Relation between methodology and advantage

In the following, I explain some more knowledge about relation between methodology and its advantage. They are intuitive results of crude facts.

Close Pursuit System

In a close pursuit system, every behavior can be completely explained by earlier behaviors and will influence future behaviors.

Society, economy and research are not close pursuit systems. A close pursuit system is isolated: it does not produce waste and does not input new materials. Advantage of methodology is measured for close pursuit systems. If a system inputs lots of wealth from outside, it might develop fast, but that does not represent advantage. If society were close, human beings can live forever and there is no pollution. But there are many technical problems waiting to be solved to make consumer-worker circulation a close one.

It is not impossible. For example, sex relation between man and woman is a close circulation, similar to charge interaction between charges.

People can always deduce, finding reasons and results, in the universe because it is close. If some field or particles disappear without any result, we will reach the end of a clue.

A perfect pursuit system has the shortest circulation: A-B-A. Mutual attraction and mutual repulsion in a perfect pursuit system makes it possible to give each pursuer a descriptive quantity: charge. If the circulation were A-B-C-D-...-A, it would be very complex to describe.

Unify Various Pursuit

In a pursuit system, there is a set of occupying and a set of occupied. New occupying or occupied can be added to or taken away from the two sets, the result is also a pursuit system.

Unification of two pursuit systems means to merge the two systems’ set of occupying and set of occupied. Unification of any two pursuit systems is also a pursuit system. So unification of infinite pursuit systems is also a pursuit system, and there is no upper limit for unification.

In society, countries ought to be unified into one, although different cultures can co-exist.

Infinite Development

Intensity of occupying and occupied increases with development from zero to positive infinity. So there is no upper limitation for a pursuit system. When discussing a perfect pursuit system, this property is used implicitly. If there were upper limit for the pursued quantity, when reaching the limit, best methodology would be unnecessary. Pursuers do not need the best methodology to maintain states. They need the best methodology to improve staes. So there is no end for pursuit and expansion.

Property of History

In a pursuit system, if all behaviors in a region is called history in the region. History of a smaller region is always subset of history of a larger region. After realized, history cannot be changed. There is one and only one history in any region.

I am not sure about the following problem:

When history of an enough large region is given, methodology is uniquely decided.

This is related with whether people can uniquely decide basic natural laws by observing the universe. Without simiplicity, my answer is no. The same phenomenon can be explained by infinite possible theories.

Properties about Methodology

Unlike set of occupying and set of occupied, a complete and consistent methodology cannot be included by another methodology, because any part of a methodology must be useful. If M were included by M', M'-M could not be used in any situation.

When two methods have the same applicable conditions, they are called relevant methods; when two applicable conditions have the same method, they are called relevant conditions. Relevant methods and conditions can be mixed together to construct new methodologies. For example, lying and honest are both methods for propagating information, and is mixed in society.

The following property might be an axiom:

(1) For any method or applicable condition, there are infinite independent relevant methods or conditions. Independent relevant methods or relevant conditions can be mixed freely to form new methodologies.

If there were only one method, choosing method would be impossible. In society, there are always many independent methods to choose from, and people have created, better to say discovered, many independent methods.

From (1), there are infinite independent methods not included in any methodology. Every method and condition can be used in infinite methodologies. From (1), there are infinite methodologies.

Since mixing is a continuous process, there are always many continuous substitution processes between any two methodologies. Methodology is not single-connected, because methods cannot substitute each other freely. Distance between two methodologies can be measured by methodology substitution, dM.

For two groups of methods and their applicable conditions, when they have no common method and no common applicable condition, and their union group is a methodology, they are mutually called "complementary method group". From (1), for a group of methods and conditions, if it is included by one methodology at least, there are infinite complementary method groups for it.

For any group of methods and applicable conditions, its advantage depends on its complementary method group. For most methods, their average advantage with all possible complementary method groups is zero. So there is no good or bad method. There is just good and bad methodology.

Advantage and Unprovability

Advantage of a methodology, A(M), is not influenced by history earlier than adopting the advantage. From the same initial state, when measuring A(M) in infinite long history, measured A(M) is uniquely determined. In a pursuit system, history is the only possible fact to measure A(M). There are infinite histories with the same measured advantage.

In a perfect pursuit system, if behavior Y has more pursued quantity than behavior X, X can not happen.Normally, it is impossible to measure system-forever influences of a behavior, so we cannot prove that a behavior is better than all possible behaviors. A behavior can be proved to be an extremely well behavior. There are some methodologies in which future history can be predicted, so unpredictable is not a property for all pursuit systems.

In a perfect pursuit system, if system-forever influence of a behavior could be deduced, one intelligent brain would be enough to guide a pursuit system and central planned economy would be the best. So a perfect pursuit system cannot be guided by one intelligent individual, no matter how great he is (including God). A perfect system must have many intelligent individuals, like infinite particles in the universe.

Experience and Democracy

Basic natural laws are proved to be the best laws, because they satisfy largest negative action principle. In society, people usually prefer to choose social system by democracy. How large is the difference between the two choices?

Just like all truth, the best methodology can be both chosen rationally and empirically. Let's see how to prove, or find, best methodology from experiences. Since most human beings are empiricists, experience is the key to persuade people and win their supports for a new social system.

Democracy is a way to calculate pursued quantity. The best democracy is "pursued quantity democracy", which is total pursued quantity in the pursuit system. In current social system, democracy is "pursuer democracy": calculating number of pursuers benefit from a methodology.

Perfection of a methodology is time invariant. If a methodology makes past history the best, it will also make future history the best. If we cannot deduce future pursued quantity, at least we can remember past pursued quantity from experiences.

Since total pursued quantity is pursued in a pursuit system, total pursued quantity in whole system is the quantity deciding the advantage of a methodology. So the correct way to calculate experience ought to be democracy method:

Total pursued quantity in a larger part of a pursuit system is a better criterion to judge advantage.

But total pursued quantity is "Not" calculated in present democracy, at most total pursued quantity in several years (so deficit is supported) and in a region (so trade protection and race discrimination is supported).

In society, pursued quantity is calculated by number of pursuers in present democracy, which is "pursuer democracy" at most. So a person with more satisfaction does not have larger right in voting. This leads to discriminate against pursuers with more pursued quantity, like progressive taxation.

"Pursued quantity democracy" in whole system is the best way to choose methodology, but not the best to choose pursuer's behaviors, which ought to be chosen by pursuer himself. Similarly in universe, basic natural laws are given, but pursuer's freedom is almost unhurt. In present democracy, there are many democratic decisions choosing behaviors for pursuers, like working time, public expenditure.

Best methodology cannot be empirically rigorously proved, because human beings cannot live in all possible methodologies and compare their total pursued quantity. So ration must be used in choosing methodology, maybe a bad news for human beings.

Logic and Methodology

For human beings, their belief about logic came from thousands of years' experience in universe. Truthfulness of logic does not come from logic itself. If observers lived in a world with discrete space, his knowledge about continuity will be totally different. They would not establish infinitesimal analysis. If observer lived in a world where particles and photons move randomly in space-time, he would not have the belief on causal law and would not think about speaking logically or establishing a science logically.

So causality comes from perfect pursuit methods, and logic is not valid in all pursuit system. So behaviors in a pursuit system are not necessary to be deductible.

People checked the truthfulness of logic by its correct prediction about universe; people will believe the perfection of basic natural laws after being guided for thousands of years. In fact, people have already believed some of them in the past two hundred years, like law equality, freedom, market, etc, although they are never proved to be better methods.

In any pursuit system, its logic is uniquely decided by its methodology. Mathematical truth in a pursuit system depends on its methodology, like continuity, honesty, instant reaction, etc. There are infinite pursuit systems that are unreasonable by observers, without order, etc. Our sensation about mathematics came from perfect pursuit system only. Can we use result of a methodology to prove advantage of a methodology?

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