekhine, Euwe and Keres (we will get back to this at a later time).

While the above is pretty straightforward, positional play and strategy make up an intricate composite of basic and higher-level concepts:

(3) System purpose

There is no organization of parts in a system without a definite purpose. Structural piece relationships are always organically linked to collective direction that the chess armies are taking during battles. Power structure follows objectives, and objectives follow power structure. One doesn't exist without the other.

This is the domain of strategy. Once we have learned to "read" the power structure in a position, strategy is all about how to change this formation on the board in one's favor following the Supreme Law of Activity.

Movement serves this purpose again. Physical maneuvering forces a sudden change of front which dislocates the distribution and organization of enemy forces. The opponent may get out of balance which creates weaknesses in their camp (=lack of control over important strategic points), so that our forces can focus on them as tactical targets.

We will see few chess theorems next time.

NOTE:

* Pick any chess primer. You will see that all of them start with pure technicalities, not with true basic concepts to help start forming the proper mindset on a blank slate.

Here is an example: The other day I randomly picked a primer at my local Barnes & Nobles bookstore. Chapter 1, The Basics, starts with 10 (ten!) pages on the Board (no one has patience to read all of that in the 21st century). Nevertheless, one can read this very useful stuff in the book.

For example, in paragraph one it reads that "most serious players stick to a standard size of about 16-22"." Does that have anything to do with mind set? Of course not. In the second paragraph, the author boldly touches on strategy already, wow! Listen to this, "Everyone has sixty-four squares to work with. Half of sixty-four is thirty-two. Therefore, here is your first rule of strategy: If you control thirty-three squares, you will have an advantage. Keep this in mind." Absolutely stunning!

And if you think this primer is an exception, well, not so much. Good chess primers, in any language, can be counted on the fingers of one hand.