Some Propertities for Inequality and Development

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 development.

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

In universe, pursuer's energy increases slowly, about10^{10} years to double, while its state changes very fast, about 10^{-20} second. Similarly in economy, personal happiness usually changes much smaller than his state changes. In universe, each particle pursues correctly, but the average result is close to zero in a short time¡ªaction increase and action decrease is nearly symmetrical. Similarly in economy, for a market full of intelligent pursuers, like in stock market, pursuers have average pursued quantity statistically. So, theorem of equality:

For a system with intelligent pursuers only, there is equality for average pursued quantity in a long term.

With a perfect methodology, pursuers¡¯ average pursued quantity in unit time will increase. The increase is statistical in a shorter time, and is inevitable after infinite long time. Probability for a pursuer to have pursued quantity larger than a given value grows with time. If success is defined as pursuer¡¯s pursued quantity larger than a given value,

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 certain electromagnetic field, repulsion 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 development is 100% safe, because feedback always increases total pursued quantity in whole system. So a perfect pursuit system develops monotonously.

A bonded charge is a better state than a free charge now because its energy is lower. Being a bonded charge forever is not the best pursuit behavior. Similarly, a person is not necessary to work for one company or to consume one company's product forever. Because a free charge has larger feedback statistically, and will have larger mass after enough long time. Both bonded charges and free charges have their advantage for pursuit: the former feel better now than the latter; the latter develop faster.

In 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 after tax income is proportional to contribution, inequality of pursued quantity will be as large as contribution difference. So taxation ratio ought to be the same for all income.

How large is contribution difference in society?

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