Without counting, adult and infant humans and many other animals are able to compare amounts of solids, intensities of stimuli, and quantities of discrete objects or stimuli – if the sizes of the sets being compared differ by a large enough ratio. For example, an infant of a given age might be able to identify the larger of two sets, where one set consists of forty items and the other set ten items, so a ratio of 4:1. The same infant might not be able to recognize which was larger, a set of 10 items and a set of 5. The cognitive system that makes these > or < discriminations is called the analog magnitude system, or the approximate magnitude system (AMS). The principle neuropsychological substrate of this system is in the lateral segment of the intraparietal sulcus. This same region is activated when people compare social ranks.

To conform equality matching, the most effective, frequent, intuitive, and widespread conformations consist of concrete operations of one-to-one correspondence. This may take the form of aligning things side by side, or doing rounds of “one for you, one for you, and one for you.” Starting together and then stopping at the same time assures temporal equality of labor. Piaget originally formulated the concept of concrete operations to describe what he inferred to be a stage of cognitive development in which children inferred equality between quantities. Humans have developed various technologies for doing concrete operations of one-to-one correspondence, such as ballots, pan balances, and placeholder items showing whose turn it is. It turns out that even infants recognize concrete operations of one-to-one correspondence, which they expect agents to use by default when distributing items between agents. Nonhuman animals have not been observed to do this.

There four fundamental relational models: communal sharing, authority ranking, equality matching, and market pricing. Each of them utilizes a distinct conformation system to represent, communicate, coordinate, motivate, and evaluate social relationships of that kind. The conformation systems are indexical equivalence of bodies, iconic dimensions of rank, concrete operations of one-to-one matching, and purely conventional symbolism of proportions. The chapter also introduces complementarity theory, which posits innate structures that can function only in conjunction with cultural complements. It concludes by saying that the book is intended to be an antitheses to symbolic anthropology.

People imagine high-status persons as tall, and in premodern art often depict rulers as bigger than others. Similarly, to evoke suitable emotions while representing the “greatness” of the Buddha and high gods, people often make statues of them as large as their technology permits. Rulers usually wear headdresses that make them seem tall, and are depicted wearing them. Rulers also tend to wear voluminous robes that make them appear especially large. Modern banners and statues of great political leaders depict them as huge, and their statues are often placed atop tall columns. Another conformation of authority ranking consists of lowering one’s head, bowing, kneeling, or prostrating oneself so as to be below a ruler or other person of “higher” rank. Rulers may place themselves on a dais.

Many cognitive experiments have shown that iconic dimensional conformations are prominent in implicit thought and perception of authority ranking relations. Cognitive experiments are designed to isolate the parameters of interest, or hold other parameters constant, so as to be able to make strong causal inferences. Schubert’s 2005 study showed pairs of role terms to German participants and told them to respond as quickly as possible to indicate with the UP or DOWN key to indicate whether the more powerful role terms was above or below the other role term. Participants responded significantly more slowly when the powerful role was displayed on the screen below the less powerful, compared to when the powerful role was displayed above the less powerful (Schubert 2005). Other researchers have replicated Schubert’s results, and extended them to surface area and to mass. Also, preverbal infants readily recognize that iconic dimensional conformations mean authority ranking relationships.

This chapter describes raised platforms, burial mounds, and topographic conformation of authority ranking in which elites’ dwellings are at higher elevations. Emperors palaces were often surrounded by vast private plazas, massive walls with high and strong gateways, and often stairs that have to be climbed to reach the palace. These are examples of iconic conformations of authority ranking using elevation, mass, and surface area. In cartography, the status of nations is conformed by their relative sizes and their position on the vertical axis of a map. For thousands of years, rulers have built massive, imposing monuments, including earthen mounds, pyramids, and huge, tall stone monoliths. The chapter concludes by explaining why these conformations of authority ranking cannot be fully explained by theories of costly signals, not by theories of conspicuous consumption of energy.

To conform market pricing, people typically use symbols whose meaning is purely a matter of common knowledge of widespread use of the symbols in a given social network or community. Like the other three conformation systems, market pricing symbols conform representationally, emotionally, motivationally, and morally. Signatures on a contract, for example, are symbolic legal and moral commitments. Beyond writing and bookkeeping, many technologies have been developed and continue to be invented to facilitate the use of symbolic conformations of market pricing. Before and after the invention of currency, measurements of weights, volumes, and land-areas depend on convention-based symbolism. Commerce is especially dependent on such symbolism to conform prices, rents, wages, interest rates, and other rates and proportions.

This chapter considers Moosé forms of the four conformation systems: iconic dimensions and magnitudes, indexical consubstantial assimilation, concrete operations of one-to-one correspondence, and purely conventional symbolism. It discusses the ineffability of Moosé sacrifices: they have no explanation for sacrifices, and are not comfortable even describing them. But they are eager to discuss prices paid in the local market.

The discovery of iconic dimensional conformations raises many interesting questions. Are the conformational effects of iconic dimensions on superiors equal in degree to their effects on subordinates? What are the mathematical functions that link “amounts” of conformational dimensions to their effects? How do the conformation effects combine when there are repeated with the same dimension? What are the felicity conditions, under which the iconic dimensional conformations actually do conform authority ranking? When a pyramid brilliantly reflects sunlight, or an enormous bell peals, when and how are their percepts linked to an emperor who commanded them, rather than, say, the engineers or the workers who built them? Does sensitivity to the conformational effects of all ten dimensions emerge simultaneously in ontogeny? Why are these ten dimensions prevalent in conformations of authority ranking, but other dimensions, such as distance, apparently are not often used?

Since at least Sumer and ancient Egypt, people have conformed supreme rank using surfaces perfected to reflect sunlight. In both the Old World and the New, people developed technologies of mining and metallurgy in order to fabricate the shiniest possible surfaces on rulers, their palaces, their temples, and statues of divinities. Glimmering shells and beetle elytra were widely used for personal wear. Olmec, Mayan, and some Asia elites wore highly polished mirrors and shiny clothing and accoutrements. Artists depicted rulers and gods with a nimbus, areole, or halo to evoke their literal brilliance. The Rigveda, and Sumerian, Akkadian, Hebrew, Persian, Zoroastrian, and Greek texts represent divinities, kings, and heroes as brilliantly shining, conforming their rulership. It is common to make loud noises to salute rulers, or praise divinities. In the British empire, the number of cannons fired in salutes marked the top levels of political hierarchies.

Language is a symbolic system, but it is often used metarepresentationally for indexical conformations of communal sharing, iconic conformations of authority ranking, and concrete operation one-to-one correspondence conformations of equality matching. Speakers of English, Mooré, Chinese, and, apparently, Proto-Indo-European and Turkish, rely on words whose original, nonsocial-relational meaning concerns dimensions or magnitudes. There are several reasons why typological study of lexicons is illuminating with regard to conformations. Language always provides the opportunity to convergently validate the other kinds of evidence available for any society. Also, there may be conformational dimensions apparent in language that are not easily seen in other media. Language also conforms third-party relationships that are otherwise difficult to conform, and makes it possible to formulate complex ideas about conformations. Finally, language provides enormous samples of metarepresentations of conformations, permitting analyses that could not be done with the smaller available samples of conformations themselves.