Player A has built up thickness in one part of the board. Player B plays so as to blunt the utility of this thickness while player A has not gotten anything of equal value in return. In the process, suppose player A transfers her thickness to another part of the board. If this "second generation" thickness is less useful or less imposing than the original thickness, one might say there has been thickness attenuation.
SnotNose: I've seen this happen in my games. One of the players spends his time transfering his thickness around the board. With each transfer, it becomes less and less useful. In the end, the player has all kinds of thick shapes but nothing to attack and no substantial territory. I think this is common for Black in high handicap games. Especially if the black player has learned enough to make "box shapes" but not learned enough to know how to use those thick walls to attack effectively.
BobMcGuigan: Seems to me that this "attenuation" is a sign of erroneous play rather than a natural occurrence. Sometimes (often?) a thick position, say a wall, gets transferred to a different part of the board where it might appear to have less potential than before but that might be because some benefit came elsewhere during the "transfer". If the over-all balance between thickness, influence, and territory changed then a mistake was made, I think.
SnotNose: Agreed. I think the definition implies that the one whose thickness has been attenuated has played in error. If one has exchanged thickness for something of equal or greater value, then that is not an error. The term seems to describe an affliction that affects those who know how to build thickness but not how to use it (no easy thing!). If I'm not paying attention I can find myself in this situation. I'm playing along thiking, "Okay so you make that thickness useless but here, how about this new thickness...D'oh nothing to attack with it!!! Oops. My thickness has been attenuated."
Alex: In my experience, this usually occurs when the thickness is in the possession of an overly passive player, facing an overly aggressive, unreasonable player. As the aggressive player makes one unreasonable invasion after another, the passive player keeps backing down and transferring his thickness elsewhere. The aggressive player's strategy is "eventually, you're not going to have anywhere else to switch to, so at some point, you're going to have to commit to trying to kill me." If the passive player is too chicken to drop the hammer when the situation calls for it, his thickness becomes attenuated.
zinger: Alex, I know just the kind of player you mean. The first few encounters with such a player can be confusing: we have been told by stronger players that it is often wrong to try to kill, so we make the opponent live small ... and then again ... and again, until we have nothing left. It takes a readjustment to realize that some players just plain force you to kill them.
Alex: I've been both. :) These days, I play thickly, but I used to play my own clumsy, amateurish variation on an amashi strategy because many online players don't use their thickness effectively.
Actually, I still do try for a "thickness attenuation" strategy on my opponents once in a while, but it's a more sophisticated version these days... "overconcentration trap" is a better term for it, though.
Bill: While I realize the theoretical possibility of thickness attenuation, in my experience the opposite happens. As a rule, thickness does not transfer, it accumulates.
Say that you have made thickness and you use that thickness to attack the opponent, who makes life, yielding you more thickness. Meanwhile, you still have the original thickness. Thickness accumulates.
Also, as a rule, the new thickness is not attenuated by comparison with the old thickness. Why? Because the old thickness aided in the attack, making the creation of the new thickness easier that it might otherwise have been.
One danger, as Alex points out, is overconcentration, not attenuation. This is especially so when the old thickness did not aid in the attack that created the new thickness. Then the new thickness can easily be too close to the old thickness.
Alex: I think the point is that the game is of finite length. If the board was infinite, you could go on accumulating thickness forever and get further and further ahead. However, as the transition from middlegame to endgame approaches, there are fewer targets to attack and fewer open areas to make territory, so the value of thickness declines. At some point, that thickness needs to be converted, either by attacking for territory, or killing an unreasonably deep moyo invasion. Otherwise, it becomes depreciated as the rest of the board becomes settled.
In other words, although you can keep attacking to build more thickness indefinitely, if that's all you know how to do then eventually the "rate of inflation" will surpass the rate at which you're accumulating thickness, and your currency will be devalued. So you need to liquidate your thickness into a more stable currency before the bubble pops. ;-)
Bill: Alex, two games of mine come to mind. One was one of the most pleasurable games I have played, one was one of the least pleasurable. The first was a true case of thickness transfer. Playing White sans komi I made -- and lost (!)-- three walls. In losing each wall I made another one, of course, transfering thickness. You can imagine Black's shock when, having won three sizable battles, he lost by five points. ;-) In the second game I took two stones from a five dan. Early on I made thickness outside of my top right corner. Then my opponent also lived in my bottom left corner but got a weak group running into the center, which I proceeded to attack. From time to time he would tenuki and make what seemed to me to be unreasonable invasions. I even felt insulted. But he was very good at shinogi and would live, giving me more thickness. Finally the attack ran into my original wall, his huge central group died, and he resigned. If his group had lived, I would have had to resign. If I had lost, I suppose that we could talk about thickness attenutation, but....
Anyway, in both games the finiteness of the go board played to the advantage of the thickness. The idea of the devaluation of thickness over time as the board fills up does not mesh with my experience.
Alex: Okay, but in both cases, you did manage to convert your thickness eventually. In the latter game, the guy lost a group. In the former, you don't say it explicitly, but if he managed to capture three walls, you must have made some territory eventually in order to end up ahead.
It's a well-known principle that thickness becomes devalued if it faces a settled position. How can it fail to be true that all unused thickness gradually depreciates in value as a greater and greater percentage of the board becomes settled?
Put another way, a ponnuki in an open area of the board is worth 30 points. At the end of the game, it is worth 2. If you haven't, in the meantime, used it to make 28 points of territory by attacking or destroy 28 points of the opponent's by invading, then you've allowed it to become devalued. You can also use it to attack to make more thickness, but say you let it get boxed in by solid stones of both colours so it has no more influence, but get two more ponnuki on the outside in the process. Well, that's good, but if you don't make good use of those, it's still only 4 points. You're not, realistically speaking, going to turn that one ponnnuki into 15 before the end of the game, so you aren't going to get your full value out of the original one if you just keep trading it for more thick shapes and never switch to making territory or killing something.
Bill: It is not always easy to indicate the points inherent in thickness. That does not indicate anything special about thickness. The average move in go gains somewhere around 6 points. But if you make 120 moves, you will not end up with 720 points of territory(!). Typically you will end up with around 60 points, which comes to about 1/2 point per move. The effectiveness of most moves lies not so much in making territory as in reducing the opponent's potential territory.
Now, of course, the value of a ponnuki, for example, will depend upon context. If the opponent is already strong in the surrounding area, it may be worth very little. However, when you make thickness after thickness, whether transfer or accumulation, you tend to get, as in the first game I mentioned, thickess facing thickness, or as in the second, thickness facing the opponent's weakness. Neither fit the picture of the thickness getting weaker or less effective as time goes on, i. e., thickness attenuation.
The way my opponent played, the second game was going to be a disaster for somebody. But I had more control in the first game. Consider the point at which I sacrificed the third wall for more thickness. That gave me a huge central territory of thickness facing thickness. (They say not to make territory from thickness, but hey! ;-)) The real danger, as Alex points out, was overconcentration. Then I would not make enough central territory. In that case my only hope would have been to save my wall and carry the fight out into the center, attempting to kill or capture enough of the opponent's stones to win the day.
Thickness attenuation is a theoretical possibility. However, in my experience, the major problems with making thickness lie in making thickness too close to your opponent's strength or too close to your own strength.
Bob McGuigan: There is also the fact that the value of the thickness might be partially turned to cash during the transfer so, in terms of overall potential, there has been no loss. I've been wondering whether there might be some kind of conservation of value in Go. I guess this would assume some sort of "perfect" play, but the idea would be that each maneuver by one player that accrues a certain value would leave the other player some corresponding maneuver that would restore the balance. In the world of real go this could mean that if, say, Black has something (e.g. thickness) with a certain overall value and White plays to take that away then Black should be able to recover the value someplace else, though maybe not in the original form.