Imagination, intuition and inspiration

Source: Guangming Daily

Imagination, intuition and inspiration

【Science and Technology Essay】

On how to do learning, Su Shi has a famous saying: "Bo guan and about to take, thick accumulation and thin hair." Here are three examples of "thick accumulation and thin hair":

Zeng Jiong, a famous algebraic mathematician on the mainland, studied in Germany in his early years, and he wrote and published only three papers in German in his lifetime, making him one of the algebraists who made significant contributions to the development of recent algebra in the 20th century.

The famous mathematician Feng Kang has published only 22 papers in mathematical journals, including two papers in foreign journals. But he had two major breakthroughs in computational mathematics in his lifetime: one was to pioneer the finite element method, and the other was to create the Hamilton system's symplectic geometry algorithm. Four years after his death, he was posthumously awarded the first prize of the National Natural Science Award in 1997.

The most legendary is the Chinese mathematician Zhang Yitang, who made a breakthrough in the study of twin prime conjectures in 2013 (at the age of 58) and won several international awards, after he had published only two articles before.

Scientific research is expensive in innovation. What is innovation? The famous statistician C.R. Rao, in his book Statistics and Truth, has the following statement: "Innovation can have different kinds. The highest level of innovation is the emergence of new ideas and new theories... Another different level of innovation refers to a new discovery within the scope of an existing law that has great significance in a particular field. "Innovations like Newtonian mechanics and Einstein's theory of relativity are the highest levels of innovation. The vast majority of scientific research innovations belong to the second level.

How can research achieve some kind of innovation? I have the following experience.

First, innovation requires long-term accumulation of knowledge, which is the basis of innovation. Albert Einstein once said, "Creating a new theory is not like destroying an old barn and then building a skyscraper in place." It's like climbing a mountain, gaining new, broader horizons, and discovering unexpected connections between our starting point and its rich environment. ”

Second, innovation requires a rich imagination. The so-called imagination is the ability to create a thought or picture in the mind, that is, the ability to think imagely. In terms of innovation, Einstein believed that "imagination is more important than knowledge." He added: "Asking a problem is often more important than solving a problem, because solving a problem may be just a mathematical or experimental skill, and asking new questions, new possibilities, and looking at old problems from a new perspective requires creative imagination." "How do you expand your imagination?" The German poet Goethe said: "Imagination can only be activated through art, especially through poetry." "It seems that imagination is more closely related to a person's artistic accomplishment. Einstein loved to play the violin and was a master violin player. He once confessed: "Physics gives me knowledge, art gives me imagination, knowledge is limited, and the imagination opened up by art is infinite." ”

Third, innovation requires intuition. The so-called intuition is the understanding and judgment of something without conscious reasoning. In his speech to mark Planck's 60th birthday, Einstein said: "The supreme mission of physicists is to obtain universal fundamental laws, so that the world system can be established by simple deductive methods." There is no way to lead to these laws, only through the intuition that is based on the understanding of empathy of experience. The physicist Born was even more convinced: "All the great discoveries in experimental physics are derived from the intuition of some people." Mathematics historian Klein said: "Mathematics is also a subject that requires creativity. Mathematicians use a high degree of intuition and imagination in anticipation of what can be proved, as they do when conceiving methods of proof. The famous French mathematician Poincaré said: "We rely on logic to prove, but we rely on intuition to invent." The "invention" referred to here refers to predicting what can be proved and the method of conceiving proof. Mathematician Tao Zhexuan said: "Only by combining strict reasoning and intuition can we solve complex mathematical problems: the former is used to correctly solve some detailed problems, and the latter is used to grasp the whole." The lack of any of them will keep you groping in the dark for a long time. ”

Fourth, innovation requires inspiration. The so-called inspiration is an almost unconscious or subconscious non-logical creative thinking activity, which is a sudden spark of thought after long-term thinking about a certain problem. Einstein said that his innovative thinking activity "arose before there was a logical structure that could communicate with others with words or other symbols," which was an inspiration. Inspiration usually comes when you are engrossed in thinking about a problem, but sometimes it is inadvertently or in the haze of consciousness. German chemist Kekuler was awakened by a dream during his lunch break that a small snake had its head bitten on its tail, and then he spent the night proposing a hypothesis of a benzene ring structure. This is the inspiration that arises in the haze of consciousness. Inspiration also sometimes comes from analogies and associations with different phenomena. In the autumn of 1834, Scott Russell, a British naval architect, was walking along the river when a small wooden boat passed by him, when he observed a rapid wave rolling up at the bow, but the wave unusually traveled forward in the form of a single peak. Later, after careful study of this phenomenon, he proposed the famous "isolated wave" theory.

Fifth, innovation requires a certain opportunity, but "opportunity is only for the prepared mind" (Basti german). But I don't subscribe to the statement that "opportunities are unattainable". I think that under certain conditions, it is possible to artificially create an environment that generates opportunities. For example, in order to keep my research alive and fresh about research questions, I change my research field every other period (8 to 10 years). There will naturally be more opportunities in new areas of research. During the transition period when changing the field of study, I often study several related fields at the same time.

In recent years, I have often gone to college or middle school to give public lectures under the title of "Science and Art in My Mind". After the report, people often ask me if I can give examples of reading classical poetry that are helpful to my scientific research, and my answer is: there are no specific examples, but the influence of artistic accomplishment on my scientific research topics and writing is subtle. In my research, I like to pursue the sufficient necessary conditions for obtaining the validity of a certain theorem or proposition, and my articles on several important results are very short, which may be the subtle influence of classical poetry on me. Regarding scientific innovation, I once wrote a testimonial: "Scientific research and innovation is like a chemical reaction, knowledge is the carrier, intuition, imagination and inspiration are the catalyst." ”

(Author: Yan Jia'an, Academician of the Chinese Academy of Sciences, Researcher of the Academy of Mathematics and Systems Science, Chinese Academy of Sciences)