For a pursuer, his pursued quantity does not increase monotonously. Pursued quantity difference between pursuers is called inequality of pursued quantity. Theorem of inequality:

Inequality of pursued quantity in unit time will grow with system expansion.

In order to develop, inequality is necessary. Equality, pursuers having the same pursued quantity, will sacrifice expansion speed. If all pursuers have the same pursued quantity everywhere, there is no acceleration and so no expansion. Inequality of pursued quantity is an inevitable property for a pursuit system.

In the universe, pursuer's energy increases slowly, about 10¹⁰ years to double, while its state changes very fast, about 10^-20 second. In economy, personal happiness usually changes much smaller than his state changes. In universe, each particle pursues correctly, but the average result is zero (when expected pursued quantity of field is not considered): increase and decrease of Lagrangian is nearly symmetrical. Similarly in economy, for a market full of intelligent pursuers, pursuers have average results in a long time. So, theorem of equality:

For identical pursuers in a perfect pursuit system, there is equality for their pursued quantity in a long term.

With a perfect methodology, pursuers' average pursued quantity in unit time will increase, because of the expected influence of field. The increase is statistical in a small area, but is inevitable in a large scale. If success is defined as pursuer's pursued quantity larger than a given value. Probability for the success of a pursuer grows with time. Theorem of success:

In a perfect pursuit system, probability of success increases with time.

Growth of pursuer's pursued quantity is not a uniformly divergent process--it is possible to find a pursuer that its pursued quantity is smaller than now after any given time. For example, in strong attractive field, correction for pursued quantity will be strong enough. Maybe this is a little disappointing for a perfect pursuit system, but risk always accompanies with single pursuer.

On the other hand, systematical expansion is 100% safe, because feedback always increases total pursued quantity in whole system. So a perfect pursuit system expands monotonously.

A bonded charge's negative action is larger than a free charge now, while a free charge has larger feedback statistically, and will have larger negative action after enough long time. So both bonded charges and free charges have their advantage and disadvantage for pursuit: the former feels better now; the latter develops faster. Always pursuing present benefit is not the perfect pursuit behavior.

In the universe, a proton in cosmic ray can be billions of times of a static proton's energy. So the problem for human beings is that inequality is not enough. The reason is discrimination to pursuers with high income. If pursuers can live healthy, it is unnecessary to protect those below average pursued quantity. If happiness reward (not monetary reward) is proportional to contribution, inequality of pursued quantity will be as large as contribution difference.

In the following, I explain three principles about equality: occupying equality for pursuers, possible contract equality for exchange and possible state equality for market.

Desire freedom between different pursuers and different time is part of desire equality. For a perfect pursuer, desires at different time have equal rights to choose contracts by themselves. Present desires do not have the right to choose for future desires. Present behaviors ought to choose for present desires, no earlier and no later. Of course, desire of one pursuer does not have the right to decide pursuit behaviors for other pursuers.

Possible contract is propagated to search pursuers. In space, field searches region with high density of pursuers the same as region with no pursuer. In society, there is serious discrimination between realized desires and unrealized desires. This will reduce the probability for possible desires to be realized. Unrealized desires have their right to be treated as realized desires. In society, there is a long way to go for desire freedom--to treat every unrealized desire the same as realized desire. So desire freedom can also be called equality for realized and unrealized desires. Generally, equality is a more broad condition than freedom.

Similar to law equality in society, there is method of methodology equality:

In universe, all pursuers follow the same laws about motion; field from all pursuers follows the same laws about propagation.

In society, big companies have privileges in field distribution. Methodology equality is also result of desire equality.

Field is similar to possible contract because field has the following property, method of possible contract:

When a pursuer receives field, it has the corresponding potential energy; when it does not receive field, it will not have the potential energy.

In society, a pursuer normally exchanges with familiar pursuers. This will reduce other pursuers' probability to exchange with him, so he will pay more because of fewer choices. Exchanging with familiar pursuers is reasonable in an imperfect system, but in a perfect pursuit system, you can trust everyone. In universe, there is method of exchange:

Exchange between two pursuers includes three independent steps: one pursuer output field to open market, field propagating in market, and another pursuer input field from market.

So a contract between two pursuers can be reached when both agree. Any relation between two pursuers is a kind of contract. For two pursuers without contract exchange, distance is infinitely large. Contract agreed by one and disagreed by the other is forbidden in a perfect pursuit system, but happens in society everyday.

Method of propagating widely:

Possible contracts from any pursuer are propagated to all the other pursuers.

So, in society, information about goods and services ought to be spread the widest.

In universe, an electron in an atom can be excited by photons, so a contract can be terminated at any time. In a perfect pursuit system, contract is similar to an intensity contract, which regulate the intensity of the contract only. Method of renting:

A pursuer can change the intensity of any possible contract at any time.

Renting is a way to replace ownership exchange by intensity ownership exchange.

In universe, pursuer's field is propagated from near to far. In perfect society, possible contracts from a pursuer ought to be propagated from the largest profit ratio to the smallest profit ratio. Method of order:

Possible contract is propagated from near to far.

So motion order and field propagation order is identical.

Method of searching equality:

Electromagnetic field is propagated with constant velocity.

Method of independence:

If a pursuer connecting with all the other pursuers by exchanging possible contracts, it is an independent pursuer who decides his motion by himself.

In society, few pursuers have enough independence, because public opinions influence personal decisions strongly.

With the unification of Europe, people have realized the advantage of unified market to some extent. In universe there is method of unified market:

There is only one space-time in universe.

In society, there are too many trade barriers. In a perfect market, trade between any two pursuers is free of charge.

In society, immigration and emigration is not free. In universe, there is method of free migration:

In universe, every pursuer can move to any place (in order to get largest feedback negative action, there is upper limit for velocity).

Method of instant reaction:

A pursuer changes its state at once when field arrives.

It is obviously a good method for personal pursuit. Human beings cannot follow it well because their bodies are not good enough: they need rest. Human beings can discover causality in universe easily because of the method. Suppose that particles reacting to interaction after a randomly chosen time (like people do in society), causal law cannot be discovered easily in universe.

In society, personal behavior is not just influenced by his feelings because he plays games with others' feelings. Method of honesty:

For a pursuer in the same field, his behaviors, including motion and field output, are irrelevant with other pursuers' behaviors (decisions).