elite. power. few and many. law of small numbers. Randall Collins. sociology of philosophers. society of mind. distribution of wealth. power. democracy. elections. Pareto. shark fin distribution. econophysics. sociophysics. sociochemistry.

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     Essay 35. Crowds and Elites, Bottlenecks and Demons

From poverty to its opposite and back, from the beginning to the end: this Essay continues Essay 31, On Poverty, which was its true beginning.

I believe that the topic of distribution of wealth and power, as soon as we start asking simple questions, leads us to the most general understanding of society, similar to the understanding of matter and life in terms of thermodynamics. Moreover, the two understandings can be just one. Power, money, energy of a physical system, psychological stress of an individual or society—all that is actually the measure of the probability of change, applicable to any natural system.

I do not pretend that I have this kind of understanding, but I believe that the major categories we need for it are: large and small, many and few, short time and long time. The generalized energy of complex systems can be measured only relatively, but this should suffice. I don't see any reason why a new term would be needed instead of the familiar energy.

Let us take molecules of gas and people as comparable models. There is a radical difference between molecules in bottle and people in society, in spite of many similarities (both are dynamic systems). We can see the differences with the naked eye, but there is also a radical difference between a very large number of molecules (people) and a small number of them which is not quite so obvious and needs some mental tools to see.

The difference is: the large dynamic system tends to come to the most probable state—it can be equilibrium or steady state—which makes many other imaginable states not just extremely improbable, but outright impossible, while a small system can go through all its imaginable states in any order. Thus, molecules in a bottle of air cannot even for a fleeting moment gather in one half of the bottle. Moreover, they cannot create even a slight difference in the density of molecules between the halves.

On the contrary, ten flies in a bottle can all gather in one half, although not for a long time, unless there is a speck of food, and ten people in a room not only avoid homogenous distribution but can (and like to) gather in groups of two and more, and even all together if there is a tidbit of news to discuss.

This is the same as to say that small systems do not have history: they do not distinguish between the very first and all the subsequent repetitions of the same state.

A small group can be in a moderate number of  states. Five people can answer a single question with YES or NO in 2*2*2*2*2=32 ways:  YES, NO, NO, YES, NO;  NO, YES, NO, NO, YES, NO  , etc. The probability of accidental unanimity is significant: 1/32=0.03125.  The probability of a unanimous answer by a group of 1000 people is negligible because the number of possible combinations of answers is astronomical (2¹ººº) and people can have all kinds of ideas, even very weird ones. And nevertheless, millions are ready to vote for Donald Trump because electoral choice is a very small system.

There are very few artificial unrealistic questions that a thousand people can answer unanimously, unless this group is artificially selected, heavily brainwashed, or watched by Big Bad Brother. Examples are: "do you want to die today? do you want to pay less tax? do you want to get a million dollars?" A small group, especially with a leader, can easily work out a single stand on a practical issue, even if there are internal disagreements. It is never a problem if there is a leader with a decisive advantage or the other choice is ridiculous.

A small group is capable not only of mulling over a wide range of  pros and contras but also of issuing a decision or answer as if it were one man. A small group works as a single brain, only much better (a single brain can work poorly enough). There are reasons to believe that the power of human minds can be additive and it is possible to create a better mind by hooking several individual minds in a certain way. This is how the theoretical physics of the first half of the twentieth century was made: in small groups of elite scientists and their students. Usually, however, human ambitions produce three opinions for two people.

The system of  US elections shows how little the important decisions are entrusted to the large population (and for good reasons). Two candidates are often promoted by small groups in such a way that they are expected to have close chances and cause a maximal division of voters, i.e., into halves close in size. The Bush-Gore elections of 2000 are an example, although the candidates could hardly be more different.  Of course, any trace of elitism is a deadly flaw for a candidate's chances.

No party puts forward a hopeless candidate. There are local referendums, but has anybody ever suggested a national referendum on "do you want to pay less tax" or "do you want a million dollars now?" Politics is similar to the principle of trial lawyers: never ask a question if you don't know the answer in advance. And yet Election 2016 starts as a true revolution against established order.

As the large number of molecules is governed by the laws of nature, the large number of people is governed by the laws of human nature. How different both laws are is a separate question. Here I am interested in the difference between the crowd and the elite, the large and the small, the few and the many.

Crowd is a society or its large segment, i.e., a large number of independent but interacting members. All scientists form a crowd: they exchange ideas, knowledge, praise, and criticism. A crowd of companies interact through business transactions, lobbying, advertisement, competition, and partnership. Investors in stock market form a different crowd: they lose and gain, gambling for a fluctuating resource. Members of competing crowds interact through cooperation and struggle. What is important about the crowd, it is its large size, so that most of its parameters have a meaningful statistics and the crowd can be described not through a list of its members and their properties but through statistical distributions and parameters.

Crowd is an example of a system. System, however, is a more abstract concept, Systems can be small, built of dependent parts, of mostly identical entities, etc. Crowd is a large human system built of interacting individuals or groups. All of them are different even if they want to be like the other guy.

A member of a crowd tries to maximize a certain value, for example, limelight, wealth, prestige, power, authority, and influence. The higher the value, the easier to increase it. At the same time, because the total value of a crowd in the short run is approximately the same, the more one member gets, the less the others have. This is why the higher the value, the more difficult to increase it, but for different reasons.

I will call the value resource. It is something that can be transferred, shared, multiplied, or destroyed in the interactions between the members of the crowd, so that the total cumulative resource is approximately constant and changes slowly.

Examples of a catastrophic change of resource: severe drought, sharp depression, war and embargo, sharp change of oil prices, stock bubble.

It is the main axiom of classical capitalist economics of Adam Smith that every human wants to maximize wealth. Kenneth Galbraith noted that power, too, must to be in the picture, although it is not a classical economic notion. According to my observations, the generalization about the universality of the will to wealth and power does not seem obvious. There are two main reasons for that.

First, what all people want (with very small exception) is happiness. It was noted by the ancient Greeks long before not only capitalism, but even feudalism. It may take various forms, including stability, attention of others, altruistic service, pursuing a goal, leisure, even sloth. The desire of wealth and power belongs to independent properties of individuals. The intensity of my desire for wealth and power is by no means influenced by other people's desires and vice versa.

The fact is that people vary very widely in what they want and how much they want it. For immigrants from poor or devastated by war countries the desires may be limited by stability and peace, which are not economic values at all. Many who go to the academe do so for the sake of stability, among other reasons. Some others do it for the love of the profession. Some people need respect and praise as much as others need wealth and power and one set does not guarantee the other.

Moreover, even from the theoretical standpoint, in a statistical crowd, any independent property must be distributed more or less symmetrically along a bell curve, with a few having a high value of this property (height, strength, ambition, drive for wealth, drive for power, imagination, etc.). Whether we are tall or short, it has no influence whatsoever on the height of other unrelated to us people. Whether we are rich or poor, it has an influence on the well-being of other people, if we assume that the total amount of wealth is approximately constant.

I use the vague but popular term "bell curve" because it is the general shape of distribution that matters most, regardless of its mathematical form. There are two extreme cases: symmetrical (bell curve)  and strongly shifted (shark fin) distributions, compared in Figure 1.

The shark fin shape appears when the members of the crowd depend on each other in their personal values, which is possible in the case of competition for a resource.

    Figure 1. Bell curve and shark fin distributions

Elite is a smaller part of the crowd, with the highest cumulative amount of the resource. Elite represents the higher (right) end of the shark fin distribution (see Essay 31. On Poverty). The high (right) wing of the bell curve is also an elite, it may be the highest IQ intellectual elite, but neither political nor the financial one because people do not depend on other unrelated people in their IQ and there is no limit on total IQ. Physical strength, height, IQ, and inborn melancholy are intensive values while wealth and power are extensive values. By elite I mean here only the "extensive" elite.

Energy is a measure of the ability of a system to change. High energy means instability, i.e., high probability of change. Life—biological or social—happens only in open systems where a certain order can be maintained only by a supply of physical energy. Energy (known in physics as free energy, see Essay 7, On the Smell of Money) has two components: physical energy and internal order.  The difference between the two tells how much work could be done by this energy.

Social synonyms of energy, however, are a very poorly researched subject. Social thermodynamics (part of it is emerging as econophysics and sociophysics), together with social psychology and sociology, might contribute to our understanding of social and individual energy. The problem with physics, however, is that it is not accustomed to dealing with structures of high and irreducible complexity which cannot be shrunk to a few equations. This might be the subject of sociochemistry, however.

To illustrate the problems with energy, here are some examples of arising questions:

1. What happens during the transfer of knowledge? A scientist of a lower rank may increase both the status of a higher rank scientist who uses the knowledge of the former, and his/her own status. What is lost? What is preserved?

GUESS: No loss. Knowledge is growing and is very far from being a conservative resource. A steady state is theoretically possible, at least, imaginable. The prestige of the low rank scientist slowly accumulates, while the high rank scientist who refers to the other creates a possible competitor.

2. Money in a crowd can be regarded as energy (Essay 31, appendix). Is a transferred quantity of money really preserved or part of it is dissipated? Or the transfer creates value, as in a loan or investment?

GUESS: The entire modern economic system is a device to dissipate the energy of  mineral and other fuel. While the fuel lasts, economy is still growing and money is being created at transactions. A steady state is possible, but it is not in sight, yet.

3. What is the difference between voluntary competition (or exchange of knowledge), and forced one, as in a chess championship where a master has to prove his title?

GUESS: Fame, like in cases of champion status or beauty crown, is the most conservative resource. If it still expands, it is because advertisement and media industries need stars as raw material for growth. A star is a vehicle for money-making. Exchange of fame is still unhindered. Exchange of knowledge is one of the most restricted transactions in industry and increasingly in academia because of patent law.

Entropy is a measure of disorder in the crowd: the higher entropy, the lower order, the higher chaos. Energy can be used to increase order, which is possible in natural or man-made machines such as organisms and pop stars. Order means that there are rules of interaction and some changes are facing strong opposition, while others are alleviated.

Temperature is the price of a unit of energy  in terms of order it can create. In other words, it is the conversion rate between energy and order. A different view—compatible with the first one—is that the temperature of the crowd is the average value of the resource. Example: gold fever.

The factor of an underestimated importance is time. History consists of events and processes in time.  Bottleneck is the slowest stage of a multistage process. It is also known as the weakest link: the location of most probable change. They both are limiting factors.

Demon is part of the system that increases the order in spite of the general tendency to disorder. Demon can work very efficiently if it sits at the bottleneck. Bureaucracy, government, and corruption create bottlenecks and assign demons to collect toll for a passage. Government agencies are demons, not in any derogatory sense, but...  mafia is also a demon. See APPENDIX 2.

Star is the winner in contest for attention and recognition. Everything linked to a star is supposed to attract attention, too. The star is a temporary member of star elite, which is very fluid. The star for a snickers company is like gold rush for a spade trader.

What is political power, then? Power in society is a very tricky phenomenon. It is easy to tell what it is not: it is not the ability to maintain order, i.e., keep entropy low by using energy, usually, in monetary form. Same low entropy corresponds to different arrangements of society. Equal powers can be used to maintain incompatible orders. Loose autocracy and inefficient democracy may keep the same entropy of society. A person who has great corporate power may be powerless in his own family.

Power is a social mechanism of applying energy (in the form of money, of course) for creating a particular order against another power that applies energy for creating a different order. Political power is not just money or any other resource. Like the power station, transformer, power line, local transformer, and electrical outlets in a neighborhood, or like the engine, transmission, steering, and wheels of a car,  power is a device that performs a certain function and maintains a certain structure of order by consuming energy, dissipating part of it, and transforming the rest into order. Social power is never universal, neither it is abstract.

This is why political power can be bought. It is a kind of a Thing: a machine, an organization, and even an organism, like horses in agriculture or elephants in the army of Hannibal. The one who buys a power device must also buy fuel every day. Power feeds on money.

Power is a mechanism, an engine: it needs to be designed, built, painted in cheerful colors, oiled, maintained, served by specialists, supplied with energy, and used. This is why not just government or a big corporation can have power. In capitalist democracy, everybody who has money or can raise funds can buy components and build a mechanism of power, possibly, as a little corg (Essay 33, The Corg). This is exactly why the corg is possible: it is a gadget manufacturing a certain increment of a general political order. For the elephants of power, voluntary contributions are a very inefficient way to graze.

Corgs of a very limited scope are already  built into large corporations, as Kenneth Galbraith noted, but what I personally see is the evolutionary divergence of the corporate host and its internal symbiont. The loose anti-globalization movement and global terrorism are both examples of yet imperfect corgs that are free of material production. They have a corporate nature and are completely focused on social and political change. Note that in modern world destruction is the cheapest activity: it goes on even if you don't move a finger (See Essay 34, On Loss).

The Russian Bolsheviks, who built the party machine, overturned the social order in 1917, and kept refining the new order, were the evolutionary predecessors of modern corgs. Interestingly, the Bolsheviks created also a giant national manufacturing conglomerate, but destroyed all its competitors up to the last man. The external competitors, however, toppled the classical black-leather-jacket Bolshevik in the 60's.

Kenneth Galbraith believes in the spirit of team work and genuine dedication and pride of the employees of a large corporation. I am less idealistic, and although team enthusiasm cannot be denied, it is the material reward (or fear of punishment, as in Soviet Russia) that keeps it burning. The Bolsheviks maintained the team enthusiasm by telling the people that they worked if not for themselves then for their children who would be in worker's paradise. Remarkably, the terrorists, too, promise paradise, as well as justice on earth.

Whatever subject of these Essays we touch upon, it points to enormous amount of available literature. Art, entropy, poverty, energy, liberalism, competition, Technos… thousands of books, papers, and web pages. Does it make sense to squeeze a droplet out of each giant fruit of knowledge, all the more, if this droplet can evaporate right before our eyes?

It is exactly the tiny size of the droplet that makes sense. Only a small volume of knowledge, like an ancient saying or a modern aphorism, can be applied to large multitude of situations.

I do not believe in utilitarian benefits of general knowledge, small in volume, portable, and as applicable to any problem as a lock-pick. I believe in the benefits of detailed, profound, and professional knowledge, which cannot be found in one person and is distributed among specialists. My Essays are not a source of this kind of professional knowledge. It is a source of some questions and answers. The answers can be disputed and changed for better ones: they are just seeds of professional answers. The questions point to the places where to plant them. The Essays belong neither to sciences, nor to humanities, but, as I hope, to a narrow tidal strip between them where the waves of humanities wet the dry sand of sciences, rolling back and forth.

As I believe in art, I believe in esthetic qualities of general knowledge.

If poetry and art have any function, it is to obscure the essence of human nature, to complicate and embellish it (sometimes with dirt), and to turn into mystery. This is what poet does in the most intimate poetry. Art makes life look more complex than life really is. If one asked why the modern art makes an opposite impression, I would say that modern art is not about life: it is about art. Similarly, abstract knowledge, which is concerned with the most general properties of the world, is not about the world: it is about knowledge. There is even a disturbing similarity between modern art and abstract knowledge: they both are reducible to a small number of principles and they both dehumanize our view of the world by rejecting its anthropocentric design.

NOTE (2016). To be objective, whatever that means, science should not depend on properties of humans . Individual humans are not present in equations, other than in their authorship.  But science is free to ask any question.  The question on my mind is: then how can the science (real science) of human matters be possible? The answer is: by using patterns instead of equations.    

Looking back at my life, I see that nothing, except my family, enriched my life as much as my interest in understanding the world around me, whether it was the science of chemistry, which was the source of my income, or completely useless knowledge about things with no relation to my life, like the cuneiform dream books of ancient Babylonians.

Do I understand what I am writing about?

The process of understanding is like listening to music or reading a novel: it captures my attention and gives a kind of satisfaction which no physical pleasure can give. Like art, it takes me to a different world. Probably, it is not such a big paradox because knowledge consists of ideas, and ideas are certainly nothing we can feel with our senses. Understanding is the most refined of all human pleasures: you acquire the ability to touch and feel ideas as if they were pebbles on the beach. It does not last, and if you once enjoyed understanding, you want it again and again. Even wrong understanding is a treasure: it can be exchanged for a better one.

The ancient advice "know thyself," which Socrates heard from the Oracle of Delphi, does not seem as enlightening as "know the nature of things." While Thales of Miletus said that to "understand thyself" is extremely difficult, Albert Einstein was optimistic about understanding the world. "The most incomprehensible thing about our universe is that it is comprehensible" is ascribed to him, although I was unable to find the reference.

I see the subject differently: it is extremely hard to understand the world, but easy to understand myself, even if it is difficult to accept the unflattering self-understanding. This is why self-knowledge is discouraging while exploration of the world is a source of unending joy. As soon as we know ourselves, life ends because nothing can add to it. We lose the mystery of our existence and become predictable, though unreliable, cogs in the mechanism of the world, even if we do not know how the mechanism works.

The world is enormous in size and complexity. Why can we understand it? There are several reasons, but all of them have the same pattern: we represent a large number of objects by a small number of ideas. As Henry Poincare said, mathematics names many things with one name, and the same is true about physics and any science.  

We operate with ideas, and ideas, like modeling clay, fuse together into a small number of large pieces which are also ideas. Unlike clay, however, all ideas, regardless of generality, have the same size and weight because they are immaterial. This is what makes them so different from the pebbles: one cannot find two identical material objects, unless they are stamped out by some machine, which is also a realization of some idea.

NOTE: Having said that, I suddenly realize the origin of the idea of equality: it regards human beings as ideas. Or, to put it differently, it is an idealized picture of the real world.

There is a natural limit to a volume of knowledge a single average specialist can manage. The size of this area is, probably, defined not just by the mental capacity of an individual, but by a limited number of intellectual leaders in the area—a property noticed by Randall Collins in his marvelous and radical  Sociology of  Philosophies A Global Theory of Intellectual Change (Cambridge, Mass.: Belknap Press, 1995). I would like to retell his vision in somewhat different terms because, among others reasons, this is a fascinating picture of an elite, in this case, the elite of philosophers: self-proclaimed elite of elites.

There is an intellectual space, which can be compared with an area of land populated by packs of  sophisticated animals who, believe it or not, graze mostly on grass, and only occasionally kill and eat devour each other. The packs (sounds more appropriate than "herds") have a certain hierarchy, with dominant males as leaders.

My biological interpretation of Collins' ideas is strongly influenced by his own eloquent imagery:

Imagine a large number of people spread out across an open plain—something like a landscape by Salvador Dali or Giorgio de Chirico. Each one is shouting, “Listen to me!” This is the intellectual attention space (p. 38). [See APPENDIX 2]
.............................
The tribe of attention seekers, once scattered across the plain, is changed into a few knots of argument. The law of small numbers says that the number of these successful knots is always about three to six. The attention space is limited; once a few arguments have partitioned the crowds, attention is withdrawn from those who would start yet another knot of argument (p.38).

I substitute animals for people in order to emphasize the competitive and compulsive nature of interaction.

There is a certain limit of density of intellectual animals on feeding grounds. If it is exceeded, the extra males have to leave the pack. Conversely, if the number of animals too low, they cannot breed. Thus, Collins establishes the number of coexisting and competing intellectual families (or packs; schools, to be exact) in the area as three to six. This is his law of small numbers, which can be interpreted as the power of an elite.

Collins' picture is much larger and richer than that: he describes the networks of  intellectual relationships between different schools and rituals of the interaction between individuals. I would say that an intellectual needs to mate with other intellectuals, and there are as many sexes as there are intellectuals. In the fight for a mate, instead of joining the leader and waiting for an opportunity, one might either become hostile to other seekers. One projection of the entire multidimensional picture gives a shadowy impression of biological struggle for existence on a limited resource. Naturally, it leads to evolution.

This seems to be a very realistic picture for philosophy and humanities in general, where fashion plays a certain role, limiting the number of "designers," but natural sciences avoid overpopulation by splitting and self-fragmenting into specialized area, as it happened with chemistry, sociology, and anything else. Conflicting "schools" is a rare phenomenon in modern experimental sciences but can be seen at the level of hypotheses. Thus, the area of biological evolution, which cannot be observed in all detail and can be subjected only to a very limited experiment, consists of schools of thoughts, and even creationists try to be one.

The sociology of philosophers along Randall Collins seems to differ little from the sociology of politicians. Modern natural sciences, in an extraordinary fashion, are moving closer and closer to politics and philosophy, at least in America, because science today is a competition for limited resources of money and attention. The scientists, too, attract money either by demonstrating their traditionalism and loyalty to proven leaders, or by splitting off new branches and brandishing the novelty and revolutionary promises of their research.

The result of the fragmentation of science is that not only most scientists lose the general view of the world, but they lose any interest in such a view. All they want is to breed, compete for dominance, and stop slightly above their level of incompetence, and this is perfectly normal today.

Pareto's distribution (Essay 31, On Poverty) applies to production of knowledge as much as it applies to production of wealth: a few leading intellectuals (dominant "males;" some of them females) produce a vast majority of publications—a well-researched fact . It is among a few leading thinkers that the larger picture of the world can be found, and Ilya Prigogine, Ulf Grenander, Randall Collins, Edward O. Wilson, and, probably, Neill Ferguson are those I would think about among my contemporaries.

I believe there are two reasons why the larger world can be understood:

1. Because it can be split into small areas which can be seen in all details. Their modest complexity is quite easily manageable by postgraduates because standard elements and relations between them are identified in larger areas. The interests of most intellectuals, whose function is teaching and generation of published ideas, are limited by a small list of topics, as anybody can see in the listings of department faculties.

2. Because only a small volume of knowledge applies to all its small areas. Hierarchy of intellectuals, leaders, knowledge, wealth, and power, as well as hierarchy of abstract principles descending down the scale toward the ground is the reality. The principles, however, range from completely untestable, as religion and philosophy (all religions and philosophies are equally true and false) to those experimentally testable before the jury of peers.

Therefore, an intellectual needs a small volume of general abstract knowledge applied to a small area of research. Very general and abstract principles, however, are difficult to interpret. We can see big disputes—burnt out as well as ongoing—about such fundamental things as information, entropy, life, and evolution.

My thesis in this Essay is the universal importance of the opposition between large and small. It is definitely inspired by the Randall Collins' law of small numbers Not only the volume of all knowledge is large and that of most important general principles is small, but also the power of small number of people vastly surpasses the power of large masses. Power, knowledge, and wealth are productive only when they are concentrated. This is why this world can be not only understood but also managed by creating a hierarchy of concentration with either elite or a single sovereign at the top.

But what about the will of the people and democracy?  To express and execute their will, the people elect the government. What self-respecting freedom-loving people would form a such a giant mechanism for the function that could be performed by a small elite?

Da capo al fine.

hat is democracy, then? It legitimizes the fight for dominant position. It establishes the Pareto distribution of wealth and influence. It typically (with some exceptions) gives people as much power as they have wealth. Do the people decide? No. A crowd cannot decide anything because decisions can be made only in small groups. A crowd can select between presented options and every vote is already largely ordered by the presentation of options and has only a limited random component in it. "It is not that anything's wrong with it" (Seinfeld). It is natural. But it is not what many people think: it is not about equality.

Absolute equality is absolute zero of social temperature.

Fine.

APPENDIX:

1. Sociophysics.

Arnopoulos, P. (1993). Sociophysics: A General Theory of Natural and Cultural Systems (Nova Science Publishers)
 "Sociophysics is constructed within the conceptual framework of a Systems Unification Model which bases the political, economic, and cultural sectors of human society upon the physical, chemical and biological aspects of nature."

I could not find it in the libraries and, unfortunately, it costs over $100. I am not a good example to illustrate the theories of Adam Smith.

 2. Pandemonium.

Metaphorically we can think of a set of workers, all looking at the same blackboard: each is able to read everything that is on it, and to judge when he has something worthwhile to add to it. This conception is just that of  Selfridge  Pandemonium ([Oliver] Selfridge, 1959): a set of demons, each independently looking at the total situation and shrieking in proportion to what they see that fits their natures (Allen Newell, 1962).
   Quoted from The Handbook of Artificial Intelligence, Volume IV, p. 18. Avron Barr, Paul R. Cohen, and Edward A. Feigenbaum, Editors. Addison-Wesley, 1989.

Also, on Pandemonium  and other topics:  Mark Humphrys' site. I see in it a general concept of sociology of mind, from which I conclude  that the society of philosophers is, actually, a collective mind, working as the single mind in Artificial Intelligence (AI).

A good recent book on AI: Stan Franklin, Artificial Minds, Cambridge, MA: MIT Press, 1995.  That one I bought and did not regret.
 

  3. Statistics as the study of crowds

There are objects and there are their measurable properties. Any such property is ordered: for any two values we can say which is larger. Time, energy, position, and other physical variables are naturally ordered: one variable is larger than other. So are IQ, wealth, creative productivity, sports achievements, etc. Physics expresses the dependence of one variable on another in the form of mathematical function.

Some human properties, for example, ethical ones, cannot be exactly measured, but there are other ways, see Essay 13, On Numbers.

Objects cannot be ordered. All we can say about them is that one is not the other.  People, animals, plants, seeds, words, events, molecules, etc., and, actually all objects, not their properties, do not have numbers on their backs. If they have, they can be numbered in any order: the number is just a name tag, as on the back of a football layer. This is what crowd is by definition. Mathematics cannot  arrange a crowd in line, unless by some property. Statistics looks at their measurable properties per se and  tries to find out how a property is distributed over the crowd of objects. It analyzes the connection between the value of a property and the number of members of the crowd that have it. Clearly, statistics cannot say anything about a particular objects, except in terms of probabilities. One needs very special skills to use the fruits of such apparently idle occupation, but the results could be powerful.  Still, using probability theory, born from the card games, for personal goals may be as much a winning as a losing business. Mathematics of crowds works better for crowds themselves.

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