Identifying something as a sphere (or region) of influence is an application of "influence". The effect of stones on intersections (possibly carrying) other stones can mean that a particular intersection has better influence values for one of the players. A string of such intersections then can be called a "sphere" of influence. More precisely, consider for every intersection the c-connected, a-alive and t-territory values for Black and the d-connected, b-alive and u-territory values for White. If c>d && a>b && t<u, then we call the intersection "belongs to a sphere of influence of Black". If c<d && a<b && t>u, then we call the intersection "belongs to a sphere of influence of White". In the other cases, neither player has an advantage for all three aspects (connection, life, territory). Alternatively it would be possible to consider only one or two of the three aspects or to make additional requirements like non-negative connection and life values for an intersection to be part of a player's sphere.



Given very limited calculation time?) I think though that every parameter value in my model can be determined within hours for almost all very difficult cases. My model assesses whether an intersection can be territory at all while you ask for the precise CGT-territory value. Naturally that can be much more difficult to assess.



The intersections are *-connected and *-alive for Black.

They are -2-connected, -1-connected, *-connected for White.
They are -2-alive, -1-alive, *-alive for White.

They are 0-territory, 1-territory, not t-territory for Black.

They are not u-territory for White.

Click Here To Show Diagram Code

[go]$$
$$ X X X X X O
$$ X . . . . O
$$ X X X X X O[/go]

They are 0-territory, 0-territory, 1-territory, not t-territory for Black.

The CGT-territory method is more precise on the tiny, endgame scale than the n-territory, which is designed for the large influence scale.



This is a different kind of influence from what my model considers. Maybe a different term can be used?



Each inside intersection is Black's 1-territory. After a black play, it reverts to your first example.

Magicwand asked whether particular fundamental findings (such as rules-related or ko definition) of mine are useful for getting stronger and I have replied that they are a bit useful in that respect. This misses two major points though:

1) The major purpose of fundamental research is to lay the basis of later applied research, which then can have much impact on getting stronger or (in case of science) making everybody's life richer. Einstein's general relativity theory was fundamental research. Later applied research enabled the installation of satellites with which GPS has become possible. My Japanese 2003 Rules are, for the sake of go theory, mostly fundamental research. Later reuse of their "force" concept has made practically useful definitions like n-connected and, relying on them, definitions of influence and thickness possible.

2) Not all my research has only marginal relevance for becoming stronger. While my fundamental research itself has an only marginal relevance for becoming stronger, my applied research, e.g., related to influence and thickness has great relevance for players becoming stronger. Of course, this does not include you, Magicwand, because you have an aversion against everything different from intuition and reading. Everybody open for conceptual learning can profit a lot though. a) My characterisation of influence and thickness to depend on connection, life and territory is much clearer than what existed before as a rough explanation: "nearby friendly stones bring an area under that player's influence". b) My degrees of influence and thickness allow whichever precision is needed while before the most precise descriptions were like "more and nearer friendly stones mean greater influence".

For other topics or concepts described by me, similar observations can be made.

_________________
"The more we think we know about
The greater the unknown"
Words by neil peart, music by geddy lee and alex lifeson

I can only conclude that either:

a) You have not read the TOS

or

b) You want to read more posts by Robert.

_________________
Patience, grasshopper.

Ignorance of contents does not make it crap but means that the ignorants do not enable themselves to judge from first hand.

Everybody is invited to discuss the contents of my books!

My books (those I have published so far) are not research (a documentation of the research process) but contain a lot of my research's results. Therefore your statement "what you call research" is wrong.



I do not know if a comment like "Robert is a very careful and methodical researcher."
viewtopic.php?p=48756#p48756
qualifies for your perception of "highly".

In general though public(!) comments really appreciating my (or, for that matter, any other go researcher's) research are sparse. I do not know why. Maybe consumption is so much easier than acquiring knowledge with which to properly identify contents as being new and comparing it with other literature.

EDIT: There is systematic observation though: Many more comments are about the fine details of English grammar than about factual research mistakes, if any. E.g., my ko definition paper still awaits a hint of any first factual mistake.



You do ignore evidence presented earlier.



You do ignore evidence presented earlier. Let me repeat: I have learned more from some weaker players (e.g. Andre Engels, then about 1 kyu) than I have learned from most professionals of those each having spent more time to teach me. James Davies (said to be about my strength) made me a lot stronger when I was a kyu.



You have never shown as clearly before that you cannot judge.

[...] you have yet to convince me that your work [...is...] worth something.

[admin]
Much of the above post was removed for being in violation of the TOS. -JB
[/admin]

_________________
"The more we think we know about
The greater the unknown"
Words by neil peart, music by geddy lee and alex lifeson

Do not expect me to spend months on repeating explanations in my work and let me concentrate on the thread subject.

My description of influence has newly introduced these aspects and added it to the previous understanding of being given due to the impact of stones:
1) Influence is said to depend on connection status.
2) Influence is said to depend on life status.
3) Influence is said to depend on territory potential.
4) Influence can be measured by precise and always meaningful degrees.

I can convince you only if you share my view that
1) knowing that influence depends on connection status is more valuable than not knowing this,
2) knowing that influence depends on life status is more valuable than not knowing this,
3) knowing that influence depends on territory potential is more valuable than not knowing this,
4) knowing influence's precise degrees is more valuable than having an only imprecise understanding of degrees.

Therefore you need to admit that you accept at least one of these conditions. Otherwise I can never convince you.

As the devil's advocate, you will of course also doubt whether indeed I have been the first to invent the mentioned conditions or whether they existed earlier. You have the chance to provide any possibly existing, still unknown to me evidence of earlier existence.

For the historians, my earliest public draft of such an idea might have been here on 2005-08-08:

http://www.dgob.de/yabbse/index.php?topic=1651.0

Peace out, dudes.

Tangentially, I don't believe anyone's mentioned Ishida Yoshio's All About Thickness. I found it pretty lucid, and the style is pleasant.

_________________
Revisiting Go - Study Journal
My Programming Blog - About the evolution of my go bot.

I did. Since I do not possess the book (it appeared when I was too strong for it), I do not recall all its contents though.



What DOES it say about what influence are thickness ARE? I recall that it gives basic (and IIRC useful) advice about how to USE thickness but that is a different topic from saying what the concepts mean.

I suspect that most people buying go books are more interested in how to use a concept than what exactly it means. I personally would have preferred more of the former and less of the latter in Joseki 2.

_________________
Patience, grasshopper.

So this is along the lines of your researches Robert,

but I remember a while back I was doing some influence maps of my own, using reflection of an influence-generating function off walls. (Using a method of images, take the board and make 8 reflected boards around it. Then compute influence for this "mega-board")

Ex:
X X X
X O X
X X X

(I believed that a high density of influence could be considered territory, and this would be an explanation for why a 3rd line stone is so much better than a 4th line stone for territory. The reflected portion in that same region is much higher, because of the exponential attenuation)

Another step I took was to have each stone contribute its influence to every point it could "see"(compute the relative angle of every group of stones, for each stone, find the closest group for each angle, and eliminate any points with a greater radius at the same angle)

I'm not sure the second part is accurate though. Influence ought to bend around groups,

In this way it should be more like a flow of water and less like a luminous source.

Any thoughts of how to improve these maps? I'd like to sit back down with them again...

_________________
Tactics yes, Tact no...

In relation to josekis, concepts must first of all be understood for the sake of building corner sequences and why they are built in particular manners. There understanding the concepts as such is more important than usage. Usage is also very interesting but I will discuss that in much greater detail for books about the middle game to be written later. Usage often occurs at a distance or in relation to positional context farther away. Such requires lots of full board diagrams. Instead of splitting the joseki series into too many volumes, I consider it more useful to discuss usage for the middle game.

This seems too artificial to be useful. Interpretation would be hard.



I started with such light models in the 90s, then tweaked a bit with stone circle shapes on a truely square board absorbing light, then revised again to let dead stones pass light etc. The pure light model (black positive, white negative light) is good enough for a very rough intuition of where the spheres of influence are and whether the light emitting stones are near. Beyond that it tells us almost nothing useful. It also cannot tell us precise things because we are not super-computers which could add all the stones' light ray functions for various (not always orthogonal) angles.

The light model is so attractive because we love light:) I needed 10 years to overcome that feeling and create the idea of connection and life degrees.

Forget it! It is not worthwhile! Instead I suggest to study applications of my model. E.g., it is interesting to ask when it suffices to consider only connection or only life and the other aspects are dominated (currently cannot provide additional relevant information).

Thinking about it again, I could not quite believe it and so I have counted Joseki 2 Strategy's bold (= most important) text paragraphs (sometimes blocks of factually related paragraphs) with these results:

85 definitions (of terms, concepts, methods)
176 applications (principles, applying conditions for concepts etc.)

That is 67.4% application, although the many examples are not even included in the counts.

For the influence and thickness chapters, matters are different though:

19 definitions
8 applications

This is 29.6% application.

***

EDIT: So I think what you mean is maybe not the ratio definitions : applications but the ratio general_idea : number_of_examples? More examples per principle etc. would only have been possible if the number of definitions, concepts, principles would have been much smaller.

I agree with Robert. Light in Newton's particle interpretation is a linear theory. Light from two sources just plainly adds. I don't think influence works in this way. In Huygens wave interpretation things are even worse. I can't imagine influence from one black stone to be annihilated by influence from another black stone.
Also other physical systems like two dimensional spin lattice models are linear and hence of no use as model for influence.
First it should be established that influence is a linear concept. I doubt this is possible.

Influence is not linear:

Click Here To Show Diagram Code

[go]$$c 23 black stones
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . O . O . O . O . O . O . O . . . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . O . X X X X X . , . . . O . , . . . |
$$ | . . . X X X . X . . . . O . . . . . . |
$$ | . O . X X X X X . O . . . O . . . . . |
$$ | . . . X . X X X . . . . O . . . . . . |
$$ | . O . X X X X X . . . . . O . . . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . O . O . O . O . O . O . O . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

Click Here To Show Diagram Code

[go]$$c 24 black stones
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . O . O . O . O . O . O . O . . . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . O . X X X X X . , . . . O . , . . . |
$$ | . . . X X X . X . . . . O . . . . . . |
$$ | . O . X X X X X . O . . . O . . . . . |
$$ | . . . X X X X X . . . . O . . . . . . |
$$ | . O . X X X X X . . . . . O . . . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . O . O . O . O . O . O . O . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

I don't see this as an example of non-linearity of influence, I think the influence map shows how that formation can effect the surrounding stones. I just don't think the influence map is the only variable in play.

That's why I never made provision for dead stones, the influence map shouldn't be the sole metric for the game state, but I think it can give information.

As far as the validity of the light model. I think the reason why the light model is a good place to start, is that light operates on a shortest path principle.

The limitation of this approach is that it assumes continuity, rather than computing shortest paths on a grid, (the shortest path may be degenerate, and the degree of degeneracy may have value)

But I think that kind of path-ing approach is a good start, and is approximated by the continuous approach.

_________________
Tactics yes, Tact no...

did you tried something like collaborative diffusion ?
http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&ved=0CDQQFjAB&url=http%3A%2F%2Fwww.cs.colorado.edu%2F~ralex%2Fpapers%2FPDF%2FOOPSLA06antiobjects.pdf&ei=YAlIT7WyH4ntOeu4tfsN&usg=AFQjCNEH_hMVBLfFWPZqB2HMxpdYRTrQMA

i learned of it while playing on the ants ai challenge, seems to be close to what you want: it does find "path" "around" ennemy stones.

i Should NOT ener this discussion but concerning your examples Robert, the influence map can be quite easily corrected to avoid the issue you mention by tweaking the diffused influence if the stones are alive or dead (or almost one or the other), and collaborative diffusion would take care of not diffusing the influence of a stone blocked by some others.

_________________
In theory, there is no difference between theory and practice. In practice, there is.