The question is why everything adheres to these exponential curves and grows so rapidly. A likely answer is related to the idea of cumulative knowledge. Anything new – an idea, discovery, or technological breakthrough – must be built upon what is known already. This is generally how the world works. Scientific ideas build upon one another to allow for new scientific knowledge and technologies, and are the basis for new breakthroughs. When it comes to technological and scientific growth, we can bootstrap what we have learned towards the creation of new facts. We must gain a certain amount of knowledge in order to learn something new.
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. The answer is that in addition to knowledge accumulation, we need to understand another factor that’s important to knowledge progression: population growth.
In an incredibly sweeping and magnificent article, entitled Population Growth and Technological Change: One Million BC to 1990, economist Michael Kremer argues 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 population, whether through more efficient food production, more efficient waste management, or other similar considerations. Conversely, Kremer also states that technological growth should be proportional to population size. If invention occurs at the same rate for each person, the more people there are, the more innovation there should be. (More recent research, however, shows that population density often causes innovation to grow faster than population size, so this seems like an underestimate.)
Travel and communication must also play a significant role in the spread of facts and knowledge. For instance, David Bradley, a British epidemiologist, discovered the extent to which populations have spread in an elegant way.
He plotted the lifetime distances travelled by the men in his family over four generations. His great grandfather only travelled around the village of Kettering, north of London – which could be encompassed in a square that is about 25 miles (40 kilometres) on each side. His grandfather, however, travelled as far as London, defined by a square that is about 250 miles (400 km) on each side. Bradley’s father was even more cosmopolitan and travelled throughout Europe; his lifetime movements could be spread throughout a space around 2,500 miles (4,000 km) on each side. Bradley himself, a world-famous scientist, travelled across the globe. While the Earth is not a square grid, he travelled in a range that is around 25,000 miles (40,000 km) on a side, about the circumference of the Earth. A Bradley man moved ten times farther throughout the course of his life with each successive generation, an exponential increase of an order of magnitude more extensive in each direction than his father.
Bradley was concerned with the effect that this increase in travel would have on the spread of disease. But the Bradley family’s exponentially increasing travel distances illustrates not only advances in technology; it is indicative of how technology’s march can itself allow for the greater dispersal of other knowledge.