have had no crucial role in epochal events: the Reformation, the Enlightenment, the Industrial Revolution, and so on. Whenever events outside of (topological) Europe assume significance, as during the ages of exploration and mercantilism, Europeans themselves play the active role. Here we have the first property of the boundary: selective permeability. Major forces in cultural evolution cannot filter through it in a centripetal direction, although raw materials can do so; likewise Aztec gold. 3 All non-European cultures are more or less primitive, at the time of colonization, by comparison with Europeans in the abstract and by comparison with the particular Europeans who colonize a given area and pass judgement on its inhabitants. All such cultures are unprogressive. All are either standing still or declining at the time of colonization. (China is usually conceded to have barely reached the “European” civilization level of pre-Enlightenment times, but is the very model of decadence.) All such cultures are barbarous and heathen. In sum, the non-European world is less strong, less intelligent, and less virtuous than Europe. Hence there is a kind of osmotic differential in power, knowledge, and righteousness. 4 The outward expansion of Europe, like the rise of Europe itself, is, sui generis, a product of internal forces and motives. It is a “striving outward,” an “urge to expand.” There is self-generated evolution within the boundaries of Europe and there is osmotic pressure across the boundary. The result is unidirectional flow: a diffusion process, not an equilibrating system. (By no coincidence, classic diffusionism in European social science was imperialistic, ethnocentric, and often racist in tone. Does this perhaps hold true for some of diffusion theory today?) As a corollary, any given part of the non-European world gains its important attributes from the European impact. Therefore the non- European world as a whole—excepting the areas depopulated and settled by Europeans, thus becoming pseudopoda of Europe itself—displays the pattern created by a decay function; the farther one gets from Europe (in the sense of connectivity, not true distance), the less intense the attribute. This can be described in part as a series of age-area or wave-diffusion bands, and in part as a continuous cline. Thus, whenever non-European areas display qualities indicative of importance, progress, and the