Part 1: Research is a Pursuit System--17 Principles
In research, knowledge progress is pursued to be the fastest. So a perfect research system can also imitate universe, just like society. Research methodology for some great researchers is fairly good. In the following, I shall establish mapping between the universe and a research system.
In research, facts and theories are generally called "pursuers", similar to protons and electrons in universe.
In research, knowledge is the pursued quantity, similar to negative action in universe.
There is mutual contradiction between theories, similar to repulsion between like charges. When a fact verifies a theory, it is also explained by the theory, this mutual explanation-verification relation is similar to mutual attraction in universe. When a theory explains better or when a fact proves a theory more, it corresponds to larger negative potential energy in universe.
In research, every fact and theory pursues more explanation-verification relation and less contradiction relation. In the universe, particles are attracted to places with low potential energy. A fact or theory is always accelerated to states with more knowledge. Researching in the opposite way, accelerating toward bad states, cannot succeed. In science of pursuit, this is an experimental proof for the advantage of basic natural laws. In research, a serious contradiction influences research stronger; similarly in the universe, acceleration is proportional to field strength.
In research, importance of a theory or fact is similar to particle's momentum-energy in the universe.
In research, each fact is explained by many theories together, and each theory participates to explain many facts. Similarly in universe, a charge interacts with all the other charges.
In research, a theory or fact outputs its possible influences to all the other pursuers. In universe, particles output field.
When there are many possible solutions for a problem, a researcher thinks the one with the largest probability to succeed first. Thinking from the largest expected knowledge to the smallest expected knowledge is similar to field propagating from the nearest to the furthest in universe, and similar to searching possible contracts from large expected profit to small expected profit in economy.
In the universe, there is gravity between mass. Similarly, there is attraction between knowledge in a research system. A theory with larger truthfulness tends to be used more. For example, theories like mechanics and geometry are used in many sciences. So, there are subjects and subject groups in research, similar to that there are stars and galaxies in universe, and similar to that there are many cities and city groups in economy.
A mature theory, stable relation between pursuers, is similar to atoms in universe.
An unexplained fact or unproved theory is similar to a free charge. Stable explanation-verification relation is similar to an atom. Sometimes, in order to solve a contradiction or explain a fact well, some stable knowledge can be partially or totally sacrificed. Similarly in the universe, an atom can be excited and lose electron(s).
Contradiction in research is different from contradiction in a mature theory. In research, contradictions help knowledge progress, similar to that photons help the universe to expand. Research system makes progress by solving contradictions, similar to that universe expands by absorbing photons.
If you have understood freedom in universe and economy from other articles at this site, you will understand why research freedom is also a good method.
1 Knowledge Judgment
Principle 1:
There is more knowledge when explanation-verification relation is stronger and when contradiction is weaker.
This principle is about the measurement of knowledge. Similarly in the universe, Lagrangian will be larger when attractive potential energy is larger and competitive potential energy is smaller.
When there are several competing theories with similar expected knowledge, it is very possible that no one is true. The correct theory might be a combination of them; or there is an undiscovered theory with much larger expected knowledge. Similarly in the universe, no charge will be the absolute winner of competition.
The main reason for knowledge progress is that there is mutual explanation-verification relation and mutual contradiction relation between pursuers, and that pursuers choose states toward places with more knowledge. This is also the reason for universe expansion. Having correct judgment for knowledge and expected knowledge is the premise for correct reaction. The judgment is invariant with some transition, similar to gauge invariance in the universe. There is no absolute correct value for judgment. Relative judgment decides pursuit behaviors.
Principle 2:
Expected knowledge for a problem or idea is product of probability for its realization and knowledge from realization. For the same discovery, its expected knowledge is about 1/n of its original value when there are n researchers with identical ability.
This principle is about the measurement of expected knowledge in current society, an imperfect pursuit system.
Normally, a researcher should not expect that he could defeat all competitors, the result is just 1/n. If he really has high ability, it is better to use his ability in an original area, not to defeat other researchers by several weeks. There are many cold topics even in very hot subjects. Strong competition greatly reduces research efficiency, although it is still much higher than other social behaviors. Human beings should change their habits of just honoring the first discoverer, especially when competition is too strong.
An important discovery often has small probability and large expected knowledge. If expected knowledge is large, even if it is very unlikely to be true, it can be more important than knowledge with high reliability. So knowledge with high reliability can be sacrificed for knowledge impossible to be true, when the latter has larger expected knowledge. If researcher discovered such an expected knowledge, he ought to be happy because a researcher is always searching miracles.
If many researchers compete for the same discovery, importance of the discovery decreases sharply. Original research road has much larger expected knowledge progress.
Keep away from high ability researchers. This is researcher's basic skill, and ought to be instinct of ambitious researchers. There are enough many undiscovered truths. If a researcher cannot find a low competition topic, he ought to increase his imagination, not to be more competitive.
Theorem:
Researcher ought to reduce competition.
When other conditions are the same, original research road increases the probability to succeed.
The decisive judgment for pursuit is velocity. In research, velocity is more important because of the overlapping between researchers' works. If some of other researchers' efforts can be trusted, keep away from their works, unless you cannot find an original topic for yourself.
For a researcher researching and learning simultaneously, his startup ability is well under the threshold ability. So it is not important how much knowledge progress he makes. Even if he had, like myself in university, the results would not be correct. All efforts ought to aim at increasing ability and form a close research system. Independence, even solitude, will be researcher's good character if the system can self-expand. A close system will monopoly a research area. Great researchers are usually those with no competitor in his specialty, they also take on a much larger risk.
There are two kinds of risks. One is researcher's expected risk; the other is real risk. Since researchers are not perfect, expected risk is not the same as real risk. Great researcher's expected risk is more close to real risk because his knowledge structure is better. Beginners cannot believe his judgment, especially in difficulty. Judgment must be tested thousands of times before reliable. For example, whether research is a rational pursuit took me a lot of time from middle school.
There is attraction between researchers' expected risk: a researcher tends to accept most researchers' expected risk.
For knowledge progress, meaningful new concepts and facts are the most important and scarce resources. Most of our knowledge progress came from a few outstanding researchers. Other researchers make use of their discoveries by fully digesting them. Some good researchers generating problems through induction, comparison, just like generating problems through nuclear reaction. Some solve these problems, just like charges absorbing kinetic energy through electromagnetic interaction.
Principle 3:
The way society evaluates knowledge and expected knowledge will directly influence the distribution of researchers' efforts.
"Ultimate truth" is the most important knowledge. Its value increases exponentially with time. Even knowledge with close relation with ultimate truth has much larger value than people thought.
Application sciences have larger value at the start, but it cannot grow forever because of competitions from new technologies. Its growth speed is normally smaller than ultimate truth.
For example, 2000 years ago, worth of Euclidean geometry was at most $100,000 dollars per year. Now, its worth is at least $1000,000,000 dollars per year, about 1 dollar per year for every educated adult. If ultimate truth can be viewed as a public company, then its share price will be infinite because its interest rate increases exponentially to infinite future.
How much work was needed for such a large value? Euclid at most worked 30000 hours for the discovery. A typical Greece at that time earned no more than 1 cent per hour. So Euclid had a much larger productivity. Theoretical research is the best behavior for a person in a developing country, because he has the same environment and the same reward as researchers in developed countries. If technical condition is bad, then it is offset by that there are fewer competitive desires.
Now many companies with thousands of employees and millions of dollars cannot have the same productivity as an ancient person thinking and writing in his small house.
After another two thousand years, if the growth speed is invariant, Euclidean geometry will worth $10,000,000,000,000 per year, close to the current total GDP in the world. So Euclid will contribute more happiness to human beings than the total contribution from all business persons, but not all researchers. The main reason is that material wealth cannot last forever. Other reasons include the growing population and growing desire for knowledge.
But no great researcher was well supported in history, and no researcher has ever been the richest person, just because the discovered truth is the cheapest commodity (nearly free).
In economy, a person wants to earn money, not bad debt. People never sent the same quantity of happiness to great researchers as great researchers sent to them. In economy, the happiness deficit is called "debt". People want to pay all the debt by "fame", but its marginal utility is small for good researchers.
Pursuing largest knowledge progress is the only purpose for an ideal researcher, but it is impossible. Other desires of human beings will influence research inevitably. For total happiness in society, a good researcher doubling his happiness is far below increasing 0.01% research progress. So society ought to provide more mechanism to stimulate the desire to research: to provide happiness difference for researchers, similar to field difference in the universe. If pursuers have much better methodology, large research desire and good research environment, I believe knowledge progress will be largely accelerated in the new millennium.
Present research system is similar to an insurance system, most researchers share good reputation and high salary with some good researchers. This really reduces researchers' worry about risk, but it leans toward researchers in good environment.
With the development of digital technology, the cost to store and to teach knowledge decreases sharply. This makes productivity of research even higher. After researcher makes a discovery, or even establishing a digital tutorial, nothing is necessary. Research process is the only cost.
Knowledge progress normally simplifies theory about the same facts, so human beings need less effort to study the same knowledge. A more complicated theory must explain more facts.
Since future desires are the main beneficiary of present research, deficit is a useful and reasonable tool to fund research.
Sometimes, wrong research results are harmful for human beings, but it is not the reason to stop research. On the contrary, human beings have strong desires for truth because of the serious harm from various fallacies.
From science of pursuit, we can learn some more properties about knowledge.
In a pursuit system, pursuer's state is described relative to other pursuers. When a fact changes its explanation, it is better to say there is relative change between the fact and the other facts and theories. Every fact and every theory can be treated as invariant no matter how large its relative change is. It is similar to relative motion in physics. An interesting problem is:
Is it possible to create a new language invariant with this relativity?
In all present languages, reference system is defined in the language. For, example, "a researcher changes his subject" uses the definition "a subject is defined to be static", similar to "a star is appointed to be static".
Sensations are basis of our description for natural laws. Formalization helps to describe abstractly, but is there a way to express truth with sensation-invariance?
"Just do it" might be the only way. If so, all intelligent living things observing a perfect pursuit system can understand its laws, no matter how weird their sensations and languages are. Invariant methods behind behaviors are the only things could be understood by all sensations with enough intelligence. By imitating universe, most intelligent living things in the universe will be perfect and will not oppress human beings. Maybe all perfect living things in the universe have already established a unified society by imitating universe, and the only way for human beings to enter the society is to perfect our society.
In a close pursuit system, a pursuer's pursued quantity totally comes from exchange with other pursuers. So, knowledge exists in the relation between facts and theories. Without other facts and theories, a fact or theory contains no knowledge. In the universe, this means mass of a particle comes from interaction with all the other particles.
In a pursuit system, the pursued quantity exists in whole pursuit process. In research, knowledge exists in whole knowledge pursuit process, not just contained in the final mature theory. A mature theory just means some static relation between pursuers. Its stability represents how well a local structure of pursuers is.
From above, mechanism for research is also the nature for intelligence. If a perfect pursuit system could be artificially established, then perfect intelligence can also be artificially realized. The converse proposition is also true.
A unified market to exchange opinions freely and a unified knowledge judgment will greatly accelerate knowledge progress. They are two long-term tasks for society.
In science of research, the emphasis is personal research methods. Because idea exchange between researchers is very weak compared with that inside a researcher. But it is also necessary to improve whole research system: making exchange between researchers stronger. It is necessary to establish a system in which knowledge can be exchanged in a common market freely. I think it is unnecessary to explain why self-sustained economy is worse than free market economy. So exchange between researchers will increase. If exchange between researchers is strong enough, all researchers will form a unified research system.
In present research system, a researcher usually thinks independently and cannot exchange opinions with others well. When methodology is the same, a larger research system is always better than many isolated research systems. Science has developed to a level at which a scientist has become more and more specialized, so exchange is more and more important for research.
Another important task is to establish a commonly accepted pursued quantity in research, just like action invariance in universe or "money invariance" in economy. Then in perfect research system, a new theory will be result of many researchers' working, similar to that many workers participate in producing a product in present economy. Contribution of each researcher is clearly marked.
Maybe establishing research currency is a good method. A researcher can be both producers and consumers. Ideas are exchanged in a common market. Each idea marked with a pursued quantity, similar to price.
2 Macroscopic Properties of Knowledge Progress
Principle 4:
Possible states with the same expected knowledge ought to be treated equally, but realized progress will have large difference.
This is a common property for pursuit systems with the universe-like mathematical expression.
Expected knowledge is called "short-term potential for knowledge progress". In universe, expected energy of electromagnetic field is the short-term source for particles' energy increase. Similarly in research, problems are the sources for expected knowledge progress.
In research, some problems can remain the same very long without any influence to knowledge progress; some have much higher influence to knowledge progress than expected. It is permitted because expected progress is just statistical. Researchers often have strong impression on the undulation of realized progress, but overlooked the stability of statistical results.
Realized progress can be much more larger or smaller than the expected progress. Similarly in universe, a photon can propagate in universe for a long time without interacting with particle, sometimes it participates interaction just after generated.
Effort to predict which expected progress will be realized better can be called "speculation". It will increase researcher's risk. It is unnecessary to regret missing a big realized progress or to celebrate seizing a chance. Expected progress is the only judgment standard before progress is realized. In a long time, realized progress will be just equal to the expected progress. For researcher with high ability, lifetime is enough long to have a correct statistical result. But for researcher with low ability, lifetime is not long enough to have the correct statistical result, so fate is more important for them. For many researchers with low ability, their total realized progress equals to the statistical result.
If time is shorter, more researchers should be included to make realized progress equal to the expected progress. For example, present knowledge progress for human beings equals to expected knowledge progress for all researchers.
So if ability can be enough high, success will be a nearly 100% result. If 10,000 hours' high quality research is enough, the ability is not hard to get. An excellent researcher can succeed at teenage!
Since a researcher is just a small pursuit system, he is more likely to be influenced by statistical fluctuation. He ought to shift his attention from realized progress to expected progress.
For children, zero point of researchers, they have different ability, but they have the same expected progress: zero. So competition, from proposing problems to solving problems, is rather fair for all researchers.
In society, people realized the importance for equality among all persons. Why researchers keep on discriminating original theories? In the universe, particles far away from others are never discriminated. Probability for an original theory to become truth is small. But if it becomes a mature theory, it develops knowledge much more than an "orthodox" theory. "Expected knowledge progress"(knowledge progress when it is true multiplied by possibility to be true) is the standard to value a research task. This is a typical mistake of judging by probability of results.
Every dominating theory came from evolution, and had been a bad theory once. A bad theory should not be discriminated. Give a bad theory some time and let it evolve with the system, it will be quite different from its original form. Researchers often underestimate potential of development. A bad explanation is often better than no explanation, because the wrong part can be gradually substituted, but a good theory cannot jump out. In the universe, a particle's mass increases gradually, but a new particle is hard to create.
Principle 5:
Researcher ought to pay attention to medium term progress and long-term progress to ensure the stability of knowledge progress. In a research area, when new problems lead to knowledge progress, and the knowledge progress lead to more problems, it is called "chain reaction".
In order to increase short-term expected progress, the only way is to generate new problems. The ability to generate new problems is called "medium term expected progress". If short-term expected progress is not enough, medium term expected progress can not be high. Similarly in universe, there is threshold temperature and threshold mass for nuclear reaction. In order to propose many original problems through analogy, researcher must have many problems and many theories in a small research area, similar to the condition for nuclear reaction. So a good researcher ought to be both an expert and a critic at the start.
In order to maintain the knowledge progress speed, it is also necessary to pay attention to long-term progress: independent new concepts and facts. In universe, physicists have not found a mechanism to create new particles (not in pairs). But from Truth Evolutionism, the mechanism must exist. This will prevent the universe from having no independent protons.
Main sources of new concepts are experiment (new facts), induction (generating new principle from facts). Sometimes, new theorems can be generalized to become new principles (a combination of deduction and induction).
Principle 6:
With fixed methodology, a self-researcher's ability increases exponentially with effort. The largest benefit from exponential progress is in the future.
If methodology is also improved, progress will be even faster. For exponential progress, many years' growth at the start just need several months after some time. In economy, current growth in one year equals to that in one hundred years hundreds of years ago. So, if cannot keep on researching for a long time, it is better not to research.
A researcher must be patient. From this principle, most pursuit results are created in the final stage. A great researcher often prepares ten years or more for the final brilliant stage, at which great ideas spurt from his mind.
The best things we can learn from great researchers are their research methods, especially on forming a close research system. It is also important to read their thoughts, but mainly limited in the original text. Great researcher often thinks much more complex than trivial researchers, so it is often much more difficult to understand the original text than the textbooks, but they contain much more indistinct feelings, author's ability often ensures that these feelings are valuable.
In order to protect researcher's original knowledge structure from assimilation, it is often better not to exchange opinions well before the formation of an original knowledge structure. Large original research system grows from a tiny original research system. So it is better to protect the originality of your research system from its origin.
Ability difference between personal ability and threshold ability is one of the decisive factors for knowledge progress. Knowledge progress grows exponentially with the difference.
Considering that ability also increases when knowledge makes progress, knowledge progress is accelerated. Similarly, expansion of the universe accelerates--faster than exp(Ht).
If ability is under the threshold value, there is no easy problem with enough importance. But when researcher's ability is a little above the threshold value, there will exist many such problems between the threshold ability and his ability. Then researcher's effort will be highly rewarded, enough to compensate his earlier efforts. If researcher's ability increases with the effort, more and more problems will become easy to solve. Because of insufficient time, researcher even has choice freedom: choose those important problems to solve. At this stage, he will be a great researcher. Of course it is important to prepare many problems in the research area. This is the third form of "point discharge".
Now, most research ability deposits around a very narrow region around the threshold value, it means research is a low temperature region. When temperature is low in whole research system, it means slow short term progress. This is often a difficult time. The difficulty cannot be solved easily. It needs a long system evolution.
Some think that if knowledge progress is slow, it means wrong research methods. This is wrong. If one's ability is under the threshold value, he cannot solve a problem, even if he follows correct methodology. A perfect researcher can have lower ability than an imperfect researcher, but will have higher ability if he goes on research. For an exponentially expanding research system, the largest knowledge progress always exists in the future. One must always remember, knowledge progress is very slow at the start.
It is impossible to solve a problem completely with one idea. In universe, a photon is absorbed by particles after nearly infinite interaction. A larger system need more time to digest a photon completely.
Ability difference mainly has two representations. Firstly, one cannot imagine all important possibilities. Normally, it is important for our brains to imagine all possibilities, but missing an important one will be a high cost (it is still possible, good researchers just do not make such mistakes often.) Secondly, one cannot make the correct judgment from imagination results. Maybe the difference is not very large between good researchers on judgment. But old researcher might make serious mistakes.
In researcher's ability increase is linear, he will surpass x% competitors every year. It means surpassing 90 million at the first year has the same difficulty as surpassing 9 at the last year. When I was in middle school, I thought my ability was among the top 10%. In order to become a top researcher, my plan was to surpass 90% children with the same age every two years. So I can have the top ability in 16 years. The result is a little better than my plan. If a researcher has a stable progress, he will surpass a fixed ratio of competitors in unit time, not a fixed number. So a researcher ought to aim at surpassing a fixed ratio of competitors in unit time.
A researcher's competitors are all over the world. If one lives in a place with bad education, he must remember to surpass competitors in the world, not around him. Relatively good students in bad environment are often too optimistic about their status.
Principle 7:
Faster knowledge progress will increase research desire, so effort will increase and knowledge progress will be even faster.
This is similar to acceleration principle in macroscopic economics: increase of investment will create more investment. In research, knowledge progress increases and decreases faster than desire does.
When other desires are the same, the principle causes undulations in knowledge progress, similar to economy fluctuation, or even crisis when the fluctuation is too large. A typical "research cycle" includes four stages: acceleration, boom, deceleration and depression. A crisis normally refers to research cycle with long period and large amplitude. I had a "research boom" from 1991 to 1995, and then I had "research depression" from 1996 to 2000. I finished my first article at the turning point.
When ability is far above the threshold value, classical physics is a good description. For those around the threshold value, statistical theory (similar to quantum mechanics) is necessary.
When research efficiency is high (knowledge progress is fast), researcher increases effort, so he gets more progress and faster ability progress. After he reaches the best effort, he cannot increase effort any more, research stops acceleration and reaches "boom". Sometimes researcher increases effort from optimistic anticipation of future progress, this increases the danger of a crisis (similar to expansionary fiscal or monetary policy in boom).
Similarly, researcher decreases effort when research efficiency decreases.
Several factors can change research efficiency. Firstly, change of environment, including emotion, will change the best effort. The second important reason is the exhaustion of problems with high priority. Thirdly, research itself will reduce the expected knowledge from problems (gradually resolved). So, deceleration is unavoidable unless enough many new problems are proposed. Fourthly, a problem with super high difficulty (or a series of fairly difficult problems) will slow the research.
Sometimes, ability increase is not stable. Deceleration will lead to a small decrease of ability: researcher cannot understand his earlier thoughts.
Cycling is a general property for all pursuit systems. Normally, researchers need not adjust the amplitude or period. When system is large enough, fluctuation will be small. For example, amplitude of current economy is relatively smaller than crisis in 19th century. This is also the reason for why universe has no expansion crisis.
Low ability researchers have few high priority problems, and face more depression. So interval between difficult problems is short. Crisis is also longer because they need more time to solve a difficult problem. Young researchers are easier to be influenced by environment because research is often not the strongest desire.
So the most difficult time is at the beginning of research. Most researchers failed at this stage. Good research state is researcher's most precious wealth.
Principle 8:
A perfect research system is a close pursuit system.
If research system is not close, when expanding to a large scale, expanding velocity will reduce, because input from outside has an upper limit (cannot always increase as fast as the system at least). This is the fatal disadvantage for learning, for which input quickly drops to zero when ability is above the threshold ability. After enough long time, a good close research system without weakness will surpass researcher with fatal weakness.
If learning is the main source of a researcher's ability, his ability cannot increase well after he reaches the threshold ability. Many researchers' ability stops at the threshold value whole life. So learning is not the most important method for a researcher. Although it provides a fast start-up, researcher cannot become a close research system by learning.
Boom and Crisis
In a research area, effort is not a constant. Total effort can be measured by number of researchers approximately.
Researcher with high ability is more likely to enter research areas with strong competition, similar to particle with high kinetic energy can enter region with strong repulsion. But this is not an important correction for the distribution of effort.
When other researchers propose many important problems but make little knowledge progress, this is the best chance for a normal researcher. Because he need not generate problems by himself, need not establish a close research system. This is a very large advantage. At the start of this century, physicists had such a good opportunity. Several great researchers proposed many important problems. When such an opportunity emerges, a lot of researchers will be attracted and activated (by large research efficiency: larger knowledge progress in unit effort).
After some time, relatively simple problems will be used up and there will be too much ability in the area. Then the chance becomes bad, because threshold ability is very high and the remained problems are very difficult. Researchers will be gradually repelled away because of low research efficiency. After a long time of slow evolution, chance will be good again. The evolution includes accumulation of new concepts and problems, simplification of difficult problems and decrease of threshold ability.
At the turning point, the area reaches the "coldest" time and knowledge progress begins to accelerate. This is the best chance for a great researcher. A researcher need some time to exceed the threshold ability (normally 10 to 20 years from zero ability), so he should start researching a little earlier than the best chance.
At the turning point, although expected risk is high, real risk is low, much lower than risk in hot topics at least. In a hot researcher area, researcher faces strong competition. Although expected risk is low, real risk can be high if competition is strong enough. It will be very difficult to be well above the threshold ability.
In the universe, two particles cannot have the same state. In perfect research, it should also be true. Overlapping of effort reduces efficiency.
Approximately, the threshold ability in a research area is function of number of researchers. Researcher's ability forms a distribution. When number of researchers increases, it is more likely to find researchers with high ability. So researcher will be easier to exceed the threshold ability in areas with fewer researcher and more problems. Rigorously speaking, researchers ought to be weighted by ability; problems ought to be measured by importance.
In a research area, when problems increase and knowledge is the same, it is similar to heating (random kinetic energy increases). It is easier to make knowledge progress in hot research areas. Iit is also easier for chain reaction (if there are enough knowledge and problems, similar to threshold mass and temperature).
For ability well under the threshold ability, they can not be observed in knowledge progress. If one's ability cannot be observed in any research area, it means he does not exist in research when observed by natural observation. This will not happen if he is a perfect researcher.
3 Zero Point and Threshold Ability
Principle 9:
Compared ability difference from method difference and diligence difference, inborn ability difference for researchers can be neglected.
By now, unlike artists, no great researcher is great from their childhood. It means that children cannot have many important research abilities.
If methodology is the same, the start point will be decisive. But current researcher is far from a perfect pursuit system. The exponential difference in velocity will catch up with any start-up difference. Even if there is no advantage difference, diligence (more effort in unit time) will also help to catch up.
The word "genius" represents the ignorance to science of research: do not know the source of ability. From above, even one has some inborn abilities, if he can not establish a close research system, his ability cannot be higher than the threshold value too much.
Ability increases exponentially with effort, so start-up difference has smaller value for high ability researcher, maybe just one hundred hours' effort.
Effort is a better measurement than working time. Effort is the effective working time.
Many argued that some great scientists have special brain structure. If ability can be judged by brain structure, I suppose that brain structure will be influenced by research effort.
Although the inborn ability difference is very small for babies, it is much larger when children can judge the results of their behaviors. There are mainly two reasons. The well-known factor is environment influence. On the other hand, if children follow their natural instincts, the difference will increase. But I still think the difference is no larger than two years' effort.
Principle 10:
There is an upper limit to get research ability from learning.
The reason is that researcher can not learn original problems and knowledge structure. A researcher must be very careful to learn knowledge structure, unless from the great researchers (long time ago researchers need to be greater). Problems depreciate with time quickly, but important and fundamental problems depreciate slowly. Knowledge structure depreciates rapidly with usage. When a knowledge structure has been used by a researcher, there is normally not many useful things left. But the greatest researchers' knowledge structures still have some potential.
Knowledge structure includes value of reliability, importance and knowledge for each theory. Different researchers have different judgment for reliability and importance of the same theory.
The limit is often a little under the threshold ability in the area, because a student will increase his ability a little from researching. A good tutor can raise the limit a little if he teaches more problems.
An independent researcher is called a "self-researcher". Many researchers can reach the threshold ability easily if they keep on researching, and stay there for many years. A self-researcher reach the threshold ability slowly, but he can keep the velocity at and above the threshold ability.
A beginner's choice (reaction to environment) is often not as good as teacher's choice, but it still helps to improve knowledge structure. At the start of a "self-researcher", his ability and knowledge accumulation is slower than good students. But he will improve his research methods and knowledge structure.
Learning and self-researching are similar to different strategies for a race. A learning researcher runs with constant velocity; a "self-researcher" accelerates his speed. When efforts are enough, the latter will surpass the former.
A well-learned researcher should have strong desire to destroy current knowledge, to partially offset the restriction from the learned knowledge.
The main difficulty for a pure "self-researcher" is to insist on researching when he drops behind. It is very difficult to stand lagging behind others longer and longer. So it is better to train ability with a blending of learning and self-researching. This sacrifices expanding velocity but gains more effort. A blending researcher will have smaller progress after surpassing the threshold value. So a research should try his best to be similar to a self-researcher, even to sacrifice some efforts.
This is also true for economic development. A developing country cannot establish all development by itself. It is important to learn from other developed countries. So the most developed countries develop slower than some less developed countries.
One advantage for self-researcher is: research ability under the threshold value does not produce knowledge progress. So self-researcher does not succeed (make important discovery) later.
To surpass the threshold value need a long time to accumulate problems and to form original knowledge structure. Hope to reach the value quickly by learning and to surpass the value slowly by self-research can not succeed.
4 How to distribute efforts the bestPrinciple 11:
In order to increase research ability in a research area, more efforts ought to be spent on areas with large conversion coefficient and slow fatigue velocity.
Conversion coefficient is e(ij). Research area is similar to space-time coordinates. Each small research effort locates in a research area. Each effort not only influences research ability in the area, but also influence ability in all areas. When the influence is larger, e(ij) will be larger. So "distance" between the two areas is closer. For perfect pursuit systems, 1/e(ij) is proportional to distance.
So a researcher ought to concentrate efforts on highly related areas. For example, mathematics is highly related with physics. Areas with small conversion coefficient and small fatigue velocity is also important, because they can increase efforts. For example, there are many games that can help researchers to train their abilities.
If one could predict the answer of a problem very well, he should simply work on the answer. But it seldom happens. For a long unsolved problem, its answer is almost unpredictable. From my experience, it is better to escape from predictable answers--this shows your respect to other researchers' works.
So in order to minimize risk, it would be better to have a much larger research area. Answer for a longer problem will be stranger, so researcher needs broader knowledge and ability.
Research ability is monotone function of thinking time. Intellectual games and recreations, like go and violins, can largely increase thinking time, so although their e(ij) is small, sometimes they help to increase ability.
If knowledge structure (and structure of any pursuit system, like society) can be directly viewed as we observe universe, research will be much easier (and interesting). Researcher can adjust the relation (distance) between concepts and knowledge of concepts.
Principle 12:
For any research effort, probability to overcome a difficulty is proportional to exp(priority*effort).
priority=importance+difficulty+ability
Priority is marginal knowledge.
(1) A=¶K/¶x
(1) is similar to relation between energy and negative action. More rigorously, priority is a vector, similar to canonical momentum. Although ability is often mentioned in my articles, priority can be measured, not ability (similar to relation between momentum and canonical momentum).
When sum of importance and difficulty is zero, effort ought to be distributed proportional to ability. Similarly in universe, pi is proportional to dxi when field is zero. Research behaviors with low priority can have large importance.
Difficulty can be treated as "negative importance".
In classical physics,
Lagrangian=potential energy+kinetic energy=repulsive potential energy+attractive potential energy+kinetic energy
In research, negative Lagrangian (negative action in unit time) corresponds to the priority order of choices. Repulsive potential energy corresponds to difficulty, or negative importance. Attractive potential energy corresponds to importance of a research work. Momentum is research ability in the area.
In a low temperature universe, particles cannot enter regions with strong field, expected negative action (proportional to F2ik) will be small.
In economics, a consumer manages to pursue the largest marginal utility of money. The marginal utility is similar to marginal priority in research and to marginal negative action in the universe.
Marginal priority decreases with effort when research effort is distributed the best. Behaviors with low marginal priority ought to be discarded.
Choice theorem:
Researcher ought to work on problems with higher priority, important problems that is easy to solve (more important, low difficulty and high ability).
When effort is the same, ability is very important. When ability is smaller than difficulty, priority is negative, so probability to overcome difficulty is very small. This is similar to low energy particle enter high potential barrier, penetration probability decreases quickly. Sometimes, inspirations help to solve such problems earlier. High ability researcher has more inspiration, but inspiration is not the thing to depend.
Diligence cannot fully compensate large ability difference, unless ability increases through diligence. I discovered this principle in middle school, when I observed the difference between different students facing the same problem. I called the principle "point discharge". So ability training has superior importance.
If priority is positive, the difficulty is not a problem. So a problem difficult for low ability researcher is not a problem for high ability researchers. This is why high ability researchers are so productive.
When a problem is too difficult, its priority is low. Researcher ought to change his route, similar to being reflected from potential. For research efforts on low priority problems, their contribution to knowledge progress is small.
Priority can be measured in two ways. One is to measure by probability to overcome a problem; the other is to measure by the logarithm of probability. The latter is similar to Lagrangian in physics.
In physics, compared with potential, photon exchange is a more accurate description. Similarly in research, idea exchange is a more accurate description.
Difficult problems needn't to be important, although important problems are often difficult (because of competition). Every moment, there are many problems waiting to be solved. Priority is the decisive factor. It is important to check whether there is a important and relatively easy problem. Deduction difficulty from A to B is similar to negative action from A to B. Difficulty of a problem is similar to expected energy of a photon, representing the difficulty to absorb the photon into mass.
When researcher thinks a problem, he considers its instant difficulty. Since concepts' adaptive behaviors will change difficulty of problem, similar to charges adaptive behaviors change field. In universe, charges' absorb energy from electromagnetic field statistically; in research, concepts reduce difficulty of problem and increase their own importance.
Long-term research considers both problems' influences to concepts and concepts' influences to problems. More basically, it considers the pursued quantity of problems.
Long-term research also allows researcher to think about influences from less important problems and less important concepts. So the result is more rigorous.
Facing the same problem, different theories have different reaction. This represents "charge", sensitivity to difficulty of problem. Problem can be classified into two kinds: waiting to be explained and waiting to be proved. This is similar to electromagnetic field from positive and negative charges.
This is also valid for other choices. For example, suppose a team faces two matches, A and B. When difficulty for match B increases, the team ought to transfer some power from match B to A. Since result of a match is not a continuous quantity, benefit will not increase for a big win. So the decision is valid when opponents have similar strength. Similarly in the quantum mechanics, a particle will change its choices when potential energy for a choice changes.
5 Calculation of ability
Principle 13:
Ability in an area is the product of imagination ability, A(x), and judgment ability, A(m). Total ability is sum of all parallel abilities (Ai)
(2) A=SAi(m)Ai(x)
A researcher ought to be good at both imagination and judgment. They are necessary abilities for any theoretical research. If good at one and inept at the other, total ability is not strong. When I started my research, I learned some judgment ability but very little imagination ability on physics, so I found I could not propose a new theory. I spent one year to propose various problems and theories. Then in university, I could propose a new theory easily, but was unable to judge its truthfulness, so I had many possible theories and little progress. Then I spent about four years to judge all kinds of thoughts, from physics to society. After I finished my training, the remained task was to establish specialized theory group(s).
Stronger imagination ability provides more choices so that there is larger probability to include a better, and the best, choice. The strongest imagination will include all possible choices in his mind, similar to space-time of universe. Inspiration is statistical result of imagination and correct judgment. If a researcher has thousands of original ideas before the right one, it is not lucky.
Stronger judgment is similar to the ability to choose the best state from all possible choices. In universe, a particle always makes the correct choice, satisfying largest pursued quantity principle, representing its perfect judgment.
Relation between different abilities can be classified into two kinds. One is parallel, similar to ability in independent subjects. The total ability is the sum of all parallel abilities. The second is in series, similar to relation between imagination and judgment. This is also similar to parallel circuit and series circuit.
For parallel abilities, researcher ought to fully utilize the strong ability. For unrelated abilities, because the same effort will lead to the same growth speed of ability, it will be better to throw effort in the area with the largest ability. A good researcher will have a subject because a little difference in parallel abilities will be amplified.
For abilities in series, researcher ought to increase the lowest ability. A researcher ought to have approximately the same imagination and judgment ability.
Principle 14:
Expected knowledge for a theory or fact is product of ability and effort. Ability increase in an area comes from the decrease of importance and difficulty of problems.
dKe=S(Aidxi)
Ke is expected knowledge. Since good environment and bad environment will offset each other, the long-term decisive factor is ability. When possible states become continuity, sum will become integral.
This is similar to expected negative action for electromagnetic field is:
dVi is similar to probability for its realization. Pi is similar to knowledge from realization. The integral on a close surface(C) means to include all possibilities. Serious problems and good ideas have large expected knowledge.
In universe, particles' energy increase is expected to be (E2+H2). Increase of ability is similar to the increase of particle's kinetic energy.
When ability is above the threshold ability, research effort will lead to knowledge progress, similar to Fik2dW. Since importance and difficulty can be approximately treated as a scalar in most situations (similar to static electric field), knowledge progress (E2-H2) often leads to larger ability increase (E2+H2).
For a large pursuit system, expected pursued quantity in whole space is realized progress. So expansion depends on two factors: expected pursued quantity in unit effort (increases with importance and difficulty) and total effort.
Research efforts can both succeed and fail. They are inevitable for knowledge progress. If there is success only, progress velocity will be infinite large.
When research gets on well, researcher ought to increase effort. This increases both progress and ability. This also leaves researcher enough space to reduce effort when meeting difficulty. This is similar to particle's acceleration and deceleration.
When researcher encounters unavoidable problems everywhere and has nothing else to do, research simply becomes waiting for the right inspiration. This situation mostly happens at the early stage of research. After a researcher enters the third research stage, he will have many independent works. So he will not sit there waiting for inspirations when having a difficult problem. At the early stage, hunting inspirations is the most important research works.
I remembered having 12 inspirations in one day, when tried to establish mapping between economy and the universe. I had about ten thousand inspirations in the early stage (in 7 years), among them about one hundred are correct. I had the most important inspirations at the final stage of research, averagely one per day. At the final stage, research direction is fairly clear and the quality of inspiration is also much better. Although great researcher cannot forsee the correct answer either, his judgment is much higher: he knows that many ideas cannot be true.
6 Mathematical Expression for Knowledge Progress
The best methodology for a pursuit system is complete decided by the mathematical expression of the pursued quantity. So it is important to find the expression. Because human beings are far from perfect researchers, the expression is difficult to establish. But I think the following expression is a very good one.
In science of research, main variables are knowledge progress(K), ability(A), importance and difficulty(F), effort(x) and research area(i). Compared with the universe, "K" is similar to negative action; "A" is similar to mass; "i" is similar to coordinates; "x" is similar to displacement. Ability is defined to be positive. Importance is defined to be negative, and difficulty is defined to be positive, similar to that attractive potential energy is negative in physics. Because better environment reduces real desire.
In science of pursuit, mathematical expression of pursued quantity decides the best pursuit methods. All principles in science of research are results of pursuing largest knowledge progress. Mathematical expression for knowledge progress in area j is:
(5) Aj= S[e(ij)
Ai](6) Fj= S[e(ij)Fi]
Ai is research ability in area i, dxi is research effort in area i, b j is threshold ability in the area. e(ij) is the correlation between area i and j. When doing research in area i, ability in area j also increases. (4) is in effect only when ability is higher than the threshold ability bj. (5) describes "gravity" between abilities. (6) describes relation between concepts and facts, similar to electromagnetic interaction.
When researcher's ability is under bj, he is called a "beginner"; when ability is above bj, he is called an "expert"; when ability is well above bj, he is called a "great researcher". A beginner mainly aims at accumulating ability and knowledge structure; an expert aims at knowledge progress.
Compared with the mathematical expression for negative action, (Aj-bj) is similar to negative action from gravity (development difference); dxj is similar to displacement; Fj is the correction from pursuit condition, similar to electromagnetic potential at area j; 1/e(ij) is similar to distance between i and j. "Expected knowledge" is similar to negative action for field, mainly electromagnetic field.
Ability increase is similar to the growth of particle's energy. (4) is similar to the mathematical expression for negative action in the universe, so the perfect research methods are similar to basic natural laws. Knowledge progress is very similar to universe expansion. A perfect researcher is very close to a mini-universe.
The above equation is correct for a perfect researcher and does not consider methodology improvement. For practical researchers, there is another way to get ability: learning. An imperfect researcher faces two research areas: his subject and science of research. Researchers compete with rivals by improving methodology and increasing efforts. When science of research is correctly established, perfect researchers will face his subject only. Efforts and initial ability will determine who will succeed.
The equations are foundation for science of research. But the detailed theory will not include too much mathematics.
7 How to make risk the smallest
Principle 15:
Generally, pursuer should not estimate a long time risk from his current state, because risk will be smaller when ability is larger. Larger ability difference from start to end will cause larger difference between experienced risk and expected risk.
The risk observed by researcher himself is called marginal risk, or experienced risk. The risk observed from a fixed state is called renormalized risk, or expected risk. This is why a beginner cannot imagine the difficulty to become a great researcher as Einstein, but Einstein himself thought there was nothing surprise. Researcher is often scared by expected risk from himself, because they want to predict total risk.
Difference between experienced risk and expected risk averagely increases exponentially with the ability difference between the start and the end, while marginal risk averagely increases linearly. Observer's ability exponentially amplifies ability difference and risk.
Risk is unavoidable, even in perfect pursuit. Every unit of pursued quantity is accompanied by risk. If one unit is 100% safe, a perfect pursuer ought to have more until risk emerges. When pursued quantity is large enough, resource will be scarce and the pursued quantity will be risky.
Human beings often measure risk by the probability of failing to overcome difficulty. But such measured risk exponentially amplifies difficulty. Similarly in the universe, energy cannot be measured by penetration probability. Researcher's ability cannot be measured by number of pursuers with the ability; the error will be smaller when there are more chances (problems). Similarly in universe, occupying number amplifies energy difference; difference will be larger when temperature is lower. In sport matches, competition results greatly amplify ability difference.
A great researcher cannot fully take advantage of his ability advantage, partially because that his total effort is limited. For a good researcher, he can make more discoveries by enhancing his knowledge standard, increasing effort (going on research after success, late accepting from dominant scientists, etc).
It is very harmful to estimate risk by result. When having an original idea, a researcher sometimes thinks it is impossible to be true. This judgment measures risk by results. This is an important reason for researchers to stop many high-risk ideas.
Since a close research system need a lot of independent pursuers (concepts and facts), it is very important to start research as early as possible. Common knowledge is not as important as personally explained knowledge. Personally explained knowledge refers to the knowledge that researcher himself has a better understanding. For example, I had a series of personal explanations for "freedom": independence leads to freedom; any combination of permitted states ought to be permitted; pursuers without desire contract ought to be free; an independent particle in space has the largest freedom. Personal original explanations, especially when unique, are productive.
On the other hand, more common explanations provide more bondage, similar to that larger mass moves slower. So it is not always beneficial to learn as much as possible, especially when compared with the marginal efficiency of other behaviors: proposing and solving problems, creating new concepts, etc.
For perturbations around the best value, marginal utility will decrease above the best value and increase under the best value. This is similar to the situation around the realized state in physics.
Any present knowledge has reliability and is possible to be rewritten. If knowledge is learned too well, it is possible to become obstacle for future knowledge progress. When learning knowledge, researcher must try to answer the problem: how large is its reliability? For Einstein and myself, we studied many subjects carelessly, because we gave those subjects low reliability. Sometimes I even underrated the value, like electrodynamics. But the mistake is not as large as give it 100% reliability.
For researchers, it is a common mistake to discriminate future knowledge. The nature is "risk phobia": avoiding risk too much. It comes from the limitation of finite life: researchers are afraid of researching whole life in vain. So they give present knowledge a very high reliability, and manage to study as well as possible, as if they are ultimate truths, 100% correct.
More problems now will lead to more knowledge in the future. So learning more problems might be better than learning more knowledge.
Keep in mind that knowledge process is an evolution. Any theory can become a good one in a good researcher system. If research process is correct, the wrong part of a theory will be abandoned, misplaced truth will be rearranged, and some more truth will be absorbed. Researcher ought to believe that knowledge progress is statistical result of research, and is unavoidable.
If condition were suitable, any creature would be possible to become the dominating intelligent life on the earth. Anthropoid is just one possibility.
State of a theory includes knowledge structure (similar to distribution of potential energy) and change (similar to kinetic energy). Solving a contradiction, similar to the decrease of positive potential energy, will lead to change, similar to energy conservation.
It is an important principle that "correct process will lead to correct result". When one believes that achievement is result of correct choices, he will not accept opinions from those with few records of correct choices. If some common accepted "correct choices"(like good education, good scores, etc) do not lead to good pursuit results, they are doubtful. This simple principle will help many puzzled youth. When I was in middle school, I thought the problem for many years: whether I should follow advices from failures, like teachers and parents.
Similar to venture capital, the earliest risk has the highest profit. So for a child, his correct judgment will benefit him whole life.
Principle 16:
Reliability of solving N problems is much larger than solving one. The effort to solve N problems is not N times the effort to solve one problem.
A stronger form will be: Marginal effort to solve the Nth problem decreases with N. Marginal reliability for solving N problems increases with N.
Research is mainly pulled by problems, not pushed by answers. A researcher seldom makes discovery by deducing from current knowledge.
In a perfect pursuit system, a pursuer interacts with all the other pursuers. Similarly in research, explanation of a theory is not local. But problems can be localized, similar to photons.
This is an advantage of starting research early. A researcher with not enough time can not spend enough effort.
Searching truth is similar to a puzzle. Researcher cannot work at one place only (similar to research on one concept). He must start at many places, so as to have many problems simultaneously.
Although research effort is a little longer, but the better research efficiency (more results in unit effort) and reliability is a good reward.
When there are enough charges, it is not difficult to absorb many problems. Larger percentage of free charges will lead to faster absorption of photons, so researcher need unexplained facts and unverified theories to increase research efficiency. Although a large research system has the same expanding velocity as a small one, its absolute increase is larger (more discoveries).
Since more problems are beneficial for knowledge progress, a researcher ought to learn and find more problems. Knowledge is necessary just because they help to resolve problems.
The most important task for a researcher is to create a knowledge system with original knowledge structure and many problems, with low cost (not to sacrifice too much current knowledge). The cheapest problems, also the most difficult and with the weakest competition, are the hopeless problems after long research. Many of such problems become philosophy problems, because most scientists think they have little hope to be solved in the near future.
Principle 17:
A theory or fact can have many contradictory evolutions simultaneously.
Similarly in quantum mechanics, a particle can be a combination of many states. Although all choices cannot be true together, researcher ought to allow all choices to co-exist. This both reduce risk and threshold judgment ability for a researcher. Facing several possible theories, if a researcher must make the correct choice, it will be very difficult. He should manage these possibilities independently, just like the superposition of quantum states.
When there are many possibilities with different expected knowledge intensity, the best way is to make a combination of all possibilities, not choosing the one with the largest expected knowledge intensity.
Those states do not have the same weight. Sometimes one or two possibilities have the main contribution. Different possibilities often have different priority, so have different knowledge in the same time(similar to phase of a quantum state). The weight will change with the evolution, including difficulty, importance etc.
So a researcher should try all possibilities, this will largely reduce risk. Many researcher thinks research like a classical system: contradicted states can not exist simultaneously. They tend to think all opinions other than their choices are wrong. This is a wrong method and often makes mistakes.
When there is a new theory, give it a small weight and let it evolve with other choices. If it is a good theory and is not discriminated, its weight will increase with time--reliability increases.
Generally in a pursuit system, quantum mechanics helps pursuer to change states continuously, from a totally wrong choice to a combination of correct and wrong choices, and to absolute correct choice(this seldom happens in research if researcher keeps on proposing new problems). It is not easy to change one's opinion suddenly. Quantum mechanics is the nature of "trial and error", in both research and economy.
Notice that methodology is not the reason for the wrong choice. A pursuer cannot predict other pursurs' behaviors, or it will destroy the equality between pursuers. For two intelligent pursuers, they cannot predict each other correctly simultaneously. If A can predict B, A can pursue better than B.
Rigorous deduction is more suitable for theories with 100% reliability, similar to that classical physics describes particles with unique choice. Practical research is a combination of many independent deductions, although there is contradiction between these deductions.
If a theory is not 100% reliable, you will be closer to truth when you keep its "enemy" in mind. If ignorance is defined as zero truthfulness; fallacy is defined as negative truthfulness. Statistically, "tolerance" will increase "average truthfulness".
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