Demography plays a large role in cultural evolution through its effects on the effective rate of innovation. If we assume that useful inventions are rare, then small isolated societies will have low rates of invention. In small populations, complex technology will tend to be lost as a result of random loss or incomplete transmission (the Tasmanian effect). Large populations have more inventors and are more resistant to loss by chance. If human populations can grow freely, then a population-technology-population positive feedback should occur such that human societies reach a stable growth path on which the rate of growth of technology is limited by the rate of invention. This scenario fits the Holocene to a first approximation, but the late Pleistocene is a great puzzle. Large-brained hominins existed in Africa and west Eurasia for perhaps 150,000 years with, at best, slow rates of technical innovation. The most sophisticated societies of the last glacial period appear after 50,000 years ago and were apparently restricted to west and north-central Eurasia and North Africa. These patterns have no simple, commonly accepted explanation. We argue that increased high-frequency climate change around 70,000–50,000 years ago may have tipped the balance between humans and their competitor-predators, such as lions and wolves, in favor of humans. At the same time, technically sophisticated hunters would tend to overharvest their prey. Perhaps the ephemeral appearance of complex tools and symbolic artifacts in Africa after 100,000 years ago resulted from hunting inventions that allowed human populations to expand temporarily before prey overexploitation led to human population and technology collapse. Sustained human populations of moderate size using distinctively advanced Upper Paleolithic artifacts may have existed in west Eurasia because cold, continental northeastern Eurasia—Beringia acted as a protected reserve for prey populations.