On inequality
1. Inequality in nature
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 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 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.
At the same time, systems with higher differential require higher cost to build. An engine that can withstand higher temperature and pressure is more expensive to build. 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.
Because of the need to maintain differential, systems generally have barriers to separate inside from outside. Engines have combustion chambers that separate inside from outside. Dams are constructed to separate inside from outside. Cells have membranes, where concentration of many materials and the electric potentials are different inside and outside. A system maintaining higher differential need to withstand greater pressure. It is more rigidly built. This is true for engines, dams, or transmission lines.
2. Inequality in human societies
There is a strong parallel in human societies. Human societies everywhere are unequal. In businesses, there are supervisors and subordinates. In academics, military and government, there are different ranks. Among different countries, there are rich countries and poor countries.
Greater inequality often means greater profits. Companies can raise prices when they have great competitive edge. Universities that are more exclusive can charge higher tuitions. Companies often move production facilities to lower wage places to increase profit margins.
At the same time, systems with higher differentials with respect to the environment are more costly to maintain. At the US Mexico border, US side maintains an expensive border screening system while people can enter Mexico freely from the US side. An affluent society requires extensive education system to maintain its social structures.
For the designers of a system, the choice of the level of inequality depends on the tradeoff between marginal 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 less resource efficient but safer options. 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 resource, its internal inequality is often low. However, such system can utilize abundant resources as “energy slaves” or impose inequality on other weaker social systems. In a social system that controls less resource, its internal inequality is often high. In such system, efficiency is very high for the elites, the designers of the system. However, such systems also have a higher probability of experiencing violent revolution.
It requires higher fixed cost to maintain a more unequal society. Dominant parties of a society do not necessarily hope to increase inequality all the time. When the British Empire was expanding rapidly in the 19th century, it abolished slavery, a more extreme form of inequality. By adopting less unequal social systems, Britain was able to maintain and expand a huge empire with relatively little cost and huge profit. The inequality of a system also depends on how long the dominant parties expect the system to last. When we go fishing, we hope to have some inequality over fish. We use a fishing line to hook fish. However, if the general public is allowed to use fishing nets in rivers, lakes and oceans, fish population will decline rapidly in a very short period of time. For an unequal system to last, the level of inequality cannot be too extreme. This applies both in nature and in human societies. 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.
In popular terms, the inequality in gravitational potential, chemical potential, electric potential and other potentials is called energy. From thermodynamic theory, inequality in potential, or energy is the driving force in the nature. It is also a destructive force. We all need energy provided by oxygen. At the same time, our body produces many antioxidants to prevent oxygen from reacting with and destroying our tissues. Sugar is a vital energy our body needs. But too much sugar in our blood system, and in cells, will damage our health. When we cannot maintain a low level of sugar in our blood system, we get diabetes.
3. Maintaining inequality
Human societies depend very much on high energy input. However, we carefully regulate the energy sources. “Playing with fire” is always considered dangerous. Whenever possible, systems with high gradient, or high inequality are carefully regulated. They are contained in isolated or remote places. Furnaces are usually located in basements. Electric generators are usually placed very far from residential areas. When factories are located in wealthy countries, much resource is used to control pollution and to ensure safe working conditions. This lowers the ratio of output over resource input. But when factories are moved to poor countries, where local population has little political power, little resource is allocated to control pollution and to ensure safe working condition. This increases the ratio of output over resource input. Pollution is the reduction of chemical potential. Increasing pollution is the increase of inequality in chemical potential. By increasing inequality, the designers of the system gain higher efficiency and higher profit margin as a result. The increase of inequality improves profit margin. The elites of a society always try to maintain inequality as much as possible. In a wealthy and democratic society, it is often difficult to maintain a high level of inequality. The elites will move production to authoritarian countries where inequality is high and profit margin is high. That is why elites in Western countries often support governments in authoritarian countries and suppress democratic movements in these countries.
4. Inequality in public discussion
Inequality is everywhere. If so, why most people, especially the richest and the most powerful, claim to fight for equality? This is because most people are at the lower end of the society. Today the richest person has more than a hundred billion asset. Half in the middle is fifty billion. Only few people have more than fifty billion asset. Most people have far less than a billion asset. This is why almost all the public announcements, whose main listeners have very little asset, promote equality. People promoting equality gain higher moral grounds than others. And people with higher moral grounds gain higher social status.
Almost everything we do 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. The people who become prominent fighting against inequality often are able to send their kids to join exclusive universities. We want to obtain and maintain competitive edge. We try to gain knowledge premium to generate higher profit. We produce patents to create monopoly. Our gods and political systems are superior to others.
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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