I would suggest that what is going on here is that we are seeing the human penchant for probabilistic thinking. We just look at a situation, subconsciously recognise topological features (edges, lack of liberties, throw-in possibilities), and make a judgement based on past experience as to how likely there is to be something there. Japanese technical vocabulary even acknowledges this in the phrase "te ga aru." In the present case I'd guess most stronger players would posit something like 98% certainty "there is something there."

We use this probabilistic thinking instinctively and in strong preference to other, more onerous, thinking modes. This is how most of us amateurs play go, and in blitz games it accounts or almost every move. In a whole game, where the guesstimates are tested very many times, we probably screw up several times, but when applied in moderation and in a slower game, probabilistic thinking is a boon in the amateur world. We could perhaps say it is our equivalent to Monte Carlo playouts and we know how spectacularly successful that was.

Hi Bill,

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Click Here To Show Diagram Code

[go]$$Bc
$$ | . . . . . . . .
$$ | . . X . . . . .
$$ | X X . X X O . .
$$ | X O X X O O . .
$$ | . O O X O . . .
$$ | O . . O . . . .
$$ +----------------[/go]

I count myself as a non-visualizer. I guess the way I do this is:

• Boy, there probably is a shortage of liberties, isn't there?
• After the standard try of throw-in at C1, capture at B1, atari at A2, fill at C1, all of those three empty points in the corner (A2, B1, C1) have been filled. (I don't think I really even think about what color they are at this point, and certainly don't visualize a group of seven White stones and count its liberties.)
• Therefore E1 captures at the end of that sequence.
• Can White productively bail out at any point? No, A2 actually threatens five stones, not just one.
• OK, it works!

I've written it all out in slow motion but it probably takes just a couple of seconds, with most of that actually coming on the last step where I confirm that I'm not just threatening to take the single stone at A1 or something.

Hi Bill

Reference:

Now, here is a problem which is difficult for me to visualize, even after I see the solution. My mind gets confused at move 10 or so.

Click Here To Show Diagram Code

[go]$$B white to play and capture some stones
$$ O . . O . . . . O O X . |
$$ . . . O X O O . . X O X |
$$ X . X X O O X O , O O . |
$$ . X . . X . X . O . . . |
$$ X . . . . . . X X O . . |
$$ . . . . . . . . X X O . |
$$ -------------------------+[/go]

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

A trick I learned in contract bridge is to visualize (in whatever fashion you may do so) the goal position. With that position in mind you can work out the intermediate steps to get there.

One thing that makes this problem difficult is that it is not a one lane road. There are branches that must be clear in your mind.

I think that it might be helpful, instead of trying to visualize the whole tree, visualize the key nodes, which are only a few.

Edit: Actually, I think that pros would call this a one lane road. But we amateurs have branches to explore.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Here I think are two positions to visualize.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

This discussion seems to lack an agreement on what is meant by visualisation, and the last example perhaps muddies the waters even further. It would be fascination to hear theories on what it is.

Visualisation presumably is some combination of at least a couple of processes. I'd guess it starts with recognition, a variable skill that increases with grade and which must be extremely high in pros. There is then some skill that enables one to set a goal (as Bill describes) and to work towards it. Stiil, while iff you have the subsequent skill set you can really get to work, you can't do anything if there is no recognition to start with.

But this example seems to suggest at least two kinds of recognition. I recognised it instantly as a blunder by a very eminent player (and so also knew the answer instantly). That kind of whole-shape recognition is actually quite common even among amateurs (L group, notchers etc) and the fame element is just icing on the cake here.

But unlike us, the player concerned here would not have seen the position before and so could not recognise it in that sense. Yet clearly it was expected of him that he should have recognised something there, otherwise it wouldn't have gone down in history as a famous blunder, and he wouldn't have felt so mortified afterwards. The question then is what was he meant to recognise?

The elements of what he is supposed to have recognised (topological features?) are probably listable. I say that in the light of various technical books I've seen outwith go where an expert contrasts how the average punter looks at something and how an expert looks at it - books such as "How to Read Water" or "How to Read the Weather." What would the go list include?

Also, it seems unconscionable that if Famous Player X had recognised the relevant features that he would have gone on to make his blunder, so there must have been something that interfered with his recognition process. On the assumption we amateurs suffer from that interference a lot, what is that something (leaving aside alcohol and similar potions)?

Bill:

Visualisation/visualization means having a mental representation of stone positions. For me, it doesn't mean I can see black and white stones, I can only see gray shadows. Other people's brains work differently. The consequence for me is that if there are some captures, and if the position doesn't become obvious by move 8, it can become very difficult for me to read variations. So, for the famous pro who made the blunder, we can assume that

• was the obvious potential danger to look at ;
• the pro has a superior ability to form mental images, and/or the position at move 8 (or perhaps even before!) looked completely obvious to him.

Why he made the mistake anyway, well, we are not computers, and it's not easy to maintain a high degree of concentration throughout a whole game.

Moi, when I talk about conscious visualization I mean having a more or less clear and distinct mental image. That's all.



I mentioned the goal position to jlt because he said he had trouble with visualization around move 10, even though he had seen the solution. If he had visualized the position after move 12, IMX, he would have found it relatively easy to work out the variation to get there. I did not mean to imply that he should somehow have seen the goal state to start with.



In bridge there is an advanced play called a squeeze. It used to be the mark of a master, but nowadays the level of play has improved so that the equivalent of 2 kyus can run squeezes. But there are a number of squeezes, some quite advanced, so that the order of play is very important. There are rules about how to decide the correct order of play, and learning those rules can be quite a challenge. But there is a technique, discovered, I believe, by Sidney Lenz, called visualizing the squeezed position. I found that, if I learned the squeezed positions of these advanced squeezes, I could work out the order of play to get there. For go problems, I have found that visualizing the goal position also helps to figure out how to play. OC, the goal position is not always obvious.



My guess is that if he had seen the first play he would have found it easy to read the position out, given his level of play. The goal position is of a kind that he would have been familiar with. (Not that he would have seen it before doing any reading.)

Knowing that this was a problem, I had no trouble finding the first play. Would I have found it in a real game? Probably not.



Black has two strings, each of which has 3 dame, but they share 2 of those dame, so that together, they have only 4 dame. (Wilcox points out that with only 4 dame they may be vulnerable.) Furthermore, one of those shared dame is adjacent to two White stones, so connecting the two strings on that shared dame will leave them with only 3 dame. And if White puts a stone on the other shared dame, then if they make that connection they will have only 2 dame, and Black to play can put them in atari and then capture them. That other shared dame is the first play.

If White makes that first play, Black will have to capture that played White stone in order to connect the two strings. That being the case, there are other familiar features to the play. And in addition there are other familiar features, such as an atari with sente that takes away a liberty, and a connect-and-die of the sort that occurs in many tsumego.

Edit: Actually, that atari is not necessarily sente, is it?

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Thanks.

OK, so you only have one goal position to visualize.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Is this (working differently) really true? One of the things that struck me when reading "Make It Stick" was that the widely held belief that some people learn better via visual means and others learn better aural means is a load of ****. People certainly have preferences, which may in turn have some effect on motivation, but as regards what goes on in the actual grey matter, it makes no difference.

I suspect almost everyone "sees" just some fuzzy images, whether grey or some other hue, and in reality it is recognition that accounts for almost the entire visual aspect. For the calculation part, I'd suspect chunking or something similar deriving from recognition takes over as far as possible - in other words, the brain tries its utmost to avoid actual hard work - and actually stepping through individual moves is a last resort. I'd further suspect that people who claim to be able to step through a lot of individual moves are deluding themselves, and are using some other technique. Again I pray "Make It Stick" in aid - it seems there are quite a few mental processes where even (or especially) intelligent people refuse to accept what is really going on because it is somehow counter-intuitive.

I am aware that some people do have clear mental images but in my experience they are treated as exceptions. For example there was a tv programme here about a young lad who was in no other way remarkable (indeed was considered below average) but when he was taken to Trafalgar Square in London (which is very busy and very varied - in height as well as at ground level). But back home he could draw the entire square in stunning detail. It was not just his recall that was remarkable but that he had the hand-eye coordination (without any special training) to produce immaculate line drawings.

In my own case I remember chunks. For example, take Constable's famous picture The Hay Wain which I have seen many times in the National Gallery and elsewhere. All I really "see" when I recall that is cart in a river. My memory has the cart pointing to the right. In reality it points left (I've just looked it up). I can remember there is a boy or man apparently looking towards open fields in the background, but I couldn't remember if he was in the cart or in the stream (I wrongly guessed at stream). I "remembered" one horse not several - but maybe that was an assumption rather than a memory given the poverty associated with the countryside. I had no memory of the house, dog or boat, but maybe that was because of Constable's skill. I could easily assume these were framing elements to help make the cart (and the wistful look into the distance) memorable.

Similarly, when I say I remember the Shuho position above, I really just remember the chunk where the atekomi applies. The rest is left "as an exercise for the reader" but as that is easy here, I assume I am also remembering somewhere what the goal of this position is.

So I am having a mental image which is useful to me in problem solving, but I wouldn't class it as clear or distinct. If for some reason I feel I need try clarity I'm apt to reach a pen and paper and to produce something I really can see. If it's something I also want to remember, I'm apt to try to chunkify it and/or make mental associations rather than try to burn an image into my brain. If I appear to be staring at something I'm not really using my eyes - I am just trying to concentrate.

My sense is that most other people use the same techniques as their routine approach to such problems, but of course I too could be deluding myself.

Yes, it is. There is a lot more literature on the subject now than there used to be when I first realized that I couldn't visualize around 20 years ago. The condition now has a name, aphantasia, searching for which will lead you to plenty of writing on the subject. In short, there is a continuum of visualization all the way from "sees and manipulates images in their head perfectly clearly" down to "sees only black when they close their eyes". From your description of your own experiences, it sounds like you are maybe slightly below the median in this ability, whereas I and jlt are way down at the bottom. (My "auralization" abilities are excellent, so I have a sense of what it is like to be good at this sort of projected imagination.)

I do agree that reading/calculation in Go/chess is not entirely a matter of visualization; otherwise I would be hopeless at both games. The kind of pattern recognition and chunking you bring up describes my experience as well. Another thing that works for me is to classify configurations of stones/pieces so that I can identify the contents of a point/square by working out how it relates to one of the configurations.

In order to think concretely about go, chess, tic-tac-toe, Othello, etc., you have to have some kind of mental image. That does not necessarily involve the visual cortex. But you need to have a representation of the state of the game. When I talk about visualizing the goal position, I do not mean seeing stones on the board, or a go diagram. I do mean having a mental image of some sort.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Yep, I agree. Unfortunately the term "visualization" has become overloaded, and people are using it in this thread and elsewhere to mean both "seeing visual images in your head" and "managing mental representations of local positions that can be queried efficiently and accurately".

This was my process, FWIW. There is a combination of visualization and just suspecting certain things lead to goodness.

From this thread it certainly sounds like it is true. My mind produces nothing that I would describe as "gray shadows".

I don't believe I have aphantasia, but I do have trouble forming images in my mind, but I have music pieces on playback all the time. Images are harder, they are fuzzy, and I can only ever get small parts of them in focus, but then I lose the rest of them. Reading on the go board is more like mentally putting down markers - black stone here, white stone here, and it becomes error-prone after a number of moves. That number varies: pattern recognition is a powerful shortcut. The throw-in on the first line example from earlier is such an example, you just know what will happen. Trying to visualize it as I type this, I can see the shape of the four critical white stones, and I know abstractly where black stones would have to be to make the problem work.

Reading a ladder I just follow the staircase up to the point where it threatens to collide with something, and then I reconstruct the markers - white stones would have to be here, then there, then there, so that's atari, so the ladder doesn't work.