Understanding the concept of a half-life will change what you read and how you invest your time. It will explain why our careers are increasingly specialized and offer a look into how we can compete more effectively in a very crowded world.
A half-life is the time taken for something to halve its quantity. The term is most often used in the context of radioactive decay, which occurs when unstable atomic particles lose energy. Twenty-nine elements are known to be capable of undergoing this process. Information also has a half-life, as do drugs, marketing campaigns, and all sorts of other things. We see the concept in any area where the quantity or strength of something decreases over time.
Radioactive decay is random, and measured half-lives are based on the most probable rate. We know that a nucleus will decay at some point; we just cannot predict when. It could be anywhere between instantaneous and the total age of the universe. Although scientists have defined half-lives for different elements, the exact rate is completely random.
Half-lives of elements vary tremendously. For example, carbon takes millions of years to decay; that’s why it is stable enough to be a component of the bodies of living organisms. Different isotopes of the same element can also have different half-lives.
Three main types of nuclear decay have been identified: alpha, beta, and gamma. Alpha decay occurs when a nucleus splits into two parts: a helium nucleus and the remainder of the original nucleus. Beta decay occurs when a neutron in the nucleus of an element changes into a proton. The result is that it turns into a different element, such as when potassium decays into calcium. Beta decay also releases a neutrino — a particle with virtually no mass. If a nucleus emits radiation without experiencing a change in its composition, it is subject to gamma decay. Gamma radiation contains an enormous amount of energy.
The Discovery of Half-Lives
The discovery of half-lives (and alpha and beta radiation) is credited to Ernest Rutherford, one of the most influential physicists of his time. Rutherford was at the forefront of this major discovery when he worked with physicist Joseph John Thompson on complementary experiments leading to the discovery of electrons. Rutherford recognized the potential of what he was observing and began researching radioactivity. Two years later, he identified the distinction between alpha and beta rays. This led to his discovery of half-lives, when he noticed that samples of radioactive materials took the same amount of time to decay by half. By 1902, Rutherford and his collaborators had a coherent theory of radioactive decay (which they called “atomic disintegration”). They demonstrated that radioactive decay enabled one element to turn into another — research which would earn Rutherford a Nobel Prize. A year later, he spotted the missing piece in the work of the chemist Paul Villard and named the third type of radiation gamma.
Half-lives are based on probabilistic thinking. If the half-life of an element is seven days, it is most probable that half of the atoms will have decayed in that time. For a large number of atoms, we can expect half-lives to be fairly consistent. It’s important to note that radioactive decay is based on the element itself, not the quantity of it. By contrast, in other situations, the half-life may vary depending on the amount of material. For example, the half-life of a chemical someone ingests might depend on the quantity.
In biology, a half-life is the time taken for a substance to lose half its effects. The most obvious instance is drugs; the half-life is the time it takes for their effect to halve, or for half of the substance to leave the body. The half-life of caffeine is around 6 hours, but (as with most biological half-lives) numerous factors can alter that number. People with compromised liver function or certain genes will take longer to metabolize caffeine. Consumption of grapefruit juice has been shown in some studies to slow caffeine metabolism. It takes around 24 hours for a dose of caffeine to fully leave the body.
The half-lives of drugs vary from a few seconds to several weeks. To complicate matters, biological half-lives vary for different parts of the body. Lead has a half-life of around a month in the blood, but a decade in bone. Plutonium in bone has a half-life of a century — more than double the time for the liver.
Marketers refer to the half-life of a campaign — the time taken to receive half the total responses. Unsurprisingly, this time varies among media. A paper catalog may have a half-life of about three weeks, whereas a tweet might have a half-life of a few minutes. Calculating this time is important for establishing how frequently a message should be sent.
“Every day that we read the news we have the possibility of being confronted with a fact about our world that is wildly different from what we thought we knew.”
— Samuel Arbesman
The Half-Life of Facts
In The Half-Life of Facts: Why Everything We Know Has an Expiration Date, Samuel Arbesman (see our Knowledge Project interview) posits that facts decay over time until they are no longer facts or perhaps no longer complete. According to Arbesman, information has a predictable half-life: the time taken for half of it to be replaced or disproved. Over time, one group of facts replaces another. As our tools and knowledge become more advanced, we can discover more — sometimes new things that contradict what we thought we knew, sometimes nuances about old things. Sometimes we discover a whole area that we didn’t know about.
The rate of these discoveries varies. Our body of engineering knowledge changes more slowly, for example, than does our body of psychological knowledge.
Arbesman studied the nature of facts. The field was born in 1947, when mathematician Derek J. de Solla Price was arranging a set of philosophical books on his shelf. Price noted something surprising: the sizes of the books fit an exponential curve. His curiosity piqued, he began to see whether the same curve applied to science as a whole. Price established that the quantity of scientific data available was doubling every 15 years. This meant that some of the information had to be rendered obsolete with time.
Scientometrics shows us that facts are always changing, and much of what we know is (or soon will be) incorrect. Indeed, much of the available published research, however often it is cited, has never been reproduced and cannot be considered true. In a controversial paper entitled “Why Most Published Research Findings Are False,” John Ioannides covers the rampant nature of poor science. Many researchers are incentivized to find results that will please those giving them funding. Intense competition makes it essential to find new information, even if it is found in a dubious manner. Yet we all have a tendency to turn a blind eye when beliefs we hold dear are disproved and to pay attention only to information confirming our existing opinions.
As an example, Arbesman points to the number of chromosomes in a human cell. Up until 1965, 48 was the accepted number that medical students were taught. (In 1953, it had been declared an established fact by a leading cytologist). Yet in 1956, two researchers, Joe Hin Tjio and Albert Levan, made a bold assertion. They declared the true number to be 46. During their research, Tjio and Levan could never find the number of chromosomes they expected. Discussing the problem with their peers, they discovered they were not alone. Plenty of other researchers found themselves two chromosomes short of the expected 48. Many researchers even abandoned their work because of this perceived error. But Tjio and Levan were right (for now, anyway). Although an extra two chromosomes seems like a minor mistake, we don’t know the opportunity costs of the time researchers invested in faulty hypotheses or the value of the work that was abandoned. It was an emperor’s-new-clothes situation, and anyone counting 46 chromosomes assumed they were the ones making the error.
As Arbesman puts it, facts change incessantly. Many of us have seen the ironic (in hindsight) doctor-endorsed cigarette ads from the past. A glance at a newspaper will doubtless reveal that meat or butter or sugar has gone from deadly to saintly, or vice versa. We forget that laughable, erroneous beliefs people once held are not necessarily any different from those we now hold. The people who believed that the earth was the center of the universe, or that some animals appeared out of nowhere or that the earth was flat, were not stupid. They just believed facts that have since decayed. Arbesman gives the example of a dermatology test that had the same question two years running, with a different answer each time. This is unsurprising considering the speed at which our world is changing.
As Arbesman points out, in the last century the world’s population has swelled from 2 billion to 7 billion, we have taken on space travel, and we have altered the very definition of science.
Our world seems to be in constant flux. With our knowledge changing all the time, even the most informed people can barely keep up. All this change may seem random and overwhelming (Dinosaurs have feathers? When did that happen?), but it turns out there is actually order within the shifting noise. This order is regular and systematic and is one that can be described by science and mathematics.
The order Arbesman describes mimics the decay of radioactive elements. Whenever new information is discovered, we can be sure it will break down and be proved wrong at some point. As with a radioactive atom, we don’t know precisely when that will happen, but we know it will occur at some point.
If we zoom out and look at a particular body of knowledge, the random decay becomes orderly. Through probabilistic thinking, we can predict the half-life of a group of facts with the same certainty with which we can predict the half-life of a radioactive atom. The problem is that we rarely consider the half-life of information. Many people assume that whatever they learned in school remains true years or decades later. Medical students who learned in university that cells have 48 chromosomes would not learn later in life that this is wrong unless they made an effort to do so.
OK, so we know that our knowledge will decay. What do we do with this information? Arbesman says,
… 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 evolution can we be better prepared for its change.
Recent initiatives have sought to calculate the half-life of an academic paper. Ironically, academic journals have largely neglected research into how people use them and how best to fund the efforts of researchers. Research by Philip Davis shows the time taken for a paper to receive half of its total downloads. Davis’s results are compelling. While most forms of media have a half-life measured in days or even hours, 97 percent of academic papers have a half-life longer than a year. Engineering papers have a slightly shorter half-life than other fields of research, with double the average (6 percent) having a half-life of under a year. This makes sense considering what we looked at earlier in this post. Health and medical publications have the shortest overall half-life: two to three years. Physics, mathematics, and humanities publications have the longest half-lives: two to four years.
The Half-Life of Secrets
According to Peter Swire, writing in “The Declining Half-Life of Secrets,” the half-life of secrets (by which Swire generally means classified information) is shrinking. In the past, a government secret could be kept for over 25 years. Nowadays, hacks and leaks have shrunk that time considerably. Swire writes:
During the Cold War, the United States developed the basic classification system that exists today. Under Executive Order 13526, an executive agency must declassify its documents after 25 years unless an exception applies, with stricter rules if documents stay classified for 50 years or longer. These time frames are significant, showing a basic mind-set of keeping secrets for a time measured in decades.
Swire notes that there are three main causes: “the continuing effects of Moore’s Law — or the idea that computing power doubles every two years, the sociology of information technologists, and the different source and methods for signals intelligence today compared with the Cold War.” One factor is that spreading leaked information is easier than ever. In the past, it was often difficult to get information published. Newspapers feared legal repercussions if they shared classified information. Anyone can now release secret information, often anonymously, as with WikiLeaks. Governments cannot as easily rely on media gatekeepers to cover up leaks.
Rapid changes in technology or geopolitics often reduce the value of classified information, so the value of some, but not all, classified information also has a half-life. Sometimes it’s days or weeks, and sometimes it’s years. For some secrets, it’s not worth investing the massive amount of computer time that would be needed to break them because by the time you crack the code, the information you wanted to know might have expired.
(As an aside, if you were to invert the problem of all these credit card and SSN leaks, you might conclude that reducing the value of possessing this information would be more effective than spending money to secure it.)
“Our policy (at Facebook) is literally to hire as many talented engineers as we can find. The whole limit in the system is that there are not enough people who are trained and have these skills today.”
— Mark Zuckerberg
The Half-Lives of Careers and Business Models
The issue with information having a half-life should be obvious. Many fields depend on individuals with specialized knowledge, learned through study or experience or both. But what if those individuals are failing to keep up with changes and clinging to outdated facts? What if your doctor is offering advice that has been rendered obsolete since they finished medical school? What if your own degree or qualifications are actually useless? These are real problems, and knowing about half-lives will help you make yourself more adaptable.
While figures for the half-lives of most knowledge-based careers are hard to find, we do know the half-life of an engineering career. A century ago, it would take 35 years for half of what an engineer learned when earning their degree to be disproved or replaced. By the 1960s, that time span shrank to a mere decade. Today that figure is probably even lower.
In 1966 paper entitled “The Dollars and Sense of Continuing Education,” Thomas Jones calculated the effort that would be required for an engineer to stay up to date, assuming a 10-year half-life. According to Jones, an engineer would need to devote at least five hours per week, 48 weeks a year, to stay up to date with new advancements. A typical degree requires about 4800 hours of work. Within 10 years, the information learned during 2400 of those hours would be obsolete. The five-hour figure does not include the time necessary to revise forgotten information that is still relevant. A 40-year career as an engineer would require 9600 hours of independent study.
Keep in mind that Jones made his calculations in the 1960s. Modern estimates place the half-life of an engineering degree at between 2.5 and 5 years, requiring between 10 and 20 hours of study per week. Welcome to the treadmill, where you have to run faster and faster so that you don’t fall behind.
Unsurprisingly, putting in this kind of time is simply impossible for most people. The result is an ever-shrinking length of a typical engineer’s career and a bias towards hiring recent graduates. A partial escape from this time-consuming treadmill that offers little progress is to recognize the continuous need for learning. If you agree with that, it becomes easier to place time and emphasis on developing heuristics and systems to foster learning. The faster the pace of knowledge change, the more valuable the skill of learning becomes.
A study by PayScale found that the median age of workers in most successful technology companies is substantially lower than that of other industries. Of 32 companies, just six had a median worker age above 35, despite the average across all workers being just over 42. Eight of the top companies had a median worker age of 30 or below — 28 for Facebook, 29 for Google, and 26 for Epic Games. The upshot is that salaries are high for those who can stay current while gaining years of experience.
In a similar vein, business models have ever shrinking half-lives. The nature of capitalism is that you have to be better last year than you were this year — not to gain market share but to maintain what you already have. If you want to get ahead, you need asymmetry; otherwise, you get lost in trench warfare. How long would it take for half of Uber or Facebook’s business models to be irrelevant? It’s hard to imagine it being more than a couple of years or even months.
In The Business Model Innovation Factory: How to Stay Relevant When the World Is Changing, Saul Kaplan highlights the changing half-lives of business models. In the past, models could last for generations. The majority of CEOs oversaw a single business for their entire careers. Business schools taught little about agility or pivoting. Kaplan writes:
During the industrial era once the basic rules for how a company creates, delivers, and captures value were established[,] they became etched in stone, fortified by functional silos, and sustained by reinforcing company cultures. All of a company’s DNA, energy, and resources were focused on scaling the business model and beating back competition attempting to do a better job executing the same business model. Companies with nearly identical business models slugged it out for market share within well-defined industry sectors.
Those days are over. The industrial era is not coming back. The half-life of a business model is declining. Business models just don’t last as long as they used to. In the twenty-first century business leaders are unlikely to manage a single business for an entire career. Business leaders are unlikely to hand down their businesses to the next generation of leaders with the same business model they inherited from the generation before.
The Burden of Knowledge
The flip side of a half-life is the time it takes to double something. A useful guideline to calculate the time it takes for something to double is to divide 70 by the rate of growth. This formula isn’t perfect, but it gives a good indication. Known as the Rule of 70, it applies only to exponential growth when the relative growth rate remains consistent, such as with compound interest.
The higher the rate of growth, the shorter the doubling time. For example, if the population of a city is increasing by 2 percent per year, we divide 70 by 2 to get a doubling time of 35 years. The rule of 70 is a useful heuristic; population growth of 2 percent might seem low, but your perspective might change when you consider that the city’s population could double in just 35 years. The Rule of 70 can also be used to calculate the time for an investment to double in value; for example, $100 at 7 percent compound interest will double in just a decade and quadruple in 20 years. The average newborn baby doubles its birth weight in under four months. The average doubling time for a tumor is also four months.
We can see how information changes in the figures for how long it takes for a body of knowledge to double in size. The figures quoted by Arbesman (drawn from Little Science, Big Science … and Beyond by Derek J. de Solla Price) are compelling, including:
- Time for the number of entries in a dictionary of national biographies to double: 100 years
- Time for the number of universities to double: 50 years
- Time for the number of known chemical compounds to double: 15 years
- Time for the number of known asteroids to double: 10 years
Arbesman also gives figures for the time taken for the available knowledge in a particular field to double, including:
- Medicine: 87 years
- Mathematics: 63 years
- Chemistry: 35 years
- Genetics: 32 years
The doubling of knowledge increases the learning load over time. As a body of knowledge doubles so does the cost of wrapping your head around what we already know. This cost is the burden of knowledge. To be the best in a general field today requires that you know more than the person who was the best only 20 years ago. Not only do you have to be better to be the best, but you also have to be better just to stay in the game.
The corollary is that because there is so much to know, we specialize in very niche areas. This makes it easier to grasp the existing body of facts, keep up to date on changes, and rise to the level of expert. The problem is that specializing also makes it easier to see the world through the narrow focus of your specialty, makes it harder to work with other people (as niches are often dominated by jargon), and makes you prone to overvalue the new and novel.
As we have seen, understanding how half-lives work has numerous practical applications, from determining when radioactive materials will become safe to figuring out effective drug dosages. Half-lives also show us that if we spend time learning something that changes quickly, we might be wasting our time. Like Alice in Wonderland — and a perfect example of the Red Queen Effect — we have to run faster and faster just to keep up with where we are. So if we want our knowledge to compound, we’ll need to focus on the invariant general principles.
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