Chapter 24 "Neural Tree"

The human brain hides infinite possibilities. ——Zhang Yaqin In 1968, Ling Xiaoning was 16 years old, Xu Yingqing was 9 years old, Zhang Hongjiang was 8 years old, Li Kaifu was 7 years old, Wang Jian was 6 years old, Guo Baining was 5 years old, Zhu Wenwu was 3 years old, Zhang Yaqin and Shen Xiangyang were only two years old, Li Shipeng was one year old, Zhang Yizhao and Ma Weiying has just been born, and Liu Ce still has to wait Not born until 9 years later.It was this year that something extraordinary happened in the field of physiology: Roger Sbury published his research on the function of the human brain, for which he was awarded the Nobel Prize.

Prior to this, scientists' understanding of the human brain has always been "emphasis on left and right".They believe that people's language ability, logical ability, and other related abilities are all realized by the left brain.The human brain is thus divided into "smart" and "dumb" parts—the "smart," "primary," "dominant" left brain, and the "silent," "secondary," The right brain in the "obey" position.This argument has dominated the field of brain science for the past 200 years, and until recently it is still prevalent. The final result is that the entire society is discriminating against the right brain.The education system and scientific system seem to completely ignore the wisdom of the right brain, and one scientist even regards the right brain as a "degenerative organ".Another typical example is that parents desperately correct their children's habit of using their left hands, and teachers absolutely do not allow students to use their left hands to write.And everyone knows that the left hand is dominated by the right brain.

Now, Roger Sberry has shown astonishingly that the two brains of man possess equally complex intellectual functions and are equally intelligent.Humans also have two completely different modes of using the brain, one is linguistic, logical, analytical and continuous, with the ability to judge right from wrong and distinguish interests; the other is non-verbal, intuitive, visual, Stimulating and sudden, it is a kind of fantasy that does not distinguish between right and wrong, regardless of interests.Everyone can switch from one way of thinking to another, it is an innate ability. "Although we always feel that we are one person, a separate entity, we have two brains," Betty Edwards explained Roger Sperry's theory, "Each half of the brain has its own cognition and perception. The way things are externally real, in a sense, each of us has two intelligences, two consciousnesses, fused by nerve fibers connecting the two hemispheres."

In this way, the human brain has two modes when processing external information: left-brain mode and right-brain mode.The left brain allows us to analyze, refine, calculate, describe, plan, and make rational statements and judgments based on logic; the right brain enables us to have imagination, creativity, understand the symbolism of things, see images in dreams, and Everything that exists only in the ocean of spirit.It is for this reason that Betty Edwards and all those who believe in "Sbury Theory" agree: "Knowing both sides of your brain is an important step in unlocking your creative potential."

If this theory is correct, then people have two brains, one is a mathematician, linguist, and scientist; the other is a dreamer, inventor, and artist.It is clear that in our schooling mathematicians, linguists, and scientists are favored in particular, while dreamers, inventors, and artists are largely repressed, transformed, and buried.Our curriculum - Chinese, mathematics, physics, chemistry, foreign languages, biology, history, geography, politics, almost all based on the training of the left brain, our examination system - whether it is "3+2" or " 3+X" is nothing more than selecting students with developed left brain.

But there's more to it than that. The surface of our brain is covered by at least 14 billion brain cells, a huge number.Only about 500 million of these brain cells are truly associated with intelligence.In ordinary people, they are called "intelligence"; in physiologists, they are called "nerve cells", also called "neurons". Regardless of whether people of yellow race, black race or white race, no matter whether they are the top scorers in the college entrance examination or those who failed the exam, whether they have a Ph. of. Since there is no obvious difference in the "neurons" that determine human intelligence, how can humans be divided into smart and non-smart?

According to Zhang Zhengyou's explanation, "Human intelligence does not depend on neurons, but on the connections between neurons." Zhang is a doctor who graduated from Paris-Sud University and is now a researcher at Microsoft Research. One of his hobbies It is to understand the physiological structure of the human brain: "There is a saying in Chinese that you look old at the age of three. This is because the neurons in the human brain begin to connect before the age of three. Can your neurons quickly form a line? The spacious access is related to the education you have received and the things you have been in contact with. Some accesses, if you continue to use them, they will be strengthened, and some accesses, if you do not use them, they will shrink.” Based on his own experience, Zhang believes that "When a person reaches the age of 15, the connection of neurons is finalized." The research results of physiologists seem to prove that he is right.The brain is not made up of individual "neurons" that are not related to each other.In fact, "neurons" are intertwined and extend each other to form a complex circuit. Its shape is like a tree with luxuriant branches, so physiologists call it "neural tree".The gap in human intelligence is related to the speed and complexity of "neurons" intertwined and stretched, and the growth and connection of "neurons" need external factors to activate.

However, there is another characteristic of the "neurons" in our brains. Whether you activate them or develop them, they will metabolize, die or regenerate.In fact, when we sleep every day, at least 100,000 brain nerve cells die, but we have never used them yet. This fact is depressing: most people only use 10%-15% of the neurons in their brains in their lifetime. Of course this fact is also exciting.Because, you only need to wake up 1% of the sleeping "neurons", and you can make a leap in your intelligence.If you can double the utilization rate of "neurons", say to 30%, then you will become a great genius like Newton, Galileo, and Einstein.

A Japanese psychologist named Taisaku Inada based his education on these theories, and his education included numerous inspirational aphorisms: "I can't do it because I make myself no good." "As long as the brain can be used rationally, it can develop." "People sometimes fail for many reasons, one of which is not using their brains more fully." This man wrote an exciting book called "The Mind Is Bigger Than The Sky".In his book, he put together all kinds of human intelligence factors, called "brain index", which is a bit like what we usually call "IQ".

Zhang Yaqin studies computers, not the human brain, but he obviously understands the human brain very well. "The human brain hides infinite possibilities, and at the same time it has its own structure. I can draw you a map of the brain structure." One day he talked with a friend about the problem of memory, while drawing on the table with his hands , said at the same time: "If you remember this, you must forget that. This is a memory choice. A good education method makes you remember the most important things, and a bad education method makes you remember a lot of unimportant things. Things. For example, do a lot of exercises, do it several times or even dozens of times, this is the process of making the brain rigid, and in the end even I am confused.”

American children can't recite the multiplication table, but they know what multiplication is.Chinese children can memorize multiplication tables, but they don't know what multiplication is. --Kai-fu Lee The first exam that Pan Zhenglei encountered at Washington State University had a plot that she could not forget after many years: The teacher allows the students to bring a piece of paper into the examination room and write anything on it.For example, various formulas, concepts and data that I can't memorize but may be used in the exam. "American teachers don't want you to memorize it. They think it's a waste of time." She later said, "You just need to know where to find what you want. The test is not a test of your memory, but a test of your memory." Thinking skills and problem-solving skills." Kai-fu Lee also talked about the same issue: "Fundamentally speaking, education is not to instill a lot of knowledge in children, but to shape children's brains. Of course, 'instilling' is also a kind of shaping." Then he talked about his ongoing Daughter in elementary school: You should look at my daughter's homework when you get a chance.Now my youngest daughter is also in school.I also want to educate children.My wife can’t teach it, and she gets angry every time she teaches it, because she always blames her daughter, saying, “This formula is so simple, why can’t I remember it?” I don’t go home until 8:30 every night.My daughter sometimes asks me to teach her homework, and I ask her, "What did you do during the five hours from 3:30 to 8:30?" She said, "I don't understand what my mother taught me." I let her understand first Why, explain to her from the beginning, what is going on.He also told her that once she understands the reason, she will not forget it easily. Even if she forgets, she can think of some reasons to remember it easily. Some of the plots here involve two completely different ways of education. The American education method requires you to understand the why and the concept first, and then tell you how to do it. It does not require you to memorize a bunch of formulas and numbers by rote.If something must be recited, it is also the last step.For example, "triangle", the teacher asked the children to go home and draw all the triangular things at home.Another example is the "nine-nine multiplication table", Chinese children may memorize it as soon as they come up.Teachers in the United States must first tell you how multiplication is going on, give you some examples in life, let you understand the concept of "multiplication", and then tell you how to do it, such as 2×3, 4×3, and finally ask you to memorize "Ninety-Nine Multiplication Table".Another example is when a teacher explains fractions, he first tells you how the concept of "fractions" came about and why.In China, you will know what fraction it is, but you don't know what it is useful for. Children don't ask why, and teachers don't explain it.He learned the problem of "chickens and rabbits in the same cage", but if he changed to "dogs and ducks in the same cage", he would not be able to do it.In order for the students to learn how to do it, the teacher keeps repeating it. As a result, the students have to do a rule dozens of times, or even a hundred times. No matter how interested the children are, they will be boring. There is a "culture of memorization" in Chinese education.It's no wonder that there are more than 6,000 Chinese characters in common use, and it is absolutely impossible not to memorize them.Because of this characteristic of writing, reciting has become the most important learning method.You have to memorize formulas, numbers, place names, how many meters above sea level, "chicken and rabbit in the same cage", how many digits after the decimal point of pi... I was very interested in "why" when I was in school, but now my daughter is not interested in "why".If I ask her whether she is willing to understand or memorize, she may be willing to recite it, but she will forget it if she recites it.It may be different for children who like math. My daughter doesn't like math, but her brain has been molded into a shape. If you don't tell her why, she can't remember it.If you understand the "why", it is not easy to forget, even if you forget the concept, you can still think of the "why".For example, she learned a four-arithmetic a while ago, she memorized it back and forth, but she still couldn't understand it. The next day she took the exam and took a "re-examination".I came home very late that day, so I ended up teaching her, let her know why first.She didn't want to learn from me either, but she didn't seem to be able to pass the exam if she didn't learn. Finally, she understood and got a perfect score in the exam.It can also be seen from this that a child's brain can be shaped into a shape. Yang Zhenning once said that Chinese education is suitable for ordinary students, while American education is suitable for smart students.Kai-fu Lee said that he was not sure if this was true.He feels that "it is right for smart students to be educated in the American way, but I am not sure whether it is good for most ordinary students to be educated in the Chinese way." "American children can't recite the multiplication table, but they know what multiplication is. Chinese children can recite the multiplication table, but they don't know what multiplication is." Li Kaifu said.He often complains that Chinese teaching methods are too rigid, and he cannot fully agree with the teaching methods of American elementary and middle schools, saying that it is "too loose and too inattentive to memorization."His daughter recited the "nine-nine multiplication table" from the age of 7 to 8, but she still couldn't. "She can't put it into her head. The teacher doesn't ask her to memorize it. When she asks questions in class, she just asks her what she likes and how many friends she has." Everyone has two brains.Very few children learn to use their two brains. ——Liu Ce Both teachers and parents can get a sense of satisfaction in the process of children acquiring knowledge.A preschool child will recite "Moonlight in front of the bed, it is suspected to be frost on the ground" today, and "Ninety-Nine Multiplication Table" tomorrow, and these will be in the surrounding The adults were amazed, everyone said that the child was "extraordinarily smart", and believed that this was the child's growth, but almost no one noticed that the accumulation of knowledge and the growth of the brain were not exactly the same thing. For the young Liu Ce, learning mathematics is a process of growth, and learning painting is also a process of growth, but anyone who understands the structure of the brain can imagine that there is a huge difference between the two processes-he must use two different methods. way of using the brain. For many years the whole life of this child was alternated between mathematics and drawing, even on weekends.There are only two classes in school on Saturday afternoon, and school ends at three o'clock.He left school, boarded the bus, and rushed to attend the "mathematical top training class".The math teacher said that he was training the students' rigor and logic, but in fact he just found some weird questions to make things difficult for these children.Every question is very difficult. Some questions really require you to have a strong mathematical ability, and there are many questions that are just "brain teasers".It would be bad for children who are not interested in mathematics to encounter this, but the students sitting in the mathematics training class are the students who are most interested in mathematics and have the strongest ability in mathematics in this city. Excited to solve the problem, Liu Ce was no exception in it. The exception occurred during the next three hours.After the mathematics training, the other children went home, only Liu Ce went straight to the Children's Palace, where a drawing training was still waiting for him, starting at 6:00 pm and continuing until 9:00 pm.Three hours of painting and two hours of mathematics are closely connected, and Liu Ce is very focused from the beginning to the end.A few minutes ago, he was immersed in the digital world, desperately mobilizing his logical ability, reasoning ability, analytical ability, abstract ability, and ability to judge right and wrong, which made his left brain extraordinarily active, but now, he began to mobilize His right brain is gone. Almost all children have their right brains at one point or another.When they were two or three years old, they knew how to graffiti on the walls and floors at home, and when they were four or five years old.They start to see the world with their own eyes.Boys who love cars will let a racing car take up two-thirds of the screen.The car must be going fast, so there are a lot of straight arrows pointing backwards through the white clouds.There are also curved and extended lines behind the wheels, like flowing air or rolled up dust, and the red sun in the upper right corner, only a quarter of which remains on the screen, showing the child's imagination The power has surpassed the limitation of paper and flew to the sky. Once such intuitions form a picture, the image is active in the brain.If children are encouraged to put in more imagination, emotion, and effort, their right brain fires again and again. Too bad our education system doesn't pay attention to this.The fact may be the opposite. When a child is six or seven years old and reaches the age of school, a well-formed knowledge system composed of language and numbers dominates his memory, controls his brain, and expels all those intuitive and visual things. go out.As the psychologist Karl Buhler said in 1930: "As education, which is essentially language, becomes the dominant force, the child abandons attempts at expression in pictures to rely almost exclusively on words. Language is first Disturbs the painting, and then devours it all." Maybe we can put it more thoroughly: today's school education mode is to stimulate children's left brain while burying children's right brain.The left brain completely eats the right brain.Only a very few children are lucky enough to escape this unintentional destruction by accident and learn how to use their two brains.Liu Ce is one of them. Painting is image, intuition, perception and imagination.Its entire process is entangled with vision, without the logic in the digital world, without reasoning, right and wrong, right and wrong.According to Betty Edwards, the mysterious drawing ability is actually an ability to continuously switch the state of the brain between the visual mode and the logical mode.This person is one of the most amazing art educators in the United States. She wrote "Think Like an Artist", which has sold 2.5 million copies in 13 languages ​​worldwide.The charm is that she encourages people who don't want to be professional painters, or who have never even had an interest in painting, to learn to paint, because "in learning to paint, you're going to tap into that part of your brain that's hidden by the endless details of everyday life." .” She bases her painting education on the "right-brain mode theory" of physiology. "I see you as someone with creative potential expressing yourself through painting," she tells her students who don't want to be painters, "and my purpose is to provide the means to unleash that potential, to help you get into A level of consciousness that is creative, intuitive, and imaginative, one that is underdeveloped because of our cultural education system that overemphasizes language and technology.” In fact, most of her students are not artists, but scientists and manager. Now let us go back to Liu Ce's childhood and explore his spiritual world every Saturday afternoon to five hours at night.When the math teacher gave him some strange questions, he would concentrate on them, so time stopped, and he stopped in the digital world of the left brain.His mind is very active and he is very confident.Two hours later, he changed a place, sat down, and according to the request of the painting teacher, stared at a certain still life with his eyes for a long time, such as an eagle, a potted flower, or a landscape painting, just as he faced a few minutes ago. Like those abstract numbers and symbols. He got out of the "left brain mode" dominated by numbers and symbols, and got rid of it very quickly and naturally.He now finds these solid figures very interesting, and cannot help relying on the visual perception of the large number of details and the relationship between each detail, discovering how the various parts fit into each other, from one line drawn to adjacent lines, from one line to the next. A space draws to another adjacent space.Unknowingly, he becomes one with his purpose, calmly but passionately.He found his confidence again. Time stopped again, but now in the right brain.This is a world of art.His thinking no longer consists of numbers, symbols, language and logic, but of lines, spaces, colors and imagination. When people change something from their left hand to their right hand, they can clearly feel the power transfer.Oddly enough, the brain allows people to distinguish between left and right hands, but not its own left and right.The key point of brain growth happens precisely in this unnoticed place.Liu Ce's thinking is constantly switching between the two brains, and digitally develops his of his left brain, while art developed his right brain. The mastery of knowledge is often considered the most difficult skill in teaching, and the mastery of the brain is even more difficult.Unfortunately, this integration is often accidental.A shift in consciousness has taken place, but few are aware of it. Now let us observe the child's "consciousness shift" again.For many years his rhythm was tense, and he rarely had a leisure time, but he always felt energetic, and he never felt tired in the brain, because he was using two brains alternately, when he was using one brain intensely. At this time, the other brain is freed from tension.Only rarely did he experience a sense of shattering, which occurred when he was jumping from one mode of thinking to another. He called it "the conflict of switching."That feeling is like climbing a dangerous mountain, the last step is often the steepest, you grit your teeth and survive, and there is infinite scenery ahead. It was already very late when he got home. After spending the most exciting time of the week, Liu Ce felt physically and mentally exhausted, especially tired.He didn't expect that in the past 5 hours, he wandered into two completely different spiritual worlds. His alternating training of "two brains" started from childhood and continued into adulthood without interruption.The failure of the junior high school entrance examination did not make him change course. Although his mother was disappointed, she did not say anything about her complaints.It is no surprise that his passion for painting is unquenchable, and his skill is growing with each passing day.The strangest thing was that he felt that his brain was getting bigger, faster, stronger and more durable.He hated things in class more and more, especially hated the teacher's "cramming teaching method".But the lesson of that exam failure was heavy after all. He began to understand that the courses he didn't like had to pass, because it involved the entrance to high school and then to university.Oddly enough, his grades at school were also getting better.In the third year of junior high school, he scored 100 points every time in the math test, 100 points in physics, and 100 points in chemistry.He became always number one in the class. When he took the high school entrance examination, he got his wish and entered the best middle school in Chengdu.In the following three years, as always, he completed his school homework while learning painting. Whenever there was a mathematics, physics and chemistry competition, he took part in it. Whether it was winning the competition or getting good grades in the exam, he felt very relaxed.In fact, the time he spent on the lessons did not increase at all, and he went to learn painting as usual.His traditional Chinese paintings are getting bigger and bigger, usually eight or even ten feet wide.The home was too small to accommodate his paintings, so the middle school student got into the children's palace and spread the paper on the floor.Sometimes he performs in public and achieves it all at once, and sometimes he concentrates on managing it. It takes several weeks for a painting to be conceived and completed.He felt that there was infinite potential in his brain, no matter what he did, he was like a fish in water.These experiences convinced us that the mind can be trained.To train the mind is to train the brain.Therefore, the purpose of learning is not to increase knowledge, but to let the brain grow up in the most perfect way. In this way, he continued to draw until the third year of high school. He has won many competitions, is also the chairman of the student union, and has excellent grades in exams.When he graduated from high school, China's three most famous universities - Tsinghua University, Peking University and China University of Science and Technology - all wanted to have this student, not requiring him to take the college entrance examination at all, and letting him choose his favorite major.Only the teacher wants him to take the exam, because the teacher believes that he can create a provincial champion and win glory for the school. He did not follow the teacher's "advice".He doesn't want to be the "No. 1 Scholar", and he is not interested in "winning glory". "That's not very interesting," he said, "and it will take a lot of time." He chose the automation department of Tsinghua University and went home.When his classmates were struggling in "Black July", he spread a piece of rice paper on the ground, walked to the window, cast his eyes to the distant place, and began to conceive a new painting. Many years later, he graduated from Tsinghua University and entered Microsoft Research Asia.He chose the direction of "artificial intelligence".Almost all of his papers are of world-class quality.Three papers were published in the world's highest-level conference, and one was published in the highest-level conference in Europe.According to Shen Xiangyang, Liu Ce's current achievements are not even achieved by many professors. But Liu Ce's mind was still flooding with fantastic ideas.When he boarded the plane to the United States, there were two questions on his mind. He found that computer scientists are using numbers to realize intelligence. All elements in the field of mathematics are assembled and defined, but "human intelligence always jumps out of the definition and continues to expand, which is completely opposite to mathematics. One idea is to break the constraints of set theory on artificial intelligence." The second thought was even more bizarre.He wanted to "describe aesthetics by mathematical means".Mathematics can do optimization problems, such as how to minimize the cost of a project, how to arrange your daily time to be the most efficient, these are all optimization.But Liu Ce believes that this is not the whole of intelligence.Until today, no one has thought of expressing beauty with numbers, and computers cannot tell whether a painting is beautiful or not.Aesthetics is not only a matter of optimization, but also of emotion.Who you like and who you want to live with in the future cannot be optimized.Therefore, Liu Ce has been thinking, "Can mathematics be used to describe 'Beauty is in the eye of the beholder'?" He was talking about these thoughts with a reporter one day, and this led to the following conversation: Q: You like mathematics, but also like aesthetics.I also heard that many great mathematicians are also artists.Do you think these two things really have anything in common? A: I think so. Compared with mathematics or engineering, art is very different in content, and it is indeed two ways of thinking.But in terms of human cultivation, the two methods have many similarities. Q: You mean that the similarities between the two processes are not in the technical aspect, but in the mental state? A: Drawing has cultivated some of my spirit.It inspires you to think about many questions: how can you draw better, where is Important, what is secondary, this is something you can't learn in the classroom.A large painting can take several weeks to complete, and classroom education rarely gives you the opportunity to complete a thing from start to finish in such a long time.This has also trained me to finish everything I do, to know how to allocate energy, to solve all problems by myself, and to enjoy it. Q: Is it the same when studying mathematics? Answer: When we were in high school, the teacher asked us to do analytic geometry, and the process of solving problems felt like drawing a picture.Many people do exercises and forget what problem they were trying to solve. They get stuck in the specific steps and feel that they are doing it step by step. Sometimes they solve it after doing it. But it's not that I'm going in that direction consciously.There are also such problems in painting, both of which must have a long-term goal, and how do you achieve your goal.There are many temptations in the middle process, you have to bypass it.When doing math problems, if you get entangled in it, it is impossible to make it in a short time. When drawing, if you stick to the details, you will ignore the whole.My painting teacher told me that painting is not to draw likeness, but to understand the purpose of painting, what you want to paint and what you can't paint.So I feel that I am exercising two abilities at the same time, the ability of the master and the ability of the engineer. Question: Most people think that art and mathematics are two completely different things, and they have completely different requirements for people's thinking. Answer: The highest guiding ideology of these two things is completely different. Mathematics emphasizes that your logic must be rigorous without any mistakes; there is no right or wrong in art.Therefore, the ultimate pursuit of these two fields is in different directions.But from their methodology, they do have a lot in common. Q: Looking back now, did you benefit more from mathematics, or from painting? A: It's hard to say, but there is one point where you can see the difference between painting and mathematics.Painting is to encourage you to dare to think and paint, to be innovative.What I think in my heart is not right or wrong, but to draw some new things, and I have to dare to try.The teacher also encourages you to draw boldly, even if you violate the rules.This is very difficult to be encouraged in school education.For example, when I was in elementary school, one day I thought of some interesting number patterns, so I went to discuss them with the teacher, but the teacher thought these things were meaningless, and instead tested me on many things that I memorized by rote. Q: Dare to think is a kind of ability or a kind of character? Answer: Many human abilities are innate, but acquired training is also very important. In China, primary and secondary schools, mathematics does not encourage you to dare to think, but encourages you to be rigorous. You can only passively do the questions and receive knowledge. So many people have become slaves of knowledge rather than masters of knowledge.At the beginning of painting, there is also a process of being a slave. I will also draw lines and circles on paper very boringly. You do have to master these skills, but it encourages you to become the master of these skills. These skills are just tools in the end. Exercises, test papers, scores, rankings, these things surround students, leaving them no time and space to think.They get high marks but lose the ability to think. ——Zhang Hongjiang There is a very common view that Chinese engineering students are better than American students, and Chinese students have better math skills than American students Okay, but Zhang Hongjiang disagrees. "I used to think the same way," he said once. "Then what I saw was not the case. What I saw was that Chinese students spent much more time studying mathematics than American students. To say mechanical calculations Ability, that is, to do the questions, Chinese students are indeed better than American students. But I have seen that only a few Chinese students can redefine some concepts and form their own mathematical thinking framework." The listeners were very interested, because there seemed to be something unheard of in Zhang Hongjiang's words. "A student who really understands mathematics must visualize mathematics." Zhang Hongjiang continued, "In his mind, many problems can form the concept of mathematics. For example, when you see a hammer, you think of nails, but how do you What about turning things around into nails? A person who is really good at mathematics has this ability. If mathematics is not good, or it is only fake good, not really good, then you can only look for ready-made nails.” "Hammers and nails?" Someone interjected, seemingly unable to understand his metaphor. "Chinese students learn mathematics as a tool. In fact, mathematics is a kind of understanding." Zhang Hongjiang said, "All great mathematicians are because they have realized something." "But we have always believed that it is a good concept to be able to use mathematics as a tool. Many people learn mathematics as knowledge. Why do you say that mathematics is perception?" Zhang Hongjiang said: "If you learn a good mathematical model, can you integrate a practical problem into this model well? This is what Chinese students lack, and this is the strength of Westerners. I see that many students in the United States have a good understanding of mathematics. Another difference is that some people can also take the problem, but if they can't solve it or the solution is not very good, he can't tell whether it is Why. People who are really good at mathematics can solve problems. If they don’t solve problems well, they can analyze the state of failure very beautifully. Those who are inferior do not have this ability. He just regards mathematics as a kind of Simple reasoning, a correct answer. In fact, the requirements of mathematics are higher, it is not only reasoning, not only an answer, but a kind of perception." "Is savvy more important than the correct answer?" "A person's superiority, in the end, is often not determined by the amount of knowledge, but by the amount of understanding. When I look at the people around me, such as Kaifu, Yaqin, and Xiang Yang, they are all superior in understanding. I think people's savvy is innate and educated. I don't believe that Chinese people's savvy is poor, but I believe that this problem has a lot to do with the educational environment." "You mean, a child with a high test score may have a poor understanding?" "I'm not entirely sure. But I believe that to cultivate good understanding, you need a relaxed environment, just like you need a relaxed environment to make good research results. Originally education is to teach students to understand things, but It is difficult for children to do so in China’s educational environment. Although some schools are very good, teachers work hard and explain a lot of things incisively, but they always surround students with exercises, test papers, scores, rankings, etc. .Students are desperately trying to earn high grades, and have no time and space to think at all. Over time, they lose the habit of thinking. They get high grades, but lose the ability to think.” If Zhou Ke had the opportunity to discuss "savvy" with Zhang Hongjiang, they would definitely resonate.他是微软公司的一个技术总监，在主持了一系列的面试之后，产生一种强烈感受：“中国学生的思维特点，是线型的，而不是跳跃的。”他仔细观察那些中国学生，觉得他们都很优秀，但却受到根深蒂固的影响。比如他总是对应聘者提出一个问题：“现在你的工作是卖饼干。你还有两个同事，你们三个人都很优秀，你怎样才能比另外两人做得更好？”这是一个很普通的问题。中国学生的回答常常是：“我要拼命工作，加班加点。”问他们还有什么，他们会说，“我要了解老板的意图，执行老板的计划一丝不苟”，等等。可是有个美国学生就不是这样回答，他说：“老板，你把饼干降价，让另外两人离开。我能让你卖得更多，你还能降低成本。” “这反映了一个人的思维方式是线型的还是跳跃型的。”周克说，“线型思维，就是你的想法总是按照逻辑顺序，一二三四排列下来，不跳跃；跳跃型思维，就是从一到三，从五到九，跳来跳去。” 周克认定“线型思维方式是中国人的特征”。这不是先天的，是后天训练出来的。根据他的经验：“我们在学校做数学题，总是因为什么、所以什么。每个步骤是多少分，错一步就扣一步的分。这是一种严格训练。它培养了学生的严谨，但却埋葬了学生的悟性。” 张亚勤：我更喜欢形象思维 张宏江说，一个数学真正好的人，“一定是把数学形象化的”，很少有人注意到其中深意。我们发现这些“E学生”尽管今日全都徜徉在“数字世界”，但他们都曾对“形象思维”有着特别的偏好。 有一次，《科学时报》的一个记者问张亚勤：“喜欢形象思维还是逻辑思维？”张亚勤毫不犹豫地说：“形象思维”。那记者正在意外，就听张亚勤继续说：“我小时候特别喜欢绘画，有过许多素描和速写，要不是考上少年班，我原来想将来要去美术学院的。” 杰出人物身上总是有某些相似之处，但是谁也不会想到，张亚勤小时候的梦想，也正是刘策小时候的梦想。这两个人，一个出生在60年代中期，一个出生在70年代后期；一个现在是美国电气电子工程师协会100年历史上最年轻的院士、全世界公认的杰出的计算机科学家，一个是沈向洋预测的“未来的大师”。按照一般人的理解，计算机的世界应当是逻辑思维的天堂，令人惊讶的是，这两个人在喜欢“形象思维”这一点上，竟是不约而同的。 然而还有更加令人惊讶的事：我们研究微软亚洲研究院大部分人的经历，可以发现，他们几乎全都喜欢“形象思维”，而且全都从小经历了“形象思维”的训练。 郭百宁：有些东西是在教室里永远不能得到的 郭百宁的蹊跷之处，与刘策如出一辙：他喜欢数学，还曾是北京大学数学系的学生，但他更喜欢绘画。 郭百宁出生在四川，与刘策同乡。80年代中期刘策刚刚开始读小学的时候，郭百宁已经是北京大学的二年级学生。那时候出国潮还没有兴起来，像北大清华这样的学校，已经是孩子们向往的科学殿堂。郭的学习成绩相当出色，高考成绩尤其出色，可他一进北大就发现：“这里聪明人太多了，我觉得自己在北大肯定不是最好的。像我这样的人很多，比我棒的也不少。” 画画是他的业余爱好，但他在这里用了很多时间。多年以后他最喜欢回忆的一段经历就是：“我从中学就开始喜欢画画。”这时候他已经是微软亚洲研究院的高级研究员，领导着一个图形学研究小组，在世界计算机图形学领域已相当有名，还异常怀念当年和老师一起作画的情形：“如果现在回去听我的老师讲画，我会津津有味，觉得很充实。” 他学的是油画。老师是个专业画家。每天放学以后，他就在老师的指点下作画，画静物，画模特，还临摹了很多石膏像。如果时间充裕，他就跟着老师到郊外去写生。老师是一个博物馆的管理员，工资不高，是最常见的那种普通人，但是此人有着非同寻常的经历，画人物的功力非常强，百宁在他的画上，一眼就能找出哪个是四川人。老师擅长人物画，因为这是他身边的生活，更因为他对生活有着精确而又深刻的直觉。 学画的人都有一种奇怪的执著，百宁也不例外。老师看着这孩子一副全神贯注的样子，都说他将来即使不成画家，也必成大器，因为琴棋书画可以陶冶人的情操，而成大器者都是以情操立身的。 在很长一段时间里，百宁只觉得绘画是一种爱好，此外没有什么特别。但是日子久了，他渐渐感觉到画画真有陶冶情操的作用，对人的智力也有极大影响。因为每逢画画的时候，他总能感觉到脑子特别开放，挥洒自如，胸中满是激情，眼睛里面充满了探索性。 他的家在一个小县城里，这地方现在已经人满为患，到处都是污染，乱七八糟，完全不是他小时候的那幅景色了。那时候这里山清水秀，人口不多，空气新鲜，坐在涪江岸边，沐浴在清风明月之中，周围鸟语花香，流水潺潺。他感受着这一切，不由得常常想起老师的教诲：“画画一定要去写生，而不能拍个照片回去比着画。” 在山水之间、天地之间、日月之间，这孩子不知不觉地获得了在教室里面永远不能得到的东西： “视觉会给人的思维带来新的东西。” “绘画和数学之间可能有互补的东西。” “在画画的过程中可以领悟到很多做人的道理。” “你会发现做学问做得好的人，往往做人也做得好。或者反过来说，做人做得好的人，才能做好学问。” 当时一起学画的那些孩子们，后来都从美术学院毕业了，成了画家，只有百宁去了北大数学系，然后出国留学，又走进计算机科学的大门。1999年他回到国内，来到微软亚洲研究院，从此全身心地投入到数字世界中，闲下来的时候，便无限怀念那个山清水秀的家乡，还有少年时代的艺术天地。 有一天，有个记者问他：“你在绘画时的那种感觉，就是那种对线条、色彩、空间的感觉，和你从事计算机研究时对数字、符号、逻辑的那种感觉，有联系吗？” “在国外，很多数学家同时也是很好的音乐家。你知道这是为什么吗？”他停了一会儿，自己回答：“艺术的确不是逻辑，而是视觉，是听觉，是直觉，是想象力，是观察能力和感悟力。但是，在数字科学的殿堂里，形象思维是很重要的。” 徐迎庆：那是一个锻炼我的空间思维的过程 “有一个对我一生都很有影响的事情，就是我小时候去了少年宫。”徐迎庆终于成为微软亚洲研究院里的一个研究员的时候，总是对别人这样说。 像郭百宁一样，徐迎庆的专长也是数学，他在大学里读的是数学专业，等到在中国科学院里读博士的时候，他又成了“三维动画”领域里的佼佼者。所谓“三维动画”，其实就是用电脑画画，迎庆的“三维动画”有一年获得了全国冠军。 他从未接受过专门的绘画训练，但是对色彩，线条和构图有一种特别的感悟力。这不是从娘胎里带来的，他把它归功于北京景山的少年宫。 他上中学的时候，中国还是“文革岁月”，到处一片混乱。说是上学，其实也是“上而不学”，老师不仅不敢训斥学生，而且提心吊胆，怕被学生训斥。每一个孩子都觉得自己无拘无束，没有什么“重点中学”和“名牌大学”，没有考试的压力，没有父母的督促，整天只知道玩儿，直到长大成人以后才特别想读书。 迎庆的家在北京。他经常早出晚归，到景山附近的少年宫去。他喜欢那里的航模小组，因为在那里可以自己动手制作飞机模型。那时候的飞机模型可不像今天的儿童玩具，现在的制造商把所有零件都准备好了，孩子只要组装在一起就大功告成。那时候迎庆要自己去找所有材料，有一种桐木，既轻盈又坚固，还有桐油、万能胶水、橡皮筋和一种薄纸，还要学会使用锯、刀、锉、钳、钻之类的全套工具。他做的第一架飞机并不大，用木材制作成骨架，下面安上铁钩，拉开橡皮筋弹射出去。此后，他的飞机越做越大，动力也不再是橡皮筋，而是一台发动机。他带着它去参加比赛，看着它飞向蓝天。 对一个孩子来说，这是非常兴奋的时刻。其实，最激动人心的变化发生在飞机起飞前的整个过程中。 他要做的第一件事就是绘制一张图纸，这要求他长时间地把眼光停留在一个物体上，他的潜意识开始感觉飞机的整体结构，理解一个空间与另外一个空间之间的相互关系，理解各个细节如何组成一个整体。这个形象跃然纸上，同时也存在于他的意识中，生动活跃，就像未来翱翔在天空的那个真飞机一样。 “那是一个锻炼我的空间思维和形象思维的过程。”徐迎庆这样说。 多年以后他加入微软亚洲研究院，就像我们在《追随智慧》中叙述过的，他在计算机图形学的领域里大有建树，而且一直认定自己今天的成就和那一段少年宫的经历有关系。但他从没想到，类似的感悟不只发生在他一个人身上。有一天他去参加一个国际会议，遇到第31届国际数学奥林匹克协调委员会主席齐旭东。齐是他大学时代的老师，这位数学家居然也是一个酷爱绘画的人，而且画得相当专业，所以被迎庆视为知音。老师当年总是对学生说：“不仅应该学会合理的'正向思维'，而且应该学会合理的'逆向思维'。”现在，师生攀谈起来，学生发现老师的思维方式依然非常新奇。 “什么事情你都要反过来想一想，”国际数学奥林匹克委员会的主席对迎庆说：“比如你在做饮料实验，做坏了，但你不要停下来，看看可不可以给做成杀虫剂。这就是换一个角度想问题。实际上有人就是这样做了，而且获得很大的成就。” “他的想法有时候不是逻辑的，而是非逻辑的，不是理性的，而是直觉的。”迎庆说，“与其说他是个科学家，倒不如说他是个艺术家。” 王坚：我不是绘画天才，不过，我的思维发生了很大变化 王坚的办公室非常凌乱，12个黑色大理石碑表明，他在计算机领域里面已经拥有12项国际专利。事实上他被公认为微软亚洲研究院里最富有想象力和创造力的研究员，而且他还有一种生生不息的激情，脑子里面总是花样百出，其中一个花样叫做“数字笔”。 关于王坚的故事，我们在后面还要详细谈到，现在只想先说，此人也曾酷爱绘画。他的最得意的作品是一幅周恩来的肖像画，用水彩画在纸上，然后贴在校园，有两层楼那么高，异常触目。画这幅画的时候，他只有14岁。 在他所有的获奖作品中，最让他激动的是一幅儿童画。那是他读小学时画的，画面上，一个孩子在给另一个孩子理发。那时候这样的场面很常见，但这幅画清楚地表现了一个孩子内心里积累起来的对外界的感觉，而且还有一种神奇的童趣，所以感动了那些担任评委的老师。 王坚在奖状上看到自己的名字，这是他第一次看到“王坚”二字被印成铅字，不免激动：“那时候印一个东西还挺贵的。” 他从小学二年级开始学画，一直学到初中。先学素描，然后是水粉画，后来又学油画，他的老师挺有名，当时是浙江美术学院副院长。 王坚对绘画非常认真，不想随便画画了事。他跟着老师学了几年。渐渐学会用艺术家的眼光去观察世界。“那时候画家们都说我很会看画，给他们提的意见都是一针见血，所以经常拉我去批评他们的画。” 这样的情形一直持续到高中。忽然有一天，他不再继续画画了。一方面是升学的压力越来越大，更重要的是他发现自己的绘画技巧总是不能进步，于是相信自己不是一个绘画天才。不过，因为绘画的基本训练，他觉得他的思维已经发生了很大变化： 画画对我的思维有不可缺少的影响。我认为人的一部分能力是从外面灌输进去的，比如语言和数学。但是人还有另外一些能力，是随着人的成长逐渐进化来的。一个小孩儿看房子，是前是后是左是右，他刚一出生的时候是不知道的，以后慢慢地可以分辨出来，这是不教就会的。比如绘画方面的视觉能力，音乐方面的听觉能力，体育方面的平衡能力和爆发能力，人类的这些能力是与生俱来的，不用去学就明白，你会了以后也很难讲出来你是怎么会的。画画这个东西，你画得好，是没有办法讲出来你为什么画得好的。这是人类的非常重要的一个特点，遗憾的是大多数人都把这些能力压抑了，后天灌输进去的知识把本来就有的天赋给淹没了。Why is this so? 高剑峰：衣服每天被颜料弄成五颜六色，我和同学彼此都觉得很酷 除了下围棋，高剑峰在学生时代最多的业余活动全都和体育有关。有我们在前边提到的长跑，还有足球和篮球，他还是上海交通大学排球队的领队。不过，他进入这所名牌大学的经历却让他和美术结了缘。 1989年春季的一天，高剑峰走进上海交通大学，对一个老师说他将要高中毕业，希望来读工业造型设计专业。老师看了这个学生在高中三年的一大堆成绩单，说他没有问题，但又补充一句： “你的美术绘画行吗？ “我只练过书法，不会画画。” “那你为什么想学工业造型设计？” “我也不知道为什么，”剑峰老实地说，“只觉得这是一个多方面结合的学科，挺好玩的。”停了一会儿，他又补充道，“小的时候，别人一直表扬我是'全面发展'，我觉得'全面'这个词很重要。” 老师是个系主任，经验丰富，看看眼前这个学生，忽然感觉到他身上有一种异乎寻常的力量，不由得喜欢起来，就说：“你现在就开始学绘画吧。离高考还有三个月，也许能行。” 剑峰回到家里就去找美术老师，说他想学画画。老师大奇，心说这孩子在高中这么多年，从没把绘画放在心上，现在临到高考，人家每天复习数理化，恨不能把一分钟掰成两半用，他却如此节外生枝。 事实上高剑峰的“备战高考”的确与众不同，他从此开始了他的绘画历程。每天的大部分时间用来学习素描，家里成了美术速成班，父亲是学物理的，现在也期望儿子能学物理，不仅因为儿子的物理成绩最棒，而且因为他和大多数父亲一样，觉得子承父业是一种难得的际遇。尽管如此，他还是再次成了儿子的坚定支持者。就像他当年支持儿子练长跑和踢足球一样。 剑峰学画和刘策不一样，他没有时间去磨练基本功，上来就画。可是这一画就让他真的有了兴趣，还觉得整个“备战高考”阶段都特别开心，一点也不像别人说的是个“黑七月”。到考试的时候，他的基本功虽然还欠着很大火候，但对于最简单的技法已经不是外行。有个考试题目是“静物写生”，还有一个是命题画，后者有点像是用线条和颜色来写作文。他表现出来的绘画能力让他的美术老师大为吃惊，也让他如愿以偿。他真的进入上海交通大学，学习工业造型设计。 如果说中学时代是在运动的旋律中度过，那么大学就是艺术的殿堂。剑峰进入大学以后的第一感觉是，这“工业造型设计”，并非他想象中的那种艺术，实际上也就是工业领域的平面设计和立体设计，有点像现在的广告装潢。这不是他喜欢的，但他仍然很开心。他每天滚在画室里面，学了很多以前不知道的东西，还拿到一等奖学金，衣服每天被颜料弄成五颜六色，他和同学彼此都觉得很酷，说自己像艺术家的样子。这是夸张的，事实上他永远成不了艺术家，但是他的绘画技巧也的确娴熟起来，还找到了色彩的感觉，知道怎样像艺术家那样表达自己的思想和自己的感受。