2. Go Memories of an Amateur Mathematician
In Honor of Go Seigen who is 100 years old Jun12, 2014 --Herb Doughty
September 2014 version
Through my father's influence, from my days as a toddler, my main joy has been exploration.
A decade later in 1950 in Lima Ohio, Cosmology and Planetary Science were my biggest interests.
One year later, with similar enthusiasm, I began to explore the sequence of binary operations,
which begins with addition, multiplication, exponentiation, and towers of exponents. I explored many
ways to nest such recursion very deeply. With inspiration from Archimedes' The Sand Reckoner, I
began to suspect that the geometry we live in has only a finite number of points and lines and involves
no infinite sets.
While in the seventh grade, I founded the Lima Astronomy Club, which later became the Lima
Astronomical Society (http://limaastro.com). Two sources that inspired me a great deal were Edwin
Hubble's book The Realm of the Nebulae and the article Our Universe Unveils New Wonders, by the
founding director of the Mount Palomar Sky Survey, Albert G. Wilson, in the February 1952 National
Geographic.
In a picture on the last page, Wilson showed us what my heroes, the Mount Palomar
astronomers, did for fun when they were not working: They were playing Go, an interesting looking
Asian board game that I had not yet heard of.
While briefly at Caltech in 1956/7, I was very inspired by Feynman's Physics-X lessons on
exploring technique, and I was delighted to hear, from my fellow students at Caltech, about Gauss and
his exploration of finite geometry with coordinates in finite fields and his frustration with colleagues in
Astronomy and Physics who would not take finite fields seriously. At Caltech, top faculty and students
loved Go. But I, desperately struggling to keep up, didn't dare even watch a game. I soon moved to
Ohio State.
In 1959/60 I took a break, working fifteen months in satellite tracking at Smithsonian
Astrophysical Observatory and regularly attending Harvard's Astronomy colloquia, where I met several
of the Cosmologists, whose work I had admired for a decade. I was disappointed that, in contrast to
Caltech Physicist Richard Feynman, and to the best Mathematicians I had met, it seemed that none of
these Astronomers would take finite geometry seriously. (Fifty years later I found out that at least one
Astronomer had taken it seriously back then, Albert G. Wilson, in several ways my inspiration since
1952. Why him and not the others? He got his PhD from Caltech in Mathematics.)
Back at Ohio State, I changed my major to math and won the local ΠΜΕ Math Competition.
About the same time that I won the local mathematics competition, my Latvian friend Arturs Zagaris
won the local chess competition. As we were congratulating each other on our small triumphs, we
confessed our dreams for the future. For about a decade, each of us had wanted to learn Go! We sent
away for Go sets and books by Arthur Smith and Edward Lasker. With our friends, we began
exuberantly grinding in by rote the habits of playing Go like complete beginners.
About a year later, I had a remarkable remarkable stroke of good fortune! Minoru Tajima,
then head of earthquake prediction research for the government of Japan, came to Ohio State to attend
Professor Heiskanen's three month research meeting on Geodesy using Earth satellites. The day he
arrived for the meeting, Tajima San found out that I was trying to learn Go, so he moved into the
rooming house where I lived, to be my teacher for the three months that he would be in town.
He impressed me so much that although only once before had my parents had an overnight
guest from outside our family, the day I met him, I was confident that they would want me to bring him
home for Christmas the next week. I called them, and they were delighted. So I invited him.
3. On being introduced to me, he had said that he was an amateur four Dan Go player, which,
although it sounded overwhelmingly strong to me at the time, was still at least two big amateur steps
plus nine smaller professional steps from the top. I quickly began to see how very understated his
description of his strength was. One weekend, he went to New York, spotted their 5 Dan players 2
stones, and won all his games. Back in Japan, he played about ten games of Go per week while hanging
onto a strap on a crowded commuter train with his friend, just telling each other their moves with no
board. Even most pro's can't do that! He was a friend of the great champion Sakata Eio, holder of the
Honinbo and Meijin titles. In their teaching games, he played Sakata Sensei with only a two stone head
start, winning about half, as would a low level pro. He was also able to win many of his even games
from low level pros.
Tajima San also had remarkable expertise in conflict resolution, because of which, the
government employees union had prevailed upon him to also head their Tokyo office. The day after I
met him, he said “I expect that you have noticed that when two people are arguing, they rarely change
each other's mind or learn from each other.” I said “Of course!” He said that usually each of them has
reached his position through a long chain of valid inferences from things that he had believed for a long
time. If their positions really contradict each other, one of them must be false. Valid inferences with a
false conclusion must depend upon a false uninferred premise which we will call the false axiom.
He said that if you could guess the false axiom and the chain of inferences, then without
upsetting him, you would be able to change his mind about his conclusion within ten minutes, in the
following way ─
1. Picture, from multiple perspectives if possible, the issue the false axiom claims to answer.
2. Pose as a question, the issue from the perspective most clearly showing that his false axiom is not
the answer. If you guessed right, he will seem stunned and will give the correct answer.
3. Pose the issue sequentially from each of the other perspectives that you were able to find,
watching each time his confidence in his new understanding grow.
4. Step by step, lead him down his tree of inferences, watching his opinions flip. Provide
reinforcement. He will now agree with the other party, while feeling enlightened and undisturbed.
I said that his method sounded great in theory, but I could not imagine it working in practice.
He smiled, and asked whether there were any social issues over which my father and I had been unable
to reach agreement over the years. I said that there were. He asked me to name three. I did. He picked
out one, saying, “I can change his mind about this one in ten minutes!” I really had my doubts.
The next week at my parents home, after dinner Tajima San began a conversation with Dad.
After his first question, Dad seemed stunned and gave the correct answer. Less than ten minutes later,
Dad was in agreement with me on the issue. I was astounded to see his method work, step by step,
exactly as he had described. Dad and Mother were delighted to have had Tajima San with us, and
remembered him fondly for the rest of their lives.
Notice that this is not a general technique for making arbitrary changes in peoples'
opinions but is precisely a debugging tool with which we may help each other to gracefully shed
false beliefs!
Tajima San said that the reason that this technique is not in widespread use throughout the
world is that very few people have much success guessing the false axiom. He said that his own
success in guessing the false axiom came primarily through extensive experience with high level Go!
Almost every evening Tajima San gave me at least two hours of lessons, often including
important subtly related topics far from the Go board.
4. The rest of my life has been greatly enriched by my three months with Tajima San.
For thousands of years, Go has had a prominent place in east Asian culture.
The Four Arts (四藝, siyi), or four main accomplishments required of the Chinese gentleman scholar,
were qin (the guqin, a stringed instrument. 琴), qi (the strategy game of Go, 棋), shu (Chinese
calligraphy 書) and hua (Chinese painting 畫). Long famous as an avenue toward mental
improvement, looking for the big picture, and making better decisions, Go has through the ages
attracted many of Asia's greatest minds, not only Go Masters (top pros}, but also top amateurs, who
include the most outstanding people in many fields, like Tajima San.
Until quite recently in the western world there has been no opportunity to reach top amateur
level. Nevertheless, during the twentieth century, top westerners in many fields have loved Go,
preferred it to chess, and eagerly tried to learn it, for example: Physicists Albert Einstein, Richard
Feynman, and Edward Witten, & Mathematicians Ralph Fox, Paul Erdös, John Forbes Nash, John
Horton Conway, and Elwyn Berlekamp and Chess players Edward and Emanuel Lasker.
In this picture, long time World Chess Champion and Pioneer Ring Theorist Emanuel Lasker playing
Go with German Go Champion, Felix Dueball. Both had first heard about Go around 1906 & 7 through
Edward Lasker, Emanuel's younger close friend, also among the worlds thirty top Chess players, author
of Chess and Go books, co founder of the American Go Association professional engineer, and inventor
of the Breast Pump for saving mothers milk.
See http://en.wikipedia.org/wiki/Edward_Lasker and
http://users.eniinternet.com/bradleym/America.html
Near the end of his life Emanuel with a genealogist said “See Edward we are related way back here!”
Here is link to a different Dr. E. Lasker vs Felix Dueball game. Is it with Edward or Emanuel?
http://www.lifein19x19.com/forum/viewtopic.php?f=12&t=7833
5. In Berkeley, on October 12, 1967, Walt McKibben and I started the Berkeley Go Club. I was
president of our local club, and Walt was president of the American Go Association. Walt had invited a
very good reporter, Bonnie Yee, from the campus paper. At our first meeting, we had twenty people
including the reporter. Walt had me reserve a larger space for our second meeting, at which we had
sixty, mainly beginners. We averaged fifty people per meeting for our first ten years. There was no
Internet, and Go was only available in Berkeley on Thursday evenings. Seeing so many people doing
Go was a big attraction. Faculty and students had no fear of addiction. This was good for attracting
beginners, but limited their further development.
At first our strongest players were around amateur 1 or 2 Dan. Mark Okada, arrived in Berkeley around
1980 and and taught students, who then quickly became 5 or 6 Dan. Later he brought Go and Internet
together by starting IGS, the original Internet Go Server. http://pandanet-igs.com/
Kaoru Iwamoto – Honinbo Kunwa
About 1968 Walt introduced me to a real Go Master, Kaoru Iwamoto, who, after winning the
Honinbo Title (effectively the World Go Championship at the time), devoted the rest of his life to
spreading Go in the western World. As Walt was driving me to San Francisco to be in a simultaneous
exhibition (a simul) with Iwamoto Sensei, a very long freight train delayed us enough to miss the event.
But, we did see him replay enough of each game to show how the largest mistakes could be avoided.
6. Walt then arranged a one on one game for me. While playing me, about an hour after the
simul, out of the corner of his eye, noticing one of the players about twenty feet away writing numbers
on a small piece of graph paper to record his game in the simul, Iwamoto Sensei yelled over to him
“That wasn't forty-seven. We exchanged two pairs of moves before that.” I was surprised by his acute
vision and his remarkable memory, and I was impressed by his brilliance in Go; by the warm, kind way
in which he related to each of us; and also by his humility.
In the course of a long conversation, he was asked his feelings about the answer given by a
more recent Honinbo title holder, Takagawa Kaku, to the question ,“How far are top humans from
perfect play?” Takagawa Sensei had given a hasty answer— “With two stones I could beat God.”
Iwamoto Sensei smiled and chuckled at being asked to comment on that answer. He carefully prefaced
his comment with, “To begin with I must say that I have no idea what perfect play looks like.” He then
contrasted his feelings in three much more easily imagined situations:
“Suppose that I was playing another player of my own strength, but my life depended upon
winning the game with a two stone head start. I would feel frightened, because I can remember just
last year making a blunder serious enough to lose such a two stone game.
Suppose that I was playing another player of my own strength, but my life depended upon
winning the game with a three stone head start. I would feel a bit of anxiety, because I remember
several years ago making a blunder serious enough to lose such a three stone game.
Suppose that I was playing another player of my own strength, but my life depended upon
winning the game with a four stone head start. I would feel no more anxiety than if my life did not
depend on winning, because I need to look back to my childhood to remember making a blunder
serious enough to lose such a four stone game.
But I must remind you, I have no idea what perfect play looks like. It may be very different.”
Later in the long conversation, someone asked Iwamoto Sensei which player he most admired
of all the go players who ever lived. He said, “Over the centuries there have been many great ones—
Dosaku, Shusaku, . . . The one that comes to my mind first is someone I have gotten to play over the
decades, Go Seigen.”
In his seventies, although usually away from Japan and spreading Go around the world,
Iwamoto Sensei still maintained a Go academy in his native country and was still a contender in major
tournaments. In his eighties he retired from tournament play and sold his Go academy. With the
proceeds he created international Go centers in New York, Sao Paulo, Amsterdam, and Seattle.
In 1986 I got to sit next to him at the 1986 Banquet celebrating the 50th
Anniversary of the San
Francisco Go Club, being a chapter of the Japan Go Association. Remembering from his previous visits
that I helped beginners in Berkeley, he asked, “So, Herb, when you are playing someone their first
game, how do you play them? What size board? And how many handicap stones?” I said, “I use a 9x9
board with 5 handicap stones.” With a twinkle in his eye, he smiled and chuckled. I knew that he had
spotted something I should learn, so I said, “Sensei, I know that since winning the Honinbo title, you
have spent many years teaching people around the world, so I expect that you have played many
beginners their first games. How do you play them?” He said, “I use a 9x9 board with 4 handicap
stones. Both for the student and for the teacher, it is far better for the teacher to play each move, taking
into account the past mistakes but no future mistakes. The student sees good moves to copy, and the
teacher does not develop positive feelings toward moves that only work against weak players.”
Living in the San Francisco Bay Area, over the decades, I have greatly enjoyed meeting and
playing several other awesome Go Masters—Fukuda, Miyashita, Okubo, Haruyama, Kobayashi Chizu,
Michael Redmond, Jimmy Cha, Jiang Jiujo, Jiang Mingjiu, Kim Mung Wan, Yang Yilun, and, most
memorably, Go Seigen, (Wu Chin Yuan in Chinese) felt by most Go players to be the greatest Go
Master of all time. Go Seigen played an eighteen board simul at the SF Go Club November 21, 1971.
7. John Givens, above,
was the only local player to win his game
with Go Seigen.
I am the left most player in the main
picture.
John was immediately to my right,
just outside the main picture.
http://gogameguru.com/go-seigen-turns-100-today/
www.advancedstudyroom.com/go-seigen-wu-bio-by-his-brother/
Before starting the simul, seeing that there were many more eager local players than the
eighteen boards that could fit around the tables, via an interpreter, Go Seigen said that if someone
resigns early, then someone else can sit down and start a game. Therefore, I don't know how many
people he played that day.
Then, with the interpreter, he came around to each of us, asking our name and how strong we
thought we were, remembering both our names and our strengths.
When I said that I thought I was about 6 kyu, he said that a nine stone head start would not be
enough. “You will have the 9 move head start, but I will make it interesting in another way. I'll tell you
now, before we start, that right here in this place (putting his hand down centered at about the (7,7)
point in my lower left quadrant), I will catch a large group of your stones.” I believe that he did some
such special thing on all of the boards of players as weak as I was and perhaps even on all boards with
kyu players.
Once the games began, he maintained a brisk walking pace (at least three miles an hour) as he
walked around the tables, placing a white stone on each board as he walked past, until about the
twentieth time around, when he stopped to think on John Givens' board.
Nearly every one was playing Go Seigen with at least a nine stone head start. John, underrated
as an Amateur 2 Dan, was playing him with only six stones.
After thinking a few seconds on John's board, he placed a white stone, then hurried around
the tables, again stopping at John's board, a little longer this time. He placed a white stone and hurried
around the tables again, stopping a third consecutive time at John's board, this time for about two
minutes, I believe. When he placed a white stone, John immediately responded with an excellent move,
and Go Seigen resigned. He then resumed his brisk pace around the tables, never again stopping. Some
local players had resigned and been replaced. No other local players won their games.
8. When all the games were finished, then for each game, including the replacements games,
starting where people had resigned, Go Seigen replayed about the first third, explaining how the first
three or four big blunders could have been avoided. When players asked questions about the latter part
of their game, he replayed that part, too, and explained it.
He had saved John's game for last. From the moment Go Seigen resigned, John had been
struggling to analyze the very complex position on the board, trying to imagine how it would have
proceeded if they had continued. Although John's remarkable intuition had led him to focus on an
excellent line in which the move he made was essential, white had too many other good lines for John
to read.
When Go Seigen was finished replaying the other games, he came over to John's board, looked
across at him, bowed deeply, and said “You won!” John stood up his full 200 cm, bowed deeply, and
said, “Thank you Sensei! Would you please be so kind as to show me how you think the game should
have proceeded if we had continued?” He did.
I was flabbergasted! It seemed to get ever more complex for about another seventy moves.
I know that John believed that there was no way that he could have found his way through that maze.
And I expect that Go Seigen did, too. So, I guess that John got an honorary win, but a very impressive
honorary win indeed. Go Seigen promoted John to 3 Dan, remarking that even at 3 Dan. John was
likely still underrated.
Go Seigen did make good on all his special supplements to nine stone head starts. I don't
know how he did it on the other boards, but on my board it went like this:
First he knew that after hearing what he had said, I wouldn't want to play anywhere near that
place. So he was able to set up a circle of white stones there. He knew that if I was approximately 6
kyu, I would know how to use the 6 points inside tactic to kill his one eyed group, and he correctly
guessed that I would not realize that as I was beginning to sacrifice 6 stones; then 5 ; then 4; then 3;
then 2; and then 1 to catch his group, I needed to have fourteen breathing spaces on my large group
surrounding his, and I would not notice that I could never get more than thirteen.
Go Seigen's day with us was both awesome and delightful. I will treasure the memory as long
as I live. But that is not why we think of him as the greatest go Master of all time. Throughout the
1950's he was conspicuously stronger and more creative than anyone else. But that is also not why we
think of him as the greatest go Master of all time. On a grander scale than anyone else, he created new
paradigms in Go and raised the understanding of present and future players to a new level. That is why
we think of him as the greatest go Master of all time. He has been doing that for more than 80 years.
Go anecdotes tend to be cheerful. A favorite concerns two young professionals who were
arguing about the details of game tree algorithms applied to Go. Go Seigen, standing near them
interrupted to say, "You both have it wrong. Go isn't a game of competition; it's a game of coexistence.
If you try to claim more space than your previous play entitles you to, you will lose. And if you don't
take what your previous play entitles you to, you lose. So the winner is the best co-exister." I don't
think this is an attitude often found in chess players.
In the early 1990's a brilliant young Chinese woman, Rui Naiwei, became the first female 9
Dan Pro. She moved from China to Japan, as Go Seigen had back in 1928. For several years she went
weekly to his home for lessons in the use of his latest insights, a rapidly developing dramatic departure
from then current beliefs, which by the late 1990's had stunned some top title holders. (See Go Seigen's
1997 book, now in English, A WAY of PLAY for the 21st
Century.)
In 1999 Rui Naiwei, through her expertise with these new insights became the first woman to
win a major open world tournament. For months she was winning her games from all the top players.
9. Paul Erdös Elwyn Berlekamp Rui Naiwei
One night around 1980, the 20th century's most prolific mathematician Paul Erdös came to our
Berkeley Go Club. He loved Go! Over four games of Go, he told me that the culture shock of his life
was seeing the top Go Masters in action. He said that he knew the top people in several sciences, and in
classical music, and knew their accomplishments, but had always felt it was a reasonable guess that if
he had given his attention to the things that they worked on, he might have been able to think of those
things too; but seeing the top Go Masters in action was exactly the opposite experience. It seemed to
him that if he had begun as a kid and done nothing else, there was no way he could ever get to where
they were. He said that he had never encountered expertise on that scale in any other discipline!
He mentioned playing in a Go simul, sometime around 1950. Among the local players were
many stars of Math and Physics including Fox, Einstein, Bohnenblust, Nash, and Erdös. Each player
had felt that he had almost been able to win his nine stone game from the Pro, until later comparing
notes, they realized that each of them had lost by the same exact number of points.
Leading edge advances in decision making from the sharing of insights between Go Masters,
Mathematicians, and Computer Scientists, is pioneered by Berkeley Professor Elwyn Berlekamp, and
his colleagues in all three disciplines around the world, especially by his many students, three of whom
wrote their Ph. D. dissertations on Go. Most Dissertations on Go are in either Math or CS.
Ernest Brown I am with Hugh and Gian Zhang at a SF Go Tournament
10. I think that in America the only exception is the dissertation of Psychologist Ernest Brown, an
early American Go Association VP for Education; several times director of the Ing foundation's World
Youth Goe1
Tournament; and current leader of the San Francisco Go Club. http://sfgoclub.com/ Dr.
Brown received his Ph. D in East/West Psychology from the California Institute of Integral Studies. He
has worked for the past twenty years at Walden House in San Francisco particularly with adolescents.
Around 1991, inspired by Elizabeth O'Shaughnessy's Chess in the Schools program in
Berkeley, and especially by Ernest Brown's success in teaching Go to kids in San Francisco, I started a
program in the Berkeley and Oakland schools, called Go in the Schools. A few years later, heart
problems forced me to give it up. Sadly it is gone.
Since then, at Bay Area Go tournaments, I give introductory lessons to people sometimes very
young who came just to watch, and since April, 2012, I am again president of the Berkeley Go Club,
where on Sunday afternoons from 2:00 PM I help beginners, young and old. You are invited!
http://www.berkeleygoclub.org/ & https://www.facebook.com/BerkeleyGoClub For tournaments and
other special events, see: http://www.bayareago.org/
A few years ago at Go tournament I met Gian Zhang and his 5 year old son Hugh who played
me his first game, and made it very clear that awesome things were coming. Now in high school, he is
8 Dan in Go, and is also a contender in national computer programming competitions.
In Go as in Math, the key is lots of early, eager, self motivated exploring; accompanied as
soon as possible by friendship with and lessons from Masters. In Go as in Math, very young people
have a chance to make their awesome talent clear, and meet great teachers. Never push, interest them.
Go Masters and Math Professors, first seeing their student make a mistake can usually spot the
level of generality at which the mistake is made and immediately help the student to understand it at
that level, preventing the formation of a long lasting bad habit. Most parents have no idea that such
help is available for their kids. Available Masters of Go and Math can be located through Go Clubs, and
Math Circles. To start, google Sensei's Library, Go Federations; National Association of Math Circles,
Berkeley Math Circle, Evan O'Dorney, Laura Pierson, Arav Karrighattam and Proof School.
We are not all born with equal potential, but the differences at birth pale into insignificance,
when compared to the differences later as we miss more and more opportunities to gain experience that
would build a craving to understand better, and build habits of exploring as we try to improve our
understanding. In our society girls, and kids from some minority groups are especially at risk of not
being encouraged to want that kind of experience. Most of us know that there is a window when we are
very young, in which it is especially easy to learn languages. But most of us don't see that window in
its full generality, as a time when it is especially easy to learn new modes of thought.
What every mother should know about how to help her young kids have fun trying to get
better at thinking: Where does very early eagerness to explore come from? I saw in action a technique
that really worked and can be copied. I have, on three occasions, given first Go lessons to kids not quite
two years old. All three learned their first lessons, but unlike the other two, Sammy Zhang was having
great fun, learning fast, and immediately eager to get better at Go. What was different? He was at his
third Go tournament! Sammy's older brother Tony played in Go tournaments. He was brought by his
mother, Stanford Professor Sue Weng. who came with her baby in her arms. All through the
tournament, she held his head up so he could watch the people having fun. Although not quite two, by
his third tournament, Sammy was really eager to get in on the fun. I seized the opportunity.
About 9 years later, at the U. S. Go Congress in 2011, Sammy came in second nationally
among kids twelve and under in the Junior Redmond Cup, named for Michael Redmond the first
westerner to reach Professional 9 Dan. A few hours later Sammy showed that he could spot me 9
stones and still win. Sammy is now also a Math star at the San Jose Math Circle led by Professor
Tatiana Shubin. Similarly, with early Go experience the Jain-Sharma brothers, Vishank and Niraek
with have become Math Circle Stars. Vishank is now a student at Princeton.
11. In my retirement, with a view toward Cosmology, I explore finite geometry with computer
graphics and some newer algebra, while amateurishly speculating on the nature of cosmos, life, mind,
and the role we each have: explorer and participant in a situation that we do not understand at all, yet!
Looking for the big picture and attempting to keep our choices and actions consistent with our
feeble but growing understanding seems indicated. That is easy to say, and very hard to do. Among all
the activities that I have encountered, Go is the one which seems most conducive to developing this
badly needed combination of skills.
Doing Go and Mathematics is wonderful not only for brilliant people, but also for the rest of
us. Having lived seventy six years with extreme Attention Deficit Disorder, I know I will never be great
at these things, but having fun with them contributes to habits that help me in every thing I do.
And I am blessed! In my later years through Go and through Mathematics, I have gotten to
exchange ideas with some of the most creative minds on Earth, sometimes while they are still young.
On very special occasions, I have experienced the remarkable delight of seeing a question that
I had pondered for decades cleared up quickly by the creative insight of a young friend.
Think deeply about simple things.
--Motto of the Arnold Ross Summer Math Program for young people.
___________________________________________________________________________________
1
Although he did not invent it, Ing Chang-ki, the greatest philanthropist of the Go world
preferred the spelling “Goe”, to reduce the confusion with the English verb to go. I feel that that
confusion has been a surprisingly serious obstacle for potential beginners. One alternative solution
which does seem to be gaining ground is to use the easy to pronounce, unique, Korean name Baduk.
