Absorption of endpoints
In order to get more insight in the absorption process, I focus on the problems that are only 3 plies deep. They show all the endpoints you need to know. It is easy to imagine how the absorption of these endpoints will help your calculation ability tremendously. Have a look at the following diagram:
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| Diagram 1. White to move |
Black has just given a check with Qb6. White has three possible answers, which all lead to a different mate.
All three mates consists of a hammer (the black Queen) and an anvil against which the white King is crushed. The swallowtail mate and the dovetail mate have a lot in common. It is essentially the same mate, rotated over 45 degrees.
There are an an incredible amount of ways how a dovetail mate can manifest itself.
The anvil can consist of the own pieces of white (Queen, Rook, Bishop or pawn)
The anvil can be replaced by one or two squares that are covered by five different pieces of the attacker. The anvil can even be formed by the rim of the board. There are 64 different squares on which the white king can be mated. The attackers can be close by or act from any distance. The queen can be protected by five different pieces.
You see, there are a tremendous amount of ways to execute the dovetail mate. It is nonsensical to learn all possibilities by heart. If it is even possible. So the question is, what and which positions need we to absorb as a minimum, in order to inspire system 1 to work its magic to drum up the required dovetail mate in any position.
In diagram 1, you need three endpoints to be SEEn. You don't see them at the same time. You see them one by one, when system 2 focuses the attention on one of the three possible answers to the check.
Temposchlucker says (in part):
ReplyDelete"It is nonsensical to learn all possibilities by heart. If it is even possible."
This is why doing hundreds, thousands, even tens of thousands of specific exercises without figuring out common elements is (generally) an exercise in futility. It’s what we SEE (the elements, the preconditions, the abstracted “essence”), not what we KNOW that counts from System 1’s perspective.
Multiplying the various combinations of pieces and squares results in a Great Big Number of potential piece-on-squares configurations for just this one mate type (dovetail mate pattern). Dr. Lasker is proven right again.
"A spirit with a large and roomy brain who without error could keep in mind millions of variations would have no need of planning. Frail, weak man can clearly keep in mind [System 2] only half a dozen variations since he has but little time to spare for Chess. And if he by chance had more time for it and in addition had genius for the game, to see through hundreds of variations would turn his brain. His reason was not made to be a substitute for a printed table. His mind has a marvelous faculty which enables him to conceive deep and far-sighted plans without being subject to the necessity of examining every possibility."
Too bad he lived prior to the advent of modern computer chess programs. I’m sure he would have been intrigued by a machine that CAN keep millions of variations in its “brain” and find the optimal variation with no planning whatsoever.
Regardless, he would still be correct with regard to the various ways that HUMANS must approach the game—with knowledge and skill, not mindless brute force calculations.
I have seen several different researchers affirm that expertise in chess consists of a complicated web of mini-skills.
One such mini-skill is the recognition of the necessary preconditions for the dovetail, swallow’s tail, and epaulette mates.
In the given example:
Variation 1 is a swallow’s tail mate.
Variation 2 is a dovetail mate.
Variation 3 is none of the above, although (if using the edge of the board as part of the “anvil”) it could be seen as a quasi-dovetail mate.
What I found useful for me is to “SEE” that the two “obstructions” (or the controlled squares; for purposes of visualization, it does not matter WHY the King cannot move to either of those two squares) which prevent the King fro escaping the mating net are at a knight’s move away from the focal point for the queen. That’s what I use as the “trigger” to start looking for that type of mate.
All of the named mates and tactics have similar features in common. These common features are what allows for a more abstract (broader) multi-level categorization. The more that we can “SEE” at the higher level as being applicable (those features that are common), the easier it becomes for System 1 to “trigger” recognition of a known pattern and the associated moves in one fell swoop. The entire mini-process (pattern plus associated moves) instantly jumps into consciousness [System 2]. All that remains is to VERIFY [using System 2} that what has been SEEn WORKS in that specific concrete position.
I looked at all mates, and I found that most mates need the edge or the corner of the board. For a mate in the middle of the board, you usually need a dovetail or swallow's tail mate. Of course you can have an Arabian mate in the middle of the board, when the pieces form some artificial corner.
ReplyDeleteI focus on problems with exactly 3 plies. Since those show the cleanest patterns, with the least distractions. All tactical motifs come along. Usually, a dovetail mate cannot be executed when one of the anvil pieces is a knight. Since a knight would cover the "hammer square" where the queen is supposed to deliver mate. But when the knight is pinned, there is no problem to deliver the mate. All tactical motifs can play a role in a dovetail mate.
The question is, how many distinctive patterns do you need? Sometimes I said somewhere jokingly "there is just one mate". But it is useful to discriminate between a dovetail mate and an Anastasia's mate. Since they both have distinctive features that can trigger system 1. OTOH I said, when you have seen 10 Anastasia's mates, you have seen them all. And there is some truth in that as well.
When we assume 32 different mates and 18 different tactical motifs, you might argue that you need 32x18 = 576 positions to absorb all mates.
If there are 6 wood gaining motifs (duplo moves of some sort) and 12 preliminary moves, you need 6x12 = 72 positions to absorb all wood gaining motifs.
All and all, I try to identify all relevant 50 motifs (32 mates, 6 wood gainers and 12 preliminary moves) in any position. What I left out to keep matters simple: all piece traps and pawn promotion.
The core of the business is to absorb the 50 motifs. I called them the endpoints of the calculation. Albeit that might not be the best term.
ReplyDeleteYou can only visualize one endpoint at a time. In the position above, a dovetail mate, a swallow's tail mate or a mate with no distinct name.
Chess logic is the way to guide your system 2. The tree of scenarios, that is. There are a limited amount of branches. With system 2 you guide your attention along the board. System 1 can only follow your attention and jumps in whenever something is recognized.
With system 2 you judge whether system 1 has found something useful.
FEN: 8/pp4kp/3p1np1/8/1q6/1Q4P1/PPP4P/6BK b - - 2 33
ReplyDeleteThis is a recent lichess puzzle. It's an easy puzzle to solve—given some common "principles" to trigger System 1.
"Always check: it might be mate!" is a trivially obvious System 1 "cue."
Odd but true: the discussion of the dovetail mate complex triggered the solution for me. There are two components that System 1 tossed up:
(1) The White King in the corner is flanked (diagonally) by two White pieces.
(2) The Black Knight "protects" (not really, since White does not "attack" e4 after the check) the Black Queen if it moves to e4.
(3) That diagonal check is the "hammer"; the "anvil" is the edge of the board, and the two White pieces.
(4) The White Queen can (uselessly) interpose, delaying the mate by one move.
It is the conceptual similarities (NOT exact pieces-on-squares) that triggers System 1 recognition. All that remains is to become aware [System 2] of that "itch" and follow the rabbit down into Alice's underground world.
How many distinct puzzles must one “SEE” in order to ingrain the “pattern” into System 1? I think it depends on what we do to identify and “SEE” the salient preconditions and the essence of the conceptual framework. For any given pattern, it should fewer than a dozen puzzles to permanently ingrain the recognition trigger(s). If the conceptual pattern is not absorbed from a small number of puzzles, doing a lot more puzzles (while focusing on the SOLUTION rather than on the recognition of the abstract concept and the salient preconditions) will NOT embed a trigger in System 1.
(Okay, it was more than two components; I failed to go back and correct the count.)
ReplyDelete