On the ThoughtFoundation of Science and Engineering Practitioners

 In science and engineeringeducation, people have generally realized the importance of independentthinking, but about the complex intension of the central thing ‘independent thinking’,so far there is not a rich and deep understanding, and people’s understandingof it has stayed at a vague and general stage; in this paper, we try to have acompletely new discussion on some essential features of independent thinking(our discussion is mainly based on scientific majors, like mathematics,physics, chemistry and biology, and will also discuss some engineering majors,like electrical engineering and computer science). Our basic opinion is: themain intension of independent thinking is to learn related knowledge in anartistic and thoughtful way, which is the central argument of this paper, andwe think this view is clear and simple, and the complex discussion of thefollowing parts is all based on this basic view. 

                                                           (I)

In mathematics and physics fields, good researchers generally agreethat physics and mathematics are both arts, and therefore, people’s pursuit forbeauty forms a basic motivation in mathematical and physical research. Forexample, the great algebraist, Sylvester, had a strong interest in literature,asBellsaid: “Inaddition to the English and classical literatures he was well acquainted withthe French, German, and Italian in the originals. His interest in language and literatureform was keen and penetrating.”[1]Wiener once wrote: “Mathematicsis in essence one kind of art.”[2]Atiyah also once wrote: “Forexperts, mathematics is both science and art, and truth and beauty are equallyrespected.”[3]If we read some books written by great scientists, likeNature and the Greeksby Schrodinger,Einstein’s collection of essays,A Mathematician’s Apologyby Hardy,The Philosophy of Mathematics and Natural Scienceby Weyl,Ex-Prodigy, I am a MathematicianbyWiener andThe Pleasure of Finding Things

Outby Feynman, we will be deeply impressed by the elegance of thesemasters’ language. Among scientific researchers, ‘beauty’ is a central thing,and I think it is a widely recognized basic notion.

The reason why artistic mindset is so important in science and engineering is naturally somewhat complicated. Firstly, in science and engineering, beauty and significance are often closely interrelated; take mathematics as an example, the Liouville theorem in Complex Analysis (every bounded entire function must be constant) is very elegant and simple, meanwhile, it has a wide range of impact, and the Gauss’s theorema Egregium in differential geometry (Gaussian curvature is an intrinsic invariant) is also a deep and elegant theorem, and the whole theory of Riemannian Geometry emerges from it; with these two theorems, we can preliminarily feel that elegant, simple and deep theorems often have a wide range of impact, and they will constantly emerge in many concrete problems and situations, while complex and ugly conclusions often can merely influence few questions. Secondly, science and engineering courses are often hard and obscure, thus, the process of learning them is often dull, while many artistic expressions can make this whole process vivid and lively, namely, art enhances the pleasure of learning process. Thirdly, one of the essential characteristics of science and engineering is innovation, and we all know that art requires creativity, but conversely, creativity also requires art, because artistic expressions are often novel, rich and full of changes and intelligence, and they are not so stiff and tedious like ordinary and standard expressions, while these elements are often highly important basic ingredients for innovation. To sum up, we list some arguments from different perspectives, though they are somewhat limited, we can already see that artistic mindset is indispensible in science and engineering, for instance, when we learn some courses like algebraic topology, it seems that we have arrived at a beauty spot, and every theorem, approach and problem in them is a beautiful scenery, while there are tens of thousands of beautiful scenery in the whole course, therefore, the process of learning them is very pleasant. (Considering this is an issue many brilliant scientists have discussed, our discussion here is somewhat concise)

                                                               （II）

In fact, many science and engineering workers also realize the importance of literature and artistic expressions, and they also try to achieve this, meanwhile, they often believe that their writing is already elegant enough and they have enough graceful humanistic cultivation, but we think the difference among these scientific workers who have certain artistic cultivation is enormous, why?

  Here, one writer’s view isquite meaningful, de Botton writes: “It is remarkable to what extent badpaintings of spring resemble, though are still distinct from, good ones. Badpainters may be excellent draughtsmen, good on clouds, clever on buddingleaves, dutiful on roots, and yet still lack a command of those elusiveelements in which the particular charms of spring are lodged. They cannot, forinstance, depict, and hence make us notice, the pinkish border on the edge ofthe blossom of a tree, the contrast between storm and sunshine in the lightacross a field, the gnarled quality of bark or the vulnerable, tentativeappearance of flowers on the side of a country track-small details, no doubt,but in the end, the only things on which our sense of, and enthusiasm forspringtime can be based.” This quotation has rich information, which can let usget some deep understanding of the difference between 1stclassworks and 2ndor 3rdclass works, namely, between goodand bad works, the difference “is ‘not very much’, or at least, surprisinglylittle.”[4]To sum up, some scientificworkers think that they have deep humanistic cultivation, and they indeed readmany books, but the internal quality of their writing is still far from reallygood ones.

  Therefore, one passage of Goethe deserves our special attention: “Percipientcan not be cultivated by reading mediocre works, and only by reading the bestworks can we cultivate percipient, thus, I just let you see the best works. Ifyou lay a solid foundation in the best works, then you will have a benchmark tomeasure other works, and for other works, you should not overly praise but shouldappropriately evaluate.”[5]To sum up, reading manybooks does not mean elegant expressions, and the writings and mindset amongdifferent scientific workers have a subtle but evident, decisive difference;beautiful writing and mindset are not so easy to achieve, and they need carefulincubation.

                                                                 (III)

However, we think, there exist some internal defects in the widespread basic notion “beauty is highly important for mathematical and physical research”-we think, besides artistic expressions, thoughtful understanding is also an indispensible part of independent thinking. Namely, independent thinking should include two major parts: thoughtful thinking and artistic one.

I think the reason why thoughtful understanding plays such an important role in science and engineering majors is not very hard to understand: since scientific knowledge is broad, complex and deep, if we just have certain understanding in the artistic level, then we cannot well control such broad and deep content, and in order to well comb these broad knowledge into ordered system, in order to establish internal connections between these complex knowledge, in order to clearly understand these objective knowledge in a rational way, we need to have thoughtful understandings. In summary, in scientific fields, speculative understanding at least includes two aspects’ value: firstly, after all, scientific knowledge is objective knowledge in the natural world, and it cannot be viewed from a completely artistically subjective perspective, objectivity is one of the main features of scientific knowledge, while artistic understanding has certain degree of subjectivity; secondly, scientific knowledge is both broad and intricate, and in order to clarify these knowledge and get a clear understanding, we also must have thoughtful perceptions.

About the internal meaning of thoughtfulness in science and engineering fields, we can also consider it from another basic perspective, namely, the importance of “idea”. For science and technology, the importance of “idea” is widely known, but people often have a misconception, namely, an idea often suddenly comes to a person and needs good luck, but in fact, what the birth of good ideas relies on is certainly not luck, but the solid basic training and strong independent thinking ability of one scholar, and only by effectively combining these two basic aspects together can he get good ideas, while for independent thinking, it naturally requires a person to have a profound thought foundation. For instance, for mathematical and physical research, basic knowledge and problem solving are certainly important, but it is also meaningless if we can just solve problems, instead, we also must have good ideas and need to have important new ideas and new concepts; and if one mathematical scholar does not have understandings in conceptual and notional level and just can compute and has basic training, then the height he can reach will also be somewhat limited. Fundamental and problem solving are certainly important for scientific innovation, but it is far from enough that one scholar just has fundamental, instead, he also must have many understandings in conceptual level, and only in this way can he make some truly profound and important new discoveries, which I think is easy to understand. About this, we can give an appropriate example, namely, Selberg’s analytic number theory research, when Selberg studies this complex and deep field, he certainly has good basic training and can solve problems and compute, but if Selberg can merely solve problems and lack the support of some deep thoughts and notions, he is naturally also impossible to get many deep results. In conclusion, for scientific and technological research, “idea” is very important, while as a basic condition to produce good ideas, thoughtfulness is certainly much more important than artistry, and in this sense, thoughtful understanding is important for scientific research.

                                                           (IV)

In terms of the high importance of thoughtful perceptions, we canhave a brief discussion by listing some concrete examples. If we observe fourwell known mathematicians, Weyl, E Cartan, Bell and Halmos, we will find outthat their expressions all belong to the elegant and fresh type from theartistic perspective, and their writings are all elegant enough, but why doonly the former two become great mathematicians and the latter two’s researchis a bit worse? The reason is that the writings of the former twomathematicians both have enough thoughtful thinking, while the latter two’sspeculative depth is somewhat worse, though Bell and Halmos also have certainspeculative depth, their depth of thinking is worse than some masters like Weyland Cartan, and this is definitely one significant reason which leads to thedifference of their academic achievements. The speculative tendency in Weyl’s andCartan’s papers are very strong, while works by Bell and Halmos are mainlyartistic style, and the deeper reason which leads to the difference of theirstyles is naturally their different personalities. (Bell is a member of UnitedStates National Academy of Sciences, and his major research field is numbertheory, his writing actually has quite depth of speculation, but still notsufficient, he and Halmos are probably both 2.5thclassmathematicians, and these differences are somewhat subtle and not very obvious,but are also decisive.)

Take contemporary mathematical world as an example, all the masters can store mathematical information speculatively and artistically, including Wiles, Atiyah, Lax, Perelman, Thurston, Milnor, Serre, Hirzebruch and etc, otherwise they cannot discover some fundamental results, and in the meantime, an incredible basic fact is that only these masters’ writings have both true thoughtfulness and artistry (in them, thoughtfulness is the main aspect and more decisive, but artistic writing is also indispensible).

If we consider the past mathematical and physical world, we thinkthat many brilliant mathematicians and physicists probably can be divided intothe following levels: Ahlfors, Liouville, Weil, Lebesgue, Artin, Chern,Gelfand, Whitney, Faraday, Dirac, Heisenberg, Yang and others belong to the 1stclass, Zariski, Hecke, Levy, L Schwartz, Quillen, Mobius, A Borel, Schwinger,Tomonaga, Pauli, Chadwick, Millikan, Rabi among others belong to the 1.5thclass, O Stern, Carl Anderson, Menger, Wald and others belong to the 2ndclass. In general, the writings of these brilliant scientists all have enoughartistry, and the difference of their achievements mainly stems from thethoughtful aspect.

In chemistry and biology, the situation is also similar, and take some basic breakthroughs in these fields as examples, like Pasteur’s many biological contributions, the periodic law of elements discovered by Mendeleev, Fleming’s discovery of Penicillin, and law of inheritance found out by Mendel, these significant discoveries are all based on the thoughtful and artistic writings of specific scientists (thoughtfulness is the main thing). We need to point out that works of most of the winners of Nobel Prize in Chemistry and Nobel Prize in Physiology or Medicine are also difficult to be described as fundamental, since they just have local impacts, and are not principle, while fundamental discoveries can have overall impacts. In brief, there are also different levels like brilliant and great among Nobel Prize winners, and we can call normal Nobel Prize winners as brilliant, famous or genius, but will definitely not say that they are masters or great scientists, while people will call some masters like Pauling, Schrodinger, and Bohr as great scientists, which is true in the fields of physics, chemistry, biology and so on; in academia and the public these two different fields, people will normally not make mistakes, though some people will make mistakes, the overall judgement will not be wrong, while the masters in mathematics, physics and etc, are actually quite a few. I think the above fact is easy to understand, and we think that the reason for the differences of these scholars’ achievements is mainly the differences of their writings’ thoughtfulness. (At the same time, in everyday life, sometimes people will also call one scholar or people as a master, which is a second-meaning, broad statement)

Here, we need to add that it is meaningless to superficially talk about scientists’ mental qualities, like thoughtfulness and artistry, and scientific research should always be down to earth, and I think that all the mathematicians need to conduct tens of thousands of specific computations and deductions, and most contents of all the mathematical papers are also symbolic; in summary, scientific research needs to be based on solid concrete knowledge and we should not overly exaggerate the value of thoughtful and artistic writings.

                                                              (V)

Then why is it so important for scientific practitioners to thoughtfully and artistically think about certain issues? The reasons are certainly complex, and one of the reasons is that only independent thinking can make our papers and works have long-term vitality. Indeed, we have many students whose foundation is very solid, but in the later research or work, they do not make excellent contributions, and the underlying reason is that they lack understanding in the thoughtful and artistic level, due to the lack of this essential level, their papers are often repetitive and mechanical work, and are often repetitions of the past ideas, approaches, concepts and skills, and don’t have essentially novel ideas. The foundation of our many students is very solid, but when they do independent research, their papers are usually model and standard, which is not because they do not want to write original papers, but stemming from the fact that they lack independent thinking and understanding in thoughtful level, therefore, they are not able to write original papers even if they want to; good papers often require a number of novel notions and only one inspiration is usually not enough, and due to lack of a solid reserve of notions, these good students can merely do some mechanical and simple research by using existing approaches, theories and concepts, and their research often does not have profound originality.

As we have expounded, storing knowledge in a thoughtful and artistic way can doubly enrich the amount of information, since the information stored in mind is not rich, deep and vibrant enough, namely, there exist internal defects in some aspects, like information breadth, depth and quality, for many students, and they naturally cannot make valuable innovations. In summary, practitioners lacking thoughtful perceptions cannot do some both complex andoriginal research.

One passage of Atiyah can supplement our above discussion, he says:“One of the main characteristics of mathematics is its universality, and nearlyevery branch of knowledge has some aspects which can be analyzed by mathematics.The first step of such kind of analysis is to focus on some special issues,strip away all the irrelevant materials and then convert the left content intoappropriate mathematical form. The success of this kind of work relies onwhether we can find suitable mathematical concept and representation form, andthen whether we can find appropriate analytical and computational skills.Therefore, working out an abstract language and making it have the flexibilityand power to be applicable to many possible aims becomes the essential featureof mathematics. In this kind of abstract world, simplicity and beauty haveabsolute importance.” “It is difficult to predict the importance of a specificproblem in advance. In this respect, the choice of problems and systematicexposition is an art relying on one mathematician’s intuition. No doubt, forintuition, aesthetic standard is very important.”[6]Through this paragraph, wecan roughly understand the partial reason why aesthetic taste is so importantin scientific research, and in today’s scientific and engineering world, theimportance of taste and style is widely recognized, since “taste” is indeed oneessential ingredient in scientific research. 

                                                               (VI)

From the above analysis, we can feel the importance of independent thinking in science and engineering education, and we can make some deeper analysis about this phenomenon. People often think that the difference among researchers only begins to appear at PhD stage, and at this stage some people do good research and some do mediocre one, but this view is somewhat defective. In fact, the difference between different individuals already arises in the undergraduate stage when we learn knowledge, and for two students who both have gift, perhaps their grades are both good, but one of them just has accumulation in knowledge level, while the other already begins to learn broad and complex undergraduate knowledge thoughtfully and artistically, and therefore, the professional quality of them already has a huge difference at graduation, and the amount of information of the individual who has thoughtful understanding is twice as the other one. This difference directly leads to the different research quality of these two students in the future. Namely, for good students, they should not just learn knowledge at undergraduate, and instead, they should have rich thinking at multiple levels.

Meanwhile, we want to point out that these basic qualities, thoughtfulness and artistry, are not fixed, and they can be gradually improved, and through many ways, like interpersonal contacts, wide reading and deep thinking, we think that a scientific worker’s mental qualities can greatly improve, however, it requires a somewhat long process. Generally speaking, even for some masters, their thoughtfulness is probably also not enough when they are about 20, and only later, with the expansion and deepening of learning experience and independent thinking, do they gradually mature.

                                                            (VII)

If we savor the writings of some brilliant mathematicians like Bonnet and Moser, we will be deeply touched by the great beauty and mature ideas of their works, indeed, their achievement is somewhat lower than Abel, Siegel and some others, but the power of personality and ideas displayed in their academic journey is worth our respect and admiration. Obviously, one people’s mindset can not be separated by his personality and academic experience, and what we face is concrete individuals, not abstract thinking pattern and research method; outstanding mathematicians and physicists often have profound personality, and this shapes their depth of thinking and artistic cultivation. No one can get high quality by mechanically using simple concepts like “thoughtfulness” and “artistry”, and independent thinking in thoughtful and artistic level stems from long-term positive work and deep love for one’s own field, and they are all complex qualities, which must be fostered for a long time, and there are basic backgrounds in many aspects behind them, like professional knowledge, work experience, life course, emotional power, personality tendency, etc. Every outstanding scientific worker has extraordinary personality, and it is these personalities that shape their thinking in thoughtful and artistic level.

In brief, “thoughtfulness” and “artistry” are not simple concepts, and they both have complex intension: thoughtfulness requires many intellectual qualities, including global perspective, precise analysis, comparison and connection, imagination and integration, etc, and artistry requires many artistic features, like elegance, subtleness, richness and changes. The root of these two basic qualities is the power of thought and character in positively thinking workers.

                                                     (VIII)

We say that good scientific workers all have thinking in thoughtfuland artistic level, but it does not mean that they are thinkers or artists,what thinkers and artists have are quite different intellectual andtemperamental ingredients. For instance, Milnor’s writing is extremely elegant,and is also with enough depth of speculation, but he once says: “I suppose Ilike to relax by reading science fiction or other silly novels.” “I enjoy musicbut I don’t have a refined musical ear or a talent for it. I certainly enjoyreading, although, as I said, I tend to read nonserious things for relaxationmore than trying to read serious things.”[7]Siegel also had a similardescription, and he said: “People generally think that mathematical gift isclosely related with musical talent, but I am aware that there are certainlymany mathematicians who do not have musical gift, and I am one of them.”[8]To conclude, the thoughtfuland artistic writings of mathematicians and physicists mainly concentrate inmathematics and physics aspects, and they are notably different from thinkersand artists, which is a somewhat basic fact.

In the meantime, many practitioners in social sciences and humanity also do not have some intellectual qualities of technical practitioners, and as we all know that some artists and thinkers’ mathematical, physical and computer abilities are not very good. Compared with people working on liberal arts, scientific workers often have many technical qualities, like good computing skills, ability to think about mathematical notations and ability to analyze natural phenomena, etc. Moreover, for one scientific worker and one liberal arts employee who both have enough thought depth, there is still an obvious difference between their expressions, and the former one’s style is more technical oriented, which is also a somewhat easily observed fact.

We want to note that, in the broad actual life, these differences are not so clear-cut, and most people have many abilities in both these two sides, meanwhile, the scientific side and the social side are usually intertwined in life, and some extreme cases are only a few.

                                                            (IX)

For engineering majors, the practitioners naturally donot need a very high level of thoughtful and artistic expressions, but they also need a great deal of independent thinking in thoughtful and artistic level with their own professional knowledge, and it is also the foundation for the innovations in engineering fields. For example, the development of Google does not merely require professional knowledge like algorithms and stochastic process, but also requires thoughtful understanding about these knowledge, in fact, there are many technicians in computer field who well master courses like algorithms and stochastic process, but the majority of them do not have enough independent thinking ability, and therefore, they cannot make some valuable, new creations and development.

For engineering majors, like mechanical engineering, electronic engineering, computer science and communication engineering, there are technical jobs and administration jobs. For workers in technical position, they need to master their professional knowledge very proficiently, subtly and deeply, since engineering directly faces consumers, for example, medical equipment and engineering equipment companies’ products are directly oriented to a number of consumers, thus, the manufacture process needs to have a high quality standard, otherwise if the made products have many flaws, then the sales will be greatly affected, namely, if we deal with our products impatiently and carelessly and they have many defects, then it will bring direct economic losses (moreover, the losses are often large amount). In a word, engineering majors also have a very high demand for the technicians’ professional expertise, and relevant workers must be expert at their professional skills, and only vague, superficial understanding is hard to meet the market demand. Some people probably have a false view and they think that for engineering fields, if one can make usable products then we donot need to care about whatever methods are used; indeed, engineering fields do not pursue the rigor of theory like scientific majors, and their work process includes many empirical, flexible and non-theoretical operations, but practitioners in engineering also need to finely and proficiently master professional knowledge, because it is very hard to get good products by casual accidents and luck (though we do not deny the existence of such occasions), in most cases, we need to have a solid foundation. For some highly precise products like medical equipment and engineering equipment (like the products of Cisco, Intel, Ericsson, Sony, Siemens and LG), their design and structure are very complex, and the workers more urgently need to delicately and deeply master their professional knowledge, and if their skills are vague and coarse, then they are hard to qualify for the frontline work, and it is hard to believe that a team which has a poor mastery of related professional skills about medical equipment can make some important product innovations. In fact, in all technical companies, the technicians often have heavy maintain and development pressure, and many good technicians usually have a systematic, broad, proficient and detailed understanding of their professional knowledge. In a word, engineering workers also need to hone their own professional ability through learning by themselves and communicating with their colleagues.

In the meantime, a bit different with scientific majors, engineering fields also have broad and active connections with many upstream firms and selling companies, thus, even technicians also need to know much business information about their industry, and need to be familiar with their partner companies. Since engineering companies need to face consumers, only theory and new notions are not enough, and to get high quality and marketable products, technicians in engineering also need to know the business situation and social experience of their industry, which is an organic part of their mastery about the purposes and applications of their products. To conclude, the knowledge structure and basic quality of engineering workers are indeed somewhat different from scientific workers.

For the administration positions in engineering fields, some of them are from technical positions and some are from non-scientific fields, and they need to be familiar with their company’s products and also be familiar with information of the market, industry and society, which we do not want to further discuss here.

In summary, for science and engineering workers, we not only need accumulation in knowledge level, but also need a great deal of understanding in thoughtful level (for scientific workers, the main thing should be the independent thinking about their own professional knowledge, while for engineering employees, they should have both the independent thinking about their expertise and about market and society). Considering the whole essay, our simple conclusion is: in order to make good innovations in the future, scientific workers need to learn and think about certain knowledge in their own way.

                                                               May 28, 2019

[if !supportFootnotes]

[endif]

[1]See E T Bell, Men of Mathematics, the discussion about Sylvester in Chapter XXI, especially pp. 422-425, London: Penguin Books, 1953.

[2]See Nobert Wiener, I am a Mathematician, chapter II, p. 47, Shanghai: Shanghai Science and Technology Press, 1987.

[3]See the paper “Identifying Progress in Mathematics” inThe Unity of Mathematics, the relateddiscussion on pp. 167-169,Dalian: Dalian University of Technology Press, 2009.

[4]See Alain de Botton, How Proust Can Change Your Life, Chapter XI, "How to Open Your Eyes".

[5]See Conversations with Goethe, Feb 26, 1824, p. 57, Nanjing: The Yilin Press, 2000.

[6] See the previous paper “Identifying Progress in Mathematics”, pp. 168, 169.

[7]See “Interview with John Milnor”, Notices of the AMS, Volume 59, Number 3, p. 408, March 2012.

[8] See the introduction of Siegel in Contemporary Mathematical Masters, p. 13, Beijing: Beijing University of Aeronautics and Astronautics Press, 2005.