The Half-Life of Facts

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Authors: Samuel Arbesman
the core idea of cumulative knowledge.
    So while exponential growth is not a self-fulfilling proposition, there is feedback, which leads to a sort of technological imperative: As there is more technological or scientific knowledge on which to grow, new technologies increase the speed at which they grow.
    But why does this continue to happen? Technological or scientific change doesn’t happen automatically; people are needed to create new ideas and concepts. Therefore, in addition to knowledge accumulation, we need to understand another piece that’s important to the growth of knowledge: population growth.
    .   .   .
    SOMEWHERE between ten thousand and twelve thousand years ago, a land bridge between Australia and Tasmania was destroyed. Up until that point individuals could easily walk between Australia and what became this small island off the southern coast of the mainland. Soon after the land bridge vanished, something happened: The tiny population of Tasmania became one of the least technologically advanced societies on the planet.
    By the time European explorers came to Tasmania in the seventeenth century, the Tasmanians had only twenty-four distinct devices, as classified by anthropologists, in their toolkit. These twenty-four included such basics as rocks and clubs. In contrast, the Aborigines not far across the strait had hundreds more elements of technology: fishing nets, boats, barbed spears, cold-weather clothing, and much more.
    The Tasmanians either never invented these technologies or simply lost them over the millennia.
    Joseph Henrich, an anthropologist, constructed a mathematical model to account for how such a loss of technology, or even such a long absence of innovation, could have occurred. The model ultimately comes down to simple numbers. Larger groups of interacting people can maintain skills and innovations, and in turn develop new ones. A small group doesn’t have the benefit of specialization and idea exchange necessary for any of this to happen.
    Imagine a small group of randomly chosen people stranded on a desert island. Not only would they have just a small subset of the knowledge necessary to re-create modern civilization—assuming Gilligan’s professor wasn’t included—but only a tiny fraction of the required skills could be done by each person. Much like the economic concept of division of labor, even if we each have two or three skills, to perform all of them adeptly, and also pass them along to our descendants, is a difficult proposition. The maintenance and creation of cultural knowledge are much more easily done with large groups of people; each person can specialize and be responsible for a smaller area of knowledge.
    In fact, many economists argue that population growth has grown hand in hand with innovation and the development of new facts. The George Mason University economist Bryan Caplan writes:
    The more populous periods of human history—most obviously the last few centuries—clearly produced more scientific, technological, and cultural innovations than earlier, less populous periods. More populous countries today produce many more scientific, technological, and cultural innovations than less populous countries.
    A classic paper by economist Michael Kremer argues this position, in an incredibly sweeping and magnificent article: “Population Growth and Technological Change: One Million B.C. to 1990.”
    Such a timescale is not for the weak-kneed. In an analysisworthy of someone as well traveled as Doctor Who, Kremer shows that the growth of human population over the history of the world is consistent with how technological change happens.
    Kremer does this in an elegant way, making only a small set of assumptions. First he states that population growth is limited by technological progress. This is one of those assumptions that has been around since Thomas Malthus, and it is based on the simple fact that as a population grows we need more technology to sustain the

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