Exploring the boundaries
Not only have I found a way to train tactics that works, but by focusing on 2 movers (3 ply) recently, I have found a way to do it in an efficient way too.
Since May 1st I focused on mate exercises solely. Since I adhere the adage that the fastest way to come to a conclusion is to make extreme choices. A 2 mover usually involves two or three logical narratives at average. So far 6 narratives is the maximum that I have found. This means that a mate in two is complex enough to study everything that is important around mates. It doesn't make sense to start with 3 movers until you fully master the 2 movers. If that is even possible.
This weekend I have been busy to inventorize the logic of 100 mate in 2 exercises and combine it in one coherent logical framework. It turns out that all logic can be captured in the PoPLoAFun system when I extend that with some logic concerning killboxes.
There are only about 8-10 logical actions to choose from when working on a mate in 2. Think of clearing a line of attack, build the wall of a killbox, herding the king into a killbox et cetera.
Furthermore there are about 8-10 salient cues that you must learn to recognize. Think about the line of attack, the point of pressure, the defender of the point of pressure and the like. So that is pretty straight forward.
Currently I'm trying to do the same with all the other tactics. There are about 10 times as much occurrences of tactical motifs that don't lead to a mate. So it is 10 times as likely that you encounter these logical ideas in a game. Whether this means that the logical framework is 10 times as vast remains to be seen. I will keep you posted.
PART I
ReplyDeleteIn Hofstadter and Sander’s excellent non-chess book (with several illustrations from chess) Surfaces and Essences: Analogies as the Fuel and Fire of Thinking, there is an implicit ‘definition’ of pattern recognition: an “implicit perception of sameness, which is to say, based on an analogy.” This perception can occur on multiple levels, depending on the level of expertise of the perceiver (perhaps best captured in the aphorism “Beauty is in the eye of the beholder.”). To a novice with a hammer, the entire world looks like a nail. The salient features change (become more abstract and on a deeper level) with increased expertise. A novice cannot “see” beyond the purely surface features because, to them, those features ARE the salient features!
As I was contemplating these ideas, I realized that an increase in skill corresponds to the ability to abstract. A very narrowly defined category can be broadened through digging deeper into the salient characteristics using the notions of commonality and differentiation – what do two (or more) things share in common and how do they differ from each other? It is only as we perform a process of abstraction that we become aware of commonalities (the shared essence) in situations (positions) that have nothing at all in common on their surfaces.
I reread Linhares and Brum’s excellent paper Understanding Our Understanding of Strategic Scenarios: What Role Do Chunks Play?. The original papers on ‘chunking’ postulated that chunks are built by encoding combinations of pieces-on-squares and that chunks are formed mostly by “close” pieces (in a Euclidean sense). A complementary hypothesis is that chunks are encoded as abstract, semantic information. The article shows that chess players are able to perceive strong similarity between very different positions (different on the surface level of pieces-on-squares) IF the pieces retain the same abstract roles in both of them. The key encoding involves the abstract roles that pieces (and sets of pieces) play dynamically (IE, what are the pieces DOING or potentially capable of DOING). This corresponds closely with the intuition underlying PoPLoAFun.
PART II:
ReplyDeleteThe authors used a set of 20 constructed problems which I’ve referenced previously; refer to the article. The task is to match pairs of positions on the basis of strategic similarity and NOT on the basis of the numbers of pieces, the sets of pieces, the types of pieces, the positions of pieces in various areas of the board and the underlying search trees. Part of the problem set is used as a control: the pairs of these problems have a strong surface similarity but little or no strategic similarity. Novices and lower rated players cannot successfully pair the strategically similar positions, whereas experts can.
While thinking about those problems, I came up with the idea of treating problems differently, focusing on the strategic similarity rather than the surface designations that usually differentiate problem sets. For example, instead of looking for Philidor’s Mate (also known as the smothered mate), I began looking for commonalities and differentiations completely separate from the classification of the problem. I used the lichess.org Puzzle Storm as my test bed.
I would play a set of Puzzle Storm, trying to “see” beyond the obvious to the inner essence while also solving the problems, without concern as to how many puzzles I completed or solved correctly. At the end of a specific Storm, I went back over all the puzzles, looking for positions that were strategically similar. To my surprise, I was able to clearly “see” those similarities in several puzzles, whereas before I was only looking at them at a much shallower level of abstraction. Surprisingly, the “cues” for those similarities turned out to be rather simple (though not obvious) and much more abstract.
I think we are traveling parallel (if not totally similar) paths toward a better capability to “see” those abstract roles. PoPLoAFun provides a very useful thinking framework!
I assume we are on the same path. I gave up my addiction to moves and pieces for the more abstract chess logic lately. Which is piece and position independent. Thus solving the transfer problem. Blogger is acting weird lately. So if you hear nothing from me for some time, feel free to send me an e-mail.
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