## Tuesday, May 21, 2019

### How to educate system I?

There are a few tasks which can be done immediately when a new chess problem is presented:
• See the material balance
• See whether a position is about mate, promotion or gaining wood
• See the points of pressure
• See the lines of attack
• See the function of the pieces
The first two skills seems to be invented especially for chess problems. Since when you play a game you already know what the material balance is, and what the position is about. I consider it a waste of time to hone these skills. I don't want to become better in puzzles, I want to become better in OTB play. I don't think it is bad or harmful to train those skills, if you feel happy about it, you should train them. But I don't consider it to be worth the effort for myself.

How useful is it to train the PoPLoAFun skills? What are the advantages, what the drawbacks?

The testimony of Robert seems to indicate that training the PoPLoAFun skills is beneficial for his game. Maybe he is willing to elaborate (again) on how he trained it. I must admit I haven't paid attention to his method sofar. (As you can see, this was written some time ago, in the mean time Robert has already shed more light on the subject).

Behind the the board I simply forget to apply the PoPLoAFun system. Usually a telltale sign that a task isn't automated.

Transferring intelligence from system II to system I
In order to become semi intelligent, system I must imitate the intelligence from system II. How is that accomplished?
From my youth I remember that my king often was chased by a knight in the endgame. And that I could win a tempo by placing the king at the same diagonal as the knight, but at one square distance. This knowledge was poured into a pattern as a kind of mold. System I retrieved the pattern whenever it was appropriate.

Working magic
What keeps haunting me though,is the metaphor of learning how to drive a car. There is no such thing as the transfer of knowledge from system II to system I. How does system I master to calculate the best speed when slowing down for a bend in the road, when to shift gears based on the sound of the motor, the speed of the car and the prevailing position of the planets? No math seems to be involved, yet the skill is performed accurate. Even on autopilot.

That is why I keep saying that system I seems to work by magic.

1. PART I:

Temposchlucker states:

"There is no such thing as the transfer of knowledge from system II to system I."
"No math seems to be involved, yet the skill is performed accurate. Even on autopilot."

Obviously, there is no DIRECT transfer of knowledge from System II to System I. No cap that we can open and just pour in the knowledge/skill. System I is non-verbal and not step-by-step logical. However, I maintain that System I is quite capable of higher math skills, such as integration and differentiation of physical motions. If it was not, you would not be able to walk, never mind "and chew gum at the same time." Consider the "simple" act of moving toward a thrown ball and catching it. Those (and similar activities) illustrate the application of higher math skills that System II could only wish it had at its conscious command. Although the brain is modelled as a digital system, it is much more likely that the brain/body system is a huge analog machine. Unfortunately, physical analog systems have been supplanted by digitally controlled systems, and the lessons of analog systems have been “lost.”

I started out in the mid-1960s in the flight simulator field based on analog systems, using vacuum tubes and servo systems. After a few years, I transitioned to systems controlled by digital computers. I started out in digital computers writing diagnostics in machine code, thumbing the code and data into computer memory using a front panel control system. That gave me the fundamental basis for all higher level coding. Each higher level language gave more productive programming power (you can DO considerably more in less time at a higher level of abstraction). Yet at the same time, you lost the capacity to "grab the metal" of the machine directly. I found it extremely helpful in understanding higher level concepts because I knew how it was implemented at the machine (hardware) level.

When learning to drive initially, you have a coach, giving you simple knowledge (System II) of the functionality of the various controls. You get instructions on the control and how it works, along with suggestions for how to use each control as part of the (eventual) skill of driving unassisted. Even in the absence of a coach, you can perform a series of trial and error attempts (based on knowledge gained and directed by System II) which will rapidly get you to where you want to be regarding driving skills. System I automatically integrates and coordinates the appropriate muscle movements because there is a built-in memory and kinesthetic feedback system. System II very rapidly makes smaller and smaller conscious corrections until System I just "does it" on its own, with little or no controlling from System II.

2. PART II:

The exact same process occurs in martial arts. At first, the muscle movements are large, even "gross" and totally uncoordinated. Yet, over time, with repetition AND effective feedback and System II analysis, you learn to refine and integrate those gross motor movements into smaller and smaller subtle movements. Eventually (if you practice and pay attention and learn from what works as well as what does NOT work), you reach a level of skill in which "it" (System I) just "does it." I started training at age 40, earned my 1st degree black belt in a little over 5 years, and eventually earned a 4th degree black belt.

The exact same process occurs with learning to play a musical instrument. I taught myself how to play a harmonica. I started with simple sounds. I read everything I could get my hands on. I quizzed my older brother (a professional musician) on music theory (knowledge). I then applied that knowledge to the instrument. Lather, rinse, repeat - over and over and over and over again. I did NOT exactly repeat the same things. Each time, I approached it from a slightly different angle. Initially, I focused on just the individual notes. I worked at trying to make each note clear. I worked on "knowing" (System II) where each note was located - its "address", if you will. I then moved up a level. I started stringing individual sounds together into small fragments of melodies. I then applied a knowledge of chords (System II) to those strung together notes. At each level, I kept expanding my knowledge base, and then applying it to the instrument. Within 4 years, I went from no knowledge of either the instrument or music theory to the point where I was teaching other people and playing with bands. I now play at the level where I can sit in with a group I’ve never practiced with, pick up the melody of a new song and play it after hearing one complete verse. I’ve been playing with a local bluegrass band now for over a year. Oh, I also picked playing electric bass (on my own without an instructor) exactly the same way.

My approach to any activity (physical or mental) which I want ingrained into System I is similar in every case. You start with knowledge. "If you don't know where you are going, any road will take you there." I refer to it as "left corner nibbling." You pick a little corner, bite off a little "chunk" and digest it. Learn everything you can about it. Then, you observe it, bend it, twist it, look for analogies with things already learned, and you repeatedly attempt to apply it. All of this activity is directed by System II - at first. After internalizing that little piece of knowledge, bite off another small chunk that is closely related, and repeat the process. After repeatedly performing all those different activities and making connections to previously known things, System I (eventually) automagically brings those things back to System II's attention whenever the cues (triggers, signals, whatever you call them) trigger recognition. If you continue the process long enough, you will reach the point where System I just "does it."

Chess skill is not a single skill; it is a combination of lots of little skills, miniskills, if you will. You gave a perfect example:

From my youth I remember that my king often was chased by a knight in the endgame. And that I could win a tempo by placing the king at the same diagonal as the knight, but at one square distance. This knowledge was poured into a pattern as a kind of mold. System I retrieved the pattern whenever it was appropriate.

I am in the process of doing my usual thing for chess; it’s working so far. I have no idea how much skill I can gain ultimately, but I do not see any limit (other than running out of lifetime, since I’m 71 years old). It really doesn’t matter what my eventual ceiling may be, as long as I keep improving and enjoying the process!

3. An observation about my parenthetical statement above:

(you can DO considerably more in less time at a higher level of abstraction)

I think this may be one of the areas where we get the cart before the horse. We START our investigations/training at some higher level of abstraction, without any grounding in the underlying basic principles/methods. There is a "sweet spot" that is not too low, and not too high.

Analogically, if we try to start our programming at the transistor level, it is highly unlikely that we will ever get anything done in software; the level of abstraction is just too low. On the other hand, if we start with a 5th generation language, we may "feel" that we know what's going on down below, but that is merely a "familiarity" illusion.

In a different context (management/leadership), I often heard the trite statement, "I know what's going on in MY part of the organization." The reality was quite different. The person making that statement rarely left their executive office and went out into their subordinates work spaces. They relied on upline reports for their information and the "feeling" that they had a handle on everything. Yet, time after time, these same people expressed great "surprise" when their subordinates failed to deliver "on time, and on schedule." That information was readily available at the working level; they just never had the interest nor took the time to find out what REALLY was happening. In order to gain that information, it would have been necessary to "move down a level." But their attitude was that doing so was beneath them and not worth their time.

We have to find the appropriate "sweet spot" to apply to our chess training.

4. PART I:

Prior to addressing the specific question above (How to educate system I?) in the context of chess improvement, I’ve excerpted some points from a great book on how to achieve SUCCESSFUL LEARNING. I provide the following information from the book without comment. If you are interested in learning more effective proven educational/training methods, I highly recommend it!

From prior experience in other fields, I know that there will be some people who “already know all this stuff” and/or have no interest whatsoever in being “sidetracked” from the “pure” subject of chess improvement. If you’ve already read this book (and others on the subject) and have absorbed the lessons, just ignore my comments because you will get absolutely NOTHING from them. On the other hand, if you genuinely want to “learn how to learn” so as to improve your chess SKILL, then at least give some thought to these ideas.

[I make use of square brackets when I insert something of my own. I use capitals and bold type to emphasize a word or point.]

make it stick – The Science of Successful Learning

Learning: Acquiring knowledge and SKILL and having them readily available from [long-term] memory.

Immutable aspects of learning:

• Learning requires memory.
• We need to keep learning and remembering all our lives.
• Learning is an acquired SKILL.
• The most effective strategies for learning are often counterintuitive.

Principal claims:

1. Learning is deeper and more durable when it’s effortful.

The repeated solution of massive numbers of simple problems may have some short-term benefit, but will likely NOT significantly increase the ability to apply that SKILL in an actual situation. Deliberate practice requires continual “stretching” just a little beyond the “comfort zone.”

2. We are poor judges of when we are learning well and when we are not.

It is important to either be ruthlessly objective OR to have a coach to assess our learning.

3. Rereading text and massed practice of a SKILL or new knowledge are preferred study strategies that are among the LEAST productive.

Single-minded rapid-fire repetition, rereading, cramming, and “practice, practice, PRACTICE” are conventional wisdom for establishing long-term durability of SKILLS that is WRONG!

5. PART II:

4. Retrieval practice (short quizzes requiring recall of facts or concepts from memory and using flashcards) is a more effective learning strategy than review by rereading.

Retrieval strengthens the memory and interrupts forgetting.

5. Periodic repetitious spaced out practice (retrieval and practice of the material [or SKILL]) is essential for retaining knowledge.

Spaced out repetition of a task (allowing some forgetting) or interleaving the practice of two or more subjects produces longer lasting learning and enhanced versatility in applying the new knowledge [or SKILL] in diverse situations.

6. Attempting to solve problems before learning the solution leads to better learning, even when errors are made in the attempt.

7. Preferred learning styles do NOT significantly impact learning and are not supported according to empirical research.

“Go wide” using as many different styles of learning as possible, in as many different concurrent (auditory, visual, kinesthetic) modes as possible.

8. Attempt to formulate and understand the underlying principles or “rules” that differentiate the types of problems to be solved. Try to reformulate these principles in your own terms, trying to connect (by analogy) to other things previously learned. This SKILL is better acquired through interleaved and varied practice than massed practice.

9. We are all susceptible to illusions that hijack our judgement. Use testing to identify and improve areas of weakness.

10. All new learning requires a foundation of prior knowledge.

11. Mechanical repetition will quickly hit a limit of what can be kept in mind. However, practiced elaboration (giving meaning to new material by expressing it in your own words and connecting it with what you already know) will enhance learning durability and add to the SKILL of applying the new knowledge to unfamiliar situations.

12. Putting new knowledge into a larger context aids learning.

13. Every time you learn something new, you change your brain.

The elements that shape your intellectual abilities lie (to a surprising extent) within your own control. Making mistakes (and learning by correcting them) is essential for advanced learning.

6. PART III:

make it stick – The Science of Successful Learning

How Learning Occurs

Encoding

The brain converts your perceptions into chemical and electrical changes that form a mental representation of the PATTERNS you’ve observed. This process of converting sensory perceptions into meaningful representations in the brain is still not perfectly understood. [The encoding process creates new representations as memory traces in short-term memory.] The experiences and learning we want to salt away for the future must be made stronger and more durable. . .

Consolidation

The process of strengthening these mental representations for long-term memory is called consolidation. New learning is labile: its meaning is not fully formed and therefore is easily altered. During consolidation, the brain reorganizes and stabilizes the memory traces. This may occur over several hours or longer and involves deep processing of the new material, during which scientists believe that the brain replays or rehearses the learning, giving it meaning, filling in blank spots, and making connections to past experiences and to other knowledge already stored in long-term memory. Prior knowledge is a prerequisite for making sense of new learning, and forming those connections is an important task of consolidation. . . . sleep seems to help memory consolidation, but in any case, consolidation and transition of learning to long-term storage occurs over a period of time.
. . .
Similarly, the process of learning something often starts out feeling disorganized and unwieldly; the most important aspects are not always salient. Consolidation helps organize and solidify learning, and, notably, so does retrieval after a lapse of some time, because the act of retrieving a memory from .long-term storage can both strengthen the memory traces and at the same time make them modifiable again, enabling them, for example, to connect to more recent learning. This process is called reconsolidation. This is how retrieval practice modifies and strengthens learning.
. . .
This effort to reconstruct what you learned the day before is ragged, but in making it, critical elements of the maneuver come clearer and are reconsolidated for stronger memory. If you are practicing something over and over in rapid-fire fashion, . . . you’re leaning on short-term memory, and very little mental effort is required. You show gratifying improvement rather quickly, but you haven’t done much to strengthen the underlying representation of those skills.

7. PART IV:

Retrieval

Learning, remembering, and forgetting work together in various ways. Durable, robust learning requires that we do two things. First, as we recode and consolidate new material from short-term memory into long-term memory, we must anchor it there securely. [A “CLUE” AS HOW TO TRANSFER LEARNING FROM SYSTEM 2 TO SYSTEM 1!] Second, we must ASSOCIATE the material with a diverse set of CUES that will make us adept at recalling the knowledge later. Having effective retrieval cues is an aspect of learning that is often overlooked. The task is more than committing knowledge to memory. Being able to retrieve it when we need it is just as important.

The reason we don’t remember how to tie knots even after we’ve been taught is because WE DON’T PRACTICE AND APPLY WHAT WE’VE LEARNED.
. . .
Knowledge, skills, and experiences that are vivid and hold significance, and those that are periodically practiced, stay with us.

Extending Learning: Updating Retrieval Cues

There’s virtually no limit on how much learning we can remember, as long as we relate it to what we already know. In fact, because new learning depends on prior learning, the more we learn, the more possible connections we create for further learning. Our retrieval capacity, though, is severely limited. Most of what we’ve learned is not accessible to us at any given moment. . . .

Knowledge is more durable if it is deeply entrenched, meaning that you have firmly and thoroughly comprehended a concept, it has practical importance or keen emotional weight in your life, and it is connected with other knowledge that you hold in memory. How readily you can recall knowledge from your internal archives is determined by context, by recent use, and by the number and vividness of CUES that you have linked to the knowledge and can call on to bring it forth. . . . It’s not the knowledge itself that has been forgotten, but the CUES that enable you to find and retrieve it.
THE END (of my excerpts from the book)

8. PART I:

Continuing with practical applications to chess:

The idea of following a formal step-by-step logical process is very appealing and is touted by such exemplary chess teachers as NM Dan Heisman. Unfortunately, doing this requires us to depend on s-l-o-w System 2 and very limited short-term (working) memory. So how can we transfer knowledge into long-term memory through training (using System 2) and then rely on System 1 to recall it, or at least have it regurgitate “cues” which will guide us to the approximately correct line of play?

The way I train to learn any formal process (regardless of complexity) is to simply apply it directly to problems without trying to formally follow it. Start with simple knowledge (the “basics”) and then apply those basics in as many ways as possible to various tasks. I try to perform activities that loosely follow the process, but I focus my attention on the context (performing the activity) rather than the process. After acquiring certainty that I can apply those basic principles, raise the level and repeat the process again. If I sometimes forget a step or two, or fail to consciously follow the entire process, so what?!? The purpose of the training process is to increase the likelihood of increased skill based on long-term memory and eventual success at the activity, not at applying the process rigidly. I followed such a process with martial arts and with music training (and other things in my professional career, but that’s another story).

I think the best way to explain something is through examples. So, without further mental gymnastics, let’s look at a “process” and then some example problems. The purpose is NOT to establish some “best practice” but to merely show what I do to train my system 1 for pattern recognition.

In the current post, Temposchlucker laid out a set of (relatively) simple “things to do”. I’m not sure there was any significance to the order given, but I don’t think the order is necessarily important. However, I do think that we need to at least consider these things as we begin to figure out what is going on (orientation to and determination of the goal of the problem). Most importantly, we need to do this automatically, without having to dredge up each item in this list via effortful recall and conscious application. The only way I know to make this process automatic is to repeat it consciously each time I try to solve a problem until I no longer think about the process. The list of things to do is not the focus; the current problem to be solved is the focus. After doing this formally several times, consciousness of the process begins to recede into the background. This is how we train System 1 using System 2.

9. PART II:

I’ve been working at making my investigative “process” automatic. This involves knowledge (what I need to do each time) and practice (repeating the “process” until it becomes automatic and almost instinctual - hopefully). I decided to try a specific approach to each problem. I also try to apply this same approach when playing a game. I try to do this at every move, but especially if I think the game is at a critical moment. Think of it in the same way as a blunder check just prior to making a move. One of the critical aspects is to use the method of elimination early on AND throughout the process. In other words: do everything possible to eliminate some (or most) of the various alternatives without going into a long System 2 tree of variations search. I do the following “steps”, usually in this order:

1. Which player is to move?

This is important because I have found myself at times working on a problem on a tactics server or a book from the wrong side of the board. It is not as important to do this in a game; you just “know” which side is to move.

2. What is the material balance?

Sometimes I do this and sometimes not. Sometimes the material balance is important; sometimes not. If it’s a game situation, you should already “know” the material balance without having to add everything up. Mostly, I’m aware of the relative material balance just by glancing at the position for a few seconds.

3. What are the MOTIFS?

Motifs are the “cues” that trigger recognition of corresponding patterns and the recall of potential tactical “solutions”. Aox’s questions regarding what the problem is about are some categories of motifs (Lasker) or “signals” (Neiman). This is the first part of eliminating some of the alternatives. For me, this is where the notion of the “vulture’s eye view” comes into play. I’m not trying to find a solution based on randomly chosen moves, but trying to narrow the scope of the problem.

4. “Seeing” PoPs and LoAs

This is the stage at which I begin identifying points of pressure (such as “loose pieces”, B.A.D. pieces and vulnerable squares in the King’s field or near vicinity) and mentally “drawing” the lines of attack from the pieces I think are important all the way to the edge of the board. Initially I actually used a highlighter (sometimes different colored highlighters) to mark the lines of attack one at a time. Of late, I’ve stopped using the highlighter when working from a book, because I obviously cannot do that when solving online or during a game. I’m not trying to develop a set of “candidate moves”; I’m just trying to “see” what is important and what may safely be ignored in the specific position. As I go through this process, I begin to “see” specific tactical ideas that might be applicable.

10. PART III:

5. Beginning tentative calculations, and noting the functions of various pieces on both sides. Here I begin “seeing” what possibilities and restrictions are applicable to specific pieces and Pawns. I try to narrow focus down to the critical area(s) of the board. Sometimes this is confined to one side or corner; sometimes relevant pieces are located in different areas. I also note those pieces and areas of the board that seem NOT relevant (actually, that are not a priority in the current position). I’m not calculating moves but just “seeing” potentialities.

6. Through the process of elimination, begin figuring out what needs to be done for the side to move, and figuring out what resources (if any) are available to frustrate that goal. There may be some tentative variations investigated, looking for a quick evaluation to see if that particular variation seems promising or not.

All of the above starts to become “second nature” after repeating it over and over on many problems. The important thing is to TRUST SYSTEM 1 BUT VERIFY YOUR INTUITIONS USING SYSTEM 2 (in the next step).

7. Choosing one specific variation to investigate as deeply as possible, or at least until I’m satisfied that it is either highly likely or has a refutation.

8. Investigate all likely candidate moves following step 7 until all candidates have been investigated or one specific solution seems to be mandatory.

9. Perform a blunder check (usually only in a game).

10. Make the “best move” found AND REPEAT THE PROCESS from the other side. Obviously, there is “carry over” from one move to the next. I don’t generally have a problem keeping relevant details in mind as I search for the final move.

11. PART IV:

The first position is the first problem taken from Emmanuel Neiman’s excellent book “Tune Your Chess Tactics Antenna – Know when (and where!) to look for winning combinations.” I commented about this book and position on December 28th, 2015. I suggest first looking at the position with fresh eyes.

FEN: k7/8/P1N5/8/2K5/6p1/5bB1/8 w - - 0 65

http://temposchlucker.blogspot.com/2015/12/zooming-outpiece-awareness.html#comment-form

As noted, this position was taken from a master game: Lignau, Carsten-Orso, Miklos, Budapest 1992 (4).

You should FIRST get a “feeling” for what the position is about. Try to follow the process outlined above. If you don’t first determine what the position is about, and you apply typical endgame “rules” such as “Centralize your King in an ending”, you will most likely NOT “see” the solution. Master Lignau did not “see” it, and ended up drawing the game because he could not figure out how to make progress following typical “rules”. As soon as you figure out the goal of the position, the correct moves will also magically seem to be obvious. Simple counting may be involved, but nothing particularly complicated is required.

12. PART V:

Uh-oh! It seems I’ve gotten ahead of myself. Some of what I do in each position/problem was NOT listed in the “formal” chess process given above. Sorry about that; sometimes what we do has become so ingrained that we are no longer aware that we do it. Isn’t that exactly what we are looking for – storing knowledge in long-term memory and having System 1 bring it back to mind when it might be applicable?!?

One of the crucial things that I do automatically (having done this for most of my life) is to elaborate and speculate on potentially related things while doing any activity. For example, if I’m reading a nonfiction book, as ideas that are related “pop” into my mind, I make annotations in the margins of that related idea. (it’s one of the reasons I prefer to continue reading books rather than use online ereaders.) I’ve made connections between things like various types of databases (hierarchical, network, relational, object) and corresponding organizational structures, or martial arts principles and leadership principles. I firmly believe that once one particular Way has been mastered, we have the potential to master anything else; see Musashi’s quote previously. One of my coworkers once remarked that my books were so much more interesting to read after I had finished them because of the highlighting of key points and the copious notes in the margins, connecting the ideas presented to something else that might seem totally unrelated on the surface (at least to a casual observer).

Using the make it stick terminology, I try to encode CUES about new information in as many different ways as possible. That’s why I try to learn by making analogies (with a hat tip and nod to Douglas Hofstadter and the FARG organization). I also try to consolidate new information by reiterating in my own terms. It’s the retrieval and reflection on what is being learned and the learning process itself that I’m trying to make stick.

13. PART VI:

In the example position given above, a casual look at the position shows that the Black King is stalemated – this is the significant “motif”. TRIGGER THE “LOOK FOR A CHECK” PATTERN! Alas, there are no obvious checks except by moving the Knight, which breaks the current stalemate. There is a possibility that if the White Bishop moves away from its current location that Black may be able to queen his Pawn. Perhaps a 7-man tablebase could give us a definitively solution which might run into hundreds of moves; not a practical solution. Let’s dredge up some more (perhaps related) memories. Assume that the White Knight, the Black Bishop and the Black Pawn magically vanished from the board. Suddenly, we have the possibility of winning because the White Bishop controls the queening square. (This is related knowledge that MIGHT be applicable.) Fantasizing, presume the Black King, White Knight and White Pawn were transposed to the h8-corner. The corresponding Bishop and Pawn ending would no longer be won. I doubt there is a way to force the White King into the a8 corner, thereby rooting out the Black King, especially given that Black can control black squares. Okay, so what if the White Knight releases the Black King and goes after the black Pawn? On and on we go, thinking of different scenarios that might bring about an eventual winning position. For instance, if the White Bishop was replaced by a White Rook, it might make sense to use the Knight to go after the black Pawn and Bishop because a Rook and King are capable of checkmate.

But what about our initial “motif”? If there was just a currently “unused” piece that could give check to the Black King, it would be checkmate. Hmmm. . . there IS a White piece currently not engaged with the black King AND (pattern recognition) it IS capable of checkmating IFF it can land on b7. OKAY! Let’s forget about King or Knight moves, and focus on Bishop moves. 1. Bh3, 2. Bc8, 3. Bb7 is the only path available. But what if Black makes a Queen in the mean time? It really won’t impact the solution: it takes two moves for Black to promote his Pawn AND there is no check when the Pawn is promoted Consequently, the solution has been found!

The “hidden” learning process does not end with the solution. What has been “learned”? It’s now time to prioritize and repeat the key “aha!” experiences. (1) When a King is stalemated, look for a check, any check, no matter how difficult it may be to achieve. (2) Simple counting can often tell us whether a particular line is feasible or not. (3) Just becoming aware of (“seeing”) the potential checkmate is sufficient to trigger the correct solution.

This “hidden” process is what enables learning of patterns to take place in accordance with the earlier insights regarding learning. By engaging in this process repeatedly, it is highly likely that similar positions may trigger the appropriate System 1 response.

This is also why I have been skeptical of the efficacy of massed practice based on trying to blitz through an enormous number of tactical problems, whether simple or complicated. There is no time for reflection and consolidation of any pattern, which requires at least 12 seconds per pattern. Consequently, System 1 will provide a feeling of familiarity from the sheer repetition of problem solving and having a fleeting glance at known positions, but the effect will NOT last because it is not encoded into long-term memory AND not connected with other knowledge.

14. INTERMEZZO

I just had a perfect illustration of the difference between people about learning by analogy. My special needs granddaughter was working on a math app on her IPod. It was using sections of a pizza to illustrate halves and quarters. As she was working on the quarters, I remarked to her that it was like having four quarters in a dollar. My wife chided me for "confusing" her with something that was not related, because she was trying to learn fractions, not learn money. I explained that I was trying to help her "cement" the idea of fractions by giving her a different situation to relate to the concept of fractions, thereby making it more likely that she would be able to remember at least one of the examples and be able to use the idea of fractions in the future. She seemed skeptical because she does NOT think in analogies. She's also not a chess player - not a surprise.

I have a t-shirt that says, "There are 10 kinds of people in the world: those who understand binary and those who don't." My wife doesn't understand either binary or why that t-shirt is an inside joke for computer nerds. Lest anyone think I'm dissing her, she has an IQ in the 130+ range.

Chess skill is NOT a single skill; instead , it is a relatively large collection of miniskills. The more "cues" (connections) we can create to any given piece of knowledge or miniskill, the greater the likelihood that System 1 will be able to recall that information or something similar when it is needed. Patterns don't have to be about the same subject; in fact, the more distance between the subjects the easier it is to create reliable memory cues for retrieval for BOTH of them.

End of rant.

1. You seem to have mastered speed writing too, lately ;)

15. PART I:

Sorry, I'm just trying to help (I hope!) answer your question. Unfortunately, the answer is not simple. I hope that at least some of that extended verbiage is useful. My apology to anyone who gets nothing from all this verbiage.

Aox made the observation that he's tried different methods, and is waiting for a "new" one. I certainly am NOT proposing a "new" method nor ideas that originated with me. I'm just trying to describe what I do and why it works, at least for me; YMMV.

One of the notions that we humans seem to have is that relationships between things are linear, i.e., one-to-one. One of the harder parts to grasp regarding conceptual connections is that the number of potential relationships are combinatorial, not linear. Without special math training or thinking beyond the obvious, it's fairly easy to fall for linear assumptions. I'm reminded of Frederick Brookes, Jr.'s description of the linearity of management thinking in The Mythical Man-Month: "Most managers seem to operate under the assumption that if 1 woman can make a baby in 9 months, 9 women should be able to make a baby in 1 month." We laugh (or cry) about that description but still fail to grasp the significance of nonlinear relationships.

Brookes gave a simple equation which captures the reason so many large projects get bogged down in communication issues. It has to do with the number of communication links between participants. The equation is: [N * (N-1)]/2, where N is the number of communicants. The first flaw in our thinking is assuming (wrongly) that communication is a one-way process; it's actually bidirectional; that's what the "2" in the equation represents. If 2 people have to communicate about a particular topic, there is one bidirectional communication connection; 3 people will have 3; 4 people will have 6; 5 people will have 10; 10 people will have 45; 100 people will have 4950. Each of those communication links has a "cost" associated with exercising it.

1. "Sorry, I'm just trying to help (I hope!) answer your question. Unfortunately, the answer is not simple. I hope that at least some of that extended verbiage is useful. My apology to anyone who gets nothing from all this verbiage."

I'm just joking, of course. The area we try to cover is huge, and since I suffer a bit from a lack of energy to write all thoughts down, I'm glad you do. This helps me to focus on distilling some new insights from all the stuff that is relevant to the subject.

16. PART II:

The same equation holds true for neural connections. If you "connect" two specific pieces of information, then there is 1 bidirectional connection between them, with the number of neural connections increasing combinatorically as more pieces of information are connected to these and others. The marvel of System 1 is that it not only can make new connections, it can also strengthen existing connections (since the connections are analog, not digital), remove connections (or, more likely, diminish the strength of the retrieval cues) and retrieve that "information" and give a plausible reason for connecting those different things in a specific way. System 2 usually just goes along with and accepts whatever "story" seems most plausible. Unfortunately, System 2 is totally unaware when System 1 puts things together in such a way that it just is not true. This is the reason for "Trust but verify."

This helps explain why it is critically important for learning, retention and especially retrieval to attempt to provide as many analogies and connections to new material while learning it. Passive viewing and focus on just one thing without attempting to connect the new information to already stored information is an exercise that will not prove to be successful over a longer time period. Cramming via massed practice works for a very short period of time, but the gain in immediate familiarity comes at the price of long-term retention.

It also helps explain why learning initially proceeds rapidly, and then slows down (with diminishing returns for the same level of effort) over time. As more learning occurs, more connections are made, and so it is possible to "know" more without actually learning the same amount of new knowledge. When first learning to drive, everything is new. After absorbing some knowledge and the skill to apply it, the remainder to be learned is less and the rate of increase in skill level approaches stasis as the total skill is acquired. Essential, we plateau as we approach an "acceptable" level of skill. The only way to break through a plateau is to acquire new knowledge OR make new connections between old knowledge subjects (which is actually new knowledge). Unfortunately, the law of diminishing returns comes into play and most of us settle for reaching the level of "good enough" rather than the best level possible, because we simply don't have the time nor energy to continually force ourselves to improve.

17. @Robert
if you want to do a training of the right way of thinking , trying to make it faster and faster: use "mixed mode" at chesstempo, there you have ~5+ min per puzzle
i did that for more than a year.. did not work for me

At present i do it more the other way around, i repeat my blunders, do some aftermath with them, i did that now for more than 1 year too.. same effect ;)

You will reach your plateau / rating at ct-blitz soon ( usually you can tell the typical rating of a tactician after 1000-4000 attempts , then the right / average ct-rythm is found ). Seemingly you will be at somthing around 1800. Then we can see if your method will work

18. @Aox:

Thank you for the description of things you've tried; it's very helpful.

I've started working on the puzzles I've gotten wrong, without any timing. I work through several of those at random, and then analyze and think about what caused me to get the problem wrong. Afterwards, I switch to blitz mode for a short period of time to see if I can improve my rating (using the rating as an indirect indicator that I'm improving in tactical vision). I'll start intermingling problem sessions in mixed mode as well.

I have no idea what my ultimate rating ceiling might be; you have a better insight to that than me. Even if I plateau at 1800 in blitz, that's still over 300 rating points above where I was stuck before. When that plateau inevitably occurs, then I will have to analyze why I'm stuck there, and try to figure out a different way to improve - which I may (or may NOT) find because it is not a certainty that such a path exists.

19. You had been at ct with a different nick before and where stuck at a ct-blitz rating of 1500?

1. My chess handle has always been "crazybob", regardless of the chess server. I first started playing on Chess Tempo with a free membership. My rating stats show the earliest I played on Chess Tempo was Standard Mode on 2010-11-04; the earliest Blitz Mode was 2016-01-27; and the earliest Mixed Mode was on 2017-12-23 (not much Mixed Mode practice at all). I joined with a Gold membership on 2018-12-13. I'm still don't use the site regularly, primarily due to using books, and only having occasional time to devote to online tactical training sessions.

My USCF history began in 1970 and ended in 1975, I went from an initial rating of USCF 1523 to USCF 1810 during that time, on the basis of approximately 70 long time control games.

As Temposchlucker noted, I've been "speed writing" of late with my comments. I'm going on vacation for my wife's birthday tomorrow, and won't be back online until after May 30th. So, y'all gonna get a break!

2. you cant compare a USCF Rating with a CT-Blitzrating.
A chain is as strong as its weakest link, you might be weak in strategy or positional play or will to win, opening play, endgame, thought process...

And you cant compare the standard rating with the blitz rating. You might have solved the standard puzzles to fast.. or extremly slow. A friend of mine was a DWZ 1600+ ( = maybe a USCF 1700+? ) and had a standard rating 2300+. He was thinking about each puzzle several hours, sometimes even some days.

After 1000-4000 ct-blitz attemps we can guess your tactical skill much better.. and then we can see if you can improve from there

GM Sortis? said that after ~8 years of serious chessplay someone reaches their "final" chess-rating.

20. I started chess training with the help of chesscom (I was convinced to practice Puzzle Rush and I bought a premium account about 2 months ago).

I started with 28-32. After 6 weeks I am able to reach 34-36.

What is the minium score at Puzzle Rush (5 minutes to solve all the puzzles and after 3 mistakes you are out), to make a statement that I made an improvement? 40, 45, 50, 60? :).

Let me know guys what do you think about that :).

21. @tomasz
would be interesting if your ct-blitz rating did change?
I have no data how people improve or perform at puzzle rush.
If your performance did change from ~30 to ~35 than your speed did increase bye more than 1/6 ( hard to tell how much in real, the puzzles get harder too!).

The best available method to measure or compare the tactical skill is the ct-blitz rating.

1. @Aox

My dear friend. Here are my stats (2019-05-30)

Stats for blitz tactics (2019-05-30)
Rating: 1816.6 (RD: 363.83) (Best Active Rating: 1921 Worst Active Rating: 1705)
Active Rank: Not Active/2410 (Best Active: 254 Worst Active: 856)
Problems Done: 1800 (Correct: 1444 Failed: 356)
Percentage correct: 80.22%

Can we estimate my tactics is 1820-1840 as for now? (without the progess we want to observe and exeperience). And my percentage of correct answer is 80%.

What is the minimum score I have to achieve to say I made a chess progress at tactics? I will try to solve some puzzles at CT-blitz mode and we will see what happpens.

My last attempt at blitz tactics at CT was performed on 2016-12-22.

Can you tell me what will be a minimum progress in my case to call it "a chess tactics progress"? Shall I achieve 2000 rating with 70% correct anserws or 2100/60, 2200/55, 2300/45?

22. If your rating did reach the "ceiling", then an other 200 points woud be very suprising for me. Can you please tell me your nick at ct?

1. My nickname is "demon_szybkosci". You can check it out and tell me what rating would be suitable (enough) to confirm I made a chess tactics improvement (by your standards and CT as a tool).

23. @Robert
you are solving the mixed puzzles way to fast, you have 5 min per puzzle.. use them

1. Aox: Thank you for taking a look, and for the advice!

24. @tomasz
i checked your ct.blitz rating
you already had a rating of 1900 so you are at least a 1900
you just race through the puzzles
often you use only 20% of the "average time" estimatingly you are already a 2000 or even more?
I suggest you do a quick blundercheck before you move, its better to be to slow than to make errors

1. Do you mean my OTB rating or CT blitz rating or online rating at blitz (Lichess, chesscom, etc.)?

I want to break my tactical ceiling and break into 2100 level. I am not sure if it possible, but at least I will try :).

25. i was looking at your ct-blitz rating
you never reacheed your ceiling because you never started thinking long enough
your peak rating was 2016 with 1900. you need to play slower, for example make a blundercheck

26. Hi, here Munich. Need to tell you guys that I improved considerably in bullet games. Something like 100, maybe 200 bullet rating points. I am still behind other expert/master players, but at least I am not sooo bad anymore.

What have I done to become better in bullet? It is just the attitude. I "let go" and play rubbish moves.
I have often lost positions, but then I sometimes win on time, manage to keep my opponents long enough occupied to flag them. Before I lost most games on time.
My board vision hasnt improved, I am very likely below Tomasz's check mate board vision numbers.
Actually I have trouble to keep following. In the last seconds I only look at my pieces, I have no idea what my opponent does, I am blind and move something. Anything! I have sometimes no Idea if I am up in material, I lose track of almost everything, and then I win. It is awful, but somehow exciting and fun.

I played Tomasz today, and so far I had a negative score against him in Bullet. but Today I did way better than I did before. Not just a little better. But I'd say it was significiantly better. Before I lost like 2 thirds of the fast games, today it was rather the other way round, over about 20 games or more.
And he confirmed - I became faster.
During Bullet I feel very stressed. Before I was not stressed. I disliked bullet and lost often. But I did not feel stress.
Now it is different: After 20-30 bullet games I am shaken. Washed up. Need a break. It costs a lot of energy. And "dopamin" says Tomasz. Is that true? Anybody knows something about this?

Anyway, even though I just improved my bullet ratings for 3 days, I doubt this is just a good run. Why? Because it feels totally different. So I dare to say, my bullet improvement is rather permanent. And since I played bullet only for 2 or 3 days (I even lose track on this here), who knows? --> maybe I get even the more the hang of it.

For curiosity reasons: After I took part in a 1/2 minute bullet tournament, I tried CT Blitz at chesstempo. Today. And my CT Blitz rating rose close to former ATH rating. Could be co-incident, but I hardly do have such good days (especially not after 22:00, because at that time I am rather tired), and somehow, these Bullet games, well, hard to say, but I somehow had the feeling I calculate faster. Dont know for sure though, because it is hard to compare. I intend to do now more CT Blitz puzzles, and if I reach new heights never reached before, I would not be surprised.
Or is there a rating inflation at chesstempo?

27. ...just remembered: there is an effect right after playing bullet (So I was right, though this is nothing new), because it was recommended that solving a few very easy puzzles (fast) before playing chess is beneficial. So the other way round should work, too. The effect doesnt last long, though. Probably it just gets you in the right mood, kinda warm up for the brain. Aox, you probably remember the science behind that effect a bit better?

(there is a rating boost possibility if you take advantage of playing weaker players. Best seems to be to play players who are rated about 200-300 lower than your own rating. The rating general formular doesnt seem to be accurate in very fast time controls and I have the suspicion that it favours the stronger player. Meaning you get more rating points (as the stronger player) than you should, because the winning probability is wrong predicted by the general rating formular used in Blitz/rapid/classic. Why? I guess that the variable "losing on time" is a bigger factor in Bullet, and it is likely that the stronger player can see checks and captures faster. An effect that hardly plays a big role in longer time controlls, but at 1 min Bullet games the 10th of seconds "seeing things faster" add up.

28. I want to confirm Munich conclusions and experiment :). We played a dozen of bullet games and as I predicted I could win most of these due to moving faster at the end of the game (time). And after I told our friend Munich, he cannot win this way (playing good moves and losing precious time at the end of the game)... he decided to change his habit. And the sides were reversed (upside down). It was me who lost every game on time even if sometimes I had an advantage.

Generally I think at bullet (1+0 or less) you have to play strong and fast and if there is 8-10 seconds to the end of the game (time) you have to play as fast as possible - and if you want to win in a "dirty win" you should play moves that are shocking and stupid - you would hardly play these at any other time control.

I can confirm Aox's observation and conclusion - I am very fast at very easy puzzles, but I do not and I cannot analyse the position :(. I simply play what looks good and if often fails.

29. I played in the monthly club Ricochet Quick [8 minutes per game with 3-second delay] Tournament last night, winning 4 out of 5 games. I was the second highest rated player [USCF 1642 Quick], and lost to the highest rated player because of a hallucination. All I can say is "NEVER RESIGN!!" Here's the game:

[Event "Ricochet Tournament"]
[Site "Asheboro NC"]
[Date "2019.06.11"]
[Round "2"]
[TimeControl "8 minutes, 3 second delay]
[White "Hales, William Thomas"]
[WhiteUSCF "1737 (Quick)"]
[Black "Coble, Robert Perry"]
[BlackUSCF "1642 (Quick)"]
[Result "1-0"]
[ECO "D26"]
[Annotator "Stockfish 9 64 (60s)"]
[PlyCount "51"]
[EventDate "2019.06.11"]
[EventType "game (rapid)"]
[EventRounds "5"]
[EventCountry "USA"]

{A08: King's Indian Attack} 1. e4 c6

{A first time for me to play the Caro-Kann, although Fritz 11 classifies it as a King's Indian Attack. I usually play some variation of the Sicilian, but didn't want to face Tom's usual Smith-Morra Gambit, although I've usually been able to get out of the opening without committing seppuku against him.]

2. c4 d5 3. exd5 cxd5 4. cxd5 Qxd5 5. Nc3 Qd8

{I considered 5. ... Qa5, but wanted the Queen back home close to the King for defensive purposes - I figured Tom would throw everything he had at me - and he did!}

6. Nf3 Nf6 7. d4 a6 8. Bc4 e6 9. O-O b5 10. Bb3 Bb7 11. d5 b4 12. dxe6 bxc3
13. exf7+ Ke7 14. Re1+ Be4 15. bxc3 Qxd1 16. Ba3+ Kd8

{Simply 16. ... Qd6!! leaves Black way ahead on material, and the immediate attack has been beaten off.}

17. Raxd1+ Kc7 18. Bxf8 Rxf8

{Now I felt a little more comfortable, because I can prevent White from forcing promotion of that devilish f7-Pawn for the near future.}

19. Ng5 Bf5 20. Re5 Bc8

{I began to think I was going to get away with my "Crazy Bob" opening play. I retreated the Bishop so I could prevent the White Knight from getting to e6.}

21. Nxh7 Nxh7

{Now Pawn promotion is stopped for good - I thought.}

22. Re8 Bd7 23. Re7 Ra7

{Focused on holding d7 securely against all attackers. In addition to stopping the f7-Pawn, the Rf8 also protects the BNb8.}

24. Be6?? Kd8

{Trapping the e7 Rook.}

25. Re8+ Rxe8 26. fxe8=Q+

{Black RESIGNED??? I had the "retained image" illusion that the White Pawn still sat on f7!! This has NEVER happened to me before!}

1-0

I learned that I CAN play at Tom's level, even in openings which he is very familiar with, and about which I know nothing. I think this is a good illustration that my tactical play has improved as a result of my training regimen, notwithstanding my oversights on moves 16 and 26.

I also had a mad time scramble against the 3rd highest player [USCF Quick 1634], eventually reaching an ending ahead by two Rooks and two passed Pawns. For the last 15 moves or so, both of us had 1 second left on our clocks. (We were playing with a 3 second delay.) I promoted one of the Pawns and checkmated him, just as my clock went to 0. The Tournament Director ruled that the checkmate occurred before the clock expired, so I won. That was my first win against this person under tournament conditions. He is absolutely amazing when extremely short of clock time (under 10 seconds); no one is able to cause him to lose on time.

30. Tonight we played another bunch of bullet games with Munich.

It looks like his progress was just a temporary change. We stand on the position that pattern recognition is very important while playing bullet games. You simply have to check out it there is simple tactics (especially 1-2 moves!) BEFORE you make your move.

No doubt Munich is a way stronger than me, but I seem to be faster at pattern recognition and simple tactical tricks. This way I can match him at very fast time control. Of course if we would be forced to play 5+0 games I would lose 100 games with the score 10 vs 90.

31. Good experience. Now I decoded another secret I wasnt aware off: in Bullet, you lose if you look too much at your own pieces, and thus dont know what your opponent has just moved.
However, if you drive a car with gears, you do not look at the gearing handle when you shift the gears.
You can do it without looking. And analogue you can play chess without reassuring yourself all the time by looking at the piece you want to move next.

Today I tried to look mainly at my opponent pieces. Where my pieces are I know, and thus there is not so much need to look at them.
The result was immediatly better, here first try with not looking at my pieces (well, of course I look at my pieces, but not as often):
https://lichess.org/tournament/1WSrHFQ1
Performance of 1933, and I feel I could have done even better. It is amazing how much this changes your rating if you do Bullet the "right" way.

32. PART I:

While mulling over my weird resignation in the Hales-Coble game, I realized (perhaps) why I resigned in a totally winning position. (I do NOT consider time pressure to be an excuse; playing within the allotted time is just another part of the game to me.)

Once Tom established the Pawn on f7, I primarily focused on how to maintain a blockade of it on f8. I did not want him to be able to promote the Pawn. As part of that blockade, I kept the Knight on f6 until he sacrificed his Knight on h7. After capturing it, I realized that I could permanently prevent the Pawn from advancing to f8. If a White Rook settled on e8, I would just maintain the blockade - by NOT capturing on e8 with the Rook. When he played 25. Re8, on the previous move I had trapped his Rook, and KNEW I could safely capture on e8 if he moved there. However, when he actually played that move, I panicked, because I thought I had misplayed it, allowing a Queen. Strange how the mind does NOT work!

Back to the subject of PoPLoAFun.

"However obviously the majority of Chess-players may be divided into two big classes of combination- and position-players, in the Chess-master this antagonism is transformed into a harmony. In him, COMBINATION PLAY IS COMPLETED BY POSITION PLAY. By combination the master aims to show up and to defeat the false values, the true values shall guide him in his position play, which in turn shall bring those values to honour. The master is like a man in a learned dispute who knows sophistry but does not make use of it, except for the purpose of exposing the sly subtleties of an artful opponent who disputes a true, sound, vigorous thesis with mere trickery."

IM Eric Kislik (in Applying Logic in Chess repeatedly emphasizes the importance of weaknesses and focal points as some of the first things to consider when trying to determine the next move.

What in heck does that have to do with PoPLoAFun?!?

33. PART II:

Our usual combinational process is to look for tactical themes/devices, working FORWARD on the basis of forcing moves toward an eventual mating attack or gain of material (including Pawn promotion). Our usual positional process is to envision a future favorable position (perhaps on the basis of the Pawn structure), and to work BACKWARDS to find a sequence of forcing moves, (again) with the goal of an eventual mating attack or gain of material (including Pawn promotion).

Suppose we take a different approach using PoPLoAFun.

We no longer look forward or backward on the basis of potential tactical themes/devices; we leave that to the calculation phase. We may be aware of those themes/devices (through pattern recognition) but that is not the focus at this stage. We identify PoPs (focal points) and LoAs for both attacking and defensive purposes. After getting a “feel” for what exists in the specific position, we have identified both the opponent’s and our own weaknesses. We can then begin identifying the Functions of the various pieces that are in conflict (or that may be in conflict) with each other within a few moves and the focal points of those conflicts (the intersection of the LoA). Identification of B.A.D. squares (whether occupied or not) is an amalgamation of weaknesses, focal points and Functions. If a B.A.D. square cannot be attacked with more attackers than defenders, then it is not a weakness at the moment (but may become a weakness in the future).

By focusing FIRST (N-O-T only) on PoPLoAFun, we are much more likely to plan and conduct our play coherently over several moves, rather than haphazardly.

Does this negate the idea of “trial and error”? I don’t think so. Without prefect chess “vision,” we will always have a certain amount of trial and error in our play. I merely seek to reduce it, in favor of KNOWING what the heck I’m trying to accomplish!

The important thing IMHO is to provide a framework within which we can play reasonably good moves, regardless of the situation. I don’t consider a formal step-by-step thought process to be useful. However, a generic prioritized approach (which is NOT dogmatic and allows the flexibility of changing the order of what we are trying to “see” and do) enables us to spiral down from the vulture’s eye view toward the important aspects of the position. How do we know that PoPLoAFun does that? Because PoPs, LoAs and Funs identify the weaknesses. The remainder of the “process” framework is to figure out how to take advantage of the opponent’s weaknesses (if attacking) or to mitigate those weaknesses (if defending), which may be occurring simultaneously on different areas of the board. This involves “seeing” (recognizing the presence of) the various tactical themes/devices (available through System 1 pattern recognition).

By approaching each and every position in this way, we can incorporate the fundamentals of both combination and positional play.