it's rather delightful to come across a position where the side extension is favored over a corner move.
This leads me to a hypothesis: the correct timing for a side extension is when both corners are exerting significant influence towards the side.
I haven't got the answers, but I have a feeling that I know where the answers lie. I have come to this feeling after having recently looked at a lot of old Chinese commentaries where the terms used are rather different from the ones the Japanese and thus we tend to use. They are looking at similar positions but through a different prism. It is often startling how much difference that makes. Another related thing that affects perception is different emphasis. The old Chinese seem to stress timing far more than the modern commentators.
I suspect therefore that, to make progress with learning from AI, we are going to have to devise a new vocabulary.
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$$ | . . . O . O . . . . . . . . . . . . . |
$$ | . . O , . . . . . , . . . . X , X . . |
$$ | . . O X . . . . . . . . . . . . . . . |
$$ | . . X X . . . . . . . . . . . . . . . |
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$$ | . . X , . . . . . , . . . . . a . . . |
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$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . X X X . . |
$$ | . . . O . . . . . . . . 1 X O O O b . |
$$ | . . . . . . . . . . . . . O . . . . . |
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- Click Here To Show Diagram Code
[go]$$Bc
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$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . O . . . . . . . . . . . . . |
$$ | . . O , . . . . . , . . . . X , X . . |
$$ | . . O X . . . . . . . . . . . . . . . |
$$ | . . X X . . . . . . . . . . . . . . . |
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$$ | . . X , . . . . . , . . . . . a . . . |
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$$ | . . . , . . . . . , . . . . X X X . . |
$$ | . . . O . . . . . . . . 1 X O O O b . |
$$ | . . . . . . . . . . . . . O . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
For example, in your example above (which I will call Diagram 1), you talk (as we all would) get away from the concept of extensions: "both corners are exerting significant influence towards the side."
But, as you also note, that way of talking lets us down in the following case (Diagram 2):
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$$ | . . X . . . . . . . . . . O . . . . . |
$$ | . . . , . . . . . , . . . . . O . . . |
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$$ | . . . X . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . O O O . . |
$$ | . . . X . . . . . . . . a O X X X b . |
$$ | . . . . . . . . . . . . . X . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------
- Click Here To Show Diagram Code
[go]$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . O . . . . . |
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$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . O O O . . |
$$ | . . . X . . . . . . . . a O X X X b . |
$$ | . . . . . . . . . . . . . X . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
Extensions are rarely mentioned in old Chinese, expect in the very limited sense of two- or three-space extensions. That tells us straightaway that we don't actually have to talk about extensions at all! The Chinese put the emphasis instead on expanding "power" (势) or what we might call a sphere of influence. For similar reasons they don't talk about thickness, so again that tells us we don't have to, either.
Let us therefore try to look at Diagrams 1 and 2 by eschewing the concept of extensions, but without going overboard and trying to apply the Chinese world view. Let us use the western concept (Matthew Macfadyen's) of "virtual territory."
The basis of VT is that you map out a large area that is big enough to be divided in two, and say that, "If he invases on one side - I don't care which - he will live small but I will get a large confirmed territory on the other side.
This does work out that way in practice, but the theory doesn't seem very popular. In think that's because it may work as predicted but doesn't give good overall results. I think AI shows why.
If we look at Diagram 2, the VT area can essentially be divided into
two areas. Bad.
But if we look at Diagram 1, the VT area can be divided into
three areas. Good.
My speculation about what is happening (which seems to fit with games by pros who study with AI) is that the gain from a VT area split in two is not enough. The lone "safe" area that results after an invasion of the other side is still subject to erasure and so on. You end up over-protecting your investment.
With a three-area VT, however, you end up two safe-to-safish areas after invasion of the other, and instead of the opponent being able to apply pressure at his leisure on your one big nest egg, he ends up instead having to chase two rabbits at once.
If there is anything in that or a similar theory, it seems to be that we should get a away from the idea of talking about extensions, which have strong connotations about territoru on the side. Instead, we should find a term that forces us to think about potential territory in a more VT or "sphere of influence" way, and to use terms such as fence post or claim markers, or whatever. It may be that a move chosen that way coincides with the spot chosen for an extension, but the mindset is very different. In particular, the VT or SOI mindset might usefully lead you to
reject a move on an extension point and, indeed, encourage to play moves on points you never looked at before because they were not extensions.
I think this language-controlled mindset comes up in other ways. In Diagram 2, for example, generations of us, pros included, have always assumed that a Black move at 'a' is only natural. That is because we have been bombarded with testosterone-laden advice. We must apply "kiai", we mustn't let White play 'a' and "force" us to connect. we must "bully" the opponent and "press" him into the corner, etc etc.
But if we strip away all of that language and look at the position dispassionately, we could alternatively say White 'a' "helps" Black to connect. We could note that there is no loss because it is the exchange of a third -line move for a fourth-line move, which we know to be normally equal. And of course, not playing 'a' means Black gets sente to play elsewhere first. Bots do that a lot. Old Chinese commentaries stress that a lot. A recurring phrase in OC commentaries which you don't see in Japanese commentaries is 'fighting for the initiative' 争先.
The Jesuits used to say, give me the child and I will give you the man. The main tool in their armoury to achieve that result was, quite simply, words.
Using new words in go may be like switching from using a donkey to power a grinding stone to using a two-stroke engine. One small step for man. A large leap for donkeys.
here, intending to more or less complete white's framework. This move is suboptimal by 1.5 points. Incidentally, a or b would be perfectly good moves here, and perhaps worthy of study. However, right now I'd like to focus on another continuation, also endorsed by KataGo, that is a bit closer to my intention in playing 
, black's shape is much stronger, so a second push is not so threatening). Second, my move was in not quite the right spot (the two-space jump is suboptimal by 1 point even after the 
is a joseki position I've been seeing more of lately, but I actually haven't studied this position much. I vaguely recall seeing it in a New York Go Center video (but don't remember which one) -- I believe the video said black can kill white with a. Based on this recollection, my intuition has been that a is the best local follow-up for black, and also probably the best move for white to avoid being killed.
instead of a, after white 
I unfortunately followed up with a anyway. In fact, KataGo thought I should play tenuki in this case. But assuming I'm tempted to play a local follow-up, 
is 2.3 points better than a.
threatens a severe cut at b, so black must defend. An alternative to