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On Inequality (Revised)
送交者: jingchen 2023年01月01日05:08:57 於 [新 大 陸] 發送悄悄話

On Inequality (Revised)

 

Boundaries and Inequalities in Nature and Society

 

Boundaries and inequalities are two parts of the same story, and both parts are necessary for life and for human societies.

 

A dam is a boundary. The water level inside a dam is higher than that outside the dam. The difference of water levels drives the movement of electricity generators to produce electricity. The air pressure inside an engine is higher than that outside the engine. The difference of air pressure propels the movement of the engine. The biggest source of energy on the earth is from the sun. The temperature on the sun is much higher than the temperature on the earth. The difference in temperature drives much of the atmosphere movement, ocean currents, rainfalls, and photosynthesis on the earth. Without inequality, the world is a dead place.


From thermodynamic theory, the efficiency of an engine is determined by the difference of temperature inside and outside the engine. The higher the temperature differential, the more efficient an engine becomes. This is a general principle. The efficiency of a dam to generate electricity is determined by the height of the dam. The higher the dam, the more electricity can be generated. The efficiency of transmitting electricity over long distance is determined by the voltage differential. The higher the voltage differential, the less energy loss during transmission.

Because of the need to maintain differentials, systems generally have barriers to separate inside from outside. Engines have combustion chambers. Dams are constructed to separate water above from water below. Cells have membranes, where concentration of many materials and the electric potentials are different inside and outside. A system maintaining a higher differential needs to withstand greater pressure.

 

At the same time, systems with higher differentials are more costly to build. An engine that can withstand higher temperature and pressure is more expensive. So are higher dams and high voltage transmission systems. Systems with higher differentials, when they fail, can cause greater damage. A higher-pressure engine causes greater damage when they explode. A higher dam causes greater flood when it collapses. A nuclear power plant, which uses high density nuclear energy as fuel, can cause great environmental damage when accidents occur. Inequalities are necessary but they are dangerous.

There is a strong parallel in human societies. Human societies everywhere are unequal. In businesses, there are supervisors and subordinates. In academics, in the military and in government, there are different ranks. Among different countries, there are rich countries and poor countries.  Enormous efforts go into building and maintaining these inequalities.  At the same time, excessive inequality is dangerous – it can cause a human society to explode.

 

In human societies, boundaries exist to create and preserve social inequalities. This is obvious, since as organizations or societies come to control more resources, they increase their exclusivity and the difficulty of getting in.  Education (from the beginning of time) has two elements.  One is the imparting of a specific skill, for instance, in a medieval village, weaving or carpentry or blacksmithing.  The other is the acquisition of the right to practice that skill – admission to membership in the guild.  This dual practice continues to the present day, in ever more complex forms.  Law and medical schools train lawyers and doctors.  Bar associations and hospitals admit (or exclude) graduates of those schools to practice.  A major purpose of professional education is social advancement – and this is a relative process, requiring and enforcing inequalities.

 

Greater inequality often means greater profits. Companies can raise prices when they have a great competitive edge. Universities that are more exclusive can charge higher tuition. In a wealthy and democratic society, it is often difficult to maintain a high level of inequality. The elites will therefore move production to authoritarian countries where inequality is high and profit margin is high. They can take advantage of lax environmental standards, low taxes, lucrative profit-sharing agreements and cheap labor.  That is why elites in Western countries often support governments in authoritarian countries and suppress democratic movements in these countries, even while they are willing to accept a certain amount of taxation, and environmental and labor standards at home.  Moving inequality across recognized (and tough) boundaries makes it less of a political risk.

 

In short, inequality is everywhere. If so, why do many people, especially the richest and the most powerful, claim to fight for equality? This is partly because they worry about their own safety in an excessively unequal system.  But it is also because most people are at the lower end of the society. Today the richest person has more than a hundred billion dollars in assets. But most people have less than a few thousands in net assets. Thus, almost all public statements, whose main listeners have very few assets, promote and celebrate equality and solidarity and similar values. People promoting equality gain higher moral ground than others. And people with higher moral ground gain higher social status. Equality breeds inequality.

Indeed, almost everything we do personally or in small groups is to increase or maintain inequality. However, we avoid the term inequality. We try to stand out, or to be outstanding. We want to excel, to be distinguished. Many people who become prominent fighting against inequality send their kids to exclusive universities. We produce patents to create monopoly. We hope our books, protected by copyright, will sell. Our gods, our political systems and our moral standards are superior. We profess equality as a political and moral goal but subvert it every day in our daily life. If equality is equilibrium, we work against it. This is the way of the world. 

Regulation and Inequality

We have discussed inequality as an artifact of boundaries and a necessary feature of all life systems.  However, though inequality is necessary, it must also be kept under control. Safety and resilience require that the inequality that is permitted not become too extreme.

For the designers of a mechanical or (say) electrical system, the choice of the level of inequality depends on the tradeoff between efficiency and maintenance costs. In North America, electric voltage in residential areas is 110 V while in most other parts of the world, the electric voltage is 220 V. To carry the same amount of electric energy in a 110 V system requires much thicker wire than in a 220 V system. However, when accidents occur, 110 V causes less shock than 220 V. In a system with abundant natural resources, such as North America, we often choose options that are safer but less resource efficient. In systems with scarce natural resources, we often choose more resource-efficient but riskier options.

There is a parallel in social systems. In a social system that controls more resources, the internal inequality is often low. Low inequality may be less efficient, but it is much safer.  For this reason, dominant parties of a society do not necessarily hope to increase inequality all the time. Rich societies can afford to be relatively egalitarian, and in fact wealthy countries are systematically more equal than poor countries. Rich countries can utilize abundant resources as “energy slaves” – so that humans can live in relative equality, and with the security and quality of life that equality makes possible. Indeed rich countries have elaborate wage structures that are determined by social and political decisions, and not in markets.  This is the basis of the social element in a theory of value, which we will discuss later.  Rich societies purchase internal resilience and safety through institutions that limit and mitigate inequalities.

In a social system that controls fewer resources, the internal inequality is often high. In such a system, efficiency is very high for the elites, the designers of the system. They can afford many servants, retainers, and cheap factory hands. Their living standards are higher – often much higher – than those of wealthy people in richer countries. The living standards of the poor are lower – much lower – than those of poor people in richer countries. The protections of social valuation do not apply. However, such systems also have a higher probability of experiencing revolts, rebellions, and revolution. Elites in poor societies usually live behind high walls and employ security guards – even sometimes private armies.

Measures to limit inequalities within a national community are necessary to preserve the concept of a national community – of a common social system to which all members (qualified persons, or citizens) have a plausible degree of access.  Oligarchs – if they are wise – generally prefer to operate in the shadows, so that the extent to which they enjoy exclusive wealth, privileges and power is not widely visible to lesser members of the same community.

 

Fixed investments like railroads and highways and parks and libraries are shared by the whole society; they reduce inequality, but they are costly to maintain. When the British Empire was expanding rapidly in the 19th century, it built many public works and abolished slavery, an extreme form of inequality. By adopting a less unequal social system, Britain was able to maintain and expand a huge empire with relatively little cost and huge profit. Victorian Britain issued bonds, called Consols, that were to be paid in perpetuity and never redeemed.  The British Empire expected to last forever. Similarly, great egalitarian movements in the United States, such as the New Deal, combined massive public investments in energy, transportation, public buildings, and education with comprehensive social insurance. It was a program designed to create a society that would last, and dominate the world economy, for a long time.

 

The inequality of a system thus depends in part on how long the dominant parties expect the system to last. For an unequal system to last, the level of inequality cannot be too extreme. This applies both in nature and in human societies. When we go fishing, we hope to have some inequality over fish. But not too much. For this reason, we use a line to hook fish – this gives the fish a sporting chance. A fishing net would be more efficient. However, if everyone were allowed to use fishing nets to an unlimited degree in rivers, lakes and oceans, the fish population would decline rapidly.  When the dominant parties expect the system to end soon, the inequality of the social system tends to increase so that dominant parties can extract more profits while the system lasts.  It may be that when a society is governed largely by older people, the tolerance for inequality goes up as time horizons shorten.  When Ronald Reagan became President of the United States in 1981, he was both the most inegalitarian modern president and the oldest president in the United States to that date.

 

水壩越高,發電的效率就越高。同樣,電壓越高,輸電過程中損失越小,效率越高。但是水壩越高,造價也越高。同樣,輸電線路的電壓越高,變電站的造價也越高。社會也是一樣,工人的工資越低,資本的效率越高,但同時,工人的不滿也越多,維護社會穩定的成本也越高。中國這幾十年經濟持續高速發展,主要得益於戶籍制度,農民工沒有多少權力,也沒有多少選擇,儘管中國對外貿易長期大量順差,農民工的收入增加很慢,這就保證了中國企業長期的競爭力。但是,大多數底層人士對中國巨大的貧富差距非常不滿,使得維穩的成本很高。在世界範圍內,美國是唯一的超級大國,享有很多特權,但美國必須在軍事上大量花銷,以維持其超級大國的地位。


並非所有時候,人們都會追求短期的高效率。當高壓電輸送到用戶的時候,會把電壓降下來,世界上大部分地方是 220 伏,但北美是 110 伏。其中一個原因,是北美資源豐富,所以對效率要求低,對安全要求高。十九世紀,當英國快速擴張,殖民地不斷增加的時候,廢除了奴隸制。這樣,就減少了統治者和被統治者的矛盾,使英國人可以統治更多的地方。香港曾是英國的殖民地,很多港人依然懷念過去的時光。

任何一個生命系統和和社會系統,都是物理系統的一部分,都服從物理規律。而某些物理系統之所以能成為生命系統和社會系統,在於它們能夠自然環境中的不平等,或者梯度。水電站利用了大壩兩側,水位的梯度。植物的光合作用利用了太陽溫度和地球溫度的梯度。

卡諾給出了系統的梯度與有用功之間的關係,熱量轉化為有用功的效率是 1-  T1/T2, T1, T2 是系統兩側的溫度,如果兩側的溫度相等,系統不能輸出任何有用功,兩側的溫差越大,轉化的效率越高。柴油的燃點高於汽油,所以柴油機的效率高於汽油機,但柴油機的造價也高於汽油機,因為需要承受更高的溫度和壓力。

當一個系統,攝取的總資源長期高於消耗的總資源,這個系統就能長期生存下去,否則,就會逐漸衰亡。一個生物如此,一個投資項目如此,一個社會也如此。


附錄:溫差與熱量轉化為有用功的效率的推導


設想一個內燃機,汽缸內的高溫是T2,環境的低溫是T1,內燃機對外做功為W,環境和汽缸內的熵值變化分別為 dS1 和 dS2, 汽缸內向外輸送的熱量是q,由熱力學第一定律,我們得到

    -T2dS2 = q = T1dS1 + W, 

所以

     W = -T2dS2 - T1dS1,

從熱力學第二定律,我們得到

    dS1 + dS2 >= 0

或者

    dS1 >= -dS2

所以

    W <= -T2dS2 + T1dS2 = (T1-T2)dS2

從上面,

    dS2 = -q/T2

因而

    W <= (T1-T2)(-q/T2) = (1- T1/T2)q

所以,熱功轉換效率

   W/q <= 1- T1/T2




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