Robert and I seem to be struggling with the precise role of perception and verbalization in the acquisition of tactical skills. Let's try a different angle of attack.
I'm very fond of the Reti manoeuvre. There is a whiff of magic in it. And it seems to express the core of chess: striving for two goals with one move.
But before we can strive for two goals, we must first learn to strive for one goal. That is not as easy as it sounds. My ordinary method of throwing everything to the wall and see what sticks is abysmal inefficient when the tree of analysis transforms into a jungle.
The core of my new method is to use logic as a machete. But logic is awfully inefficient too, because it is applied by system 2, which is notoriously slow by its very nature.
In order to speed up things, we must siphon as much tasks as possible from system 2 to system 1. How to do that?
- look for a goal
- generalize the goal without accepting trivialities
- look for patterns that accompany the goal
Let me experiment with this position:
 |
| Diagram 1. White to move |
1Q6/p3q1k1/1p2p1p1/r2b4/3P2R1/8/6P1/5R1K w - - 0 34
Varuzhan Akobian vs. Blas Lugo (2005)
I had serious trouble to solve this position in trial and error mode.
So how does that logical narrative stuff work?
It helps if you see the following salient cue:
 |
| Diagram 2 |
It is all about the smooth interaction between system 1 and system 2. System 1 might even whisper in your ear "opera mate".
Once you know that h8 is the focal point, the question is how to get there. Via which LoA (line of attack) does the rook reach h8?
Have a look at the LoA:
 |
| Diagram 3. White to move |
The LoA goes via the pivotal point h4. As you notice, h4 is covered by the black queen. So now system 1 should retrieve a logical standard scenario "remove the defender". System 1 does so much more than only pattern recognition. It takes care of every memory retrieval that system 2 might need.
From diagram 1:
34. Qe5+ Kh7
35. Rf7+ Qxf7
36. Rh4+ Kg8
37. Rh8# 1-0
We shouldn't worry too much about how system 1 works its magic. By creating a logical narrative by system 2, we give system 1 the chance to look over its shoulder and create whatever it needs to solve these types of position.
The position might be about an opera mate, what happens after 34.Qe5+ ?
The black king must stay in contact with the pawn, otherwise the white rook invades via Rxg6
The black king must stay in contact with h8, otherwise the white queen will invade
So 34.Kh7
The black queen defends the pivotal square h4. How can I deflect the queen?
The rook sacrifice 35.Rf7+ is a double attack on the black Queen and King. It can't be ignored.
Notice that Rf7+ is difficult to find for trial and error but easy to find for logical reasoning.
35. ... Qxf7 happens to place the black queen on the only escape square of the black king.
This logical narrative should be worked out for every variation like
34. ... Kh6
34. ... Kg8
34. ... Qf6
You know you have absorbed the solution when you start to become bored by your own created word salad (the logical), because you SEE everything with clarity, so there is no need for words anymore. Because words are to sluggish and imprecise.
The LoA system provides a simple logical framework which makes it easy for system 2 to build its narratives around. Those verbal logical narratives are just temporary side wheels.
What goals are we talking about?
ReplyDeleteFirst there is a big goal. Getting the rook to h8. In an ideal world, we start with the goal and work backwards.
But every move is guided by one or more goals. Look at the little goals when the black king is in check after 1.Qe5+
- prevent invasion of the queen
- protect pawn on g6
The big goal is Rh8. But the little goals are how to get there
- free h4
The logic narrative is geared around the big goals and the little goals. The task of system 1 is to retrieve those goals from memory from previous games with similarities. The more you can retrieve from previous positions, the less you need system 2 for it.
There is a finite amount of goals (protect the pawn, prevent invasion). If you know the goal, you usually find ways to reach them. Initially, you need system 2 to find the goals. The training must accomplish that system 1 retrieves the standard goals from memory.
Do I need a grand scheme of generalized opera mates so system 1 recognizes it in every position where an opera mate is hidden?
ReplyDeleteOr do I need a list of standard goals (like continue to protect that pawn, prevent invasion) that can be accomplished by one move?
Or do I need a list of standard scenarios (like remove that defender from guarding the pivotal square)? A scenario is often implemented by a series of moves.
Probably all three. It are all three tasks that are suited to be siphoned from system 2 to system 1.
They all have a different frequency of occurrence.
The individual goals of a move happen every move.
The goal of a scenario is based one or a series of moves.
The goal of an opera mate happens from time to time in a game.
Hence our emphasis must lie on the first two types of goals.
All three types of goals are fairly finite. Wouldn't it be a great help when system 1 would let them pop up when needed and relevant? That would be a grand trick!
PART I:
ReplyDeleteTemposchlucker asked the following rhetorical questions (simplified):
Do I need a grand scheme of generalized opera mates?
Or do I need a list of standard goals that can be accomplished by one move?
Or do I need a list of standard scenarios?
My answer would be a qualified “No.” Those things are not needed in order to increase chess SKILL.
The basic problem with any “grand scheme” (especially a generalized scheme that is devoted to a specific theme/device) is that it attempts to cover too much territory succinctly. The only way to develop such a scheme is to abstract far beyond any useful level. It is the same problem illustrated by the idea of “general principles.” Such “rules” are very useful for NOVICES to avoid some of the most egregious problems caused by lack of skill. Unfortunately, as skill increases linearly, the number of exceptions to those “rules” increase exponentially, with a corresponding increase in memory load that becomes unusable.
The problem with the second two is similar. There are myriad potential “goals” for any given move. There are any number of standard “scenarios.” As those numbers increase, so does the memory load. Given the limited time available (assuming tournament games), going through the lists becomes prohibitively expensive.
As you noted, “All three types of goals are fairly finite. Wouldn't it be a great help when system 1 would let them pop up when needed and relevant? That would be a grand trick!”
The number of moves in a game of chess ARE [NOT “fairly”] finite, but for practical purposes, they are infinite.
That brings us to the “grand trick.” Simply put, this is the child prodigy “trick.”
I have emphasized PERCEPTION as the basis of that “trick.” A child does not have either the logical or verbal skills of an adult. A child also does not have the educational “process” hammered into his psyche through endless repetition in every subject.
The fact that MDLM needed only 1134 problems to gain 400 rating points is an indicator that the amount of scenarios is finite AND that you can use almost any suited problem set.
DeleteThe amount of COMBINATIONS which you can create with the scenarios is infinite.
PART II:
ReplyDeleteGM Abhimanyu Mishra (the current record holder for being the youngest grandmaster in chess history at age 12 years, 4 months and 25 days) learned how to play chess from his father at age 2.5 years and began tournament play at age 5. He gained the IM title at age 10. His father (his first teacher) estimated his own approximate rating as 1400-1500 USCF (that would be approximately 1200-1300 FIDE). It hardly seems possible that someone so young could build any kind of “grand scheme” or lists of standard goals and scenarios. Too bad that László Polgár only published the exercises he gave his three daughters, and not a detailed explanation of the course of training he used with each of them.
Let’s try a perception example, not directly related to chess. Take a glance at the following picture. (Sorry: you’ll have to follow the link; I don’t know how to embed an image in a Blogger comment.)
What do you SEE in that first instant?
LINK: https://i.ebayimg.com/images/g/vTIAAOSw4aRdOUtj/s-l1600.webp
Now, after that first impression, how is that image associated with one of the most famous of optical illusions? Have you ever seen it previously?
If you answered “It’s a variation of the Vase and Two Faces illusion,” congratulations! You just demonstrated System 1’s marvelous ability to instantly take in different stimuli and arrive at the most likely answer — with no “grand scheme,” and no lists to be searched linearly, even though the usual picture is black and white, and readily allows for the foreground and background to be mentally switched back and forth without any effort (called “figure-ground reversal).
Out of curiosity, I counted the number of puzzles associated with each category of tactics given in Frank Erwich’s book 1001 Chess Exercises for Club Players. It seems that 50-100 exercises are considered (by him) sufficient to extract the essence and “cement” a particular theme/device into System 1. That number of different contexts/examples for the same perception/conception should provide all the information needed for System 1 to subconsciously generalize that information and trigger recognition whenever a new (slightly different) situation is encountered.
Or, as usual, am I missing something important?
Yes, Virginia, there really is a Santa Claus!
Source: https://publicdomainreview.org/collection/yes-virginia-there-is-a-santa-claus-1897/
Lying about Santa learns your children two things:
DeleteLying is allowed and you can't trust your parents.
If that is what you want to learn your children, then it is ok, I guess.
"Or, as usual, am I missing something important?"
ReplyDeleteThe grand schemes and things are meant for system 2 so that it creates its word salad more efficient.
That the amount of scenarios is finite is an observation, not an assumption.
There is no need to create a perfect word salad. Since the word salad acts as side wheels and is only temporary. You abandon it as soon as system 1 has worked its miracles.
What you might be missing is the role of perception. In the next post I discovered accidentally what that role might be. Inspired by your perseverance to have a look at perception despite my bias.
Every problem has a basic scenario, and often a lot of distractions. The first skill to learn is to see the basic scenario. That what makes the combination tick. Where the gain comes from. Once that is learned, when you see that for every problem in your problem set, you can go a step further.
ReplyDeleteEvery "distraction" has its own scenario too. You will have to learn to SEE those scenarios too.
"Too bad that László Polgár only published the exercises he gave his three daughters, and not a detailed explanation of the course of training he used with each of them."
ReplyDeleteActually, I belief he had done that. In hungarian. Maybe mr. Z can have a look at it, if he is still reading this blog (which I doubt).
I found this online PDF of Polgar's book Raise a Genius!:
DeleteLINK: https://slatestarcodex.com/Stuff/genius.pdf
(This is Robert. For some reason, I log into Google but Blogger refuses to acknowledge the login. No idea how to get back to commenting as me.)
(Robert here as Anonymous)
DeleteIn the Polgar book Raise a Genius!, Chapter III., Section 2. How did the Polgar sisters learn how to play chess?
I know that you possess a large library and card file system with 200 thousand records. How did you use this at the start, and how are you able to use it now?
We have a library with 4-5 thousand volumes that greatly helped with the children’s instruction and learning. It is well organized and provided with several different catalogues. We organized the card file system (which we have just supplemented with a computer database) by the names of players, variants of openings and types of middlegames. The girls knew how to use it from a young age, and if they need anything, they can find it in seconds. The chess books serve us as manuals.
We use the card files for openings as a first step in inventing new openings. For a single variant we look through 50-100 matches, to choose - mainly for comparison - the most appropriate, but my daughters themselves are capable of inventing novelties. And because this catalog contains complete games, they can on those occasions study the middlegames of those matches. The database is similarly suitable for writing articles and analyzing matches.
We use the catalog by names to prepare for opponents. We developed the catalog of middlegames for two purposes: one is strategy, the other is the tactics of middlegames. A section of middlegame strategy contains 40-50 types. For example, an isolated pawn, castling long, occupying open lines, etc. In a section of tactics, for example: gambits for major pieces in squares f7, g7, h7, g6, h6, f6, d5, c3, or intuitive pawn and major piece gambits, etc. If I want the children to look over some type, for example, they research 50-100 examples of it, and after this study they become informed enough to be certain of the legalities and induce generalizations. We do not have an organized collection of end-games in the form of card files, but we have enough related books. The encyclopedia of endgames published in Yugoslavia, and the collection of pawn and rook endgames, etc., are very good material. They substitute for the most part for the card file.
Children at an early age like mate combinations of two or three moves very much. These are not too difficult, but aesthetically very beautiful and entertaining and help the children master the mate, develop their combination ability, and enjoy the game of chess. We have already released two books about two-move mate combinations, and we still have a lot of material in manuscript form.
~+~+~+~+~+~+~+~+~+~+~+~+~+~+~+~+~+~+~+~+~+~+~+~
Aha! Empirical confirmation of my “guess-timate” regarding 50-100 examples being sufficient for training purposes of a particular aspect.
Furthermore, in March 2025, an autobiography of Susan Polgar will see the light.
ReplyDelete(Robert here)
ReplyDeleteThis is the message I get from Blogger when I try to comment using my Google account:
Unable to sign in to comment. Please check your browser configurations to allow sign-in. Learn more. You can still comment anonymously, or with name and URL.
I signed out completely, then signed back into Google, and then into Blogger. When I click on "Google Account", I still get the message. This is very Irritating!
Any suggestions for how to get around this will be greatly appreciated!
I think I have finally figured it out. If you make a comment from a different device (switching from my laptop to my iPhone), there is a "Recent security activity" message that REQUIRES confirmation that it was YOU who signed in on the other device. If you do not confirm it was you, then Blogger will not accept your Google account for comments. I just verified that it was me on both my laptop and iPhone, and now I can comment as me (as is evident from this comment). Bizarre: I was thinking about this problem while asleep, and had this sudden insight into why it might be happening. (I have been away from the silicon software war too long.).
DeleteExcellent!
ReplyDelete