Tag: Science

The Disproportional Power of Anecdotes

Humans, it seems, have an innate tendency to overgeneralize from small samples. How many times have you been caught in an argument where the only proof offered is anecdotal? Perhaps your co-worker saw this bratty kid make a mess in the grocery store while the parents appeared to do nothing. “They just let that child pull things off the shelves and create havoc! My parents would never have allowed that. Parents are so permissive now.” Hmm. Is it true that most parents commonly allow young children to cause trouble in public? It would be a mistake to assume so based on the evidence presented, but a lot of us would go with it anyway. Your co-worker did.

Our propensity to confuse the “now” with “what always is,” as if the immediate world before our eyes consistently represents the entire universe, leads us to bad conclusions and bad decisions. We don’t bother asking questions and verifying validity. So we make mistakes and allow ourselves to be easily manipulated.

Political polling is a good example. It’s actually really hard to design and conduct a good poll. Matthew Mendelsohn and Jason Brent, in their article “Understanding Polling Methodology,” say:

Public opinion cannot be understood by using only a single question asked at a single moment. It is necessary to measure public opinion along several different dimensions, to review results based on a variety of different wordings, and to verify findings on the basis of repetition. Any one result is filled with potential error and represents one possible estimation of the state of public opinion.

This makes sense. But it’s amazing how often we forget.

We see a headline screaming out about the state of affairs and we dive right in, instant believers, without pausing to question the validity of the methodology. How many people did they sample? How did they select them? Most polling aims for random sampling, but there is pre-selection at work immediately, depending on the medium the pollsters use to reach people.

Truly random samples of people are hard to come by. In order to poll people, you have to be able to reach them. The more complicated this is, the more expensive the poll becomes, which acts as a deterrent to thoroughness. The internet can offer high accessibility for a relatively low cost, but it’s a lot harder to verify the integrity of the demographics. And if you go the telephone route, as a lot of polling does, are you already distorting the true randomness of your sample size? Are the people who answer “unknown” numbers already different from those who ignore them?

Polls are meant to generalize larger patterns of behavior based on small samples. You need to put a lot of effort in to make sure that sample is truly representative of the population you are trying to generalize about. Otherwise, erroneous information is presented as truth.

Why does this matter?

It matters because generalization is a widespread human bias, which means a lot of our understanding of the world actually is based on extrapolations made from relatively small sample sizes. Consequently, our individual behavior is shaped by potentially incomplete or inadequate facts that we use to make the decisions that are meant to lead us to success. This bias also shapes a fair degree of public policy and government legislation. We don’t want people who make decisions that affect millions to be dependent on captivating bullshit. (A further concern is that once you are invested, other biases kick in).

Some really smart people are perpetual victims of the problem.

Joseph Henrich, Steven J. Heine, and Ara Norenzayan wrote an article called “The weirdest people in the world?” It’s about how many scientific psychology studies use college students who are predominantly Western, Educated, Industrialized, Rich, and Democratic (WEIRD), and then draw conclusions about the entire human race from these outliers. They reviewed scientific literature from domains such as “visual perception, fairness, cooperation, spatial reasoning, categorization and inferential induction, moral reasoning, and the heritability of IQ. The findings suggest that members of WEIRD societies, including young children, are among the least representative populations one could find for generalizing about humans.”

Uh-oh. This is a double whammy. “It’s not merely that researchers frequently make generalizations from a narrow subpopulation. The concern is that this particular subpopulation is highly unrepresentative of the species.”

This is why it can be dangerous to make major life decisions based on small samples, like anecdotes or a one-off experience. The small sample may be an outlier in the greater range of possibilities. You could be correcting for a problem that doesn’t exist or investing in an opportunity that isn’t there.

This tendency of mistaken extrapolation from small samples can have profound consequences.

Are you a fan of the San Francisco 49ers? They exist, in part, because of our tendency to over-generalize. In the 19th century in Western America and Canada, a few findings of gold along some creek beds led to a massive rush as entire populations flocked to these regions in the hope of getting rich. San Francisco grew from 200 residents in 1846 to about 36,000 only six years later. The gold rush provided enormous impetus toward California becoming a state, and the corresponding infrastructure developments touched off momentum that long outlasted the mining of gold.

But for most of the actual rushers, those hoping for gold based on the anecdotes that floated east, there wasn’t much to show for their decision to head west. The Canadian Encyclopedia states, “If the nearly 29 million (figure unadjusted) in gold that was recovered during the heady years of 1897 to 1899 [in the Klondike] was divided equally among all those who participated in the gold rush, the amount would fall far short of the total they had invested in time and money.”

How did this happen? Because those miners took anecdotes as being representative of a broader reality. Quite literally, they learned mining from rumor, and didn’t develop any real knowledge. Most people fought for claims along the creeks, where easy gold had been discovered, while rejecting the bench claims on the hillsides above, which often had just as much gold.

You may be thinking that these men must have been desperate if they packed themselves up, heading into unknown territory, facing multiple dangers along the way, to chase a dream of easy money. But most of us aren’t that different. How many times have you invested in a “hot stock” on a tip from one person, only to have the company go under within a year? Ultimately, the smaller the sample size, the greater role the factors of chance play in determining an outcome.

If you want to limit the capriciousness of chance in your quest for success, increase your sample size when making decisions. You need enough information to be able to plot the range of possibilities, identify the outliers, and define the average.

So next time you hear the words “the polls say,” “studies show,” or “you should buy this,” ask questions before you take action. Think about the population that is actually being represented before you start modifying your understanding. Accept the limits of small sample sizes from large populations. And don’t give power to anecdotes.

Half Life: The Decay of Knowledge and What to Do About It

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.

The Basics

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.

Conclusion

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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Activation Energy: Why Getting Started Is the Hardest Part

The beginning of any complex or challenging endeavor is always the hardest part. Not all of us wake up and jump out of bed ready for the day. Some of us, like me, need a little extra energy to transition out of sleep and into the day. Once I’ve had a cup of coffee, my energy level jumps and I’m good for the rest of the day. Chemical reactions work in much the same way. They need their coffee, too. We call this activation energy.

Understanding how this works can be a useful perspective as part of our latticework of mental models.

Whether you use chemistry in your everyday work or have tried your best not to think about it since school, the ideas behind activation energy are simple and useful outside of chemistry. Understanding the principle can, for example, help you get kids to eat their vegetables, motivate yourself and others, and overcome inertia.

How Activation Energy Works in Chemistry

Chemical reactions need a certain amount of energy to begin working. Activation energy is the minimum energy required to cause a reaction to occur.

To understand activation energy, we must first think about how a chemical reaction occurs.

Anyone who has ever lit a fire will have an intuitive understanding of the process, even if they have not connected it to chemistry.

Most of us have a general feel for the heat necessary to start flames. We know that putting a single match to a large log will not be sufficient and a flame thrower would be excessive. We also know that damp or dense materials will require more heat than dry ones. The imprecise amount of energy we know we need to start a fire is representative of the activation energy.

For a reaction to occur, existing bonds must break and new ones form. A reaction will only proceed if the products are more stable than the reactants. In a fire, we convert carbon in the form of wood into CO2 and is a more stable form of carbon than wood, so the reaction proceeds and in the process produces heat. In this example, the activation energy is the initial heat required to get the fire started. Our effort and spent matches are representative of this.

We can think of activation energy as the barrier between the minima (smallest necessary values) of the reactants and products in a chemical reaction.

The Arrhenius Equation

Svante Arrhenius, a Swedish scientist, established the existence of activation energy in 1889.

Arrhenius equation

Arrhenius developed his eponymous equation to describe the correlation between temperature and reaction rate.

The Arrhenius equation is crucial for calculating the rates of chemical reactions and, importantly, the quantity of energy necessary to start them.

In the Arrhenius equation, K is the reaction rate coefficient (the rate of reaction). A is the frequency factor (how often molecules collide), R is the universal gas constant (units of energy per temperature increment per mole), T represents the absolute temperature (usually measured in kelvins), and E is the activation energy.

It is not necessary to know the value of A to calculate Ea as this can be figured out from the variation in reaction rate coefficients in relation to temperature. Like many equations, it can be rearranged to calculate different values. The Arrhenius equation is used in many branches of chemistry.

Why Activation Energy Matters

Understanding the energy necessary for a reaction to occur gives us control over our surroundings.

Returning to the example of fire, our intuitive knowledge of activation energy keeps us safe. Many chemical reactions have high activation energy requirements, so they do not proceed without an additional input. We all know that a book on a desk is flammable, but will not combust without heat application. At room temperature, we need not see the book as a fire hazard. If we light a candle on the desk, we know to move the book away.

If chemical reactions did not have reliable activation energy requirements, we would live in a dangerous world.

Catalysts

Chemical reactions which require substantial amounts of energy can be difficult to control.

Increasing temperature is not always a viable source of energy due to costs, safety issues, or simple impracticality. Chemical reactions that occur within our bodies, for example, cannot use high temperatures as a source of activation energy. Consequently, it is sometimes necessary to reduce the activation energy required.

Speeding up a reaction by lowering the rate of activation energy required is called catalysis. This is done with an additional substance known as a catalyst, which is generally not consumed in the reaction. In principle, you only need a tiny amount of catalyst to cause catalysis.

Catalysts work by providing an alternative pathway with lower activation energy requirements. Consequently, more of the particles have sufficient energy to react. Catalysts are used in industrial scale reactions to lower costs.

Returning to the fire example, we know that attempting to light a large log with a match is rarely effective. Adding some paper will provide an alternative pathway and serve as a catalyst — firestarters do the same.

Within our bodies, enzymes serve as catalysts in vital reactions (such as building DNA.)

“Energy can have two dimensions. One is motivated, going somewhere, a goal somewhere, this moment is only a means and the goal is going to be the dimension of activity, goal oriented-then everything is a means, somehow it has to be done and you have to reach the goal, then you will relax. But for this type of energy, the goal never comes because this type of energy goes on changing every present moment into a means for something else, into the future. The goal always remains on the horizon. You go on running, but the distance remains the same.
No, there is another dimension of energy: that dimension is unmotivated celebration. The goal is here, now; the goal is not somewhere else. In fact, you are the goal. In fact, there is no other fulfillment than that of this moment–consider the lilies. When you are the goal and when the goal is not in the future, when there is nothing to be achieved, rather you are just celebrating it, then you have already achieved it, it is there. This is relaxation, unmotivated energy.”

— Osho, Tantra

Applying the Concept of Activation Energy to Our Daily Lives

Although activation energy is a scientific concept, we can use it as a practical mental model.

Returning to the morning coffee example, many of the things we do each day depend upon an initial push.

Take the example of a class of students set an essay for their coursework. Each student requires a different sort of activation energy for them to get started. For one student, it might be hearing their friend say she has already finished hers. For another, it might be blocking social media and turning off their phone. A different student might need a few cans of Red Bull and an impending deadline. Or, for another, reading an interesting article on the topic which provides a spark of inspiration. The act of writing an essay necessitates a certain sort of energy.

Getting kids to eat their vegetables can be a difficult process. In this case, incentives can act as a catalyst. “You can’t have your dessert until you eat your vegetables” is not only a psychological play on incentives; it also often requires less energy than constantly fighting with the kids to eat their vegetables. Once kids eat a carrot, they generally eat another one and another one. While they still want dessert, you won’t have to remind them each time, so you’ll save a lot of energy.

The concept of activation energy can also apply to making drastic life changes. Anyone who has ever done something dramatic and difficult (such as quitting an addiction, leaving an abusive relationship, quitting a long-term job, or making crucial lifestyle changes) knows that it is necessary to reach a breaking point first. The bigger and more challenging an action is, the more activation energy we require to do it.

Our coffee drinker might crave little activation energy (a cup or two) to begin their day if they are well rested. Meanwhile, it will take a whole lot more coffee for them to get going if they slept badly and have a dull day to get through.

Conclusion

To understand and use the concept of activation energy in our lives does not require a degree in chemistry. While the concept as used by scientists is complex, we can use the basic idea.

It is no coincidence that many of most useful mental models in our latticework originate from science. There is something quite poetic about the way in which human behavior mirrors what occurs at a microscopic level.

For other examples, look to Occam’s Razor, falsification, feedback loops, and equilibrium.

Alexander von Humboldt and the Invention of Nature: Creating a Holistic View of the World Through A Web of Interdisciplinary Knowledge

In his piece in 2014’s Edge collection This Idea Must Die: Scientific Theories That Are Blocking Progress, dinosaur paleontologist Scott Sampson writes that science needs to “subjectify” nature. By “subjectify”, he essentially means to see ourselves connected with nature, and therefore care about it the same way we do the people with whom we are connected.

That’s not the current approach. He argues: “One of the most prevalent ideas in science is that nature consists of objects. Of course, the very practice of science is grounded in objectivity. We objectify nature so that we can measure it, test it, and study it, with the ultimate goal of unraveling its secrets. Doing so typically requires reducing natural phenomena to their component parts.”

But this approach is ultimately failing us.

Why? Because much of our unsustainable behavior can be traced to a broken relationship with nature, a perspective that treats the nonhuman world as a realm of mindless, unfeeling objects. Sustainability will almost certainly depend upon developing mutually enhancing relations between humans and nonhuman nature.

This isn’t a new plea, though. Over 200 years ago, the famous naturalist Alexander Von Humboldt (1769-1859) was facing the same challenges.

In her compelling book The Invention of Nature: Alexander Von Humboldt’s New World, Andrea Wulf explores Humboldt as the first person to publish works promoting a holistic view of nature, arguing that nature could only be understood in relation to the subjectivity of experiencing it.

Fascinated by scientific instruments, measurements and observations, he was driven by a sense of wonder as well. Of course nature had to be measured and analyzed, but he also believed that a great part of our response to the natural world should be based on the senses and emotions.

Humboldt was a rock star scientist who ignored conventional boundaries in his exploration of nature. Humboldt’s desire to know and understand the world led him to investigate discoveries in all scientific disciplines, and to see the interwoven patterns embedded in this knowledge — mental models anyone?

If nature was a web of life, he couldn’t look at it just as a botanist, a geologist or a zoologist. He required information about everything from everywhere.

Humboldt grew up in a world where science was dry, nature mechanical, and man an aloof and separate chronicler of what was before him. Not only did Humboldt have a new vision of what our understanding of nature could be, but he put humans in the middle of it.

Humboldt’s Essay on the Geography of Plants promoted an entirely different understanding of nature. Instead of only looking at an organism, … Humboldt now presented relationships between plants, climate and geography. Plants were grouped into zones and regions rather than taxonomic units. … He gave western science a new lens through which to view the natural world.

Revolutionary for his time, Humboldt rejected the Cartesian ideas of animals as mechanical objects. He also argued passionately against the growing approach in the sciences that put man atop and separate from the rest of the natural world. Promoting a concept of unity in nature, Humboldt saw nature as a “reflection of the whole … an organism in which the parts only worked in relation to each other.”

Furthermore, that “poetry was necessary to comprehend the mysteries of the natural world.”

Wulf paints one of Humboldt’s greatest achievements as his ability and desire to make science available to everyone. No one before him had “combined exact observation with a ‘painterly description of the landscape”.

By contrast, Humboldt took his readers into the crowded streets of Caracas, across the dusty plains of the Llanos and deep into the rainforest along the Orinoco. As he described a continent that few British had ever seen, Humboldt captured their imagination. His words were so evocative, the Edinburgh Review wrote, that ‘you partake in his dangers; you share his fears, his success and his disappointment.’

In a time when travel was precarious, expensive and unavailable to most people, Humboldt brought his experiences to anyone who could read or listen.

On 3 November 1827, … Humboldt began a series of sixty-one lectures at the university. These proved so popular that he added another sixteen at Berlin’s music hall from 6 December. For six months he delivered lectures several days a week. Hundreds of people attended each talk, which Humboldt presented without reading from his notes. It was lively, exhilarating and utterly new. By not charging any entry fee, Humboldt democratized science: his packed audiences ranged from the royal family to coachmen, from students to servants, from scholars to bricklayers – and half of those attending were women. Berlin had never seen anything like it.

The subjectification of nature is about seeing nature, experiencing it. Humboldt was a master of bringing people to worlds they couldn’t visit, allowing them to feel a part of it. In doing so, he wanted to force humanity to see itself in nature. If we were all part of the giant web, then we all had a responsibility to understand it.

When he listed the three ways in which the human species was affecting the climate, he named deforestation, ruthless irrigation and, perhaps most prophetically, the ‘great masses of steam and gas’ produced in the industrial centres. No one but Humboldt had looked at the relationship between humankind and nature like this before.

His final opus, a series of books called Cosmos, was the culmination of everything that Humboldt had learned and discovered.

Cosmos was unlike any previous book about nature. Humboldt took his readers on a journey from outer space to earth, and then from the surface of the planet into its inner core. He discussed comets, the Milky Way and the solar system as well as terrestrial magnetism, volcanoes and the snow line of mountains. He wrote about the migration of the human species, about plants and animals and the microscopic organisms that live in stagnant water or on the weathered surface of rocks. Where others insisted that nature was stripped of its magic as humankind penetrated into its deepest secrets, Humboldt believed exactly the opposite. How could this be, Humboldt asked, in a world in which the coloured rays of an aurora ‘unite in a quivering sea flame’, creating a sight so otherworldly ‘the splendour of which no description can reach’? Knowledge, he said, could never ‘kill the creative force of imagination’ – instead it brought excitement, astonishment and wondrousness.

This is the ultimate subjectivity of nature. Being inspired by its beauty to try and understand how it works. Humboldt had respect for nature, for the wonders it contained, but also as the system in which we ourselves are an inseparable part.

Wulf concludes at the end that Humboldt,

…was one of the last polymaths, and died at a time when scientific disciplines were hardening into tightly fenced and more specialized fields. Consequently his more holistic approach – a scientific method that included art, history, poetry and politics alongside hard data – has fallen out of favour.

Maybe this is where the subjectivity of nature has gone. But we can learn from Humboldt the value of bringing it back.

In a world where we tend to draw a sharp line between the sciences and the arts, between the subjective and the objective, Humboldt’s insight that we can only truly understand nature by using our imagination makes him a visionary.

A little imagination is all it takes.

The Danger of Oversimplification: How to Use Occam’s Razor Without Getting Cut

Occam’s razor (also known as the ‘law of parsimony’) is a problem-solving principle which serves as a useful mental model. A philosophical razor is a tool used to eliminate improbable options in a given situation, of which Occam’s is the best-known example.

Occam’s razor can be summarized as such:

Among competing hypotheses, the one with the fewest assumptions should be selected.

The Basics

In simpler language, Occam’s razor states that the simplest solution is correct. Another good explanation of Occam’s razor comes from the paranormal writer, William J. Hall: ‘Occam’s razor is summarized for our purposes in this way: Extraordinary claims demand extraordinary proof.’

In other words, we should avoid looking for excessively complex solutions to a problem and focus on what works, given the circumstances. Occam’s razor is used in a wide range of situations, as a means of making rapid decisions and establishing truths without empirical evidence. It works best as a mental model for making initial conclusions before adequate information can be obtained.

A further literary summary comes from one of the best-loved fictional characters, Arthur Conan Doyle’s Sherlock Holmes. His classic aphorism is an expression of Occam’s razor: “If you eliminate the impossible, whatever remains, however improbable, must be the truth.”

A number of mathematical and scientific studies have backed up its validity and lasting relevance. In particular, the principle of minimum energy supports Occam’s razor. This facet of the second law of thermodynamics states that, wherever possible, the use of energy is minimized. In general, the universe tends towards simplicity. Physicists use Occam’s razor, in the knowledge that they can rely on everything to use the minimum energy necessary to function. A ball at the top of a hill will roll down in order to be at the point of minimum potential energy. The same principle is present in biology. For example, if a person repeats the same action on a regular basis in response to the same cue and reward, it will become a habit as the corresponding neural pathway is formed. From then on, their brain will use less energy to complete the same action.

The History of Occam’s Razor

The concept of Occam’s razor is credited to William of Ockham, a 13-14th-century friar, philosopher, and theologian. While he did not coin the term, his characteristic way of making deductions inspired other writers to develop the heuristic. Indeed, the concept of Occam’s razor is an ancient one which was first stated by Aristotle who wrote “we may assume the superiority, other things being equal, of the demonstration which derives from fewer postulates or hypotheses.”

Robert Grosseteste expanded on Aristotle’s writing in the 1200s, declaring that:

That is better and more valuable which requires fewer, other circumstances being equal… For if one thing were demonstrated from many and another thing from fewer equally known premises, clearly that is better which is from fewer because it makes us know quickly, just as a universal demonstration is better than particular because it produces knowledge from fewer premises. Similarly, in natural science, in moral science, and in metaphysics the best is that which needs no premises and the better that which needs the fewer, other circumstances being equal.

Early writings such as this are believed to have led to the eventual, (ironic) simplification of the concept. Nowadays, Occam’s razor is an established mental model which can form a useful part of a latticework of knowledge.

Mental Model Occam's Razor

Examples of the Use of Occam’s Razor

Theology

In theology, Occam’s razor is used to prove or disprove the existence of God. William of Ockham, being a Christian friar, used his theory to defend religion. He regarded the scripture as true in the literal sense and therefore saw it as simple proof. To him, the bible was synonymous with reality and therefore to contradict it would conflict with established fact. Many religious people regard the existence of God as the simplest possible explanation for the creation of the universe.

In contrast, Thomas Aquinas used the concept in his radical 13th century work – The Summa Theologica. In it, he argued for atheism as a logical concept, not a contradiction of accepted beliefs. Aquinas wrote ‘it is superfluous to suppose that what can be accounted for by a few principles has been produced by many.’ He considered the existence of God to be a hypothesis which makes a huge number of assumptions, compared to scientific alternatives. Many modern atheists consider the existence of God to be unnecessarily complex, in particular, due to the lack of empirical evidence.

Taoist thinkers take Occam’s razor one step further, by simplifying everything in existence to the most basic form. In Taoism, everything is an expression of a single ultimate reality (known as the Tao.) This school of religious and philosophical thought believes that the most plausible explanation for the universe is the simplest- everything is both created and controlled by a single force. This can be seen as a profound example of the use of Occam’s razor within theology.

The Development of Scientific Theories

Occam’s razor is frequently used by scientists, in particular for theoretical matters. The simpler a hypothesis is, the more easily it can be proved or falsified. A complex explanation for a phenomenon involves many factors which can be difficult to test or lead to issues with the repeatability of an experiment. As a consequence, the simplest solution which is consistent with the existing data is preferred. However, it is common for new data to allow hypotheses to become more complex over time. Scientists chose to opt for the simplest solution the current data permits while remaining open to the possibility of future research allowing for greater complexity.

Failing to observe Occam’s razor is usually a sign of bad science and an attempt to cover poor explanations. The version used by scientists can best be summarized as: ‘when you have two competing theories that make exactly the same predictions, the simpler one is the better.’

Obtaining funding for simpler hypothesis tends to be easier, as they are often cheaper to prove. As a consequence, the use of Occam’s razor in science is a matter of practicality.

Albert Einstein referred to Occam’s razor when developing his theory of special relativity. He formulated his own version: ‘it can scarcely be denied that the supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience.’ Or “everything should be made as simple as possible, but not simpler.” This preference for simplicity can be seen in one of the most famous equations ever devised: E=MC2. Rather than making it a lengthy equation requiring pages of writing, Einstein reduced the factors necessary down to the bare minimum. The result is usable and perfectly parsimonious.

The physicist Stephen Hawking advocates for Occam’s razor in A Brief History of Time:

We could still imagine that there is a set of laws that determines events completely for some supernatural being, who could observe the present state of the universe without disturbing it. However, such models of the universe are not of much interest to us mortals. It seems better to employ the principle known as Occam’s razor and cut out all the features of the theory that cannot be observed.

Isaac Newton used Occam’s razor too when developing his theories. Newton stated: “we are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.” As a result, he sought to make his theories (including the three laws of motion) as simple as possible, with the fewest underlying assumptions necessary.

Medicine

Modern doctors use a version of Occam’s razor, stating that they should look for the fewest possible causes to explain their patient’s multiple symptoms and also for the most likely causes. A doctor I know often repeats, “common things are common.” Interns are instructed, “when you hear hoofbeats, think horses, not zebras.” For example, a person displaying influenza-like symptoms during an epidemic would be considered more probable to be suffering from influenza than an alternative, rarer disease. Making minimal diagnoses reduces the risk of over treating a patient, or of causing dangerous interactions between different treatments. This is of particular importance within the current medical model, where patients are likely to see numerous different health specialists and communication between them can be poor.

Prison Abolition and Fair Punishment

Occam’s razor has long played a role in attitudes towards the punishment of crimes. In this context, it refers to the idea that people should be given the least punishment necessary for their crimes.

This is to avoid the excessive penal practices which were popular in the past, (for example, a Victorian could receive five years of hard labour for stealing a piece of food.) The concept of penal parsimony was pioneered by Jeremy Bentham, the founder of utilitarianism. He stated that punishments should not cause more pain than they prevent. Life imprisonment for murder could be seen as justified in that it may prevent a great deal of potential pain, should the perpetrator offend again. On the other hand, long-term imprisonment of an impoverished person for stealing food causes substantial suffering without preventing any.

Bentham’s writings on the application of Occam’s razor to punishment led to the prison abolition movement and our modern ideas of rehabilitation.

Crime solving and forensic work

When it comes to solving a crime, Occam’s razor is used in conjunction with experience and statistical knowledge. A woman is statistically more likely to be killed by a male partner than any other person. Should a female be found murdered in her locked home, the first person police interview would be any male partners. The possibility of a stranger entering can be considered, but the simplest possible solution with the fewest assumptions made would be that the crime was perpetrated by her male partner.

By using Occam’s razor, police officers can solve crimes faster and with fewer expenses.

Exceptions and Issues

It is important to note that, like any mental model, Occam’s razor is not failsafe and should be used with care, lest you cut yourself. This is especially crucial when it comes to important or risky decisions. There are exceptions to any rule, and we should never blindly follow a mental model which logic, experience, or empirical evidence contradict. The smartest people are those who know the rules, but also know when to ignore them. When you hear hoofbeats behind you, in most cases you should think horses, not zebras- unless you are out on the African savannah.

Simplicity is also a subjective topic- in the example of the NASA moon landing conspiracy theory, some people consider it simpler for them to have been faked, others for them to have been real. When using Occam’s razor to make deductions, we must avoid falling prey to confirmation bias and merely using it to backup preexisting notions. The same goes for the theology example mentioned previously – some people consider the existence of God to be the simplest option, others consider the inverse to be true. Semantic simplicity must not be given overt importance when selecting the solution which Occam’s razor points to. A hypothesis can sound simple, yet involve more assumptions than a verbose alternative.

Occam’s razor should not be used in the place of logic, scientific methods and personal insights. In the long term, a judgment must be backed by empirical evidence, not just its simplicity. Lisa Randall best expressed the issues with Occam’s razor in her book, Dark Matter and the Dinosaurs: The Astounding Interconnectedness of the Universe:

My second concern about Occam’s Razor is just a matter of fact. The world is more complicated than any of us would have been likely to conceive. Some particles and properties don’t seem necessary to any physical processes that matter—at least according to what we’ve deduced so far. Yet they exist. Sometimes the simplest model just isn’t the correct one.

Harlan Coben has disputed many criticisms of Occam’s razor by stating that people fail to understand its exact purpose:

Most people oversimplify Occam’s razor to mean the simplest answer is usually correct. But the real meaning, what the Franciscan friar William of Ockham really wanted to emphasize, is that you shouldn’t complicate, that you shouldn’t “stack” a theory if a simpler explanation was at the ready. Pare it down. Prune the excess.

I once again leave you with Einstein: “Everything should be made as simple as possible, but not simpler.

Occam’s razor is complemented by other mental models, including fundamental error distribution, Hanlon’s razor, confirmation bias, availability heuristic and hindsight bias. The nature of mental models is that they tend to all interlock and work best in conjunction.

How To Mentally Overachieve — Charles Darwin’s Reflections On His Own Mind

We’ve written quite a bit about the marvelous British naturalist Charles Darwin, who with his Origin of Species created perhaps the most intense intellectual debate in human history, one which continues up to this day.

Darwin’s Origin was a courageous and detailed thought piece on the nature and development of biological species. It’s the starting point for nearly all of modern biology.

But, as we’ve noted before, Darwin was not a man of pure IQ. He was not Issac Newton, or Richard Feynman, or Albert Einstein — breezing through complex mathematical physics at a young age.

Charlie Munger thinks Darwin would have placed somewhere in the middle of a good private high school class. He was also in notoriously bad health for most of his adult life and, by his son’s estimation, a terrible sleeper. He really only worked a few hours a day in the many years leading up to the Origin of Species.

Yet his “thinking work” outclassed almost everyone. An incredible story.

In his autobiography, Darwin reflected on this peculiar state of affairs. What was he good at that led to the result? What was he so weak at? Why did he achieve better thinking outcomes? As he put it, his goal was to:

“Try to analyse the mental qualities and the conditions on which my success has depended; though I am aware that no man can do this correctly.”

In studying Darwin ourselves, we hope to better appreciate our own strengths and weaknesses and, not to mention understand the working methods of a “mental overachiever.

Let’s explore what Darwin saw in himself.

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1. He did not have a quick intellect or an ability to follow long, complex, or mathematical reasoning. He may have been a bit hard on himself, but Darwin realized that he wasn’t a “5 second insight” type of guy (and let’s face it, most of us aren’t). His life also proves how little that trait matters if you’re aware of it and counter-weight it with other methods.

I have no great quickness of apprehension or wit which is so remarkable in some clever men, for instance, Huxley. I am therefore a poor critic: a paper or book, when first read, generally excites my admiration, and it is only after considerable reflection that I perceive the weak points. My power to follow a long and purely abstract train of thought is very limited; and therefore I could never have succeeded with metaphysics or mathematics. My memory is extensive, yet hazy: it suffices to make me cautious by vaguely telling me that I have observed or read something opposed to the conclusion which I am drawing, or on the other hand in favour of it; and after a time I can generally recollect where to search for my authority. So poor in one sense is my memory, that I have never been able to remember for more than a few days a single date or a line of poetry.

2. He did not feel easily able to write clearly and concisely. He compensated by getting things down quickly and then coming back to them later, thinking them through again and again. Slow, methodical….and ridiculously effective: For those who haven’t read it, the Origin of Species is extremely readable and clear, even now, 150 years later.

I have as much difficulty as ever in expressing myself clearly and concisely; and this difficulty has caused me a very great loss of time; but it has had the compensating advantage of forcing me to think long and intently about every sentence, and thus I have been led to see errors in reasoning and in my own observations or those of others.

There seems to be a sort of fatality in my mind leading me to put at first my statement or proposition in a wrong or awkward form. Formerly I used to think about my sentences before writing them down; but for several years I have found that it saves time to scribble in a vile hand whole pages as quickly as I possibly can, contracting half the words; and then correct deliberately. Sentences thus scribbled down are often better ones than I could have written deliberately.

3. He forced himself to be an incredibly effective and organized collector of information. Darwin’s system of reading and indexing facts in large portfolios is worth emulating, as is the habit of taking down conflicting ideas immediately.

As in several of my books facts observed by others have been very extensively used, and as I have always had several quite distinct subjects in hand at the same time, I may mention that I keep from thirty to forty large portfolios, in cabinets with labelled shelves, into which I can at once put a detached reference or memorandum. I have bought many books, and at their ends I make an index of all the facts that concern my work; or, if the book is not my own, write out a separate abstract, and of such abstracts I have a large drawer full. Before beginning on any subject I look to all the short indexes and make a general and classified index, and by taking the one or more proper portfolios I have all the information collected during my life ready for use.

4. He had possibly the most valuable trait in any sort of thinker: A passionate interest in understanding reality and putting it in useful order in his headThis “Reality Orientation” is hard to measure and certainly does not show up on IQ tests, but probably determines, to some extent, success in life.

On the favourable side of the balance, I think that I am superior to the common run of men in noticing things which easily escape attention, and in observing them carefully. My industry has been nearly as great as it could have been in the observation and collection of facts. What is far more important, my love of natural science has been steady and ardent.

This pure love has, however, been much aided by the ambition to be esteemed by my fellow naturalists. From my early youth I have had the strongest desire to understand or explain whatever I observed,–that is, to group all facts under some general laws. These causes combined have given me the patience to reflect or ponder for any number of years over any unexplained problem. As far as I can judge, I am not apt to follow blindly the lead of other men. I have steadily endeavoured to keep my mind free so as to give up any hypothesis, however much beloved (and I cannot resist forming one on every subject), as soon as facts are shown to be opposed to it.

Indeed, I have had no choice but to act in this manner, for with the exception of the Coral Reefs, I cannot remember a single first-formed hypothesis which had not after a time to be given up or greatly modified. This has naturally led me to distrust greatly deductive reasoning in the mixed sciences. On the other hand, I am not very sceptical—a frame of mind which I believe to be injurious to the progress of science. A good deal of scepticism in a scientific man is advisable to avoid much loss of time, but I have met with not a few men, who, I feel sure, have often thus been deterred from experiment or observations, which would have proved directly or indirectly serviceable.

[…]

Therefore my success as a man of science, whatever this may have amounted to, has been determined, as far as I can judge, by complex and diversified mental qualities and conditions. Of these, the most important have been—the love of science—unbounded patience in long reflecting over any subject—industry in observing and collecting facts—and a fair share of invention as well as of common sense.

5. Most inspirational to us of average intellect, he outperformed his own mental aptitude with these good habits, surprising even himself with the results.

With such moderate abilities as I possess, it is truly surprising that I should have influenced to a considerable extent the belief of scientific men on some important points.

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Still Interested? Read his autobiography, his The Origin of Species, or check out David Quammen’s wonderful short biography of the most important period of Darwin’s life. Also, if you missed it, check out our prior post on Darwin’s Golden Rule.