The Half-Life of Facts (10 page)

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DAVID
Bradley, a British epidemiologist, decided in 1989 to make a special sort of map. 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 transportation 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 Berlin 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 spread 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.

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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.

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 interviewers 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. 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, specifically 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.

This occurs most clearly in science itself.

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WHILE
it may be an extreme case, Tai’s mistake is far from the exception in the world of science. When it comes to science, too often knowledge simply doesn’t spread as quickly, or as evenly, as we might expect. Disciplines grow rapidly and ramify; it becomes difficult for any one person to know all that has been discovered in a single area.

There has been rapid growth in interdisciplinary research in the past few decades. Molecular biologists work with applied mathematicians, sociologists work with physicists, economists even work with geneticists. If you can think of two fields, you can think of a way to combine a prefix from one and a suffix from the other in order to get a new discipline. People often flippantly acknowledge that an area is about to undergo a shift if the physicists begin to move into it. They have already begun a steady colonization of biology, economics, and sociology, as evidenced by such newfangled terms as
biophysics, econophysics
, and
sociophysics
.

This trend is a welcome one, on the whole, because it often leads to ideas that are well-known in one field finding wonderful applications in another area, where they have not yet been considered. This can lead to an exciting synthesis of ideas, yielding something new and vibrant. But when multiple areas are linked together only superficially, and knowledge is not truly combined, it occasionally leads to a situation in which someone thinks they’ve discovered something new, yet they’re only re-creating something that has been known for a long time in another field. Tai’s experience is an extreme example of this, but smaller examples abound.

My own research, which draws from many different disciplines, has not been immune to this problem. In the fall of 2010, when I was a postdoctoral research fellow at Harvard, I was working with Jukka-Pekka Onnela, a fellow postdoc and currently a professor at Harvard’s School of Public Health, on a project involving a large anonymized data set of cell phone network calls from a country in Europe. In addition to knowing who called whom, which was important for understanding social ties, we also had information about the callers’ locations down to the level of the cell tower. Using our data we could map a community of callers on a country map.

When you do this sort of mapping you get a nice scatter of points on a grid. As part of our work, we wanted to know whether there were clusters of points on this grid, and if so, how many groups of people were there in the points we were examining. I already knew of many sophisticated ways to cluster data points based on their locations, but you often need to know the number of clusters in advance. For example, if you know that there are three groups of data, these algorithms will take your data and place them into three different groups. But what if you didn’t know the number?

Onnela and I began searching online for help with this problem, and while we found a lot about clustering, we didn’t find the answer to our problem. At one point in this long process one of us might even have recommended thinking about how to create our own method. Then I came up with a solution: “Why don’t we just go down the hall and speak to Alan?” Alan is Alan Zaslavsky, a statistician in the Department of Health Care Policy at Harvard, and someone you can count on to be knowledgeable about all things relating to statistics and mathematics (and most other subjects as well). So we walked down the hall and knocked on his door. He wasn’t busy, so we went in for a chat, and within five minutes we had the answer: something called the Akaike Information Criterion, created decades ago, was exactly what we needed.