The Half-Life of Facts
The Half-Life of Facts

The Half-Life of Facts

We can measure the amount of time for half of a subject’s knowledge to be overturned. (Location 92)

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. (Location 107)

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. (Location 132)

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 (Location 134)

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. (Location 136)

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. (Location 142)

They embrace the mesofacts of medicine, teaching physicians that changing knowledge is the rule rather than the exception. (Location 155)

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. (Location 156)

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. (Location 158)

We accumulate scientific knowledge like clockwork, with the result that facts are overturned at regular intervals in our quest to better understand the world. (Location 161)

are also part of the universe of facts that change with regularity. (Location 163)

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. (Location 163)

Instead, he realized, the heights of the volumes fit a specific mathematical shape: an exponential curve. (Location 184)

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. (Location 187)

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. (Location 200)

Science can develop only as quickly as we can figure out things about the world. Grand opera, however, is not limited by what is true, only by what is beautiful, and should therefore be able to grow more rapidly, since it doesn’t have to be rigorously subjected to experimentation. (Location 257)

The closer two people are, the higher the impact of the research that results from that collaboration. They found that just being in the same building as your collaborators makes your work better. (Location 276)

The more important a work is, the more likely it is to be referenced in many other papers, implying that it has had a certain foundational impact on the work that comes after it. (Location 278)

By examining the average number of times articles in a given journal are cited, we can get what is known as the impact factor (Location 285)

The journals with the highest impact factors have even penetrated the public consciousness—no doubt due to the highly cited individual papers within them (Location 287)

this can vary from field to field, but Zuckerman took it as a useful rule of thumb. What she found was that Nobel laureates are first authors of numerous publications early in their careers, but quickly begin to give their junior colleagues first authorship. And this happens far before they receive the Nobel Prize. (Location 308)

By their forties, Nobel laureates are first authors on only 26 percent of their papers, as compared to their less accomplished contemporaries, who are first authors 56 percent of the time. (Location 313)

is even a Web site named TheoryMine to which anyone can go and get a novel mathematical theorem created by a sophisticated computer program that automatically generates a mathematical proof and have it named after you or a loved one. (Location 332)

The principle is rather elegant. While computers are good at lots of things, from adding numbers to counting words in a document, they are often very bad at many simple things: We (Location 336)

Simple tasks are given to lots of people to perform, often either for a small amount of money or because someone has cleverly hidden the task in a game. One of the most well-known examples of these are the distorted (Location 339)

Several intrepid scientists turned a fiendishly difficult problem—how to predict what shapes proteins will fold into based on their chemical makeup—into a game. They found that the best players of a simple online game known as Foldit are actually better than our best computers. (Location 347)

knowledge. So, in truth, the facts that are changing are not changing simply without the involvement of the general population. We are part of the scientific process now. Each of us, not just scientists, inventors, or even explorers, are able to be a part of the process of creating knowledge. (Location 350)

Eurekometrics is about studying scientific discoveries themselves. More traditional scientometric approaches that use citations are still very important. They can teach us how scientists collaborate, measure the impact of scientific research, and chart how scientific knowledge grows, but they often tell us nothing about the content of the discoveries themselves, or their properties. (Location 358)

One simple example of eurekometrics—and one that I was involved in—is examining how discoveries become more difficult over time. (Location 362)

Each dataset adhered to a curve with the same basic shape. In every case, the ease of discovery went down, and in every case, it was an exponential decay. (Location 379)

For example, the sizes of asteroids discovered annually get 2.5 percent smaller each year. In the first few years, the ease of discovery drops off quickly; after early researchers pick the low-hanging fruit, it continues to “decay” for a long time, becoming slightly harder without ever quite becoming impossible. (Location 381)

In fact, I only know of one area where scientific research has exhausted all discoveries: the “field” of the discovery of new major internal organs. (Location 390)

For example, in pharmaceutical research, drug companies counter the decreasing number of drugs created per dollar spent by pouring more money into drug discovery. (Location 407)

Some scientists arrive at new discoveries without a significant investment in resources by becoming more clever and innovative. (Location 410)

When one area of research becomes difficult, the scientists in that field either rise to the challenge by investing greater effort or shift their focus of inquiry. Physicists have moved into biology, raising new questions that no one had thought to ask before. (Location 413)

But the impossible had been done: A supposedly extinct species had been discovered alive and well. (Location 445)

Then they checked to see how many were eventually recategorized as nonextinct. The answer: More than a third of all mammals that allegedly were lost to time in the past five hundred years have since been rediscovered. (Location 451)

AS scientific knowledge grows rapidly, it leads to a certain overturning of old truths, a churning of knowledge. While this churning is hard to deny—recall my inability to recall the health benefits of red wine despite having seen it in the newspapers many times—it is difficult to measure. (Location 456)

They found something striking: a clear decay in the number of papers that were still valid. (Location 463)

Medical knowledge about cirrhosis or hepatitis takes about forty-five years for half of it to be disproven or become out-of-date. (Location 466)

But ultimately, while we can’t predict which individual papers will be overturned, just like we can’t tell when individual radio active atoms will decay, we can observe the aggregate and see that there are rules for how a field changes over time. (Location 480)

addition, these results are nearly identical to a similar study that examined the overturning of information in surgery. Two Australian surgeons found that half of the facts in that field also become false every forty-five years. (Location 483)

takes 50 years to get a wrong idea out of medicine, and 100 years a right one into medicine.” (Location 486)

One simpler way to do this is by looking at the lifetime of citations. As mentioned before, citations are the coin of the scientific realm and the metric by which we measure the impact of a paper. (Location 493)

Their libraries were being inundated. They needed ways to figure out which volumes they could safely discard. If they knew the half-life of a book or article’s time to obsolescence, it would go a long way to providing a means to avoid overloading a library’s capacity. (Location 504)

The story of why facts get overturned—sloppy scientists or something else?—is for chapter 8, and has to do with how we do science and how things are measured. But shouldn’t the very fact that most scientific knowledge decays be somewhat distressing? It’s one thing to be told that a food is healthy one day and a carcinogen the next. But it’s something else entirely to assume that basic tenets of our scientific framework—gravity, genetics, electromagnetism—might very well be wrong and can possibly be part of the half-life of knowledge. (Location 529)

It’s not that when a new theory is brought forth, or an older fact is contradicted, what was previously known is simply a waste, and we must start from scratch. Rather, the accumulation of knowledge can then lead us to a fuller and more accurate picture of the world around us. (Location 554)

While they explain a good fraction of what’s out there, there is a long tail of smaller movies or cities that exist and are still important. Understanding how they are distributed can give us a better picture of how the world consumes popular culture or lives in cities. (Location 596)

As mentioned earlier, when a field is young the discoveries come easily, and they are often the ones that explain a lot of what is going on—or, in the case of species, are the really big ones. (Location 598)

So what we’re really dealing with is the long tail of discovery. Our search for what’s way out at the end of that tail, while it might not be as important or as Earth-shattering as the blockbuster discoveries, can be just as exciting and surprising. (Location 602)

Clearly our technological knowledge changes rapidly, and this shouldn’t surprise us. But in addition to our rapid adaptation to all of the change around us—which I address in chapter 9—what should surprise us is that there are regularities in these changes in technological knowledge. (Location 634)

He didn’t arrive at this conclusion through exhaustive amounts of data gathering and analysis; in fact, he based his law on only four data points. (Location 646)

Moore’s Law becomes the latest in a long line of technical rules of thumb that explain extremely regular change in technology. (Location 656)

By lining up one technology after another, one thing becomes clear: Despite the differences among all of these technologies—human brains, punch cards, vacuum tubes, integrated circuits—the overall increase in humanity’s ability to perform calculations has progressed quite smoothly and extremely quickly. Put together, there has been a roughly exponential increase in our information transformation abilities over time. (Location 671)

It might be better than what is currently in use, but it is clearly a work in progress. This means that the new technology is initially only a little bit better. As (Location 677)

But then a limit is reached. And when that limit is reached there is the opportunity to bring in a new technology, even if it’s still tentative, untested, and buggy. (Location 680)

At first, as they gobble the nutrients in the dish, they obey the doubling and rapid growth of the exponential curve. (Location 683)

No one has it yet, so its usage can only grow. As people begin to buy the newest Apple device, for example, each additional user is gained faster and faster, obeying an exponential curve. But of course this growth can’t go on forever. (Location 692)

These curves are also often referred to as S-curves, due to their stretched S-like shapes. (Location 695)

IN chapter 8, I explore how advances in measurement enable the creation of new facts and new knowledge. But one fundamental way that measurement is affected is through the tools that we have to understand our surroundings. (Location 723)

These technological doublings in the realm of science are actually the rule rather than the exception. (Location 738)

Even the field of neuroscience is able to move forward at a pace similar to Moore’s Law: The technological advances related to recording individual neurons have been growing at an exponential pace. Specifically, the number of neurons that can be recorded simultaneously has been growing exponentially, with a doubling time of about seven and a half years. (Location 741)

sciences. Technology, in its broadest sense, is the process by which we modify nature to meet our needs and wants. (Location 749)

Henry Petroski, a professor of engineering and history at Duke University, puts it even more succinctly: “Science is about understanding the origins, nature, and behavior of the universe and all it contains; engineering is about solving problems by rearranging the stuff of the world to make new things.” (Location 751)

But not only isn’t it always clear which one occurs first, it is just as often the case that it’s difficult to distinguish between scientific and technological knowledge. Iron’s magnetic properties demonstrate this well. (Location 757)

However, soon the limits of these approaches became evident, and the discoveries slowed. But, following a Moore’s Law–like trajectory, a new technology arose. (Location 777)

Technological growth facilitates changes in facts, sometimes rapidly, in many areas: sequencing new genomes (nearly two hundred distinct species were sequenced as of late 2011); finding new asteroids (often done using sophisticated computer algorithms that can detect objects moving in space); even proving new mathematical (Location 781)

theorems through increasing computer power. (Location 783)

Sometimes they have the potential for fundamentally changing the very nature of humanity. We can see the true extremes of the possibilities of change in the facts of technology by focusing on our life spans. (Location 810)

If this acceleration continues, something curious will happen at a certain point. When we begin adding more than one year to the expected life span—a simple shift from less than one to greater than one—we get what is called actuarial escape velocity. (Location 815)

THERE are those who, when confronted with regularities such as Moore’s Law, feel that these are simply self-fulfilling propositions. (Location 844)

The Hawthorne effect was defined as “an increase in worker productivity produced by the psychological stimulus of being singled out and made to feel important.” While (Location 855)

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. (Location 862)

Koh and Magee argue that we should imagine that the magnitude of technological growth is proportional to the amount of knowledge that has come before it. The more preexisting methods, ideas, or anything else that is essential for making a certain technology just a little bit better, the more potential for that technology to grow. (Location 866)

proportional to its current size gets exactly what we hoped for: exponential growth. What this means is that if technology is essentially bootstrapping itself, much as science does, and its growth is based on how much has come before it, then we can easily get these doublings and exponential growth rates. (Location 870)

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. But let’s see where Kremer’s math takes us. (Location 903)

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. (Location 908)

In physics, a simple model that explains the largest amount of the system being studied is often termed a first-order model. (Location 922)

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. (Location 927)

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. (Location 935)

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. (Location 952)

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. (Location 964)

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. (Location 971)

Berlin’s general shape was dictated by the development of ever more powerful technologies. (Location 973)

the distance reachable by current technologies in thirty minutes or less. (Location 974)

All of these facts, ever changing, are subject to the rules of technological change. Ultimately, each often follows its own mini–Moore’s Law. (Location 980)

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. (Location 996)

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. (Location 1014)

But why does knowledge spread unevenly? Certainly geography is one component: People within reach of the telegraph knew about Lincoln’s election much more quickly than those in California, and the closer you were to Washington, D.C., the sooner you knew about the end of the War of 1812. But does that fully explain it, or are there other factors? (Location 1055)

used metallurgical developments to create metal type that not only had a consistent look (Gutenberg insisted on this), but type that could be easily cast, allowing whole pages to be printed simply at once. He used chemical innovations to create a better ink than had ever been used before in printing. Gutenberg even exploited the concept of the division of labor by employing a large team of workers, many of whom were illiterate, to churn out books at a rate never before seen in history. (Location 1076)

This is the rule when it comes to how facts spread: social networks spread information. Of course, back in the day of the printing press, geography and social connectivity were harder to disentangle. (Location 1092)

understand how social groups are distributed across countries, and even how we make and break friendships over time. In these ways, and many more, we are beginning to truly understand the social structures that we are embedded in, and how these ties influence us. (Location 1113)

Therefore, much of a social network should consist of clusters of tightly knit groups that are connected by their strong ties into little triangles. But these tight-knit groups are occasionally connected to other strong clusters by weak ties. (Location 1138)

Of those who said they got a job through personal contacts, he found that most of these personal contacts were quite “weak.” (Location 1144)

When they tested the network and ran this experiment, they discovered that weak ties aren’t that important to spreading knowledge. While weak ties do in fact hold the network together, much as Granovetter suspected, they aren’t integral for spreading facts. Weak ties, while bringing together disparate social groups, aren’t strong enough to spread anything effectively. (Location 1157)

So Granovetter wasn’t quite right. Ultimately it’s the medium-strength ties that are the most important. They are that happy medium between ties that are too weak to spread anything and those too strong to be found in anything but socially (and informationally) inbred groups. (Location 1162)

even discovered that Popeye seems to have eaten spinach not for its supposed high quantities of iron, but rather due to vitamin A. While the truth behind the myth is still being excavated, this misinformation—the myth of the error—from over thirty years ago continues to spread. (Location 1246)

Michael Mauboussin, the chief investment strategist of Legg (Location 1250)

The problem was, when Mauboussin tried it, it didn’t work. It turned out that his source was riddled with errors, ranging from one number that was ten times too small to another that contained a rounding error, completely changing the meaning of the equation. Only when Mauboussin tracked down the original scientific paper did he find the correct version. (Location 1252)

One good rule of thumb when examining how errors propagate over time is to look for a simple phrase: contrary to popular belief. (Location 1259)

myself was a victim when I actually propagated the myth that a frog, if boiled slowly, will not jump out of a pot. I mentioned this in passing in the Boston Globe, using it to explain how people don’t notice factual change if it happens slowly. (Location 1289)

The group of chemical machines responsible for duplicating a strand of DNA occasionally makes mistakes. That’s what canmake up a mutation: an incorrect copying, or even a piece of DNA getting hit by a cosmic ray. However it happens, some error is introduced into the sequence. (Location 1316)

There is a common scribal error known by the Greek term homeoteleuton. This refers to a type of deletion, in which there are two identical word phrases separated by some other text and the scribe accidentally skips to the second phrase without transcribing the intervening portion, including the first instance of the phrase. For example, there is a verse at the end of the creation story in Genesis that reads, (Location 1324)

Simkin and Roychowdhury conclude, using some elegant math, that only about 20 percent of scientists who cite an article have actually read that paper. This means that four out of five scientists never take the time to track down a publication they intend to use to buttress their arguments. (Location 1362)

Too often not knowing where one’s facts came from and whether it is well-founded at all is the source of an error. We often just take things on faith. (Location 1404)

The spirit that infused this time period brought forth a whole host of new knowledge, and the disproving of facts that had existed for centuries, if not millennia. The Scientific Revolution has made the swift changes in modern-day knowledge possible. (Location 1408)

Many of the papers presented in the early years at the Royal Society were devoted to trying to understand errors, to root out misunderstandings, or to test the veracity of tales told to them that often seemed too good to be true. (Location 1410)

One’s knowledge is dependent upon it being knowable to you specifically, on it having been spread to you. As we’ve seen, this spread relies on social networks, and sometimes on the all-too-human tendency to corrupt information as it spreads. But as long as we remain true to the spirit of the Scientific Revolution, by not taking things on faith and by spreading true facts, we are far from being overwhelmed with error. (Location 1418)

As a researcher, he is fond of the unexpected hypothesis and the counterintuitive concept. (Location 1426)

He realized that while an expert might solve a hard problem 20 percent of the time, simply giving it to five experts won’t always yield results. There’s a good chance that all the experts will fail. (Location 1429)

Perhaps, Bingham argued, there was a “long tail of expertise” (his term, not mine) of lots of people who are all interested in solving a technical problem but each of whom has a very small chance of success. (Location 1431)

Instead of working in the same area for a quarter of a century, you can open up the question to a larger group and get an answer from an unexpected source. And more important, an unexpected field. (Location 1445)

My father is not a neurologist, nor does he have any specialized knowledge in the area of neurodegenerative diseases. However, he is an expert in something else: undiscovered public knowledge. (Location 1459)

Similarly, there is often knowledge that is in fact hidden in plain (Location 1468)

It’s one thing for a result to be ignored—that’s a specific instance of this sort of knowledge, which will be discussed later. (Location 1470)

Building on this, Swanson continued to develop methods of combing through the newly digitized literature. He expanded his use of MEDLINE, an online database run by the National Library of Medicine, which is housed at the National Institutes of Health. MEDLINE allowed Swanson to search rapidly for medical key words, and then to combine research that had remained separate. In the late 1980s, such databases were still in their relative infancy, but Swanson recognized their potential. (Location 1480)

These scientists had found that, even though this was a neurological disease, it could affect other parts of the body, including the skin. My father realized that this was the critical clue. (Location 1495)

Prize money in hand, my father went to researchers at the dermatology and neurology departments of Columbia University and suggested that they all collaborate on testing his hypothesis. They conducted a pilot study with ALS patients, and it seems that my father’s undiscovered public knowledge was right: There are quantitative changes as the patients got sicker. (Location 1500)

ONE of the most fundamental rules of hidden knowledge is the lesson learned from InnoCentive: a long tail of expertise—everyday people in large numbers—has a greater chance of solving a problem than do the experts. (Location 1512)

But while prizes help tease out innovations and ideas that would otherwise remain hidden and accelerate the pace of knowledge diffusion, hidden facts unfortunately remain a far too common part of how knowledge works. (Location 1525)

But knowledge can be hidden for other reasons. There are occasions in science when knowledge is hidden because it is so far ahead of its time. (Location 1560)

THERE is a rule in online circles known as Godwin’s law. It states that as the length of an Internet discussion approaches infinity, the probability that someone will be compared to Hitler or the Nazis approaches one. (Location 1562)

related to grain and baked goods, produced a variety of unbelievable innovations in mathematics and physics. Two of his contributions are known as Green’s theorem and Green’s functions, the latter of which are complex enough to vex many mathematicians and physicists. (Location 1572)

But however Green learned advanced mathematics, Einstein once remarked that Green’s contributions were decades ahead of what was expected. As a result of his work being so ahead of its time, and coming from far outside the mainstream, Green’s work was almost completely unknown until after his death in 1841. (Location 1578)

There are many instances when knowledge is not recognized or not combined, because it’s created by people who are simply too far ahead of their time, or who come from backgrounds that are so different from what is traditionally expected for scientific insight. (Location 1581)

facts can remain hidden for a long time, whether the problem is because they are very advanced or because they come from a different discipline. But is there a way to measure this? Specifically, how often is knowledge skipped over? (Location 1588)

Based on everything I’ve mentioned so far, the answer likely will be no. But then, what fraction of the time do we ignore (or simply don’t know about) what has come before us? (Location 1593)

Meta-analysis is a well-known technique that can be used to extract more meaning from specific papers than could be gained from looking at each one alone. A meta-analysis combines the results of papers in a specific area in order to see if there is a consensus or if more precise results can be found. They are like the analyses of thermal conductivity for different elements mentioned in chapter 3, which use the results from lots of different articles to get a better picture of the shape of what we know about how these elements conduct heat. (Location 1600)

The more papers in the field, the smaller the fraction of previous papers that were quoted in a new study. (Location 1607)

The newer ones are far more likely to be mentioned. This shouldn’t be surprising after our discussion of citation decay and obsolescence in chapter 3. And it is hardly surprising that scientists might use the literature quite selectively, perhaps to bolster their own research. But when it comes to papers that are current, relevant, and necessary for the complete picture of the current state of a scientific question, this is unfortunate. (Location 1609)

This type of analysis is known as cumulative meta-analysis. What Lau and his colleagues realized was that meta-analyses can be viewed as a ratchet rather than simply an aggregation process, with each study moving scientific knowledge a little closer to the truth. (Location 1627)

In the fall of 2010, a team of scientists in the Netherlands published the first results of a project called CoPub Discovery. Their previous work had involved the creation of a massive database based on the co-occurrence of words in articles. If two papers both have the terms p53 and oncogenesis, for example, they would be linked more strongly than words with no two key terms in common. (Location 1640)

This type of program has provided a foundation for other automated proof systems, such as TheoryMine, briefly mentioned in chapter 2, which names a novel, computationally created and proved theorem after oneself or a friend, for a small price. (Location 1680)

Eureqa takes in a vast quantity of data points. Let’s say you’re studying a bridge and trying to understand why it wobbles. Or an ecosystem, and how the relative amounts of predators and prey change over time. You dump all the data you’ve collected into Eureqa—how many predators there are on each day, as well as the quantity of prey, for example—and it attempts to find meaning. (Location 1689)

In addition, he calculated the half-lives of these books: how long they would last before the destruction of half of the copies. He found that the half-lives were between four and nine centuries, a surprisingly long time. Cisne was able to conclude that most documents from the early Middle Ages, and perhaps even antiquity, have, in fact, survived. We have certainly lost a great deal; time ravages much knowledge. But when it comes to hidden knowledge, it’s heartening to know that many facts aren’t lost to history; they can indeed be discovered. (Location 1738)

Tools related to hidden knowledge are being created for everyone, enabling a certain renaissance in the discovery of knowledge; facts can be spread and mixed in novel ways, unburied and shown the sunlight. One of these tools is Mendeley, which is designed for the average scientist. (Location 1747)

WHEN facts change we can often anticipate the speed at which the change occurs. Populations grow according to certain rules, medical knowledge accumulates in a regular fashion, and new technologies allow us to do things at faster and faster rates—but all in a way that is well understood and regular. (Location 1813)

The iPhone appeared so rapidly in the world of technology that executives from a rival company thought many of its claimed specifications were lies, and Marc Andreessen has argued that it’s as if it appeared from the future, incredibly ahead of its time. (Location 1817)

Astonishingly enough, there is in fact an order to these rapid shifts in our knowledge. We can find regularities in them, and sometimes even predict them before they happen. (Location 1820)

In general, through a small change of an underlying parameter, such as temperature, we get a small change in the overall properties of what we’re looking at. Warm a cup of water by a small amount and it becomes a bit hotter. (Location 1826)

But as the system cools down, things start becoming more clumpy, because now neighboring cards are affected when a card is flipped. So whole patches of cards can change color quite rapidly. (Location 1861)

In the Ising model, we change something slowly and continuously—temperature—and this change yields a sudden jump in something else: the state of the system, from gas to solid, for example. In the world of facts, this sort of thing can also happen: A sudden jump in our knowledge might be due to some other facts changing and being slowly accumulated. But this still sounds very abstract; how might this work in practice? (Location 1872)

In fact, it’s not even the few missions just prior to the moon landing that could help explain the transition; hundreds of years of smooth data can actually be used to explain this steady march. (Location 1884)

If they extrapolated the exponential curve outward, the data showed that speeds necessary to leave the Earth’s surface could be reached within four years! A curve had implied the existence of the first artificial satellite well before Sputnik’s launch, and exactly as predicted (Sputnik went into orbit on October 4, 1957). (Location 1887)

What this means is that the factual phase transition of the moon landing was long in the cards—it was simply due to a steady change in the underlying speeds we could achieve. (Location 1892)

These steady progressions are the underlying slow temperature changes that result in the fast phase transition that we see when looking at everything from a different scale. (Location 1904)

In fact, this upward trend conformed to our old friend the logistic curve. Just as scientific output in general fits exponential and logistic curves, the march toward the discovery of a potentially Earth-like planet fits one of these omnipresent functions as well. (Location 1929)

SOMETIMES, though, it’s not that easy to determine the underlying change and see when a phase transition will happen. Even so, there are still mathematical regularities to how sudden changes in our knowledge occur, at least in the aggregate. One of these areas is in the proof of mathematical concepts. (Location 1953)

So while I can’t know exactly when any individual problem will be solved in advance, I can look at the aggregate of hard problems and see if there are any regularities. In doing this we can begin to put some bounds on our uncertainty about solving hard problems. (Location 1995)

RECENTLY, physicists have begun to take mathematical tools from their own field and apply them to understanding the relationship between the populations of cities and how they use energy and produce new ideas. (Location 2011)

But infinite growth can’t happen, either for organisms (cancer eventually overwhelms its own resources) or for cities. For cities, then, the only way to not be overwhelmed by this infinite growth is to undergo what the researchers deemed paradigmatic innovations, essentially to reset the parameters of growth. (Location 2025)

In past years these innovative resets occurred every few hundred years, and for any single person, these large-scale changes in facts were manageable. But no longer; we are living during the first time in history when multiple rapid changes can occur within a single human lifetime. (Location 2030)

The world around us seems to be ever poised on the edge of some rapid shift in facts and knowledge. A small change can cause a large shift in our knowledge at any moment. (Location 2040)

In 1987, they published a simple mathematical model that aimed to understand why small changes can yield a system that is always on the verge of large shifts. (Location 2047)

turns out that this sort of system, one that organizes itself to always be at the edge of a total avalanche, is the hallmark of actual systems we find in the real world, perhaps even including the world of knowledge. While a bit overly metaphorical, a world with the constant potential for rapid knowledge change would look just like ours. (Location 2054)

We understand how they behave in the aggregate, through the use of probability, but we can also predict these changes by searching for the slower, regular changes in our knowledge that underlie them. (Location 2061)

making its location also a mesofact, one of those slowly changing pieces of knowledge. (Location 2090)

From the incorrect number of chromosomes to the misclassification of species, our increased preoccupation with measuring our surroundings allows us to both increase our knowledge and find opportunities in which large amounts of our knowledge will be overturned. (Location 2110)

However, we were also taught that the number of neutrons in each atom can vary. If an element, as defined by the number of protons, can have different numbers of neutrons in its nucleus, these different versions are known as isotopes. (Location 2226)

Anytime a scientist tries to discover something new or validate an exciting and novel hypothesis, she tests it against something else. Specifically, our scientist tests it against a version of the world where the hypothesis would not be true. (Location 2247)

Enter p-values. Using sophisticated statistical analyses, we can reduce this complicated question to a single number: the p-value. This provides us with the probability (Location 2258)

His 2005 paper in the journal PLoS Biology was titled “Why Most Published Research Findings Are False.” As of late 2011, it has been viewed more than four hundred thousand times and cited more than eight hundred times. (Location 2345)

But this is absurd. Prior to the testing of a hypothesis, there is a certain expectation of what might happen. As another scientist interviewed by The Daily Show stated, there is a 0 percent chance of the earth being destroyed, based on what we already know about the fundamental laws of physics and how particle accelerators work. (Location 2354)

Ioannidis then uses this ratio, along with something known as our hypothetical experiment’s discriminating power—a number that encapsulates the ability of the experiment to actually yield a positive result—to calculate whether the experimental result is valid. (Location 2362)

ONE simple way to minimize a lot of this trouble is through replication, measuring the same problem over and over. Too often it’s much more glamorous to try to discover something new than to simply do someone else’s experiment a second time. In addition, many scientists, even those who want to replicate findings, find it difficult to do so. Especially when they think a result is actually wrong, there is even more of a disincentive. (Location 2384)

But none of those critics had actually tried to replicate the initial results. That would take months of research: getting the bacteria from the original team of scientists, rearing them, setting up the experiment, gathering results and interpreting them. Many scientists are leery of spending so much time on what they consider a foregone conclusion, and graduate students are reluctant, because they want their first experiments to make a big splash, not confirm what everyone already suspects. (Location 2389)

Science is not always cumulative, as the philosopher of science Thomas Kuhn has noted. There are setbacks, mistakes, and wrong turns. Nonetheless, we have to distinguish the core of science from the frontier, terms used by SUNY Stony Brook’s Stephen Cole. (Location 2414)

it’s unlikely that the basic mechanism of encoding genes in DNA is some sort of mesofact. (Location 2417)

That’s where the scientists live, and in truth, that’s where the most exciting stuff happens. The frontier is often where most scientists lack a clear idea of what will become settled truth. (Location 2422)

The errors at the frontier are many, from those due to measurement or false positives, to everything else that this book has explored. But it’s what makes science exciting. Science is already a terribly human endeavor, with all the negative aspects of humanity. But we can view all of this uncertainty in a positive light as well, because science is most thrilling and exciting when it’s unsettled. (Location 2429)

Mueller compiled all of the data since 1946 from a variety of sources and showed that, after an increase from the beginning of the data set until the end of the Cold War, the number of wars has plummeted precipitously. He also showed that the vast majority of wars are civil wars. (Location 2442)

There is a burgeoning group of scientists who use such data, which has been derived through careful measurement, to discover whole new ways of thinking about our world. The patron saint of this kind of careful measurement is Francis Galton. (Location 2447)

Soon he was involved in fields ranging from biology and mathematics to photography and anthropology, making numerous contributions in each of these areas. (Location 2453)

Galton was not a man to shy away from data. While many of his results may no (Location 2466)

longer be accepted, he combined analysis and mathematical techniques to great effect, and in so doing, brought many new facts to light, facts that could only be learned through careful, exhaustive, tedious measurement. (Location 2466)

WHAT can be measured, and when, affects what can be learned. If we can’t measure something, this can actually create a bias in what we know. For example, in biology, there is something known as taxonomic bias. (Location 2483)

These were the easiest dinosaurs to find—the low-hanging terrible lizard fruit, as it were. They had the first-mover advantage in fossils, and have therefore gained an outsize share of our brains’ stock of dinosaur knowledge. (Location 2500)

MEASUREMENT is a double-edged sword. It can create errors where none existed before. It can lead us to information about certain topics more frequently than we might have expected, creating a sort of informational (Location 2504)

When John Maynard Keynes was asked about why he switched his position on monetary policy, he uttered the immortal, though likely apocryphal, bon mot: “When the facts change, I change my mind. What do you do, sir?” All too often, we don’t act like Keynes. (Location 2530)

becomes what we expect to be normal. This condition is known as shifting baseline syndrome, and it refers to how we become used to whatever state of affairs is true when we are born, or when we first look at a situation. Since we are only capable of seeing change over a single generation, if slow change occurs over many lifetimes, we often fail to perceive it. (Location 2536)

Why do we believe in wrong, outdated facts? There are lots of reasons. Kathryn Schulz, in her book Being Wrong, explores reason after reason why we make errors. Sometimes it has to do with our desire to believe a certain type of truth. (Location 2566)

What was the topic of this song? Cognitive bias. There is a whole set of psychological quirks we are saddled with as part of our evolutionary baggage. (Location 2574)

This is akin to Daniel Kahneman’s idea of theory-induced blindness: “an adherence to a belief about how the world works that prevents you from seeing how the world really works.” (Location 2607)

Confirmation bias is only one of many cognitive biases, and it is related to another problem of our mental machinery: change blindness. This refers to a quirk of our visual-processing system. When we concentrate on one thing or task very intently, we ignore everything else, even things that are important, or at the very least, surprising. (Location 2613)

I decided to conduct a simple experiment to actually get a handle on people’s factual inertia. To do this, I used a Web site created by Amazon called Mechanical Turk. The label Mechanical Turk derives from a well-known hoax from the eighteenth and nineteenth centuries. The Turk was a complex device that was displayed all throughout Europe. While appearing to be a chess-playing automaton, the Turk actually had a person in a hidden compartment, controlling the machine. (Location 2646)

As part of my scientific research, I’ve been part of a team that has developed software infrastructure for running online experiments to see how people cooperate in networks on Mechanical Turk. But due to this, I have also gained an appreciation for Mechanical Turk. To get a sense of people’s factual inertia, I thought it would be a good place to quickly survey a population about their beliefs and knowledge. (Location 2654)

But all of our earlier knowledge remains in stasis. Instead of it all growing and developing in a rigorous fashion, like whatever we choose to make our careers in, it generally stays the same. Unless we happen to stumble upon an article in a magazine or newspaper about a certain scientific finding, or unless something is so important and earth shattering that we can’t help but remark upon this new fact’s novelty, we remain stuck at the factual level of our grade-school selves. (Location 2682)

And these jumps occur at precise intervals: the length of a single human generation. (Location 2690)

we do return to the subject, if only when our own children have reached the same point. Rather than seeing these mesofacts change slowly, in a relatively smooth advancement of knowledge, you only encounter them in bursts, when the next generation does, such as when your child comes home and informs you that dinosaurs were warm-blooded and looked like birds. This generational knowledge appears staccato, even though the knowledge changes and accretes steadily. (Location 2694)

Of course, what generation means needn’t be literal, although it is often the case that the facts in our brain—and their lifetime—are tied to childbirth. We can also understand what a generation is more figuratively. For example, when it comes to university-specific knowledge, a generation time is far closer to four years than multiple decades, due to the turnover of students. Institutional memory, and its attendant facts and knowledge, are only as permanent as its generation time. (Location 2705)

We both were simply rejecting anything newer than our own childhood. Just as many of us only view “technology” as anything invented after we were born, we took our baseline—when we started playing with LEGO—as the way things should be in the realm of LEGO. (Location 2718)

Having more than a few contrarians keeps everyone honest. But it can also be very bad, as when people irrationally hold onto ideas for too long, refusing to admit the errors of their ways. (Location 2732)

Pritchett argues that a more apt way to describe how these ideas are adopted is that they often follow this trajectory: “Crazy. Crazy. Crazy. Obvious.” (Location 2738)

Kuhn argued that switching from one paradigm to another is a messy process and often involves scientists digging in their heels to the extent that their retirement or death—with their attendant replacement by younger and more open minds—might be required for the new paradigm to become accepted. (Location 2745)

Language is a complex mix of flux and stability. On the one hand, there is evidence that the frequencies of the sounds of consonants in Old English are by and large the same as those in modern English, even though we modern English speakers are separated from Old English by one thousand years. (Location 2783)

Most of the facts we have examined so far are either what we as a society think is true (as in scientific truth) or what is the current state of the world (such as the speeds of the fastest computers). (Location 2792)

We are often like objects being dragged through mud. We change, but slowly, and with the residue of where we came from upon us. (Location 2822)

was fascinated. Apparently there were linguistic equivalents to the Black Death, the Great Awakening, the Enlightenment, and the Industrial Revolution. When I looked more carefully, though, it wasn’t quite as dramatic as I first expected. (Location 2824)

Ultimately, the facts of language—in this case, the prescriptive rules that we learn as schoolchildren—are those that are based on our own language experiences. Just as we view technological innovation, facts about dinosaurs, and even the acceptability of different types of LEGO pieces with a perspective formed in the crucible of childhood, the same thing happens with language. (Location 2860)

On the other end of the spectrum there is the Long Now Foundation, which is geared toward fostering long-term thinking and awareness. They get people to think in terms of millennia, and are even constructing a clock out in the Texas desert. Designed to operate for ten thousand years. They also have a sporadically used news-clipping service that highlights articles that might be relevant centuries from now, as a way to keep on top of really big and important changes. (Location 2872)

There is a straightforward, though not always easy, solution to dealing with changing facts: constant education and the omnipresence of information. How each of us implements these rather difficult solutions is certainly a personal choice, but the following are a number of suggestions. (Location 2877)

Paradoxically, by not relying on our own memories, we become more likely to be up-to-date in our facts, because the newest knowledge is more likely to be online than in our own heads. Medicine has exploited this idea through a constantly updated online medical reference site called UpToDate; looking something up guarantees the most current information. (Location 2920)

As I mentioned in chapter 6, the innovative pace of cities is ever quickening. In order to continue growing, cities seem to actually require periodic drastic innovative reboots—from advanced sewage systems to building methods that allow for skyscrapers—that are happening more quickly. For the first time in human history these rapid changes are occurring multiple times in a single generation, and they don’t seem to be slowing down. (Location 2966)

The same sort of limits could be argued to hold with transportation speeds. We have had an astonishing sequence of technologies that have allowed us to go faster and faster, but an exponential pace doesn’t seem sustainable forever. While going to the moon for our lunch break sounds wonderful, it just isn’t likely. (Location 2983)

That being said, as humans we are very good at being pessimistic and underestimating our ability for continued innovation. Even though each individual technology might reach its limits, a new one comes along so often to innovate around these limits that the change around us might not be slowing down for a long time to come. (Location 2987)

albeit at a slower place, and we certainly do not seem to be leaving the exponential regime anytime soon. But even if everything continues to grow rapidly, there might be certain limits to how we perceive this change and adapt to it. (Location 2997)

However, as humans, we seem to have certain cognitive limits on what we can know and what we can handle in our daily lives. (Location 3013)

fast growth and culminating in what many would argue was the crossing of some sort of singularity threshold. In the case of Portugal, the country established a nearly globe-encompassing maritime empire, and in the case of clocks, timepieces became so advanced that measurement of time was far more precise than human perceptions. (Location 3047)

We are getting better at internalizing this. For example, many medical schools inform their students that within several years half of what they’ve been taught will be wrong, and the teachers just don’t know which half. But too often—whether because change is still too slow to notice or because of quirks in how we learn and observe our surroundings—we don’t really live our lives with the concept that facts are always changing. (Location 3060)