Follow the wise old men - and solve problems faster

[Boidhre]

The immersive method to learn a language works well if you frequently communicate with people who speak the language well. If you only interact within a community of people who make mistakes, you will reproduce these mistakes and teach them to other people.

In the same way, the immersive method can work in go if you frequently play against stronger players. This is not possible for everyone.

This comes up a lot with minority languages since they usually have relatively little native level material available, or what is available is narrowly specific. E.g. Irish has this issue but there is a very good free native radio station available to listen to, the issue is you're going to want to be interested in Irish rural matters, weather, farming, Irish politics etc. You're going to have to shape your interests to what's available. If you are going to delve into the literature, again you'll have to live with what kinds of genres, time periods and stories are available. You don't get to go in with a mindset of "I only read Science Fiction" unless you're happy with only a handful of books to work with.

It feels you're going to hit the same wall with go. I think things have massively improved since pro and extremely strong amateur players started to stream games. It's a "light" way to feed your "go ear" a lot of high quality moves. In general though, we have access to this material, it perhaps just isn't in the form we'd most enjoy. If you want to attain native level Irish spending your time talking to and reading works from non-native speakers of middle-upper middle level is worse than a dead end. In go maybe there's something similar, if most of you time is spent watching/playing other middling amateurs, why should we expect to play above that level? Similar to Irish, once you're happy to just speak it and don't care about accuracy etc it doesn't matter. If you want to play better, or similar to with a language not necessarily attain native level but be able to appreciate it, then yes, the answer seems obvious to me now in retrospect.

[Boidhre]

As for interacting with people who make mistakes, I have warned against weak players playing even games if they wish to advance. That's a good way to pick up and reinforce bad habits. Better to play against stronger players, and then, when they get better, to return the favor and play some against weaker players. OC, if your aim is to have fun, then do as you will.

Yes, much later did I realise that I really, really should have listened to you when you said that to me. Fortunately long breaks from the game offer wonderful opportunities to forget bad habits as well as good ones.

[Ian Butler]

It feels you're going to hit the same wall with go. I think things have massively improved since pro and extremely strong amateur players started to stream games.

I don't agree with you. I think for 99% of all Go players, we could still benefit massively from pro's even of 100 years ago. I don't think it hurts to try and learn from guys like Shusaku, Dosaku, Shuei... Professional players and high amateur players, sure, they'll have to keep up with the most modern trends, but I 100% believe you can become a very strong player even if you ignore everything AI. I don't think it's entirely comparable with a language that changes. I'd compare it with just more vocabulary being added to a language.

You don't get to go in with a mindset of "I only read Science Fiction" unless you're happy with only a handful of books to work with.

I read a lot. And I almost only read Sci-Fi and Fantasy. I can tell you, you can fill an entire lifetime with just those two genres But I see what you mean

[Bill Spight]

There is a tendency, it seems to me, for players to recommend what they did to reach their level, what they believe worked for them. OC, that is only anecdotal evidence, and everybody is different. Moi, I try to make suggestions based upon research. But there is no question that from an early age I have been strongly influenced by Znosko-Borovsky's advice in How Not to Play Chess. Namely,

1) Analyze the position.
2) Make a plan.

Also: Do not get lost in "a maze of calculations."

I read the relevant chapters of Jon Tisdall's book last night. May main reaction was, "At last!" A chess grandmaster finally demolished Kotov's approach, and in clinical Joran Peterson fashion using common sense in place of dogma. I had always felt uncomfortable with Kotov. At first I thought it was me. Then I thought it was a combination him and me - he was a numbers man, I'm not. Then I eventually came to the view was wrong that his status came from piggy-backing on the Soviet School of Chess.

There are elements to Kotov that do make sense, and Tisdall stresses his good advice to make a list of candidate moves, for example. But essentially, even if Kotov's method worked for a Soviet tractor it doesn't work for humans.

AFAIK, the only part of Kotov's method that has been debunked by research is not revisiting previously explored nodes of the game tree. Everybody else does it. Moi, I found reading each branch only once to be good discipline. If you know you're not coming back, you do your best the first time. As Tommy Armour said, A cow could do it right the second time.

As I recall, Kotov begins talking about his method of calculation in Think Like a Grandmaster with an example he used in talks before an audience. He illustrates how a hypothetical player might decide upon a play in a particular position. He explores one move, but after searching a few moves deep, he decides he doesn't like it, and tries another move. After a search he doesn't like that play either, and returns to the first move. After further search he still doesn't like it, and returns to the other play. He goes back and forth for a while, and then sees another play, which he makes without further ado. The audience laughs and applauds, recognizing that they have done the same thing. (I have, too. ) This is what Terence Reese calls dithering. Don't dither.

Making allowances for the differences between go and chess, I'd say that the methods Tisdall and I propose are almost in synch. There are differences - he proposes pausing every few moves to burn a visualised image into the brain; I focus more on the time element. But I suspect these are superficial things and probably not real differences.

I have also found it helpful to spend some time just looking at the board, but without any effort to visualize it. As far as problems go, however, it is important to know where the key stones are. Often, when reviewing a problem, we may recognize it based upon some trivial details. Then, when a similar position arises in a game, we may play the problem solution, but it does not work because the game position is slightly different. I have observed this in real life.

There is, however, one discrepancy. Jon says he came to his method as the result of noticing that his own powers of analysis (= reading) were waning with age. His method was therefore recuperative, and worked. But he doesn't appear to say what was different about his (even more natural?) method when he was younger.

Kotov's method was also remedial. At some point he realized that he was relying too much on intuition and general principles, I have the same problem, which is why I appreciate his way of overcoming it.

So why is go not taught by the immersive method in the west?

Until the advent of online go it was hardly possible. And the lack of FTF contact is also an obstacle.

Why does the hairshirt approach prevail? I think the reason is the prevalence of mathematicians here, and it was interesting to me to watch a recent Michael Redmond video where he made the same point, though more diplomatically than me (yet more tellingly, because he has a mathematical background himself).

I strongly doubt it. The mathematical approach is to make things easier. The woodshedding necessary to accomplish that may be hard work, but that is not go.

AFAICT, it comes from the practice of strong Eastern players, who recommend what worked for them.

[Boidhre]

It feels you're going to hit the same wall with go. I think things have massively improved since pro and extremely strong amateur players started to stream games.

I don't agree with you. I think for 99% of all Go players, we could still benefit massively from pro's even of 100 years ago. I don't think it hurts to try and learn from guys like Shusaku, Dosaku, Shuei... Professional players and high amateur players, sure, they'll have to keep up with the most modern trends, but I 100% believe you can become a very strong player even if you ignore everything AI. I don't think it's entirely comparable with a language that changes. I'd compare it with just more vocabulary being added to a language.

I was not for a second suggesting it wasn't worthwhile studying older games or that only go post-AlphaGo is worth having! What I was getting at is that this is a *very* digestible format for the modern age and being able to hear a pro comment on the game as they play it live is something new and very welcome. It also gives people an excellent opportunity to play "where would I play here?" and get instant feedback on it. Which I think is a very good way of actively engaging in watching stronger players play.

[Boidhre]

What I mean is, similar to a lot of games, hearing a pro give a snapshot of their thinking as their playing can often open people's eye to "how the game is supposed to be approached" and hearing your thinking refuted live is helpful. You're not necessarily improving in terms of mechanical skills in the sense of a games in general but something closer to how higher level thinking should be shaped. You're not going to become strong just by doing this but it offers an excellent chance to catch some misconnections about the game that you may have picked up along the way or introduce you to new ways to apply what you've been learning. It has to be part of a bigger toolbox, but there's definitely value to this *alongside* kifu and commented game collections.

[SoDesuNe]

Visualisation was never a problem but compared to the common way a solution to a tsuemgo is shown I needed a lot more time.

This sentence leads me to infer that you are using visualisation in a different way from me.

Let's imagine you are walking to a new destination - a church on yon side of a brae. But you can see the spires of two churches. You have to choose and you don't want to get lost.

[...]

I wish to stress: the coordinates themselves are not an issue. They are just a symbolic way of representing a sequence of steps in time. Variation diagrams represent sequences in space, which is confusing in itself but is also heinous if their apparent convenience tempts us into not spending the time to learn the steps. How many of us can learn to dance by looking at pictures of dance steps. You have to tread the light fantastic.

Hm, I don't know if I truly understood your "paths to churches"-metaphor. But I guess within your metaphor my (obviously bad) reading approach is best described as running towards the spire I see first, neither looking at terrain nor checking probabilities. And then I do what Bill Spight wrote Terence Resese calls dithering. But I also have not really any ambition, motivation nor interest in improving my go skill anymore. I'm only here for the show.

But actually my point was that I don't see any benefit on the learning effect when solutions to problems are presented as coordinates. As someone not used to dividing up the board in letters and numbers (or numbers and numbers) it just takes more time checking moves. I also don't see the time/space-difference between writing coordinates by referencing letters and numbers and showing a board position with the correct moves labelled by numbers. In both examples moves precede one another, are sequential so both have your "time"-attribute? But a board position shown is much easier to understand.

[Boidhre]

Visualisation was never a problem but compared to the common way a solution to a tsuemgo is shown I needed a lot more time.

This sentence leads me to infer that you are using visualisation in a different way from me.

Let's imagine you are walking to a new destination - a church on yon side of a brae. But you can see the spires of two churches. You have to choose and you don't want to get lost.

[...]

I wish to stress: the coordinates themselves are not an issue. They are just a symbolic way of representing a sequence of steps in time. Variation diagrams represent sequences in space, which is confusing in itself but is also heinous if their apparent convenience tempts us into not spending the time to learn the steps. How many of us can learn to dance by looking at pictures of dance steps. You have to tread the light fantastic.

Hm, I don't know if I truly understood your "paths to churches"-metaphor. But I guess within your metaphor my (obviously bad) reading approach is best described as running towards the spire I see first, neither looking at terrain nor checking probabilities. And then I do what Bill Spight wrote Terence Resese calls dithering. But I also have not really any ambition, motivation nor interest in improving my go skill anymore. I'm only here for the show.

But actually my point was that I don't see any benefit on the learning effect when solutions to problems are presented as coordinates. As someone not used to dividing up the board in letters and numbers (or numbers and numbers) it just takes more time checking moves. I also don't see the time/space-difference between writing coordinates by referencing letters and numbers and showing a board position with the correct moves labelled by numbers. In both examples moves precede one another, are sequential so both have your "time"-attribute? But a board position shown is much easier to understand.

I read it as thinking along the same lines as: Reading a list of the declensions of a noun or tenses of a verb and writing out those declensions in context as part of a correct sentence. The latter takes much longer but is probably better for recall, understanding and just developing a general sense of the language. There is value to be had in language learning by actively revising instead of passively revising material some of the time. It's an inefficient way to always revise though.

[SoDesuNe]

Still not sure how this translates to the tsumego shown and how it advocates presenting a solution in form of coordinates. Disregarding for a moment a more proper way to attempt the tsumego, every way will involve reading to various degrees. At the end of your reading you will check the solution.

When I understand it correctly, the coordinates-form will need more engagement from me and thus should be more effective learning-wise?

But the flaw in that is that it only needs more engagement (and time) due to me being unfamiliar with the form. When I'm fluid in translating intersections to coordinates I will likely need the same time checking the solution compared to it being presented in the (now) usual way. The question is now whether the time needed to learn the coordinates for 361 intersections by heart has any impact on my go skill?

My take is, it doesn't.

In my earlier post I referenced the way chess players store the answer to problems in their head: They instinctively translate their sequence into coordinates because that's what they have to do in chess to check the answer. But this translation of moves into coordinates is anything but effortful. It's like remembering multiplication tables. I don't calculate 9*9, I know it's 81. No effort needed.

[Boidhre]

How I thought about is this, what is different? My first thought was that perhaps this is similar to looking at a kifu in a book and playing out that kifu on a board. My feeling is that I get more from doing the latter, perhaps I am naturally giving more thought to the move by physically placing it. With having to see via co-ordinates the answer instead of seeing it laid out in a diagram I think about the difference between holding a problem in mind and solving it without visual aids versus solving a problem while looking at it on a board or screen. The former generally is more difficult than the latter for most people I've spoken to about this suggesting it's working more or different areas of the mind than the latter. Finally I thought about laying problems out on a board before trying to solve them. I think this is good, if time consuming, but there is perhaps a chance to engrain more sense of shape here? I don't know.

In all these I don't think that they're equivalent even though they are effectively doing the same thing. Where I feel there's something to the co-ordinate system approach is not with very difficult problems but problems that are reasonable for the player as they add a little more difficulty to seeing the solution but also give more opportunity for training reading by in the mind's eye with a change of context from searching to verifying. I think there is value in finding and fixing the image of the solved position in your mind as opposed to seeing it akin to real-game situations where you are always working in this mental view of the game. I'm deeply sceptical of the value of this however when the problems are difficult for the player, I think at that stage they need to be fed the solution/tesuji/etc rather than train their ability to visualise it. I also think that there's value in drilling many easy problems quickly as a form of light reading workout to verify your fast reading is accurate for simpler shapes and the coordinate system is less useful here, though the solutions are only hopefully very rarely useful also.

Maybe my take's all kinds of wrong here though.

[jlt]

I sometimes find that the diagram with the final position is disturbing because it's hard to visualize an intermediate position, i.e. it's harder to mentally remove stones from the final position than to add them from the initial position.

[Ian Butler]

I sometimes find that the diagram with the final position is disturbing because it's hard to visualize an intermediate position, i.e. it's harder to mentally remove stones from the final position than to add them from the initial position.

I share that sentiment. If I need to go back to the problem after looking at the solution diagram, I go back to the problem diagram, 100%. Taking away 2 stones is a lot more confusing than adding 6.

I was not for a second suggesting it wasn't worthwhile studying older games or that only go post-AlphaGo is worth having! What I was getting at is that this is a *very* digestible format for the modern age and being able to hear a pro comment on the game as they play it live is something new and very welcome. It also gives people an excellent opportunity to play "where would I play here?" and get instant feedback on it. Which I think is a very good way of actively engaging in watching stronger players play.

Oh, I misunderstood you then. Yeah I agree. Watching pro's play won't make you a better player, but it'll help staying engaged and it might reinforce some general principles.

[Boidhre]

Yeah I agree. Watching pro's play won't make you a better player, but it'll help staying engaged and it might reinforce some general principles.

Oh I think you can become a better player by watching strong players play for certain. Especially if you're watching actively and thinking where you'd play next etc.

[John Fairbairn]

But actually my point was that I don't see any benefit on the learning effect when solutions to problems are presented as coordinates. As someone not used to dividing up the board in letters and numbers (or numbers and numbers) it just takes more time checking moves. I also don't see the time/space-difference between writing coordinates by referencing letters and numbers and showing a board position with the correct moves labelled by numbers. In both examples moves precede one another, are sequential so both have your "time"-attribute? But a board position shown is much easier to understand.

Several points emerge from this.

1. You don't need to divide up the board into coordinates. The book editor can do that for you - see below.

2. When you are seeing a board position with all the moves on it together - the typical variation diagram - there is an implied sequence (1, 2, 4, 5...) but you are seeing it, at a single moment in space. You are also seeing the garbage left my captured stones. You are not seeing the move order in any meaningful sense. You only see it as a sequence if you play it out on a board so that each move (not just a single diagram) gets its own moment in time.

A typical situation is that you are reading a tsumego book on a train. You probably do not have a board and stones, but let's assume you do. You plonk down a dozen stones. Purely mechanical, but better than nothing. So far so good. You then have to remove them, but probably end up picking up too few or too many stones and have to waste time reconstructing the original position. This builds up resentment or other negative feelings which chip away at your motivation to do tsumego in the first place.

You may instead be using a smart phone. You could click through the moves on an app, but experience shows we all get click happy and the procedure ends up as a speed exercise for the thumb. Again, you also have to go through the negative and time-consuming process of unwinding the sequence.

You could watch a video and let somebody else do the work for you. That's filling in time, not using. In any case, while the demonstrator is picking up played stones and reconstructing the position, you will be switching off and thinking about what you'll have for lunch or "did I really turn the tap off?"

Or you could put in a bit of "effortful practice". Since this is a euphemism for "hard work" it's not a pleasant topic on the face of it. But if you try it and stick with it, various benefits accrue that either do not occur with the above methods, or which may occur but much more slowly and patchily. Effortful practice in his case means visualising the moves by following a prompt. The prompt may be via coordinates on the side of the diagram, or letters on the diagram, and/or by the use of words. The use of words is especially useful when you a reviewing a problem (e.g. atari, connects, hane underneath, nobi to extend liberties....). With any of these methods you are not just solving the problem but you are also training your mind, and there is no need for equipment and no need to unwind back to the original position - so, no negative feedback.

3. "But a board position shown is much easier to understand." Only sometimes, and more importantly understanding is not the aim of the exercise. The aim is internalising the solution so that it becomes a tool in your tool chest, and one that you actually know how to use.

Examples:

$$Bc Black to play
$$ ---------------------------------------
$$ | . . . . . O X X . . . . . . . . . . . |
$$ | O O O X O . O X . . . . . . . . . . . |
$$ | O X X . O . O X . . . . . . . . . . . |
$$ | X . . X O O O X . , . . . . . . . . . |
$$ | . X . X X X X . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |

Click Here To Show Diagram Code

[go]$$Bc Black to play
$$ ---------------------------------------
$$ | . . . . . O X X . . . . . . . . . . . |
$$ | O O O X O . O X . . . . . . . . . . . |
$$ | O X X . O . O X . . . . . . . . . . . |
$$ | X . . X O O O X . , . . . . . . . . . |
$$ | . X . X X X X . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |[/go]

A problem by Hashimoto Utaro. You may care to note that it is called Soma 相馬 by Hashimoto and is one of a trio of problems called Iwaki, Soma and Miharu, these being three villages mentioned by Basho on his journey on the Narrow Road to the Far North. There he saw Shadow Pond, so called because it was reputed to reflect an exact image. But when Basho was there it was cloudy day and there was no reflection of anything but grey skies. His disappointment matched the scene. Does the tsumego problem represent the pond. Will I end up looking at grey skies? All waffle of a kind, but making such associations is a useful and enjoyable part of effortful practice. You are both more likely to pursue the problem and to remember it later.

The solution in the book (though actually without coordinates there buy I don't know how to turn them off here):

$$Bc Black to play
$$ ---------------------------------------
$$ | . . 4 1 5 O X X . . . . . . . . . . . |
$$ | O O O X O 3 O X . . . . . . . . . . . |
$$ | O X X 2 O . O X . . . . . . . . . . . |
$$ | X . . X O O O X . , . . . . . . . . . |
$$ | . X . X X X X . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |

Click Here To Show Diagram Code

[go]$$Bc Black to play
$$ ---------------------------------------
$$ | . . 4 1 5 O X X . . . . . . . . . . . |
$$ | O O O X O 3 O X . . . . . . . . . . . |
$$ | O X X 2 O . O X . . . . . . . . . . . |
$$ | X . . X O O O X . , . . . . . . . . . |
$$ | . X . X X X X . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |[/go]

Grey skies or sharp image? Do you understand? Do you see? Like Basho, you are ona journey to the far north - you have jo go board and cell reception is awful.

The solution if you use coordinates and visualisation:

$$Bc Black to play
$$ ---------------------------------------
$$ | . . . . . O X X . . . . . . . . . . . |
$$ | O O O X O . O X . . . . . . . . . . . |
$$ | O X X . O . O X . . . . . . . . . . . |
$$ | X . . X O O O X . , . . . . . . . . . |
$$ | . X . X X X X . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |

Click Here To Show Diagram Code

[go]$$Bc Black to play
$$ ---------------------------------------
$$ | . . . . . O X X . . . . . . . . . . . |
$$ | O O O X O . O X . . . . . . . . . . . |
$$ | O X X . O . O X . . . . . . . . . . . |
$$ | X . . X O O O X . , . . . . . . . . . |
$$ | . X . X X X X . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |[/go]

Black D19, White D17, Black F18, White C19, Black E19.

Better, if you use words as well: Black placement D19, White cuts D17, Black throws in at F18, White prevents Rooster on One Leg with C19, Black captures with E19 and makes a false eye. (Hashimoto doesn't go this far but he does add a touch of associational humour which helps the memory; he ends his answer with the haiku-style phrase: Kanashii kana, kakeme desu - Oh woe is me, the eye is false!)

To reinforce my claim that seeing a single picture is deceptive, or even useless, consider the following. (I'm using a discipline that most go players won't be familiar with, to ensure assumed knowledge does not get in the way of the point.)

BalletPortdeBras.jpg (16.18 KiB) Viewed 12609 times

The typical presentation in a go book would actually be only pictures 1 (Figure 1 in go) and 4 (Variation 1). But as a concession, if you really do believe variation diagrams show sequences clearly, I present a sequence here. What is going on?

it's actually very simple - a standard port de bras exercise usually done at the end of a lesson, and any dancer would recognise it instantly. It has been internalised and she can do it easily. In fact you can do it easily, once shown - but from the diagram? There is also no need to understand it. You just need to do it. Go's not much different. It just feels different because those pesky numbers create an illusion of meaning. Conjurers call it misdirection.

There is one other point that needs addressing. People often say: that's OK for simple positions, but it doesn't work when there's more than one variation. If you are one of these nay sayers, your everyday experience proves you wrong, I'll bet.

Think of a variation diagram as a picture of the destination. Now a destination doesn't have much relevance without a journey. What I am proposing is that you choose a destination - you don't need a picture of it - then you plan the journey. If you make the journey many times you will probably want to work out an efficient way to get there.

Let's say I want to drive from London to Edinburgh. A very long trip - over 400 miles. I have chosen my destination. I don't need a picture postcard. I've been there before. I therefore also don't need a map. Still, because it's a very long trip there are many variables. In go terms, I look at the the surrounding position and the stage of the game - what time of day (or night) will I be travelling, what time do I need to be there, what's the weather forecast, is my car in good nick and so on. Once I've got that kind of stuff sorted, I can think about the actual journey/ Do I need a tesuji - e.g. start off at 3 in the morning to beat the traffic. Do I take the straight M1 with all its traffic or the much quieter A1 with all its twisty roads and fewer service stations. Do I take the quicker route across the mountains - or will there be snow and ice there - or do I take the coastal route. Or shall I go west first then whizz up to Glasgow and approach Edinburgh from a different angle. Maybe depends on where the hotel is. And so on and so forth.

My point is that we all do this sort of thing all the time without hard thinking for familiar journeys. We make choices, we look at many variations (routes), we take account of strategy (weather) and tactics (location of petrol stations). We solve the tsumetravel problem easily, quickly, efficiently.

Now if I wanted to go to Pontyprydd instead, for me that would be a different kettle of fish. Not only do I not know how to get there, I don't even know where it is - except that it's (I assume) in Wales somewhere. In that case I will need a map. I might well find pictures useful - is it in mountains, for example? I can't really make any assessment about which route is best, and will have to do a fair bit of analysis (reading), and I may even decide I want to avoid the worst route rather than find the best one.

Again this is an experience we are all familiar with.

And I'll bet again that everybody does what I do if I have to go to Pontyprydd again. I'll try to skip the map and the pictures, maybe experiment with a possibly faster or safer route, and so on, all with the explicit goal of eventually reducing that journey to the same kind of travel experience as the trip to Edinburgh.

It doesn't take much digging to realise that go problems can be reduced to the same sort of journey + destination process. But how may people do that? Those who sit on a train with a standard tsumego book may feel they are travelling, but that's just because they are being pulled by a locomotive. They are not driving, even in the book. They are getting barely anything out of the book. In the book they are just turning from picture to picture. If they sat with a map and followed their train journey on that, would they feel they were getting anything out of it? If no, then why should they expect to get anything out of the picture-postcard kind of tsumego book?

It's very easy to scoff at this in some solipsistic way and say, "Well, I don't do that sort of thing!" Really? Next time you are on a plane, notice how many passengers (yourself, too, maybe?) sit gazing catatonically at the route map on your seat tv screen. (I own up to doing it. I fool myself by pretending I'm improving my geography.)

Another problem is a kind of being wise before the event. Telling your self that every journey begins with the first step can make you feel wise, which can make you feel you've understood the problem, therefore you've solved the problem, therefore you can go and do something else. You skate over the real problem - that fact that you haven't made any steps after the first one and so never reach your destination.

In short, the journey (the work, the effortful practice) is that matters most in making progress. And the fact that that is bleeding obvious never seems to make a blind bit of difference. Look at the constant drip, drip, drip of people asking on forums (not just go) for the best way to do this or the best way to study that. What they are really saying is, "I know you are supposed to work hard at this, but what's the best way to avoid actual work?" And they only listen to advice that comes without that rude four-letter word.

My advice is to substitute the rude word for a nice one: a journey. Going to the Far North, well away from normal temptations and distractions, might be the ideal, but even short journeys can show you new things you never suspected were there.

[Bill Spight]

How about this?

$$B Black to play
$$ ---------------------
$$ | . . . . . O X X . .
$$ | O O O X O . O X . .
$$ | O X X . O . O X . .
$$ | X . . X O O O X . ,
$$ | . X . X X X X . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .

Click Here To Show Diagram Code

[go]$$B Black to play
$$ ---------------------
$$ | . . . . . O X X . .
$$ | O O O X O . O X . .
$$ | O X X . O . O X . .
$$ | X . . X O O O X . ,
$$ | . X . X X X X . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .[/go]

(BTW, John, to remove coordinates remove the c in the title line.)

$$B Goal
$$ ---------------------
$$ | . . O . X . X X . .
$$ | O O O . O X O X . .
$$ | O X X O O . O X . .
$$ | X . . X O O O X . ,
$$ | . X . X X X X . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .

Click Here To Show Diagram Code

[go]$$B Goal
$$ ---------------------
$$ | . . O . X . X X . .
$$ | O O O . O X O X . .
$$ | O X X O O . O X . .
$$ | X . . X O O O X . ,
$$ | . X . X X X X . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .[/go]

Edit:

$$B Failure
$$ ---------------------
$$ | . X . O . O X X . .
$$ | O O O . O X O X . .
$$ | O X X O O . O X . .
$$ | X . . X O O O X . ,
$$ | . X . X X X X . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .

Click Here To Show Diagram Code

[go]$$B Failure
$$ ---------------------
$$ | . X . O . O X X . .
$$ | O O O . O X O X . .
$$ | O X X O O . O X . .
$$ | X . . X O O O X . ,
$$ | . X . X X X X . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .[/go]