Friday, December 16, 2016

Geometry

So far, our findings weren't just limited to the pin. Which is great, since it makes them more often applicable. The following might look familiar, because I already posted about it before. When I came across it lately, I saw the geometry of it. Luckily there was a pin involved, so I could use it in this series about pins.

Diagram 1. White to move
2b1r3/3n1p1p/p1Nb1nk1/3p2p1/N7/2B2PPB/PPR2K1P/8 w - - 1 1
[solution]

This is a position where my mind wanders around for quite some time. With trial and error the wrong cues are triggered first. I have done an awful lot of analysis on this kind of positions. And although that often leads to a deep understanding of the specific position at hand, it usually doesn't yield anything that goes beyond that very position. The reason for that is, that the positions differ so much. Chess is such a rich game, that no game resembles another. And even the tactical combinations are extremely rich. Which is the main reason we don't come any further, even after hours and hours of analysis of a position. The analysis doesn't transfer to other positions.

The geometry coat hook
The coat rack is intended to go beyond that limited application. Geometry is our next hook. The straight line is the most prominent geometric property of the pin. As Robert pointed out, a line is a distinct feature of other duplo attacks as well, like a skewer, roentgen attack, the discovered attack and a subset of the double attacks. Rooks, bishops and queens all move in straight lines. Only the knight limps in a strange way over the board, which probably means that a knight should have his own geometrical system.

The line
That justifies a closer look at the line. Lines come in different flavors. With or without targets and/or attackers on the line. Presumably we should start with the most simple situation, there where an attacker and a target are already in place.

Cues
Which cue should fire in the position above? What should the implanted Robert Coble chess module shout in our ear? I think if it would shout c8!!, I probably would solve this position must faster.
Both the attackers Rc2 and bishop h3 bear down on c8. As Robert pointed out, a line of attack which is blocked by pieces (or pawns) gives you a glance into the future. I posted about the relationship of time and geometry long ago. There are a lot of pieces that stand in the way between the attacker and the target. If you can move them (own piece) or force them (hostile piece) out of the way, then all of a sudden c8 is outnumbered (encircled). The bishop on c8 is an important defender of Nd7 (function). This seems to imply that I must add to other coat hooks: encircling and function.

Now we have:
  • Value
  • Defenders
  • Geometry
  • Encircling
  • Function
  • Initiative
  • Target placement
  • Exploiting immobility
  • Opening of the line of attack
  • Connection to other tactical themes
If we can look at the line of attack as if there were no pieces in the way, we look into the future in a way that is not taxing for the mind.
  • c8 is outnumbered (encircled)
  • Nd7 has as function to block the line of attack between Bh3 and c8, so it is pinned
  • This means that Nf6 is not defended by Nd7 (Nd7 is immobilized by another function)
  • Bc8 is not yet immobilized by its function to defend Nd7, but after Bxf6, it is
So rather unexpected, I stumbled upon mister Lasker here. His advice always remained rather theoretical to me, but now it appears to be critical to fire the right cues. The immobility of the head piece in a pin, is just another form of immobility caused by the function of a piece that has obligations. This means that our coatrack changes into a tree with branches.

Only geometry guides my attention towards c8.
Encircling tells me that c8 is outnumbered. Not yet, but in the future.
Function tells me that c8 and d7 are immobile because of their obligations.
Encircling tells me that d7 is BAD (Barely Adequate Defended) after Bxf6
Function tells me that Nf6 defends d7

The other hooks like Value, Defenders and Exploiting immobility are closely related to the three motifs of Lasker. The clues lead to the cues.

The other tactical themes like the knightfork and the discovered attacks play a minor rule. When their cues fire we get distracted from what is really important. I'm going to have a closer look at the motifs of mister Lasker. So now we have a tree in stead of a coatrack.



19 comments:

  1. I have returned to mister Lasker many times over the years. The introduction by Fred Reinfeld opines that most people view mister Lasker's Lasker's Manual of Chess as too much like a philosophy or psychological treatise and not enough like a practical chess book. I respectfully disagree. When I first read his book, I readily identified those aspects that smacked of general philosophy, especially the concept of Struggle. I made observations in the workplace, trying to see if these concepts were applicable; in short, they were! It was only by carefully going back through his book that I observed something rather strange (to me): every time, I gained more insight into Lasker's approach to playing chess, which was available to anyone willing to really STUDY it hard. Those "general" philosophical concepts and principles turn out to be the bedrock of learning to play good chess. (At least that's what MY implanted "Robert Coble chess module" tells ME! ;-)

    This is GREAT stuff! (I claim NO CREDIT for any of it whatsoever; paraphrasing Newton, If I can "see" a little bit farther, it is only because I'm looking over the shoulders of giants.)

    ReplyDelete
    Replies
    1. Usually I start writing a post with a question in the back of my head. During the writing I try to find an answer to the question by logical reasoning. In general, I have a vague notion of how the answer might look like. But in this case I genuinely had no idea that I would end up with the motifs of mister Lasker beforehand. It came as much as a surprise to me as it will be for most readers, I suppose. (Except for you, of course ;) )

      Delete
  2. This position is an "introduction to the classical motif of pin IN ACTION".

    To me this position is a way harder than you explained it! When I have some spare time I will share my observations and findings at this position. In short: I would look at white and black's checks too (Bf5+, Ne7+ and Ne5+ from white and Ng4+, Ne4+ and Re2+ from black) not to mention assesing Black's counterplay.

    "I have done an awful lot of analysis on this kind of positions. And although that often leads to a deep understanding of the specific position at hand, it usually doesn't yield anything that goes beyond that very position. The reason for that is, that the positions differ so much. Chess is such a rich game, that no game resembles another. And even the tactical combinations are extremely rich. Which is the main reason we don't come any further, even after hours and hours of analysis of a position. The analysis doesn't transfer to other positions."

    --> I STRONGLY disagree. In fact I am completely on the opposite view. In my opinion all the important observations which we can call CONCLUSIONS are based on the specific characteristic (features) of the position. If we extracts many features and build (merge) them into Metaconclusions we would have "a system" (or a method) of finding the most important features of ANY positions. This way we are building upon our chess mastery! Of course it is hard to say how many elements we have to discover to build the (complete) system of tactical awereness, but anyway the more conclusions we change into methods... the better system we can build! That's what I think about that!

    ReplyDelete
    Replies
    1. "I STRONGLY disagree" I explained why my analysis of positions in the past didn't bear fruit for current positions. I don't say it is impossible that it might become helpful, I'm just saying I used the wrong method of analysis to be helpful in the past.

      What lacks is a good system of analysis. When you and I look at this position for the first time, tactical themes pop up all over the place. But those are the wrong cues. It is extremely difficult to derive the combination from the tactical themes. Even if all tactical themes have popped up.

      Now our coatrack has grown into a tree of motifs. The right cues are not the tactical themes, but the underlying motifs.
      Geometry: it shows the lines of attack, regardless the pieces that stand in the way.
      Encircling: it tells you which targets are under attack.
      Function: it tells you which pieces of your opponent have obligations to fulfill. These obligations can make a piece vulnerable because such piece is less mobile.

      Motifs form a deeper layer under the tactical themes. The tactical themes are just a means to execute what is revealed by the motifs.

      The task at hand is clear: we must have a greater knowledge of the motifs. We must make that knowledge practical. Then the right cues will be able to be formed.

      Delete
  3. At issue currently is the question of what "cue(s)" should be identified and studied in order to QUICKLY trigger analytical exploration in the direction of the "best solution" (in a chess sense). I cannot be certain, but it is my humble opinion that the study of the tactical themes is (somewhat) putting the horse before the cart. (Given the near universal experience of massive study of tactical themes with little long-term improvement in tactical skill seems to support my conclusion.) The first phase (pre-calculation of variations) is to just "see" (triggered by cues) what is important/significant/interesting in the specific position. Only when that trigger fires quickly can we move on to the means (tactical themes) which will take advantage of the available tools to the end of "seeing" the "idea" of the overall combination. Interestingly, when we follow this progression, the ability to "look ahead" is considerably enhanced. Not because it enables us to do the usual, "I go here, he goes there, etc." calculations but because of two interrelated things. First, there is a pruning away of irrelevant lines of investigation. If we can avoid following the rabbit down the hole in the wrong direction, we will have made significant progress in speeding up the response time. Second, there is (implicitly) an ability to think in terms of a sequence of related moves (the tactical themes) that can be fitted together as "chunks" which allows "analysis" to be performed much quicker and easier. Looking ahead (via concrete calculations) is considerably easier when using multi-move sequences rather than individual moves.

    Mister Lasker proposes that motifs (motives; motivation, i.e., the reason WHY a favorable continuation exists in a specific position) must be studied FIRST in order to get the thinking process going in the right direction. The means to the end are the various tactical themes. The entirety of the motifs and the tactical themes are subsumed in the concept of the "idea." The "idea" is nothing more (or less) than the threading together of the motifs and the tactical themes as a "solution" to a SPECIFIC problem. Mister Lasker states that the the motifs and the tactical themes must be burned into memory, because the type and number of motifs and tactical themes are limited. On the other hand, the number of "ideas" (the blending together of a specific "combination" of motifs and tactical themes) is unlimited and ALWAYS unique to the specific position.

    If his analysis of the situation is correct (and I have every reason to believe he is correct), then we should strive to identify and learn to blend together the motifs and tactical themes in as many ways as possible. This will enable us to have "ideas" of what to do in every specific position.

    BTW, Mister Weteschnik also alludes to the "motifs" following mister Lasker, but his terminology is different. (Mister Weteschnik uses the term "motifs" to refer to tactical themes.) He glosses over (as do most chess pedagogues) the pre-analysis pre-analytic phase - until he gets to the chapter on conducting a "survey" of the specific position.

    I may be wrong, but I think that the direction of the current discussion will prove to be very fruitful for improving our vision and our speed.

    ReplyDelete
    Replies
    1. "I cannot be certain, but it is my humble opinion that the study of the tactical themes is (somewhat) putting the horse before the cart."

      I think that putting the horse before the cart is a good idea ;)
      There is little need to study tactical themes because we are already so familiar with them that their pooping up distracts us from a deeper look of what is going on in the position.

      Delete
    2. I sometimes write dyslexically! Let's get that horse out in front of the cart by all means, where it can begin "pooping" tactical plops! ;-)

      Delete
  4. I am interested in your opinion about one specific issue.

    Imagine a position (similar in difficulty with the one in the article) you have to solve.

    1. Normally you use 300 seconds to solve the position.
    2. With one hint (cue) you need only 200 seconds.
    3. With two hints (cue) you need only 150 seconds.
    4. With three hints (cue) you need only 60 seconds.

    This way we can state:
    One hint is worth speeding factor of 1,5x
    Two hints are worth speeding factor of 2,0x
    Three hints are worth speeding factor of 5,0x

    I rememeber Aox/Tempo was/were talking about the speeding factor and "if we only could do the same 3-5 times faster we could reach a progress of 300-400 rating points in tactics/combinations".

    Let me know what do you think about it and if such hints would be really our boost (turbo mode) to crack the positions A LOT faster. As far as I see we have not invented such turbo mode - is it true? Am I right?

    I am going to give it a try to a few dozens of positions and see if these hints (cues) may be really beneficial (especially in a more complex positions). Anyway I want to hear your opinion: Tempo, Aox, Robert - what do you think about such turbo mode? ;) :)

    ReplyDelete
    Replies
    1. Suppose, your are an avid smoker. Every time your opponent makes a move, the first thing you do is to go outside and smoke a cigarette. After 9 minutes, you come back and think for a minute. Then you move. So your average speed is 1 move per 10 minutes.

      On a good day, you decided to quit smoking. When your opponent makes a move, you think for a minute, and make your move. Your average is 1 move per minute now. So you have become 10 times faster. But where is the turbo in that? You do everything as fast (slow) as you did before.

      Try to understand the essence of a cue. It is not a clue, nor a hint. Only if you grasp the essence, you can start experimenting with it. Read a bit about cues in cognitive literature.

      Delete
    2. Suppose you are playing a game that lasts 40 moves (after that the advantage is so big there is no need to think, but just realize the advantage).

      And the first case (scenario):

      1. Suppose, your are an avid smoker. Every time your opponent makes a move, the first thing you do is to go outside and smoke a cigarette. After 9 minutes, you come back and think for a minute. Then you move. So your average speed is 1 move per 10 minutes.

      Conclusion: You spent 40x10 = 400minutes for the game. 10% of time consumption was efficient and the rest was a waste of energy.

      2. Suppose, you think for 3 minutes per move and after 10 moves you waste 3 minutes for relax, walking and rest. After 40 moves you spent 40x3 + 4x3 = 132 minutes. 90% of time consumption was efficient and the rest was a waste of energy.


      Now let's compare these two cases.

      What would it be if we could find (invent/create) such a "reverse habit machine"? How much we could improve our level of play?

      Maybe I express my thoughts not the precise. My intention was to show (ask) what would it be if we simply could "cut off" all the waste of energy for irrational thinking and searching.

      I apologise for any confusion I could make with this.

      Delete
    3. The problem is, that I feel that I'm not in the lead of the variations. The variations govern me. I feel that it should be possible to gain the lead though. I felt that the past 18 years that I'm busy with chess improvement. Actually, I'm quite surprised that I didn't already got sofar. But with hindsight, I can explain every failure.

      I now follow a road that seems the only possible alternative to me. It is very logical, and it answer all my questions. Assuming that I indeed manage to make things work, I would be very surprised if it wouldn't gain me 300 points at CT. That is 2000.

      That's why I abandoned chess. I will only return to OTB play when I reach 2000 at CT. Look how silly my mistakes at CT are. There must be a lot room for improvement. And I mean A LOT. It just doesn't make sense to play OTB as long as I make these silly mistakes. And I mean SILLY.

      Delete
    4. I had the same feeling and I quit playing OTB chess for a period of 7-8 years now (with a few exceptions for a dozen of one day fast control tournaments). However nowadays (from August) I started reading chess books and solving puzzles. It is a painful experience and sometimes I am wondering why I am doing it ;) :). Anyway I am extremally curious what it is like to play at the level of 2200 (FICS standard games level). Nowadays I am only 2050-2070, but before the year 2020 I want to reach 2200.

      And you give/share you some warm feelings - I make stupid mistakes, too! However I try to limit these and avoid repetition of the same ones.

      And what about tactics? I have solved about 20K easy puzzles (from paper workbooks) and now I want to do the same with much harder ones (in the range of 1800-2200). I solve most of these by "brute force" and I really hate such artificial approach. The only serious problem (drawback) is that... this method works for me!

      I am going to make some research at the tactical books and see what (valuable) things I can find. I simply cannot believe tactics and counting variations has to be that dumb process as we realize it nowadays. I want it to be really logical, efficient and smooth. Of course it can require hard work to create or invent the system (method) of solving these puzzles, but good heavens - it must be a lot more efficient!

      What I discovered (while playing serious games at FICS) is the opportinity to exploit tactical mistakes by ANY players... with the reasonable method of spotting the key positions and points (squares) we have to focus our attention and make good conclusions to find the best solution.

      I keep fingers crossed on you and you inventions (discoveries). I hope you will be able to make a breakthrough with all your ideas tested and extracted to the final conclusions (a system similar to Weteschnik's one).

      Delete
    5. PART I:

      I took a look at Wikipedia’s article on cues. The relevant section (for cues in chess) seems to be environmental cues.

      Environmental cues are all of the sensory cues that exist in the environment. [In the context of chess, this would be the board, the pieces on the board and the interrelationships of the pieces/squares.]
      With directed attention an environmental cue becomes an attended cue. [I understand this to mean that one consciously or subconsciously ones attention is directed to the important factor(s) by the cue(s).] However, most environmental cues are assimilated subconsciously, as in visual contextual cuing. [This implies that the cuing mechanism (the association between the cuing stimulus and the memory of what to do if that cue is triggered) has already been ingrained into the subconscious.]

      Environmental cues serve as the primary context that shapes how the world is perceived and as such they can prime prior experience to influence memory recall and decision making.

      The cues that trigger the mind in the proper direction in a specific position must be subconscious in order to be timely. Conscious logical processes will work, but will also consume considerable time, which is undesirable when trying to solve tactical problems OR when playing chess under a time constraint.

      I think of it this way: I want to “see” (instantaneously, if possible) not just the tactical possibilities inherent in the specific position, but also the differentiation as to which of those possibilities are the most promising lines, without requiring a sequential process of logical thinking.

      Using the example position above, there are any number of potential distractors from the solution. For example, let’s start with Nunn’s notion of Loose Pieces Drop Off.

      As I previously stated, one of the most important “cues” is: Who is to move? This is important because only that player to move can control the initiative (at least for one move). This is also true for actual games, not just for problems. White is to move. There are two White pieces that are loose: the WNa4 and the WBh3. (I’m going to ignore the White Pawns that are unprotected.) If one proceeds on that basis, the WNa4 is not threatened by any Black “attack” at present or in the near future, so it is eliminated from consideration. The WBh3 IS indirectly “attacked” by the BBc8. So if the cuing mechanism is based on the idea of defending/protecting loose pieces, this would come to the surface for attention almost immediately. Knowing that the “solution” does not lie in protecting loose pieces, we KNOW this problem is not about protecting loose pieces, but because of our trained cuing mechanism, we waste precious time examining possible ramifications of this “red herring.”

      As a second distraction, suppose that we ALWAYS look at potential tactical themes first (because that is how we have trained our cuing mechanism). Let’s start with Knight forks, because that is the simplest and most obvious. The WNc6 seems to draw our attention because there are possible forks on e5 and e7. Additionally, there is a check to the Black King! The immediately perceived problem is that both of those squares are firmly in the grip of the Black pieces. We bounce around the various possibilities and MORE TIME PASSES; another “red herring.”

      Delete
    6. PART II:

      As a third distraction, we try to combine two or more tactical themes. If we capture the BNf6 and Black responds by capturing with the BNd7, we now have the possibility of a tactical sequence that just might work! We capture the BBc8, and then we can attack the Black King with WNe7+, opening the “attack” of the WRc2 on to the BRc8 and winning the exchange. So we play around with this idea until we realize that Black is not obligated to recapture on f6 with the BNd7; he can recapture BKxf6 and the WNe7+ is gone. Oops, lots more time spent examining these possibilities.

      I’ll stop with the distractions at this point, since it should be obvious that we are delving deeper and deeper into the position, but – THAT IS NOT THE CURRENT ISSUE! The current investigation is into developing cues that trigger almost instantaneously and EFFICIENTLY guide subsequent thought toward the best solution with a minimum of distractions.

      This is where the motifs (as defined by mister Lasker) come into play. These cues are “lying on the surface in plain view” so to speak. If we utilize (burn in) just the three motifs given in Temposchlucker’s tree of motifs (there are many more BUT there is a limited number of motifs, just as there is a limited number of tactical themes), they should be sufficient to trigger the appropriate line of thought.

      The geometrical motif cues thoughts about the line-moving long-range pieces (Q, R, B). Simply “looking” at the WBh3 to c8 and the WRc2 to c8 reveals a superiority of force by White on c8 (2:1). This stimulates thinking based on the encircling motif – superior force and immobility. The BBc8 is limited in mobility (it can only move to b7). At this point the function motif comes into play. We need to quickly determine what the functions of the various pieces are. The BNd7 is protecting the BNf6 and also preventing the WBh3 from exchanging on c8. Can we exploit that somehow? Yes, by capturing WBc3xBNf6. This also accomplishes an efficient line-opening between WRc2 and c8. So, the BNd7 has TWO functions to perform, which limits Black’s possible responses. Forcing lines are always fruitful for investigation! There is also another way to double up on BBc8: WNc6-a7, double attack on c8. This provides some additional clarity. We have insight into how to clear the c2-c8 line of the White pieces.

      I’m not going to give the variations, simply because most readers will have worked them out.

      The point is NOT to “see” all of the specific moves in all possible variations; instead, it is to “see” the most fruitful direction for our immediate attention almost instantaneously, i.e., to develop training methods that will create and cement those type of “cues”. The knowledge of tactical themes and the ability to utilize them quickly is assumed to already exist in memory. The notion of using motifs (in the sense mister Lasker defines them) as cues seems to be a fruitful way of inculcating the cues into the subconscious. For training, we have to consciously think about the motifs, until they no longer require conscious thought. This training can be done fairly quickly.

      Delete
    7. It is surprising to notice that tactical themes randomly popping up, act like red herrings that distract us. As I said before, I often have the feeling that the tactical themes lead me in stead of that I am in charge. That is the optimal trial and error state. Often you hear people (me) complain "I knew which tactical themes were involved, but I couldn't get the order of the moves right".

      The reason for that, is that tactical themes are confined within themselves. There is no logic beyond the limits of the theme involved.

      Motifs operate a level deeper than tactical themes. They are made of logic, as it were. Logic is the fabric of motifs. If you start with the motifs, tactical themes act as tools to make a motif work. That way the logic of the motif is in the lead.

      Even after solving a problem and studying the solution for quite some time, I often am left with a feeling of fuzziness, concerning certain parts of the board. That are issues that I can calculate, but I cannot see it. While in the mean time, I feel that it is possible to see it in stead of calculating it. I'm going to inventory these issues.

      Delete
    8. When I started focusing on "seeing" mister Lasker's motifs BEFORE exploring the available tactical themes/devices, I noticed that I WAS "seeing" much more of the tactical possibilities than I ever had before. It grounds the orientation to the specific position. When I have failed to "see" the direction of the solution, in almost every case, it is because I failed to consider a particular "aura" (line of movement all the way to the edge of the board) of a particular piece, or I did not pay sufficient attention to ALL of the functions of a particularly critical piece. As soon as I notice that failure to "see", I spend time burning that lesson into my mind. ALWAYS START WITH THE MOTIFS!

      As for "fuzziness": I sometimes have the feeling that the solution should lie in a particular direction, involving specific pieces, without having a clear sight of all of the moves required. Formerly, I would just go ahead and throw out the first move(s) that came to mind, not caring whether it worked or not. Now I focus on forcing myself to work through to the solution, no matter how long it takes. While I work on it (using s-l--o---w logical thinking, I try to understand which motif(s) I have overlooked or disregarded. In almost every case, the "answer" pops into my mind rather quickly. Not quickly enough to gain any rating points, but relatively quickly. The problems I fail are the means to teach myself what I am not "seeing." The ones that I "see" immediately really don't teach me anything. Maybe it's just me. . .

      There is a time and place for intuitive thinking, but NOT while in the woodshed training.

      Delete
  5. I have just compared our ratings at blitz puzzles at CT.

    You have solved so far: 11278 and me only 1724.
    Your percent score is 71.42% vs mine 80.80%.

    Your highest rating (at blitz) is 1806 while mine is 1921.


    I have no patience to figure out the best variations. Sometimes I had to waste as much as 5-7 minutes to figure out 2-3 moves puzzle (!). It is ridiculous and it shows how weak I am at the analysis of variations.

    Anyway I noticed how many gaps I have in my chess knowledge and how poor is my pattern recognition with adjustment to the original positions.

    In general my approach is to find the mate final in every puzzle or win the Queen in 1-2 moves. It is pointless to comment such an approach, isn't it? I have to work HARD on this weakness, but when I finally do it - I will be able to achieve 2000-2100 at CT rated puzzles.

    ReplyDelete
  6. @ Tomasz:

    The point of this quest is to find ways to NOT work so hard. If we are working hard (using sequential logical thinking), then I submit that we are going to be disappointed with our eventual (lack of) improvement. This was the "lesson" I took away from the MDLM training approach. There MUST be a training approach that works in considerably less time than we have experienced so far. That doesn't mean the training itself will be easy. I think the current road is the most promising investigated to date. Only time and extensive trials will tell the final story. I'm happy so far with the results that I am "seeing" (pun intended).

    ReplyDelete