Tag: Critical Thinking

Ayn Rand on Why Philosophy Matters

Reading Time: 3 minutes

Nearly four decades after her death, many of Ayn Rand’s works remain controversial and divide people into two camps: love them or hate them. Her lesser known book on philosophy provides broad, timeless insights. Here are her thoughts on the value of philosophy.

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A note on keeping an open mind:

Ayn Rand is a controversial figure. Responses to her ideas seem to land on extremes. The problem with this kind of discourse is that it prevents dialogue. We encourage taking advantage of grey thinking and trying to avoid viewing people and ideas as good/bad binaries. We can learn from people we both like and dislike. We can agree with one idea from someone without having to buy into all their ideas.

There is no doubt that Rand’s essays are polemic. Her writing, like all recorded knowledge, needs to be understood in context. The 1970s saw the height of the Cold War, when capitalism versus communism was set as a battle that would decide the fate of humanity. One need not agree with her political and economic prescriptions to get something interesting from her writing. Accepting this complexity is aligning with the complicated nature of the world. With this in mind, let’s continue!

In Philosophy: Who Needs It, Rand raises questions that dive into the heart of metaphysics, the branch of philosophy that seeks to explain the nature of reality. What can be known? What are our core responsibilities as human beings? The title of the book comes from a talk she gave at the United States Military Academy in 1974. It is a collection of essays written mostly in the 1970s, and explores ideas about the requirements of living a full life and participating well in the world.

Here are two key takeaways from this book:

We All Need Philosophy

To answer the original question of who needs philosophy, Rand argues that everyone does.

She suggests we need philosophy to help develop our values, and to defend ourselves against manipulation and control. Rand posits that everyone has a personal philosophy. In her view:

[y]our only choice is whether you define your philosophy by a conscious, rational, disciplined process of thought and scrupulously logical deliberation—or let your subconscious accumulate a junk heap of unwarranted conclusions, false generalizations, undefined contradictions, undigested slogans, unidentified wishes, doubts and fears, thrown together by chance, but integrated by your subconscious into a kind of mongrel philosophy and fused into a single, solid weight: self-doubt, like a ball and chain in the place where your mind’s wings should have grown.

She goes on to advocate for the process of learning to identify first principles in our thinking processes. This involves picking apart assumptions about the foundations of our knowledge by asking questions like, “Why?” or, “How do I know this to be true? What are the standards a statement must meet in order to be considered true?” This kind of questioning is an important component of deliberate thinking. When we avoid challenging ourselves and others, we remain vulnerable to the influence of ideas that would ultimately do us harm.

Reflection is the key to thinking well

Rand claims that reflection is a responsibility we all have, and that it is a critical step in gaining useful knowledge.

The men who scorn or dread introspection take their inner states for granted, as an irreducible and irresistible primary, and let their emotions determine their actions. This means that they choose to act without knowing the context (reality), the causes (motives), and the consequences (goals) of their actions.

Letting our emotions dictate our actions results in rationalizing experience to fit what we feel, instead of dealing with the world as it actually is.

Rand makes an interesting distinction when she says, “What objectivity and the study of philosophy require is not an ‘open mind,’ but an active mind—a mind able and eagerly willing to examine ideas, but to examine them critically.” Being willing to listen isn’t enough. We must be willing to engage with what we hear, not accepting at face value the often misinformed opinions of others.

She discusses how lazy thought processes hinder progress. Discussing the person who avoids reflection, she writes, ‘When such a man considers a goal or desire he wants to achieve, the first question in his mind is: “Can I do it?”—not “What is required to do it?”’ It’s a handy approach to keep at the forefront. When confronted with obstacles, we can first consider the conditions necessary to tackling them, not if we have the capacity to do so.

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There are many philosophers and essayists that we continue to learn from, even as we gingerly pick our way around their flaws. One disappointment in the book is that Rand’s philosophy often doesn’t live up to the requirements she herself argues for. But she isn’t the first thinker whose questions are far more interesting than her answers.

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Poker, Speeding Tickets, and Expected Value: Making Decisions in an Uncertain World

Reading Time: 13 minutes

You can train your brain to think like CEOs, professional poker players, investors, and others who make tricky decisions in an uncertain world by weighing probabilities.

All decisions involve potential tradeoffs and opportunity costs. The question is, how can we make the best possible choices when the factors involved are often so complicated and confusing? How can we determine which statistics and metrics are worth paying attention to? How do we think about averages?

Expected value is one of the simplest tools you can use to think better. While not a natural way of thinking for most people, it instantly turns the world into shades of grey by forcing us to weigh probabilities and outcomes. Once we’ve mastered it, our decisions become supercharged. We know which risks to take, when to quit projects, and when to go all in.

“Take the probability of loss times the amount of possible loss from the probability of gain times the amount of possible gain. That is what we’re trying to do. It’s imperfect but that’s what it’s all about.”

— Warren Buffett

Expected value refers to the long-run average of a random variable.

If you flip a fair coin ten times, the heads-to-tails ratio will probably not be exactly equal. If you flip it one hundred times, the ratio will be closer to 50:50, though again not exactly. But for a huge number of iterations, you can expect heads to come up half the time and tails the other half. The law of large numbers dictates that the values will, in the long term, regress to the mean, even if the first few flips seem unequal.

The more coin flips, the closer you get to the 50:50 ratio. If you bet a sum of money on a coin flip, the potential winnings on a fair coin have to be bigger than your potential loss to make the expected value positive.

We make many expected-value calculations without even realizing it. If we decide to stay up late and have a few drinks on a Tuesday, we regard the expected value of an enjoyable evening as higher than the expected costs the following day. If we decide to always leave early for appointments, we weigh the expected value of being on time against the frequent instances when we arrive early. When we take on work, we view the expected value in terms of income and other career benefits as higher than the cost in terms of time and/or sanity.

Likewise, anyone who reads a lot knows that most books they choose will have minimal impact on them, while a few books will change their lives and be of tremendous value. Looking at the required time and money as an investment, books have a positive expected value (provided we choose them with care and make use of the lessons they teach).

These decisions might seem obvious. But the math behind them would be somewhat complicated if we tried to sit down and calculate it. Who pulls out a calculator before deciding whether to open a bottle of wine (certainly not me) or walk into a bookstore?

The factors involved are impossible to quantify in a non-subjective manner – like trying to explain how to catch a baseball. We just have a feel for them. This expected-value analysis is unconscious – something to consider if you have ever labeled yourself as “bad at math.”

Parking Tickets

Another example of the expected value is parking tickets. Let’s say that a parking spot costs $5, and the fine for not paying is $10. If you can expect to be caught one-third of the time, why pay for parking? The expected value of doing so is negative. It’s a disincentive. You can park without paying three times and pay only $10 in fines, instead of paying $15 for three parking spots. But if the fine is $100, the probability of getting caught would have to be higher than one in twenty for it to be worthwhile. This is why fines tend to seem excessive. They cover the people who are not caught while giving an incentive for everyone to pay.

Consider speeding tickets. Here, the expected value can be more abstract, encompassing different factors. If speeding on the way to work saves 15 minutes, then a monthly $100 fine might seem worthwhile to some people. For most of us, though, a weekly fine would mean that speeding has a negative expected value. Add in other disincentives (such as the loss of your driver’s license), and speeding is not worth it. So the calculation is not just financial; it takes into account other tradeoffs as well.

The same goes for free samples and trial periods on subscription services. Many companies (such as Graze, Blue Apron, and Amazon Prime) offer generous free trials. How can they afford to do this? Again, it comes down to expected value. The companies know how much the free trials cost them. They also know the probability of someone paying afterward and the lifetime value of a customer. Basic math reveals why free trials are profitable. Say that a free trial costs the company $10 per person, and one in ten people then sign up for the paid service, going on to generate $150 in profits. The expected value is positive. If only one in twenty people sign up, the company needs to find a cheaper free trial or scrap it.

Similarly, expected value applies to services that offer a free “lite” version (such as Buffer and Spotify). Doing so costs them a small amount or even nothing. Yet it increases the chance of someone’s deciding to pay for the premium version. For the expected value to be positive, the combined cost of the people who never upgrade needs to be lower than the profit from the people who do pay.

Lottery tickets prove useless when viewed through the lens of expected value. If a ticket costs $1 and there is a possibility of winning $500,000, it might seem as if the expected value of the ticket is positive. But it is almost always negative. If one million people purchase a ticket, the expected value is $0.50. That difference is the profit that lottery companies make. Only on sporadic occasions is the expected value positive, even though the probability of winning remains minuscule.

Failing to understand expected value is a common logical fallacy. Getting a grasp of it can help us to overcome many limitations and cognitive biases.

“Constantly thinking in expected value terms requires discipline and is somewhat unnatural. But the leading thinkers and practitioners from somewhat varied fields have converged on the same formula: focus not on the frequency of correctness, but on the magnitude of correctness.”

— Michael Mauboussin

Expected Value and Poker

Let’s look at poker. How do professional poker players manage to win large sums of money and hold impressive track records? Well, we can be certain that the answer isn’t all luck, although there is some of that involved.

Professional players rely on mathematical mental models that create order among random variables. Although these models are basic, it takes extensive experience to create the fingerspitzengefühl (“fingertips feeling,” or instinct) necessary to use them.

A player needs to make correct calculations every minute of a game with an automaton-like mindset. Emotions and distractions can corrupt the accuracy of raw math.

In a game of poker, the expected value is the average return on each dollar invested in the pot. Each time a player makes a bet or call, they are taking into account the probability of making more money than they invest. If a player is risking $100, with a 1 in 5 probability of success, the pot must contain at least $500 for the bet to be safe. The expected value per call is at least equal to the amount the player stands to lose. If the pot contains $300 and the probability is 1 in 5, the expected value is negative. The idea is that even if this tactic is unsuccessful at times, in the long run, the player will profit.

Expected-value analysis gives players a clear idea of probabilistic payoffs. Successful poker players can win millions one week, then make nothing or lose money the next, depending on the probability of winning. Even the best possible hands can lose due to simple probability. With each move, players also need to use Bayesian updating to adapt their calculations, because sticking with a prior figure could prove disastrous. Casinos make their fortunes from people who bet on situations with a negative expected value.

Expected Value and the Ludic Fallacy

In The Black Swan, Nassim Taleb explains the difference between everyday randomness and randomness in the context of a game or casino. Taleb coined the term “ludic fallacy” to refer to “the misuse of games to model real-life situations.” (Or, as the website logicallyfallacious.com puts it: the assumption that flawless statistical models apply to situations where they don’t actually apply.)

In Taleb’s words, gambling is “sterilized and domesticated uncertainty. In the casino, you know the rules, you can calculate the odds… ‘The casino is the only human venture I know where the probabilities are known, Gaussian (i.e., bell-curve), and almost computable.’ You cannot expect the casino to pay out a million times your bet, or to change the rules abruptly during the game….”

Games like poker have a defined, calculable expected value. That’s because we know the outcomes, the cards, and the math. Most decisions are more complicated. If you decide to bet $100 that it will rain tomorrow, the expected value of the wager is incalculable. The factors involved are too numerous and complex to compute. Relevant factors do exist; you are more likely to win the bet if you live in England than if you live in the Sahara, for example. But that doesn’t rule out Black Swan events, nor does it give you the neat probabilities which exist in games. In short, there is a key distinction between Knightian risks, which are computable because we have enough information to calculate the odds, and Knightian uncertainty, which is non-computable because we don’t have enough information to calculate odds accurately. (This distinction between risk and uncertainty is based on the writings of economist Frank Knight.) Poker falls into the former category. Real-life is in the latter. If we take the concept literally and only plan for the expected, we will run into some serious problems.

As Taleb writes in Fooled By Randomness:

Probability is not a mere computation of odds on the dice or more complicated variants; it is the acceptance of the lack of certainty in our knowledge and the development of methods for dealing with our ignorance. Outside of textbooks and casinos, probability almost never presents itself as a mathematical problem or a brain teaser. Mother nature does not tell you how many holes there are on the roulette table, nor does she deliver problems in a textbook way (in the real world one has to guess the problem more than the solution).

The Monte Carlo Fallacy

Even in the domesticated environment of a casino, probabilistic thinking can go awry if the principle of expected value is forgotten. This famously occurred in Monte Carlo Casino in 1913. A group of gamblers lost millions when the roulette table landed on black 26 times in a row. The probability of this occurring is no more or less likely than the other 67,108,863 possible permutations, but the people present kept thinking, “It has to be red next time.” They saw the likelihood of the wheel landing on red as higher each time it landed on black. In hindsight, what sense does that make? A roulette wheel does not remember the color it landed on last time. The likelihood of either outcome is exactly 50% with each spin, regardless of the previous iteration. So the potential winnings for each spin need to be at least twice the bet a player makes, or the expected value is negative.

“A lot of people start out with a 400-horsepower motor but only get 100 horsepower of output. It’s way better to have a 200-horsepower motor and get it all into output.”

— Warren Buffett

Given all the casinos and roulette tables in the world, the Monte Carlo incident had to happen at some point. Perhaps some day a roulette wheel will land on red 26 times in a row and the incident will repeat. The gamblers involved did not consider the negative expected value of each bet they made. We know this mistake as the Monte Carlo fallacy (or the “gambler’s fallacy” or “the fallacy of the maturity of chances”) – the assumption that prior independent outcomes influence future outcomes that are actually also independent. In other words, people assume that “a random process becomes less random and more predictable as it is repeated”1.

It’s a common error. People who play the lottery for years without success think that their chance of winning rises with each ticket, but the expected value is unchanged between iterations. Amos Tversky and Daniel Kahneman consider this kind of thinking a component of the representativeness heuristic, stating that the more we believe we control random events, the more likely we are to succumb to the Monte Carlo fallacy.

Magnitude over Frequency

Steven Crist, in his book Bet with the Best, offers an example of how an expected-value mindset can be applied. Consider a hypothetical race with four horses. If you’re trying to maximize return on investment, you might want to avoid the horse with a high likelihood of winning. Crist writes,

The point of this exercise is to illustrate that even a horse with a very high likelihood of winning can be either a very good or a very bad bet, and that the difference between the two is determined by only one thing: the odds.”2

Everything comes down to payoffs. A horse with a 50% chance of winning might be a good bet, but it depends on the payoff. The same holds for a 100-to-1 longshot. It’s not the frequency of winning but the magnitude of the win that matters.

Error Rates, Averages, and Variability

When Bill Gates walks into a room with 20 people, the average wealth per person in the room quickly goes beyond a billion dollars. It doesn’t matter if the 20 people are wealthy or not; Gates’s wealth is off the charts and distorts the results.

An old joke tells of the man who drowns in a river which is, on average, three feet deep. If you’re deciding to cross a river and can’t swim, the range of depths matters a heck of a lot more than the average depth.

The Use of Expected Value: How to Make Decisions in an Uncertain World

Thinking in terms of expected value requires discipline and practice. And yet, the top performers in almost any field think in terms of probabilities. While this isn’t natural for most of us, once you implement the discipline of the process, you’ll see the quality of your thinking and decisions improve.

In poker, players can predict the likelihood of a particular outcome. In the vast majority of cases, we cannot predict the future with anything approaching accuracy. So what use is the expected value outside gambling? It turns out, quite a lot. Recognizing how expected value works puts any of us at an advantage. We can mentally leap through various scenarios and understand how they affect outcomes.

Expected value takes into account wild deviations. Averages are useful, but they have limits, as the man who tried to cross the river discovered. When making predictions about the future, we need to consider the range of outcomes. The greater the possible variance from the average, the more our decisions should account for a wider range of outcomes.

There’s a saying in the design world: when you design for the average, you design for no one. Large deviations can mean more risk-which is not always a bad thing. So expected-value calculations take into account the deviations. If we can make decisions with a positive expected value and the lowest possible risk, we are open to large benefits.

Investors use expected value to make decisions. Choices with a positive expected value and minimal risk of losing money are wise. Even if some losses occur, the net gain should be positive over time. In investing, unlike in poker, the potential losses and gains cannot be calculated in exact terms. Expected-value analysis reveals opportunities that people who just use probabilistic thinking often miss. A trade with a low probability of success can still carry a high expected value. That’s why it is crucial to have a large number of robust mental models. As useful as probabilistic thinking can be, it has far more utility when combined with expected value.

Understanding expected value is also an effective way to overcome the sunk costs fallacy. Many of our decisions are based on non-recoverable past investments of time, money, or resources. These investments are irrelevant; we can’t recover them, so we shouldn’t factor them into new decisions. Sunk costs push us toward situations with a negative expected value. For example, consider a company that has invested considerable time and money in the development of a new product. As the launch date nears, they receive irrefutable evidence that the product will be a failure. Perhaps research shows that customers are disinterested, or a competitor launches a similar, better product. The sunk costs fallacy would lead them to release their product anyway. Even if they take a loss. Even if it damages their reputation. After all, why waste the money they spent developing the product? Here’s why: Because the product has a negative expected value, which will only worsen their losses. An escalation of commitment will only increase sunk costs.

When we try to justify a prior expense, calculating the expected value can prevent us from worsening the situation. The sunk costs fallacy robs us of our most precious resource: time. Each day we are faced with the choice between continuing and quitting numerous endeavors. Expected-value analysis reveals where we should continue, and where we should cut our losses and move on to a better use of time and resources. It’s an efficient way to work smarter, and not engage in unnecessary projects.

Thinking in terms of expected value will make you feel awkward when you first try it. That’s the hardest thing about it; you need to practice it a while before it becomes second nature. Once you get the hang of it, you’ll see that it’s valuable in almost every decision. That’s why the most rational people in the world constantly think about expected value. They’ve uncovered the key insight that the magnitude of correctness matters more than its frequency. And yet, human nature is such that we’re happier when we’re frequently right.

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Footnotes
  • 1

    From https://rationalwiki.org/wiki/Gambler’s_fallacy, accessed on 11 January 2018.

  • 2

    Steven Crist, “Crist on Value,” in Andrew Beyer et al., Bet with the Best: All New Strategies From America’s Leading Handicappers (New York: Daily Racing Form Press, 2001), 63-64.

What’s So Significant About Significance?

Reading Time: 7 minutes

How Not to be wrong

One of my favorite studies of all time took the 50 most common ingredients from a cookbook and searched the literature for a connection to cancer: 72% had a study linking them to increased or decreased risk of cancer. (Here’s the link for the interested.)

Meta-analyses (studies examining multiple studies) quashed the effect pretty seriously, but how many of those single studies were probably reported on in multiple media outlets, permanently causing changes in readers’ dietary habits? (We know from studying juries that people are often unable to “forget” things that are subsequently proven false or misleading — misleading data is sticky.)

The phrase “statistically significant” is one of the more unfortunately misleading ones of our time. The word significant in the statistical sense — meaning distinguishable from random chance — does not carry the same meaning in common parlance, in which we mean distinguishable from something that does not matter. Don’t worry, we will get to what that means.

Confusing the two gets at the heart of a lot of misleading headlines and it’s worth a brief look into why they don’t mean the same thing, so you can stop being scared that everything you eat or do is giving you cancer.

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The term statistical significance is used to denote when an effect is found to be extremely unlikely to have occurred by chance. To make that determination, we have to propose a null hypothesis to be rejected. Let’s say we propose that eating an apple a day reduces the incidence of colon cancer. The “null hypothesis” here would be that eating an apple a day does nothing to the incidence of colon cancer — that we’d be equally likely to get colon cancer if we ate that daily apple.

When we analyze the data of our study, we’re technically not looking to say “Eating an apple a day prevents colon cancer” — that’s a bit of a misconception. What we’re actually doing is an inversion— we want the data to provide us with sufficient weight to reject the idea that apples have no effect on colon cancer.

And even when that happens, it’s not an all-or-nothing determination. What we’re actually saying is, “It would be extremely unlikely for the data we have, which shows a daily apple reduces colon cancer by 50%, to have popped up by chance. Not impossible, but very unlikely.” The world does not quite allow us to have absolute conviction.

How unlikely? The currently accepted standard in many fields is 5% — there is a less than 5% chance the data would come up this way randomly. That immediately tells you that at least 1 out of every 20 studies must be wrong, but alas that is where we’re at. (The problem with the 5% p-value, and the associated problem of p-hacking has been subject to some intense debate, but we won’t deal with that here.)

We’ll get to why “significance can be insignificant,” and why that’s so important, in a moment. But let’s make sure we’re fully on board with the importance of sorting chance events from real ones with another illustration, this one outlined by Jordan Ellenberg in his wonderful book How Not to Be Wrong. Pay close attention:

Suppose we’re in null hypothesis land, where the chance of death is exactly the same (say, 10%) for the fifty patients who got your drug and the fifty who got [a] placebo. But that doesn’t mean that five of the drug patients die and five of the placebo patients die. In fact, the chance that exactly five of the drug patients die is about 18.5%; not very likely, just as it’s not very likely that a long series of coin tosses would yield precisely as many heads as tails. In the same way, it’s not very likely that exactly the same number of drug patients and placebo patients expire during the course of the trial. I computed:

13.3% chance equally many drug and placebo patients die
43.3% chance fewer placebo patients than drug patients die
43.3% chance fewer drug patients than placebo patients die

Seeing better results among the drug patients than the placebo patients says very little, since this isn’t at all unlikely, even under the null hypothesis that your drug doesn’t work.

But things are different if the drug patients do a lot better. Suppose five of the placebo patients die during the trial, but none of the drug patients do. If the null hypothesis is right, both classes of patients should have a 90% chance of survival. But in that case, it’s highly unlikely that all fifty of the drug patients would survive. The first of the drug patients has a 90% chance; now the chance that not only the first but also the second patient survives is 90% of that 90%, or 81%–and if you want the third patient to survive as well, the chance of that happening is only 90% of that 81%, or 72.9%. Each new patient whose survival you stipulate shaves a little off the chances, and by the end of the process, where you’re asking about the probability that all fifty will survive, the slice of probability that remains is pretty slim:

(0.9) x (0.9) x (0.9) x … fifty times! … x (0.9) x (0.9) = 0.00515 …

Under the null hypothesis, there’s only one chance in two hundred of getting results this good. That’s much more compelling. If I claim I can make the sun come up with my mind, and it does, you shouldn’t be impressed by my powers; but if I claim I can make the sun not come up, and it doesn’t, then I’ve demonstrated an outcome very unlikely under the null hypothesis, and you’d best take notice.

So you see, all this null hypothesis stuff is pretty important because what you want to know is if an effect is really “showing up” or if it just popped up by chance.

A final illustration should make it clear:

Imagine you were flipping coins with a particular strategy of getting more heads, and after 30 flips you had 18 heads and 12 tails. Would you call it a miracle? Probably not — you’d realize immediately that it’s perfectly possible for an 18/12 ratio to happen by chance. You wouldn’t write an article in U.S. News and World Report proclaiming you’d figured out coin-flipping.

Now let’s say instead you flipped the coin 30,000 times and you get 18,000 heads and 12,000 tails…well, then your case for statistical significance would be pretty tight.  It would be approaching impossible to get that result by chance — your strategy must have something to it. The null hypothesis of “My coin flipping technique is no better than the usual one” would be easy to reject! (The p-value here would be orders of magnitude less than 5%, by the way.)

That’s what this whole business is about.

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Now that we’ve got this idea down, we come to the big question that statistical significance cannot answer: Even if the result is distinguishable from chance, does it actually matter?

Statistical significance cannot tell you whether the result is worth paying attention to — even if you get the p-value down to a minuscule number, increasing your confidence that what you saw was not due to chance. 

In How Not to Be Wrong, Ellenberg provides a perfect example:

A 1995 study published in a British journal indicated that a new birth control pill doubled the risk of venous thrombosis (potentially killer blood clot) in its users. Predictably, 1.5 million British women freaked out, and some meaningfully large percentage of them stopped taking the pill. In 1996, 26,000 more babies were born than the previous year, and there were 13,600 more abortions. Whoops!

So what, right? Lots of mothers’ lives were saved, right?

Not really. The initial probability of a women getting a venous thrombosis with any old birth control pill was about 1 in 7,000 or about 0.01%. That means that the “Killer Pill,” even if was indeed increasing “thrombosis risk,” only increased that risk to 2 in 7,000, or about 0.02%!! Is that worth rearranging your life for? Probably not.

Ellenberg makes the excellent point that, at least in the case of health, the null hypothesis is unlikely to be right in most cases! The body is a complex system — of course what we put in it affects how it functions in some direction or another. It’s unlikely to be absolute zero.

But numerical and scale-based thinking, indispensable for anyone looking to not be a sucker, tells us that we must distinguish between small and meaningless effects (like the connection between almost all individual foods and cancer so far) and real ones (like the connection between smoking and lung cancer).

And now we arrive at the problem of “significance” — even if an effect is really happening, it still may not matter!  We must learn to be wary of “relative” statistics (i.e., “the risk has doubled”), and look to favor “absolute” statistics, which tell us whether the thing is worth worrying about at all.

So we have two important ideas:

A. Just like coin flips, many results are perfectly possible by chance. We use the concept of “statistical significance” to figure out how likely it is that the effect we’re seeing is real and not just a random illusion, like seeing 18 heads in 30 coin tosses.

B. Even if it is really happening, it still may be unimportant – an effect so insignificant in real terms that it’s not worth our attention.

These effects should combine to raise our level of skepticism when hearing about groundbreaking new studies! (A third and equally important problem is the fact that correlation is not causation, a common problem in many fields of science including nutritional epidemiology. Just because x is associated with y does not mean that x is causing y.)

Tread carefully and keep your thinking cap on.

***

Still Interested? Read Ellenberg’s great book to get your head working correctly, and check out our posts on Bayesian updating, another very useful statistical tool, and learn a little about how we distinguish science from pseudoscience.

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Daniel Dennett’s Most Useful Critical Thinking Tools

Reading Time: 7 minutes

We recently discussed some wonderful mental tools from the great Richard Feynman. Let’s get some more good ones from another giant, Daniel Dennett.

Dennett is one of the great thinkers in the world; he’s been at the forefront of cognitive science and evolutionary science for over 50 years, trying to figure out how the mind works and why we believe the things we believe. He’s written a number of amazing books on evolution, religion, consciousness, and free will. (He’s also subject to some extreme criticism due to his atheist bent, as with Dawkins.)

His most recent book is the wise and insightful Intuition Pumps and Other Tools for Critical Thinking, where he lays out a series of short essays (some very short — less than a page) with mental shortcuts, tools, analogies, and metaphors for thinking about a variety of topics, mostly those topics he is best known for.

Some people don’t like the disconnected nature of the book, but that’s precisely its usefulness: Like what we do here at Farnam Street, Dennett is simply trying to add tools to your toolkit. You are free to, in the words of Bruce Lee, “Absorb what is useful, discard what is useless and add what is specifically your own.”

***

The book opens with 12 of Dennett’s best “tools for critical thinking” — a bag of mental tricks to improve your ability to engage critically and rationally with the world.

Let’s go through a few of the best ones. You’ll be familiar with some and unfamiliar with others, agree with some and not with others. But if you adopt Bruce Lee’s advice, you should come away with something new and useful.

Making mistakes

Mistakes are not just opportunities for learning; they are, in an important sense, the only opportunity for learning or making something truly new. Before there can be learning, there must be learners. There are only two non-miraculous ways for learners to come into existence: they must either evolve or be designed and built by learners that evolved. Biological evolution proceeds by a grand, inexorable process of trial and error–and without the errors the trials wouldn’t accomplish anything. As Gore Vidal once said, “It is not enough to succeed. Others must fail.”

[…]

The chief trick to making good mistakes is not to hide them–especially not from yourself. Instead of turning away in denial when you make a mistake, you should become a connoisseur of your own mistakes, turning them over in your mind as if they were works of art, which in a way they are. The fundamental reaction to any mistake ought to be this: “Well, I won’t do that again!”

Reductio ad absurdum

The crowbar of rational inquiry, the great lever that enforces consistency, is reductio ad absurdum–literally, reduction (of the argument) to absurdity. You take the assertion or conjecture at issue and see if you can pry any contradictions (or just preposterous implications) out of it. If you can, that proposition has to be discarded or sent back to the shop for retooling. We do this all the time without bothering to display the underlying logic: “If that’s a bear, then bears have antlers!” or “He won’t get here in time for supper unless he can fly like Superman.”

Rapoport’s Rules

Just how charitable are you supposed to be when criticizing the views of an opponent? […] The best antidote I know for [the] tendency to caricature one’s opponent is a list of rules promulgated by the social psychologist and game theorist Anatol Rapoport (creator of the winning Tit-for-Tat strategy in Robert Axelrod’s legendary prisoner’s dilemma tournament).

How to compose a successful critical commentary:

1. You should attempt to re-express your target’s position so clearly, vividly, and fairly that your target says, “Thanks, I wish I’d thought of putting it that way.”
2. You should list any points of agreement (especially if they are not matters of general or widespread agreement).
3. You should mention anything that you have learned from your target.
4. Only then are you permitted to say so much as a word of rebuttal or criticism.

Sturgeon’s Law

The science-fiction writer Ted Sturgeon, speaking at the World Science Fiction Convention in Philadelphia in September 1953, said,

When people talk about the mystery novel, they mentioned The Maltese Falcon and The Big Sleep. When they talk about the western, they say there’s The Way West and Shane. But when they talk about science fiction, they call it “that Buck Rogers stuff,” and they say “ninety percent of science fiction is crud.” Well, they’re right. Ninety percent of science fiction is crud. But then ninety percent of everything is crud, and it’s the ten percent that isn’t crud that’s important, and the ten percent of science fiction that isn’t crud is as good as or better than anything being written anywhere.

This advice is often ignored by ideologues intent on destroying the reputation of analytic philosophy, evolutionary psychology, sociology, cultural anthropology, macroeconomics, plastic surgery, improvisational theater, television sitcoms, philosophical theology, massage therapy, you name it. Let’s stipulate at the outset that there is a great deal of deplorable, stupid, second-rate stuff out there, of all sorts.

Occam’s Razor

Attributed to William of Ockham (or Occam), the fourteenth century logician and philosopher, this thinking tool is actually a much older rule of thumb. A Latin name for it is lex parsimoniae, the law of parsimony. It is usually put into English as the maxim “Do not muliply entities beyond necessary.” The idea is straightforward: Don’t concoct a complicated, extravagant theory if you’ve got a simpler one (containing fewer ingredients, fewer entities) that handles the phenomenon just as well. If exposure to extremely cold air can account for all the symptoms of frostbite, don’t postulate unobserved “snow germs” or “arctic microbes.” Kepler’s laws explain the orbit of the planets; we have no need to hypothesize pilots guiding the planets from control panels hidden under the surface.

Occam’s Broom

The molecular biologist Sidney Brenner recently invented a delicious play on Occam’s Razor, introducing the new term Occam’s Broom, to describe the process in which inconvenient facts are whisked under the rug by intellectually dishonest champions of one theory or another. This is our first boom crutch, an anti-thinking tool, and you should keep your eyes peeled for it. The practice is particularly insidious when used by propagandists who direct their efforts at the lay public, because like Sherlock Holmes’ famous clue about the dog that didn’t bark in the night, the absence of a fact that has been swept off the scene by Occam’s Broom is unnoticeable except by experts. 

Jootsing

…It is even harder to achieve what Doug Hofstadter calls joosting, which stands for “jumping out of the system.” This is an important tactic not just in science and philosophy, but also in the arts. Creativity, that ardently sought but only rarely found virtue, often is a heretofore unimagined violation of the rules of the system from which it springs. It might be the system of classical harmony in music, the rules for meter and rhyme in sonnets (or limericks, even), or the canons of good taste or good form in some genre of art. Or it might be the assumptions and principles of some theory or research program. Being creative is not just a matter of casting about for something novel–anbody can do that, since novelty can be found in any random juxtaposition of stuff–but of making the novelty jump out of some system, a system that has become somewhat established, for good reasons.

When an artistic tradition reaches the point where literally “anything goes,” those who want to be creative have a problem: there are no fixed rules to rebel against, no complacent expectations to shatter, nothing to subvert, no background against which to create something that is both surprising and yet meaningful. It helps to know the tradition if you want to subvert it. That’s why so few dabblers or novices succeed in coming up with anything truly creative.

Rathering (Anti-thinking tool)

Rathering is a way of sliding you swiftly and gently past a false dichotomy. The general form of a rathering is “It is not the case that blahblahblah, as orthodoxy would have you believe; it is rather that suchandsuchandsuch–which is radically different.” Some ratherings are just fine; you really must choose between the two alternatives on offer; in these cases, you are not being offered a false, bur rather a genuine, inescapable dichotomy. But some ratherings are little more than sleight of hand, due to the fact that the word “rather” implies–without argument–that there is an important incompatibility between the claims flanking it.

The “Surely” Operator

When you’re reading or skimming argumentative essays, especially by philosophers, here is a quick trick that may save you much time and effort, especially in this age of simple searching by computer: look for “surely” in the document, and check each occurrence. Not always, not even most of the time, but often the world “surely” is as good as a blinking light in locating a weak point in the argument….Why? Because it marks the very edge of what the author is actually sure about and hopes readers will also be sure about. (If the author were really sure all the readers would agree, it wouldn’t be worth mentioning.)

The Deepity

A “deepity” is a proposition that seems both important and true–and profound–but that achieves this effect by being ambiguous. On one reading it is manifestly false, but it would be earth-shaking if it were true; on the other reading it is true but trivial. The unwary listener picks up on the glimmer of truth from the second reading, and the devastating importance from the first reading, and thinks, Wow! That’s a deepity.

Here is an example. (Better sit down: this is heavy stuff.)

Love is just a word.

[…]

Richard Dawkins recently alerted me to a fine deepity by Rowan Williams, the Archbishop of Canterbury, who described his faith as a

silent waiting on the truth, pure sitting and breathing in the presence of a question mark.

***

Still Interested? Check out Dennett’s book for a lot more of these interesting tools for critical thinking, many non-intuitive. I guarantee you’ll generate food for thought as you go along. Also, try checking out 11 Rules for Critical Thinking and learn how to be Eager to be Wrong.

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Atul Gawande and the Mistrust of Science

Reading Time: 3 minutes

Continuing on with Commencement Season, Atul Gawande gave an address to the students of Cal Tech last Friday, delivering a message to future scientists, but one that applies equally to all of us as thinkers:

“Even more than what you think, how you think matters.”

Gawande addresses the current growing mistrust of “scientific authority” — the thought that because science creaks along one mistake at a time, that it isn’t to be trusted. The misunderstanding of what scientific thinking is and how it works is at the root of much problematic ideology, and it’s up to those who do understand it to promote its virtues.

It’s important to realize that scientists, singular, are as fallible as the rest of us. Thinking otherwise only sets you up for a disappointment. The point of science is the collective, the forward advance of the hive, not the bee. It’s sort of a sausage-making factory when seen up close, but when you pull back the view, it looks like a beautifully humming engine, steadily giving us more and more information about ourselves and the world around us. Science is, above all, a method of thought. A way of figuring out what’s true and what we’re just fooling ourselves about.

So explains Gawande:

Few working scientists can give a ground-up explanation of the phenomenon they study; they rely on information and techniques borrowed from other scientists. Knowledge and the virtues of the scientific orientation live far more in the community than the individual. When we talk of a “scientific community,” we are pointing to something critical: that advanced science is a social enterprise, characterized by an intricate division of cognitive labor. Individual scientists, no less than the quacks, can be famously bull-headed, overly enamored of pet theories, dismissive of new evidence, and heedless of their fallibility. (Hence Max Planck’s observation that science advances one funeral at a time.) But as a community endeavor, it is beautifully self-correcting.

Beautifully organized, however, it is not. Seen up close, the scientific community—with its muddled peer-review process, badly written journal articles, subtly contemptuous letters to the editor, overtly contemptuous subreddit threads, and pompous pronouncements of the academy— looks like a rickety vehicle for getting to truth. Yet the hive mind swarms ever forward. It now advances knowledge in almost every realm of existence—even the humanities, where neuroscience and computerization are shaping understanding of everything from free will to how art and literature have evolved over time.

He echoes Steven Pinker in the thought that science, traditionally left to the realm of discovering “physical” reality, is now making great inroads into what might have previously been considered philosophy, by exploring why and how our minds work the way they do. This can only be accomplished by deep critical thinking across a broad range of disciplines, and by the dual attack of specialists uncovering highly specific nuggets and great synthesizers able to suss out meaning from the big pile of facts.

The whole speech is worth a read and reflection, but Gawande’s conclusion is particularly poignant for an educated individual in a Republic:

The mistake, then, is to believe that the educational credentials you get today give you any special authority on truth. What you have gained is far more important: an understanding of what real truth-seeking looks like. It is the effort not of a single person but of a group of people—the bigger the better—pursuing ideas with curiosity, inquisitiveness, openness, and discipline. As scientists, in other words.

Even more than what you think, how you think matters. The stakes for understanding this could not be higher than they are today, because we are not just battling for what it means to be scientists. We are battling for what it means to be citizens.

Still Interested? Read the rest, and read a few other of this year’s commencements by Nassim Taleb and Gary Taubes. Or read about E.O. Wilson, the great Harvard biologist, and what he thought it took to become a great scientist. (Hint: The same stuff it takes for anyone to become a great critical thinker.)

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Eager to Be Wrong

Reading Time: 3 minutes

“You know what Kipling said? Treat those two impostors just the same — success and failure. Of course, there’s going to be some failure in making the correct decisions. Nobody bats a thousand. I think it’s important to review your past stupidities so you are less likely to repeat them, but I’m not gnashing my teeth over it or suffering or enduring it. I regard it as perfectly normal to fail and make bad decisions. I think the tragedy in life is to be so timid that you don’t play hard enough so you have some reverses.”
— Charlie Munger

***

When was the last time you said to yourself I hope I’m wrong and really meant it?

Have you ever really meant it?

Here’s the thing: In our search for truth we must realize, thinking along two tracks, that we’re frequently led to wrong solutions by the workings of our natural apparatus. Uncertainty is a very mentally demanding, and in a certain way, physically demanding process. The brain uses a lot of energy when it has to process conflicting information. To show yourself, try reading up on something contentious like the abortion debate, but with a completely open mind to either side (if you can). Pay attention as your brain starts twisting itself into a very uncomfortable state while you explore completely opposing sides of an argument.

This mental pain is called cognitive dissonance and it’s really not that much fun. Charlie Munger calls the process of resolving this dissonance doubt avoidance tendency – the tendency to resolve conflicting information as quickly as possible to return to physical and mental comfort. To get back to your happy zone.

Combine this tendency to resolve doubt with the well-known first conclusion bias (something Francis Bacon knew about long ago), and the logical conclusion is that we land on a lot of wrong answers and stay there because it’s easier.

Let that sink in. We don’t stay there because we’re correct, but because it’s physically easier. It’s a form of laziness.

Don’t believe me? Spend a single day asking yourself this simple question: Do I know this for sure, or have I simply landed on a comfortable spot?

You’ll be surprised how many things you do and believe just because it’s easy. You might not even know how you landed there. Don’t feel bad about it — it’s as natural as breathing. You were wired that way at birth.

But there is a way to attack this problem.

Munger has a dictum that he won’t allow himself to hold an opinion unless he knows the other side of the argument better than that side does. Such an unforgiving approach means that he’s not often wrong. (It sometimes takes many years to show, but posterity has rarely shown him to be way off.) It’s a tough, wise, and correct solution.

It’s still hard though, and doesn’t solve the energy expenditure problem. What can we tell ourselves to encourage ourselves to do that kind of work? The answer would be well-known to Darwin: Train yourself to be eager to be wrong.

Right to be Wrong

The advice isn’t simply to be open to being wrong, which you’ve probably been told to do your whole life. That’s nice, and correct in theory, but frequently turns into empty words on a page. Simply being open to being wrong allows you to keep the window cracked when confronted with disconfirming evidence — to say Well, I was open to it! and keep on with your old conclusion.

Eagerness implies something more. Eager implies that you actively hope there is real, true, disconfirming information proving you wrong. It implies you’d be more than glad to find it. It implies that you might even go looking for it. And most importantly, it implies that when you do find yourself in error, you don’t need to feel bad about it. You feel great about it! Imagine how much of the world this unlocks for you.

Why be so eager to prove yourself wrong? Well, do you want to be comfortable or find the truth? Do you want to say you understand the world or do you want to actually understand it? If you’re a truth seeker, you want reality the way it is, so you can live in harmony with it.

Feynman wanted reality. Darwin wanted reality. Einstein wanted reality. Even when they didn’t like it. The way to stand on the shoulders of giants is to start the day by telling yourself I can’t wait to correct my bad ideas, because then I’ll be one step closer to reality. 

*** 

Post-script: Make sure you apply this advice to things that matter. As stated above, resolving uncertainty takes great energy. Don’t waste that energy on deciding whether Nike or Reebok sneakers are better. They’re both fine. Pick the ones that feel comfortable and move on. Save your deep introspection for the stuff that matters.

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