I have defined some important terms. Usually, others' descriptions of them are not definitions in a (semi-formal) mathematical sense. Therefore, usually, there are not two different definitions. Your problem may be that you confuse 'definition' and 'very ambiguous informal description' in this thread. With the latter, rational choice is difficult, of course. Rational choice must rely on clear, preferably unambiguous definitions. You know because you have provided some definitions of terms, too.

Bill: I think this is the most important insight here (though perhaps the word 'definition' will lead some down the wrong path). At any rate, it gave me a bit of a sleepless night! I realised for the first time that in essence this is a re-statement of the Gestalt principles of grouping. I'm kicking myself for not having made the connection before. In my own defence, Gestalt was in common use when I was a student but it seems to have disappeared down the rabbit hole in recent years. I suspect this may have been when the term was hijacked by people like novelists.

But it does seem applicable to go. As I understand it, the Gestaltists were concerned with how disparate qualitative elements merge into a whole (a 'configuration') that is recognised by everyone but which cannot be understood in terms of its parts, as these are not measurable. I believe the original prompt for their speculations was music. They were fascinated by the notion that all humans can identify the same melody even when it is played in different key with occasional different wrong notes, irrespective of whether it is played on a trumpet or sung, and whether it is sung to one set of lyrics or another. It's a very human skill, and although there are now apps like Shazam that can attempt to identify tunes, humans seem to do it so much better.

For myself I devised a different configuration, using the old "can't see the wood for the trees" saw. You climb a hill and can instantly see various unmeasurable elements. Sounds obvious, but it's a great skill. One element is a large stand of trees. Aha, a wood, you say. But what do you make of it? That depends on what your plans are. If you are a traveller, you want to know where it is and how to avoid it. You don't care what's inside. If you are a fugitive, however, you still don't care much what's inside but you don't want to avoid it - you want to enter it. But if you are a carpenter looking for oak to build ships, you do care what inside - and you may also care about how much there is (but "lots" will be sufficient description). Then again, you might not see even it as a wood at all. If you are hungry and looking for free food and you spot apples in the trees, you will think of it as an orchard. And yet again, you might just be a tourist who says, "Ooooo" and moves straight onto the next sight.

All these hill climbers are seeing exactly the same unmeasurable, fuzzy thing but interpreting it differently.

I suspect this is what happening in go. Pros and amateurs see the same thing (so it's irrelevant whether it's measured or not, or defined or not) but interpret (or "understand") it in startlingly different ways. I came across an example myself very recently. It was the position below.



The reader was being asked to choose between Black A and B. Since it was a book on a specific topic (surrounding) there was of course an implication that you had to justify your choice with reasons. So this was an example of the sort of test Gladwell was talking about.

In a real game I would have played A without thinking (i.e. intuitively). But because I knew this was being set as a problem with a theme - and also because I know I play almost every move without thinking and that's a habit I feel I should correct - I gave it some thought. My first thought was to do with the triangled stone. This involved a little reading but I quickly decided that White would make himself heavy by running away, and Black, with a preponderance of stones in the area would chase White and make more territory in doing so, while not being in any danger himself on either side of the fleeing White stones.

So I then turned my attention to the Black group on the lower side and tried to see the merits of B. I could accept that Black was somewhat thinner down there than he was on the right side, and, since White dominates the left side, a move that looks in that direction to erase that dominance could be useful. There was also the point that Black A instead would run the risk of ippoji (one big territory). Note that I did have several reasons, which is perhaps different from the amateurs in the Gladwell experiments. Still, in the end I couldn't convince myself that B was right, and went with A. But it was a close-run thing, and it shouldn't have been.

That uncertainty made me feel bad enough, but I was gobsmacked by the pro's explanation. A was correct, but the main reason was that it covered the weakness around the triangled stone. What weakness????!!!! Like my hill climbers, the pro and I had seen exactly the same thing but perceived something quite different. I am very used to observing that pros very often make early safety plays that I feel are too slow, so I don't find it hard to accept the pro was right here, but to say my understanding is incomplete is being generous to me. (There's a very similar thing in shogi I had trouble with - "Early escape by the king [i.e. castling] is worth nine moves.")

Now in my sleepless state I was trying to work out how this state of affairs (which I think applies to most amateur players) comes about and what can we do about it.

Without going into the inner workings of my thoughts, I came to the conclusion that I already held but now hold even more strongly: that attempts to measure or define strictly the various aspects of go that we can identify (e.g. thickness) are not just doomed to failure but are detrimental. They are trying to teach us to do things algorithmically, which is not something humans do very well, and certainly not when faced with a brand-new problem (i.e. a position we have never seen before).

It may seem glib to say that this is mainly a western problem, but I think it probably is - we see these attempts to measure and define an awful lot in chess. We maybe see this much less in western go (though the "noise" factor may be higher ) but that could be because it's harder in go. Chess has also had a much longer recent tradition of devising algorithms for computers (though I can't help but remark that the algorithms pale into insignificance alongside depth of search). I think the only objection that might confirm glibness is that we occasionally see things like formulas for counting thickness in Japanese books. OK, but first, they are much rarer. Second (and this point might not come over too well if you are not used to reading the Japanese text - things like the prefaces as well as what's under the diagrams), I believe the western authors of such systems (in chess and go) are trying to teach us how to think algorithmically whereas the Japanese pros are trying to improve our perception. The westerners want to teach us that a specific thickness is worth definitely 27.67 points. The Japanese pro wants us to "feel" more usefully that it and similar positions are worth about 30 points. The common western complaint that the Japanese pros leave their explanations fuzzy is therefore misguided - dangerous even.

It can be a subtle difference. Wilcox talked about sector lines. Takagawa talked about boxes and trays. If sector lines have a purpose it is just demarcation - not specially useful because we can see the invisible lines for ourselves already. But boxes and trays have contents and can hold different amounts according to shape and size - don't need to conform to a strict geometric definition of their sides. This seems to offer so much more in getting to grips with perception.

Perception is what the Gestalt grouping principles are concerned with. They try to offer a guide to the way humans perceive, which is important because we have an innate disposition to see patterns, or configurations. I think the most basic elements are proximity, similarity, continuity, closure, and connectedness, though they seem to have several different names. They are all relevant to go positions.

I recall, though maybe wrongly, reading that Gestalt workers failed to come up with a satisfactory theory of how perception works but that they were so convinced that they were on to something that they instead insisted on the word 'principles' rather than 'theory.' I find that a useful distinction. It has been common to translate Japanese kiri as 'go theory', and I've done that myself, but it's bit sloppy. 'Go principles' (plural) would be more accurate. Apart from the etymology of the -ri part and the typical definitions (as genri - basic principles of go), I think it is telling that the usual way to say someone is good at kiri is 'kiri ni akarui' where the etymology of akarui, suggesting brightness and seeing clearly, is really all about perception.

Since I am effectively suggesting perception as a new buzz word (possibly more useful than intuition), it may be useful, somewhat paradoxically, to define it. My Oxford English Dictionary says: the ability to see, hear or become aware of something through the senses. It also adds a more technical sense: The neurophysiological processes, including memory, by which an organism becomes aware of and interprets external stimuli.

Either way, that sounds much more useful than numbers and mathlish. A lot harder to achieve, of course, but for many (?most) of us that's where the appeal of go ultimately lies.

Edit: clarified it was Black to play.

As usual, you spread fear (a myth of having to determine the hundredth of a point, a warning of reasoning being dangerous) when it comes to comparing reasoning to subconscious thinking. Instead, I promote verification when applying a definition and reasoning.

In [13], I define a group to have thickness if it is connected and alive. (Note: this is independent of points so we need not even get a multiple of 10 right.) Obviously, the strings of the tentative black wall on the upper side are alive. We use tactical reading to determine and verify its weakness: White can cut, see the SGF below. Connection of those strings is important, therefore Black's move must establish it.

This is never about perception. Connection is verified by tactical reading. Any pro will confirm this. Fujisawa Shuko might even play the honte N15.

Robert, I think you wanted to say "obviously, the strings of the tentative Black wall at the upper side are NOT alive"

On another note, I can check the OP using this example by John: intuitively I play A. When trying to reason about it I may ask myself which one White would play. And then B looks more attractive to White.

But there's another argument: A allows Black to cut through the keima, using the double atari tesuji, confining White. So it does 2 things, while B does only 1 thing.

This reasoning backs up my original intuitive choice.

So, intuition provides a clue. Some heuristics (my opponent's good move ...) may mislead, other heuristics (make double purpose moves) lead to the proper answer. Perhaps most importantly, my second heuristic involved "seeing" a variation.

This is the opposite of what I say.

I know that I thought you omitted "not" from your sentence. So you really meant to say "obviously, the strings of the tentative Black wall at the upper side are alive".

If those are obviously alive and both are connected to themselves, then both are thick, according to your definition. However, you go on to prove that they can be cut and as such are not thick.

It may be obvious to you but it isn't to me. What does it mean for a string to be "obviously alive"? That they are still on the board?

Alive in this context is independently alive (can make two eyes). Obvious, if White does not have the slightest chance of preventing that. (White can cut, but doing so the most obviously does not prevent any of the black wall strings from living independently.)

Here is a problem that I plan to include in my Capture Go Tutorial which illustrates at least one low level, basic, well defined concept.

Click Here To Show Diagram Code

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

I think everybody reading this sees Black's play instantly. Most of us have the named concept that White has a half eye on the bottom. White to play can make an eye there (in gote) and Black to play can take away the potential eye (in gote).

But just a while ago, as I was looking at this position I realized that I have an unnamed concept about the bottom. Black has one dame there. And when she plays there, she still has one dame.

Click Here To Show Diagram Code

[go]$$B Still one dame on the bottom
$$ -------
$$ | O . X |
$$ | O O X |
$$ | . 1 X |
$$ -------[/go]

Now this kind of micro position, a corridor on the first line where the dame count is significant, occurs in tsumego and sometimes in real games. I have been aware of its properties for some time. But the dame situation has no name that I am aware of.

In terms of capture, a dame is a liberty. As long as it is not filled, the stone or stones with that dame is not captured. The dame represents a potential play by the opponent to capture the stone or stones. (Looking at the whole board, White may not wish to make that play, but let's abstract away the rest of the board and focus on the bottom corridor.) When Black plays into the corridor, she does not lose a dame, but she does not gain one, either. White can still fill it. That means that the original dame is worth less than one liberty, but not measurably less. We may then think of such a dame like a negative infinitesimal, one that is worth something to White. (See the CGT pages on SL for more.) For this to work there has to be a payoff for Black at the end of the corridor, and how to think about these kinds of dame will depend on those payoffs.

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

Visualize whirled peas.

Everything with love. Stay safe.

SO both strings, which can be cut apart by white, are alive (can make two eyes)? And both are connected strings (but not to each other). So according to your definition, you have two thick strings there. Yet, pros are worried about the cut. Rightfully so, because, when cut, both strings have bad aji, i.e. need to live independently.

I refrain from starting a debate on the proper definition of thickness, but yours isn't one that will meet with the pros' assessment, or I misunderstood.

If Black captures that cutting stone firmly, the capture represents an eye and a connection. That leaves 1 eye to be made by either string. The pressure on these strings goes from having to make 4 eyes to just 1. That's good aji.

The tentative wall consists of three strings.

You do not understand what is alive? Come on. It does NOT mean to have surrounded eyes. Do not pretend to be an absolute beginner.

That a string is a string does NOT mean that the three strings are connected to each other. Yes, we know that a string consists of stones. Their string-constituting connection (string-connection) does not automatically establish a connection between the strings.

Yes, you misunderstand.

I may also have misunderstood your definition. Is it correct to say that, according to your definition, the group consisting of the string of three stones is thick, the group consisting of the two strings of 5 and 2 stones is thick, but the whole group of 10 stones is not?

In terms of the OP, we seem to be confusing rational choice with reason-based choice. The many undesirable effects of the latter are quite well reported over the last thirty years.

I found the original paper ("Thinking Too Much: Introspection Can Reduce the Quality of Preferences and Decisions", Wilson and Schooler 1991) but only behind a paywall. One interesting point was

"...The Consumer Reports rankings were based on the ratings of seven consultants who were trained sensory panelists. These experts rated 16 sensory characteristics (e.g., sweetness, bitterness, aroma) of 45 jams; these ratings were averaged to compute the ranking of each jam..."

In other words the experts agreed on a list of reasons in order to rate the jams. Did this make the experts' list less reliable?

One of the sources cited in the original paper was "The disruptive effects of explaining attitudes: The moderating effect of knowledge about the attitude object". The abstract of that paper explains... [Emphasis added]


I found all this interesting. Of course YMMV.

_________________
Dave Sigaty
"Short-lived are both the praiser and the praised, and rememberer and the remembered..."
- Marcus Aurelius; Meditations, VIII 21

Yes.

Next, the question arises why would you even consider thickness of part of the tentative wall? Concentrate your study on important aspects of a position.

If we only assessed thickness of the top right two strings, we would only be judging on how well these two contribute to protecting the right edge. If we assess the three strings together, being or not being thickness affects most of the board. This is important.

***

Similarly, imagine a large tentative territory region of yours. If only fragments of your surrounding strings are thickness, they protect little territory. If all essential surrounding strings are thickness, they have the potential to protect the large territory region. It is important to have them all as thickness and not allow large parts of your surrounding strings to fall into pieces. (As a related study, we must also assess whether - despite the surrounding thickness - an invasion life is possible.)

This portion of the discussion has turned into a discussion of thickness, and a discussion of a highly idiosyncratic definition of thickness at that. FWIW, the pro does not mention thickness at all and instead mentions that if White is allowed to play at A that would make Black thin at the top. Furthermore, he mentions a "weakness" at the top which Black A helps to cover. Embedded in all that is the implication that there are tactics available here. None of this would allow us to apply the standard definition of thickness here.

IOW, for him, it's not a thickness problem, it's a direction of play problem.

That in turn means the true decision has been made at a level one notch up. It was a problem of perception. The pro perceived it is a DOP issue. The amateur perceived it is a faux-thickness problem. Take your pick.

I probably misunderstood something again. Isn't thinness related to thickness?

Thickness, as an English go term, usually refers to a thick shape or local position. The Black wall on the top side is too weak to qualify as thickness, whether White plays at or around A or not. It is not a matter of degree. OTOH, the Black position at the top can be to a greater or lesser degree thick or thin.

Edit: I see from a previous note that Jasiek defines thickness as something that a position has. The standard usage is that thickness is something that a position is.

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

Visualize whirled peas.

Everything with love. Stay safe.

It's related but there's a dichotomy in Japanese. The adjective atsui can be converted to two kinds of noun, atsumi and atusa, which are both used in go but are different but both usually translated as thickness in English. That's the real source of confusion (even before other people come along and try to create new definitions). But usui = thin converts to just usumi in go.

That's understandably too esoteric for most people, so I recommend just going with what Bill said.

From my understanding of rational, the better a choice's reasoning, the more rational a choice is. Amateur jam tasters can talk themselves into reasoning far worse than the subconscious. So the conscious cannot do the subconscious job well without training.

I'm not too competent with go engines, but it seems self-learning AI are based upon the human brain. For any position, your brain comes up with the best options in an instant. Most moves are rated as really low (such as first line plays and senseless self-captures), leaving a couple of candidates in the green. Second, you verify them through search, the ones you feel to be most likely best getting searched more than others, each position repeating the process for the first one. Then you change the values the more you search. Better players usually have fewer candidate moves, but sometimes weaker players discard moves that a stronger player wouldn't. This can be due to assuming a move is bad because it doesn't seem to follow some strict rule— and could explain why many amateurs are often surer of their opinions than pros!

I guess when speedily solving many easier tsumego or when playing a fast-paced game, you have to rely more on perception, and your reading must be accurate and quick. Solving a hard tsumego or playing a long game, you need the will to last and conduct a thorough search many times.

What about a situation where A wins more against B, B wins more against C, C wins more against D and D wins more against A? This hearkens back to the style discussion, but it may also show those players have developed different perceptions. I wonder what kind of perception today's young future pros would have from studying AI games.

Maybe it just means that we should be wary of our reasoning, rather than abandon it. More accurately, be wary of oversimplifying. So far this discussion tells me that when reviewing games, you should try to describe your feelings during the game, then explain your reasoning as to why you felt that way, then explain your verification process. In addition to you avoiding false reasoning, reviewers may be able to identify separate problems with perception, reasoning and reading.

_________________
On Go proverbs:
"A fine Gotation is a diamond in the hand of a dan of wit and a pebble in the hand of a kyu" —Joseph Raux misquoted.

Most definitely. It is especially important to follow such a process when using a bot to review games; it's easy to fall into a trap of looking for justifications and explanations of the percentages and their deltas instead of analysing the process of selection of a move, i.e. becoming biased. First go through a game and pick out the points you focused on during the match, then perform a more thorough, perhaps written analysis and only in the end should you look at whatever feedback a bot can provide you with. At least I find this to be a much more efficient method of review than only utilizing the last stage.