The Great Mental Models

by Shane Parrish

  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’s 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.

  Insurance Companies

  The most probability-acute businesses in the world are insurance companies—because they must be. When we think of insurance, we might think of life insurance (the probability of a policyholder dying at a certain age), or auto insurance (the probability of being in a car accident), or maybe home insurance (the probability of a tree falling on the house). With the statistics available to us, the probabilities of these things are easy to price and predict across a large enough population.

  But insurance is deeply wide-ranging, and insurers will insure almost any event, for a price. Insurance policies have been taken out on Victoria’s Secret models’ legs, on baseball players’ arms, on the Pepsi Challenge and the NCAA tournament, and even on a famous country singer’s breasts!

  How is this possible? Only with a close attention to probability. What the great insurance companies in the world know how to do is pay attention to the important factors, even if they’re not totally predictable, and price accordingly.

  What is the probability of a Victoria’s Secret model injuring her legs badly enough to end her career? One in 10,000? One in 100,000? Getting it right would mean evaluating her lifestyle, her habits, her health, her family history—and coming up with a price and a set of conditions that are good enough to provide a profit on average. It’s not unlike handicapping a race at the horse tracks. You can always say yes to insuring, but the trick is to come up with the right price. And for that we need probability.

  Supporting Idea:

  Causation vs. Correlation

  Confusion between these two terms often leads to a lot of inaccurate assumptions about the way the world works. We notice two things happening at the same time (correlation) and mistakenly conclude that one causes the other (causation). We then often act upon that erroneous conclusion, making decisions that can have immense influence across our lives. The problem is, without a good understanding of what is meant by these terms, these decisions fail to capitalize on real dynamics in the world and instead are successful only by luck.

  No Correlation

  The correlation coefficient between two measures, which varies between -1 and 1, is a measure of the relative weight of the factors they share. For example, two phenomena with few factors shared, such as bottled water consumption versus suicide rate, should have a correlation coefficient of close to 0. That is to say, if we looked at all countries in the world and plotted suicide rates of a specific year against per capita consumption of bottled water, the plot would show no pattern at all.

  Perfect Correlation

  On the contrary, there are measures which are solely dependent on the same factor. A good example of this is temperature. The only factor governing temperature—velocity of molecules—is shared by all scales. Thus each degree in Celsius will have exactly one corresponding value in Fahrenheit. Therefore temperature in Celsius and Fahrenheit will have a correlation coefficient of 1 and the plot will be a straight line.

  Weak to Moderate Correlation

  There are few phenomena in human sciences that have a correlation coefficient of 1. There are, however, plenty where the association is weak to moderate and there is some explanatory power between the two phenomena. Consider the correlation between height and weight, which would land somewhere between 0 and 1. While virtually every three-year-old will be lighter and shorter than every grown man, not all grown men or three-year-olds of the same height will weigh the same.

  This variation and the corresponding lower degree of correlation implies that, while height is generally speaking a good predictor, there clearly are factors other than height at play.

  In addition, correlation can sometimes work in reverse. Let’s say you read a study that compares alcohol consumption rates in parents and their corresponding children’s academic success. The study shows a relationship between high alcohol consumption and low academic success. Is this a causation or a correlation? It might be tempting to conclude a causation, such as the more parents drink, the worse their kids do in school.

  However, this study has only demonstrated a relationship, not proved that one causes the other. The factors correlate—meaning that alcohol consumption in parents has an inverse relationship with academic success in children. It is entirely possible that having parents who consume a lot of alcohol leads to worse academic outcomes for their children. It is also possible, however, that the reverse is true, or even that having kids who do poorly in school causes parents to drink more. Trying to invert the relationship can help you sort through claims to determine if you are dealing with true causation or just correlation.

  Causation

  Whenever correlation is imperfect, extremes will soften over time. The best will always appear to get worse and the worst will appear to get better, regardless of any additional action. This is called regression to the mean, and it means we have to be extra careful when diagnosing causation. This is something that the general media and sometimes even trained scientists fail to recognize.

  Consider the example Daniel Kahneman gives in Thinking Fast and Slow:5

  Depressed children treated with an energy drink improve significantly over a three-month period. I made up this newspaper headline, but the fact it reports is true: if you treated a group of depressed children for some time with an energy drink, they would show a clinically significant improvement. It is also the case that depressed children who spend some time standing on the
ir head or hug a cat for twenty minutes a day will also show improvement.

  Whenever coming across such headlines it is very tempting to jump to the conclusion that energy drinks, standing on the head, or hugging cats are all perfectly viable cures for depression. These cases, however, once again embody the regression to the mean:

  Depressed children are an extreme group, they are more depressed than most other children—and extreme groups regress to the mean over time. The correlation between depression scores on successive occasions of testing is less than perfect, so there will be regression to the mean: depressed children will get somewhat better over time even if they hug no cats and drink no Red Bull.

  We often mistakenly attribute a specific policy or treatment as the cause of an effect, when the change in the extreme groups would have happened anyway. This presents a fundamental problem: how can we know if the effects are real or simply due to variability?

  Luckily there is a way to tell between a real improvement and something that would have happened anyway. That is the introduction of the so-called control group, which is expected to improve by regression alone. The aim of the research is to determine whether the treated group improves more than regression can explain.

  In real life situations with the performance of specific individuals or teams, where the only real benchmark is the past performance and no control group can be introduced, the effects of regression can be difficult if not impossible to disentangle. We can compare against industry average, peers in the cohort group or historical rates of improvement, but none of these are perfect measures.

  The test of a first-rate intelligence is the ability to hold two opposing ideas in mind at the same time and still retain the ability to function. One should, for example, be able to see that things are hopeless yet be determined to make them otherwise.

  F. Scott Fitzgerald1

  The People Who Appear in this Chapter

  Jacobi, Carl.

  1804-1851 - German mathematician who made fundamental contributions to elliptic functions, dynamics, and number theory.

  Bernays, Edward.

  1891-1995 - Austrian-American. Known as “the Father of Public Relations”. Although his influence cannot be doubted, his legacy is one of brilliant but sometimes unethical strategies that consumers and citizens are still navigating today.

  Bogle, John.

  1929 - American investor, business magnate, and philanthropist. He is the founder and retired chief executive of The Vanguard Group.

  Lewin, Kurt.

  1890-1947 - German-American psychologist. Often recognized as the founder of social psychology, he was one of the first to study group dynamics and organizational development.

  Nightingale, Florence.

  1820-1910 - English social reformer, statistician, and the founder of modern nursing. By turning nursing into a profession and collecting detailed statistics on hospital conditions, she improved the lives of people all over the world.

  Inversion

  Inversion is a powerful tool to improve your thinking because it helps you identify and remove obstacles to success. The root of inversion is “invert,” which means to upend or turn upside down. As a thinking tool it means approaching a situation from the opposite end of the natural starting point. Most of us tend to think one way about a problem: forward. Inversion allows us to flip the problem around and think backward. Sometimes it’s good to start at the beginning, but it can be more useful to start at the end.

  Think of it this way: Avoiding stupidity is easier than seeking brilliance. Combining the ability to think forward and backward allows you to see reality from multiple angles.

  There are two approaches to applying inversion in your life.

  Start by assuming that what you’re trying to prove is either true or false, then show what else would have to be true.

  Instead of aiming directly for your goal, think deeply about what you want to avoid and then see what options are left over.

  Set your assumptions: The 19th century German mathematician Carl Jacobi became famous for a number of reasons—including solving some ungodly difficult problems—but is perhaps best remembered for his advice to “invert, always invert.” Jacobi solved a range of problems by starting with the endpoint. When faced with proving an axiom in a difficult math problem, he might instead assume a property of the axiom was correct and then try to determine the consequences of this assumption. From that point, he could work out surprising, and at times counterintuitive, insights.

  — Sidebar: The Most Successful Detective of All Time

  Jacobi was not the first mathematician to use inversion. In fact, inversion is a staple of mathematical, philosophical, and scientific inquiry. We can look around today and appreciate that we can’t see atoms and quarks, but we know they exist because we can make predictions about their behavior and test those predictions.

  Or we can go back 2,300 years and look at the work of the Greek Hippasus, a follower of Pythagoras.2 (Yes, the one with the Theorem.) His attempts to derive the square root of 2, and his original direct approach to solving the problem (essentially, dividing larger and larger whole numbers into each other) were both fruitless and time consuming. He hit an impasse, realizing that he’d never be able to definitely solve the problem by thinking forward. In his increasing frustration, Hippasus decided to take the reverse route, thinking about what the square root of 2 might imply, and working backwards from there. If he couldn’t find it the way he had expected to, he’d start by proving what the number couldn’t be. His quest forever changed what we understood about mathematics, and led to the discovery of the first irrational number.

  Mathematics is not the only area where using inversion can produce surprising and non-intuitive results. In the 1920s the American Tobacco Company wanted to sell more of their Lucky Strike cigarettes to women. Men were smoking, but women weren’t. There were pervasive taboos against women smoking—it was seen as a man’s activity. Women therefore presented an untapped market that had the potential of providing huge revenue. The head of the company thought that they needed to convince women that smoking would make them thinner, riding on the slimness trend that had already begun, so he hired Edward Bernays, who came up with a truly revolutionary marketing campaign.3,4

  In the style of the inversion approach described above, Bernays did not ask, “How do I sell more cigarettes to women?” Instead, he wondered, if women bought and smoked cigarettes, what else would have to be true? What would have to change in the world to make smoking desirable to women and socially acceptable? Then—a step farther—once he knew what needed to change, how would he achieve that?

  The Most Successful Detective of All Time

  The first great detective to capture the public imagination was Sherlock Holmes. He solved cases in ways that were unfathomable to others, yet seemed obvious in retrospect. He gave the appearance of being a magician, but really he was an excellent observer. He was also a master of inversion.

  In his third case, “A Scandal in Bohemia,”5 Holmes is hired by a king to recover a compromising photograph in which the king appears with an American opera singer, Irene Adler. The king is fearful that Adler will use the picture of the two of them to prevent his upcoming marriage or to blackmail him in the future. He does not want to live under this threat, and so hires Sherlock Holmes to retrieve the picture from Adler.

  Presented with this task, what does Holmes do? What would you do? Does he study Adler for months to determine where, based on her personality, she is likely to hide the picture? Does he break into her house and perform a systematic exploration of every nook and cranny? No. Instead, he inverts the problem.

  If it is true that Adler has this compromising picture of the king and is planning to blackmail him, what would also be true? Likely that she would greatly value the photo as it will bring her money, and that it would be hidden in an accessible location so she could retrieve it in a hurry. We tend to keep our most prized possessions where we can easily grab them in
case of emergency.

  So Holmes contrives a scenario in which he is able to be in her house while Watson creates an illusion of a fire on the street outside. Believing the threat, Adler takes the photo out of its hiding place before escaping. In one instant Holmes both confirms the existence of the photo and now knows its whereabouts. By starting with the logical outcome of his assumptions and seeking to validate those, he advances his case with significantly more efficiency and accuracy than if he had searched first for proof of the assumptions themselves.

  _

  Bernays never believed his own propaganda on smoking, for years pressuring his wife to quit.

  To tackle the idea of smoking as a slimming aid, he mounted a large anti-sweets campaign. After dinner, it was about cigarettes, not dessert. Cigarettes were slimming, while desserts would ruin one’s figure. But Bernays’s real stroke of genius lay not just in coming out with adverts to convince women to stay slim by smoking cigarettes; “instead, he sought nothing less than to reshape American society and culture.”6 He solicited journalists and photographers to promote the virtues of being slim. He sought testimonials from doctors about the health value of smoking after a meal. He combined this approach with

  …altering the very environment, striving to create a world in which the cigarette was ubiquitous. He mounted a campaign to persuade hotels and restaurants to add cigarettes to dessert-list menus, and he provided such magazines as House and Garden with feature articles that included menus designed to preserve readers ‘from the dangers of overeating’…. The idea was not only to influence opinion but to remold life itself. Bernays approached designers, architects, and cabinetmakers in an effort to persuade them to design kitchen cabinets that included special compartments for cigarettes, and he spoke to the manufacturers of kitchen containers to add cigarette tins to their traditional lines of labeled containers for coffee, tea, sugar, and flour.7