Quote:
OC, reading to the end makes use of depth first calculation, and trying other moves emphasizes exploration. The idea is not just to solve a problem, but to understand it thoroughly.
I just read this in another tsumego thread by Bill in which he looks at the use of iterative deepening in solving problems. My vague reaction was somewhat along the lines of "Yeah, good point" and then I quickly read on. I think most people read forum stuff that slapdash way. We understand all the words, the idea expressed is in line with our own knowledge/prejudices or whatever - let's get down to the interesting stuff.
For me the real interest was in the mention of iterative deepening. That was because I clearly remember reading, very many years ago, an article about Newell and Simon's discovery that this technique worked wonders in chess programming. As I recall, there were two main benefits. One was that each iteration allowed an ordering of the moves so far, which helped enormously with pruning the alpha-beta tree efficiently. This was very counter-intuitive at the time. How could the huge amount of time to do a complete search at a low ply number with the hardware available in that era possibly be justified?
The other benefit, probably rendered nugatory now by modern hardware, was that if the computer was interrupted by the chess time control before it could search very deeply, it had at least looked at every move at a low ply and so could make a half-decent move without overlooking obvious (to us) little traps.
Anyway, that was enough for me to make a mental note to follow that thread.
Then, purely by chance, I turned next to my computer files and started doing a little bit of housekeeping - putting several files in a new directory. In the course of that I saw a file I had marked "Igo Tsumekata". It meant nothing to me until I opened it, and what I saw was the image below. And that got me thinking.
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The first thing I did was to recall Bill's post, but the bit that re-surfaced was not the glittering bauble of iterative deepening. It was mainly the humdrum word "understanding."
This image is the beginning of a book by Kobayashi Tetsujiro, which I had taken a mild interest in long ago because Kobayashi was a rival of Honinbo Shuei. He was somebody Shuei did not treat very well. I therefore always had a soft spot for K.
This illustrates what was for a very, very long time the usual way to present tsumego collections. It's what appears in ancient Chinese classics such as Xuanxuan Qijing and Guanzipu and goes back over a millennium. It was also retained in Japan in the early 19th century, an era when go publishing bloomed and many presentational innovations were tried. Tsumego essentially resisted these innovations until well into the 20th century. There were some apparent nods towards novelty, such as the diagram on the right, which shows the notation at use in the book, but even that was more common-sense than innovation, since there were other notations in use at the time (e.g. the iroha notation).
I had always assumed this was because publishing was then an expensive undertaking and the idea was to save on paper. The fact that several problems appear on the same whole-board diagram supports that. The fact that the solutions are scribbled in the margins of the same page also seemed to support that. That could arguably be seen as an innovation, as a typical approach in older books was to put the answers on the same board as the problems. But the ancients did have recourse to the margins for text notes on variations. That required the use of a notation, and the same idea in the image above can bee seen even in the ancient Carefree & Innocent Pastime - our oldest diagrammed manual.
Yet I have always had a niggling doubt that survival of this practice really was just a matter of publishers' parsimony. Thinking about Bill's post is, however, the first time I have let that doubt have some wiggle room.
While I was marshalling my thoughts, the problem in the lower right caught my eye (Black to play). I think the reason was some unconscious thought along the lines of "why is such an easy problem in this book?"
Needless to say there was more than a touch of hubris there. I could do the problem, and I could even identify a couple of themes, so I could even claim I "understood" it. More hubris.
But I didn't really
know the answer as I still had to check my so-called understanding. (I only knew how to
get the answer.) I therefore had to read the text at the top. That was my Damascene revelation.
If the problem been presented in a modern book, I would have just turned the page, looked at an answer diagram, and said, "Yup, I've got it." And moved on.
But in this case I had to do
two things I would not normally do. One was to convert the notation to a version I am more familiar with (e.g. 3-2 to S3) and the other was to visualise the moves for myself on the board. It was in the painfully slow (but therefore valuable) course of doing that that I realised my understanding was defective. I don't mean wrong. In fact what I understood was 100% right. It was defective because I had seen the themes as separate items in a list. Lists are usually a bad way of thinking. This was another example. I had to learn to see the elements as part of an organic whole. Or, as Bill says, "understand it thoroughly."
Still, I think the most valuable lesson for me was how powerful it is to be led move by move so as to visualise the solution on the bare board. if you think about it, this is 100% efficient training because you are not just practising visualisation - you are also following the route of the correct solution, thus reinforcing your intuition in the optimum way.
This was of special interest to me because it's essentially the way I have been presenting my most recent books in Go Wisdom format. There I have been concerned with complete games rather than problems, but I have likewise eschewed variation diagrams in favour of describing the variations within the text, either in coordinate form as here or by giving a detailed clue as to the outcome (e.g. it ends as a capturing race that Black wins by one move). I am forcing the reader to actually do some study work. In other words, I am being cruel to be kind.
I am inclining now towards believing that the old method of presenting tsumego problems was actually the best. I am even minded, therefore, to maybe publish Kobayashi's little book in precisely that format - answers in coordinates - so that other people can try out the technique for themselves.
If you want to try it at once, the solution to the problem above is: S2, R3, S3, Q4, S6, S7, S5.
You will see that this does not solve the problem down to the bitter end. But that was the aspect that led me to realise I had a poor (inorganic) understanding. It was thinking about why the author stopped his solution there that led me to
framing the problem - or, rather, both problem and solution - in a more organic way. Although my thoughts are continuing and may change, at present I believe this "framing" is actually a human version of iterative deepening - it is ordering my thoughts in a way that makes the deeper search much, much more efficient.