Introduction

That’s quite enough about memory, memory, and more memory, don’t you think? Now that we have a clear picture of how information is stored, accessed, and lost in our minds, let’s return to talking about what we do with all that information. So far, we’ve covered visualizing and organizing it. What about using it to solve problems?

Suppose Agatha is faced with the following math problem.

312.757 x 4

She can approach this problem in a couple of different ways – you can see them in Figure 8.1.

Agatha can either do all the math to get the exact answer (1251.028), or she can do a quick approximation in her head and get “about 1200”. Which route she takes will depend a little on why she needs the number, but the question for us to consider is more general. What kind of calculation does a computer always do? And what kind of calculation do our brains default to?

A computer, as you likely guessed, is built to perform precise calculations. A calculator will never tell you “about 1200.” It will tell you the exact answer. And while we learn in school all the steps to come to the exact answer through multiplication, that process is not automatic or natural to our brains. When given the option, our brains will almost always choose “easy and mostly accurate” over “lots of work and always accurate.” In the case of math, that sometimes means rounding numbers and ignoring precision. Other times, it means ignoring the digits completely and simply turning the numbers into concepts, like “a lot” and “way too much.”

When our brains simplify things like this, we call it a heuristic: a cognitive shortcut designed to generalize about a problem, to be accurate most of the time instead of all the time. And because they are accurate most of the time, we don’t always notice them. But we can expose these heuristics in the rare occasions during which they do make a mistake. In the following sections, we’ll highlight some of these errors to understand what they reveal about the assumptions our brains make.

Representativeness

Let’s learn a bit more about Agatha.

Agatha is 37, likes reading mystery novels, doing puzzles, writing poetry, playing with her cat, and baking soft pretzels.

Is Agatha more likely to be a librarian or a saleswoman?

You might be leaning towards librarian. After all, Agatha likes books and quiet indoor hobbies! It seems to fit her personality a lot better than saleswoman. But according to a dominant cognitive scientific perspective, you’d be dead wrong.

Why? Because there are many, many more salespeople in the world than librarians. In the United States (as of around 2020) there are around 13 million salespeople, and 166 thousand librarians. That means any random person in the United States is about 78 times more likely to be a salesperson than a librarian!

According to traditional cognitive science, Agatha’s personality is irrelevant. Much more important is something called the base rate: the natural amount that something occurs. Personality varies across people, but the fact remains that there are far more salespeople than librarians, so if you draw a random human out of a bag, you should always bet on that person being a salesperson rather than a librarian.

The error that people make when they assume Agatha should be a librarian is an example of the representativeness heuristic: we classify things based on their traits. Why do we think Agatha should be a librarian? She has traits we often associate with libraries. Why does a tomato seem like a vegetable, when it is not one? It shares a taste profile with vegetables and often goes in the same context as vegetables. Why does a dolphin seem like a fish, even though it is a mammal? Because it shares many traits with fish, like its shape and habitat. The thing is, we are usually correct when we make assumptions like this. Most fish-like things are fish. That’s what makes this mental shortcut useful—it’s correct most of the time.

Anchoring/Adjustment

Time for a pop quiz! Please answer the following questions to the best of your ability.

• How many known species of bees do you think there are in the world? For reference, there are over 300 species of monkey.

• About how many people do you think lived in the city of Westbrook, Maine, as of the 2020 census? For reference, that year about 550,000 people lived in Portland, Maine.

Take a look at your answers. How did you come up with them? Did you guess wildly? Did you use prior knowledge? Did you use my helpful reference facts?

Was your answer to #1 smaller than your answer to #2?

Odds are that even if you ignored my helpful reference facts (or intentionally tried to block them out of your mind) they may have wormed their way into your brain to influence your answers. While both are true, the reference I gave you for #1 is much smaller than the reference for #2. If your brain was nudged at all by this information, you were employing the anchoring/adjustment heuristic: when we have to make a guess, we often latch on to nearby and potentially irrelevant values to help us along.

Off the top of my head, I don’t have a good idea of how many bee species there are, so when evaluating #1, my thought process might be something like, “Well, I know there are a lot more insects than monkeys, so maybe there are 10,000 species of bee.” For #2, my thought process would be, “Should I know Westbrook, Maine? Is that a famous city? Maine is a beautiful state. But does it have a lot of people? Portland is probably its most populous city. Westbrook must be much smaller. 500,000 people smaller. Let’s say it has 50,000 people.”

So my final answers would be:

• 10,000
• 50,000

In fact, both answers are about the same: around 20,000.

You can see the result of a very simple example of anchoring/adjustment in the example below, which shows what happened when experimenters asked subjects to guess the answer to a math problem. In this example, subjects fixated on the first few numbers they saw: if the first couple numbers were small, they ended up guessing a smaller number for the answer. If the first couple numbers were larger, they guessed a larger number.

You likely use the anchoring/adjustment heuristic all the time, because it saves you a large amount of mental effort! At the grocery store, how do you know if a bottle of lemonade is too expensive? Do you do a lot of mental math to figure out the optimal price of lemonade, or do you just compare it to the price of a different juice next to it, or the price at another store? It’s usually a lot easier to find a point of reference when we make judgments about value, and this is usually effective! Using the price of other juices or the same lemonade at another store is a great way to decide whether you think it’s worth it to buy the lemonade now. Like most heuristics, your brain uses anchoring/adjustment to help you out. It’ll usually only cause a problem if someone is actively trying to trick you, like in the example below.

Availability

Our next heuristic links back to our discussion of concept representation and learning by association! Specifically, the idea that thinking about concepts more makes their bonds to other ideas stronger in your mind. Recall that this can happen even if the bonds are “incorrect,” like associating dolphins with fish when they are not fish, or tomatoes with vegetables when they are berries. The availability heuristic describes how if something comes to mind easily, we assume it is true, important, or common. Ideas that are especially interesting or relevant to us are “loud” in our minds, and we tend to overestimate their relevance to the world. On the other hand, we underestimate the prevalence of boring things we usually don’t think about. Here’s an exercise you can try: list what you believe the top three Google searches were in the past month!

Of course, I don’t know what month you’re reading this, but the odds are your mind went to big news items of the past month or year. However, the top Google searches every month are almost always things like “YouTube,” “Gmail,” “Amazon,” and so on—people just trying to get to very popular and common websites. This is such a mundane process that it usually doesn’t come to mind when we think about what people search on the internet!

Another common example of how the availability heuristic works is when you ask people to think about causes of death. Death is a very dramatic event in most of our minds, and when we think about the ways in which lives can end, we often overestimate the more “dramatic” ways and underestimate the more “boring” ways. You can see an example of this in Figure 8.6, which shows how subjects over and underestimated the frequencies of various causes of death in Sweden².

In the experiment, subjects predicted the frequencies of many different causes of death, and the researchers reported these predicted frequencies alongside the actual frequencies. In Figure 8.6, I’ve pulled out a few of these causes of death and plotted either how many times larger the subjects’ estimation was than the actual value (yellow bars, positive values) or how many times larger the actual frequency was than the subjects’ guesses (purple bars, negative values). People tend to believe that dangers like lightning strikes and venomous bites are much more frequent than they actually are, probably because they are very interesting and stick in our brains. Conversely, people usually underestimate the frequency of death from everyday causes like heart disease and diabetes.

Once again, heuristics usually work. The availability heuristic works for you most of the time because most of the time two things are very “loud” in your brain, it’s because they are frequent, important, or true. Can you guess what the most common pets are in the United States? If you thought of dogs and cats, you’d be right, and it’s probably because that’s what your brain is used to. In this case, your experience is a good representation of reality.

The Gambler’s Fallacy

Agatha is playing a board game with six-sided die. She keeps rolling low numbers…1, 3, 2, 3, 3, 1…a high number is bound to come up sometime, right? Isn’t it due?

We use the gambler’s fallacy when we assume random events are connected. If we’re flipping a coin and it comes up heads six times in a row, it really feels like that means tails should be up next. This is a fallacy because it’s mathematically wrong. The math of probability dictates that every coin flip has exactly a 50/50 chance of coming up heads or tails, regardless of what happened before. Want to think about something confusing? The following two outcomes of ten coin flips in a row have exactly the same odds of happening (H = heads, T = tails):

• T H H T H T T T H H
• H H H H H H H H H

Doesn’t that feel wrong? But it’s the truth! If you flip a coin ten times, the odds of any specific pattern is ½ * ½ * ½ * ½ * ½ * ½ * ½ * ½ * ½ * ½. Now, that doesn’t mean that getting ten heads in a row has the same odds as getting any tails in that set of ten coin flips; it just means it has the same odds as any other exact pattern of coin flips. If this is easy for you to wrap your head around, great! If not, don’t worry! You’re a human, and human brains don’t work this way. We aren’t computers, and we’re not good at naturally doing probability math. We use our gut. We use shortcuts.

Humans likely assign meaning and patterns to random events because most natural things in our lives are not random. Randomness is an infinite resource; every time you flip a coin or roll a die, all values are available. Rolling a 3 doesn’t reduce the number of 3’s you could roll. In real life, if you eat five apples from an apple tree, you’re now less likely to find another apple on that tree. You’ve depleted the resource! So, while it’s called the gambler’s fallacy, it’s not really fair to call it a fallacy. It’s very reasonable for human brains to assume that events follow natural rules. However, if you find yourself playing a game, gambling, or doing anything that involves randomness, it’s good to keep in mind not to assume that independent events are linked!

The Hot Hand Fallacy

The hot hand fallacy is the gambler’s fallacy’s mirror image. Sometimes, instead of assuming that random values are a limited resource that need to “even out,” we assume that a streak will keep going. The term hot hand comes from basketball: when a player is scoring a lot of points, we often believe they are “hot” and will be more likely to keep scoring points. Similarly, when we see streaks in random events, we like to give them meaning. Imagine a slot machine that has given you several small payouts in a row. You might think, wow, this machine is on a roll! I better stay here! When in truth, streaks are a normal part of random patterns.

Consider this randomly generated list of zeros and ones:

0 0 0 0 1 0 0 1 0 1

1 1 1 0 1 0 1 0 0 1

1 0 1 1 0 0 1 0 1 0

0 0 1 0 0 1 1 0 0 0

1 1 0 1 1 1 0 0 0 0

0 0 1 1 0 0 0 1 1 0

0 0 0 0 1 0 1 1 0 1

0 0 0 0 0 1 1 1 0 1

1 1 0 0 1 1 0 0 1 0

0 1 1 0 0 1 1 1 0 1

If you look it over, you’ll see parts that look “nicely random,” where it alternates frequently between 1 and 0, and you’ll also see parts where there are longer streaks of zeros or ones. None of it has any meaning; each digit is generated independently. But when patterns like this happen around us, we are very quick to attribute meaning.

Again, this “fallacy” isn’t that ridiculous. Many things in real life do work in streaks. If you see seven blades of grass, you are very likely to see another. If you dig twelve wells in an area and don’t find water in any of them, the area probably doesn’t have water. Things in nature are not purely random; they are clumpy, streaky, or follow patterns that have some kind of meaning. When we apply this reasoning to things that are more random (e.g. games, math, or gambling), we can make mistakes – but this does not mean we are being irrational.