The goals of this post are modest. The previous post about chess thinking outlined how humans don’t first generate a list of legal moves that they filter down. It hand-wavingly claimed that moves “pop up” in our minds. This post shows one possible mechanism of such popping up.

The analysis will be based on what I call “situational categories” (or situations, for short), a term I prefer over the overused term pattern. I hope to sidestep the rigid imagery that the term pattern evokes: it makes some people think of assorted pieces arrayed in some specific configuration. By contrast, the term situational categories includes “being in check,” which can be attained by many piece arrangements. The next section details how situations are being used in this post.

We will then consider one possible mechanism for how we come to see moves. We will look at:

  1. How situations, once perceived, suggest actions and direct attention.
  2. How that directed attention can cause us to perceive other situations, thus forming a virtuous cycle.
  3. How we discover different situations, refine these, and recognize them in novel positions.

As promised, the next post will reuse these ideas in the seemingly unrelated domain of language understanding. People employ the same cognitive machinery for both tasks, making these distant connections possible.

Situations

At any point during a chess game, a lot is going on. Maybe the enemy rook has put us in check. Our rook is under threat. The center is closed. We can force a trade of our bad bishop for a knight. A pawn is marching toward queenhood. Enemy pieces are gathering for a decisive attack. The list goes on. The question “what is it that is going on” is ill-posed since it demands a single simple answer.

The way I use the term, each of the items listed above is “a situation”, short for “a situational category”. “Being in check” is a situation that arises from many piece configurations. More surprisingly, these following three are different situations, although of course closely related: being “in check from a knight”, “in a double check”, and “in check-mate”. These three situations are not equivalent because how you deal with them is different. Situations are not exclusive, and many exist simultaneously. You cannot be in check mate without also being in check.

Situations differ along many dimensions. They may refer to present reality on the board (e.g., checkmate) or to what may happen soon (forced mate in 3). They may be objective (“I am a queen up in material”) or subjective (“I am winning”). Three other dimensions along which situations differ need to be called out: blurriness, depth and namelessness.

Situations may be blurry vs clearly delineated. We can easily verify some situations on the board while others are blurrier. For instance, there is never any doubt whether we are in check. Similarly, you either have a bishop pair or you don’t. The situation “I can force a trade of a bishop for a knight” is less clear cut: you make a move and the most sensible response for the opponent may be the trade, but the opponent may play something else, giving up material for some other positional benefit. A particular position may be a perfect example of the situation “can force a trade”, another may be a perfect non-example, and yet others may lie somewhere in between these extremes. The category is blurry, with ill-defined boundaries.

Situations may be surface level or deeper. I do not intend deeper to mean better. The term just refers to whether seeing that situation involves many layers of seeing more superficial situations. We may identify the situation that we have an extra pawn from just the pieces alone, but seeing a piece as supported involves interaction among pieces. Going deeper, spotting an “overworked piece” involves having seen which pieces are supported by which.

Situations may be named or unnamed. Chess teaching makes use of such named situations as “open files”, “forks”, “passed pawns” and Najdorf Variation. Other situations may be nameless yet familiar. If you play the Sicilian Defense, there may be a position you encounter after 10 moves that you have reached in dozens of games. There is no name, but you may know a lot about it from experience. Below, we will see the growth and development of an unnamed situation.

Perceived Situations and the Umwelt

What matters is the perception of situations. In any given position, the grandmaster perceives situations that the novice is blissfully unaware of. Even grandmasters aren’t aware of all the infinitely many situations. Indeed, today’s club players are aware of situations that the strongest players in the world were unaware of two centuries ago. For example, the notion of controlling the center (as opposed to occupying it with pawns) is taught to beginning players but is a mere century old. Some aspects that beginners in the 24th century will notice may be beyond Magnus Carlsen today.

The german word “Umwelt” is useful here to discuss what a chess player may become aware of and to talk about the differences among chess players. Daniel Dennett discusses this notion, although not in the context of chess, in his fine book “From Bacteria to Bach and Back”. The term was originally used by Jakob von Uexküll in 1920 to describe how different organisms “live in different worlds”. The bee unfortunate enough to fly into the classroom won’t be able to see the blackboard: not just is a bee’s visual apparatus and color perception different from ours, the cognitive concept of blackboard is completely outside its reach.

A related example is provided by sociologist Erving Goffman in his book “Frame Analysis”. Imagine two players, sitting at a table, engrossed in a game of chess, lost in a complex battle hinging on the control of the e5 square. Their game is interrupted by the janitor cleaning the room. The janitor’s sense of “what is going on here” makes no reference to the e5 square. What the players perceive is different from what the janitor perceives or cares about. For that moment, in this limited sense, the chess players and the janitor are inhabiting different worlds, one world with rooks and discovered checks, the other with more prosaic concerns. The difference isn’t just ability but also interest in the moment, since the janitor may be an excellent chess player and fully capable of analyzing the game, but at this moment preoccupied with getting the cleaning done.

Within the chess universe, players of different skill levels and different temperaments live in different worlds. The situations a master notices go unnoticed by the novice. The attacking player sees somewhat different situations than does a positional player. Their umwelts are different.

Perceived Situations Direct Attention

Donald Norman, the first person with the word “User Experience” in their job title, was a “User Experience Architect” at Apple Computer, and wrote the book “The Design of Everyday Things”. In this, he talks of the “action possibilities” readily perceived by an actor. In designing things, it is important that it be clear to a user what actions can be taken: for instance, in web design, a blue link suggests that it can be clicked, a slider suggests that we may be able to drag it to change some value, and so forth. To talk about action possibilities, Norman appropriated the term “affordance” from ecological psychologist James Gibson. In this terminology, blue underlined text affords clicking. Such underlining does not force you to click, but suggests clicking as a possible action. I use an analogous notion here, expanding that idea beyond visual perceptions to cover the cognitive perception of situations. Certain situations afford particular actions.

We begin with a simple demonstration of a board suggesting candidate moves. This section’s three examples feature easy-to-spot situations.

Say you are playing White and reach the following position. I only show 25% of the board below, just enough to make the point.

White to move

Of course, you cannot tell the best move with just 25% of the board displayed. What should be immediately apparent, however, is that you are under check from the Black queen. This situation (“being in check”) is something that you have often encountered, and you may already know the basic classes of responses: “capture the attacker,” “stick one of our pawns or pieces between the attacker and our king,” or “move our king.” We don’t know the best move from this fragment, but this easy-to-see situation is already directing our attention: can something capture the queen? Can we bring something in between the queen and the king? Can we move the king somewhere? Each of those three possibilities is a micro-plan not yet clothed in moves.

A second example. Consider this fragment of a position:

White to move

What could White do? One possibility to consider is suggested by the queen and rook sharing a diagonal. If you could place a bishop on that diagonal, it would “skewer” the opponent’s two pieces, possibly winning us some material. Is that a good move? That depends on the rest of the board, of course, but it is an excellent candidate to explore further. This situation (“two major pieces on a diagonal or a king and another piece on a diagonal”) can give rise to a plan to put a bishop on that diagonal.

A third example is the related situation of a piece already pinned.

White to move

Here, the bishop pins the Black knight. It cannot move since that would expose the Black king to check from the bishop. If you can threaten a pinned piece with a pawn, you stand to capture it.

It might be tempting to say that the situations “being in check,” “potential skewer,” and “a pinned piece” are suggesting moves. But no, it is more accurate to say that they offer subproblems to solve. The pin asks: can I threaten the knight? This question may lead us to search for such a threat, and a successful search could yield a move or sometimes show moves that need preparatory actions. For instance, the example above might have been slightly different:

White to move

Searching for “can I threaten this pinned knight?” might suggest the possibility of attacking it immediately with our knight, as well as the two-step combination of moving our knight away somewhere and attacking with the pawn. What that “somewhere” is is another subproblem: there are eight potential places the knight could go to, and one might work better than others. In this sense, the situations and the subproblems they evoke are directing attention, telling us where to look, telling us what to look for.

How did the connection between the situation and the subproblems get established in our minds? The answer includes both direct instruction and an associationist account.

Books exist that tell us what to look for in particular situations. For example, the Move-by-Move series from the publisher Everyman Chess is organized as a set of questions and answers, pointing out what questions to ask and what to look for in specific positions in the opening. I immensely enjoyed GM Neil McDonald’s book on the Ruy Lopez in this series and found the format effective. In the same vein, pawn structure books — such as “Pawn Structure Chess” by Soltis and “Chess Structure: A grandmaster guide” by Flores Rios — are organized by situations (such as a particular pawn structure) and talk about what to look at.

The second source of connecting situations with suitable plans comes from experience, and this is the most crucial for getting better at chess. We will soon see concrete examples of this in action.

A Situation Bestiary

A vast array of perceived situations either suggests moves or nudge our attention. Here I list a few, along with some micro-plans or subproblems they suggest. These range from easy to perceive to more subtle, range from those with immediate, actionable micro-plans to those with long term, general direction to attend.

  1. An unsupported enemy piece asks, “Can we capture it?”
  2. An overworked piece is one that is doing double duty, supporting two pieces, a job it cannot do simultaneously. This leads to a question “Can we overwhelm it by attacking one of those it supports?”
  3. The situation “We have a Bishop pair and the opponent doesn’t” suggests “Can I open up the center so that this pair is a bigger advantage?
  4. The situation “I have castled king-side, but the opponent has castled queen-side” suggests “could I orchestrate a queen-side pawn-storm?”
  5. The situation “Weak square” asks “Can I get my knight there?”
  6. Pawn structure. Pawns have been called the soul of chess, and specific structures suggest specific plans. The Caro formation, for example, often suggests planning for a white d4-d5 move.
The Caro pawn formation

The list of situations mentioned above just scratches the surface. I have said nothing about doubled pawns, an isolated queen’s pawn, opposite colored bishops, passed pawns, discovered checks, bad bishops, tempos, material-vs-development tradeoffs, and on and on. Some situations here are easy to spot. Others are situations that a novice may be completely unaware of. The fact that there is a weak square in the enemy camp that can be exploited may not register at all, and thus won’t suggest the sequence of knight moves that would make the knight immensely powerful.

A story of how situations influence thought must thus also describe how the situations are recognized in the first place, because, of course, we don’t always recognize situations.

Directed Attention Leads to Perceiving Additional Situations

We will look at three examples here of how seeing a situation directs attention that then leads to perceiving other situations. Remember that many situations co-exist, and here we will see how awareness of one situation can direct attention leading to awareness of another situation.

The first example concerns a puzzle from Lichess.com (https://lichess.org/training/s76ff). We are Black: find the best move here.

Black to play. What is the best move?

Because it is a puzzle, we know that a good move exists (unlike in an actual game, where we may be in a hopeless position).

What should Black do? Many black moves are legal. However, you may notice that White is very close to check-mating us. If it were White’s turn now, the game will be over. In puzzles, this situation “opponent’s victory is imminent” means that we probably must check the opponent king, since any move we make that is not absolutely forcing can be answered by check-mating us.

This observation leads to looking for ways of checking. The situation has directed our attention to the subproblem of exploring moves with checks, ignoring the rest. There are just two possible checks: the rook next to the white king can move one square lower or one square to the left. Moving to the left is a move we will normally not consider: the rook can immediately be captured by the king. But given the limited moves for us, we may look deeper and see another pattern: if the king captures the rook, our queen can checkmate the king from f5. If the king does not capture the rook, the only legal move is to move to h6, and our queen can again checkmate from c1.

The second example, discussed briefly, comes from the situation “the opponent just pushed a pawn”. Pawn moves can weaken the pawn chain, possibly creating weak squares. The pawn was protecting a square that it no longer is, and this may be now weak, prime for further action. Attention was thus directed to looking for newly weakened squares in a particular region of the board. We are directed to actively look for particular situations.

The final example is related: whenever an opponent moves, see what changed. What they moved may have been supporting something which is now weaker. Their movement may have opened a diagonal or blocked another, so attention should be directed to this additional or diminished mobility of other pieces. Maybe their move threatens something. When we look in these areas, we often see opportunities.

Discovery and Refinement of Situations

The goal of this section is to look at how actions may get attached to situations and how our repertoire of situations grows.

Many patterns we learn are not “discovered”: we read about them in books. But knowing a kind of situation doesn’t by itself confer the ability to use it. In this section, we begin with a trivial situation that we first learn from whoever is teaching us, book or person. But what “this situation” is will get refined over time, and our ability to spot when it is relevant and what precisely to do will become better. The “trivial” situation we will look at is back rank mate, touched on in the last post:

Black to play

This motif of a king in his unbroken pawn castle suggests that we could get a rook or queen on that row. In the trivial example above, it is immediately clear what move is needed. But sometimes a plan suggests itself but doesn’t quite work and then begins the task of patching. It feels like the plan must work, that there is some tweak that would get the job done.

We will look at a progression of three puzzles, all involving a back rank mate, each building on situations in earlier puzzles, refining the situations or associating potential actions with these. When I started solving these three puzzles, I knew they involved back rank mates since I discovered these by searching for that theme on Lichess. The puzzles are not very complex: I have chosen these to make a point more than for their beauty. Try solving these and observing yourself.

Puzzle 1. White to play.

https://lichess.org/training/backRankMate/x6mD6.

White to play

Clearly, the King is trapped in his Castle, and a Rook or Queen in that row will check him with no escape. So Queen to c8 looks good. But the Bishop can intervene (at d8, which the black rook also covers), potentially throwing a spanner into our nice plan. Not a big problem, though: we can capture the Bishop, and then capture the rook that captures us. We have enough firepower aimed at the right place to swat away these pesky annoyances.

Here is the series of moves:

Armed with that, let’s look at a second puzzle.

Puzzle 2. Black to play.

https://lichess.org/training/backRankMate/aYVbI.

Black to play

Please try solving before reading on.

One of my first thought was to try “the same thing”: queen to e1 and swat away the pesky rook when it attacks. However, this simple plan doesn’t work: the rook captures the queen, and the Black rook which captures the White rook is taken by the king. The attack peters out and all we have achieved is a sacrificed queen.

And yet, the plan looks almost right. Can we tweak it to make it work? Yes: Queen to e2 (instead of e1), gently nudging the king deeper into his castle (going deeper is the only legal move). Then, the old solution “Check from the back row and finish the check mate with a second piece when the first is captured” works out just fine.

Armed with solutions to those two puzzles, let’s look at the third puzzle.

Puzzle 3: White to play

https://lichess.org/training/backRankMate/uF0Nn

Please try solving before reading on.

White to play

Here, we can overpower the rook, but the king seems ready to flee the castle. As you may have discovered, the solution involves nudging the king back into his castle. The sub-plan “nudging the king back into his castle” has gotten associated with the situation “back rank mate with the king close to the castle mouth”. Moving the queen to g5 will put the king in check and nudge him in, since the only other legal move is moving the king to e8 and leads to immediate mate with queen to e7. Then, the queen checks again, from g4: again, the king has the unenviable choice between going deeper or be immediately mated if taking a step out d8. So he takes a step deeper into the castle. Now the solution from puzzle 1 works: Check with rook, which is captured by the Black rook, which is captured by our queen, mate.

In these last two examples, our simple plan of back row mate hit a glitch. The glitch is itself what we have been calling a “situation” (namely, the situation “king escaping castle through the castle’s mouth”), and now that glitch is associated in our minds with the sub-plan of nudging. Another common glitch in back rank mate situations is the opponent pushing one of the castle pawns to open an escape hatch, and with enough experience with such situations, your mind will associate some sub-plans with that glitch as well.

These three examples have primed you, temporarily, to try nudging when this glitch is encountered. If you right now (as opposed to a month later) go to Lichess and solve a few more back rank mate puzzles, this newly formed situation-action link might help you see some solutions. The link may weaken and disappear over time.

Next Post and a Request

The next post will deal with how situational categories and directing attention play a part in language comprehension. If you have a few moments to spare, I’d like to collect a few additional data points for my analysis of what I call the “Wandering Mind Experiment”.

The Request

I present three sentences below. Watch yourselves as you read and understand these — what questions you asked yourself, what puzzled you, what thoughts passed through your mind — and email these to me at amahabal@gmail.com. Thanks!

  1. They got married on Feb 29, 1870.
  2. Pen raised her eyebrows in dismay.
  3. BEAUTIFUL convent-educated girl, 24/25 for a handsome, W.B. Kayastha (Basu), B. Com. (H.), C.A. Inter, Senior Accounts Officer, M.N.C., 30/5'7", flat / car in Kolkata, only son

I do unsupervised concept discovery at Pinterest (and previously at Google). Twitter: @amahabal