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W to play and escape


Velobici has brought to our attention a Scientific American article about the [ext] The Expert Mind, by Philip Ross. He reviews what we have learned in Western psychology and cognitive science about expertise in chess. Presumably expertise in go is similar in many regards.

This material, including some stuff that is not said, contradicts some of what is said on SL about training and improvement at go. It has been a while since I studied learning theory, but I think that a lot of what I can add is still valid.

I make some suggestions for play and training, but it is an open question how much previous research generalizes to go. I think that even what pros recommend should be taken cum grano salis, at least as regards amateurs. Experience is a great teacher, but anecdotal evidence needs to be tested by research.

{I welcome comments, but I plan to reedit this page later, and maybe even delete it after making a more general page. Don't count on what you say here surviving an edit.}

-- Bill


One thing that the article does is to de-emphasize the importance of reading, in the sense of the calculation of variations, at least past a certain level. In general, chess masters are no better at calculating variations than good non-masters. Rather, they choose better candidate plays to start with, and their judgement is better in regard to assessing the results of the calculation.

Kotov, in Think Like a Grandmaster, would disagree about the importance of reading. Also, many go pros (if not all) would disagree. The fact that statistical experiments do not back them up does not mean that they are wrong. For one thing, the experiments are addressing a somewhat different claim, and statistics is a blunt instrument.

The article also emphasizes the importance of memory. This surprised me, because in my own learning I have de-emphasized memory, feeling that it is better, in general, to be able to work things out than to rely upon memory. And in go, after the first few moves we are usually on virgin territory. (In chess, by contrast, much of the opening may be a well-worn path.) Memory may not be so important in go, but I suspect that it is, particularly in the number of distinct patterns that professionals know (about the same as the number of words that an adult knows in his native language). It also would not surprise me if go professionals make use of areas of the brain that usually hold long term memory as working memory when playing go.

If memory is so important for playing go well, that has definite implications for training. For one thing, it de-emphasizes working things out on your own. In particular, it may be very bad advice to tell beginners to work things out on their own. (It may be very good advice for prospective professionals, for different reasons. They presumably have already committed many, many go patterns to memory. Their job is not so much to learn patterns as to utilize them.) Beginners' time is better spent soaking up as much go knowledge as possible, without having to reinvent the wheel.

Here is an experiment. Take a group of beginners and a problem book, like one of the Graded Go Problem Books for beginners, which is appropriate to their level. Give them a 10 minute test with some of the problems from the book and pair the players according to their test scores. Then give them study material. One player of each pair gets some problems from the book with no answers and is asked to try to solve the problems in her head. The other gets the same problems, along with the answers and text from the book, and is asked to read the material. Let them study for 30 minutes, and then give them a second 10 minute test with other problems from the book. Compare results.

My guess: The readers will show more improvement on the second test.

We could do similar experiments on single digit kyu players and dan players. It may be that at some level the solvers will improve more than the readers. But maybe not. Anyway, it's an empirical question.

(BTW, just because I contrast reading the text with working things out without answers does not mean that I advocate simply reading, per se. It is just that telling the players to read rather than to study or work on the problems provides a clear contrast for the purposes of the experiment.)

xela: I find these ideas very interesting. For many years, in music and in mathematics as well as in go, I tried to put a high emphasis on working things out, and tended to avoid memorisation or rote learning. I'm now in the process of reevaluating these ideas, and am finding interesting parallels between the way I've studied all three subjects, not least the fact that I've memorised an awful lot (yet not enough to make me a really good go player) without meaning to.

My current thought is that memorising and working things out are inseparable. Things that you work out yourself will be easier to remember. Having some things memorised gives you the tools to work things out when you need to. The hard thing for me is to believe that building technique through repetitive work is a good foundation for, rather than an impediment to, true creativity; but there seems to be a lot of evidence pointing that way.

It's also important to consider the value of working things out for yourself as a motivational technique. I suspect that most people, unless they're under the influence of a very charismatic teacher, have a small appetite for memorisation.

Charles In order to become strong at go, you must learn much stuff. For example, on The Appeal of Tesujis Volume 2, the first and third problem on the page I just 'know'. If I didn't see these in a game, it would be tiredness, something like that. The second I 'solved' immediately, but I didn't 'know' the answer, just that nothing else would be possible. So this is about having learned patterns, with reasoning attached. Now in my case I can say exactly how I learned the third, anyway, (going through as many tesuji books as possible). It is striking, to me, that the kind of rote 'learning' being talked about above is more like joseki variations, or life-and-death standard positions. I suspect that no one who cannot memorize these by the 1000 can get to pro level, when young enough to make a career.

Bill: Thanks for your comments, guys! :-)

Xela, to say that memory is important is not to say that rote learning is the way to go. The analogy with language has some merit. For instance, memorizing sentences in French, such as "Les enfants de l'empereur mangent dans la rue," -- That's from an actual textbook, I kid you not! ;-) -- won't get you very far with learning the language, especially if you do not learn the meanings of the words. OTOH, trying to learn a second language as an adult with no memorization practice is not so easy, either.

Your make important points about how working things out and memorization can go together and about how working things out can provide motivation.

As for building technique through repetition vs. creativity, remember what Rubinstein said: "Technique is so the fingers don't get in the way of the music."

Charles, your remark about learned patterns with reasoning attached is a good way to put it. The patterns of go are not simply visual, but include such things as dame count. And there are patterns of go reasoning, as well.

I took a look at The Appeal of Tesuji volume 2. The technique of the first problem was in memory, and I do remember how I learned it. I worked it out during a game when I was 5-kyu. The second was kind of obvious, the third I had to work out. (So much for the star system!) B1 came immediately to mind. (If there is a tesuji here, this is probably it.) Would you say that B3 is an example of your 1-2-3 principle?

Charles Not filed that way. It is a pattern related to a counter to the tower peep, for me.

'Related' pattern  

That is, the white+circle stones are doomed after B3.

But it is probably less important where it is filed. It could have been a classification of nets instead.

Bill: Thanks, Charles. :-)

Lynx: The way that I see the concept of knowing basic patterns is very simple. There is a 2d level problem on (or was it 4d)?, where you have to do several tesujis at once. Each tesuji separately is obvious and I can see "instantly" what will happen, the resulting shape as I saw "instantly" the answers to each of those three problems.

Applying this to joseki patterns is an interesting question. I do not think that even a 10k can not "see" the basic shape from the most basic 34 high approach joseki. Being able to "see" as clearly variations from the start for other problems should not be hard in terms of reading, but hard strategically.


W to play and escape  

This problem is near impossible to solve quickly if you don't know the correct tesuji. Once you know it, it is pretty easy. (The answer? Try an angle play)

By seeing the answer here, you expand your horizons and the next time you see a similar problem, you might find it, as opposed to here, where, I at least, struggled in confusion for 2 minutes then gave up.

Bill: Thanks, Lynx. :-)


What do we mean by intution in go? I think we mean the ability to come up with a good play without conscious thought.

There is good news and not so good news. First, the not so good news.

Intuition allows us to play well quickly. That does not mean that playing quickly or working problems quickly is the best way to develop intuition, or even that it does much to develop it.

Now the good news. Let us think of intuition as based upon implicit knowledge. We know more than we can consciously articulate. The good news is that increasing explicit knowledge increases implicit knowledge, as well. (Not directly, of course, but we are constantly extending our implicit knowledge beyond the fringe of our conscious knowledge.)

How, then, to expand our explicit knowledge and skill? The Scientific American article talks about taking our study and training just beyond our current level of competence. In terms of tasks we set ourselves, such as solving go problems, there is a good rule of thumb: it is best to try problems that we have about a 50% chance of success with.

Because of the accuracy of go handicapping, a player has about a 50% chance of winning a game. As the article indicates, playing is not enough for advancement, but one's own games provide a good ground for study at the frontiers of competence. Furthermore, it is not too hard to recognize many errors in hindsight. Even two beginners going over their own games together can learn something.

Overlearning to solidify what we have learned is very important. It is also important to avoid cramming. The apparent gains of cramming disappear quickly. BTW, I see now that my feeling that you should space out overlearning trials is consistent with the 50% rule. If you try a solved problem again too soon, the task is perhaps too easy. (I do not know if anyone has researched this question of spacing.)

Some pros advise doing very easy problems (for you) quickly. While that is not bad advice, let's look at it in terms of intuition, overlearning, and the 50% rule.

First, speed is an indicator of intuition. Intuition engenders speed, but does speed engender intuition? Solving familiar problems quickly is unlikely to have a direct effect upon intuition. (Not that intuition, or aspects of it, cannot be trained. More on that later.)

Second, solving easy problems is almost always a matter of recognizing what you already know. Thus, it can be important in overlearning, to put that knowledge on a firm foundation. It can boost confidence, and solving easy problems quickly can be a fun thing to do.

However, in terms of the 50% rule, solving easy problems, even quickly, may be too easy. If I am familiar with a problem, I typically see the main line of the solution in a fraction of a second. It would be a good idea to make the task of solving easy problems harder.

Here is one approach. What does it mean to solve a problem? It means that you choose the first move correctly, and that you choose a correct response for each reply of the opponent. But typically a published problem will have a single main line, showing the best or most stubborn or trickiest replies of the opponent. As a practical matter, it is normally good enough to find the main line of the solution, especially as the correct responses to other replies of the opponent are usually obvious. But when we are reviewing what should be familiar material, everything should be more or less obvious. One way to make the problem more difficult is to require seeing several lines of play within, say, 2 seconds. (It is up to you to decide what lines are worth reviewing. Some lines are surely not worth thinking about. But if you miss one that you think was worth reviewing, you flunked the test. See Go Problems - The Fudge Factor.)

You can also try loading the task. I first heard about loading at a conference lecture. The lecturer told about training novice helicopter pilots. Their first task was to take off and hover, keeping the helicopter over a one acre field. (It's not so easy to fly a helicopter!) Once they could do that successfully, their second task was to do the same thing while chewing gum. (!) That sounds like a joke, but it wasn't. Loading means adding a second, easy but irrelevant task to increase the difficulty level. The point is to increase the difficulty without increasing it too much. I have never tried this, but maybe reciting poetry or singing would be a fun way to load the task of solving easy go problems. (Freude, schoener oshibori....) ;-)

Aside from having some fun, what is the point of loading? Isn't an irrelevant task simply irrelevant? No, by loading you increase the difficulty, and thereby increase the efficiency of the main task. If problems are so easy that you cannot increase the efficiency of recognizing their solutions, why bother in the first place?

I think that the best way to improve intuition is indirectly, by expanding explicit knowledge. However, I understand that there has been some recent work on improving intuition in general, so more may be done. I do think that it is possible to improve one's utilization of intuition, and that is primarily by relying upon it and putting it to the test in games. That is also a way to develop judgement, so it is not easy to separate the two.

Some of you may know of my own experience in that regard when I had been playing go for several months. In one game, after working hard to try and figure out the local fight and find my move, I took a breather and just sat back and looked at the go board for a few seconds. Intuitively I realized that the best play was elsewhere than I had been studying for so long. And the work that I had just done studying the local area was not lost, because it helped me when the play came back to that area. I began incorporating the pause to look at the whole board before making almost all of my plays. That was worth four stones.

There are a number of things going on here. One was the new reliance upon intuition. (I was too weak to have developed anything we could call judgement.) Another was relaxation. I took a breather. That helped me be receptive to my intuition. Another was the rhythm of effort and relaxation. It may be that we can skip the effort part, at least at the intensity I experienced. Bruce Wilcox advocates playing quickly, at an average of about 4 - 5 seconds per move. OTOH, Lin Haifeng advocates spending up to 10 minutes on a move if you think it might be crucial. (I tend toward Lin's camp.) But in terms of intuition, playing quickly does not mean playing hurriedly. Intuition allows you to play quickly, but it takes time to work. The phrase, effortless effort comes to mind. If you take only a few seconds to make a play, spend the time pondering, wondering about the next play, even if a move has already come to mind. That puts you in a receptive state of mind while at the same time invoking your intuition to do its work. IMO, most of the mistakes of amateurs are sins of omission, not so much making the wrong play as not even considering the right play. Spending time in a state of receptive expectation, open to the possibilities of the whole board, may help to see the right play, at least as a possibility.

Also going on was the shift of perspective to the whole board. Here again, spending time with different perspectives may be important.

Also going on was something that I did not mention, but that I think was very important, and that was reviewing the game. If you are going to rely upon intuition, you have to put it to the test, not just in winning or losing the game, but in rigorous analysis afterwards. IMO, the most important thing for improvement at go is studying your own games.

(Well, this section has gotten pretty long. I think I will continue in this vein in a new section, which will be even more speculative. :-))

Dieter's comments

Hi Bill. I had a guitar teacher for a few weeks, recently, and both having taught in a variety of fields (mine are Go, sciences, tennis, basically) we often digressed into the matter of pedagogic skills and devices. Contemporary pedagogy schools are strongly biased towards "finding out for themselves", "guidance", "many alternative methods for one objective" ... Much to the embarassment of the authorities, my teacher in a seminar suggested "imitation", "rote learning", "drill" as efficient teaching devices.

What I firmly grasped from reading, is that memory is indeed a very powerful asset, but equally powerful in doing something wrong as doing it right. Unfortunately, we haven't all learned our first go-steps from Kitani Minoru but sometimes from amateurs who thought they understood much more than they actually did, not to mention all the bad habits that crept in just like that, after 1000 games we lost as quickly as possible on xGS. Which is why we need to unlearn about as much as we have to learn, in terms of effort. To effectively unlearn bad habits and ill shaped knowledge, we have to arm ourselves with fresh knowledge, working from the very grounds, "reinventing the hot water" as someone mentioned.

One more note: I am apprehensive of making the distinction between aspiring pros and amateurs. Should they fundamentally differ in their approach to improvement?

Velobici: The aspiring professional is studying to achieve of level of proficiency that results in a life-long income stream either from teaching (nearly all professionals) or from tournaments (very few reach this level). The amateur either has or will develop a profession apart from go. This is a significant difference. As a result, an amateur is free to play a joseki line that is slightly less profitable in exchange for a more stable/secure/less aji position. A professional does not have that luxury, but rather must press for each and every point that can be gained. In other words, the amateur may (will only?) play for enjoyment. Enjoyment is secondary for the aspiring professional; only achievement matters.

Dieter: Obviously the desired level and the approach to the game differs, I'm not doubting that. I'm doubting that necessarily the approach to improvement differs. On, they talk of horizontal growth (more songs, same technique) as opposed to vertical growth (increased level of mastery, even within the same song). As an amateur in Go, I do (did) aspire vertical growth. In order to get it, I'm not sure that I should apply another way of studying the game than a pro. Less intensity, sure, less time, definitely, less brain power, I'm afraid so. Surely I can allow myself some time of horizontal growth (more games for fun, the analogy being not quite fully applicable), a luxury the pros do not have.

Bill: Thanks, Dieter. :-)

As I indicated, I have tended to avoid the rote learning approach. But the significance of memory raises questions, at least for me. I think that motivation is very important, and allowing students to develop in a way that is more congenial to them than whatever a teacher might impose is a good idea. A student centered approach is best, I believe. As you know, I usually respond to people's questions about how to improve with a focus on them. My purpose here is to discuss what Western psychology has to say about improvement and training that an individual can utilize for herself. Pedagogy is a different and larger issue.

I do believe in imitation, however. For one thing, the best learners in the world, children, make great use of it. Pretending is also good, I think. A "primitive" fisherman may pretend to be the god of fishing. Do you think that has no positive effect on his fishing? A young golfer may pretend to be Tiger Woods. Why not pretend to be Cho U or Yi Chang Ho or Go Seigen?

Or, more prosaically, ask oneself, where would Sakata or Jowa play? One of the best tacticians locally is named Eric. Sometimes when I play him and we get into a tactical skirmish I'll tease him a little by asking at my turn, "Where would Eric play?" That's also a serious question. If I only try to solve my tactical problem by my own devices, I will not always do as well as he. But if I pretend to be him for an instant or two (a form of imitation) I may see something I would otherwise miss. And if I can't work it out, my best play under the circumstances may be where I think he would play.

Some people advise beginners not to study professional games, since they are too difficult. There is something to that, but I think that it is based on a too rational approach to learning. Improvement is not always explicit, brick by brick, step by step. If you are going to pick up bad habits anyway, why not do so by misunderstanding Shusaku or another player who inspires you? Meanwhile, you will also learn things that you do not know you are learning. Do we ask a two year old not to listen to adult conversation?

As for unlearning, except for forgetting, there really is no such thing. What we do is learn something else and inhibit the previous learning. That is one reason that we regress to the previous learning under stress. In the moment the inhibition fails. That having been said, unlearning is natural for most complex subjects, where new understanding is built upon previous, less perfect understanding.

About prospective pro vs. amateur: I do not know about fundamental differences, but purpose matters, motivation matters, and level matters. At age three I was learning both vocabulary and grammar; by age six I was focusing on vocabulary and my main tool was a dictionary (i. e., my mother); at age 14 I was focusing on style and nuance, and my main tool was the thesaurus. I also began to study writing, then, in various ways. Where you are and where you are going and the tools you have to get there -- all such things matter. One size does not fit all.

Go Savant?

What would it be like to be a go savant? There are savants in music and art, but there are also savants who can perform prodigious feats of memory and mathematical calculation, rapidly and without much conscious effort. Go playing itself is too high level to expect savant capability for go playing. However, it would be nice to be able to count a position with a glance. ;-)

Savant abilities are associated with brain dysfunction or damage. A large percentage of savants are autistic, for instance. Sometimes a blow on the head can produce savant ability, sometimes small strokes or other brain damage with age can do so. But there are also cases where people with no apparent brain damage have developed savant or near savant abilities.

One person who developed his skill as a rapid calculator was Leslie Dodds, a World Bridge Champion. Once, when he underwent an operation, just before going under anesthesia he asked the nurse to give him two six-digit numbers. When he came out of the anesthesia he gave their product!

There is research indicating that inhibiting some areas of the brain can enhance savant skills, like counting the number of matchsticks on the floor. Well, as yoga, biofeedback, and hypnosis suggest, people should be able to inhibit those areas on their own. There is hope. :-)

Is the calculation of variations something that can be done rapidly and unconsciously? Even if it were, would that be desirable? Once such a calculation is made, the resulting positions have to be evaluated. Simply producing variations without judgement makes for a lot of work assessing the results. Reading is really a higher level activity than calculating variations.

But reading can occur unconsciously, like much mental activity. How often do people wake up with a solution to a problem that they have been working on? (There is research on unconsciously working on problems, it's not just anecdotal.) There is, in fact, an example here on SL, on TsumegoFromGames42/Attempts . Several of us worked together on the problem. Finally one morning I woke up with the final plays to make the double ko.

Rapid mathematical calculation can be trained. Can the rapid calculation of variations be trained? I think it highly likely. Here is perhaps where go differs from chess (not essentially, but culturally). Go has the insei tradition, where young children train to become professionals. It may well be that some professionals have trained themselves for savant-like rapid calculation of variations.

Rarely, people like Leslie Dodds have trained themselves in rapid mathematical calculations, but there are people whose training is not so rare. Some Japanese students have been trained in rapid mathematical calculation. I do not know the details of the training, but it starts with the soroban (abacus). In fact, when they perform these calculations you can often see their fingers moving, as though manipulating a soroban.

There is an instrument for calculating variations in go, the computer. Depending on the program, you can produce variations rapidly. Now, with a soroban you can read off the answer. You cannot simply do that in go. But I do think that a training method for calculating variations in go can be developed which combines visualization training with producing variations with a computer program.

Visualization is probably a good tool for calculating variations. It is not that hard to develop, either. Anybody who dreams can visualize. With the help of a hypnotist, it can be developed within weeks, on one's own, within months. Much can be done with it. For instance, you might build a tree of variations, opening and closing nodes on the tree to view (to minimize confusion and clutter). It would be unnecessary to redo previous calculations. Breadth first search might become possible, which would normally be a strain on the brain's working memory.

It might be easier to become a go professional than to learn how to count the board at a glance. However, more modest goals, such as rapidly counting the dame of a connected group of stones, should be within reach -- again, within weeks or months. Rapidly counting small to moderate territories should be trainable, as well.

Kotov and go pros recommend reading lines of play only once. That is an antidote for dithering, going back and forth between lines willy-nilly. However, unless a line can be read out, it is probably better to read lines twice, to take advantage of unconscious processing. Research suggests that the brain continues to explore lines of play unconsciously, even when other lines are being explored consciously. It may be best to spend about 1/2 to 2/3 of one's time on a first reading, and then the remainder going over the reading again.

If you are spending one hour solving a set of problems, it is probably a good idea to allot 2/3 of the time, 40 minutes, to going through the set the first time without looking at the answers of those you could not solve, and then returning to them in the last 20 minutes, to take advantage of unconscious problem solving.

BillSpight/improvement last edited by PJTraill on September 12, 2018 - 21:31
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