Many people believe thinking is ...

By Rob Van Zeijst

Many people believe thinking is a natural process and can be applied to a variety of subjects. However, thinking and reasoning are not hard-wired skills, but they can be taught. While school subjects often involve rote learning, most, including math, reading and languages, draw on thinking skills. But none of them actually embraces and develops them. Comprising elements such as memory, cognition, decision-making and problem-solving, critical thinking is a complicated process that incorporates a number of skills such as gathering information, evaluating data and making logical inferences and hypotheses.

Reasoning is a meta-skill because it involves analyses and a decision-making process for real-world application. All of these skills are used and exercised in go, making it the ultimate tool to acquire these skills. It is finding more recognition in both academic and business circles. In fact, go is taught in a number of universities.

Diagram 1 (1-29 represent moves 123-151): Let us resume the game we started two weeks ago between titleholder Keigo Yamashita and challenger Satoru Kobayashi (Black) in the 31st Kisei title match.

Black 1 was the concluding move last time. White 2 defends in sente against the cut at A and black 3 against the one at B. After the sequence through 14, White's group seems alive. Black, however, has a trick up his sleeve when he plays at 15. He wanted to play at 19, but he got the order wrong. Instead, he should have followed Reference 1. He could have used 15 and 17 as ko threats, but since he played them prematurely, White is able to resist with 20 and fight a ko on less unfavorable terms. Black has a good ko threat at 29, but it is not nearly as good as one at 15, but he had already shot his wad.

Reference 1: Black 1 is an exquisite move. White 2 is the best response as it defends against the threat at A and stops Black playing at 15 in sente as well. If White plays at A instead, Black will force 15 for 2 in sente, which is even better than the sequence shown. On the other hand, if White plays at 15 (as in the actual game), Black can play the ko, using 3 and 5 as good ko threats-White would not stand a chance in that case. After forcing 1 for 2, Black reinforces his position against a possible counterattack by White at B, followed by black C, white D, black E and white 5. Now Black is ready to strike with 7. The moves through 21 show one example of how White's position crumbles. White cannot connect at F, because of black A.

Diagram 2 (30-56 represent moves 152-178): Since he has no ko threats, Black plays at 31, although capturing with A would have been better, since now White can play at 34 and Black has to answer at 35. White is alive after 30 and 32. Next, he strikes at 36 and gains a lot in the sequence through 46. Black takes the lower right corner, but note that White has already bottled up six black stones in the center with 34 and 48. After White 56, the difference is about 10 points with no chance to make amends. Therefore, Black resigns.

Diagram 3: This game is between Cho Chikun, holder of the Judan title, and current NHK Cup titleholder Hane Naoki for the NHK Cup. The games are broadcast every Sunday on NHK. In his inimitable style, Cho, who plays Black, usually grabs territory early in the game in exchange for giving his opponent thickness and moyo (territorial framework). Then he jumps right in there and the game is often decided by his invading group living or dying. This game is a perfect example of this strategy. The sequences in the top left and top right are both joseki (standard corner patterns). As expected, Cho chooses these joseki patterns because the corners become solid territory. The point where White can deviate is after black 29. Providing a running commentary, Takao Shinji mentioned he had played a similar game with Cho up to move 29. At that stage, he opted for A, but was crestfallen when this was answered by black B. In retrospect, he said playing at 30 immediately is probably better, which is what happened in this game. After white 36, the question is how and where Black should invade. For starters, he starts through a nozoki (peeking between two enemy stones) at 37. Would you connect at D now? If not, how would you cope with this situation?

Solution to last week's problem

Solution 1: White 1 and 3 are correct. After Black captures the marked white stone with 4, it becomes a ko. White has a good internal ko threat at A-Black must oblige with B, and White can recapture the ko.

Reference 2: If White captures the marked stone with 3, Black plays 4 and 6. White must connect with 7 (not shown) where he earlier took the marked stone. Black makes two eyes with 8. This is bad for White.

New problem

Problem: What should White do to kill the Black stones? Hint: Note the presence of the marked white stone. This will influence the solution.

Van Zeijst is a four-time European go champion and European representative at the Fujitsu World Championship.