Category: Mental Models

Deductive vs Inductive Reasoning: Make Smarter Arguments, Better Decisions, and Stronger Conclusions

You can’t prove truth, but using deductive and inductive reasoning, you can get close. Learn the difference between the two types of reasoning and how to use them when evaluating facts and arguments.

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As odd as it sounds, in science, law, and many other fields, there is no such thing as proof — there are only conclusions drawn from facts and observations. Scientists cannot prove a hypothesis, but they can collect evidence that points to its being true. Lawyers cannot prove that something happened (or didn’t), but they can provide evidence that seems irrefutable.

The question of what makes something true is more relevant than ever in this era of alternative facts and fake news. This article explores truth — what it means and how we establish it. We’ll dive into inductive and deductive reasoning as well as a bit of history.

“Contrariwise,” continued Tweedledee, “if it was so, it might be; and if it were so, it would be; but as it isn’t, it ain’t. That’s logic.”

— Lewis Carroll, Through the Looking-Glass

The essence of reasoning is a search for truth. Yet truth isn’t always as simple as we’d like to believe it is.

For as far back as we can imagine, philosophers have debated whether absolute truth exists. Although we’re still waiting for an answer, this doesn’t have to stop us from improving how we think by understanding a little more.

In general, we can consider something to be true if the available evidence seems to verify it. The more evidence we have, the stronger our conclusion can be. When it comes to samples, size matters. As my friend Peter Kaufman says:

What are the three largest, most relevant sample sizes for identifying universal principles? Bucket number one is inorganic systems, which are 13.7 billion years in size. It’s all the laws of math and physics, the entire physical universe. Bucket number two is organic systems, 3.5 billion years of biology on Earth. And bucket number three is human history….

In some areas, it is necessary to accept that truth is subjective. For example, ethicists accept that it is difficult to establish absolute truths concerning whether something is right or wrong, as standards change over time and vary around the world.

When it comes to reasoning, a correctly phrased statement can be considered to have objective truth. Some statements have an objective truth that we cannot ascertain at present. For example, we do not have proof for the existence or non-existence of aliens, although proof does exist somewhere.

Deductive and inductive reasoning are both based on evidence.

Several types of evidence are used in reasoning to point to a truth:

  • Direct or experimental evidence — This relies on observations and experiments, which should be repeatable with consistent results.
  • Anecdotal or circumstantial evidence — Overreliance on anecdotal evidence can be a logical fallacy because it is based on the assumption that two coexisting factors are linked even though alternative explanations have not been explored. The main use of anecdotal evidence is for forming hypotheses which can then be tested with experimental evidence.
  • Argumentative evidence — We sometimes draw conclusions based on facts. However, this evidence is unreliable when the facts are not directly testing a hypothesis. For example, seeing a light in the sky and concluding that it is an alien aircraft would be argumentative evidence.
  • Testimonial evidence — When an individual presents an opinion, it is testimonial evidence. Once again, this is unreliable, as people may be biased and there may not be any direct evidence to support their testimony.

“The weight of evidence for an extraordinary claim must be proportioned to its strangeness.”

— Laplace, Théorie analytique des probabilités (1812)

Reasoning by Induction

The fictional character Sherlock Holmes is a master of induction. He is a careful observer who processes what he sees to reach the most likely conclusion in the given set of circumstances. Although he pretends that his knowledge is of the black-or-white variety, it often isn’t. It is true induction, coming up with the strongest possible explanation for the phenomena he observes.

Consider his description of how, upon first meeting Watson, he reasoned that Watson had just come from Afghanistan:

“Observation with me is second nature. You appeared to be surprised when I told you, on our first meeting, that you had come from Afghanistan.”
“You were told, no doubt.”

“Nothing of the sort. I knew you came from Afghanistan. From long habit the train of thoughts ran so swiftly through my mind, that I arrived at the conclusion without being conscious of intermediate steps. There were such steps, however. The train of reasoning ran, ‘Here is a gentleman of a medical type, but with the air of a military man. Clearly an army doctor, then. He has just come from the tropics, for his face is dark, and that is not the natural tint of his skin, for his wrists are fair. He has undergone hardship and sickness, as his haggard face says clearly. His left arm has been injured. He holds it in a stiff and unnatural manner. Where in the tropics could an English army doctor have seen much hardship and got his arm wounded? Clearly in Afghanistan.’ The whole train of thought did not occupy a second. I then remarked that you came from Afghanistan, and you were astonished.”

(From Sir Arthur Conan Doyle’s A Study in Scarlet)

Inductive reasoning involves drawing conclusions from facts, using logic. We draw these kinds of conclusions all the time. If someone we know to have good literary taste recommends a book, we may assume that means we will enjoy the book.

Induction can be strong or weak. If an inductive argument is strong, the truth of the premise would mean the conclusion is likely. If an inductive argument is weak, the logic connecting the premise and conclusion is incorrect.

There are several key types of inductive reasoning:

  • Generalized — Draws a conclusion from a generalization. For example, “All the swans I have seen are white; therefore, all swans are probably white.”
  • Statistical — Draws a conclusion based on statistics. For example, “95 percent of swans are white” (an arbitrary figure, of course); “therefore, a randomly selected swan will probably be white.”
  • Sample — Draws a conclusion about one group based on a different, sample group. For example, “There are ten swans in this pond and all are white; therefore, the swans in my neighbor’s pond are probably also white.”
  • Analogous — Draws a conclusion based on shared properties of two groups. For example, “All Aylesbury ducks are white. Swans are similar to Aylesbury ducks. Therefore, all swans are probably white.”
  • Predictive — Draws a conclusion based on a prediction made using a past sample. For example, “I visited this pond last year and all the swans were white. Therefore, when I visit again, all the swans will probably be white.”
  • Causal inference — Draws a conclusion based on a causal connection. For example, “All the swans in this pond are white. I just saw a white bird in the pond. The bird was probably a swan.”

The entire legal system is designed to be based on sound reasoning, which in turn must be based on evidence. Lawyers often use inductive reasoning to draw a relationship between facts for which they have evidence and a conclusion.

The initial facts are often based on generalizations and statistics, with the implication that a conclusion is most likely to be true, even if that is not certain. For that reason, evidence can rarely be considered certain. For example, a fingerprint taken from a crime scene would be said to be “consistent with a suspect’s prints” rather than being an exact match. Implicit in that statement is the assertion that it is statistically unlikely that the prints are not the suspect’s.

Inductive reasoning also involves Bayesian thinking. A conclusion can seem to be true at one point, until further evidence emerges and a hypothesis must be adjusted. Bayesian updating is a technique used to modify the probability of a hypothesis’s being true as new evidence is supplied. When inductive reasoning is used in legal situations, Bayesian thinking is used to update the likelihood of a defendant’s being guilty beyond a reasonable doubt as evidence is collected. If we imagine a simplified, hypothetical criminal case, we can picture the utility of Bayesian inference combined with inductive reasoning.

Let’s say someone is murdered in a house where five other adults were present at the time. One of them is the primary suspect, and there is no evidence of anyone else entering the house. The initial probability of the prime suspect’s having committed the murder is 20 percent. Other evidence will then adjust that probability. If the four other people testify that they saw the suspect committing the murder, the suspect’s prints are on the murder weapon, and traces of the victim’s blood were found on the suspect’s clothes, jurors may consider the probability of that person’s guilt to be close enough to 100 percent to convict. Reality is more complex than this, of course. The conclusion is never certain, only highly probable.

One key distinction between deductive and inductive reasoning is that the latter accepts that a conclusion is uncertain and may change in the future. A conclusion is either strong or weak, not right or wrong. We tend to use this type of reasoning in everyday life, drawing conclusions from experiences and then updating our beliefs.

A conclusion is either strong or weak, not right or wrong.

Everyday inductive reasoning is not always correct, but it is often useful. For example, superstitious beliefs often originate from inductive reasoning. If an athlete performed well on a day when they wore their socks inside out, they may conclude that the inside-out socks brought them luck. If future successes happen when they again wear their socks inside out, the belief may strengthen. Should that not be the case, they may update their belief and recognize that it is incorrect.

Another example (let’s set aside the question of whether turkeys can reason): A farmer feeds a turkey every day, so the turkey assumes that the farmer cares for its wellbeing. Only when Thanksgiving rolls around does that assumption prove incorrect.

The issue with overusing inductive reasoning is that cognitive shortcuts and biases can warp the conclusions we draw. Our world is not always as predictable as inductive reasoning suggests, and we may selectively draw upon past experiences to confirm a belief. Someone who reasons inductively that they have bad luck may recall only unlucky experiences to support that hypothesis and ignore instances of good luck.

In The 12 Secrets of Persuasive Argument, the authors write:

In inductive arguments, focus on the inference. When a conclusion relies upon an inference and contains new information not found in the premises, the reasoning is inductive. For example, if premises were established that the defendant slurred his words, stumbled as he walked, and smelled of alcohol, you might reasonably infer the conclusion that the defendant was drunk. This is inductive reasoning. In an inductive argument the conclusion is, at best, probable. The conclusion is not always true when the premises are true. The probability of the conclusion depends on the strength of the inference from the premises. Thus, when dealing with inductive reasoning, pay special attention to the inductive leap or inference, by which the conclusion follows the premises.

… There are several popular misconceptions about inductive and deductive reasoning. When Sherlock Holmes made his remarkable “deductions” based on observations of various facts, he was usually engaging in inductive, not deductive, reasoning.

In Inductive Reasoning, Aiden Feeney and Evan Heit write:

…inductive reasoning … corresponds to everyday reasoning. On a daily basis we draw inferences such as how a person will probably act, what the weather will probably be like, and how a meal will probably taste, and these are typical inductive inferences.

[…]

[I]t is a multifaceted cognitive activity. It can be studied by asking young children simple questions involving cartoon pictures, or it can be studied by giving adults a variety of complex verbal arguments and asking them to make probability judgments.

[…]

[I]nduction is related to, and it could be argued is central to, a number of other cognitive activities, including categorization, similarity judgment, probability judgment, and decision making. For example, much of the study of induction has been concerned with category-based induction, such as inferring that your next door neighbor sleeps on the basis that your neighbor is a human animal, even if you have never seen your neighbor sleeping.

“A very great deal more truth can become known than can be proven.”

— Richard Feynman

Reasoning by Deduction

Deduction begins with a broad truth (the major premise), such as the statement that all men are mortal. This is followed by the minor premise, a more specific statement, such as that Socrates is a man. A conclusion follows: Socrates is mortal. If the major premise is true and the minor premise is true the conclusion cannot be false.

Deductive reasoning is black and white; a conclusion is either true or false and cannot be partly true or partly false. We decide whether a deductive statement is true by assessing the strength of the link between the premises and the conclusion. If all men are mortal and Socrates is a man, there is no way he can not be mortal, for example. There are no situations in which the premise is not true, so the conclusion is true.

In science, deduction is used to reach conclusions believed to be true. A hypothesis is formed; then evidence is collected to support it. If observations support its truth, the hypothesis is confirmed. Statements are structured in the form of “if A equals B, and C is A, then C is B.” If A does not equal B, then C will not equal B. Science also involves inductive reasoning when broad conclusions are drawn from specific observations; data leads to conclusions. If the data shows a tangible pattern, it will support a hypothesis.

For example, having seen ten white swans, we could use inductive reasoning to conclude that all swans are white. This hypothesis is easier to disprove than to prove, and the premises are not necessarily true, but they are true given the existing evidence and given that researchers cannot find a situation in which it is not true. By combining both types of reasoning, science moves closer to the truth. In general, the more outlandish a claim is, the stronger the evidence supporting it must be.

We should be wary of deductive reasoning that appears to make sense without pointing to a truth. Someone could say “A dog has four paws. My pet has four paws. Therefore, my pet is a dog.” The conclusion sounds logical but isn’t, because the initial premise is too specific.

The History of Reasoning

The discussion of reasoning and what constitutes truth dates back to Plato and Aristotle.

Plato (429–347 BC) believed that all things are divided into the visible and the intelligible. Intelligible things can be known through deduction (with observation being of secondary importance to reasoning) and are true knowledge.

Aristotle took an inductive approach, emphasizing the need for observations to support knowledge. He believed that we can reason only from discernable phenomena. From there, we use logic to infer causes.

Debate about reasoning remained much the same until the time of Isaac Newton. Newton’s innovative work was based on observations, but also on concepts that could not be explained by a physical cause (such as gravity). In his Principia, Newton outlined four rules for reasoning in the scientific method:

  1. “We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.” (We refer to this rule as Occam’s Razor.)
  2. “Therefore, to the same natural effects we must, as far as possible, assign the same causes.”
  3. “The qualities of bodies, which admit neither intensification nor remission of degrees, and which are found to belong to all bodies within the reach of our experiments, are to be esteemed the universal qualities of all bodies whatsoever.”
  4. “In experimental philosophy, we are to look upon propositions collected by general induction from phenomena as accurately or very nearly true, notwithstanding any contrary hypotheses that may be imagined, ’till such time as other phenomena occur, by which they may either be made more accurate, or liable to exceptions.”

In 1843, philosopher John Stuart Mill published A System of Logic, which further refined our understanding of reasoning. Mill believed that science should be based on a search for regularities among events. If a regularity is consistent, it can be considered a law. Mill described five methods for identifying causes by noting regularities. These methods are still used today:

  • Direct method of agreement — If two instances of a phenomenon have a single circumstance in common, the circumstance is the cause or effect.
  • Method of difference — If a phenomenon occurs in one experiment and does not occur in another, and the experiments are the same except for one factor, that is the cause, part of the cause, or the effect.
  • Joint method of agreement and difference — If two instances of a phenomenon have one circumstance in common, and two instances in which it does not occur have nothing in common except the absence of that circumstance, then that circumstance is the cause, part of the cause, or the effect.
  • Method of residue — When you subtract any part of a phenomenon known to be caused by a certain antecedent, the remaining residue of the phenomenon is the effect of the remaining antecedents.
  • Method of concomitant variations — If a phenomenon varies when another phenomenon varies in a particular way, the two are connected.

Karl Popper was the next theorist to make a serious contribution to the study of reasoning. Popper is well known for his focus on disconfirming evidence and disproving hypotheses. Beginning with a hypothesis, we use deductive reasoning to make predictions. A hypothesis will be based on a theory — a set of independent and dependent statements. If the predictions are true, the theory is true, and vice versa. Popper’s theory of falsification (disproving something) is based on the idea that we cannot prove a hypothesis; we can only show that certain predictions are false. This process requires vigorous testing to identify any anomalies, and Popper does not accept theories that cannot be physically tested. Any phenomenon not present in tests cannot be the foundation of a theory, according to Popper. The phenomenon must also be consistent and reproducible. Popper’s theories acknowledge that theories that are accepted at one time are likely to later be disproved. Science is always changing as more hypotheses are modified or disproved and we inch closer to the truth.

Conclusion

In How to Deliver a TED Talk, Jeremey Donovan writes:

No discussion of logic is complete without a refresher course in the difference between inductive and deductive reasoning. By its strictest definition, inductive reasoning proves a general principle—your idea worth spreading—by highlighting a group of specific events, trends, or observations. In contrast, deductive reasoning builds up to a specific principle—again, your idea worth spreading—through a chain of increasingly narrow statements.

Logic is an incredibly important skill, and because we use it so often in everyday life, we benefit by clarifying the methods we use to draw conclusions. Knowing what makes an argument sound is valuable for making decisions and understanding how the world works. It helps us to spot people who are deliberately misleading us through unsound arguments. Understanding reasoning is also helpful for avoiding fallacies and for negotiating.

FS Members can discuss this article on the Learning Community Forum.

The Value of Probabilistic Thinking: Spies, Crime, and Lightning Strikes

Probabilistic thinking is essentially trying to estimate, using some tools of math and logic, the likelihood of any specific outcome coming to pass. It is one of the best tools we have to improve the accuracy of our decisions. In a world where each moment is determined by an infinitely complex set of factors, probabilistic thinking helps us identify the most likely outcomes. When we know these our decisions can be more precise and effective.

Are you going to get hit by lightning or not?

Why we need the concept of probabilities at all is worth thinking about. Things either are or are not, right? We either will get hit by lightning today or we won’t. The problem is, we just don’t know until we live out the day, which doesn’t help us at all when we make our decisions in the morning. The future is far from determined and we can better navigate it by understanding the likelihood of events that could impact us.

Our lack of perfect information about the world gives rise to all of probability theory, and its usefulness. We know now that the future is inherently unpredictable because not all variables can be known and even the smallest error imaginable in our data very quickly throws off our predictions. The best we can do is estimate the future by generating realistic, useful probabilities. So how do we do that?

Probability is everywhere, down to the very bones of the world. The probabilistic machinery in our minds—the cut-to-the-quick heuristics made so famous by the psychologists Daniel Kahneman and Amos Tversky—was evolved by the human species in a time before computers, factories, traffic, middle managers, and the stock market. It served us in a time when human life was about survival, and still serves us well in that capacity.

But what about today—a time when, for most of us, survival is not so much the issue? We want to thrive. We want to compete, and win. Mostly, we want to make good decisions in complex social systems that were not part of the world in which our brains evolved their (quite rational) heuristics.

For this, we need to consciously add in a needed layer of probability awareness. What is it and how can I use it to my advantage?

There are three important aspects of probability that we need to explain so you can integrate them into your thinking to get into the ballpark and improve your chances of catching the ball:

  1. Bayesian thinking,
  2. Fat-tailed curves
  3. Asymmetries

Thomas Bayes and Bayesian thinking: Bayes was an English minister in the first half of the 18th century, whose most famous work, “An Essay Toward Solving a Problem in the Doctrine of Chances” was brought to the attention of the Royal Society by his friend Richard Price in 1763—two years after his death. The essay, the key to what we now know as Bayes’s Theorem, concerned how we should adjust probabilities when we encounter new data.

The core of Bayesian thinking (or Bayesian updating, as it can be called) is this: given that we have limited but useful information about the world, and are constantly encountering new information, we should probably take into account what we already know when we learn something new. As much of it as possible. Bayesian thinking allows us to use all relevant prior information in making decisions. Statisticians might call it a base rate, taking in outside information about past situations like the one you’re in.

Consider the headline “Violent Stabbings on the Rise.” Without Bayesian thinking, you might become genuinely afraid because your chances of being a victim of assault or murder is higher than it was a few months ago. But a Bayesian approach will have you putting this information into the context of what you already know about violent crime.

You know that violent crime has been declining to its lowest rates in decades. Your city is safer now than it has been since this measurement started. Let’s say your chance of being a victim of a stabbing last year was one in 10,000, or 0.01%. The article states, with accuracy, that violent crime has doubled. It is now two in 10,000, or 0.02%. Is that worth being terribly worried about? The prior information here is key. When we factor it in, we realize that our safety has not really been compromised.

Conversely, if we look at the diabetes statistics in the United States, our application of prior knowledge would lead us to a different conclusion. Here, a Bayesian analysis indicates you should be concerned. In 1958, 0.93% of the population was diagnosed with diabetes. In 2015 it was 7.4%. When you look at the intervening years, the climb in diabetes diagnosis is steady, not a spike. So the prior relevant data, or priors, indicate a trend that is worrisome.

It is important to remember that priors themselves are probability estimates. For each bit of prior knowledge, you are not putting it in a binary structure, saying it is true or not. You’re assigning it a probability of being true. Therefore, you can’t let your priors get in the way of processing new knowledge. In Bayesian terms, this is called the likelihood ratio or the Bayes factor. Any new information you encounter that challenges a prior simply means that the probability of that prior being true may be reduced. Eventually, some priors are replaced completely. This is an ongoing cycle of challenging and validating what you believe you know. When making uncertain decisions, it’s nearly always a mistake not to ask: What are the relevant priors? What might I already know that I can use to better understand the reality of the situation?

Now we need to look at fat-tailed curves: Many of us are familiar with the bell curve, that nice, symmetrical wave that captures the relative frequency of so many things from height to exam scores. The bell curve is great because it’s easy to understand and easy to use. Its technical name is “normal distribution.” If we know we are in a bell curve situation, we can quickly identify our parameters and plan for the most likely outcomes.

Fat-tailed curves are different. Take a look.

At first glance they seem similar enough. Common outcomes cluster together, creating a wave. The difference is in the tails. In a bell curve the extremes are predictable. There can only be so much deviation from the mean. In a fat-tailed curve there is no real cap on extreme events.

The more extreme events that are possible, the longer the tails of the curve get. Any one extreme event is still unlikely, but the sheer number of options means that we can’t rely on the most common outcomes as representing the average. The more extreme events that are possible, the higher the probability that one of them will occur. Crazy things are definitely going to happen, and we have no way of identifying when.

Think of it this way. In a bell curve type of situation, like displaying the distribution of height or weight in a human population, there are outliers on the spectrum of possibility, but the outliers have a fairly well defined scope. You’ll never meet a man who is ten times the size of an average man. But in a curve with fat tails, like wealth, the central tendency does not work the same way. You may regularly meet people who are ten, 100, or 10,000 times wealthier than the average person. That is a very different type of world.

Let’s re-approach the example of the risks of violence we discussed in relation to Bayesian thinking. Suppose you hear that you had a greater risk of slipping on the stairs and cracking your head open than being killed by a terrorist. The statistics, the priors, seem to back it up: 1,000 people slipped on the stairs and died last year in your country and only 500 died of terrorism. Should you be more worried about stairs or terror events?

Some use examples like these to prove that terror risk is low—since the recent past shows very few deaths, why worry?[1] The problem is in the fat tails: The risk of terror violence is more like wealth, while stair-slipping deaths are more like height and weight. In the next ten years, how many events are possible? How fat is the tail?

The important thing is not to sit down and imagine every possible scenario in the tail (by definition, it is impossible) but to deal with fat-tailed domains in the correct way: by positioning ourselves to survive or even benefit from the wildly unpredictable future, by being the only ones thinking correctly and planning for a world we don’t fully understand.

Asymmetries: Finally, you need to think about something we might call “metaprobability” —the probability that your probability estimates themselves are any good.

This massively misunderstood concept has to do with asymmetries. If you look at nicely polished stock pitches made by professional investors, nearly every time an idea is presented, the investor looks their audience in the eye and states they think they’re going to achieve a rate of return of 20% to 40% per annum, if not higher. Yet exceedingly few of them ever attain that mark, and it’s not because they don’t have any winners. It’s because they get so many so wrong. They consistently overestimate their confidence in their probabilistic estimates. (For reference, the general stock market has returned no more than 7% to 8% per annum in the United States over a long period, before fees.)

Another common asymmetry is people’s ability to estimate the effect of traffic on travel time. How often do you leave “on time” and arrive 20% early? Almost never? How often do you leave “on time” and arrive 20% late? All the time? Exactly. Your estimation errors are asymmetric, skewing in a single direction. This is often the case with probabilistic decision-making.[2]

Far more probability estimates are wrong on the “over-optimistic” side than the “under-optimistic” side. You’ll rarely read about an investor who aimed for 25% annual return rates who subsequently earned 40% over a long period of time. You can throw a dart at the Wall Street Journal and hit the names of lots of investors who aim for 25% per annum with each investment and end up closer to 10%.

The spy world

Successful spies are very good at probabilistic thinking. High-stakes survival situations tend to make us evaluate our environment with as little bias as possible.

When Vera Atkins was second in command of the French unit of the Special Operations Executive (SOE), a British intelligence organization reporting directly to Winston Churchill during World War II[3], she had to make hundreds of decisions by figuring out the probable accuracy of inherently unreliable information.

Atkins was responsible for the recruitment and deployment of British agents into occupied France. She had to decide who could do the job, and where the best sources of intelligence were. These were literal life-and-death decisions, and all were based in probabilistic thinking.

First, how do you choose a spy? Not everyone can go undercover in high-stress situations and make the contacts necessary to gather intelligence. The result of failure in France in WWII was not getting fired; it was death. What factors of personality and experience show that a person is right for the job? Even today, with advancements in psychology, interrogation, and polygraphs, it’s still a judgment call.

For Vera Atkins in the 1940s, it was very much a process of assigning weight to the various factors and coming up with a probabilistic assessment of who had a decent chance of success. Who spoke French? Who had the confidence? Who was too tied to family? Who had the problem-solving capabilities? From recruitment to deployment, her development of each spy was a series of continually updated, educated estimates.

Getting an intelligence officer ready to go is only half the battle. Where do you send them? If your information was so great that you knew exactly where to go, you probably wouldn’t need an intelligence mission. Choosing a target is another exercise in probabilistic thinking. You need to evaluate the reliability of the information you have and the networks you have set up. Intelligence is not evidence. There is no chain of command or guarantee of authenticity.

The stuff coming out of German-occupied France was at the level of grainy photographs, handwritten notes that passed through many hands on the way back to HQ, and unverifiable wireless messages sent quickly, sometimes sporadically, and with the operator under incredible stress. When deciding what to use, Atkins had to consider the relevancy, quality, and timeliness of the information she had.

She also had to make decisions based not only on what had happened, but what possibly could. Trying to prepare for every eventuality means that spies would never leave home, but they must somehow prepare for a good deal of the unexpected. After all, their jobs are often executed in highly volatile, dynamic environments. The women and men Atkins sent over to France worked in three primary occupations: organizers were responsible for recruiting locals, developing the network, and identifying sabotage targets; couriers moved information all around the country, connecting people and networks to coordinate activities; and wireless operators had to set up heavy communications equipment, disguise it, get information out of the country, and be ready to move at a moment’s notice. All of these jobs were dangerous. The full scope of the threats was never completely identifiable. There were so many things that could go wrong, so many possibilities for discovery or betrayal, that it was impossible to plan for them all. The average life expectancy in France for one of Atkins’ wireless operators was six weeks.

Finally, the numbers suggest an asymmetry in the estimation of the probability of success of each individual agent. Of the 400 agents that Atkins sent over to France, 100 were captured and killed. This is not meant to pass judgment on her skills or smarts. Probabilistic thinking can only get you in the ballpark. It doesn’t guarantee 100% success.

There is no doubt that Atkins relied heavily on probabilistic thinking to guide her decisions in the challenging quest to disrupt German operations in France during World War II. It is hard to evaluate the success of an espionage career, because it is a job that comes with a lot of loss. Atkins was extremely successful in that her network conducted valuable sabotage to support the allied cause during the war, but the loss of life was significant.

Conclusion

Successfully thinking in shades of probability means roughly identifying what matters, coming up with a sense of the odds, doing a check on our assumptions, and then making a decision. We can act with a higher level of certainty in complex, unpredictable situations. We can never know the future with exact precision. Probabilistic thinking is an extremely useful tool to evaluate how the world will most likely look so that we can effectively strategize.

Members can discuss this post on the Learning Community Forum

References:

[1] Taleb, Nassim Nicholas. Antifragile. New York: Random House, 2012.

[2] Bernstein, Peter L. Against the Gods: The Remarkable Story of Risk. New York: John Wiley and Sons, 1996. (This book includes an excellent discussion in Chapter 13 on the idea of the scope of events in the past as relevant to figuring out the probability of events in the future, drawing on the work of Frank Knight and John Maynard Keynes.)

[3] Helm, Sarah. A Life in Secrets: The Story of Vera Atkins and the Lost Agents of SOE. London: Abacus, 2005.

Inertia: The Force That Holds the Universe Together

Inertia is the force that holds the universe together. Literally. Without it, things would fall apart. It’s also what keeps us locked in destructive habits, and resistant to change.

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“If it were possible to flick a switch and turn off inertia, the universe would collapse in an instant to a clump of matter,” write Peter and Neal Garneau in In the Grip of the Distant Universe: The Science of Inertia.

“…death is the destination we all share. No one has ever escaped it. And that is as it should be, because death is very likely the single best invention of life. It’s life’s change agent; it clears out the old to make way for the new … Your time is limited, so don’t waste it living someone else’s life.”

— Steve Jobs

Inertia is the force that holds the universe together. Literally. Without it, matter would lack the electric forces necessary to form its current arrangement. Inertia is counteracted by the heat and kinetic energy produced by moving particles. Subtract it and everything cools to -459.67 degrees Fahrenheit (absolute zero temperature). Yet we know so little about inertia and how to leverage it in our daily lives.

Inertia: The Force That Holds the Universe Together

The Basics

The German astronomer Johannes Kepler (1571–1630) coined the word “inertia.” The etymology of the term is telling. Kepler obtained it from the Latin for “unskillfulness, ignorance; inactivity or idleness.” True to its origin, inertia keeps us in bed on a lazy Sunday morning (we need to apply activation energy to overcome this state).

Inertia refers to resistance to change — in particular, resistance to changes in motion. Inertia may manifest in physical objects or in the minds of people.

We learn the principle of inertia early on in life. We all know that it takes a force to get something moving, to change its direction, or to stop it.

Our intuitive sense of how inertia works enables us to exercise a degree of control over the world around us. Learning to drive offers further lessons. Without external physical forces, a car would keep moving in a straight line in the same direction. It takes a force (energy) to get a car moving and overcome the inertia that kept it still in a parking space. Changing direction to round a corner or make a U-turn requires further energy. Inertia is why a car does not stop the moment the brakes are applied.

The heavier a vehicle is, the harder it is to overcome inertia and make it stop. A light bicycle stops with ease, while an eight-carriage passenger train needs a good mile to halt. Similarly, the faster we run, the longer it takes to stop. Running in a straight line is much easier than twisting through a crowded sidewalk, changing direction to dodge people.

Any object that can be rotated, such as a wheel, has rotational inertia. This tells us how hard it is to change the object’s speed around the axis. Rotational inertia depends on the mass of the object and its distribution relative to the axis.

Inertia is Newton’s first law of motion, a fundamental principle of physics. Newton summarized it this way: “The vis insita, or innate force of matter, is a power of resisting by which every body, as much as in it lies, endeavors to preserve its present state, whether it be of rest or of moving uniformly forward in a straight line.”

When developing his first law, Newton drew upon the work of Galileo Galilei. In a 1624 letter to Francesco Ingoli, Galileo outlined the principle of inertia:

I tell you that if natural bodies have it from Nature to be moved by any movement, this can only be a circular motion, nor is it possible that Nature has given to any of its integral bodies a propensity to be moved by straight motion. I have many confirmations of this proposition, but for the present one alone suffices, which is this.

I suppose the parts of the universe to be in the best arrangement so that none is out of its place, which is to say that Nature and God have perfectly arranged their structure… Therefore, if the parts of the world are well ordered, the straight motion is superfluous and not natural, and they can only have it when some body is forcibly removed from its natural place, to which it would then return to a straight line.

In 1786, Immanuel Kant elaborated further: “All change of matter has an external cause. (Every body remains in its state of rest or motion in the same direction and with the same velocity, if not compelled by an external cause to forsake this state.) … This mechanical law can only be called the law of inertia (lex inertiæ)….”

Now that we understand the principle, let’s look at some of the ways we can understand it better and apply it to our advantage.

Decision Making and Cognitive Inertia

We all experience cognitive inertia: the tendency to stick to existing ideas, beliefs, and habits even when they no longer serve us well. Few people are truly able to revise their opinions in light of disconfirmatory information. Instead, we succumb to confirmation bias and seek out verification of existing beliefs. It’s much easier to keep thinking what we’ve always been thinking than to reflect on the chance that we might be wrong and update our views. It takes work to overcome cognitive dissonance, just as it takes effort to stop a car or change its direction.

When the environment changes, clinging to old beliefs can be harmful or even fatal. Whether we fail to perceive the changes or fail to respond to them, the result is the same. Even when it’s obvious to others that we must change, it’s not obvious to us. It’s much easier to see something when you’re not directly involved. If I ask you how fast you’re moving right now, you’d likely say zero, but you’re moving 18,000 miles an hour around the sun. Perspective is everything, and the perspective that matters is the one that most closely lines up with reality.

“Sometimes you make up your mind about something without knowing why, and your decision persists by the power of inertia. Every year it gets harder to change.”

— Milan Kundera, The Unbearable Lightness of Being

Cognitive inertia is the reason that changing our habits can be difficult. The default is always the path of least resistance, which is easy to accept and harder to question. Consider your bank, for example. Perhaps you know that there are better options at other banks. Or you have had issues with your bank that took ages to get sorted. Yet very few people actually change their banks, and many of us stick with the account we first opened. After all, moving away from the status quo would require a lot of effort: researching alternatives, transferring balances, closing accounts, etc. And what if something goes wrong? Sounds risky. The switching costs are high, so we stick to the status quo.

Sometimes inertia helps us. After all, questioning everything would be exhausting. But in many cases, it is worthwhile to overcome inertia and set something in motion, or change direction, or halt it.

The important thing about inertia is that it is only the initial push that is difficult. After that, progress tends to be smoother. Ernest Hemingway had a trick for overcoming inertia in his writing. Knowing that getting started was always the hardest part, he chose to finish work each day at a point where he had momentum (rather than when he ran out of ideas). The next day, he could pick up from there. In A Moveable Feast, Hemingway explains:

I always worked until I had something done and I always stopped when I knew what was going to happen next. That way I could be sure of going on the next day.

Later on in the book, he describes another method, which was to write just one sentence:

Do not worry. You have always written before and you will write now. All you have to do is write one true sentence. Write the truest sentence that you know. So, finally I would write one true sentence and go on from there. It was easy then because there was always one true sentence that I knew or had seen or had heard someone say. If I started to write elaborately, or like someone introducing or presenting something, I found that I could cut that scrollwork or ornament out and throw it away and start with the first true simple declarative sentence I had written.

We can learn a lot from Hemingway’s approach to tackling inertia and apply it in areas beyond writing. As with physics, the momentum from getting started can carry us a long way. We just need to muster the required activation energy and get going.

Status Quo Bias: “When in Doubt, Do Nothing”

Cognitive inertia also manifests in the form of status quo bias. When making decisions, we are rarely rational. Faced with competing options and information, we often opt for the default because it’s easy. Doing something other than what we’re already doing requires mental energy that we would rather preserve. In many areas, this helps us avoid decision fatigue.

Many of us eat the same meals most of the time, wear similar outfits, and follow routines. This tendency usually serves us well. But the status quo is not necessarily the optimum solution. Indeed, it may be outright harmful or at least unhelpful if something has changed in the environment or we want to optimize our use of time.

“The great enemy of any attempt to change men’s habits is inertia. Civilization is limited by inertia.”

— Edward L. Bernays, Propaganda

In a paper entitled “If you like it, does it matter if it’s real?” Felipe De Brigard[1] offers a powerful illustration of status quo bias. One of the best-known thought experiments concerns Robert Nozick’s “experience machine.” Nozick asked us to imagine that scientists have created a virtual reality machine capable of simulating any pleasurable experience. We are offered the opportunity to plug ourselves in and live out the rest of our lives in permanent, but fake enjoyment. The experience machine would later inspire the Matrix film series. Presented with the thought experiment, most people balk and claim they would prefer reality. But what if we flip the narrative? De Brigard believed that we are opposed to the experience machine because it contradicts the status quo, the life we are accustomed to.

In an experiment, he asked participants to imagine themselves woken by the doorbell on a Saturday morning. A man in black, introducing himself as Mr. Smith, is at the door. He claims to have vital information. Mr. Smith explains that there has been an error and you are in fact connected to an experience machine. Everything you have lived through so far has been a simulation. He offers a choice: stay plugged in, or return to an unknown real life. Unsurprisingly, far fewer people wished to return to reality in the latter situation than wished to remain in it in the former. The aversive element is not the experience machine itself, but the departure from the status quo it represents.

Conclusion

Inertia is a pervasive, problematic force. It’s the pull that keeps us clinging to old ways and prevents us from trying new things. But as we have seen, it is also a necessary one. Without it, the universe would collapse. Inertia is what enables us to maintain patterns of functioning, maintain relationships, and get through the day without questioning everything. We can overcome inertia much like Hemingway did — by recognizing its influence and taking the necessary steps to create that all-important initial momentum.

***

Prime Members can discuss this on the Learning Community Forum.

End Notes

[1] https://www.tandfonline.com/doi/abs/10.1080/09515080903532290

Go Fast and Break Things: The Difference Between Reversible and Irreversible Decisions

Reversible vs. irreversible decisions. We often think that collecting as much information as possible will help us make the best decisions. Sometimes that’s true, but sometimes it hamstrings our progress. Other times it can be flat out dangerous.

***

Many of the most successful people adopt simple, versatile decision-making heuristics to remove the need for deliberation in particular situations.

One heuristic might be defaulting to saying no, as Steve Jobs did. Or saying no to any decision that requires a calculator or computer, as Warren Buffett does. Or it might mean reasoning from first principles, as Elon Musk does. Jeff Bezos, the founder of Amazon.com, has another one we can add to our toolbox. He asks himself, is this a reversible or irreversible decision?

If a decision is reversible, we can make it fast and without perfect information. If a decision is irreversible, we had better slow down the decision-making process and ensure that we consider ample information and understand the problem as thoroughly as we can.

Bezos used this heuristic to make the decision to found Amazon. He recognized that if Amazon failed, he could return to his prior job. He would still have learned a lot and would not regret trying. The decision was reversible, so he took a risk. The heuristic served him well and continues to pay off when he makes decisions.

Decisions Amidst Uncertainty

Let’s say you decide to try a new restaurant after reading a review online. Having never been there before, you cannot know if the food will be good or if the atmosphere will be dreary. But you use the incomplete information from the review to make a decision, recognizing that it’s not a big deal if you don’t like the restaurant.

In other situations, the uncertainty is a little riskier. You might decide to take a particular job, not knowing what the company culture is like or how you will feel about the work after the honeymoon period ends.

Reversible decisions can be made fast and without obsessing over finding complete information. We can be prepared to extract wisdom from the experience with little cost if the decision doesn’t work out. Frequently, it’s not worth the time and energy required to gather more information and look for flawless answers. Although your research might make your decision 5% better, you might miss an opportunity.

Reversible decisions are not an excuse to act reckless or be ill-informed, but is rather a belief that we should adapt the frameworks of our decisions to the types of decisions we are making. Reversible decisions don’t need to be made the same way as irreversible decisions.

The ability to make decisions fast is a competitive advantage. One major advantage that start-ups have is that they can move with velocity, whereas established incumbents typically move with speed. The difference between the two is meaningful and often means the difference between success and failure.

Speed is measured as distance over time. If we’re headed from New York to LA on an airplane and we take off from JFK and circle around New York for three hours, we’re moving with a lot of speed, but we’re not getting anywhere. Speed doesn’t care if you are moving toward your goals or not. Velocity, on the other hand, measures displacement over time. To have velocity, you need to be moving toward your goal.

This heuristic explains why start-ups making quick decisions have an advantage over incumbents. That advantage is magnified by environmental factors, such as the pace of change. The faster the pace of environmental change, the more an advantage will accrue to people making quick decisions because those people can learn faster.

Decisions provide us with data, which can then make our future decisions better. The faster we can cycle through the OODA loop, the better. This framework isn’t a one-off to apply to certain situations; it is a heuristic that needs to be an integral part of a decision-making toolkit.

With practice, we also get better at recognizing bad decisions and pivoting, rather than sticking with past choices due to the sunk costs fallacy. Equally important, we can stop viewing mistakes or small failures as disastrous and view them as pure information which will inform future decisions.

“A good plan, violently executed now, is better than a perfect plan next week.”

— General George Patton

Bezos compares decisions to doors. Reversible decisions are doors that open both ways. Irreversible decisions are doors that allow passage in only one direction; if you walk through, you are stuck there. Most decisions are the former and can be reversed (even though we can never recover the invested time and resources). Going through a reversible door gives us information: we know what’s on the other side.

In his shareholder letter, Bezos writes[1]:

Some decisions are consequential and irreversible or nearly irreversible – one-way doors – and these decisions must be made methodically, carefully, slowly, with great deliberation and consultation. If you walk through and don’t like what you see on the other side, you can’t get back to where you were before. We can call these Type 1 decisions. But most decisions aren’t like that – they are changeable, reversible – they’re two-way doors. If you’ve made a suboptimal Type 2 decision, you don’t have to live with the consequences for that long. You can reopen the door and go back through. Type 2 decisions can and should be made quickly by high judgment individuals or small groups.

As organizations get larger, there seems to be a tendency to use the heavy-weight Type 1 decision-making process on most decisions, including many Type 2 decisions. The end result of this is slowness, unthoughtful risk aversion, failure to experiment sufficiently, and consequently diminished invention. We’ll have to figure out how to fight that tendency.

Bezos gives the example of the launch of one-hour delivery to those willing to pay extra. This service launched less than four months after the idea was first developed. In 111 days, the team “built a customer-facing app, secured a location for an urban warehouse, determined which 25,000 items to sell, got those items stocked, recruited and onboarded new staff, tested, iterated, designed new software for internal use – both a warehouse management system and a driver-facing app – and launched in time for the holidays.”

As further guidance, Bezos considers 70% certainty to be the cut-off point where it is appropriate to make a decision. That means acting once we have 70% of the required information, instead of waiting longer. Making a decision at 70% certainty and then course-correcting is a lot more effective than waiting for 90% certainty.

In Blink: The Power of Thinking Without Thinking, Malcolm Gladwell explains why decision-making under uncertainty can be so effective. We usually assume that more information leads to better decisions — if a doctor proposes additional tests, we tend to believe they will lead to a better outcome. Gladwell disagrees: “In fact, you need to know very little to find the underlying signature of a complex phenomenon. All you need is evidence of the ECG, blood pressure, fluid in the lungs, and an unstable angina. That’s a radical statement.”

In medicine, as in many areas, more information does not necessarily ensure improved outcomes. To illustrate this, Gladwell gives the example of a man arriving at a hospital with intermittent chest pains. His vital signs show no risk factors, yet his lifestyle does and he had heart surgery two years earlier. If a doctor looks at all the available information, it may seem that the man needs admitting to the hospital. But the additional factors, beyond the vital signs, are not important in the short term. In the long run, he is at serious risk of developing heart disease. Gladwell writes,

… the role of those other factors is so small in determining what is happening to the man right now that an accurate diagnosis can be made without them. In fact, … that extra information is more than useless. It’s harmful. It confuses the issues. What screws up doctors when they are trying to predict heart attacks is that they take too much information into account.

We can all learn from Bezos’s approach, which has helped him to build an enormous company while retaining the tempo of a start-up. Bezos uses his heuristic to fight the stasis that sets in within many large organizations. It is about being effective, not about following the norm of slow decisions.

Once you understand that reversible decisions are in fact reversible you can start to see them as opportunities to increase the pace of your learning. At a corporate level, allowing employees to make and learn from reversible decisions helps you move at the pace of a start-up. After all, if someone is moving with speed, you’re going to pass them when you move with velocity.

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Members can discuss this on the Learning Community Forum.

End Notes

[1] https://www.sec.gov/Archives/edgar/data/1018724/000119312516530910/d168744dex991.htm

First Principles: The Building Blocks of True Knowledge

First-principles thinking is one of the best ways to reverse-engineer complicated problems and unleash creative possibility. Sometimes called “reasoning from first principles,” the idea is to break down complicated problems into basic elements and then reassemble them from the ground up. It’s one of the best ways to learn to think for yourself, unlock your creative potential, and move from linear to non-linear results.

This approach was used by the philosopher Aristotle and is used now by Elon Musk and Charlie Munger. It allows them to cut through the fog of shoddy reasoning and inadequate analogies to see opportunities that others miss.

“I don’t know what’s the matter with people: they don’t learn by understanding; they learn by some other way—by rote or something. Their knowledge is so fragile!”

— Richard Feynman

The Basics

A first principle is a foundational proposition or assumption that stands alone. We cannot deduce first principles from any other proposition or assumption.

Aristotle, writing[1] on first principles, said:

In every systematic inquiry (methodos) where there are first principles, or causes, or elements, knowledge and science result from acquiring knowledge of these; for we think we know something just in case we acquire knowledge of the primary causes, the primary first principles, all the way to the elements.

Later he connected the idea to knowledge, defining first principles as “the first basis from which a thing is known.”[2]

The search for first principles is not unique to philosophy. All great thinkers do it.

Reasoning by first principles removes the impurity of assumptions and conventions. What remains is the essentials. It’s one of the best mental models you can use to improve your thinking because the essentials allow you to see where reasoning by analogy might lead you astray.

The Coach and the Play Stealer

My friend Mike Lombardi (a former NFL executive) and I were having dinner in L.A. one night, and he said, “Not everyone that’s a coach is really a coach. Some of them are just play stealers.”

Every play we see in the NFL was at some point created by someone who thought, “What would happen if the players did this?” and went out and tested the idea. Since then, thousands, if not millions, of plays have been created. That’s part of what coaches do. They assess what’s physically possible, along with the weaknesses of the other teams and the capabilities of their own players, and create plays that are designed to give their teams an advantage.

The coach reasons from first principles. The rules of football are the first principles: they govern what you can and can’t do. Everything is possible as long as it’s not against the rules.

The play stealer works off what’s already been done. Sure, maybe he adds a tweak here or there, but by and large he’s just copying something that someone else created.

While both the coach and the play stealer start from something that already exists, they generally have different results. These two people look the same to most of us on the sidelines or watching the game on the TV. Indeed, they look the same most of the time, but when something goes wrong, the difference shows. Both the coach and the play stealer call successful plays and unsuccessful plays. Only the coach, however, can determine why a play was successful or unsuccessful and figure out how to adjust it. The coach, unlike the play stealer, understands what the play was designed to accomplish and where it went wrong, so he can easily course-correct. The play stealer has no idea what’s going on. He doesn’t understand the difference between something that didn’t work and something that played into the other team’s strengths.

Musk would identify the play stealer as the person who reasons by analogy, and the coach as someone who reasons by first principles. When you run a team, you want a coach in charge and not a play stealer. (If you’re a sports fan, you need only look at the difference between the Cleveland Browns and the New England Patriots.)

We’re all somewhere on the spectrum between coach and play stealer. We reason by first principles, by analogy, or a blend of the two.

Another way to think about this distinction comes from another friend, Tim Urban. He says[3] it’s like the difference between the cook and the chef. While these terms are often used interchangeably, there is an important nuance. The chef is a trailblazer, the person who invents recipes. He knows the raw ingredients and how to combine them. The cook, who reasons by analogy, uses a recipe. He creates something, perhaps with slight variations, that’s already been created.

The difference between reasoning by first principles and reasoning by analogy is like the difference between being a chef and being a cook. If the cook lost the recipe, he’d be screwed. The chef, on the other hand, understands the flavor profiles and combinations at such a fundamental level that he doesn’t even use a recipe. He has real knowledge as opposed to know-how.

Authority

So much of what we believe is based on some authority figure telling us that something is true. As children, we learn to stop questioning when we’re told “Because I said so.” (More on this later.) As adults, we learn to stop questioning when people say “Because that’s how it works.” The implicit message is “understanding be damned — shut up and stop bothering me.” It’s not intentional or personal. OK, sometimes it’s personal, but most of the time, it’s not.

If you outright reject dogma, you often become a problem: a student who is always pestering the teacher. A kid who is always asking questions and never allowing you to cook dinner in peace. An employee who is always slowing things down by asking why.

When you can’t change your mind, though, you die. Sears was once thought indestructible before Wal-Mart took over. Sears failed to see the world change. Adapting to change is an incredibly hard thing to do when it comes into conflict with the very thing that caused so much success. As Upton Sinclair aptly pointed out, “It is difficult to get a man to understand something, when his salary depends on his not understanding it.” Wal-Mart failed to see the world change and is now under assault from Amazon.

If we never learn to take something apart, test the assumptions, and reconstruct it, we end up trapped in what other people tell us — trapped in the way things have always been done. When the environment changes, we just continue as if things were the same.

First-principles reasoning cuts through dogma and removes the blinders. We can see the world as it is and see what is possible.

When it comes down to it, everything that is not a law of nature is just a shared belief. Money is a shared belief. So is a border. So are bitcoins. The list goes on.

Some of us are naturally skeptical of what we’re told. Maybe it doesn’t match up to our experiences. Maybe it’s something that used to be true but isn’t true anymore. And maybe we just think very differently about something.

“To understand is to know what to do.”

— Wittgenstein

Techniques for Establishing First Principles

There are many ways to establish first principles. Let’s take a look at a few of them.

Socratic Questioning

Socratic questioning can be used to establish first principles through stringent analysis. This a disciplined questioning process, used to establish truths, reveal underlying assumptions, and separate knowledge from ignorance. The key distinction between Socratic questioning and normal discussions is that the former seeks to draw out first principles in a systematic manner. Socratic questioning generally follows this process:

  1. Clarifying your thinking and explaining the origins of your ideas (Why do I think this? What exactly do I think?)
  2. Challenging assumptions (How do I know this is true? What if I thought the opposite?)
  3. Looking for evidence (How can I back this up? What are the sources?)
  4. Considering alternative perspectives (What might others think? How do I know I am correct?)
  5. Examining consequences and implications (What if I am wrong? What are the consequences if I am?)
  6. Questioning the original questions (Why did I think that? Was I correct? What conclusions can I draw from the reasoning process?)

This process stops you from relying on your gut and limits strong emotional responses. This process helps you build something that lasts.

“Because I Said So” or “The Five Whys”

Children instinctively think in first principles. Just like us, they want to understand what’s happening in the world. To do so, they intuitively break through the fog with a game some parents have come to hate.

“Why?”

“Why?”

“Why?”

Here’s an example that has played out numerous times at my house:

“It’s time to brush our teeth and get ready for bed.”

“Why?”

“Because we need to take care of our bodies, and that means we need sleep.”

“Why do we need sleep?”

“Because we’d die if we never slept.”

“Why would that make us die?”

“I don’t know; let’s go look it up.”

Kids are just trying to understand why adults are saying something or why they want them to do something.

The first time your kid plays this game, it’s cute, but for most teachers and parents, it eventually becomes annoying. Then the answer becomes what my mom used to tell me: “Because I said so!” (Love you, Mom.)

Of course, I’m not always that patient with the kids. For example, I get testy when we’re late for school, or we’ve been travelling for 12 hours, or I’m trying to fit too much into the time we have. Still, I try never to say “Because I said so.”

People hate the “because I said so” response for two reasons, both of which play out in the corporate world as well. The first reason we hate the game is that we feel like it slows us down. We know what we want to accomplish, and that response creates unnecessary drag. The second reason we hate this game is that after one or two questions, we are often lost. We actually don’t know why. Confronted with our own ignorance, we resort to self-defense.

I remember being in meetings and asking people why we were doing something this way or why they thought something was true. At first, there was a mild tolerance for this approach. After three “whys,” though, you often find yourself on the other end of some version of “we can take this offline.”

Can you imagine how that would play out with Elon Musk? Richard Feynman? Charlie Munger? Musk would build a billion-dollar business to prove you wrong, Feynman would think you’re an idiot, and Munger would profit based on your inability to think through a problem.

“Science is a way of thinking much more than it is a body of knowledge.”

— Carl Sagan

Examples of First Principles in Action

So we can better understand how first-principles reasoning works, let’s look at four examples.

Elon Musk and SpaceX

Perhaps no one embodies first-principles thinking more than Elon Musk. He is one of the most audacious entrepreneurs the world has ever seen. My kids (grades 3 and 2) refer to him as a real-life Tony Stark, thereby conveniently providing a good time for me to remind them that by fourth grade, Musk was reading the Encyclopedia Britannica and not Pokemon.

What’s most interesting about Musk is not what he thinks but how he thinks:

I think people’s thinking process is too bound by convention or analogy to prior experiences. It’s rare that people try to think of something on a first principles basis. They’ll say, “We’ll do that because it’s always been done that way.” Or they’ll not do it because “Well, nobody’s ever done that, so it must not be good. But that’s just a ridiculous way to think. You have to build up the reasoning from the ground up—“from the first principles” is the phrase that’s used in physics. You look at the fundamentals and construct your reasoning from that, and then you see if you have a conclusion that works or doesn’t work, and it may or may not be different from what people have done in the past.[4]

His approach to understanding reality is to start with what is true — not with his intuition. The problem is that we don’t know as much as we think we do, so our intuition isn’t very good. We trick ourselves into thinking we know what’s possible and what’s not. The way Musk thinks is much different.

Musk starts out with something he wants to achieve, like building a rocket. Then he starts with the first principles of the problem. Running through how Musk would think, Larry Page said in an

interview, “What are the physics of it? How much time will it take? How much will it cost? How much cheaper can I make it? There’s this level of engineering and physics that you need to make judgments about what’s possible and interesting. Elon is unusual in that he knows that, and he also knows business and organization and leadership and governmental issues.”[5]

Rockets are absurdly expensive, which is a problem because Musk wants to send people to Mars. And to send people to Mars, you need cheaper rockets. So he asked himself, “What is a rocket made of? Aerospace-grade aluminum alloys, plus some titanium, copper, and carbon fiber. And … what is the value of those materials on the commodity market? It turned out that the materials cost of a rocket was around two percent of the typical price.”[6]

Why, then, is it so expensive to get a rocket into space? Musk, a notorious self-learner with degrees in both economics and physics, literally taught himself rocket science. He figured that the only reason getting a rocket into space is so expensive is that people are stuck in a mindset that doesn’t hold up to first principles. With that, Musk decided to create SpaceX and see if he could build rockets himself from the ground up.

In an interview with Kevin Rose, Musk summarized his approach:

I think it’s important to reason from first principles rather than by analogy. So the normal way we conduct our lives is, we reason by analogy. We are doing this because it’s like something else that was done, or it is like what other people are doing… with slight iterations on a theme. And it’s … mentally easier to reason by analogy rather than from first principles. First principles is kind of a physics way of looking at the world, and what that really means is, you … boil things down to the most fundamental truths and say, “okay, what are we sure is true?” … and then reason up from there. That takes a lot more mental energy.[7]

Musk then gave an example of how Space X uses first principles to innovate at low prices:

Somebody could say — and in fact people do — that battery packs are really expensive and that’s just the way they will always be because that’s the way they have been in the past. … Well, no, that’s pretty dumb… Because if you applied that reasoning to anything new, then you wouldn’t be able to ever get to that new thing…. you can’t say, … “oh, nobody wants a car because horses are great, and we’re used to them and they can eat grass and there’s lots of grass all over the place and … there’s no gasoline that people can buy….”

He then gives a fascinating example about battery packs:

… they would say, “historically, it costs $600 per kilowatt-hour. And so it’s not going to be much better than that in the future. … So the first principles would be, … what are the material constituents of the batteries? What is the spot market value of the material constituents? … It’s got cobalt, nickel, aluminum, carbon, and some polymers for separation, and a steel can. So break that down on a material basis; if we bought that on a London Metal Exchange, what would each of these things cost? Oh, jeez, it’s … $80 per kilowatt-hour. So, clearly, you just need to think of clever ways to take those materials and combine them into the shape of a battery cell, and you can have batteries that are much, much cheaper than anyone realizes.

BuzzFeed

After studying the psychology of virality, Jonah Peretti founded BuzzFeed in 2006. The site quickly grew to be one of the most popular on the internet, with hundreds of employees and substantial revenue.

Peretti figured out early on the first principle of a successful website: wide distribution. Rather than publishing articles people should read, BuzzFeed focuses on publishing those that people want to read. This means aiming to garner maximum social shares to put distribution in the hands of readers.

Peretti recognized the first principles of online popularity and used them to take a new approach to journalism. He also ignored SEO, saying, “Instead of making content robots like, it was more satisfying to make content humans want to share.”[8] Unfortunately for us, we share a lot of cat videos.

A common aphorism in the field of viral marketing is, “content might be king, but distribution is queen, and she wears the pants” (or “and she has the dragons”; pick your metaphor). BuzzFeed’s distribution-based approach is based on obsessive measurement, using A/B testing and analytics.

Jon Steinberg, president of BuzzFeed, explains the first principles of virality:

Keep it short. Ensure [that] the story has a human aspect. Give people the chance to engage. And let them react. People mustn’t feel awkward sharing it. It must feel authentic. Images and lists work. The headline must be persuasive and direct.

Derek Sivers and CD Baby

When Sivers founded his company CD Baby, he reduced the concept down to first principles. Sivers asked, What does a successful business need? His answer was happy customers.

Instead of focusing on garnering investors or having large offices, fancy systems, or huge numbers of staff, Sivers focused on making each of his customers happy. An example of this is his famous order confirmation email, part of which reads:

Your CD has been gently taken from our CD Baby shelves with sterilized contamination-free gloves and placed onto a satin pillow. A team of 50 employees inspected your CD and polished it to make sure it was in the best possible condition before mailing. Our packing specialist from Japan lit a candle and a hush fell over the crowd as he put your CD into the finest gold-lined box money can buy.

By ignoring unnecessary details that cause many businesses to expend large amounts of money and time, Sivers was able to rapidly grow the company to $4 million in monthly revenue. In Anything You Want, Sivers wrote:

Having no funding was a huge advantage for me.
A year after I started CD Baby, the dot-com boom happened. Anyone with a little hot air and a vague plan was given millions of dollars by investors. It was ridiculous. …
Even years later, the desks were just planks of wood on cinder blocks from the hardware store. I made the office computers myself from parts. My well-funded friends would spend $100,000 to buy something I made myself for $1,000. They did it saying, “We need the very best,” but it didn’t improve anything for their customers. …
It’s counterintuitive, but the way to grow your business is to focus entirely on your existing customers. Just thrill them, and they’ll tell everyone.

To survive as a business, you need to treat your customers well. And yet so few of us master this principle.

Employing First Principles in Your Daily Life

Most of us have no problem thinking about what we want to achieve in life, at least when we’re young. We’re full of big dreams, big ideas, and boundless energy. The problem is that we let others tell us what’s possible, not only when it comes to our dreams but also when it comes to how we go after them. And when we let other people tell us what’s possible or what the best way to do something is, we outsource our thinking to someone else.

The real power of first-principles thinking is moving away from incremental improvement and into possibility. Letting others think for us means that we’re using their analogies, their conventions, and their possibilities. It means we’ve inherited a world that conforms to what they think. This is incremental thinking.

When we take what already exists and improve on it, we are in the shadow of others. It’s only when we step back, ask ourselves what’s possible, and cut through the flawed analogies that we see what is possible. Analogies are beneficial; they make complex problems easier to communicate and increase understanding. Using them, however, is not without a cost. They limit our beliefs about what’s possible and allow people to argue without ever exposing our (faulty) thinking. Analogies move us to see the problem in the same way that someone else sees the problem.

The gulf between what people currently see because their thinking is framed by someone else and what is physically possible is filled by the people who use first principles to think through problems.

First-principles thinking clears the clutter of what we’ve told ourselves and allows us to rebuild from the ground up. Sure, it’s a lot of work, but that’s why so few people are willing to do it. It’s also why the rewards for filling the chasm between possible and incremental improvement tend to be non-linear.

Let’s take a look at a few of the limiting beliefs that we tell ourselves.

“I don’t have a good memory.” [10]
People have far better memories than they think they do. Saying you don’t have a good memory is just a convenient excuse to let you forget. Taking a first-principles approach means asking how much information we can physically store in our minds. The answer is “a lot more than you think.” Now that we know it’s possible to put more into our brains, we can reframe the problem into finding the most optimal way to store information in our brains.

“There is too much information out there.”
A lot of professional investors read Farnam Street. When I meet these people and ask how they consume information, they usually fall into one of two categories. The differences between the two apply to all of us. The first type of investor says there is too much information to consume. They spend their days reading every press release, article, and blogger commenting on a position they hold. They wonder what they are missing. The second type of investor realizes that reading everything is unsustainable and stressful and makes them prone to overvaluing information they’ve spent a great amount of time consuming. These investors, instead, seek to understand the variables that will affect their investments. While there might be hundreds, there are usually three to five variables that will really move the needle. The investors don’t have to read everything; they just pay attention to these variables.

“All the good ideas are taken.”
A common way that people limit what’s possible is to tell themselves that all the good ideas are taken. Yet, people have been saying this for hundreds of years — literally — and companies keep starting and competing with different ideas, variations, and strategies.

“We need to move first.”
I’ve heard this in boardrooms for years. The answer isn’t as black and white as this statement. The iPhone wasn’t first, it was better. Microsoft wasn’t the first to sell operating systems; it just had a better business model. There is a lot of evidence showing that first movers in business are more likely to fail than latecomers. Yet this myth about the need to move first continues to exist.

Sometimes the early bird gets the worm and sometimes the first mouse gets killed. You have to break each situation down into its component parts and see what’s possible. That is the work of first-principles thinking.

“I can’t do that; it’s never been done before.”
People like Elon Musk are constantly doing things that have never been done before. This type of thinking is analogous to looking back at history and building, say, floodwalls, based on the worst flood that has happened before. A better bet is to look at what could happen and plan for that.

“As to methods, there may be a million and then some, but principles are few. The man who grasps principles can successfully select his own methods. The man who tries methods, ignoring principles, is sure to have trouble.”

— Harrington Emerson

Conclusion

The thoughts of others imprison us if we’re not thinking for ourselves.

Reasoning from first principles allows us to step outside of history and conventional wisdom and see what is possible. When you really understand the principles at work, you can decide if the existing methods make sense. Often they don’t.

Reasoning by first principles is useful when you are (1) doing something for the first time, (2) dealing with complexity, and (3) trying to understand a situation that you’re having problems with. In all of these areas, your thinking gets better when you stop making assumptions and you stop letting others frame the problem for you.

Analogies can’t replace understanding. While it’s easier on your brain to reason by analogy, you’re more likely to come up with better answers when you reason by first principles. This is what makes it one of the best sources of creative thinking. Thinking in first principles allows you to adapt to a changing environment, deal with reality, and seize opportunities that others can’t see.

Many people mistakenly believe that creativity is something that only some of us are born with, and either we have it or we don’t. Fortunately, there seems to be ample evidence that this isn’t true.[11] We’re all born rather creative, but during our formative years, it can be beaten out of us by busy parents and teachers. As adults, we rely on convention and what we’re told because that’s easier than breaking things down into first principles and thinking for ourselves. Thinking through first principles is a way of taking off the blinders. Most things suddenly seem more possible.

“I think most people can learn a lot more than they think they can,” says Musk. “They sell themselves short without trying. One bit of advice: it is important to view knowledge as sort of a semantic tree — make sure you understand the fundamental principles, i.e., the trunk and big branches, before you get into the leaves/details or there is nothing for them to hang on to.”

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End Notes

[1] Aristotle, Physics 184a10–21

[2] Aristotle, Metaphysics 1013a14-15

[3] https://waitbutwhy.com/2015/11/the-cook-and-the-chef-musks-secret-sauce.html

[4] Elon Musk, quoted by Tim Urban in “The Cook and the Chef: Musk’s Secret Sauce,” Wait But Why https://waitbutwhy.com/2015/11/the-cook-and-the-chef-musks-secret-sauce.html

[5] Vance, Ashlee. Elon Musk: Tesla, SpaceX, and the Quest for a Fantastic Future (p. 354)

[6] https://www.wired.com/2012/10/ff-elon-musk-qa/all/

[7] https://www.youtube.com/watch?v=L-s_3b5fRd8

[8] David Rowan, “How BuzzFeed mastered social sharing to become a media giant for a new era,” Wired.com. 2 January 2014. https://www.wired.co.uk/article/buzzfeed

[9] https://www.quora.com/What-does-Elon-Musk-mean-when-he-said-I-think-it%E2%80%99s-important-to-reason-from-first-principles-rather-than-by-analogy/answer/Bruce-Achterberg

[10] https://www.scientificamerican.com/article/new-estimate-boosts-the-human-brain-s-memory-capacity-10-fold/

[11] Breakpoint and Beyond: Mastering the Future Today, George Land

[12] https://www.reddit.com/r/IAmA/comments/2rgsan/i_am_elon_musk_ceocto_of_a_rocket_company_ama/cnfre0a/

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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