I always treat research skills as a science, which is unified into science of pursuit together with science about universe and science about society. In research, knowledge progress is pursued to be the largest.
Teaching researchers how to research is more important than research. In my long research career, I realized the importance of methodology and discovered many research methods. After discovered science of pursuit, I greatly improved these methods by imitating universe. I hope these methods will help other researchers: to have the same progress with smaller difficulty; or make larger knowledge progress from the same effort. Good researchers usually have more problems, stronger ability, and better knowledge structure, but normally not more efforts.
Since almost all researchers want to be good researchers, not trivial researchers. Without enough knowledge about methods and their advantage, research becomes a high-risk job. So many talented youths do not want to be researchers. Investment on research is also insufficient because of low research effiency.
If a researcher follows correct methodology and is diligent enough, although he cannot predict what discovery he will make, it is safe to predict that he will make some discoveries.
I started to think about science of research at twelve; started physics research at eighteen; and started sociology and economics research at twenty-three. So research is the pursuit system I understand the best. Science of research provides a more detailed explanation of science of pursuit.
Many researchers do not believe that research is totally rational. They depend on hardworking and opportunity. There are two facts supporting that knowledge progress is a rational process.
Firstly, good researchers have much higher research efficiency: make more discoveries in unit time. Newton and Einstein made more discoveries in one month than thousands of trivial researchers made in whole life. Researcher with higher research efficiency usually has stronger ability.
Secondly, good researchers' ability increases much faster than their rivals. They can catch up with many wonder children, who have large advantage at the beginning.
People cannot explain the mystery source of ability, so they invented words like "genius" and "inspirations", to give ability a partially irrational explanation. Many great researchers like Einstein and Edison said repeatedly that they were not genius, but people did not believe.
Diligence, defined as efforts in unit time, is not the decisive factor either. Einstein worked about two hours daily, much less than many scientists. From his and my experiences, if methods are good, working no more than 10,000 hours is enough to solve very important problems.
Science of research lags far behind social demands. The situation is similar to that between economics and economy before Adam Smith wrote "Wealth of Nations". In society, knowledge progress is the main reason for economic development and growth of happiness, but people do not know the best methods to pursue knowledge progress.
It is difficult to establish a science, unless there are enough experiences. Economics can be established when economy system is good enough. Similarly, science of research can be established when there are enough many great researchers. An important difficulty for science of research is the lack of materials. Economy system can be gradually improved because the old one can be preserved. But research methodology were not recorded well because most researchers did not treat methodology as a universally valid truth. This is the reason why science of research is established so late.
The current education systems treat a future researcher the same as the other students. But researchers have a very different purpose, the purpose requires researcher to start research much earlier than other students starting their careers. Most of researcher's learning in school is unrelated with research. A good researcher ought to manage to reduce the efforts on those subjects. Einstein played truant to learn useful knowledge, and I imitated Einstein.
There are three steps for a complete research process. The first step is new fact discovery and new concept generating, similar to the creation of matter (although the mechanism is unknown in physics). A researcher normally does not participate this stage. Great researchers proposed most useful concepts.
The second step is analogy, which requires explaining many concepts in one theory. This is similar to nuclear reaction. This stage aims at simplifying knowledge, generalizing theories. Normally, good researchers can participate this step.
The third step is to solve problems. When enough many problems are proposed, researcher need to solve them, similar to particles absorbing energy from electromagnetic field. Most researchers just participate this step. Sometimes, in order to solve a problem, researcher also needs the first and second stage.
Human beings have sufficient knowledge about the third stage, but very little about the first and second stages. If a researcher just wants to be a researcher at the third stage, the influence of these principles and methods is not large, at most saving some efforts. But these principles and methods will largely improve the probability to be a good researcher, so the title is "How to be a Good Researcher".
I mainly use research careers of Einstein and myself as examples to explain the theory, just because I am more familiar with them.
Some Simple Analogies
Since most readers do not have long research experiences. It is necessary to explain the principles and methods in an easy way. Since all pursuit behaviors have some common properties, knowledge from other pursuit can also help to explain research process. They are inaccurate, but much easier to understand. Many of the following analogies are prototypes of the principles abuot research.
Stock market:
Researcher ought to choose topic like investor choosing stock. When competition is strong (stock price is high), it is dangerous, although it is still possible to succeed. The best choice is the good stock with low price. Generally, researchers' knowledge about topics is much less than investors' knowledge about stocks. So a good researcher has the chance to find a good topic. It is better to study many problems, similar to buying many stocks. Researcher can both makes progress and meet difficulty; similarly, stock market can both rise and fall. Statistically, researcher will make progress; similarly, stock price will rise in a long time.
If researcher establishes a new research area, he is similar to the founder of a company seeking IPO. Although risk is higher, reward is also much higher.
Training of an athlete:
An athlete cannot keep on training without competition. The only aim of his training is to solve problems in competition. Such training has the highest efficiency.
Learning in research is similar to training in sports. Research is similar to competition. So a researcher's learning ought to work for researching. It can help to improve research the fastest.
Knowledge progress is similar to athlete breaking world record. It would have been very difficult if there were not so many topics.
Strategic explanation:
The only purpose of a war is to win a decisive battle. Research is similar to a very long battle between ability and problems. Ability has had many victories. But problems have never been totally defeated, they always organized new defense successfully. Problems merely defense, never attack. Normally, there is a fairly fixed battlefield and front in a long time.
A researcher is similar to a commander of ability. He ought to find the problem with the highest priority; similar to that a commander ought to find the weakest point in the defense. He should focus his efforts (army and firepower) on the problem. A researcher cannot have many topics together; similarly, a commander ought to have a narrow battlefront (without the dangerous of being attacked, this is extremely necessary).
When being defeated, army ought to resume fighting ability as fast as possible. Similarly, researcher ought to manage to resume his research ability. But his situation is much better, there is no dangerous of being chased by the enemy. But competition is similar to another kind of chasing.
When researcher's ability is stronger than difficulty of problems, he will win the battle. Researcher should fully make use of the victory; keep on chasing problems to the line where problems are strong enough to defend. Similarly in battle, chasing is an important method to have more victories.
As the result of strong competition, important problems are always defended the best. Problems organize defense very well. Methodology is the only tool that can reduce researcher's sacrifice (risk and effort).
Before the battle, it is important to collect information about the defense. It is especially important to analyze why previous attacks fail to succeed. If attacked correctly, a problem will be solved quickly.
A researcher needs reliable foundations to start his theory. Similarly, army need base.
Random walk
Drunkard model:
As a theoretical model, suppose a researcher keeps on changing topics randomly. This is similar to a drunkard. Total effort is similar to total distance. Each topic is similar to a step. Suppose researcher's effort is the same on every topic. His success is similar to the displacement of the drunkard, proportional to N0.5. N is the number of steps.
Even if N is 2, research efficiency will drop sharply. Although topics are not randomly chosen, researcher normally changes topics many times in his life. So a good researcher ought to find a large topic, and working on the topic whole life. Normally, research process is a combination of random pursuit and ordered pursuit.
Specialty ought to be combined with ergodic theorem. It does not need much time to try all original possibilities.
Normal distribution:
If all researchers' ability forms a normal distribution,
P=exp(-x2/2)
x=(a-u)/z
P is probability density. "u" is threshold ability. "z" is root-mean-square error. "z" will be larger when there are more independent researchers. Learning more will reduce "z". Probability to find a good researcher (ability larger than a given value) increases with "z" and number of researchers. A good society ought to increase "z" and "u".
For a researcher, realized knowledge progress from unit effort also forms a normal distribution. Then "u" is explained as the expected progress from unit effor. Stronger ability will reduce "z". A researcher ought to increase ability to increase "u", and reduce risk to reduce "z".
Mountain-climbing:
Suppose truth as a high mountain. Researchers try to climb the fastest. There is no danger for climber's life. Both starting too early and too late are harmful. The best way is to climb together with learning. Apart from skills for climbing, researcher also needs to study the incomplete map of the mountain. He can get the best map from some great researchers, because they visit more places than others. Then he needs to visit the candidates for good roads by his own. A "good road" has two meanings: road to high peaks and shortcut to the same height.
Researcher must study his purpose. In most situations, simple purposes are low peaks. The high peaks hide behind the clouds and cannot be seen clearly. Researchers often discover the hill is too low after they reach the hilltop. Before making up his mind, researcher must try all candidates for shortcuts. A good researcher has a good intuition for good roads, just like an old climber. This ability can be trained
Home
All rights reserved.