The Half-Life of Facts

by Samuel Arbesman

  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 periods27 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 Kremer28 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 analysis worthy 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 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,29 however, shows that population density often causes innovation to grow faster than population size, so this seems like an underestimate. But let’s see where Kremer’s math takes us.

  Using these two assumptions,30 and a bit of related math, Kremer found that a population’s growth rate will increase in size proportionally to the current number of people. To be clear: This is much faster than exponential growth, the fastest growth rate we’ve considered so far. Exponential growth is a constant rate, and here the rate is growing, and growing along the speed at which the population increases. This is known as a hyperbolic growth rate, and if left unchecked can even result in infinite growth.

  Kremer found that until very recently, over the long sweep of human history, this result seems to be true and could be the cause of the rapid technological progress around us. The number of humans in the world has grown in proportion to the current level of the population—the larger the number of people on Earth, the faster the rate at which the population rises.

  Furthermore, he found that his model fits with other aspects of world history. For example, just as Tasmania was disconnected from Australia about ten thousand years ago, a number of other land bridges were also destroyed, leading to several populated but disconnected regions. The largest by far was the Old World, which consisted of Europe, Asia, and Africa. Next in size were the Americas, followed by Australia, Tasmania, and Flinders Island, a tiny island off the coast of Tasmania.

  And as Kremer predicted, the largest areas—meaning those capable of supporting the largest populations—were the most technologically advanced. The Old World, with its gunpowder and other technologies, led the pack. In second place came the Americas, which were dotted with massive cities, used sophisticated calendars, and had well-developed agriculture. On the other hand, Australian Aborigines remained hunter-gatherers, and Tasmania, as mentioned before, was without even some of the most basic of technologies.

  Last we have little Flinders Island, where evidence indicates that the population vanished only four thousand years after its land bridge was destroyed, possibly due to a technological regress. This is the phrase Kremer used to signify the loss of even the technologies basic for survival.

  But is population really the only story? Or is something more complex going on?

  In physics, a simple model that explains the largest amount of the system being studied is often termed a first-order model.31 The more “orders” that are added, the more precise the model will be, as this terminology is derived from the history of fitting functions to complex curves on a graph. The first order explains the general shape, the second order explains a bit of its wiggle, and so on. While each successive term—a higher order—makes the overall model more precise, they each individually explain less and less of the shape of the curve. The first-order model explains most of what’s going on, while the higher orders explain the details.

  Very likely, population is part of the first-order model of technological progress; it certainly seems that technology and population have gone hand in hand for millennia. However, we know that the likelihood of someone being innovative is not independent of population, as Kremer assumed, and we also know that higher population densities in certain regions32 need not lead to higher amounts of innovation.

  Similarly, it’s not just the size of the population that’s important, but its parts; the makeup of the population can have an effect on how our facts change. Robert Merton, a renowned sociologist of science, argued in “Science, Technology, and Society in Seventeenth-Century England” that the concerns of the English people33 during this time period affected where the scientists and engineers of that century focused their attentions. It is unsurprising that they were obsessed with the construction of precise timepieces—that is what was needed in order to carefully measure longitude on the high seas, something of an English preoccupation during this time.

  In addition, Merton argued that it wasn’t just the overall population size that caused innovation, but who these people were: It turns out that a greater percentage of eminent people of that time chose to become scientists rather than officers of the church or to go into the military. This in turn influenced the rapid innovation of England, rather than overall population size.

  The world’s evolving technologies and changing facts are not just due to churning out babies and waiting for advances that are due to population growth. New knowledge and innovative technologies are due to a whole host of factors, from the concerns of the populace to the makeup of the population. But to ignore population growth as an important factor for technological innovation is to miss a significant piece of the puzzle.

  We’ve examined technological change and how it’s mathematically regular and, even more so, often predictable. We now have a handle on why innovation fits the particular shapes that we see ar
ound us. And it’s clear that technological change can itself lead to widespread change of other facts. But there is one large area of technology that not only obeys reliable trajectories but also plays a significant role in the spread of other facts and pieces of knowledge: travel and communication.

  • • •

  DAVID Bradley, a British epidemiologist, decided in 1989 to make a special sort of map.34 He was interested in the nature of contagion and wanted to see how far people could actually spread a pathogen.

  He used data from his own family. He plotted the lifetime distances traveled by the men in his family over four generations: his great-grandfather, grandfather, father, and himself. His great-grandfather only traveled around the village of Kettering, which is north of London, in the county of Northamptonshire. His movements can be encompassed in a square that is about 25 miles on each side. His grandfather, however, traveled a good deal farther, even going so far as London. All of his travels over his lifetime can be defined by a square that is about 250 miles on each side. Bradley’s father was even more cosmopolitan and traveled throughout the continent of Europe, leading his lifetime movements to be spread throughout a space that is about 2,500 miles on each side. Bradley himself, a world-famous scientist, traveled across the globe. While the Earth is not a square grid, he traveled in a range that is around 25,000 miles on a side, about the circumference of the Earth. A Bradley man could move ten times farther throughout the course of his life with each successive generation, traveling in a space an order of magnitude more extensive in each direction than his father.

  This increase in travel is an exponential increase in distance from one generation to the next. If we look at the areas and not just the distance of the geographic footprint of each man, these also increase exponentially, at a rate double that of the increase in distance (because they are squares). Bradley was concerned with the effect that this increase in travel would have on the spread of disease, postulating that increased travel correlates with an increased 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. What is true of the men in David Bradley’s family is true of travel more generally: The speed at which individuals, information, and ideas can spread has greatly increased in the past several hundred years. And, unsurprisingly, it has done so according to mathematical rules.

  For example, the upper limit of French travel distances in a single day has obeyed an exponential increase over a two-hundred-year period, mirroring Bradley’s anecdotal evidence. Beginning in 1800, as humanity moved from horses to railways, the curve holds. Similar trends hold for air and sea transportation. The curves for sea transport begin a bit earlier (around 1750), and air transit of course starts later (no one is really flying until the 1920s), but like movement over land, these other modes of transportation35 obey clear mathematical regularities.

  Figure 5. Increases in average distance of daily travel in France over time, using all modes of transportation. Note that the distance traveled is on a logarithmic axis, meaning that the distances capable of being traveled increases exponentially over time. The thick black line shows the general exponential trend. Data from Grübler, Technology and Global Change (Cambridge University Press, 2003).

  These transportation speeds have clear implications for how the world around us changes.

  Cesare Marchetti, an Italian physicist and systems analyst, examined the city of Berlin36 in great detail and showed that the city has grown in tandem with technological developments. From its early dimensions, when it was hemmed in by the limits of pedestrians and coaches, to later times, when its size ballooned alongside the electric trams and subways, Berlin’s general shape was dictated by the development of ever more powerful technologies. Marchetti showed that Berlin’s expanse grew according to a simple rule of thumb: the distance reachable by current technologies in thirty minutes or less. As travel speeds increased, so too did the distance traversable and the size of the city. Viewed this way, a city is then a place where people can easily interact.

  Furthermore, Bradley’s intuition—that transportation speeds are important for understanding the spread of disease—is exactly correct. Just as people can spread at certain rates, so can disease. The Black Death spread37 precisely at the rate of human movement in the fourteenth century in medieval Europe.

  These examples are not exceptions. We arrive at the foundations of a variety of ever-changing facts based on the development of travel technologies: the natural size of a city; how long information takes to wing its way around the world; and how distant a commute a reasonable person might be expected to endure. All of these facts, ever changing, are subject to the rules of technological change. Ultimately, each often follows its own mini–Moore’s Law.

  • • •

  FROM communication and urban growth to information processing and medical developments, the facts of our everyday lives are governed by technological progress. While the details of each technological development might be unknown—Will we use disks or CDs? How will we cram more transistors into a square inch?—there are mathematically defined, predictable regularities to how these changes occur. Once we understand this, especially in tandem with understanding scientific progress, we can grasp how technology alters the knowledge around us.

  But how exactly do facts spread? And how does this affect how our knowledge changes over time? Just as the technologies of travel and communication affect certain facts of our world, so too do they affect how facts spread and reach each one of us, changing our own personal knowledge.

  The facts we, as people, know are due to what we are exposed to, and this requires the spread of knowledge. Is the spread of knowledge just as understandable as how knowledge grows and is overturned? To answer this question we can examine a presidential primary.

  CHAPTER 5

  The Spread of Facts

  WHILE campaigning for the Democratic presidential nomination in 1972, George Wallace was shot multiple times in the abdomen by Arthur Bremer. Wallace, the governor of Alabama, had up until that point been doing very well in the polls. This assassination attempt (he survived, though he was left paralyzed) effectively brought his campaign to an end and altered the election, leaving McGovern to capture the Democratic nomination.

  On that same day—May 15, 1972—a group of telephone interviewers1 happened to be undergoing preparation for that day’s assignment at the Consumer Research Corporation, a small market research firm. When David Schwartz, the firm’s owner, heard the news of the shooting, he realized this was a rare opportunity: They could use the assassination attempt to actually measure how long it takes for important news to travel and spread through a population. He redirected some of the phone-bank interviewers to examine this, and his team began dialing individuals in the New York City area, attempting to see how the news spread each hour. They carefully called hundreds of people over the course of several hours, and in doing so extracted a clear mathematical curve of how news diffuses over time. Each hour, a larger and larger fraction of those surveyed had heard the news of the shooting. By 10:00 P.M. that night, nearly everyone they spoke with had already heard the news, through a combination of radio, television, and personal contacts. This important piece of information spread extremely rapidly but not instantaneously. The news flashed around New York City in a measurable and predictable way.

  Facts do not always diffuse so rapidly. Consider the case of Mary Tai.2 In February 1994, Tai authored a paper in the journal Diabetes Care entitled “A Mathematical Model for the Determination of Total Area Under Glucose Tolerance and Other Metabolic Curves.” On the surface, this appears to be little more than a quantitative approach to understanding certain aspects of metabolism, and an article appropriate for such a specialized journal. But look a little closer, sp
ecifically at the first few words of the article’s title. Need help? Think about determining the area under a curve. And now think about your math classes from high school and college.

  What Tai “discovered,” even being so bold as to term it Tai’s Model, is integral calculus. Tai was not the first person to discover calculus, no doubt to her great disappointment. Rather, it was first developed in the latter half of the seventeenth century by Isaac Newton and Gottfried Leibniz, more than three hundred years before Tai’s diabetes-related calculations. Specifically, Tai rediscovered something known as the trapezoidal rule for calculating the area below a curve, which seems to have been known to Newton. And yet Tai’s article passed through the editors and has received well over one hundred citations in the scientific literature.

  A number of letters written in response to Tai in a later issue of Diabetes Care pointed out that this technique is well-known and available in many introductory calculus textbooks. But this example should allow us to recognize something often forgotten: Despite our technological advancement, and even the advances in the speeds of communication chronicled in the last chapter, in many situations knowledge can spread far slower than we might realize.

  The creation of facts, as well as their decay, is governed by mathematical rules. But individually, we don’t hear of new facts, or their debunking, instantly. Our own personal facts are subject to the information we receive. Understanding how and why information and misinformation spread or don’t spread are just as important when it comes to figuring out how we know what we know. Knowledge doesn’t always reach all of us simultaneously, whether we’re talking about big new theories or simple incorrect facts—it filters through a population in fits and starts. But there are rules for how facts spread, reach individuals, and change what each of us knows.