The Great Mental Models Read online

  In the first case, your knowledge of James (young, tall, athletic, and skilled), Allen (old, small, frail, and funny), and the game of basketball gave you a clear mental image. The disparity between the players’ abilities makes the question (and the bet) a total no-brainer.

  In the second case, your knowledge of LeBron and Durant may well be extensive, but that doesn’t make it an easy bet. They’re both professional basketball players who are quite similar in size and ability, and both of them are likely to go down as among the best ever to play the game. It’s doubtful that one is much better than the other in a one-on-one match. The only way to answer for sure would be to see them play. And even then, a one-off contest is not going to be definitive.

  A better way to answer the “who would win” question is through a remarkable ability of the human brain—the ability to conduct a detailed thought experiment. Its chief value is that it lets us do things in our heads we cannot do in real life, and so explore situations from more angles than we can physically examine and test for.

  Thought experiments are more than daydreaming. They require the same rigor as a traditional experiment in order to be useful. Much like the scientific method, a thought experiment generally has the following steps:

  Ask a question

  Conduct background research

  Construct hypothesis

  Test with (thought) experiments

  Analyze outcomes and draw conclusions

  Compare to hypothesis and adjust accordingly (new question, etc.)

  In the James/Allen experiment above, we started with a question: Who would win in a game of basketball? If you didn’t already know who those people were, finding out would have been a necessary piece of background research. Then you came out with your hypothesis (James all the way!), and you thought it through.

  _

  Who would win in a game of one-on-one?

  One of the real powers of the thought experiment is that there is no limit to the number of times you can change a variable to see if it influences the outcome. In order to place that bet, you would want to estimate in how many possible basketball games does Woody Allen beat LeBron James. Out of 100,000 game scenarios, Allen probably only wins in the few where LeBron starts the game by having a deadly heart attack. Experimenting to discover the full spectrum of possible outcomes gives you a better appreciation for what you can influence and what you can reasonably expect to happen.

  Let’s now explore few areas in which thought experiments are tremendously useful.

  Imagining physical impossibilities

  Re-imagining history

  Intuiting the non-intuitive

  Imagining physical impossibilities: Albert Einstein was a great user of the thought experiment because it is a way to logically carry out a test in one’s own head that would be very difficult or impossible to perform in real life. With this tool, we can solve problems with intuition and logic that cannot be demonstrated physically.

  One of his notable thought experiments involved an elevator.2 Imagine you were in a closed elevator, feet glued to the floor. Absent any other information, would you be able to know whether the elevator was in outer space with a string pulling the elevator upwards at an accelerating rate, or sitting on Earth, being pulled down by gravity? By running the thought experiment, Einstein concluded that you would not.

  This led to the formulation of Einstein’s second major theory, the general theory of relativity—his universal theory of gravity. Einstein’s hypothesis was that the force you felt from acceleration and the force you felt from gravity didn’t just feel the same—they were the same! Gravity must work similarly to the accelerating elevator. We can’t build elevators in space, but can still define some of the properties they would have if we could. This gives us enough information to test the hypothesis. Eventually, Einstein worked it all out mathematically and in great detail, but it started with a simple thought experiment, impossible to actually perform.

  This type of thought experiment need not only apply to physics and is actually reflected in some of our common expressions. When we say “if money were no object” or “if you had all the time in the world,” we are asking someone to conduct a thought experiment because actually removing that variable (money or time) is physically impossible. In reality, money is always an object, and we never have all the time in the world. But the act of detailing out the choices we would make in these alternate realities that have otherwise similar properties to our current one, doing the thought experiment, is what leads to insights regarding what we value in life and where to focus our energies. — Sidebar: The Trolley Experiment

  Re-imagining history: A familiar use of the thought experiment is to re-imagine history. This one we all use, all the time. What if I hadn’t been stuck at the airport bar where I met my future business partner? Would World War I have started if Gavrilo Princip hadn’t shot the Archduke of Austria in Sarajevo? If Cleopatra hadn’t found a way to meet Caesar, would she still have been able to take the throne of Egypt?

  These approaches are called the historical counter-factual and semi-factual. If Y happened instead of X, what would the outcome have been? Would the outcome have been the same?

  As popular—and generally useful—as counter- and semi-factuals are, they are also the areas of thought experiment with which we need to use the most caution. Why? Because history is what we call a chaotic system. A small change in the beginning conditions can cause a very different outcome down the line. This is where the rigor of the scientific method is indispensable if we want to draw conclusions that are actually useful.

  The Trolley Experiment

  Thought experiments are often used to explore ethical and moral issues. When you are dealing with questions of life and death it is obviously not recommended to kill a bunch of people in order to determine the most ethical course of action. This then is where a thought experiment is also extremely valuable.

  One of the most famous of this type is the trolley experiment. It goes like this: say you are the driver of a trolley that is out of control. You apply the brakes and nothing happens. Ahead of you are five people who will die should your trolley continue on the track. At the last moment you notice a spur that has one person on it. What do you do? Do you continue on and kill the five, or do you divert and kill the one?

  This experiment was first proposed in modern form by Philippa Foot in her paper “The Problem of Abortion and the Doctrine of the Double Effect,”3 and further considered extensively by Judith Jarvis Thomson in “The Trolley Problem.”4 In both cases the value of the thought experiment is clear. The authors were able to explore situations that would be physically impossible to reproduce without causing serious harm, and in so doing significantly advanced certain questions of morality. Moreover, the trolley problem remains relevant to this day as technological advances often ask us to define when it is acceptable, and even desirable, to sacrifice one to save many (and lest you think this is always the case, Thomson conducts another great thought experiment considering a doctor killing one patient to save five through organ donation).

  To understand it, let’s think about another chaotic system we’re all familiar with, the weather. Why is it that we can predict the movement of the stars but we can’t predict the weather more than a few weeks out, and even that is not altogether reliable?

  It’s because weather is highly chaotic. Any infinitesimally small error in our calculations today will change the result down the line, as rapid feedback loops occur throughout time. Since our measurement tools are not infinitely accurate, and never will be, we are stuck with the unpredictability of chaotic systems.

  And compared to human systems, one could say weather is pretty reliable stuff. As anyone who’s seen Back to the Future knows, a small change in the past could have a massive, unpredictable effect on the future. Thus, running historical counter-factuals is an easy way to accidentally mislead yourself. We simply don’t know what else would have occurred had Cleopatra not met Caesar or
had you not been stuck at that airport. The potential outcomes are too chaotic.

  But we can use thought experiments to explore unrealized outcomes—to re-run a process as many times as we like to see what could have occurred, and learn more about the limits we have to work with.

  The truth is, the events that have happened in history are but one realization of the historical process—one possible outcome among a large variety of possible outcomes. They’re like a deck of cards that has been dealt out only one time. All the things that didn’t happen, but could have if some little thing went another way, are invisible to us. That is, until we use our brains to generate these theoretical worlds via thought experiments.

  If we can also factor in the approximate probability of these occurrences, relative to the scope of possible ones, we can learn what the most likely outcomes are. Sometimes it is easy to imagine ten different ways a situation could have played out differently, but more of a stretch to change the variables and still end up with the same thing.

  So let’s try it. First, we have to ask a question. What if Serbian Gavrilo Princip hadn’t shot Austrian Archduke Franz Ferdinand? That single act has often been credited with launching World War I, so it is a question worth asking. If we conclude the assassination started a chain reaction for which war was the inevitable result, it would certainly tell us a lot about certain causal relationships in politics, diplomacy, and possibly human psychology.

  Then we need to do our background research: What do we need to know to be able to answer this question? So we look into it—treaties, conflicts, alliances, interests, personalities—enough to be able to formulate an hypothesis.

  An immediate response to the assassination was on June 30, 1914, two days later. Austria changed its policy toward Serbia. Shortly after that Germany offered full military support to Austria, and less than two months later the world was at war. Thus, a next step in our thought experiment might be to refine the question. Something like, how did Princip’s assassination of the Archduke influence Austrian policy toward Serbia?

  Our hypothesis could be one of the following:

  The assassination had no effect on the policy

  The assassination had partial effect on the policy

  The assassination had total effect on the policy

  To test any one of these, we run the experiment in our heads. We sit back and think about what the world looked like in Sarajevo on June 28, 1914. The Archduke and his wife being chauffeured in their car, Gavrilo Princip cleaning his gun somewhere. Now we imagine Princip gets stomach cramps from some bad food the night before. The Archduke’s car makes it to its destination while Princip is curled up in bed. The Archduke gives a speech, emphasizing peace. One of Princip’s gang tries to assassinate the Archduke, but fails. How does Austria react? Is it demonstrably different from what they actually did?

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  What we think of as an inevitable occurrence could have played out in many ways: Earlier on the day of the assassination, Archduke Ferdinand and his wife Sophie survived a grenade being detonated by their car. It was on the way to visit those injured, an unplanned change of schedule, that Princip got his opportunity.

  Princip wasn’t a lone wolf, and there was a lot of unrest in Serbia towards Austria. How could the situation be changed to lead to different Austrian policy? Given the climate at the time, is our hypothetical situation realistic? Meaning, can you construct an historically accurate scenario in which no events come to pass that prompt Austria’s policy change? How many Serbians would have to get the stomach flu?

  One of the goals of a thought experiment like this is to understand the situation enough to identify the decisions and actions that had impact. This process doesn’t provide definitive answers, such as whether the assassination did, or did not, cause World War I. What you are trying to get to is a rough idea of how much it may have contributed to starting the war. The more scenarios you can imagine where war comes to pass without the assassination, the weaker the case for it being the critical cause. Thus, by exploring the realistic relationships between events you can better understand the most likely effects of any one decision. — Sidebar: Reduce the Role of Chance

  Intuiting the non-intuitive: One of the uses of thought experiments is to improve our ability to intuit the non-intuitive. In other words, a thought experiment allows us to verify if our natural intuition is correct by running experiments in our deliberate, conscious minds that make a point clear.

  Reduce the Role of Chance

  Let’s try a real world example. Suppose you were to buy $100,000 of stock in Google, with 50% paid for in cash and 50% borrowed from the brokerage firm. (They call it a margin loan.)

  A few years later, the stock price has doubled: That means your $100,000 is worth $200,000. Since you still owe the brokerage $50,000, your own $50,000 is now worth $150,000—you’ve tripled your money! You consider yourself a financial genius.

  Before we land on that conclusion, though, let’s run our Theoretical World Generator a bunch of times in our head. What else could have happened, but didn’t?

  Google could have gone down 50% before it went up 100%—nearly all stocks on the exchange have had this happen to them at some time or another. In fact, Google could have gone down 90%! The whole New York Stock Exchange did just that between 1929 and 1932.

  What if something like that had happened? The brokerage would have called in your margin loan: Game over, thanks for playing. You would have been worth zero.

  Now, return to the beginning of the chapter again. If you’re going to buy Google on margin, is your bet that Google won’t go down 50% more similar to the LeBron/Allen thought experiment, or the LeBron/Durant thought experiment? Running through the scenario 100,000 times, how many times do you go broke and how many times do you triple your dough?

  This gives you some real decision-making power: It tells you about the limits of what you know and the limits of what you should attempt. It tells you, in an imprecise but useful way, a lot about how smart or stupid your decisions were regardless of the actual outcome. It makes you aware of your process, so that even if the results are good, you can recognize when this was all down to luck and that maybe you should work on your decision-making process to reduce the role of chance.

  An example of this is the famous “veil of ignorance” proposed by philosopher John Rawls in his influential Theory of Justice. In order to figure out the most fair and equitable way to structure society, he proposed that the designers of said society operate behind a veil of ignorance. This means that they could not know who they would be in the society they were creating. If they designed the society without knowing their economic status, their ethnic background, talents and interests, or even their gender, they would have to put in place a structure that was as fair as possible in order to guarantee the best possible outcome for themselves.5

  Our initial intuition of what is fair is likely to be challenged during the “veil of ignorance” thought experiment. When confronted with the question of how best to organize society, we have this general feeling that it should be fair. But what exactly does this mean? We can use this thought experiment to test the likely outcomes of different rules and structures to come up with an aggregate of “most fair.”

  We need not be constructing the legislation of entire nations for this type of thinking to be useful. Think, for example, of a company’s human resources policies on hiring, office etiquette, or parental leave. What kind of policies would you design or support if you didn’t know what your role in the company was? Or even anything about who you were?

  Conclusion

  Thought experiments tell you about the limits of what you know and the limits of what you should attempt. In order to improve our decision-making and increase our chances of success, we must be willing to probe all of the possibilities we can think of. Thought experiments are not daydreams. They require both rigor and work. But the more you use them, the more you understand actual cause and effect, and the more knowledg
e you have of what can really be accomplished.

  Supporting Idea:

  Necessity and Sufficiency

  We often make the mistake of assuming that having some necessary conditions in place means that we have all of the sufficient conditions in place for our desired event or effect to occur. The gap between the two is the difference between becoming a published author and becoming J.K. Rowling. Certainly you have to know how to write well to become either, but it isn’t sufficient to become a Rowling. This is somewhat obvious to most. What’s not obvious is that the gap between what is necessary to succeed and what is sufficient is often luck, chance, or some other factor beyond your direct control.

  Assume you wanted to make it into the Fortune 500. Capital is necessary, but not sufficient. Hard work is necessary, but not sufficient. Intelligence is necessary, but not sufficient. Billionaire success takes all of those things and more, plus a lot of luck. That’s a big reason that there’s no recipe.

  Winning a military battle is a great example of necessity and sufficiency. It is necessary to prepare for the battle by evaluating the strength and tactics of your enemy, and by developing your own plan. You need to address logistics such as supplies, and have a comprehensive strategy that allows flexibility to respond to the unexpected. These things, however, are not enough to win the battle. Without them you definitely won’t be successful, but on their own they are not sufficient for success.