After evidence was obtained in the 1920s that the universe is expanding, it became reasonable to ask: Will the universe continue to expand indefinitely, or is there enough mass in it for the mutual attraction of its constituents to bring this expansion to a halt? It can be calculated that the critical density of matter needed to brake the expansion and "close" the universe is equivalent to three hydrogen atoms per cubic meter. But the density of the observable universe-luminous matter in the form of galaxies-comes to only a fraction of this. If the expansion of the universe is to stop, there must be enough invisible matter in the universe to exceed the luminous matter in density by a factor of roughly 70.

Our contribution to the search for this "missing matter" has been to study the rotational velocity of galaxies at various distances from their center of rotation. It has been known for some time that outside the bright nucleus of a typical spiral galaxy luminosity falls off rapidly with distance from the center. If luminosity were a true indicator of mass, most of the mass would be concentrated toward the center. Outside the nucleus the rotational velocity would decrease geometrically with distance from the center, in conformity with Kepler's law. Instead we have found that the rotational velocity in spiral galaxies either remains constant with increasing distance from the center or increases slightly. This unexpected result indicates that the falloff in luminous mass with distance from the center is balanced by an increase in nonluminous mass.

Our findings suggest that as much as 90 percent of the mass of the universe is not radiating at any wavelength with enough intensity to be detected on the Earth. Such dark matter could be in the form of extremely dim stars of low mass, of large planets like Jupiter, or of black holes, either small or massive. While it has not yet been determined whether this mass is sufficient to close the universe, some physicists consider it significant that estimates are converging on the critical value.

    By the sixteenth century, the Incas of South America ruled an empire that extended along the Pacific coast and Andean highlands from what is now Ecuador to central Chile. While most of the Incas were self-sufficient agriculturists, the inhabitants of the highland basins above 9,000 feet were constrained by the kinds of crops they could cultivate. Whereas 95 percent of the principal Andean food crops can be cultivated below 3,000 feet, only 20 percent reproduce readily above 9,000 feet. Given this unequal resource distribution, highland Incas needed access to the products of lower, warmer climatic zones in order to enlarge the variety and quantity of their foodstuffs. In most of the preindustrial world, the problem of different resource distribution was resolved by long-distance trade networks over which the end consumer exercised little control. Although the peoples of the Andean highlands participated in such networks, they relied primarily on the maintenance of autonomous production forces in as many ecological zones as possible. The commodities produced in these zones were extracted, processed, and transported entirely by members of a single group.

    This strategy of direct access to a maximum number of ecological zones by a single group is called vertical economy. Even today, one can see Andean communities maintaining use rights simultaneously to pasturelands above 12,000 feet, to potato fields in basins over 9,000 feet, and to plots of warm-land crops in regions below 6,000 feet. This strategy has two principal variations. The first is "compressed verticality," in which a single village resides in a location that permits easy access to closely located ecological zones. Different crop zones or pasturelands are located within a few days walk of the parent community. Community members may reside temporarily in one of the lower zones to manage the extraction of products unavailable in the homeland. In the second variation, called the "vertical archipelago," the village exploits resources in widely dispersed locations, constituting a series of independent production "islands." In certain pre-Columbian Inca societies, groups were sent from the home territory to establish permanent satellite communities or colonies in distant tropical forests or coastal locations. There the colonists grew crops and extracted products for their wn use and for transshipment back to their high-altitude compatriots. In contrast to the compressed verticality system, in this system, ommodities rather than people circulated through the archipelago.

    Years before the advent of plate tectonics―the widely accepted theory, developed in the mid-1960's, the holds that the major features of Earth's surface are created by the horizontal motions of Earth's outer shell, or lithosphere a similar theory was rejected by the geological community. In 1912, Alfred Wegener proposed, in a widely debate theory that came to be called continental drift, that Earth's continents were mobile. To most geologists today, Wegener's The origin of Continents and Oceans appears an impressive and prescient document, containing several of the essential presumptions underlying plate tectonics theory: the horizontal mobility of pieces of Earth's crust; the essential difference between oceanic and conti nental crust; and a causal connection between horizontal displacements and the formation of mountain chains. Yet despite the considerable overlap between Wegener's concepts and the later widely embraced plate tectonics theory, and despite the fact that continental drift theory presented a possible solution to the problem of the origin of mountains at a time when existing explanations were seriously in doubt, in its day Wegener's theory was rejected by the vast majority of geologists.

    Most geologists and many historians today believe that Wegener's theory was rejected because of its lack of an adequate mechanical basis. Stephen Jay Gould, for example, argues that continental drift theory was rejected because it did not explain how continent could move through an apparently solid oceanic floor. However, as Anthony Hallam has pointed out, many scientific phenomena, such as the ice ages, have been accepted before they could be fully explained. The most likely cause for the rejection of continental drift―a cause that has been largely ignored because we consider Wegener's theory to have been validated by the theory of plate tectonics―is the nature of the evidence that was put forward to support it. Most of Wegener's evidence consisted of homologies-similarities of patterns and forms based on direct observations of rocks in the field, supported by the use of hammers, hand lenses, and field notebooks. In contrast, the data supporting plate tectonics were impressively geophysical-instrumental determinations of the physical properties of Earth garnered through the use of seismographs, magnetometers, and computers.