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diffusion

  • Julian Steward and the logic of diffusion

    Thu, 2008-10-30 00:17 -- John Hawks

    I've had a tremendous response to the last entry in the diffusion series, which discussed the treatment of cultural diffusion by the Boasian school. I really appreciate the pointers, which have taken me in some interesting directions that I might have missed. Meanwhile, I'm continuing on with my review.

    In the last post, I pointed out that Boas already had described the main elements necessary for a formal description of diffusion. Indeed, diffusion was of special importance to the Boasian view of culture, because it provided a mechanism by which culture history could come to be partially independent of race history. But despite its importance, neither Boas nor his students brought themselves to a reductive theory of diffusion. That is no surprise, in the context of early American anthropology, which was in many respects unwilling to generalize rules from the particular descriptions generated by ethnographers.

    But one of Kroeber and Lowie's students, Julian Steward, did attempt a relatively formalized description of cultural diffusion. In a short 1929 article, "Diffusion and independent invention: a critique of logic," the 27-year-old Steward showed frustration with anthropology's failure to grapple with the diffusion problem in a concrete way.

    There exists a large proportion of anthropological data which admits of no clear-cut methodology but is usually handled according to inference and common sense logic. While this method may be soundly rational, the possibility of an enormous subjective element and fallacious logic is ever present and is demonstrated by the existence of the diffusion controversy. This controversy is made possible not only by the personal bias of the investigator but also by confusion of the principles upon which the solution is based.

    It is not my purpose to present a rule-of-thumb method for the settlement of the diffusion controversy but to inquire into its logical implications and discover whether these are not capable of formulation. While this will but formulate the principles implicit in most work, it will also reveal the possibility of certain confusions and inconsistencies (Steward 1929:491).

    Why was there a "diffusion controversy"? Steward describes the controversy as emerging from two extreme viewpoints about culture history -- "extreme diffusionists" and "evolutionists." In Steward's description, this conflict comes down to a logical error of comparison.

    He describes this error with an example: "inverted speech," which is "a custom of clowns and others of saying the reverse of what is meant."

    This may be illustrated by inverted speech which occurs in North America in the Plains area, California, and the Southwest, and also occurs in Australia. Shall we account for these four occurrences by diffusion or independent invention. The solution depends upon inference from the assembled facts, but what is the logic of our reasoning? We ask: How probable is communication between these areas? How difficult an achievement is inverted speech? It is tempting immediately to postulate diffusion between the North American occurrences but independent invention for Australia. This would be solely on a basis of distribution and by this we should be prone to judge the uniqueness of the element (Steward 1929:491-492).

    Steward uses "uniqueness" as a synonym for improbability: an improbable feature shared by two societies is likely to result from a unique occurrence that had diffused to both. Continuing with inverted speech, Steward notes that the assumption of diffusion among the North American instances leads naturally to the conclusion that inverted speech is improbable -- after all, it only occurred once in the entire continent. But the assumption of independent invention of the trait in Australia

    ...lead us to regard inverted speech as not so difficult an invention after all, for it clearly has been invented a second time. What logical justification would there be for the assumption that independent invention is inherently less possible for the Plains, California, and the Southwest than for Australia because the first three happen to be geographically more accessible (492)?

    Steward claimed that this comparison amounts to question-begging. Sure, if we assume that communication between two societies is likely, we will be predisposed to interpret diffusion. But this does not give us any real information as to whether independent invention happened.

    To address this problem, Steward suggests three "principles" to guide the interpretation of shared culture elements. I'm going to list these, which Steward presents as statements about probabilities, and recast them in terms of information theory.

    (1) The probability of independent invention is directly proportionate to the difficulty of communication between the localities

    In other words, if messages may pass easily between two locations, then we predict that the information comprising culture elements may pass easily also. Steward further describes two signs that may indicate the difficulty of communication. If the two localities share many culture elements, then we can infer that a regular communication was probably present. And if the localities communicated over a very long time, they may share many more things than if they have communicated only over a short time.

    (2) The probability of independent invention is directly proportionate to the uniqueness of the element.

    Steward adds:

    The uniqueness of a culture element -- that is, the probability of its being invented -- is the most difficult problem to determine. This will be decided by the investigator upon his experience and knowledge of the cultural setting and circumstances under which it may have been invented. But his decision must not depend upon either of the other two principles stated here. To the probability of an element of culture arising in a particular culture, the existence of this element in other localities and the difficulty of communication between the localities are totally irrelevant.

    This is probably the most important point in the essay: It would be desirable to maintain a separate test of the diffusion hypothesis with reference to the "uniqueness" of the element in question, so that this test could reinforce the test based on communication. As it was, each of these tests appeared to obviate the other, resulting in a circle. But Steward's description of this point is totally unclear, and benefits from an information theoretic analysis.

    If we recast "uniqueness" as "reduction in Shannon entropy" (e.g., "information" in the technical sense), and understand that the entropy is a function of probabilities of the components of a culture element, then we can reformulate this principle: Independent invention is less probable when the shared element has a high information content. Still, this cannot be absolute: high information content is difficult to communicate. Communicating a long message across a noisy channel (like a culture contact) requires some work to maintain the fidelity of the information -- and that work requires an incentive.

    In this sense, the "uniqueness" criterion must really break down into at least three separate properties: (1) the information content of the trait, (2) its value, and (3) synergy with the existing culture system. Value may refer to function, such as status marking or foraging utility. A culture element that conflicts with existing knowledge is less likely to be transmitted accurately; whereas one that is synergistic with existing knowledge might be picked up easily from a distant culture. In effect, "synergy" refers to the extent that the information content of a culture element is already familiar within the culture background.

    (3) The probability of independent invention is inversely proportionate to the probability of derivation from a common ancestral culture.

    This is a phyletic view of shared culture elements, that they come from original populations that split into daughter cultures. Again, when many elements are shared, this increases the probability of sharing for any single element.

    Yet after this discussion of principles, Steward comes to an uncomfortable conclusion. We are still left utterly unable to assess whether inverted speech was invented independently in different North American regions, or whether it diffused from one origin. Certainly it helps to know that we don't know that, but that doesn't give us a method, just a critique.

    What the problem really requires is some kind of measurement of the probabilities of invention and transmission. In the case of genetic transmission, we have well-defined probabilities, because actually there is very little information entropy in the system of a single gene with a finite (and small) number of alleles.

    But for culture elements, the information content may be much greater. With more information, we can imagine more ways for the information to be apportioned, as well as more different ways that transmission of the information might be disrupted.

    As to the "diffusion controversy," that will be discussed further in the next post, where I cover Leslie White's record on diffusion.

    References:

    Steward JH. 1929. Diffusion and independent invention: a critique of logic. Am Anthropol 31:491-495.

    Tags: 
    diffusion
    history of anthropology
    Julian Steward
    information theory

  • Early concepts of cultural diffusion: the Boasians

    Mon, 2008-10-27 23:39 -- John Hawks

    I went looking for Lowie, because I was curious about the introduction of the diffusion concept into cultural anthropology. The mathematical description of diffusion, originally developed in thermodynamics, became important in statistical genetics during the first half of the twentieth century. In particular, R. A. Fisher introduced diffusion methods to examine the effects of natural selection in his 1922 paper, "On the dominance ratio." Diffusion methods made it possible to derive analytical approximations for many interesting biological parameters, and also came to underlie models of population dynamics outside the field of genetics.

    So I wondered: How did the use of diffusion in cultural anthropology compare to the introduction of the diffusion concept in genetics? Kroeber's systematization of the concept of cultural diffusion was certainly later than Fisher and Wright's major works on diffusion theory.

    It turns out that "diffusion" was initiated into cultural anthropology by E. B. Tylor himself. The OED has the earliest anthropological use of the term in Primitive Culture:

    How good a working analogy there really is between the diffusion of plants and animals and the diffusion of civilization, comes well into view when we notice how far the same causes have produced both at once.

    Later, Boas also makes extensive use of the concept of diffusion, in essentially the modern sense as an alternative explanation to independent invention for a cultural trait. For example, in his 1891 article, "Dissemination of tales among the natives of North America," he compares the transfer of myths and stories among groups in the New World to that in the Old. He writes:

    Then, we may ask, is there no criterion which we may use for deciding the question whether a tale is of independent origin, or whether its occurrence at a certain place is due to diffusion? I believe we may safely assume that, wherever a story which consists of the same combination of several elements is found in two regions, we must conclude that its occurrence in both is due to diffusion. The more complex the story is, which the countries under consideration have in common, the more this conclusion will be justified (Boas 1891:13-14).

    So by the time Lowie was writing his Culture and Ethnology, the concept of cultural diffusion was well-established, and the Boasian school was concerned with classifying culture similarity in terms of diffusion.

    Cultural problems tended to involve the spread of relatively large quantities of information -- reflected by the Boas quote above and its concern with the "combination of several elements." We can interpret this focus as a statistical consequence of observing culture: With so many potential observations, diffusion is difficult to distinguish from the null hypothesis of parallel development (chance similarity) unless the similarities are sufficiently detailed (involve a threshold of information) to prove otherwise.

    I have not yet found anywhere that this concept of assessing diffusion by "information content" was formalized beyond verbal descriptions like Boas' above. I will review Kroeber's contribution later; he does not provide any formalism at all.

    What I want to point out here is that this concept of diffusion is delimited quite differently from the use of diffusion models in genetics. Fisher and Wright initially introduced diffusion methods to deal with the effects of random changes of gene frequencies. In the case of Boasian cultural diffusion, random change will almost always fall short of the information content necessary to identify specific resemblances in a cross-cultural context.

    I can imagine datasets on cultural traits that would be sufficient to test the hypothesis of undirected (non-selected) diffusion. For example, phonological data on dialects is often detailed and coded to geographic locations. If we approached these data with a diffusion model, they would in many cases be sufficient to demonstrate departures from the null model of undirected diffusion.

    But most observations from ethnography are not of this character. For this reason, cultural diffusion is a priori a phenomenon involving direction by some selective mechanism. In genetics, this would be natural selection. In cultural variation, the selective mechanism may be less clear -- some combination of conscious decision, customs concerning borrowed behaviors, and functional efficacy may be involved.

    In the case of natural selection driving a gene substitution through space, Fisher's model of a wave of diffusion assumed only a single parameter determining intrinsic increase -- the "reaction" term in a reaction-diffusion equation. This was sufficient because the only relevant difference between the selected and non-selected alleles was fitness.

    The case of cultural diffusion, in contrast, makes it tempting to suggest that there might be many independent terms contributing to the spatial dispersion of a cultural trait. Traits might be different in that some are more transmissible than others; thereby spreading more widely. Some might have greater functional advantages than others. Some ideas might be impeded because they conflict with widespread taboos; others might be facilitated by the same factors.

    I write all this because I'm curious about why there was not a more formal development of diffusion in the context of cultural theory. There was every potential of it: Boas did not begin with a formalization, but the ideas critical to a formal theory are present in his description. But the development of the field quickly went in the opposite direction -- away from formalization and toward description. This was despite the fact that the concept of diffusion became incredibly important in the conflict between the Boasian school of ethnology and the cultural evolutionism of Leslie White and others.

    Others (non-anthropologists) did develop more formal theory, but this had little (if any) impact within anthropology. As I continue, I'll go back to the early cultural evolutionists Tylor and Morgan, and trace their influence on 20th century neo-evolutionists. Additionally, no account of cultural diffusion can omit the importance of the Kulturkreis school and its concept of the culture area.

    Tags: 
    evolutionary theory
    history of anthropology
    Robert H. Lowie
    E. B. Tylor
    Franz Boas
    R. A. Fisher
    diffusion
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