The Half-Life of Facts (2 page)

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HOW
exactly is knowing how knowledge changes actually useful? You may find it interesting to discover that the dinosaurs of our youth—slow, reptilian, and gray-green—are now fast moving, covered in feathers, and the colors of the NBC peacock. But if you don’t have a six-year-old at home, this is probably not going to affect your life in any significant way.

I could tell you that certain areas of medical knowledge have a churn of less than a half century—well within a single life span—and
knowing this can motivate us to constantly brush up on what we know, so we continue to eat healthy or exercise correctly and don’t simply rely on what we were told when we were young. Or I could say that by knowing how language changes, we can better understand the slang and dialect of the generation that follows us.

But really, practical examples like these, while important (medical knowledge will keep cropping up), are not the main point. Knowing how facts change, how knowledge spreads, or how we adapt to new ideas are all important for a different reason: Knowing how knowledge works can help us make sense of our world. And even more than that, it can allow us to anticipate the shortcomings in what we each might know and help us to plan for these flaws in our knowledge.

Facts are how we organize and interpret our surroundings. No one learns something new and then holds it entirely independent of what they already know. We incorporate it into the little edifice of personal knowledge that we have been creating in our minds our entire lives. In fact, we even have a phrase for the state of affairs that occurs when we fail to do this: cognitive dissonance.

Ordering our surroundings is the rule of how we as humans operate. In childhood we give names to our toys, and in adulthood we give names to our species, chemical elements, asteroids, and cities. By naming, or, more broadly, by categorizing, we are creating an order to an otherwise chaotic and frightening world.

And when we learn facts, we are doing the same thing. Facts—whether about our surroundings, the current state of knowledge, or even ourselves—provide us with a sense of control and a sense of comfort. When we see something out of the corners of our eyes around dusk, we needn’t view it as a creepy bird of the night: We call that a
bat
, which is a winged nocturnal mammal that “sees” through the use of echolocation and is probably afraid of the bipedal mammals around it. Only half as scary, right?

But when facts change, we lose a little bit of this control. Suddenly things aren’t quite as they seemed. If doctors didn’t know that smoking was bad for us for decades, we worry about what else
doctors are also wrong about today. If I’ve just learned that my parents had completely different—and, for their time, acceptable—parenting techniques from my own, I am a bit concerned about my upbringing. And if I’ve just found out that scientists have discovered hundreds of planets outside the solar system, and I was living with the assumption that there were only a handful, I might be a little shaken, or at the very least somewhat surprised.

But if we can understand the underlying order and patterns of how facts change, we can better handle all of the uncertainty that’s around us.

To be clear: I’m using the word
fact
in an intuitive way—a bit of knowledge that we know, either as individuals or as a society, as something about the state of the world. We generally like our facts to represent an accurate representation of reality, an objective truth, but that’s not always the case.

Certain fields use fact to mean an objective truth. The endeavor of science gets us ever closer to this truth, and many of the shifts in what we know occur only at the fringes of discovery, and are due to our continuous approach to truth. However, I am choosing to use
fact
in a looser fashion, simply to refer to our individual states of knowledge awareness. This can refer to a scientific fact, even if it might eventually be disproved, or even to a less ambiguous sort of fact, such as the current fastest human runner or the most powerful computer, which are facts about our surroundings.

This will not satisfy everyone, but there are two reasons for this choice. The first is to avoid being drawn down some sort of epistemological rabbit hole, which is likely to be more than a little confusing. To paraphrase Justice Potter Stewart, many of us know a fact when we see one. But second, and more important, it turns out that lots of different types of knowledge change in similar ways. While some facts are about approaching truth and some are about our changing surroundings, we can only see the similarities clearly in how they operate by bundling all of these types of facts together. (See
Notes
for further discussion.)

And there’s one simple way to organize facts, even before we
understand all the math and science behind how knowledge changes. We can organize what we know by the rate at which it changes.

Imagine we have all the facts in the world—those pieces of knowledge that contain all that we know—lined up according to how often they change. On the far left we have the fast-changing facts, the ones that are constantly in flux. These are things such as what the weather will be tomorrow or what the stock market close was yesterday. And on the far right we have the very slow-changing facts, the ones that for all practical purposes are constant. These are facts such as the number of continents on the planet or the number of fingers on a human hand.

In between we have the facts that change, but not too quickly—and are therefore that much more maddening to deal with. These facts might change over the course of years or decades or a single lifetime. How many billions of people are on the planet is one of these. I learned five billion in school, and we just recently crossed seven billion, as of 2012. My grandfather, who was born in 1917, learned there were fewer than two billion. The number of planets outside the solar system that have been discovered, or, for that matter, the number of planets in our own solar system, is also in this category. What we know about dinosaurs is in this group of facts, as is the average speed of a computer. The vast majority of what we know seems to fall into this category, which I call
mesofacts
—facts that change at the meso-, or middle, timescale.

Lots of our scientific knowledge consist of mesofacts. For example, the number of known chemical elements is a mesofact. If, as a baby boomer, you learned high school chemistry in 1970, and then, as we all are apt to do, did not take care to brush up on your chemistry periodically, you would not realize that there are at least 12 new elements in the periodic table, bringing the total up to 118. Over a tenth of the elements have been discovered since you graduated high school. And all that dinosaur knowledge I’ve mentioned is also made up of mesofacts.

Technology is full of mesofacts too, from the increase in
transportation speeds to the changes in how we store information—from floppy disk to the cloud. The height of the tallest sky-scraper has also steadily increased over time due to improving technology.

World records are constantly being broken in the realms of human ability, and we recently have begun to be humbled by machines, as they rack up wins against us in more and more games once deemed too complex for computers, from Othello and checkers to chess. All mesofacts.

Mesofacts are all around us and just acknowledging their existence is useful. It can help eliminate part of the surprise in our lives.

If my grandfather had been told in dental school that a specific fraction of the knowledge he learned there would become obsolete soon after he graduated, this could at least provide an anchor for his uncertainty. It would prevent dentists of his generation from being surprised by basic biological facts, or from working with outdated knowledge. In fact, many medical schools now do this: They embrace the mesofacts of medicine, teaching physicians that changing knowledge is the rule rather than the exception.

But simply knowing that knowledge changes like this isn’t enough. We would end up going a little crazy as we frantically tried to keep up with the ever-changing facts around us, forever living on some sort of informational treadmill. But it doesn’t have to be this way, because there are patterns: Facts change in regular and mathematically understandable ways. And only by knowing the pattern of our knowledge’s evolution can we be better prepared for its change.

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THERE
are mathematical regularities behind the headlines of changing scientific knowledge. We accumulate scientific knowledge like clockwork, with the result that facts are overturned at regular intervals in our quest to better understand the world. Similarly, the growth and change of technological knowledge, from processing
power to information storage, are also part of the universe of facts that change with regularity. And of course these two areas—science and technology—affect many other factual aspects of our lives: from the spread of disease, to how we travel, and even to the increase in computer viruses on the Internet. All of these areas of knowledge change systematically.

But just as the creation of facts operates according to certain scientific principles, so too does the spread of knowledge; how each of us hears of new information, or how error gets dispelled, adheres to the rules of mathematics. And due to a new understanding of cognitive biases, much of what each of us knows, even as it changes, now has a clear structure: These shifts obey certain scientific patterns that are explicable by findings in cognitive science.

This is not to say that we can understand everything. Much in the world is shocking and unexpected, and we still have to deal with these new facts when we become aware of them. But by and large there are ways to understand how our knowledge changes, ways to bring order to the chaos of ever-changing facts.

William Macneile Dixon, a British professor of literature in the late nineteenth and early twentieth centuries, once wrote, “The facts of the present won’t sit still for a portrait. They are constantly vibrating, full of clutter and confusion.”

We now understand how vibrations work, due to physics. We’re no longer confused by the fact that plucking a guitar string somehow gives rise to order and music. It’s time we do the same thing for the fluctuations in what we know as well, and recognize that there’s an order to all of our changing knowledge. This book is a guide to the science behind the vibrations in the facts around us.

WHEN
Derek J. de Solla Price arrived at Raffles College (now the National University of Singapore) to lecture on applied mathematics in 1947, he did not intend to spearhead an entirely new way of looking at science. But his plans to continue research in physics and mathematics were altered by the construction on the college library. Since Raffles was a small university, the library was actually giving books out to students and faculty to store in their dormitories and apartments while the construction was under way.

Price ended up with a complete set of
Philosophical Transactions
of the Royal Society of London, a British scientific journal that dates back to 1665. Once home, he stacked the journals chronologically against the walls in his apartment: Each pile was published later than the one before it, and they were all lined up one after another. One day, while idly looking at this large collection of books that the library had foisted upon him, he realized that the heights of the piles of these bound volumes weren’t all the same. But their heights weren’t random either. Instead, he realized, the heights of the volumes fit a specific mathematical shape: an exponential curve. Price’s simple observation was the origin of a sophisticated quantitative theory for how scientific knowledge advances.

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MOST
of our everyday lives revolve around linear growth, or changes that can be fit onto a line. When something increases by the same amount each year, when the rate is constant, we get linear growth. When we drive somewhere, and go at the same speed the entire way, a chart showing the distance we’ve traveled over time follows a straight line. And if we have a machine that builds widgets at a constant rate of three per hour, the number of widgets after a given number of hours grows linearly with the number of hours we’re considering.

Due to how easy it is to imagine (and our brains seem particularly well suited to this type of thinking), we often think in terms of linear growth. If the temperature was sixty-five degrees yesterday, and sixty degrees the day before that, it is not surprising if we expect it to be about seventy degrees today.

But there are many examples of change that occur differently. If you were watching when the sun set over the course of a few days early in the summer, it wouldn’t be unreasonable to expect the sunset’s timing to follow a nice linear curve: Each day the sun sets the same number of minutes later than it did the day before. But it turns out that sunsets at a specific location adhere to a sine curve—a wavelike shape that looks like a rope being shaken up and down, a shape that we aren’t particularly intuitive about. During the solstices—the shortest and longest days of the year—we are at the top or bottom of the wave, when the sunset only varies by a small amount each day; during the equinoxes (spring and fall), we are in the steep parts of the wave, and each day the sunset time is many minutes different from the day before. This is far from a curve that we can think about easily.

We are just as ill suited when it comes to noticing the many changes that adhere to exponential growth. When we encounter exponential curves all around us, we often don’t think about it this way at all, because it is harder to picture. Exponential growth is when something increases by the same fraction or percentage,
rather than the same amount, each second or minute or hour. If bacteria double every hour, that’s exponential growth, because they’re growing at a constant rate of 200 percent an hour. Compound interest is the same sort of thing: If our money grows by a certain percentage each year, we can describe this growth by an exponential curve.