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 universe because universe is close. If some field or particles disappear without any result, we will reach the end of a clue.
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 systemsí» 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. So there is no upper limit for unification.
In society, countries ought to be unified into one, although different cultures can co-exist.
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 satisfaction, when the limit were reached, best methodology would be unnecessary. So there is no end for pursuit and development.
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 can not 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.
Properties about Methodology
Unlike set of occupying and set of occupied, a complete and consistent methodology can not be included by another methodology, because any part of a methodology must be useful. If M were included by M', M'-M can not be used in any situation.
When two methods can be substituted with each other without changing applicable conditions, they are called relevant methods; when two applicable conditions can be substituted with each other without changing 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:
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. (1)
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 can not 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.
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.
Normally, it is impossible to measure system-forever influences of a behavior, so we can not deduce that a behavior is better than all possible behaviors. A behavior can be proved to be an extremely well behavior, but can not be proved to be the best one. There are some methodologies in which future history can be totally predicted, so unpredictable is not a property for all pursuit systems.
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 better social system. A perfect society must have many intelligent individuals, like infinite particles in universe. Unprovability is the reason for why a pursuit system can never be guided by one intelligent individual, no matter how great he is.