The following methods are applications of the above principles. They help to increase ability, and sometimes increase desire. The advantage of these methods cannot be fully explained. Compared with those worse methods, they also have some disadvantages. But the advantage will be larger than the disadvantage.

The following methods mainly teach how to start research the best.

For the pursuit of any quantity, the best way is to pursue the quantity directly. It is hard to imagine pursuing one quantity is the best way to pursue the other, even at a special stage. Learning is not the best way to research.

In current education systems, students basically finish their learning before start researching. Since what to learn is different for different researchers, this is not the best way for a researcher.

In a pursuit system, utility is valued by "marginal pursued quantity". Researcher will reach equilibrium between all efforts: utility from unit effort is a constant.

For a current researcher, problem learned from unit effort is statistically more important than knowledge learned from unit effort. So, researcher ought to spend more time to learn problems. Researcher needn't solve all problems. His probability to solve problem increases with the number of problems he has. His probability to solve many problems increases even faster.

Students commonly discriminate problems, because they cannot improve their scores. When there are enough many problems participating the knowledge evolution, researcher has finished 50% of his research road to success.

Start research early is very important. I think this is the largest advantage for Einstein and myself. If athletes can succeed at teenage when they become professional early, teenage good researchers will emerge in the future. The followings are the main advantages to start research early.

Firstly, it prolongs research time. For the same total efforts, it reduces effort in unit time, so pains will be smaller. If effort in unit time is the same, it increases total effort, so increases knowledge progress. It also provides more high-quality time for research. If one always has research desire, he will catch the high-quality time; if he has no such desire, he will not know it is a good moment for research. The high-quality time reduces researcher's happiness cost.

Secondly, if one starts research before entering university, he will have a chance to evaluate all knowledge, including reliability and importance, from a researcher's eyes. He will also have a chance to learn problems in every subject. This will help to establish an original research system, similar to a universe with original kinetic energy and potential energy. For two pursuit systems with different structure, the evolution results will be different. Original system structure is the best proof to reduce competition, and is the source for specialized ability. Knowledge progress, research results, can be learned easily. But system structure is hard to copy. So learning cannot make you a good researcher.

Thirdly, imagination is best, maybe only, cultured at young age. If research can change brain and gene structure, start research early will be the only choice for those "no genius".

Fourthly, it will prolong the time left after success, so a researcher will have longer time to enjoy his success. This will increase his research desire. An old researcher ought to stop researching and to enjoy life, even if he still has research ability. The problem is whether his ability is higher than those younger ones. A research system full of old researchers cannot have large knowledge progress. If there is a knowledge revolution, he ought to retire even earlier. It is a difficult decision because he wants to participate the revolution too.

Fifthly, you will have larger freedom to cope with risk. You cannot know how much effort will be needed for your research exactly. You need more time to increase your effort if your fate is not good enough. Sometimes, in order not to totally waste your earlier efforts, you need to start a new topic (partially waste some earlier effort, but not all, because you will have higher ability and more knowledge). This will reduce your risk.

I shortly changed my topic several times and finally changed back. I would not dare to change freely, or research on such a large topic, if I started after graduation. I also cannot have time to propagate my theory. I must say I have not consider the risk for a correct theory to be refused. But starting early will also reduce the harm of unexpected risk. Science of research studies phenonmena inside research.

Sixthly, researcher can utilize his most energetic time: youth. Normally, happiness is not sensitive to age, but effort is. One can enjoy most happiness very well when he is 50 or 60, but he will lose 70%-80% effort then (compared with youth).

Imagination and judgment are the two most important properties for researcher's knowledge structure.

Knowledge progress, total expected pursued quantity, will be larger when there are more possible states, so stronger imagination will make knowledge progress faster. Without strong imagination, it is impossible to have fast progress; it is also impossible to find a topic with weak competition. When judgment is correct, expected pursued quantity at every possible state will be positive.

For current researchers, it is a random choice when imagine possible states. Researcher cannot know what he will imagine, or can he imagine the correct result. For good researchers, imagination is often beyond his rational expectations.

But judgment is rational. A good researcher normally has high ability to expect the judgment result. So they mainly use intuitional expectations, this greatly reduces research time. When research ability is not high enough, researcher also uses intuitional expectation, because he cannot organize a rational judgment.

When researcher can combine different properties freely, imagination will reach its maximum, because possible states form a single-connected continuity for possible states, similar to space-time. Imagination also exists in problem proposing and solving, similar to photon absorption and radiation. It is important to record every inspiration. From my experiences, inspirations from dreams are not as good as the inspirations from daily research. I recorded some of them, but cannot remember most of them when I waked up.

Researcher need not check all possible states, he just check all typical possibilities. After finding the best choice, he will check more possibilities around it.

Different abilities have different best learning age. For a child, imagination is easier to train and has no difficulty, while it is difficult for a child to learn deduction. The judgment standard is to compare the marginal efficiency for every learning effort.

There are two advantages for starting research with the training of imagination. Firstly, imagination is little related with knowledge level and research area. Imagination ability does not change with ability and research area quickly, so it can be used in different research areas. This greatly reduces risk when researcher has not decided his topic. Secondly, it will help research to reduce his worship on the dominating theory, because he will find many possible theories. Current education system gives students a bad impression: the dominating theory is the only possible theory.

Another work unrelated with research area and ability is methodology designing and choosing. Especially when research behaviors are not perfect. Improvement of methodology will increase progress velocity. Sometimes, a researcher can be excellent in both science of research and his subject.

Establishing correct judgment in research is similar to establishing correct potential energy and kinetic energy in the universe. If a contradiction is serious than knowledge, the knowledge ought to be abandoned. A well-educated student from current education systems always has a bad judgment: overestimating knowledge and underestimating problem. So a good student often needs a long time to reorganize his knowledge structure, this waste a lot of efforts.

If a beginner establishes a knowledge structure similar to the frontier of research, any progress he makes will be a new discovery. Many good researchers paid close attention to knowledge progress from their childhood; this saves them many efforts on forming correct knowledge structure. If starting research early, the wasted effort will be very small.

When a researcher himself decides what to learn and when to learn, it will greatly reduce his and teachers' effort. If you have enough high ability to teach yourself well (so you do not need teachers), the best time for learning is when you find the knowledge is helpful for your research. Every unit of effort must have effect on knowledge progress. The effort you saved from learning knowledge can be spent on learning problems, training imagination, judgment, etc.

Before finding the similarities between economy and universe, I often puzzled whether my effort on imagination and judgment have any effect. It is hard to spend efforts on things without observable influence in a long time.

When effort is the same, researcher with higher marginal utility will have higher ability. When competition, difficulty and utility are considered together, it is difficult to make a decision. Sometimes researcher ought to avoid popular knowledge, especially when its utility is doubtful. Even if the popular knowledge has unexpected large utility, the competition will be strong. I do not mean that it is unnecessary to learn popular knowledge, but you must think of its utility.

So researcher himself must choose subjects. From my experiences, there are many subjects which utility varies with research process, so researcher ought to have the freedom to give up and continue learning any subject, even the freedom to learn several chapters of a subject. In bad education systems, Einstein and I played truant to increase marginal utility of effort.

There are two kinds of researchers' problems. One is contradiction between meanings when two propositions cannot be true together. The other is contradiction in possibility: either to explain a fact as an inevitable result or as an accidental result. The first kind of contradiction is easy to decide, while it is difficult to judge whether it is a second kind problem or not.

It is an important task for beginners to have correct research methods. A beginner does not have enough ability to distinguish good and bad methods, also cannot win arguments with teachers and parents on what are good methods. But this does not mean the teachers and parents are always correct. The few good methods that are refused by most researchers have the largest marginal value than the commonly accepted good methods (because the commonly accepted good methods often have many rather good substitutions).

So it is better to imitate good researchers, where you can find many unique behaviors. Good methods often hide behind those behaviors. For example, I wondered why Einstein researched as an amateur. I also discovered that there are few professional researchers among the greatest researchers. Many greatest researchers, like Maxwell and Einstein, ought to be called "young free researchers" (although they became professional researchers after success). They had both time and ability to research, but did not work for others' priority order. They had no task and schedule for their research. This is the kernel advantage for amateur scientist. A professional scientist cannot research freely when he is young, and his time is not enough when he is famous.

Soceity ought to pay attention to "young free researchers". From ancient Greece to modern society, they made a large contribution to knowledge progress with nearly zero social investment.

The method provides an easy method for beginners to judge advantage of methods from researcher's ability. Normally, researchers who cannot obviously surpass the threshold ability do not have any original good methods to learn, so teachers and parents cannot teach you how to be good researchers. A beginner cannot treat persons with higher ability or more knowledge as teachers. He can easily increase the marginal efficiency by choosing teachers properly.

This method can also make mistakes, but it is easy to operate. It removes very bad methods, increases the average advantage of candidate methods significantly. Researcher with low ability can have some good methods, but he cannot distinguish them from bad methods. Since a child cannot distinguish, it is better to find a researcher with high ability, even if it is impossible to learn face-to-face.

Some good teachers can teach methods without many personal opinions. If so, students can learn to judge advantage of various methods. They will spend more time on research methods. This is also a considerable method.

I thought about this method from twelve and lasted nearly ten years, and became my starting point to oppose many mainstream thoughts. The kernel problem is: if what they taught are correct methods for success, why they did not succeed? Those methods are fairly simple and everyone can do. There have been too many children following their methods but few succeeded. On the other hand, Einstein followed an original way and had a great success. I cannot believe it is accidental. I found many advantages from Einstein's methods, especially on early start, importance of imagination, choose learning, studying masterpiece, studying philosophy, etc. Then I began to study mechanism for these advantages, which are the above principles.

Of course, beginner should learn to judge the advantage of methods, or even create original research methods to gradually improve research methodology.

Following imitation method is safer than creating new methods. Knowledge progress is basically decided by methods and efforts. Researcher often doubts his methods when his ability is below the threshold value. At least, imitation ensures that one can succeed if his total efforts are enough. But pay attention to competition. If competition is too strong, the necessary total efforts will be very large.

Following imitation method, researcher can check whether your progress can keep in step with great researchers. Running behind a great researcher will help you to discover your problems. I decided to imitate Einstein at twelve, and compared my progress with him in every important stage, like proposing important problem, studying philosophy, establishing important theory, etc.

Living good researchers are scarce, so masterpiece is an important way to exchange opinions with them. The benefit from reading masterpiece increases with both the author's ability and the reader's ability. It is similar to investment that could bring you long return, and the return even increases progressively. In every pursuit system, it is important to establish several local structures that could generate high return in a long time. For beginners, reading masterpieces is a main source for such structures.

Textbooks can explain a theory much clearly because they often remove important knowledge structure, like problems that authors explained wrong or cannot explain clearly. Such problems might be valuable, especially when they are still not resolved.

Researcher's works will provide reader a chance to stimulate actual research. Masterpiece is difficult to read because it is written from the viewpoint of researcher, not teacher or student. Textbooks often use later knowledge to explain, so readers cannot experience the author's research situation.

It also helps you to measure the ability difference between you and the author. Sometimes such measurement is important to judge whether effort is enough, approximately how long will be needed to catch up with them. Einstein started research at 16. So when I had not proposed an important problem at 17, I worked hard at asking problem, and had my problem at 18. Einstein solved his problems at 26, I worked hard to follow him and established the basic theory of "science of pursuit" at 26. If you are not far nehind a great researcher, you cannot be a bad researcher.

In a pursuit system, if pursuers experience all possible states, the system will realize the expected pursued quantity safely: with zero risk. So it is important to try all possibilities, not to discriminate unrealized states. Normally, it means to try all possible states around current states.

This method encourages researcher to try new states. When good states are discovered, they ought to be remained; when bad states are discovered, they ought to be abandoned. This anti-symmetrical treatment ensures that knowledge progress is always positive. This is similar to particle's acceleration and deceleration in field. In most situations, "good" and "bad" is not absolute. Researcher changes the portion of each state, similar to quantum transition. I had a long time adjusting the portions on physics, philosophy, economy, and science of research.

Correct theory is statistical result of thousands of tries. Researcher experiencing more possible theories will have the statistical result of expected knowledge. Fate will be less important for such researchers.

Sometimes, it is important for researcher to experience various living states. This helps to increase inspirations. When research efficiency is low, it is often helpful to change living state until a good research state emerges. Normally, a living state cannot always be the best research state. Marginal utility for a state deceases with usage. Traveling is a good way because it always provides new states.

Different researchers have different roads. Without enough experiences, one cannot discover his best road, or best combination of roads. Many researchers learn a lot of knowledge before research; but a few need not. Many researchers have the same effort every year; but some have a large undulation. Many researchers have good inspirations when discussing; but some have good inspirations when thinking alone. If one finds his best road too late, the cost is too expensive.

It is also a good attitude to life. Our lifetime is finite, but we can try as many possible life styles as possible.

In a perfect pursuit system, a pursuer always remembers methodology, but does not remember his pursuit history. He makes judgment just from his current state. In the universe, identical particles have the same reaction in the same field, no matter how different their histories are. In society, personal experience is an important factor to influence his pursuit methods. For perfect human beings, memory is unnecessary.

For a researcher, it is an important and difficult work to clean memory after failures, similar to clean cache and restart computer. Memory of old research process will reduce the independence of new research works. There is no easy way to clean all bad ideas. A whole new living state is one of the ways.

A good researcher often uses short time, like five to ten minutes, to have a try. If he cannot think out anything valuable in five minutes, it is unlikely to have a valuable idea in the next five minutes because he has lost "free mind" and need some time to clean the cache. Marginal efficiency for searching ideas deceases with continuous searching time. If one has five to ten tries daily, it is better than searching four hours continuously.

Because of memory ability, a researcher cannot avoid the repetition of bad thoughts. But he should try to reduce the repetition to increase the effective efforts. The method is to increase imagination ability and to clean cache.

But if a researcher has valuable thoughts, he need to work continuously. The cache will be valuable for his research. When research goes on well, it is better to stay at the state until marginal efficiency is low enough.

Brilliant research achievement is always established on one or more basic concepts, or concept groups, where researcher's knowledge and ability is much larger than others'. They are the local structures that could generate high return in the final stage of research. New problems or theories are continuously proposed from these concepts and concept groups. As my understanding about pursuit increases, pursuit becomes one of my specialized concept groups.

Maybe a good researcher has strong ability in many research areas, but he should stay in his specialized concepts. This is similar to "law of comparative cost" in economics. In economy, even a country has high productivity on every products, it is better not to produce all. At least, a researcher ought to find several topics with comparative advantage. For a good researcher, he increases his research areas at first, so that he will not miss a topic with comparative advantage; then he should shrink his research areas to have the highest research efficiency.

At these specialized concepts, originality is much more simplified, similar to production lines. For example, when I revised my understanding in a pursuit system, I automatically check my understanding in other pursuit systems.

Specialized concepts also enhance the truthfulness of research results. Researchers will check them hundreds of times. So their reliability is much higher. If a research project fails, normally researcher need not revise these specialized concepts.

Some of these specialized concepts will become researcher's belief, like relativity (observer invariance) for Einstein. Belief comes from many times of applications and correct results. Beliefs also need revise, including correction and precision, but are much more difficult. Beliefs gained from free research will be harder to change than those gained from learning.

In order to reduce competition, some researchers pursue weird theory. They often start with a hypothesis, which no one knows whether it is true or not. This is not very bad because it really reduces competition.

But a great theoretical researcher often starts with a priori truth, which cannot be wrong. Applied sciences do not have such start. I once worked on superconductivity, but when I found that I couldn't have a reliable start, I gave up. Einstein and I pursued a priori truth, truthfulness of which is unnecessary to be tested. So Einstein could express his doubt about experimental results.

Some philosophy research often helps to find a reliable start. Project with a dangerous start is high-risk. It will greatly reduce the research desire. It is never a waste of effort to spend more efforts on foundation.

With the fast progress in mathematics and the help of computer, mathematics is not a key problem for the basic theory about the world, which must be simple. So contradiction between basic logic and our sensation is the key problem. People repeatedly found that truth contradicts with their experience to follow some simple logic. So the ability with the largest priority(marginal importance) is to have stronger ability on logic and reduce the influence from sensation(experience). The ability is important because it is scarce. It is possible that some other abilities are scarce in the future, then the most important ability will change.

Human beings pursue happiness, not knowledge, so they are imperfect researchers who cannot research forever.

Pursuer not only distributes current efforts, but also distributes present effort and future effort. Correct distribution will reduce happiness cost and increase the desire to research.

Many good researchers cannot escape from various sufferings. They sometimes need to have larger expectations from future happiness to ease present pain. This is similar to investment: reduce present happiness to increase a larger future happiness. Social system ought to reduce the suffering and help to realize reasonable expectations.

On the other hand, researchers sometimes need to have some happiness in advance to ease present pain. Normally, a given happiness increases with difficulty. In universe, acceleration is stronger when potential difference increases. This is similar to deficit: reduce future happiness to have larger present happiness. Sometimes, researcher's happiness is too low, then deficit will be an important method, similar to a company with high loss lends more debt, waiting for the recovery of market, finishing of a project, etc.

Life is a system. If researcher can sacrifice local happiness freely, he will have much more possible pursuit roads.

Another important judgment for research is whether effort is enough, similar to whether investment is enough in economy. Starting research early is similar to that investor himself have enough money to finish the investment, this is certainly safer than lending efforts from others.

An ideal purpose will be a continuously growing pursued quantity, similar to the mathematical expression of negative action.

Pursuer aiming at a future state is harmful. It is similar to giving pursued quantity at a special state with high weight, and discriminating others. Researcher often makes such mistakes because their lifetime is rather short. It will be less harmful to pursue step by step, each step is a short-term pursuit between two stable states. Since careful academic researchers welcome such research topics, competition is often strong.

Step-by-step research also discriminates many possibilities. A knowledge revolution is often a long-term purpose that cannot be resolved into a series of short-term evolution. A great researcher often has a long research process to reach another stable state. When researcher cannot see any realistic short-term goal, the topic often has weak competition.

Besides the priority order, there is another method deciding the order to handle problems.

As we know, when two problems are unrelated, they should be treated as their priority order. But when they are in series: solving problem A will significantly influence the solution of B, but solving B will not influence A much, then always solving A first.

This will reduce efforts. Even a great researcher cannot be so rational forever. There are various reasons. For example, before I explained physics in science of pursuit, although I believed the universe is a perfect pursuit system, I spent a lot of time to discover perfect methods in economy and research, just because it was a simpler work and I needed some progress to ease my pressure from stagnate.

In most situations, the relation is a mix of series and parallel: solving problem A is "possible" to help solving B easily; or solving A helps to solve B little. It will also influence the distribution of efforts a little.

Great researchers can invent various good methods themselves. So I just give the most common methods.

Close research system

A close research system refers to a researcher with the ability to fulfil a complete research process. A great researcher is an all-round researcher.

In order to establish a close research system, a great researcher spends more time to "discuss" with himself: questioning, trying a solution, criticizing, trying another solution. A possible solution is also called hypothesis.

Utility of self-research monotonously increases with efforts. Large project with long research process gets more benefit from the method, while small project gets more benefit from opinion exchange.

For a researcher whose ability is far above the threshold ability, it will be much better to exchange opinions in his mind only, unless there are other researchers with very high ability or with very good ideas. Opinion exchange in a brain is at least ten times faster than that between brains, so working efficiency is much larger. In discussion, a large part of time is spent to make others understand your opinion.

Good researchers often have an original priority order. Exchanging opinions with others will hurt the order.

When I was a child, I wondered why great researchers could not make important discoveries when they became famous? Apart from less effort, an important reason is the change of priority order. After success, most of their time was spent on answering problems from others. This changed their effort distribution and gradually changed their priority order.

From my experiences, shortly isolated from society, like staying in a little house for some weeks, is a good method to make a sprint. When a researcher facing an important and difficult problem, this is often helpful.

Pursuing perfection

Many researchers pursue perfection, some succeeded, some not. The result is decided by whether they have enough ability and effort.

Firstly, researcher must understand that pursuing perfection normally needs more effort (longer evolution process to reach a stable state). So, even if his ability is high, he must have effort reserve before increasing his goal. If a fifty years old good researcher suddenly pursues perfection, that is suicide. Normally, I spent no more than 50% of my efforts on daily research. On difficult situations (normally at the beginning ) or very good research states (normally at the final stage), the ratio was close to 100%. Because I had enough time left and enough effort surplus in daily research, I can gradually increase my goal and always pursue a better theory. Secondly, it provides stronger research desire, especially for researcher in good living conditions. A good researcher loses many research desires after success, like fame, money, etc. He needs a pure research desire, like perfection pursuit. Thirdly, severe criticism is a good method for perfection pursuit. It helps to generate more problems and will lead to better theories after spending more efforts. Fourthly, desire for perfection often squeezes out desire for normal happiness, so researcher will be more similar to a pure researcher. This will greatly reduces the competition from normal desires.

A researcher pursues two pursued quantities: happiness expansion and knowledge progress. When methodology is the same, its pursuit efficiency will be lower than unique-purpose system.

Even if researcher follows correct methods, he needs effort. Researcher following bad methods needs more effort. So, a researcher with bad methodology and strong research desire can succeed; a researcher with perfect methodology and small research desire can fail.

In this part, I mainly explain how to pursue one quantity without hurting the other too much, how to unify the two purposes the best.

For given desires, methodology and effort are the keys for knowledge progress. Stronger research desire will increase effort in unit time, but it does not change advantage of methodology.

For a researcher, there is interaction between other desires and research desire. He ought to learn the main happiness and pain for a researcher.

The main happiness for a current researcher includes: happiness from learning and researching, high rewards (money +fame), medium risk (mainly from competition), long reward time (money and the memory of success), slow decrease of ability, less contact with the imperfect society.

The main pains for a current researcher includes: long investment time, research is dull before making discovery.

From my experiences, pains from unit effort grow with total efforts; happiness from unit effort decreases with total effort, until researcher makes an important discovery. The reason might be that researcher is often more and more impatient. So beginners and great researchers are the happiest.

Principle:

For a researcher, research desire is always scarce. Stronger research desire will increase both efforts and ability. Difficulty is the main factor for stop researching.

A researcher with stronger research desire will be more similar to a pure researcher. Most of our desires want to pursue happiness, just a small portion wants to research.

I do not use time to measure efforts, because many efforts in research time might be unrelated with research. Effort is similar to the "effective research time".

Compared with pure researcher, research desire is always scarce for human beings. So any researcher can give up researching when competitive desire is strong enough.

Stop researching is the main problems for researcher. Our lifetime is much longer than the time needed to surpass the threshold ability. Lifetime mainly influences the expected happiness after success, so influences research desire indirectly.

Stronger research desire increases effort and probability of success, but also increases pains if research fails to succeed.

It is difficult to have a strong research desire suddenly, so research desire is a continuous quantity. Strong research desire is mainly a reserve for difficulties. Without the reserve, researcher will give up research easily.

Stronger research desire also increases ability a little. If researcher's ability is well above the threshold ability, the increase will lead to many discoveries.

Sometimes when various desires reach maximum together, research desire will be the strongest. So a great researcher normally makes most discoveries in a small time period. But they are not the decisive moments for researcher's success, the moments with the largest difficulties are.

The same difficulty has different influences to researchers with different ability. For example, Beethoven could go on working after he lost his hearing, but if he lost hearing ten years' earlier, he would face a tougher situation.

Desire distribution influences research in another way. Because human beings are not pure researcher, other desires will compete with the desire to research. A researcher with strong research desire can insist on researching in difficulties, while others will change their mind. Both are correct choices. If one does not have enough research desire, he'd better not to be a good researcher. I do not support to change desires intentionally, although it is an important method in some difficult situations. For example, after many years of hard research, one can consider the necessity when he needs more research desire to overcome difficulties.

Total desire=research desire +reciprocal desire +competitive desire

For two desires, they are called "reciprocal" when they mutually strengthen each other. In order to overcome difficulties, researcher ought to use more reciprocal desire, like winning award, fame, etc, to support research desire. For two desires, they are called "competitive" when they mutually weaken each other. For example, if a person has two desires: wants to be a merchant and a physicist, he will face a much larger difficulty. Researcher ought to reduce competitive desires.

Reciprocal desire is similar to attractive potential energy; competitive desire is similar to competitive potential energy. Pursuing happiness is not always harmful to research. Pursuing happiness for the reciprocal desire will help research.

Research desire includes both happiness and pains. "Interested in research" just means having happiness in a normal situation. When pain from research is enough strong, research cannot go on, unless there is strong support from reciprocal desire.

As I pointed in "Relation between advantage and purpose", advantage is different for different purposes. Different researchers have different mathematical expressions for the pursued knowledge progress. All researchers do not pursue knowledge progress only. Equation (1) is just a theoretical expression. The error will be very large when the knowledge progress is very large or when effort is very large, because most researchers will slow the pace after making important discoveries, and all researchers can not go on researching when they are old.

The following principles will help researchers to adapt the conditions better.

Principle:

Ability decreases with fatigue monotonously. The velocity is different in different environment and for different research works.

Since ability increase is proportional to the product of ability and effort, when ability decreases faster than effort increases, marginal ability increase will be negative. So there is a best diligence, after which more diligence will be a wrong choice. It is important to reduce researching in bad environment. I recommend using these "bad time" to satisfy those human desires, like eating, exercising, making friends, etc. Another choice is to do works with small fatigue velocity, like reading, learning, etc.

Different research works have different fatigue velocity. If research is full imagination and judgment for reliability, ability drops very fast. Researching two or three hours will be enough. For a pure deductive research, working time can be very long. So deduction ability can increase fairly fast, but imagination and judgment ability is hard to increase.

Principle:

Research ability increases with research desire.

Ability is also function of desire. If research is not the strongest desire, ability cannot be fully applied. Sometimes, in order to solve a difficult important problem, researcher can manage to reach his best state (full of energy and desire, in good environment) at a planned time. It is better not to suppress human desires too much, because that will lead to stronger desire and disturb research.

Principle:

Total desire=realized desire +expected desire

This is universally valid in all pursuit systems.

Realized desire is similar to particle's energy; expected desire is similar to energy of field. When expected desire equals to the statistical increase of realized desire, the expectation is called "practical", or the expectation is cheating.

Overestimated expectation on knowledge progress is similar to speculation, although it can help in some situations, it is wrong statistically. In the universe, when a particle used out of its kinetic energy, it stops, although it is possible that moving another meter will reach a very good state. So, current progress speed is the only judgment for expectation. Acceleration can be considered only when it is result of methodology improvement.

Principle:

Researcher's ability normally reaches the maximum at the middle age. When other conditions are the same, ability monotonously increases with time before the turning point; ability monotonously decreases with time after the turning point.

Research ability is the most precious for human beings. Wealthy and power can do little help for a person to have high ability. The process for a person to establish a close research system is just similar to the evolution of the universe. So a great researcher can be compared with the creator of the universe. This is a great joy.

Principle:

Utility of a research behavior changes with the research purpose. Happiness cost is invariant. Normally, judgment standard is (utility-cost)/cost, called "profit ratio", similar to profit ratio in economy.

Normally, (utility-cost) is function of priority, and increases monotonously with priority. When a problem is easy to solve, happiness cost is low; when it is important, utility is large.

Since researchers are imperfect, they cannot pursue infinite long knowledge progress, like the negative action pursuit in the universe. So there are both long term and short-term purposes. Everybody wants to be great researcher, but the cost is high and many cannot afford that. So many would like to choose a simpler topic.

If a researcher wants to be a great researcher, establishing a close research system will be very important, almost a necessary condition. But if he just wants to be a normal researcher, there many easier ways (utility decreases, so profit ratio is not the largest). Utility is also variable of research area. Mathematics has different importance for physicists and sociologists.

In a given research area, some behaviors have large profit ratio for various purposes. For those who are not sure about their goals, they ought to do such behaviors first, like knowledge learning, but need not to learn many problems.

But most behaviors do not have the same importance for various purposes. In a given research area, behaviors with large profit ratio for ambitious goals but with small profit ratio for easier goals are called high-level behaviors; behaviors with large profit ratio for easier goals but with small profit ratio for ambitious goals are called low-level behaviors.

Normally, high-level behaviors include starting research early, establishing a close research system, starting with reliable proposition, pursuing perfection, etc. There are much more low-level behaviors than high-level behaviors.

If one has decided to be a great researcher, his behaviors will not be similar to normal researchers. Sometimes, a normal researcher increases his ambition, then he ought to adjust his behaviors: to abandon those low-level behaviors and accept some high-level behaviors.

On the other hand, there are also high-level problems, and low-level problems. Normally, researcher's interest for high-level problems increases with ability, and his interest for low-level problems decreases with ability.

Principle:

When other conditions are identical, pain from unit effort monotonously increases with effort in unit time.

So a researcher always tries to avoid diligence, while society always hopes researcher to be more diligent.

The threshold ability is function of methodology and total efforts. When methodology is the same, the threshold ability will be completely decided by threshold efforts. Then, researchers with the largest total efforts and some genius will be the greatest researchers. Since the winner takes all, efforts above the threshold effort will have large marginal utility, while efforts under the threshold effort has zero marginal utility. Researchers will play game with each other. This is a bad situation. But I think it will not happen in the near future, because there is enough room to improve methodology.

For a good researcher, marginal utility of his efforts is very large, but marginal happiness increases slowly. So society hopes good researchers to work harder, but they won't.

Conversion between desires:

Researcher usually gets a lot of research desire from the happiness and pains in life. Pains are more important because realized happiness (not from research) is usually a competitive desire, while escaping from pains is a reciprocal desire. For young researchers, losing love is a common source of research desire.

A self-confident researcher will not mind short-term undulation. So expected knowledge will be turned into realized progress. But there are both advantage and shortcoming for self-confidence. If a researcher is confident of a bad methodology, it will lead to expected depression. Self-confidence might be important for a beginner too. A beginner normally has no strong belief, and self-confidence can increase his research desire. So self-confidence is very useful for good researchers and beginners, but is a little dangerous for researchers with ability between them.

Although I benefited from the method, I doubt whether a researcher should use such an irrational method. Depending on willpower too much will reduce interest, which is the basic desire for research. Self-confidence ought to be rational, established on scientific foundation.

Depression is a common state for researchers, while prosperity is seldom. Researcher must have strong nerves to endure stagnant, or his research behaviors will be worse and cannot walk out of stagnant.

Self-confidence also changes researcher's consumption. He tends to increase consumption and reduce savings.