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and Powers of Analysis through Visualization by Richard Bozulich © Copyright 2015 by Richard Bozulich All rights reserved according to international law. No part of this work may be reproduced by any mechanical, photographic, or electronic process, nor may it be stored in a retrieval system, transmitted, or otherwise copied for public or private use without written permission from Kiseido Publishing Company. Chigasaki, Japan |
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Visualization
The human mind has the ability to clearly visualize things without actually seeing them. We do this every night in our dreams. Photographic memory is the ability to memorize these visualizations. Once a person has developed the ability to visualize things, such as symbols on a printed page, on a computer screen, or a position on a game board, remembering them is the same as the ordinary process of committing something to memory. Therefore, the power of visualization and photographic memory, though not the same, are closely linked. Succinctly put, photographic memory is simply memorizing our visualizations. Like all memories, they need to be refreshed if left dormant for a time, but once learned, they quickly return. Blindfold Chess Versus Blindfold Go Although it is rare for go players to play blindfold go, blindfold chess and even blindfold shogi (Japanese chess) games are quite common. In fact, blindfold chess tournaments are sometimes held and the playing strength of the participants doesn't seem to be diminished by much, if at all. The great chess grandmaster Alexander Alekhine played 26 simultaneous blindfold games against a field of very strong opponents, some of whom were of grandmaster strength. He ended with an impressive score of 16 wins, five draws, and five losses. This achievement was later eclipsed by a number of players (including Alekhine himself with 32 simultaneous blindfold games), but not against a field as strong as in his 1924 achievement. According to The Guinness Book of Records, the record for the most simultaneous blindfold chess games played is held by George Koltanowski, who played 34 games in 1937, winning 24 and losing 10. Alekhine's best was 32 games, of which he won 22, drew five and lost five. The reasons that blindfold go is rarely played are obvious: the playing field of the chess board (8x8) is visually manageable and, as the game progresses, pieces are captured, so there are fewer items that the players must keep track of. On the other hand, the playing field of a game of go is more than five and a half times larger than that of chess (64 squares verus 361 points). Moreover, as the game progresses, the board fills up with intricate arrangements of black and white stones. Keeping track of all these stones is a monumental task. One method for increasing your power of visualization on the go board is to solve life-and-death problems without looking at the board. First, look at the problem on a board or in a book and visualize the position in your head, then solve the problem without looking at the board. The playing field of most life-and-death problems is contained within a 10x10 grid, so this is visually manageable. According to Michael Redmond 9-dan, many apprentice go professionals solve problems in this way in order to build up a go board in their heads. This gives them a clearer vision of the position as they are reading out the moves, enabling them to analyze more deeply. Building up a Go Board in Your Mind When training by this method you should start out with simple problems that have a limited playing field. Such a collection of problems can be found in Kiseido's publication 1001 Life-and-Death Problems. All the problems in this book have a playing field well under 10x10 lines and, at the start, are easy (one-move solutions). They gradually become more difficult (three-move and five-move solutions). Another collection of problems can be found in Kiseido's recent publication The Basics of Life and Death. The playing field of most of the 177 problems in Part Two of this book does not exceed 10x10 lines. Moreover, they are not just a random collection of life-and-death problems. Each one is a basic pattern that results from josekis or skirmishes in the corners or along the side, so they could easily arise in any of your games. Internalizing them will do much to improve your game. Once you have worked through the above two books, you could then try solving the more difficult problems in 300 Life-and-Death Problems, 5-kyu to 3-dan and 300 Life-and-Death Problems, 4-dan to 7-dan. The collection of problems that apprentice go professionals most often use to develop their visualization abilities is the collection of ancient Chinese problems found in Kanzufu. These are not easy problems, so they are a challenge for players 6-dan and stronger. Concentration Once you have developed the ability to visualize — even partially — the go board, you will find that solving life-and-death problems becomes faster and easier. This is because you become more focussed on the problem and there are fewer distraction. Everything is concentrated in your mind, so your concentration becomes more intense. I have the most success in solving difficult life-and-death problems in a dark room when I go to bed at night. Even when you are playing a game and looking at the board, you still have to visualize the results of your analyses. Einstein is supposed to have said, 'we only use 10% of our brains.' Visualization is certainly some part of that 90% that most people do not fully use. One often sees evidence of how professionals clearly visualize go positions in their minds. Sometimes professionals giving public commentaries on large demonstration boards look away from the board to read out sequences, as they find it awkward to read out moves on the large board right in front of their faces. I remember a public commentary on a Japanese title game given by Kajiwara Takeo in the 1980s. A complicated fight was going on in the game and the young woman professional assisting Kajiwara asked him if a certain stone could be captured in a ladder. To answer, Kajiwara looked away from the demonstration board, stared into the distance for a few seconds, then answered without looking at the board: 'No, it's not a ladder.' Clearly, he had no trouble mentally visualizing the whole position. Professional shogi players also have impressive visualization abilities. During shogi festivals or special events they often play blindfold exhibition games. This is more difficult than playing blindfold chess because shogi is played on a 9x9 board and captured pieces can reenter the game, so all 40 pieces are potentially always in play. I remember a meeting I had with the great shogi Meijin, Oyama Yasuharu, who at the time was the president of Japan Shogi Association. I had entered into discussions with the shogi association about propagating shogi in the West and how much it would cost to finance a magazine and publish some books. I presented Oyama with a rather long list of items and their cost, but I hadn't had time to add them up before the meeting. I started to do the calculations on my calculator, but, after I entered the first item, Oyama had finished adding up the entire list in his head and announced the sum. I couldn't believe that anyone could add up such a long list of numbers so quickly and in their heads as well, so I continued entering all the numbers on the list. The total I came up with was the same as Oyama's. How was Oyama able to make this calculation almost in the blink of the eye? In China and Japan, the soroban (abacus) has been used for centuries for making arithmetic calculations. Before the advent of hand-held calculators and computer accounting programs, it had been used most often by accountants who had to add up long list of numbers. Besides addition, the soroban can also be used for subtraction, multiplication, and division, and even for extracting square roots and cubic roots. Before the war, the use of the soroban in Japan was ubiquitous. Oyama was born in 1923 and in 1928 it became a compulsory subject in grade school. No doubt that is where Oyama learned how to use a soroban and he clearly became quite adept at it. Every year in Japan, the All Japan Soroban Championship is held in which children compete in preforming difficult calculations, such as multiplying two 7-digit numbers, on the soroban. The finale of this competition is Flash Anzan — AN-ZAN 暗算: 'AN' means dark and 'ZAN' means calculation) — we might translate this as 'blindfold calculation'. In less than half a minute, fifteen three-digit numbers are flashed on a screen and the contestants are required to add them up. The numbers go by so fast that it would be impossible to do the calcuations by manipulating an actual soroban. So the contestants have to do the calculations in their heads. When the first number flashes on the screen, it is instantly visualized in the contestant's mental soroban. When the second one appears, it is instantly added to the first number on their mental soroban. This process continues until they reach the final sum. In the past, many accountants and others who constantly used the soroban for their work, tended to stop using a physical soroban and made their calculations by visualizing a soroban in their heads. Not having to manipulate an actual soroban dramatically increased the speed at which they were able to make their calculations. Nowadays, with the prevelance of calculators and accounting programs, accountants rarely use a soroban. In conclusion, the younger a person starts to develop their powers of visualization, whether it be a game position, a soroban, or a printed page, such as a musical score, the more adept they will become at it. I speculate that the ideal age would be four or five, but adults, even those over 60, can benefit from such training. Next essay: Microgo |