JF mentioned why the question of why do windmills and L shapes occur during Go fighting a while back.

I would like to share some of my observations and explanations. Go is symmetric enough and general enough for its concepts to be used as a model for many more simple things. (even chess )

For example, why are the corners so important? Why is the 4-4 popular despite the 3-3 invasion. I think this comes down to the parable of the fox and the rabbit. A hunt for a fox is worth a meal but for a rabbit is worth its life. So the 4-4 can let go of the corner and still get good eyespace and territory (due to local thickness relative to any approaching opponent stone against the wall) but the 2nd player depends on 3-3 access for their own life.

Another example is that we say a 3-4 has 2 directions of development. I think you can find in AI go that it is not uncommon for the opponent to play on the wrong side of the 3-4 (but not to approach, approach is almost always the right side), but the owner of the 3-4 almost never plays on the "wrong side" before the "right side". This concept certainly had already appeared in human Go, but it somewhat different circumstances (Lee-Sedol alphago game 2). My explanation, is that approaching the "right side" is a fight, unlike the 3-3 invasion, where the normal low approach isn't alive yet, or at least can still be attacked or pressed down. A pre-emptive play on the "wrong side" can help since it might not be that easy to get eyespace there otherwise. At the same time, you don't expect the opponent to have an efficient double attack, as there is always a lot of aji on the "right side", but perhaps simply at a lower temperature.

Windmills I think are somewhat rarer in AI go than human Go because say in the centre crosscut shape, AI tends to say that you should tenuki (or lose 1-2 points if I remember correctly). Crosscuts are a good shape for sacrificing for local extra control and shape but not for making territory as they don't have much development when the opponent is also strong nearby.

The Ising model in physics still seems interesting today, though I think there is more interest in non-equilibrium thermodynamics. Without doubt concepts of phase transitions are relevant to Go. But first, what are the energies and forces involved?

In Go, if an intersection X is controlled by W, it is certainly more likely that surrounding intersections Y, Z, ... are controlled by W. Why? X needs two eyes to live, so it must find them with a chain connected, so at least one neighbour must be W control (or W eyespace, or seki neutral point etc.). Similarly if Y really were B, then it also needs B stones nearby. But X is W, so Y is less likely to be B again. This creates a repulsion force between strong groups. Basically, a group's "energy" lowers the closer it gets to settling (regardless of which colour it is), and likewise for every intersection on the board. Temperature gets higher, when a large area (intersections, stones) all depends on the same region of eyespace to live (i.e. a life and death problem), when it isn't yet clearly alive or dead. Then a move on such a hot area affects this large region, with appropriate multiplicity. We think of it as a whole group that is affected. This seems somewhat analogous to forming a complete electron shell in chemistry.

So we certainly have a sort of bonding between friendly stones that lowers the energy. Perhaps this is like metallic bonding, sharing eyespace options like electrons? Then when a group is under attack, it is like a magnet is calling it? Perhaps the analogy is starting to overstep its bounds. Perhaps it suggests that the reason we don't find magnetic monopoles is that they are rather low temperature or low entropy, or too long range, or equipment to detect them is too low entropy?

However, during fights, we also have bonding between neighbouring weak groups of opposite colours. This creates perhaps the strongest forces and temperature fluctuations. If a group's easiest way to live is by leaning on (or even killing) an opponent group, then it will certainly be attracted to it. There is probably some kind of analogy to covalent/ionic bonding here, where Pauling's electronegativity has the principle that the strongest bonds occur between the most opposite groups? I'm not sure how, but perhaps the weakest (large enough) groups of both sides tend to have the strongest attractions (perhaps semeai that attracts lots of moves)? Sometimes to the point that they cross over each other and merge in a tangle of cross-cuts, tesujis, threats to sacrifice, threats to make the opponent's sacrifice heavier, counter-sacrifice and so on. Seki also.

What can we conclude in Go?

The weaker your stones, the more attracted to faster eyespace you are (if it works to live, faster meaning fewer moves played), such as corners or sides, or weak groups of the opponent, especially if you have no stones there whatsoever. Forces are balanced by the cost of living. So if a variation doesn't work to connect to easy eyespace, then it can only be called leaning for profit. It may still be valuable, or another direction where you are more solid may be better. Of course, if you still can't live, consider sacrificing. If you are too heavy to sacrifice, then leaning may still be best, but opp will also get double attack as you get close to such valuable areas for life.
In conclusion, you may notice that in centre fights, as they spread all groups tend to swerve towards empty areas of sides of the board. Of course, such areas are just big moves anyway so there will be natural swerving there, but they become even more valuable in fights.

If a group B is close to death, then a few questions need to be asked.
Why was it created in the first place? Was it just to give another option for a more important group A to live and the opponent made it heavy? Then consider sacrificing, perhaps using the weaknesses in the opponent's surround of A.
When near death but not yet dead, we expect the opponent to play tightly squeezing every little local profit of space locally. Clamping motions squeeze dragons when both sides (think they) can extract high value locally.
Consider ladders. This is how dragons are made. Valuable semeai like moves by the opponent, perhaps to make themselves alive in a fight. Once the dragon is released, it tends to be because the opponent already has enough profit, making themselves strong enough locally and further attacks don't help, perhaps because they are too thin (normally you will be slower if chasing a dragon on 2 sides at once unless already prepared with a wall). At this point, the temperature drops, but as the dragon isn't alive, it is still very valuable to attack/defend. Hence, it is likely to start spreading out at the boundaries, forming flat clouds (stratus?) in the process, leaning on the opponent's weak and valuable points to live. Weakness is always attractive in Go unless it doesn't work or is counterbalanced by your own weakness. Another form of spreading to form L shapes from a stick is when the spreading on the 1st line. This is normally too cold for the opponent to prevent, so it is common for stones to spread sideways there during endgame or from reducing the opponent's eyespace.

Sometimes new groups will be created like hot oil jumping from a sizzling pan. This is because it oil can cool down much faster (increasing entropy) outside the pan and there is a route to do so (even at the cost of gravity) because kinetic energy is so high. A weak group can still cut the opponent if that is a more valuable way to live (or extract value by sacrifice) because living with a weak group is so valuable but it is even more valuable if it can be done by capturing the opponent. Then a fight progresses.

Once a group is alive, the probability it starts becoming clumpy and fatter as the temperature cools is much more likely, to only fight for smaller profit locally (that couldn't have been obtained by pre-existing walls). Heavy and bulky shapes at the end of the game are likely to arise from this. Either that, or their value is onesided. Namely they unlikely add much local value to the clumpy shape, unless they help it live by capturing a group on the other side of it.

One last point. Often said that Go is about territory not killing. Since the opponent stones are likely placed for a reason (to threaten to surround enough areas of big enough territory that at least one will become territory, with attacking potential on the others), the value of surrounding an opponent stone tends to be more to undermine its connection to its potential rather than capturing one stone. Killing is when that stone doesn't have any much potential territory and is actually mostly the last eyespace opportunity of a connected big group. (groups and empty intersections are related, but groups are well connected so that one move can take the entire group whereas empty areas take more time).

I think that there should be a way to describe aggressive/conservative play in terms of this sort of temperature/shape analysis, but I haven't figured it out yet.
As usual the most difficult and interesting question is how to evaluate walls and moyos. Just divide by half? How to take small shape weaknesses into account. Even working out first order approximations to ability to live would probably be progress.

Thank you very much for sharing your ideas and analogies about go.

I also enjoy reading your game reviews with your thought process explained.


The windmills are emerging in go just in hommage to el caballero de la mancha by the way.

Some random points, Daniel.

Because of my work, translating chemical patents, I often toyed with go analogies based on science, but only in a desultory way. I'm afraid that I simply concluded that the best such analogy for amateur go was Brownian motion

Your clouds analogy has some potential, I think, as a way of describing the overall flow of a game. Related ideas such as warm fronts and tornados could be in the mix! I personally have never looked at this, but someone did propose it a long time ago. It may well have been Matthew Macfadyan, as he used to work as a meteorologist. Any Brits of a certain age with a fuller recollection?



I agree with your decision to highlight this. But I think it is important to use "wall" cautiously. Another saying from the days of old British go was "walls have ears but not eyes." A wall itself is not worth much unless it is actually thickness (i.e. has more than a passing acquaintance with eyes). Thickness could, I suggest, even be taken as a first-order approximation simply by evaluating whether it is genuine thickness (i.e. not a mere wall or influence). And then we could follow the Japanese and distinguish between first-order and second-order thicknesses in the form of atsumi and atsusa. Various pros have touted theories that may be considered continuing with a third-order approximation, by doing things like counting the stones in a wall and/or the area surrounded by the wall - the barmkin, I once called it. In fact, other aspects of this medieval concept, such as tower houses, pele towers and bastle houses provide a rather accurate description of surrounding shapes on the go board, simply because of their primitiveness, I imagine. When thinking of battles in the modern age, we tend, even if only subconsciously, think of drones and tanks, and Kallies. But medieval conflicts were almost as primitive as go. With a tower house (i.e. a wall that is genuine thickness) and a protective bastle house (i.e. a small bastille) not too far away, you can expect to keep many cattle (i.e. territory) in your barmkin. Without the bastle house, the reivers will easily steal your cattle. Not to everyone's taste, I accept, especially for numbers guys

As regards moyos, I still think Matthew's concept of virtual territory is the easiest to understand and use, but I'd be interested in your view of the value of the Korean idea of counting a moyo on the basis of 6 points for each keystone. Like counting 3 points for each stone in a wall of thickness, it seems to me that it often works, but when it doesn't work, it is rather hard to (a) see why and (b) make a sensible adjustment.

re your last point.

I think that sort of question would take me years to do the research to answer properly. For now, I think of edge effects around walls as mattering more, i.e. if the opponent is weak nearby (e.g. at 3-2 in the 3-3 invasion of 4-4). For example, the effects of walls should be more prominent in the centre because neither side (hence especially the opponent) can live there easily. Rather than sides.

So walls help even out the temperature between the sides (where temperature is naturally high) and the centre. This is a physics reason for why you should keep playing tenuki when you own a wall, at least initially, and only play later than previous generations of humans might expect.

Also, I have been using a principle that a peep to cut (if it works) may subtract more than 1 from the height of the wall as nearby follow ups may more speedily reduce the influence of the wall and attack it. But it depends on how well the wall can counter attack.

____

20221016 some more analysis

What is the value of a weak point? i.e. how to count its cost?

If opp is also weak nearby, and they can say peep or threaten to counterattack by leaning on your weak point (which is presumably a hotter area than elsewhere locally in a fight, by definition), then they may gain some eyespace. These balance out each other as perhaps local territory isn't big, but if it affects the marginal cost of living when under attack, then it counts. (i.e. playing a small side move to attack doesn't profit much if opp plays a similar size move running into centre with more directions of life)

Otherwise, if opp isn't weak nearby, then perhaps the weak point can be attacked from multiple sides. If it takes 1 move to fix (i.e. 1d), then assume for evaluation that opp extends on the wide extension with most potential. If opp can say wedge, forcing you to spend multiple moves to deal with it, even if they sacrifice, they may have extra forcing moves, depending on shape.
Curiously it seems that you should often play from the smaller side first if opp weak point is more open and 2d with 2 directions of attack. Then since the follow up is bigger, you have a chance to force from both sides. But it depends on marginal values.

Local temperature can't really be higher than sum of hottest weak points around. And the marginal temperatures should tell us how to evaluate local control (i.e. expected total score). As usual, difficult is how to calculate temperature as in a fight it is only defined once something settles (which may be many moves), so some logic about how fights settle (lowering temperature, exchanging this weak point for that) is required.


I'm not familiar with your farmhouse analogy. But I think you have a point that walls need spaces where the opponent is weak nearby, whether because you have support (i.e. territory), it is open, or the opponent is weak (i.e. they have some shielding but you are strong on the other side of their shield).

20221019

Re: clouds. I'm not sure where this came from, haven't interacted much with Macfadyen. Probably a mix of Shikamaru, San Francisco weather, 3d Go.
I've just studied some plate tectonic theory.

Regarding the notion of convergent, divergent, transform boundaries. Since I already noticed an analogy between convergent/divergent series and peace/war (Antti's lecture) in Go via temperature. What then is transform? Or perhaps can it be described in terms of shape.

Go shape:
convergent when locally valuable (i.e. corners, sides), attracts stones, high pressure, capture of relatively large marginals may occur (subduction?), highest temperatures (strongest earthquakes)
divergent when locally not valuable (i.e. centre), thickness, settled semeai. Low pressure. weakest earthquakes.
transform when each has support beside unsettled area and they are fighting for it, but neither side can win everything, but must split profit. Complicated and subtle, lots of smaller profits. Many fractures. Just fighting and exchanges, no real profit?

Series:
One series only tending to what limit?
Convergent when time limit of everything is the same.
Divergent when many different time limits. Mathematically this is defined as anything non-convergent.
Transform when only two limits or one infinite limit? I know some series like 1+2+3+...=-1/12 are meaningful and others aren't like 1+1+1+...=????, a pure singularity of a zeta function. I don't understand much deeper than this phenomenological level though, what is the underlying mechanism?

Plates:
convergent: pacific rim, ocean plate gets (cyclically?) subducted under the more stable and robust continental plate. also himalayas.
divergent: mid-atlantic ridge, iceland, magma rises to fill plates moving apart. (causing hurricanes below in mantle?)
transform: san andreas, plates moving parallel to boundary. No magma involved.

In this analogy is magma like board points?