Friday, December 11, 2020

Analogies

  Something Robert said somewhere struck a chord with me. He talked about analogy being the primary language of system 1 (unconscious thinking). Since then I wondered how we could integrate analogies in our training method.




15 comments:

  1. PART I:

    This is going to be long, so bear with me.

    Suppose (just for the sake of “supposing”) that you are given the picture above and the following instructions:

    Describe what is SIMILAR in these two pictures.

    In the picture, there is a visual similarity (analogy) between the curve of the equation and the curve of the skateboard ramp. This follows the “piece(s)-on-square(s)” concept regarding chunks and patterns.

    I suspect that most (all?) of us would (without hesitation) utilize the visual similarity as the starting point for our description. System 1 instantly “sees” that perceptual similarity, reports that “it is the curved shape that is the most significant aspect of the two sides of the picture in terms of the given instructions,” and passes it off to System 2 without further comment. System 2 takes a quick look to confirm the assessment, agrees and goes back to thinking about how to achieve long-term chess improvement using analogies.

    There is also a couple of “clues” that there MIGHT be a different analogy (possibly) at work: there are two (“=” & “f(x)”) mathematical symbol in the picture. That might be a “hint” that there MIGHT be a mathematical relationship (analogy) between the two sides of the picture; the curve of the skateboard ramp MAY be a physical embodiment of the mathematical function (“f(x)”). This is a “deeper” analogy than the first one. A mathematically inclined person MIGHT “See” the similarity in terms of the mathematical evidence. Unfortunately, for those without the relevant mathematical knowledge as background, this possibility will remain totally “invisible”; System 1 will NOT be triggered and will NOT even consider this as a possibility.

    The “surface” level provides “clues” but the interpretation depends on the requisite knowledge AND CONTEXT as to the “essence” of the situation.

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  2. PART II:

    Let’s examine a different correspondence using analogy, based on chess. The following two positions are taken from:

    LINK=”https://onlinelibrary.wiley.com/doi/pdfdirect/10.1080/03640210701703725”

    Cognitive Science 31 (2007) 989–1007
    Copyright C 2007 Cognitive Science Society, Inc. All rights reserved.
    Understanding Our Understanding of Strategic Scenarios: What Role Do Chunks Play?
    Alexandre Linharesa,b, Paulo Bruma a EBAPE/FGV, Rio de Janeiro, Brazil bBrazilian Chapter, The Club of Rome Received 7 February 2006; received in revised form 9 January 2007; accepted 11 January 2007

    1.1. Observation: The flexibility of perception

    In the game of chess there are similar strategic situations in which the numbers of pieces vary, the sets of pieces vary, the types of pieces vary, the positions of pieces vary, and the underlying search trees vary in depth and in breadth.

    Different, but similar: Any student of the game will have seen similar strategic situations involving positions in which these types of variations occur. Sometimes chess masters will mention having seen “the same game” (or position) in the past, but in reality that “same” position actually varied in a number of characteristics. The following two positions offer an example from a study book (Bain) for chess players. How can a position with all the pieces on the board be strategically similar to a position with a mere five pieces? How can positions with radically different search trees be strategically similar? How can positions in which there are few (or no) piece types found in common—kings exempted—be strategically similar? How can positions in which pieces appear in radically different areas be strategically similar?

    Position A: FEN=rnbqkbnr/pppp1ppp/4p3/8/6P1/5P2/PPPPP2P/RNBQKBNR b KQkq - 0 1

    Position B: FEN=1b6/8/8/8/8/8/2k1P3/4KB2 b - - 0 1

    A “piece(s)-on-square(s)” (POS) approach (the visio-spatial or physical perception viewpoint) would insist that there is NO similarity at all between the two positions , with the possible exception of the position of the Ke1, Pe2 and Bf1! And, since there is NO similarity, neither position can be solved using pattern recognition (IFF POS is the basis for “chunks” and patterns).

    I’m willing to bet that most (ALL?) of the people reading this comment will “SEE” the “solution” to both problems immediately. Solving Position A ‘primes’ the solution to Position B by analogy. Neither position is the least bit difficult to solve for an experienced chess player.

    But if no analogy between the two positions can be discerned on the sole basis of visio-spatial (physical) aspects, then what is the corresponding analogical solution based on?!?

    Linhares gives the answer elsewhere. . .

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  3. PART III:

    From Alexandre Linhares' paper, Decision-making and strategic thinking through analogies.


    How do humans perceive similarity at a strategic level?


    Strategically similar chess positions may be explained by looking at the configurations from the point of view of sets of abstract roles. For deep understanding, that abstraction is the most efficient level of
    description. While a skeptical reader might consider that the processing of both trajectories and of roles may be redundantly inefficient, that is really not the case. It is crucial to process both trajectories and roles. The distinction is an important one. Because a particular trajectory is bound to a set of squares, it is not an adequate structure to either perceive the situation in abstract terms or to generalize to other superficially different but strategically similar scenarios. Trajectories lead to chess relations, but are different from them. Chess relations are independent of locations and of particular squares of a trajectory. And chess relations are subtly different from abstract roles: In Capyblanca’s evolving interpretation of a position, roles emerge gradually from the set of chess relations, by the process of continuous re-evaluation of the intensity of each relation.


    This is a distinction, not an argument. By structuring information in terms of abstract roles it is possible to obtain abstract representational invariance. Consider, for example, the notion that, “under a double check, the only response is to escape with the king”. This notion is generalizable to an immense set of situations. It would be unthinkable—or at least computationally intractable—to try to describe it in terms of particular pieces, particular squares, and particular trajectories. The most efficient level of description is the abstraction “piece A has a role of attacker towards piece X”, “piece B also has a role of attacker towards piece X”, and “X is a king”. It is irrelevant for understanding, and inefficient for processing, what type of piece A and B are, what their mobilities are like, or even which squares they occupy. Therefore, it is imperative, for an architecture with the ambition to model human understanding of a chess position, to use different representational structures to account for the trajectories involved in chess relations, and separate structures for the abstract roles that are found to be relevant in a particular position. Deep understanding arises by recognizing a familiar, previously seen, configuration of abstract roles. For understanding a scenario, the most efficient level of description is given by a combination of abstract relations representing the most important roles objects play. By reasoning at this level, the system is able to perceive analogies between dramatically different scenarios (Linhares 2008). This enables the eventual emergence of a global, meaningful, understanding of the constraints and key issues underlying the strategic situation one faces—
    and leads us to our final claim concerning the architecture.


    We don’t “think” in analogical terms when studying chess positions to develop SKILL. Each position is seen as unique (because the visio-spatial aspects are so different). As a consequence, we don’t create any abstraction of the relevant details that form the patterns we need to drive into System 1 and LTM. Each example we “study” is an isolated “fact” stored somewhere in the bowels of System 1, and thus (generally) inaccessible.

    The relevant question should be “How is this position/solution similar BY ANALOGY to something I already KNOW?

    Identifying the abstract similarity/commonality (AND repeating that process over and over again) is what triggers the analogical recognition process.

    This holds true for all phases of the game: opening, middlegame and ending.

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    Replies
    1. "We don’t “think” in analogical terms when studying chess positions to develop SKILL. Each position is seen as unique (because the visio-spatial aspects are so different). As a consequence, we don’t create any abstraction of the relevant details that form the patterns we need to drive into System 1 and LTM. Each example we “study” is an isolated “fact” stored somewhere in the bowels of System 1, and thus (generally) inaccessible."

      Beautifully said! You hit the nail on the head.

      Delete
  4. This must be the answer why transfer between chess positions doesn't occur by my method.

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  5. "Strategically similar chess positions may be explained by looking at the configurations from the point of view of sets of abstract roles. For deep understanding, that abstraction is the most efficient level of
    description."


    I really like that.

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  6. I respectfully refer you back in time to one of your previous posts, and the voluminous (41!!) comments to that post. There is a lot of valuable information there - and that is NOT because I wrote the comments. As I have often stated, I contribute very little original material in my comments; I am deeply indebted to those original researchers who have plumbed the depths of these subjects.

    How to educate system I? - Tuesday, May 21, 2019

    There are NO "secrets" to the knowledge/skill transfer process; all of the information we need has already been investigated and documented by experts in many fields. Our problem is that if we don't see the explanation given explicitly in chess terms, we glide right over the "clues" provided, assuming we "understand the concepts." In most cases, this "understanding" simply is not true. This is nothing more than compartmentalization of our knowledge into distinct categories, with implicit "walls" between those various categories.

    In the immortal words of Ronald Reagan: "TEAR DOWN THAT WALL!"

    (That, BTW, is a perfect example of shifting from one category to a totally different one, in order to connect the two categories using an analogy.)

    ". . . looking at the configurations from the point of view of sets of abstract roles."

    As I was thinking about this "explanation," I realized that I have missed an important learning opportunity when working through tactical problems on Chess Tempo.

    Pick any tactical problem. Look at the tags for that problem. In some cases, you will find that there is only one tag. In a lot of other cases, you will find multiple tags. THE TAGS GIVE US VITAL INFORMATION ABOUT THE DIFFERENT "CLUES" THAT SYSTEM 1 (in different people) USED TO TRIGGER A SOLUTION. It illustrates quite succinctly how people "SEE" differently - "one size does NOT fit all." Most importantly, it gives us a set of ABSTRACT ROLES as a "lens" (so to speak) through which we can look at a given position and "SEE" it in multiple ways, thereby increasing the likelihood (NO GUARANTEE!) that given a new (different) position, System 1 will trigger the appropriate response simply because there is more than one neural pathway to the appropriate information.

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  7. Let’s take a look at analogy from a slightly different perspective.

    Recall Positions A and B from a previous comment on this post. What is the commonality between those two positions? We could “see” it as an example of “King in the box.” We could “see” it as an open line leading into the King’s “box.” Alternatively, we could “see” the King as a trapped piece. Or, we could “see” it as a combination (a vulnerable King AND an open line leading to that King). Or, we could “see” it as two examples of Loose Pieces Drop Off (even though the King cannot be captured). Or, we could “see” it as two cases of domination on a weak color complex. Any one “view” of the two positions could be “correct” and could lead the player with the opportunity to reach a successful conclusion. The two positions are analogous from a strategic role perspective BUT TOTALLY DIFFERENT IN VISIO-SPATIAL STRUCTURE.

    Consider the following two positions (BY WAY OF ANALOGY to Positions A and B), from games played by World Champions against an “amateur” – a certain GM named Akiba Rubenstein. Oh, sorry, NOT an amateur! The games are in the Chess Tempo database and on chessgames.com. These two positions are also analogous to each other.

    Position 1: FEN=r1bqr1k1/1p1nbpp1/p1p4p/3p3n/3P1B2/1QNBPN2/PP3PPP/2R2RK1 w - - 0 24

    Chess Tempo
    Game 1:
    Marshall, Frank (2570) vs Whitaker, Norman (2420)
    Date: 1913
    Event: New York National, New York, NY USA


    Game 2:
    Euwe, Max (2650) vs Rubinstein, Akiba (2640)
    Date: 1928
    Event: Bad Kissingen, Bad Kissingen

    Let’s charitably “assume” that GM Rubenstein “forgot” the game by GM Marshall, although that seems unlikely, given that Rubenstein would have most certainly have played over every game that Marshall ever played. But who can remember all those old games?!?

    Maybe he should have remembered his own game. . .

    Position 2: FEN= r1bqr1k1/1p1nb1pp/p1p5/3p1p2/3PnB2/2NBPN2/PPQ2PPP/2R2RK1 w - - 0 24

    Chessgames.com
    Game 1:
    Alexander Alekhine vs Akiba Rubinstein
    San Remo (1930), San Remo ITA

    Here we have a totally different position (at least from the perspective of “piece(s)-on-square(s)”). Yet there is something “familiar” about this position, n’est ce pas?

    Here’s where analogy can enrich our System 1 retrieval. Let’s consider Positions A & B to be one “view”, and Positions 1 & 2 to be a different “view”.

    What is analogous between all four positions?

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    Replies
    1. All 4 positions have a box with no room for the trapped piece to move, and one entrance diagonal to deliver the final blow. The abstract concept of a box seems to be applicable. The box can be translated, rotated, even rotated 45 degrees, mirrored. The targets can differ, a king, a queen, a rook or a minor piece. The box can comprise exactly one square, or a whole bunch of squares. The walls can consist of different materials. They even can be invisible:

      FEN= 1r6/6p1/1N1k1p1p/Bb1Pn3/2pK4/1PR3P1/7P/8 b - - 0 0

      Roles:
      Target
      Wall of the box
      attacker

      Pathways:
      line of attack

      Actions:
      clear the line of attack
      squeeze the walls
      chase the targets
      remove defenders

      Initiative:
      who is to move
      duplo attack
      double whammy

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  8. That's a very definitive summarization! The important thing (for LTM purposes) is to become aware of all those things AFTER working out (or looking up) the solution. That's what gives System 1 more "clues" for future use. Unfortunately, it's not an obvious training step, which is why we often don't gain as much as we could from our tactical work.

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  9. "I respectfully refer you back in time to one of your previous posts, and the voluminous (41!!) comments to that post. There is a lot of valuable information there "

    I read everything again. As always I need time to digest it in view of the newly acquired insights.

    I tend to run around in a horizontal plane. I gather all kinds of horizontal stuff, in the hope I can find the vertical viewpoint from where I'm in control of my own thoughts. Metaphorically: imagine two different viewpoints. One in a train. Everything happens sequentially. The landscape glides by the windows sequentially (horizontally). And a viewpoint that is perpendicular to that: on a mountain above the train. From above you cannot only see the train riding along the mountain, but you can see its future at the same time.

    I have been focussing on the geometrics of the positions too much lately. The perpendicular view is freeing myself from the geometrics, and find a higher abstraction level from where to look. The metaphor of the box shows exactly how to do that.

    The metaphor of the spiralling vulture indicated the notion of a vertical viewpoint. But to make it actually work is an entirely different animal.

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  10. As you note, there is a "spiral", implyng a circular AND a verticle movement simultaneously. I think I got too "locked in" to the concept of the vulture circling at the top of the mountain, staying at a specific height. We have to dip down for a closer look and then soar back up to a higher (briader) look several times during the course of examining a position for "clues."

    This process is analogous to Capablanca's notion of PETITE COMBINAISON. There are several levels of abstraction between the level of individual moves and strategic plans. We have to be able to unconsciously move between those levels whenever System 1 wants to do so.

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  11. I just went back to Dr. (IM) Fernand Gobet’s book The Psychology of Chess to take another look at his recommendations for a training program in Chapter 8, Psychological Warfare and Training – How To Progress – From Beginner to Candidate Master. Just highlighting the key points:

    1. The basic tactical IDEAS should be learnt and mastered. TACTICS ARE ESSENTIAL!
    2. One should assimilate the FOUNDATIONS of strategy and planning.
    3. Endgames should be studied.
    4. A fair amount of attention should be devoted to the basic knowledge of openings.
    5. One should study the classics: famous historical games and games played by leading grandmasters, including, of course, World Champions.
    6. Play competitive games, which is an ESSENTIAL part of becoming a better player.
    7. It is important to analyze one’s own games, if possible with a coach.

    The available literature is essentially applied, in the sense that it is a compilation of principles and methods that have led to successful results. Template theory was used to develop teaching principles, which include the limited capacity of attention and short-term memory, perceptual chunks. Selective search and the fact that knowledge is domain specific. The approach includes more general principles of learning and memory, such as THE IMPORTANCE OF PROCESSING INFORMATION DEEPLY AND IDEALLY FROM DIFFERENT POINTS OF VIEW. [ANALOGY!]

    Three educational principles were highlighted (in the referenced paper):

    1. the acquisition of knowledge should proceed from simple to complex;
    2. learning is more efficient when the teacher (or a book) clearly identifies the elements to be learnt;
    3. and finally, a powerful way of assisting learning is first present the material in a simple, even over-simplified way and then to return to it several times, each time adding new information. We call this method an IMPROVING SPIRAL. [A correspondence to our vulture’s eye view! In one case, “SEEing” the implications/abstractions that are right before our eyes, and in the other case, “SEEing” how to train for improvement.]

    For example, when studying an opening [the current focus], a first pass would cover the main ideas of the opening and commonly played variations. A second pass would discuss some typical endgames frequent with this opening. The next pass could address strategic themes suggested by this opening’s pawn structure. Not only will the student learn important information, but THE MULTIPLE PASSES WILL ALSO STRENGTHEN MEMORY TRACES AND COMBAT THE RISK OF FORGETTING. A variant of this is the DECOMPOSITION METHOD, where a typical opening position is studied by removing all pieces except kings and pawns, and the resulting endgame analyzed or played in practice games. Different pieces are progressively added, and again the resulting endgame studied.

    CHESS EXPERTISE CONSISTS IN GREAT PART OF MASTERING COMMON METHODS OF PLAY. Thus, while time should be devoted to find-the-best-move exercises, the main ideas should be explicitly taught and open-ended forms of teaching such as that advocated by the discovery-based learning approach should be AVOIDED. After all, it took several centuries for very smart people to discover these ideas!


    There is a second section titled How To Progress – From Candidate Master To Grandmaster. I think we can safely leave that one until after we reach the Candidate Master level.

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  12. "Explicit is better than implicit" (to borrow a phrase) might have some value, but this has a bit of tension with the general notion that skill is best acquired through practice. Different tactics books reflect different approaches to balancing between explanation and practice (= puzzles). Some are basically just puzzle collections, though a good one (say the L. Polgar brick) will reinforce ideas through clustering and repetition of themes. Others have a lot of explanation - at a basic level there is the online book by Farnsworth. I haven't read the higher-level book by Weteschnik, but apparently that has a lot of detailed explanation too. Judging by online reviews, some people like it but it's not uniformly admired. So does it veer too far towards explaining rather than exercising skills?

    I recently went through a book by S. Polgar (the one about defensive tactics) that has separate chapters on each of the motifs discussed. It just has a tiny amount of explicit instruction at the start of each chapter (e.g. if there's a threat of mate, your options are to capture the threatening piece, block its path, pin it, move your king...) Then a lot of puzzles regarding the theme where you have to find the right option. Then a final chapter of puzzles that mixes all the motifs together. I thought this was a good balance for a tactics book.

    Chesstempo tags are useful but they are pretty limited, since there is more or less one for each chapter of a beginner tactic book. At higher levels maybe it's useful to divide the basic tags/motifs up into smaller categories with more specificity. In some cases there are characteristic combinations of motifs, like the hook and ladder pattern, that are worth knowing as well. --mfardal

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  13. mfardal asks:

    "So does it [Martin Weteschnik's book on chess tactics] veer too far towards explaining rather than exercising skills?

    I have the 2006 version Understanding Chess Tactics. There is a 2012 version Chess Tactics from Scratch: Understanding Chess Tactics 2nd Edition, which I do not have. The first edition was oriented more toward explaining rather than a collection of puzzles. I found it to be very educational, especially Chapter 10, Status examination.

    An excerpt from the 2nd edition:

    "The first edition of this book, Understanding Chess Tactics, was hailed as a modern classic. But Weteschnik was not completely satisfied with the book and decided to restructure and rewrite it completely. This expanded and improved second edition offers MORE PUZZLES to test the tactical chess skill that the reader will develop."

    On the Quality Chess blog (Aagaard), there is this note on 2 FEB 2012 regarding the books:

    "In the Quality Chess office we have had our heads down working to finish books and hiding from the winter storms. On February 17th we will publish Chess Tactics from Scratch by Martin Weteschnik. This is a fully revised and expanded second edition of Understanding Chess Tactics. The main changes are two completely new chapters and 300 new exercises/puzzles at the end of the book. An excerpt is available."

    The 2nd edition excerpt can be found at: Chess Tactics from Scratch

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