Category: Mental Models

Predicting the Future with Bayes’s Theorem

In a recent podcast, we talked with professional poker player Annie Duke about thinking in probabilities, something good poker players do all the time. At the poker table or in life, it’s really useful to think in probabilities versus absolutes based on all the information you have available to you. You can improve your decisions and get better outcomes. Probabilistic thinking leads you to ask yourself, how confident am I in this prediction? What information would impact this confidence?

Bayes’s Theorem

Bayes’s theorem is an accessible way of integrating probability thinking into our lives. Thomas Bayes was an English minister in 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 in 1763—two years after his death—by his friend Richard Price. The essay did not contain the theorem as we now know it, but had the seeds of the idea. It looked at how we should adjust our estimates of probabilities when we encounter new data that influence a situation. Later development by French scholar Pierre-Simon Laplace and others helped codify the theorem and develop it into a useful tool for thinking.

Knowing the exact math of probability calculations is not the key to understanding Bayesian thinking. More critical is your ability and desire to assign probabilities of truth and accuracy to anything you think you know, and then being willing to update those probabilities when new information comes in. Here is a short example, found in Investing: The Last Liberal Art, of how it works:

Let’s imagine that you and a friend have spent the afternoon playing your favorite board game, and now, at the end of the game, you are chatting about this and that. Something your friend says leads you to make a friendly wager: that with one roll of the die from the game, you will get a 6. Straight odds are one in six, a 16 percent probability. But then suppose your friend rolls the die, quickly covers it with her hand, and takes a peek. “I can tell you this much,” she says; “it’s an even number.” Now you have new information and your odds change dramatically to one in three, a 33 percent probability. While you are considering whether to change your bet, your friend teasingly adds: “And it’s not a 4.” With this additional bit of information, your odds have changed again, to one in two, a 50 percent probability. With this very simple example, you have performed a Bayesian analysis. Each new piece of information affected the original probability, and that is Bayesian [updating].

Both Nate Silver and Eliezer Yudkowsky have written about Bayes’s theorem in the context of medical testing, specifically mammograms. Imagine you live in a country with 100 million women under 40. Past trends have revealed that there is a 1.4% chance of a woman under 40 in this country getting breast cancer—so roughly 1.4 million women.

Mammograms will detect breast cancer 75% of the time. They will give out false positives—say a woman has breast cancer when she actually doesn’t—about 10% of the time. At first, you might focus just on the mammogram numbers and think that 75% success rate means that a positive is bad news. Let’s do the math.

If all the women under 40 get mammograms, then the false positive rate will give 10 million women under 40 the news that they have breast cancer. But because you know the first statistic, that only 1.4 women under 40 actually get breast cancer, you know that 8.6 million of the women who tested positive are not actually going to have breast cancer!
That’s a lot of needless worrying, which leads to a lot of needless medical care. In order to remedy this poor understanding and make better decisions about using mammograms, we absolutely must consider prior knowledge when we look at the results, and try to update our beliefs with that knowledge in mind.

Weigh the Evidence

Often we ignore prior information, simply called “priors” in Bayesian-speak. We can blame this habit in part on the availability heuristic—we focus on what’s readily available. In this case, we focus on the newest information and the bigger picture gets lost. We fail to adjust the probability of old information to reflect what we have learned.

The big idea behind Bayes’s theorem is that we must continuously update our probability estimates on an as-needed basis. In their book The Signal and the Noise, Nate Silver and Allen Lane give a contemporary example, reminding us that new information is often most useful when we put it in the larger context of what we already know:

Bayes’s theorem is an important reality check on our efforts to forecast the future. How, for instance, should we reconcile a large body of theory and evidence predicting global warming with the fact that there has been no warming trend over the last decade or so? Skeptics react with glee, while true believers dismiss the new information.

A better response is to use Bayes’s theorem: the lack of recent warming is evidence against recent global warming predictions, but it is weak evidence. This is because there is enough variability in global temperatures to make such an outcome unsurprising. The new information should reduce our confidence in our models of global warming—but only a little.

The same approach can be used in anything from an economic forecast to a hand of poker, and while Bayes’s theorem can be a formal affair, Bayesian reasoning also works as a rule of thumb. We tend to either dismiss new evidence, or embrace it as though nothing else matters. Bayesians try to weigh both the old hypothesis and the new evidence in a sensible way.

Limitations of the Bayesian

Don’t walk away thinking the Bayesian approach will enable you to predict everything! In addition to seeing the the world as an ever-shifting array of probabilities, we must also remember the limitations of inductive reasoning. A high probability of something being true is not the same as saying it is true. A great example of this is from Bertrand Russell’s The Problems of Philosophy:

A horse which has been often driven along a certain road resists the attempt to drive him in a different direction. Domestic animals expect food when they see the person who usually feeds them. We know that all these rather crude expectations of uniformity are liable to be misleading. The man who has fed the chicken every day throughout its life at last wrings its neck instead, showing that more refined views as to the uniformity of nature would have been useful to the chicken.

In the final analysis, though, picking up Bayesian reasoning can truly change your life, as observed in this Big Think video by Julia Galef of the Center for Applied Rationality:

After you’ve been steeped in Bayes’s rule for a little while, it starts to produce some fundamental changes to your thinking. For example, you become much more aware that your beliefs are grayscale. They’re not black and white and that you have levels of confidence in your beliefs about how the world works that are less than 100 percent but greater than zero percent and even more importantly as you go through the world and encounter new ideas and new evidence, that level of confidence fluctuates, as you encounter evidence for and against your beliefs.

So be okay with uncertainty, and use it to your advantage. Instead of holding on to outdated beliefs by rejecting new information, take in what comes your way through a system of evaluating probabilities.

Bayes’s Theorem is part of the Farnam Street latticework of mental models. Still Curious? Read Bayes and Deadweight: Using Statistics to Eject the Deadweight From Your Life next. 

Learning community members can discuss this on the member forum

The Disproportional Power of Anecdotes

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

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

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

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

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

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

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

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

Why does this matter?

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

Some really smart people are perpetual victims of the problem.

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

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

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

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

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

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

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

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

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

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

5 Mental Models to Remove (Some of) the Confusion from Parenting

Just a few days ago, I saw a three-year-old wandering around at 10:30 at night and wondered if he was lost or jet-lagged. The parent came over and explained that they believed in children setting their own sleep schedule.

Interesting.

The problem with this approach is that it may work, or it may not. It may work for your oldest, but not your youngest. And therein lies the problem with the majority of the parenting advice available. It’s all tactics, no principles.

Few topics provoke more unsolicited advice than parenting. The problem is, no matter how good the advice, it might not work for your child. Parenting is the ultimate “the map is not the territory“ situation. There are so many maps out there, and often when we try to use them to navigate the territory that is each individual child, we end up lost and confused. As in other situations, when the map doesn’t match the territory, better to get rid of the map and pay attention to what you are experiencing on the ground. The territory is the reality.

We’ve all dealt with the seemingly illogical behavior of children. Take trying to get your child to sleep through the night—often the first, and most important, challenge. Do you sleep beside them and slowly work your way out of the room? Do you let them “cry it out?” Do you put them in your bed? Do you feed them on demand, or not until morning? Soft music or no music? The options are endless, and each of them has a decently researched book to back it up.

When any subsequent children come along, the problem is often exacerbated. You stick to what worked the first time, because it worked, but this little one is different. Now you’re in a battle of wills, and it’s hard to change your tactics at 3:00 a.m. Parenting is often a rinse and repeat of this scenario: ideas you have about how it should be, combined with what experience is telling you that it is, overlaid with too many options and chronic exhaustion.

This is where mental models can help. As in any other area of your life, developing some principles or models that help you see how the world works will give you options for relevant and useful solutions. Mental models are amazing tools that can be applied across our lives. Here are five principle-based models you can apply to almost any family, situation, or child. These are ones I use often, but don’t let this limit you—so many more apply!

Adaptation

Adaptation is a concept from evolutionary biology. It describes the development of genetic traits that are successful relative to their performance in a specific environment—that is, relative to organisms’ survival in the face of competitive pressures. As Geerat Vermeij explains in Nature: An Economic History, “Adaptation is as good as it has to be; it need not be the best that could be designed. Adaptation depends on context.”

In terms of parenting, this is a big one: the model we can use to stop criticizing ourselves for our inevitable parenting mistakes, to get out of the no-point comparisons with our peers, and to give us the freedom to make changes depending on the situation we find ourselves in.

Species adapt. It is a central feature of the theory of evolution—the ability of a species to survive and thrive in the face of changing environmental conditions. So why not apply this basic biological idea to parenting? Too often we see changing as a weakness. We’re certain that if we aren’t absolutely consistent with our children, they will grow up to be entitled underachievers or something. Or we put pressure on ourselves to be perfect, and strive for an ideal that requires an insane amount of work and sacrifice that may actually be detrimental to our overall success.

We can get out of this type of thinking if we reframe ‘changing’ as ‘adapting’. It’s okay to have different rules in the home versus a public space. I am always super grateful when a parent pacifies a screaming child with a cookie, especially on an airplane or in a restaurant. They probably don’t use the same strategy at home, but they adapt to the different environment. It’s also okay to have two children in soccer, and the third in music. Adapting to their interests will offer a much better return of investment on all those lessons.

No doubt your underlying goals for your children are consistent, like the desire of an individual to survive. How you meet those goals is where the adaptability comes in. Give yourself the freedom to respond to the individual characteristics of your children—and the specific needs of the moment—by trying different behaviors to see what works. And, just as with adaptation in the biological sense, you only need to be as good as you have to be to get the outcomes that are important to you, not be the best parent that ever was.

Velocity

There is a difference between speed and velocity. With speed you move, but with velocity you move somewhere. You have direction.

As many have said of parenting, the days are long but the years are short. It’s hard to be focusing on your direction when homework needs to be done and dinner needs to get made before one child goes off in the carpool to soccer while you rush the other one to art class. Every day begins at a dead run and ends with you collapsing into bed only to go through it all again tomorrow. Between their activities and social lives, and your need to work and have time for yourself, there is no doubt that you move with considerable speed throughout your day.

But it’s useful to sometimes ask, ‘Where am I going?’ Take a moment to make sure it’s not all speed and no direction.

When it comes to time with your kids, what does the goal state look like? How do you move in that direction? If you are just speeding without moving then you have no frame of reference for your choices. You might ask, did I spend enough time with them today? But ten minutes or two hours isn’t going to impact your velocity if you don’t know where you are headed.

When you factor in a goal of movement, it helps you decide what to do when you have time with them. What is it you want out of it? What kind of memories do you want them to have? What kind of parent do you want to be and what kind of children do you want to raise? The answers are different for everyone, but knowing the direction you wish to go helps you evaluate the decisions you make. And it might have the added benefit of cutting out some unnecessary activity and slowing you down.

Algebraic Equivalence

“He got more pancakes than I did!” Complaints about fairness are common among siblings. They watch each other like hawks, counting everything from presents to hugs to make sure everyone gets the same. What can you do? You can drive yourself mad running out to buy an extra whatever, or you can teach your children the difference between ‘same’ and ‘equal’.

If you haven’t solved for x in a while, it doesn’t really matter. In algebra, symbols are used to represent unknown numbers that can be solved for given other relevant information. The general point about algebraic equivalence is that it teaches us that two things need not be the same in order to be equal.

For example, x + y = 5. Here are some of the options for the values of x and y:

3 + 2

4 + 1

2.5 + 2.5

1.8 + 3.2

And those are just the simple ones. What is useful is this idea of abstracting to see what the full scope of possibilities are. Then you can demonstrate that what is on each side of those little parallel lines doesn’t have to look the same to have equal value. When it comes to the pancakes, it’s better to focus on an equal feeling of fullness then the number of pancakes on the plate.

In a deeper way, algebraic equivalence helps us deal with one accusation that all parents get at one time or another: “You love my sibling more than me.” It’s not true, but our default usually is to say, “No, I love you both the same.” This can be confusing for children, because, after all, they are not the same as their sibling, and you likely interact with them differently, so how can the love be the same?

Using algebraic equivalence as a model shifts it. You can respond instead that you love them both equally. Even though what’s on either side of the equation is different, it is equal. Swinging the younger child up in the air is equivalent to asking the older one about her school project. Appreciating one’s sense of humor is equivalent to respecting the other’s organizational abilities. They may be different, but the love is equal.

Seizing the middle

In chess, the middle is the key territory to hold. As explained on Wikipedia: “The center is the most important part of the chessboard, as pieces from the center can easily move to either flank with great speed. However, amateurs often prefer to concentrate on the king’s side of the board. This is an incorrect mindset.”

In parenting, seizing the middle means you must forget trying to control every single move. It’s impossible anyway. Instead, focus on trying to control what I think of as the middle territory. I don’t mind losing a few battles on the fringes, if I’m holding my ground in the area that will allow me to respond quickly to problems.

The other night my son and I got into perhaps our eighth fight of the week on the state of his room. The continual explosion makes it hard to walk in there, plus he loses things all the time, which is an endless source of frustration to both of us. I’ve explained that I hate buying replacements only to have them turn up in the morass months later.

So I got cranky and got on his case again, and he felt bad and cried again. When I went to the kitchen to find some calm, I realized that my strategy was all wrong. I was focused on the pawn in the far column of the chess board instead of what the pieces were doing right in front of me.

My thinking then went like this: what is the territory I want to be present in? Continuing the way I was would lead to a clean room, maybe. But by focusing on this flank I was sacrificing control of the middle. Eventually he was going to tune me out because no one wants to feel bad about their shortcomings every day. Is it worth saving a pawn if it leaves your queen vulnerable?

The middle territory with our kids is mutual respect and trust. If I want my son to come to me for help when life gets really complicated, which I do, then I need to focus on behaviors that will allow me to have that strategic influence throughout my relationship with him. Making him feel like crap every day, because his shirts are mixed in with his pants or because of all the Pokemon cards are on the floor, isn’t going to cut it. Make no mistake, seizing the middle is not about throwing out all the rules. This is about knowing which battles to fight, so you can keep the middle territory of the trust and respect of your child.

Inversion

Sometimes it’s not about providing solutions, but removing obstacles. Sociologist Kurt Lewin observes in his work on force field analysis[1] that reaching any goal has two components: augmenting the forces for, and removing the forces against. When it comes to parenting, we need to ask ourselves not only what we could be doing more of, but also what we could be doing less of.

When my friend was going on month number nine of her baby waking up four times a night, she felt at her wits’ end. Out of desperation, she decided to invert the problem. She had been trying different techniques and strategies, thinking that there was something she wasn’t doing right. When nothing seemed to be working, she stopped trying to add elements like new tactics, and changed her strategy. She looked instead for obstacles to remove. Was there anything preventing the baby from sleeping through the night?

The first night she made it darker. No effect. The second night she made it warmer. Her son has slept through the night ever since. It wasn’t her parenting skills or the adherence to a particular sleep philosophy that was causing him to wake up so often. Her baby was cold. Once she removed that obstacle with a space heater the problem was resolved.

We do this all the time, trying to fix problem by throwing new parenting philosophies at the situation. What can I do better? More time, more money, more lessons, more stuff. But it can be equally valuable to look for what you could be doing less of. In so doing, you may enrich your relationships with your children immeasurably.

Parenting is inherently complex: the territory changes almost overnight. Different environments, different children—figuring out how to raise your kids plays out against a backdrop of some fast-paced evolution. Some tactics are great, and once in a while a technique fits the situation perfectly. But when your tactics fail, or your experience seems to provide no obvious direction, a principle-based mental models approach to parenting can give you the insight to find solutions as you go.

[1] Lewin’s original work on force field analysis can be found in Lewin, Kurt. Field Theory in Social Science. New York: Harper and Row, 1951.

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.

***

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 updating. 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 (c) 2018 Farnam Street Media Inc. All rights reserved. May not be used without written permission.

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.

(c) 2018 Farnam Street Media Inc. All rights reserved. May not be used without written permission.

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.

***

“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.

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End Notes

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