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Rewrite Axioms for Universe in General pursuit language

The way to calculate negative action in universe can also be the way to calculate happiness in society, profit in economy and knowledge in research. If happiness, profit and knowledge are calculated the same as negative action. The best way to pursue largest happiness, profit and knowledge is the same as the best way to pursue largest negative action. From least action principle in physics, universe pursues negative action the best.

In universe, growth of action depends on two principles. One is statistical theory, which ensures expected change of action equal to actually realized change of action in a long term. The other is axiom 6 in "Axioms and Theorems for a Perfect Pursuit System", which requires a particle¡¯s best behavior satisfy:

(1) d(-S_{m})+d(-S_{f})=0

From (1), a particle's realized behavior can increase its negative action and reduce others' negative action; or reduce its negative action and increase others' negative action, but the increase can not be smaller than the reduction. The choice principle is similar to a valve, just letting beneficial behaviors to pass.

In a pursuit system, microscopically perfect pursuit behaviors have macroscopic result¡ªdevelopment.

Perfect development principle: Universe is a closed pursuit system with the fastest sustainable development for the given feelings.

¡°Closed¡± means universe does not input or output energy-momentum during its evolution. ¡°Sustainable¡± means universe expands around a fairly fixed speed, so there is no end for the expanding of universe. ¡°Feelings¡± is described by the seven axioms.

It is necessary to establish a more basic science, science of pursuit, to unite all sciences about various pursuit systems. It explains what a pursuit system is. In science of pursuit, pursuit behaviors are the facts needed to be explained.

Which do you prefer, infinite truth in infinite sciences or unified truth? Human beings will discover more and more systems in the future, do we need more and more sciences? Imagine the situation that there are more sciences than scientists. I believe ultimate truth can be known by each pursuer, just like that a particle in universe know all truth, basic natural laws, about perfect pursuit.

In this part, I rewrite the seven axioms in science of pursuit. Since people are more familiar with economy, I mainly use economic language to describe pursuit. If pursuers in a pursuit system follow the seven axioms, total pursued quantity will have the same form as universe, and the best behaviors will be the same as things happened in universe.

Axiom 6 in science of pursuit: A pursuit system wants to pursue a quantity the best.

In research and society, people want to pursue the largest knowledge and happiness. In universe, action is pursued to be the least, but unlike in society and research, a particle¡¯s action is defined to be negative. So negative action is pursued to be the largest in universe. If the pursued quantity is the largest, the system is a perfect pursuit system.

If happiness is calculated just like the way negative action is calculated, then society pursuing happiness the best will be isomorphic with universe. Perfect society will follow natural laws just like universe does. If observer observes the pursued quantity only, knowledge about all ¡°perfect pursuit systems¡± ought to be identical. This will lead to science unification.

Axiom 1 in science of pursuit: For a pursuer¡¯s all possible states with the same development degree, apparent desire for a commodity is proportional to percentage of the commodity in total commodity.

Commodity is valued by expected pursued quantity. In society, a person changes his state faster when he is more dissatisfied with his state. In economy, when a person pays more on a commodity, his desire for the commodity is stronger. In research, a concept changes faster when researcher is more dissatisfied with its knowledge state.

Another form of axiom 1: For a pursuer¡¯s all possible states, average apparent desire is the lowest.

Average apparent desire is (p_{i}/u_{i}), which means desire from unit velocity. In order to have extreme value, there is

(2) p_{i}=Bu_{i}

B is a constant for the same development degree, and it is larger for higher development degree. From axiom 1, ratio between desire and commodity is the lowest; from axiom 3 and 6, product of desire and commodity is the largest. They form the foundation of a pursuit system.

Perfect human beings have a scalor mc to stand desire. After consuming the same, their satisfaction difference is proportional to mc. Perfect pursuers' desires can be called "parallel" to each other. Then, ds=dS/mc is the unified measurement for commodities.

An Euclidean space is set of all commodity combinations with identical development.

If there are two sets of possible values for commodity and desire, the axiom gives the way to establish mapping between them.

Axiom 2 in science of pursuit: Real desire is apparent desire minus price field influence.

In physics, ¡°bad¡± influence is defined to be positive, so (mcu_{i}+qA_{i}) is similar to real desire. If negative action is defined to be the pursued quantity, iP_{i} will be the real desire and idx_{i} will be commodity.

When two identical pursuers consume the same amount of commodity, the one in better field environment has smaller real desire. In universe, when two identical particles have the same velocity, the one in ¡°better¡± field has smaller energy. In society, when two identical persons consume the same quantity of commodity, the one buying cheaper has smaller desire. In research, when two identical theories have the same application, the one surrounded by more facts and less theories has smaller desire.

Similar to apparent momentum, apparent desire changes for two reasons. In (11), the term A_{i,k} comes from A_{i} changes with x_{k}. Similarly in pursuit, apparent desire is larger when environment along the direction is better. The term A_{k,i} comes from A_{k} changes with x_{i}. Similarly, when a pursuer discovers that adjacent parallel experience is better, he will increase the desire toward the experience.

Axiom 3 in science of pursuit: For a pursuer, its pursued quantity from a pursuit behavior is product of commodity and the real desire for the commodity.

Axiom 4 in science of pursuit: For a pursuer, when there are several independent sets of pursuit behaviors, total pursued quantity is sum of pursued quantity from each set.

Axiom 1 and 3 are satisfied in each set.

Each independent set is a perpendicular direction. ¡°Independent¡± means changing desire in one set does not influence desire in the other set.

General form of axiom 5: Space-time and field is evaluated by their expected total influences to action.

In science of pursuit: For market volume, price difference and development difference, their value for pursuit is expected pursued quantity for all possible feelings.

This is a general form for theorem 1 and axiom 5. In economy, price and development difference exists because they are necessary links for happiness pursuit. When considering various price adjustments, producer compares the expected total influence to profit for various possible conditions. In research, different research tasks have different value of expected knowledge. These estimates are rough and are not commonly accepted by all pursuers--a fatal imperfection for society and research, but they are enough to have development. Better precision and valuation invariance will lead to better development on the pursued quantity.

In economy, a possible project(field) might interact with both competitor and consumer, so F_{ik}^{2} is similar to expected profit. But realized profit, similar to realized potential energy, can be much larger or smaller than expected profit.

In economy, everything is man-made just in order to have the largest profit. But human beings have not found how to establish a perfect economy. So it is not easy to discover the perfect pursuit methods independently, but it will be very simple by imitating universe. Ration is not necessary for a perfect pursuit system. Even though particles just followed natural laws by instinct, universe would still be a perfect pursuit system.

Development can be explained in many ways. When a more developed state is called ¡°larger desire for the same commodity¡±, commodity is covariant vector; when it is called ¡°more commodity for the same desire¡±, desire is covariant vector. Development is an infinite progress. If the creation of unstable energy is perfect, universe will expand forever without the risk of low particle density and zero interaction.

Axiom 7 in science of pursuit: For a pursuer, there are four independent sets of pursuit behaviors, among which there is only one with positive pursued quantity.

A perfect pursuer certainly believes its state is the best, so changing state means negative pursued quantity. In such a pursuit system, changing state is not encouraged. The one-dimensional time corresponds to the set of remaining unchanged.

If development of a pursuit system is not influenced by number of independent dimensions, three-dimensional space is just an initial condition for universe. If a pursuit system with other spatial dimensions can not develop, axiom 7 will be a theorem.

Purity and Incompatibility for Pursuit Systems

Here are two axioms in science of pursuit.

Purity axiom:

A pure pursuit system only contains feelings for the pursued quantity and methodology guiding pursuit. Methodology is completely decided by making feelings the best.

A methodology is a one-one mapping between a set of methods and a set of applicable conditions. It must be both complete and consistent. In order to be complete, there exists one method at least under any condition; in order to be consistent, there is no more than one method under any condition. The seven axioms are incomplete, so they are not enough to deduce complete methodology¡ªall basic natural laws. More axioms are necessary to include quantum mechanics and the creation of unstable energy.

Purity axiom is a general form for causal law in science of pursuit. Universe is a pure pursuit system. Basic natural laws form a perfect methodology. In society, methodology consists of laws and morality; in research, methodology consists of research methods. Society and research are not pure pursuit systems, because some behaviors are not chosen to pursue better.

Incompatible axiom:

For any two independent quantities in a closed pursuit system, when both are pursued well enough, in order to pursue one better, the other must be pursued worse.

¡°Independent¡± means there is no causal relation between the two quantities. For any methodology, it can be the best methodology to pursue one quantity at most. When all methods increasing both quantities are followed, there exists method increasing one and reducing the other. So a pursuit system can not pursue equality and development the best together; can not make the pursued quantity the largest at each moment; can not make the pursued quantity the largest for each particle. Incompatible axiom brings unique aim theorem:

In a perfect pursuit system, there is only one quantity pursued to be the largest.

For universe, it is action invariance--total action is invariant with particle¡¯s feelings. A perfect pursuit system is perfect in every pursuer¡¯s viewpoint. If two pursuers had different valuations on the pursued quantity, they would pursue different quantities, which can not be the largest simultaneously.

In science of pursuit, the universe is mostly created by its own: in nothingness, if a perturbation happened to be a very small perfect pursuit system, it will expand forever by its own, so nothingness is not stable. In universe, total action increases exponentially, so it will be larger than any static pursuit system. The existence of universe, or another similar large expanding system pursuing a least or largest quantity, is unavoidable.

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