## Wednesday, April 12, 2017

### Convergence squares

If I look at the diagram of the previous post, I find it difficult to express what is needed. After studying this position for quite some time, the moves are so evident that I simply cannot understand why I didn't see the simplicity of the position before. At the mean time, I fully acknowledge that there is no guarantee at all, that I will able to see the simplicity of similar positions in the future. I can impossible tell what I need to learn from this position that will be transferable to other positions. It seems that words are a too lousy vehicle to do that.

Maybe that is a positive sign. When something descends from the conscious to the unconscious, we don't know how that happens, and words cannot express how it works. You learn how to push the breaks and to shift gears when you turn right, but you can't possibly tell how you calculate the right speed, how you judge the right noise of the engine and how you calculate the correct power to apply to push the steering wheel. But then again, maybe I'm just deceiving myself here.

One point springs out, when I considered 1. ... Ne6, I didn't realize the importance of f7. The alternative point of pressure f7 gives white a counter attack (1. ... Ne6 2.Rd7). This means that it must be good to cultivate the habit to look at the points of pressure

And maybe that is how we should formulate it. We have to develop a few good habits. These habits are mainly visual, it seems. Aox said:

"This "splitting of the whole problem in a sequence of sub-problems and then to solve them" costs---->time!!"

He  certainly has a point here. We must not look for an algorithm that guides our logical thinking. I have tried that a few times in the past, and the trade-off between better thinking and time usage has always been negative. Not to mention the drain of mental energy.

This means that it is not quite clear how to proceed. As said, it is probably best to cultivate a few good habits. The algorithm I'm busy to develop isn't a goal in itself. It is meant to identify the habits we need to cultivate.

Take for instance the following position:

 Diagram 1. White to move

4r1k1/pqr1pp1p/p1Nn2p1/3P4/5QP1/8/PP1R1P1P/4R1K1 w - - 1 1
[solution]

What habit do we need to cultivate in order to transfer something from this position to similar positions? Feel free to comment already. I will update this post later.

UPDATE
What do we fancy that our RC-chess module should shout in our ear here?: Rb8!!

I have seen this mechanism working over and over again the past months. The moment my attention is guided to the right place of the board, the missing piece of the puzzle immediately pops up.

Every square of the board is screaming for our attention. Some squares shout harder than others. b8 is not screaming hard enough, so its sound drowns in the overall background noise, and is overpowered my the squares that seems more interesting.

What is so special about b8? What makes it different from c8 or a8? The difference is of course that the white knight and the white rook converge at b8. Chances that you can post a rook on b8 safely are higher than that you can post it on c8 or a8.
We can know beforehand, that converging squares are going to play a crucial role in any combination. So if you are stuck while forward thinking, you can start to look at the converging squares of the second order. If the squares of the first order don't work. There is no reason to look at non convergence squares.

The unconscious mechanism to let pop up the right solution is already well developed and put into place. The only thing that is missing  to ignite it, is the little spark of attention that leads us to b8.

Of course it would have been nice if the black queen was recognized as a sitting duck during the initial scan of the position. But I already identified the points of pressure and the lines of attack as a toolkit to help to find the most immobile pieces. The black queen has five squares where it can stand safely, so it doesn't look immobile until a rook appears on b8.

THE METHODS FOLLOWED IN THE ANALYSIS OF A GIVEN POSITION BY COMBINATION AND BY THE CREATION OF PLANS ARE DIFFERENTIATED BY THE DIRECTION OF THE UNDERLYING THOUGHT. THE COMBINATION-PLAYER THINKS FORWARD: he starts from the given position and tries the forceful moves in his mind; THE POSITION-PLAYER THINKS BACKWARD: he conceives a position to be arrived at and works toward that position of which he is more conscious than the one on the board. He "sees" successive stages of the position aimed at and he visualizes the stage in a reverse order. If one position, according to his plan, is to follow another he "sees" the one that is to follow first and he deduces, as it were, the anterior position from it.

To be honest, I was a little worried by this citation. It seemed as if the adult-chess-tactics-improvement-method I'm developing is different from the young-prodigy-way-of-chess-tactics-improvement-method. It is unlikely that nature is so prodigal that it allows two different ways, one by forward thinking and one by backward thinking, to learn the same skill, and that the end product of both ways will be equally effective.

But Aox put me on the right track again by pointing out the danger of introducing slow thinking into the method.

I'm sure that the young prodigy has picked up a few obvious idea's along the way, and has made looking for convergence squares of the second order a habit long ago, while even not remembering that fact consciously later on. And we should do the same.

1. I have NO IDEA, but when I can move the pieces I can discover the solution pretty soon (without the engine help).

This way I think we can make a TRANSFER between the biggest duck and a very big one!

What do I mean is to do the same to the Queen what we wanted to do with the King. If we restrict completely, we can attack it and win it!

The most funny thing was the fact I KNEW the first two moves (they were "totally obvious to me"), but I could not figure out the third (key) one!

Now I got why this position is too easy to handle, but a lot of people can missed the key move! Maybe we can ask the question: If I sacrifice the Q for B+N, can I mate the king OR win the Q (or R) in this specific line? If we had asked that question, the sacrifice would have been A PIECE OF CAKE!

1. You said: " but when I can move the pieces I can discover the solution pretty soon".

I suspect since a long time that your visualisation is bad. You can solve "flat" puzzles in hyperspeed but there is a cut of at puzzles with some "depth".
I suggest to do some calculation/visualisation/memorisation training. i guess that this would boost your chess the most and quickest.

2. I suspect that there is nothing wrong with the visualization skills of Tomasz. But maybe he makes things overcomplicated. His analysis of complex positions is not unlikely to start with the story of Adam and Eve and end with the latest findings in quantum mechanics ;) When the position allows that he doesn't think too much, he performs best.

3. The reason that I suspect that there is nothing wrong with the visualization skills is this post, see last diagram

Tomasz commented:

The last puzzle was AMAZING! I have solved it within 2 minutes!!! I am really proud of myself as I noticed the theme (motif) immediately! After that I thought it is mate in 3-4 moves, but the King ran away quite a long way. Anyway I checkmated it at move 8! It was great pawn move - 8.g6 mate final! :)

4. Yes possible too,.. bad thinking habits.. unorganised thinking, lack of concentration.... Should be extremely !!! beneficial to detect exactly : what it is and to work on it

5. I probably have it all (the list is not exhausted):

- unorganised thinking
- lack of concentration
- lack of visualisation
- lack of motivation
- lack of perseverance (and persistance)
- lack of following logical observations (conclusions)
- lack of making conclusions

Anyway I like guessing tactical puzzles even if all the chess world does it methodically, logically and systematically in a correct way with organized thinking and making conclusions :)

6. @Tomasz, I didn't mean to offend you or to ridiculize your efforts. I reacted to an observation of Aox with an observation of my own. I exaggerated it a little (a lot) because I thought that was funny between all the seriousness here. If you don't like that, I will respect that in the future and I will apologize. I don't spare my own sensitivities when I write down my observations about myself, and I tend to do the same with other people. Since I don't want to deprive them from the chance to learn something.

7. Oh Jeezee... :D

It is the problem with communication without the access to the emotional side of our partner (in the discussion).

I listed these elements (traits) to show that EVEN I have a huge problems with "perfect approach" something may be done with that. It may look the way I wrote it down because I was fury, but in fact they are my problems to overcome.

I try to broaden the distance to my own and to laugt at myself every time I have a chance for it. And in addition I use irony and sarcasm quite often. I hope this explanation is a good guide for a future misunderstandings ;) :).

You can criticize me effort as much as you wish ON ONE CONDITION. Do it constructively - show me what is wrong and what should be done to overcome it. And respect my will not to do or listen to your advice.

BTW. At the last paragraph I used "you" as a plural - not just you Tempo, my dear chess friend :).

2. Part of the vision problem (IMHO) is failing to "see" potentialities that are (1) disconnected from the most "obvious" moves, and (2) that are in different areas (I almost stated "quadrants" but that is the wrong idea) of the board, and therefore "apparently" disconnected from each other. Connecting two (or more) different areas of the board is at a higher level of "chunking" than connecting various pieces into one coordinated attack in one area of the board. It is similar in IDEA to decoying away a potential defender from the target area. For example, during a king-side attack, we do NOT want a specific piece [perhaps a Knight] to be able to take up a defensive location [perhaps f6]. We decoy it away from the area that we want to penetrate with the REAL attack, using a piece that is not currently required in the REAL attack.

I think there is a "clue" that can be and should be "seen" in similar positions. The Black Queen is confined to a "T" arrangement of squares: a8-c8 and b8-b4, caused by the Black Rook move to c7. Question to be asked: Which piece can take advantage of that lack of mobility? A ROOK. It is merely coincidence that a Rook move created this possibility, and a Rook move can take advantage of that possibility. The question then becomes: Can I get a Rook to b8, and if that is POSSIBLE, HOW DO I DO IT? As Tomasz noted, the first two moves then become "obvious" (in some sense) IFF we "see" the possibility in a totally different area of the board as significant. It is that third move that requires looking at "future" PoPs and LoAs based on the limited mobility (immobility?!?) of the Black Queen. White retains an extra Knight at the end.

I'm petty sure the following position was previously posted here, but it illustrates the point I am trying to make regarding "connecting" two (or more) areas of the board into a single coherent IDEA. It is the first example in Weteschnik's Understanding Chess Tactics, Chapter 10, page 177, from the game between Borisenkov - Mezenev, USSR 1950. (I can't find this game in the USSR 1950 Championship. Borisenkov is spelled G. Borisenko. I have no idea who Mezenev is; he's not listed as playing in that championship.)

FEN: 8/8/8/8/5k2/1p3pR1/bK5P/8 b - - 0 1

3. Material : =
Tactical weaknesses : In endgames usually more or less every piece is weak ( a HE )
What is the puzzle about : Material
I "saw" that QxN PxQ RxR+ don't lose much material and did calculate some short forcing lines like Rxe7 Rxe7 Qxd6. A little confused how to continue i did start looking for the type of HE`s of the pieces and i recognised that the black queen is immobile. In this moment i did know whats going on.
What might have helped me is my present training with strategy 3.0 of chessok. At the moment i study the lesson "Disposition of pieces"

4. I don't know if anyone else looked at the game (given below) from which this position was taken. It's informative!

It is fascinating that we amateurs beat ourselves up over "missing" the "obvious" tactical "kill" shot after
23. ... Rc7 - GM Ehlvest also missed it! Either that or (probably more likely), he had already assessed the
position as "won" and continued his plan. He just continued to pile on the pressure on e7 with 24. Rde2. IM Shahade
gave up an exchange to get out of the looming kingside attack, but lost his Queen for a Rook and resigned.

[Event "56th NY Masters"]
[Site "New York USA"]
[Round "4"]
[Date "2003.5.13"]

[White "Ehlvest, Jaan"]
[Result "1-0"]

1.d4 Nf6 2.c4 g6 3.Nc3 d5 4.Nf3 Bg7 5.Qb3 dxc4 6.Qxc4 O-O 7.Bf4 Na6 8.e4 Bg4 9.Ne5 Nh5 10.Be3 Be6
11.Qa4 c5 12.Bxa6 cxd4 13.Bxd4 bxa6 14.Nc6 Qc7 15.Bxg7 Nxg7 16.O-O Rfc8 17.Rfd1 Qb7 18.Nd5 Bxd5
19.exd5 Nf5 20.g4 Nd6 21.Qf4 Re8 22.Rd2 Rac8 23.Re1 Rc7 [POSITION ABOVE] 24.Rde2 Rd7
25.b3 Qc7 26.Re3 Nc8 27.Qh6 Rxd5 28.Rh3 Rh5 29.gxh5 Qxc6 30.hxg6 Qxg6+ 31.Rg3 1-0

This reminds me of a simultaneous game I played against GM Arthur Bisguier in 1980 (the only game I've ever played against a GM). Not because I played good (I was never really in the game at all), but because he played simple lines without mind-numbing tactics and just let me implode on my own.

[Event "Simultaneous Exhibition"]
[Site "?"]
[Date "1980.10.25"]
[Round "?"]
[White "Bisguier, Arthur"]
[Black "Coble, Robert"]
[Result "1-0"]
[ECO "C66"]
[Annotator "Stockfish DD 64 SSE4.2 (10s)"]
[PlyCount "65"]

{C66: Ruy Lopez: Steinitz Defence} 1. e4 e5 2. Nf3 Nf6 3. Nc3 Nc6 4. Bb5 d6 5. d4 Bd7 6. O-O Be7 7. Re1 O-O
8. Bxc6 Bxc6 9. dxe5 dxe5 10. Qxd8 Raxd8 11. Nxe5 Bxe4 12. Nxe4 Nxe4 13. Nd3 f5 14. f3 Bh4 {last book move}
15. g3 Nxg3 16. hxg3 Bxg3 17. Re2 Rde8 18. Rg2 Bd6 19. Bh6 Rf7 20. Rd1 Kf8 21. Bf4 Re6 (21... Bxf4
22. Nxf4 Rfe7 23. Kf2 \$18) 22. Kf1 (22. Bxd6+ {seems even better} Rxd6 23. Re1 b6 \$18) 22... Ke8
(22... Rfe7 23. Bxd6 Rxd6 24. Kf2 \$18) 23. Re2 (23. Bxd6 \$5 {makes it even easier for White} cxd6
24. c4 Rh6 \$18) 23... Rxe2 24. Kxe2 Rd7 25. Bxd6 Rxd6 26. Ne5 (26. Rh1 h6 \$18) 26... Re6 \$2
(26... Rxd1 \$142 27. Kxd1 g5 \$18) 27. f4 \$18 g5 28. Kf3 g4+ 29. Kg3 Rd6 (29... a6 \$18
{there is nothing else anyway}) 30. Rxd6 cxd6 31. Nc4 Kd7 32. Ne3 Ke6 33. c4 1-0

1. Robert, good point. Do you think at the end of the tournament, they announced Ehlvest has left the Building? .....

2. Only if he was wearing blue suede shoes - LOL!

3. https://en.chessbase.com/post/us-chess-legend-arthur-bisguier-passes-at-87

5. Instructive position. This is a nice little tactic that would of been fun to play as white . I think I need a duck identification class. Second post in a row where I did not follow through to quiescence. Didn't see a useful place for the rook to move after delivering check; I stopped calculating. Most likely a lesson here for me.

6. Time for another experiment. . .

FEN: 8/5ppp/8/5PPP/1p6/1k6/8/1K6 w - - 0 1

What should be the outcome?

How did you go about forming your opinion of what to play?

Thanks!

1. FWIW:

The outcome is a White win.

There are three distinct ways of "looking" at this apparently simple endgame.

(1) Using the concept of the opposition.

Black has an outside passed Pawn and his King is ahead of the Pawn. If the other Pawns on the other side of the board were eliminated, Black would be winning because the White King must give way, allowing Black to advance his King and support the Pawn as it moves toward promotion. There is some trickery involved which requires Black to avoid a possible stalemate, but nothing that can't be worked out rather quickly at the board.

(2) Using the Silman concept of "Fox in the Chicken Coop."

Black abandons the Black Pawn to its fate, and goes after the White Pawns with his King. There is nothing that White can do to stop this idea IFF there were nothing else in the position; BUT, there is!

(3) Using tactics to force a White Pawn through to queening.

This requires special knowledge; without it, most class players would not suspect that White is winning IFF he knows how to do it.

The first point is that White can employ a duplo attack. By 1. g6! there is a fork and an immediate threat to take either the f7 or h7 Pawn, creating a passed Pawn which is very close to promotion. Black MUST capture the Pawn.

The variations now split into two branches. The procedure is the same in both variations: it is to create a second duplo attack, using two Pawns to attack two Pawns. Black must choose one or the other, allowing the second attack to succeed by bypassing and then promoting that Pawn.

(1) 1. ... fxg6 2. h6! gxh6 (2. ... gxf5 3. hxg7 and the Pawn queens) 3. f6 and the Pawn queens.

(2) 1. ... hxg6 2. f6! gxf6 (2. ... gxh5 3. fxg7 and the Pawn queens) 3. h6 and the Pawn queens.

My point is this: if you are missing specific knowledge (how to force the Pawn through in this specific configuration), then it is highly likely that you will focus on one or both of the first two general ideas, and assume (without detailed calculations) that Black is winning. It demonstrates that we have to consider Lasker's idea of "balance" across the ENTIRE BOARD at all times, not just the local situation in one specific area of the board.

Connecting the various areas of the board is very difficult to do, especially if working at the level of moves. This is the advantage of the vulture's eye view, looking for PLF FIRST, then combining these into motifs, then identifying potential tactical themes/devices and only then formulating combinations (connecting everything "seen" into a coherent whole). Since the motifs MAY be offensive or defensive in specific areas, these ideas constitute "playing in accordance with the requirement(s) of the position."

7. I have added an update to the post in blue.

8. Vis-a-vis the Lasker quote referenced in the Update. . .

The important idea (IMHO) is encapsulated in what followed that excerpt:

In looking for a combination the given position is the essential thing,
in the conceiving of plans the intended position is the root of MY thinking.

[Note: Lasker is describing his own thinking processes in THAT statement!]

THE MASTER UTILIZES BOTH DIRECTIONS OF THINKING, ALTERNATING BETWEEN THEM
WITHOUT THINKING ABOUT THE THINKING PROCESS.

I do NOT "see" a correlation between what mister Lasker stated regarding the
opposing orientations of AMATEURS (combination-player thinks forward;
position-player thinks backward) and the (potential but very unlikely) connection
between those two archtypes of AMATEURS and adult "improvers" (forward thinking combination players?)
vice young prodigies (backward thinking position players?). I don't think that is the case at all.

Please note that the following point is NOT "aimed" at anyone in particular - except (perhaps) ME.
I am as guilty of faulty "thinking" as anyone else.

I think that adult chess improvers (with extremely rare exceptions) approach "improvement" from a
totally different perspective from young prodigies. I also think this is why most adults fail to improve
as fast or to the level of which they are potentially capable.

The adult relies heavily (perhaps almost exclusively) on SLOW rational thinking (* System 2). He does this
when trying to learn patterns (or "chunks" or "templates"). He does this when trying to devise a "rational"
(perhaps all-inclusive) thinking "process." He does this when he tries to "solve" a problem or a position.
The emphasis is on logical reasoning. If you doubt this assertion, simply re-read this blog and the comments.
In every case, the emphasis is primarily on REASONING.

The young prodigy does NOT rely on rational thinking. Instead, he relies on FAST intuition (* System 1).
He is exposed to a position. He does not reason his way to a general "rule" which covers that situation.
He merely(!) "sees" (intuits) a "solution" and tries it. If it does not work, he does not REASON out why;
he simply looks for another (similar in some aspect of chess) and tries again.

I know that is a very simplistic view of the differences. IMHO, it does succinctly capture the differences.

Time after time, we collectively have arrived at a logical "solution" to how to improve - and yet, we do NOT.

Perhaps it is time to change our approach and try what the vast majority of masters suggest as the "tried
and true" method of chess improvement.

I am quite sure that anyone reading this will immediately jump to the thought "Physician, heal thyself."

I'm working on THAT!

* Thinking, Fast and Slow, Daniel Kahneman, C 2011

System 1 operates automatically and quickly, with little or no effort and no sense of voluntary control.

System 2 [consciously] allocates attention to the effortful mental activities that demand it, including
complex computations. The operations of System 2 are often associated with the subjective experience of
agency, choice and concentration.

1. we may watch on how several masters think and solve tactical puzzle. They have different methods for different types of positions but a main method seems to be to generate a prototype of the mainline, using patterns/ideas they spot, not only at the beginning (first move(s)) or end ( goal ) but at any location in this line too ( try to make use of a potential discovered attack at some point for example ) . It's a type of genetic process using methods of inverse move-orders and so on; then they try to tune the line and at the end its been blunder checked.
The videos of the actual thinking of grandmasters give a hint what should/must be improved to solve tactics at masterlevel ( not necessary how ).
To analyze the patterns of "points of pressure" and so forth as tempo does here is a type of deliberate training which might help to improve. But when i watch masters solving tactical puzzles i think there is a lot more to do.

Since 4 months i am using a modification of this method : https://drive.google.com/file/d/0B7CnosTj8wPhTjk0TDU4U1BpX2M/view with the hope to gain more and better chunks. Its a deliberate training with sequences of master-games sorted by themes.

2. But, but: what about the Kotovian 4-step process?

(1) List all candidate moves FIRST, before anything else;
(2) Calculate each variation in turn;
(3) Visualize all possible lines as a "tree of variations"; and
(4) During a GAME, each branch of the tree must be examined once and only once.

(Just kidding; GM V. Beim pretty much demolishes that process in his book How to Calculate chess Tactics. I actually prefer the much shorter question by GM A. Lein: "I don't think like a tree - do you think like a tree?", quoted in GM J. Tisdall's excellent book Improve Your Chess NOW.)

I had bookmarked GM Irina Mikhailova's training plan some time ago. Given the intensity of the training and the time requirements, I came to the reasonable conclusion that I personally was never going to be able to even attempt it.

I was amused (a little) by the Monday-Thirsday "Weekday plan of individual studies in a computer class 1998" which required 4.5 hours per day of training, for a total weekly time commitment of 16 hours. (I am easily amused by ironies, such as touting a computer based training solution and then not using the computer to check the schedule math.) At 4.5 hours per day, who cares if that would total to 18 hours per week? Oh well, as long as the proposed program achieves the planned goal of reaching FIDE 2400 (IM level), the math doesn't matter.

I applaud your choice to use sequences of master games sorted by themes.

Best of luck to you!

3. It is 4 * 45min of study + 30 min of --rest-- and this 4 times a week ( i do more ! ). 45min is 1 School-hour. So: her math is ok. The "trainingsplan" is an abstract of her PhD thesis in Pedagogics.

4. @ Aox:

Thank you for the clarification! I thought it "odd" that the math didn't work out; I was unaware that 1 school hour was only 45 minutes long.

This plan is one of the most detailed I have ever seen, especially incorporating existing computer software to assist the process.

Have you noticed any appreciable improvement so far after 4 months of intensive training?

5. The pupil in this thesis did not improve "sharp" during the first year and i dont play enough chess to see any improvement yet
The last 10 years i did tactics,tactics,tactics so i did start now with Strategy 3.0 only with ~~ 4 * 45min * 6 per week ( because it did interest me most ). It will take me estimatingly an other 3 months to reach the requested level of 80+ %. Next is planed to do endgames because the baseline requests the knowledge of 250 endgames. At the same time i will make shure that i stay at the same level in Strategy 3.0. Begining 2018 i will get closer to the trainingsplan and mix the different subjects and games as shown in the plan.

9. I consider the prodigy to be the average (grand)master in his younger years. Just to avoid misunderstandings. The scope of forward thinking is limited by numbers. I don't think that this scope is different for prodigies and adult amateurs. Since the numbers are the same, and the physical build of the brains is roughly the same.

This and the previous posts describes how the scope of forward thinking (system I) can be extended by changing the numbers. The numbers are changed by pruning the tree of analysis. Backwards thinking is able to prune the tree of analysis. We accomplish backwards thinking as system II. I hypothesize the following:

The prodigy transfers his backwards thinking from system II to system I without knowing it. His system II thinking is as slow as our system II thinking. And even his system I thinking is as fast as our system I thinking. But since he is able to recognize the squares that are the stepping stones of backward thinking FAST (since with system II), he is able to prune the tree of analysis. Which makes his forward thinking looking as much faster than our forward thinking. Which isn't true, since he calculates less due to the pruning. I predict that we can learn to transfer our backward thinking from system II to system I too.

We should automate the scan for stepping stones for backward thinking. Like the search for the b8 square in the position.

1. But since he is able to recognize the squares that are the stepping stones of backward thinking FAST (since with system II) should read: But since he is able to recognize the squares that are the stepping stones of backward thinking FAST (since with system I)

10. Interested where this will go. I spent a lot of time without much thought doing the mdlm circles. Intuition didnt follow. It wasnt until i started to understand and notice structure did intuition follow.

1. @ Jim takchess:

Thank you for the reference to Mr. Winter's remarks regarding the Theory of Steinitz, which MIGHT be better attributed to Dr. Lasker. I followed a link, and found this note by Dr. Lasker, in response to an earlier criticism.

Emanuel Lasker, on pages 464-465 of the November 1933 BCM:

Now as to my philosophy.

Mr Goulding Brown disarms me by claiming for himself no authority whatever in that domain. In speaking of the reason of a plan I did have an end in view. Many chessplayers have peculiar notions as to how a chess master does his thinking, and it is not easy to make them understand. Language is pregnant with old philosophical thought, and a new idea, in making use, as it must, of old terms, has to rely on the reader’s imagination and good will. The motive for a plan, the reason of a plan, the raison d’ĂȘtre of a plan, all these arise from valuation. I wanted to suggest this idea. If the reader grasps it he will more readily understand that a new style of planning must be generated at a period when valuations have undergone a change, and that it cannot arise nor be logically founded in any other way.

I simply note the importance that Dr. Lasker placed on developing your own valuations if you wish to progress in chess.

Thank you for the reference!

2. @ Jim takechess

I have spend a dozens of hours at salt mining... actually I am probably one of the few crazy guys who has solved (done) 120-130K positions (repetitions) of mate in 1 easy puzzles. Some people say: IT IS INSANE!!! ;) :)

There was the time we had been working on salt mines. Here you can check it out by yourself: http://temposchlucker.blogspot.com/search/label/salt%20mines

3. @tomasz. Yes i see that we share in the saltmining struggle.although mine is more measured than it was ten years ago. 8) Cheers, Jim.