Many years ago, Edmond Leach stated, “I do not want to turn anthropology into a branch of mathematics, but I believe we can learn a lot by beginning to think about society in a mathematical way” (Leach, 1961). This article shares this view and contributes to the current theoretical discussion in anthropology, exploring the possibilities of borrowing a theoretical perspective on mathematics and natural sciences, known as “chaos theory.”

Paradigms in anthropology have always used mechanical models in the sense that “their constituent elements are on the same scale as phenomena” (Levi-Strauss, 1958, p. 311). From a formal point of view, biological analogies in Anthropology are also mechanical models, as Levi-Strauss and also natural scientists define them. Mechanical models are deterministic, which means that, like any regular algebraic equation, and like most differential equations, they have only one solution. Applied to natural and social phenomena, such models are those where, given the exact same causes, the results are the same.

Deterministic, mechanical models, from a formal point of view, are opposed to stochastic models. The difference between deterministic and stochastic models is essential for understanding the concept of “chaos” as used in natural sciences and mathematics. At a meeting of the Royal Society in 1986, “chaos” was defined as “stochastic behavior occurring in a deterministic system” (Stewart 1989, l7). Thus, in this new approach, the absolute opposition between deterministic and stochastic models disappears. A typical example of this arrangement is found in Lorenz’s equations. Lorenz understood that the differential equations (a typical “deterministic model”) that he used in meteorological studies presented results with a high degree of (“random”) variations due to slight differences in their initial states. Thus, the solutions to these systems were “unstable and almost all non-periodic” (Lorenz, 1963).

Some authors (Marcus and Fisher, 1986) have associated “chaos theory” with the postmodern movement in literature, the humanities, and the social sciences. There are, however, very significant differences, despite the fact that “chaos” and literary postmodernism can be considered part of the same broad cultural movement, especially regarding the challenge to current systems of explanation. The most striking difference is that “chaos” is a comprehensive paradigm in mathematics and physics while, in the opinion of postmodern anthropology, today’s social thought would be highly suspicious of comprehensive paradigms.

“Chaos” could designate a radical new path for deterministic models in science by incorporating the random factor. It is an expansion of the territory of science and rationality, while literary postmodernism is to a large extent a critique of science and rationality.

On the other hand, the non-distinction between the frontiers of anthropology and literature, as proposed by some tendencies of postmodernism, represents a strong internal rupture for anthropology: a field that emerged in natural history museums and which has long been perceived as the most “scientific” among the social sciences.

The understanding of anthropology as a kind of story to be told, that is, just a particular kind of literary creation, is often justified in the name of ethical and political relativism.

There is no doubt that relativism represents one of the ethical and methodological premises of Anthropology. There is, however, no obvious logical association between the adoption of literary metaphor as a premise in anthropology and the abandonment of ethnocentric descriptions that exaggerate the violence, cruelty or bizarre sexual behavior of distant peoples. That is, between relativism and the “writing of culture”. On the other hand, explanations that make strange customs intelligible and therefore “rational” can make an important contribution to tolerance by those who think about human diversity. There is an old philosophical (and even theological) tradition that associates rationality with tolerance.

Tolerance and prejudice can both be found in anthropology from its beginning, but the postmodern literary metaphor may in itself be a new danger to anthropological “natives”.  “The lack of importance of the author and his irresponsibility towards the text” (cf. Foucault, 1979) – coupled with the prosaic but effective pressure to publish for a large external audience, a sort of “populist” dream – can pose a serious threat to populations studied. Literary authors write to their readers and, consequently, have the tendency to say what their audience wants to hear, or better, to read.

This reaction against rational anthropology – sometimes without a previous deeper discussion – manifests the global reaction against the rationality of today’s times.

Rationality understood as the very essence of the human condition has been considered, since the Greeks and again in the Enlightenment – to be the basis for the organization of political society: Rousseau and the “social contract” would place rationality as the basis for social life, because human beings, by the use of reason, would agree to live according to rules accepted by all. Much earlier, reason was already central to the concept of “human”. After the emergence of Christianity and Islam, it was associated with the idea of ​​”soul”, with “free will”. When Father Bartolome de Las Casas affirmed that the American Indians were human beings because they had a soul, he also said that they were able to choose freely and rationally, between good and evil.

The premise of rationality has sometimes been associated with central planning and dirigisme, state violence, and military-technocratic government, contradicting the central Weberian thesis of rationality disseminated throughout society. The problem is that the “rational state” of this kind relies on the idea of ​​reason as the privilege of the few, who in the name of their technical knowledge would make reason putatively exclusive.  This feature would make it possible for such a group to impose its will on the rest of society. On the opposite side, messianic political movements make their members feel morally superior and, as such, bearing the right to irrational behavior. This is the case with all the kinds of fascism. Nevertheless, it is still a fact that democracy is founded on the rationality of the common person and that most individuals are able to choose what is best for themselves and for the community. This is opposed to the belief that reason belongs only to the few who are identified with the state power (in a Hegelian way). It is a political and moral fallacy to reject the premise of rationality using its association with the success of some contemporary totalitarian states, such as the Chinese. The premise of democracy upholds the opposite: that reason is distributed among all individuals of different social strata.

Social sciences are ideologies that reflect and affect the societies that produce them. Thus, the choice of poetry, for example, by some lines of postmodern anthropology, as the main channel of communication between different cultures, may express the assumption of the impossibility of transcultural communication through the use of reason. Besides, in some contexts, a densely symbolic and poetic discourse may become a pretext for a supposedly irrational behavior of the described human beings; even if they are described as “wonderfully irrational,” as in Nietzsche`s Zarathustra.

The uncritical literary metaphor can also be a serious threat to high-quality anthropology because careful research is not a prerequisite for writing a literary piece. Thus, the literary identity in anthropology can produce excessive adjectives and insufficient ethnographies, as indeed has been observed in some productions of the genre.

Considering the present crisis of paradigms, so well diagnosed by postmodern social scientists, and the fragility of the solution they point out, these are good reasons to discuss alternatives. I believe that the use of new mathematical models can contribute to the theoretical advance of the question.

The main proposals for using dynamic mathematical models as a metaphor in anthropology are as follows:

  1. Disorder is the common state in nature. Organization is an exception, and only momentary, an internal discontinuity in the state of disorder.

Absolute disorder would be pure randomness. In chaos theory, however, the comprehensive explanatory model remains deterministic, despite opening space for several different alternative solutions. The deterministic model operates during a logical stage in the explanation and is suspended during the subsequent logical stage.

The transfer of this methodological position relative to nature to the field of social sciences is extremely interesting. It proposes disorder, intermediated by ordered states, as the normal situation in social life and culture. The methodological implication of this premise in the field of Anthropology is that anthropologists should give up naïve attempts at functional explanations, because, in some cases, lack of explanation may be the most faithful way of portraying the world.

The existence of vast areas of social life which anthropologists cannot explain may suppose that their model has become chaotic, and this is itself an explanation. Moreover, a methodology faithful to reality should not only seek what can be explained, but also what cannot be explained. Sometimes the inexplicable can be far more interesting than what is explained through the use of tiresome current functional explanations.

2 – Chaotic phenomena can be considered as systems of nonlinear equations (complex systems)

Due to the first premise, above, if disorder is considered to be the common state, pure description without explanation may be assumed to be an essential aspect of the anthropologist’s work. The consequence for anthropological methodology is that anthropologists should describe everything they find in their fieldwork, even those aspects that have no explanation.

Hence the analogy with complex systems of equations. Complex systems of equations have no solution, but represent efficient descriptions of very complicated relationships. When transposed to anthropology, we rediscover the rather familiar Boasian idea that while we cannot explain everything, we have an obligation to describe it in the best possible way.

The need to be “elegant”, as in the formulation of mathematical complex systems, becomes a great challenge when a large volume of data is presented. Here the “literary question” in Anthropology of ’’writing well”, would come back, but with a rather different connotation from postmodern formulations. Good writing would be a form of communication necessary for the exercise of reason. Not as a form of aesthetic or an emotional alternative to reason, but as the very necessity of the exercise of reason.

  1. Some types of phenomena are extremely sensitive to their initial conditions.

The best example appears again in the Lorenz equations. Conspicuous differences in the initial conditions affect the long-term future behavior of the system.

Lorenz, a meteorologist, has created the now well-known and popular term “butterfly effect,” meaning that the flapping of wings of a single butterfly produces infinitesimal changes over time in the short term, but in the long run it can become the cause of storms or weather changes in other regions of the world. The butterfly wing-beat factor cannot be measured.

Transferred to human society and culture, the metaphor of the “butterfly effect” is fairly interesting. The behavior of a single individual may or may not affect all of human culture and history. The butterfly itself, flapping its wings, changes the weather, which influences human decisions. The issue is not just uncertainty but also unpredictability. Chance, biography and individual will become central to the explanation, if there is any explanation. Great men in powerful positions may be strategic to understanding the molding of culture because their influence is known, but those who are powerless can also change it without their role being detected.

The question of individual power and decision is once again considered in the change and stability of culture.

4 – Differences in scale are essential in explaining

The relationship between a flying butterfly and a hurricane (and vice versa) is a complex relationship between phenomena on different scales. Mandelbrot (1982) invented fractal geometry, based on difference of scale, which has been understood as a sort of appendage to the “chaos” models.

Differences of scale have always been a crucial problem in the social sciences. A classic example of a treatment of scale, especially indicated for the study of complex societies, originates from the Marxist concept of “totality”. In this perspective, the mediation between partial totalities and their relationship with the whole is central.

Scale has been a major problem in anthropology, even for its epistemological distinction from sociology, given its preferential approach to small-scale groups. Issues related to scale in anthropology have covered such diverse issues as the explanatory role of wholes, the ethnographic notion of anthropological holism, and the boundaries of ethnic groups, for example.

Social sciences have been engaged in the formulation of mechanical models. Some of these models establish hierarchical relationships between different scales. When such models become “chaotic,” the relationship between levels of different scale becomes unstructured. From this moment on, chance and accidents characterize the relationships between levels of different scales.

These propositions are the basic ideas that can be drawn from chaos theory to create a mathematical metaphor for anthropology.

II-The Chaotic Period: The BRAZILIAN CASE

Brazilians wrote the positivist motto, “Order and Progress”, on their flag. This slogan has the meaning of a mechanical model applied to history. It brings the idea of an orderly and inexorable national growth, of constant improvement, a regular march upwards and for the better.

Brazilian history can be considered as the elite’s attempt to maintain control of society through the idea of ​​order, at the cost of a very high dose of repression and violence. The idea of ​​”order,” identified with “social peace,” that is, with the undisputed control of the elites, if necessary with the ordinary use of direct violence, is effective in explaining Brazilian history and political culture. “Order and Progress” is the synthesis of a political ideology, but is also a mechanical model applied by a group that holds power over a society. The evidence of its effectiveness is the supposed and frequently cited “political stability” of the Brazil, when contrasted with the nations of Spanish America.

On the other hand, the idea of ​​progress was also confirmed by the country’s history. Until the late 1970s, Brazil had one of the highest GDP growth rates, perhaps the highest, for a continuous period of about 100 years.

The control of the elite over society was made possible by the equilibrium conditions of the latter, that is, society was organized by a mechanical model, a model of equilibrium that reproduced over time. This model emerged from a traditional form of organization characterized by oligarchic groups composed of land-owning family networks, who built a unifying political community in their regions. The articulation between these regional oligarchies made political unity possible in Brazil. On the other hand, the poorer masses were linked to these oligarchic-employer groups, through paternalist ties of the “compadre” or “godfather” type and, through them, to political society as a whole. Personal loyalty, as a central aspect of the code of honor of the people, consisted in the bond, cementing both the internal relationship of the oligarchic groups and that of the population subordinate to these groups.

The best description of this system – through a mechanical model – is still found in Oliveira Vianna, when he identifies different types of “clans” in the Brazilian political system of the beginning of the century: the “Fiefdom Clan ” bringing together the farmer, his family and their aggregates. The aggregated Fiefdom Clans, the related families of the local oligarchy created the “kinshp clan”, but the “lower” layers have no class or kinship solidarity. They participate, as a whole, in the “kinship” and “electoral clan”, which brings together several kinship clans. Society was built through personal loyalty bonds.

The process of abandoning a mechanical model of directing history by the elite corresponds to the very process of transformation of society in which this traditional elite ceases to exist. Society becomes incapable of producing an elite committed to a locally built community, and the Brazilian elite begins to look outside the country. As society goes into a chaotic stage, so does the elite and its ability to control or its illusion about controlling the destiny of the country’s history.

The breakdown of the traditional Brazilian political system is related to economic growth and urbanization, with urban concentration of the population, industrial concentration in the Center-South of the country and accelerated growth of the middle class. It runs parallel to the process of disengagement of the elite with the national destiny. This last movement has two aspects.

The first is the replacement of the loyalty bond within the old clans described by Oliveira Vianna by other political communities. Due to academic training on a large scale, especially in the United States, and the possibility of working abroad, important elite sectors began to dedicate their loyalty to concrete communities located outside the country.

The second is the ideology that legitimates this change of loyalty stemming from universities, international institutions and multinational corporations: the concept of nation loses its symbolic and affective value to the elites. The heavily symbolic concepts of “nation” and “people” are replaced by the neutral concepts of “market” and “society” (Zarur, 2004).

2 – The Impossibility / possibility of explanation

The existence of the chaotic situation is clearly perceived by all in Brazil.

The elite’s sense of aristocratic / patrimonialist responsibility for the country and the people disappeared after 20 years of military rule. The same thing had happened to the previous set of personal relationships, which included a large traditional Brazilian political system. Loyalty ties were broken everywhere except in the small family-type groups that still represent a basic form of organization of Brazilian society.

Since the economic crisis of the 1980s, the country has become an arena for fierce fighting between groups within each of its institutions. These groups struggle to maintain their positions in an environment where opportunities are getting smaller. The collapse of interclass loyalty makes the country a battlefield, an undeclared civil war, not clearly a political war, but by no means non-violent. The old Brazilian political problem of regional disparities is aggravated by the growing concentration of wealth in the southeast and by the collapse of oligarchic arrangements. In Henry Maine’s terms, the organizational principle of status gradually disappears, but it is not replaced by the contract. Randomness triumphs, Brazil becomes perceived as an arena where fate is decided by luck and chance, replacing the previous model of an orderly progress to a bright future. Brazil, therefore, entered a chaotic period of its history.

Brazilians wonder why Brazil has entered this period of its history. No one is sure of the answer, but several hypotheses are raised, blaming:

  1. God, who left Brazil, despite the traditional expression that “God is Brazilian”;
  2. The military, who “stole Brazilian history”, that is, they took it out of its natural course;
  3. Inflation caused by various reasons;
  4. Excessive concentration of income;
  5. External debt;
  6. The people, who are lazy and do not work enough;
  7. A conspiracy led by the CIA;
  8. Excessive population growth;
  9. High levels of illiteracy;
  10. Corrupt politicians, especially the president and his ministers.
  11. Corrupt politicians, especially the Deputies and Senators.
  12. The International Monetary Fund, associated with Brazilian bankers;
  13. Economists in government;
  14. The lack of moral fiber among the people: Brazilians have lost their shame;
  15. Overly rapid cultural changes;
  16. Manipulation of the populace by the media; people not knowing how to vote;

17 The “Brazilian way” (”jeitinho brasileiro”): the Brazilian way of circumventing all the rules;

  1. The national tendency to try to take advantage of everything;
  2. Investment in the financial market, diverting investment away from productive activities;
  3. Brazilians who have lost their religious values;
  4. The lack of citizenship after decades of dictatorship;
  5. The judicial system, which does not operate well;
  6. Oligopolies everywhere;
  7. The President of the Republic (Collor), who was addicted to cocaine;
  8. The President of the Republic (Bolsonaro), who was mentally ill;
  9. The President of the Republic (Fernando Henrique Cardoso), who destroyed the state and, therefore, the nation.
  10. The President of the Republic (Lula), who was in jail because of corruption

28.Public deficit caused by an excess of public-sector jobs, social security advantages and government inefficiency;

  1. The privatization program for state-owned enterprises, which is not going as fast as it should;
  2. The privatization program for state-owned enterprises, which is going too fast and too broadly.
  3. Carnival: Brazilians prefer to dance, drink and have sex and take nothing seriously;
  4. The import substitution industrialization model, which has reached its limit;
  5. Portuguese colonization, which built societies where laziness replaces hard work.

This list could be extended ad infinitum. It is in itself a testimony to the disorder that reigns in the country. The list does not reflect how it contributes to the disorder.

  1. Sensitivity to Initial Conditions and the differences in scale.

The example of the “butterfly’s wing ” leading to hurricanes finds its sociological metaphor in the accident affecting human history. The story is full of examples of turning points, like the great battles, such as Napoleon at Waterloo and the fatal delay of one of his generals.

In the Brazilian case, a key event was the impeachment of then President Dilma Rousseff and the imprisonment of former President Lula.

From a standpoint of indeterminacy models, the difference between individuals is essential, especially among those who occupy positions of power and, therefore, are able to influence the lives of others in a more direct way. Will, perceptions and initiatives and, in turn, each person’s “fortune”, that is, chance, is of great importance.

The most evident example in this context is that of then President-elect Tancredo Neves’ illness and death in 1985. The 2018 election of Jair Bolsonaro, a retired army officer holding a radical right-wing position, partly embodied a desperate attempt by the electorate to place Brazil back on the Order and Progress track.

This is an aspect that marks a fundamental methodological difference by emphasizing long and detailed historical reconstructions. A change of mood, or illness, or even a single humble soldier who does not do his duty can transform the world. Most of these causes of historical and cultural processes will remain unknown for ever.

Thus, we can only assume that the long Brazilian crisis results from the meeting and mismatch of a myriad of individual decisions and accidents involving individuals.

III. Conclusions: Chaos in culture

I have identified four possibilities for the operation of the above described mathematical metaphor of chaos in anthropology.

The first is the recognition that disorder is a common state of social life, which emerges when a prior deterministic model becomes chaotic. This study of Brazil is framed in a deterministic model of traditional culture. The model became chaotic at the moment when the bonds of loyalty that unified the whole country were loosened. These bonds tied the social classes and, horizontally, the oligarchies themselves. The common law based on reciprocity has disappeared, replaced by randomness. From this point on, the deterministic model no longer operates and randomness takes over.

Deterministic models have been the main interest of the social sciences and the usual ingredients of national ideologies. The idea of ​​methodical growth is central to the Brazilian process of nation building. The previous deterministic path – that of “Order and Progress”   – disappeared. Chance had a role in making the present situation especially confusing – the death, for example, of a great leader, President Tancredo Neves, who fell ill on the very day he was to take office in 1985 was “bad luck” on a national scale. Although Brazilians speculate on the way in which the present situation has been reached, there is no consensus (see list above).

Today’s Brazilian society goes through the experience of deterministic chaos in three different ways:

1 – The previous deterministic system became random;

  1. The present situation cannot be adequately explained;
  2. – Chance is evidently a significant factor in the present and future of the country. Anything can happen, which is also true for the international situation, especially after the Trump period.

The second proposition is the extreme sensitivity of some types of phenomena to their initial conditions. This proposition is translated into anthropology by the influence of individual human beings on historical events. Many of the situations associated with the “butterfly wing-beat factor” remain unnoticed, by definition. In spite of this, disorder and the prevalence of chance open up a stronger possibility for the influence of the individual’s influence on history.

The third proposition for the chaos metaphor in anthropology is the analogy with systems of nonlinear equations (complex systems): they have no solution but can produce efficient descriptions of extremely complicated sets of relations. Likewise, the current Brazilian situation, as perceived by Brazilians, does not have a clear explanation, a “solution”. It can, however, be described in a rational and systematic way.

Finally, the fourth aspect brought about by the metaphor of “chaos” is the consideration of scale levels in explanation. Different levels of scale, ranging from national culture to institutions, small groups and individuals, assume a central role. At the moment that the previous deterministic model became chaotic, there was a change in the relationships between different levels of scale, with the substitution of relationships structured by new relations of random occurrence.

I hope the idea of ​​chaos can help find ways to deal with the question of methodological uncertainty in the social sciences. The assumption of the impossibility of a rational explanation is replaced by the idea of ​​randomness and the idea of ​​an explanation at such a level of detail that it is impossible to detect it. It is assumed that there is always an explanation, even when we do not know the explanation at all.

Therefore, a third level, that of randomness, can be added to the classic dichotomies, such as status and a Maine contract or community and Weberian society.

One of the conditions that define randomness, the predominance of individual choice, was not entirely neglected in anthropology. Firth (1951), for example, described “social organization” as the level of individual choice, in contrast to the permanent and stable “social structure.” He placed it, however, in a peripheral position in its interpretative scheme. Moreover, individual choice is just one of the conditions that define randomness. Simple accident is another. Accidents sometimes become known only through historical analysis.

An emphasis on scale differences, associating sociology, anthropology, history and psychology, is another feature of the metaphor of “chaos” shared with some postmodern views that disregard disciplinary boundaries. On the other hand, the emphasis on fieldwork remains an important difference from these postmodern formulations. In fact, some even disregard the importance of traditional anthropological field work.

The “chaos” metaphor offers an alternative to the perspectives that rule out rationality. From a Latin American point of view, rationality remains a highly desirable political achievement for society. On the other hand, all human beings must be considered rational because this is an essential aspect of their humanity. In this way, their actions can be explained by rational means, and anthropology becomes a way of understanding behavior that would otherwise be considered irrational.

True relativism in the social sciences must express these assumptions.

2021-01-10T15:25:11-03:00By |Artigos, Artigos - Capa, Identidade Brasileira|