## Power Laws: How Nonlinear Relationships Amplify Results

### “The greatest shortcoming of the human race is our inability to understand the exponential function.”

— Albert Allen Bartlett

## Defining A Power Law

Consider a person who begins weightlifting for the first time.

During their initial sessions, they can lift only a small amount of weight. But as they invest more time, they find that for each training session, their strength increases a surprising amount.

For a while, they make huge improvements. Eventually, however, their progress slows down. At first, they could increase their strength by as much as 10% per session; now it takes months to improve by even 1%. Perhaps they resort to taking performance-enhancing drugs or training more often. Their motivation is sapped and they find themselves getting injured, without any real change in the amount of weight they can lift.

Now, let’s imagine that our frustrated weightlifter decides to take up running instead. Something similar happens. While the first few runs are incredibly difficult, the person’s endurance increases rapidly with the passing of each week, until it levels off and diminishing returns set in again.

Both of these situations are examples of power laws — a relationship between two things in which a change in one thing can lead to a large change in the other, regardless of the initial quantities. In both of our examples, a small investment of time in the beginning of the endeavor leads to a large increase in performance.

Power laws are interesting because they reveal surprising correlations between disparate factors. As a mental model, power laws are versatile, with numerous applications in different fields of knowledge.

If parts of this post look intimidating to non-mathematicians, bear with us. Understanding the math behind power laws is worthwhile in order to grasp their many applications. Invest a little time in reading this and reap the value — which is in itself an example of a power law!

A power law is often represented by an equation with an exponent:

Y=MX^B

Each letter represents a number. Y is a function (the result); X is the variable (the thing you can change); B is the order of scaling (the exponent); and M is a constant (unchanging).

If M is equal to 1, the equation is then Y=X^B. If B=2, the equation becomes Y=X^2 (Y=X squared). If X is 1, Y is also 1. But if X=2, then Y=4; if X=3, then Y=9, and so on. A small change in the value of X leads to a proportionally large change in the value of Y.

B=1 is known as the linear scaling law.

To double a cake recipe, you need twice as much flour. To drive twice as far will take twice as long. (Unless you have kids, in which case you need to factor in bathroom breaks that seemingly have little to do with distance.) Linear relationships, in which twice-as-big requires twice-as-much, are simple and intuitive.

Nonlinear relationships are more complicated. In these cases, you don’t need twice as much of the original value to get twice the increase in some measurable characteristic. For example, an animal that’s twice our size requires only about 75% more food than we do. This means that on a per-unit-of-size basis, larger animals are more energy efficient than smaller ones. As animals get bigger, the energy required to support each unit decreases.

One of the characteristics of a complex system is that the behavior of the system differs from the simple addition of its parts. This characteristic is called emergent behavior. “In many instances,” write Geoffrey West in Scale: The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life in Organisms, Cities, Economies, and Companies, “the whole seems to take on a life of its own, almost dissociated from the specific characteristics of its individual building blocks.”

This collective outcome, in which a system manifests significantly different characteristics from those resulting from simply adding up all of the contributions of its individual constituent parts, is called an emergent behavior.

When we set out to understand a complex system, our intuition tells us to break it down into its component pieces. But that’s linear thinking, and it explains why so much of our thinking about complexity falls short. Small changes in a complex system can cause sudden and large changes. Small changes cause cascades among the connected parts, like knocking over the first domino in a long row.

Let’s return to the example of our hypothetical weightlifter-turned-runner. As they put in more time on the road, constraints will naturally arise on their progress.

Recall our exponential equation: Y=MX^B. Try applying it to the runner. (We’re going to simplify running, but stick with it.)

Y is the distance the runner can run before becoming exhausted. That’s what we’re trying to calculate. M, the constant, represents their running ability: some combination of their natural endowment and their training history. (Think of it this way: Olympic champion Usain Bolt has a high M; film director Woody Allen has a low M.)

That leaves us with the final term: X^B. The variable X represents the thing we have control over: in this case, our training mileage. If B, the exponent, is between 0 and 1, then the relationship between X and Y— between training mileage and endurance — becomes progressively less proportional. All it takes is plugging in a few numbers to see the effect.

Let’s set M to 1 for the sake of simplicity. If B=0.5 and X=4, then Y=2. Four miles on the road gives the athlete the ability to run two miles at a clip.

Increase X to 16, and Y increases only to 4. The runner has to put in four times the road mileage to merely double their running endurance.

Here’s the kicker: With both running and weightlifting, as we increase X, we’re likely to see the exponent, B, decline! Quadrupling our training mileage from 16 to 64 miles is unlikely to double our endurance again. It might take a 10x increase in mileage to do that. Eventually, the ratio of training mileage to endurance will become nearly infinite.

We know this state, of course, as diminishing returns: the point where more input yields progressively less output. Not only is the relationship between training mileage and endurance not linear to begin with, but it also gets less linear as we increase our training.

It gets even more interesting. If B=−0.5 and X=4, then Y=0.5. Four miles on the road gets us a half-mile of endurance. If X is increased to 16, Y declines to 0.25. More training, less endurance! This is akin to someone putting in way too much mileage, way too soon: the training is less than useful as injuries pile up.

With negative numbers, the more X increases, the more Y shrinks. This relationship is known as an inverse power law. B=−2, for example, is known as the inverse square law and is an important equation in physics.

The relationship between gravity and distance follows an inverse power law. G is the gravitational constant; it’s the constant in Newton's law of gravitation, relating gravity to the masses and separation of particles, equal to:

6.67 × 10−11 N m2 kg−2

Any force radiating from a single point — including heat, light intensity, and magnetic and electrical forces — follows the inverse square law. At 1m away from a fire, 4 times as much heat is felt as at 2m, and so on.

## Higher Order Power Laws

When B is a positive integer (a whole number larger than zero), there are names for the power laws.

When B is equal to 1, we have a linear relationship, as we discussed above. This is also known as a first-order power law.

Things really get interesting after that.

When B is 2, we have a second-order power law. A great example of this is kinetic energy. Kinetic energy = 1/2 mv^2

When B is 3, we have a third-order power law. An example of this is the power converted from wind into rotational energy.

Power Available = ½ (Air Density)( πr^2)(Windspeed^3)(Power Coefficient)

(There is a natural limit here. Albert Betz concluded in 1919 that wind turbines cannot convert more than 59.3% of the kinetic energy of the wind into mechanical energy. This number is called the Betz Limit and represents the power coefficient above.)[1]

The law of heat radiation is a fourth-order power law. Derived first by the Austrian physicist Josef Stefan in 1879 and separately by Austrian physicist Ludwig Boltzmann, the law works like this: the radiant heat energy emitted from a unit area in one second is equal to the constant of proportionality (the Stefan-Boltzmann constant) times the absolute temperature to the fourth power.[2]

There is only one power law with a variable exponent, and it’s considered to be one of the most powerful forces in the universe. It’s also the most misunderstood. We call it compounding. The formula looks like this:

Future Value = (Present Value)(1+i)^n

where i is the interest rate and n is the number of years.

Unlike in the other equations, the relationship between X and Y is potentially limitless. As long as B is positive, Y will increase as X does.

Non-integer power laws (where B is a fraction, as with our running example above) are also of great use to physicists. Formulas in which B=0.5 are common.

Imagine a car driving at a certain speed. A non-integer power law applies. V is the speed of the car, P is the petrol burnt per second to reach that speed, and A is the air resistance. For the car to go twice as fast, it must use 4 times as much petrol, and to go 3 times as fast, it must use 9 times as much petrol. Air resistance increases as speed increases, and that is why faster cars use such ridiculous amounts of petrol. It might seem logical to think that a car going from 40 miles an hour to 50 miles an hour would use a quarter more fuel. That is incorrect, though, because the relationship between air resistance and speed is itself a power law.

Another instance of a power law is the area of a square. Double the length of two parallel sides and the area quadruples. Do the same for a 3D cube and the area increases by a factor of eight. It doesn’t matter if the length of the square went from 1cm to 2cm, or from 100m to 200m; the area still quadruples. We are all familiar with second-order (or square) power laws. This name comes from squares, since the relationship between length and area reflect the way second-order power laws change a number. Third-order (or cubic) power laws are likewise named due to their relationship to cubes.

## Using Power Laws in Our Lives

Now that we’ve gotten through the complicated part, let’s take a look at how power laws crop up in many fields of knowledge. Most careers involve an understanding of them, even if it might not be so obvious.

### “What's the most powerful force in the universe? Compound interest. It builds on itself. Over time, a small amount of money becomes a large amount of money. Persistence is similar. A little bit improves performance, which encourages greater persistence which improves persistence even more. And on and on it goes.”

— Daniel H. Pink, The Adventures of Johnny Bunko

The Power Behind Compounding

Compounding is one of our most important mental models and is absolutely vital to understand for investing, personal development, learning, and other crucial areas of life.

In economics, we calculate compound interest by using an equation with these variables: P is the original sum of money. P’ is the resulting sum of money, r is the annual interest rate, n is the compounding frequency, and t is the length of time. Using an equation, we can illustrate the power of compounding.

If a person deposits \$1000 in a bank for five years, at a quarterly interest rate of 4%, the equation becomes this:

Future Value = Present Value * ((1 + Quarterly Interest Rate) ^ Number of Quarters)

This formula can be used to calculate how much money will be in the account after five years. The answer is \$2,220.20.

Compound interest is a power law because the relationship between the amount of time a sum of money is left in an account and the amount accumulated at the end is non-linear.

In A Random Walk Down Wall Street, Burton Malkiel gives the example of two brothers, William and James. Beginning at age 20 and stopping at age 40, William invests \$4,000 per year. Meanwhile, James invests the same amount per year between the ages of 40 and 65. By the time William is 65, he has invested less money than his brother, but has allowed it to compound for 25 years. As a result, when both brothers retire, William has 600% more money than James — a gap of \$2 million. One of the smartest financial choices we can make is to start saving as early as possible: by harnessing power laws, we increase the exponent as much as possible.

Compound interest can help us achieve financial freedom and wealth, without the need for a large annual income. Members of the financial independence movement (such as the blogger Mr. Money Mustache) are living examples of how we can apply power laws to our lives.

As far back as the 1800s, Robert G. Ingersoll emphasized the importance of compound interest:

One dollar at compound interest, at twenty-four per cent., for one hundred years, would produce a sum equal to our national debt. Interest eats night and day, and the more it eats the hungrier it grows. The farmer in debt, lying awake at night, can, if he listens, hear it gnaw. If he owes nothing, he can hear his corn grow. Get out of debt as soon as possible. You have supported idle avarice and lazy economy long enough.

Compounding can apply to areas beyond finance — personal development, health, learning, relationships and more. For each area, a small input can lead to a large output, and the results build upon themselves.

Nonlinear Language Learning

When we learn a new language, it’s always a good idea to start by learning the 100 or so most used words.

In all known languages, a small percentage of words make up the majority of usage. This is known as Zipf’s law, after George Kingsley Zipf, who first identified the phenomenon. The most used word in a language may make up as much as 7% of all words used, while the second-most-used word is used half as much, and so on. As few as 135 words can together form half of a language (as used by native speakers).

Why Zipf’s law holds true is unknown, although the concept is logical. Many languages include a large number of specialist terms that are rarely needed (including legal or anatomy terms). A small change in the frequency ranking of a word means a huge change in its usefulness.

Understanding Zipf’s law is a central component of accelerated language learning. Each new word we learn from the most common 100 words will have a huge impact on our ability to communicate. As we learn less-common words, diminishing returns set in. If each word in a language were listed in order of frequency of usage, the further we moved down the list, the less useful a word would be.

Power Laws in Business, Explained by Peter Thiel

Peter Thiel, the founder of PayPal (as well as an early investor in Facebook and Palantir), considers power laws to be a crucial concept for all businesspeople to understand. In his fantastic book, Zero to One, Thiel writes:

Indeed, the single most powerful pattern I have noticed is that successful people find value in unexpected places, and they do this by thinking about business from first principles instead of formulas.

And:

In 1906, economist Vilfredo Pareto discovered what became the “Pareto Principle,” or the 80-20 rule, when he noticed that 20% of the people owned 80% of the land in Italy—a phenomenon that he found just as natural as the fact that 20% of the peapods in his garden produced 80% of the peas. This extraordinarily stark pattern, when a small few radically outstrip all rivals, surrounds us everywhere in the natural and social world. The most destructive earthquakes are many times more powerful than all smaller earthquakes combined. The biggest cities dwarf all mere towns put together. And monopoly businesses capture more value than millions of undifferentiated competitors. Whatever Einstein did or didn’t say, the power law—so named because exponential equations describe severely unequal distributions—is the law of the universe. It defines our surroundings so completely that we usually don’t even see it.

… [I]n venture capital, where investors try to profit from exponential growth in early-stage companies, a few companies attain exponentially greater value than all others. … [W]e don’t live in a normal world; we live under a power law.

The biggest secret in venture capital is that the best investment in a successful fund equals or outperforms the entire rest of the fund combined.

This implies two very strange rules for VCs. First, only invest in companies that have the potential to return the value of the entire fund. … This leads to rule number two: because rule number one is so restrictive, there can’t be any other rules.

…[L]ife is not a portfolio: not for a startup founder, and not for any individual. An entrepreneur cannot “diversify” herself; you cannot run dozens of companies at the same time and then hope that one of them works out well. Less obvious but just as important, an individual cannot diversify his own life by keeping dozens of equally possible careers in ready reserve.

Thiel teaches a class called Startup at Stanford, where he hammers home the value of understanding power laws. In his class, he imparts copious wisdom. From Blake Masters’ notes on Class 7:

Consider a prototypical successful venture fund. A number of investments go to zero over a period of time. Those tend to happen earlier rather than later. The investments that succeed do so on some sort of exponential curve. Sum it over the life of a portfolio and you get a J curve. Early investments fail. You have to pay management fees. But then the exponential growth takes place, at least in theory. Since you start out underwater, the big question is when you make it above the water line. A lot of funds never get there.

To answer that big question you have to ask another: what does the distribution of returns in [a] venture fund look like? The naïve response is just to rank companies from best to worst according to their return in multiple of dollars invested. People tend to group investments into three buckets. The bad companies go to zero. The mediocre ones do maybe 1x, so you don’t lose much or gain much. And then the great companies do maybe 3-10x.

But that model misses the key insight that actual returns are incredibly skewed. The more a VC understands this skew pattern, the better the VC. Bad VCs tend to think the dashed line is flat, i.e. that all companies are created equal, and some just fail, spin wheels, or grow. In reality you get a power law distribution.

Thiel explains how investors can apply the mental model of power laws (more from Masters’ notes on Class 7):

…Given a big power law distribution, you want to be fairly concentrated. … There just aren’t that many businesses that you can have the requisite high degree of conviction about. A better model is to invest in maybe 7 or 8 promising companies from which you think you can get a 10x return. …

Despite being rooted in middle school math, exponential thinking is hard. We live in a world where we normally don’t experience anything exponentially. Our general life experience is pretty linear. We vastly underestimate exponential things.

He also cautions against over-relying on power laws as a strategy (an assertion that should be kept in mind for all mental models). From Masters’ notes:

One shouldn’t be mechanical about this heuristic, or treat it as some immutable investment strategy. But it actually checks out pretty well, so at the very least it compels you to think about power law distribution.

Understanding exponents and power law distributions isn’t just about understanding VC. There are important personal applications too. Many things, such as key life decisions or starting businesses, also result in similar distributions.

Thiel then explains why founders should focus on one key revenue stream, rather than trying to build multiple equal ones:

Even within an individual business, there is probably a sort of power law as to what’s going to drive it. It’s troubling if a startup insists that it’s going to make money in many different ways. The power law distribution on revenues says that one source of revenue will dominate everything else.

For example, if you’re an entrepreneur who opens a coffee shop, you’ll have a lot of ways you can make money. You can sell coffee, cakes, paintings, merchandise, and more. But each of those things will not contribute to your success in an equal way. While there is value in the discovery process, once you’ve found the variable that matters most, you should place more time on that one and less on the others. The importance of finding this variable cannot be overstated.

He also acknowledges that power laws are one of the great secrets of investing success. From Masters’ notes on Class 11:

On one level, the anti-competition, power law, and distribution secrets are all secrets about nature. But they’re also secrets hidden by people. That is crucial to remember. Suppose you’re doing an experiment in a lab. You’re trying to figure out a natural secret. But every night another person comes into the lab and messes with your results. You won’t understand what’s going on if you confine your thinking to the nature side of things. It’s not enough to find an interesting experiment and try to do it. You have to understand the human piece too.

… We know that, per the power law secret, companies are not evenly distributed. The distribution tends to be bimodal; there are some great ones, and then there are a lot of ones that don’t really work at all. But understanding this isn’t enough. There is a big difference between understanding the power law secret in theory and being able to apply it in practice.

The key to all mental models is knowing the facts and being able to use the concept. As George Box said, “all models are false but some are useful.” Once we grasp the basics, the best next step is to start figuring out how to apply it.

The metaphor of an unseen person sabotaging laboratory results is an excellent metaphor for how cognitive biases and shortcuts cloud our judgement.

Natural Power Laws

Anyone who has kept a lot of pets will have noticed the link between an animal’s size and its lifespan. Small animals, like mice and hamsters, tend to live for a year or two. Larger ones, like dogs and cats, can live to 10-20 years, or even older in rare cases. Scaling up even more, some whales can live for 200 years. This comes down to power laws.

Biologists have found clear links between an animal’s size and its metabolism. Kleiber’s law (identified by Max Kleiber) states that an animal’s metabolic rate increases at three-fourths of the power of the animal’s weight (mass). If an average rabbit (2 kg) weighs one hundred times as much as an average mouse (20g), the rabbit’s metabolic rate will be 32 times the mouse’s. In other words, the rabbit’s structure is more efficient. It all comes down to the geometry behind their mass.

Which leads us to another biological power law: Smaller animals require more energy per gram of body weight, meaning that mice eat around half their body weight in dense foods each day. The reason is that, in terms of percentage of mass, larger animals have more structure (bones, etc.) and fewer reserves (fat stores).

Research has illustrated how power laws apply to blood circulation in animals. The end units through which oxygen, water, and nutrients enter cells from the bloodstream are the same size in all animals. Only the number per animal varies. The relationship between the total area of these units and the size of the animal is a third-order power law. The distance blood travels to enter cells and the actual volume of blood are also subject to power laws.

## The Law of Diminishing Returns

As we have seen, a small change in one area can lead to a huge change in another. However, past a certain point, diminishing returns set in and more is worse. Working an hour extra per day might mean more gets done, whereas working three extra hours is likely to lead to less getting done due to exhaustion. Going from a sedentary lifestyle to running two days a week may result in greatly improved health, but stepping up to seven days a week will cause injuries. Overzealousness can turn a positive exponent into a negative exponent. For a busy restaurant, hiring an extra chef will mean that more people can be served, but hiring two new chefs might spoil the proverbial broth.

Perhaps the most underappreciated diminishing return, the one we never want to end up on the wrong side of, is the one between money and happiness.

In David and Goliath, Malcolm Gladwell discusses how diminishing returns relate to family incomes. Most people assume that the more money they make, the happier they and their families will be. This is true — up to a point. An income that’s too low to meet basic needs makes people miserable, leading to far more physical and mental health problems. A person who goes from earning \$30,000 a year to earning \$40,000 is likely to experience a dramatic boost in happiness. However, going from \$100,000 to \$110,000 leads to a negligible change in well-being.

The scholars who research happiness suggest that more money stops making people happier at a family income of around seventy-five thousand dollars a year. After that, what economists call “diminishing marginal returns” sets in. If your family makes seventy-five thousand and your neighbor makes a hundred thousand, that extra twenty-five thousand a year means that your neighbor can drive a nicer car and go out to eat slightly more often. But it doesn’t make your neighbor happier than you, or better equipped to do the thousands of small and large things that make for being a good parent.

###### Footnotes
• 1

http://www.raeng.org.uk/publications/other/23-wind-turbine

• 2

https://www.britannica.com/science/Stefan-Boltzmann-law

## Becoming an Expert: The Elements of Success

We're massively impressed by a concert pianist, or a wide receiver, or a truly skillful visual artist. Their abilities seem otherworldly.

But what makes these people so skillful? How did they start out like you and I and then become something so extraordinary?

Part of us wants to believe that it’s something innate and magical, so we can recuse ourself from hard work. The other part of us wants to believe that it’s something earned through blood, sweat, and tears — that we too could achieve amazing performance, if only we could devote ourselves to something.

In reality, it's a bit of both.

In the book Bounce: Mozart, Federer, Picasso, Beckham, and the Science of Success, Matthew Syed takes a critical look at all the factors underpinning the success of some of the most extraordinary athletes and artists in the world.

The obvious place to start is with the popular Outliers idea posited by Malcolm Gladwell, the idea that many successful people are a product of their environment rather than ‘gifted’.

Gladwell shows how the success of Bill Gates, the Beatles, and other outstanding performers is not so much to do with ‘what they are like’ but rather ‘where they come from.’ ‘The people who stand before kings may look like they did it all by themselves,’ Gladwell writes. ‘But in fact they are invariably the beneficiaries of hidden advantages and extraordinary opportunities and cultural legacies that allow them to learn and work hard and make sense of the world in ways others cannot.’”

We think if you study the life and work trajectory of experts, two patterns seem to emerge.

One, they have specific backgrounds or opportunities, as mentioned above. Two, they put an incredible amount of time and effort into deliberate, effortful practice.

But not everyone will have access to the same facilities or teachers (this goes back to opportunity and circumstance), and some rules/regulations will inevitably favor some and add roadblocks for others in the quest for their 10,000 hours.

A good example of the latter is eligibility cutoff dates for children’s sports teams. If you’ve ever signed up yourself or your kids in a sports league then you’ll know there is always a cut-off birth date for the different age groups.

Say your child plays on a soccer team for kids born any time in the year 2007. If your child is born in January, then they will have almost a 12 month head start on a child born in December, and a year is like a lifetime at that stage of physical development. Those physical skills manifest themselves in playing time, which further develops the child.

Month of birth is, of course, just one of the many hidden forces shaping patterns of success and failure in this world. But what most of these forces have in common – at least when it comes to attaining excellence – is the extent to which they confer (or deny) opportunities for serious practice. Once the opportunity for practice is in place, the prospects of high achievement take off. And if practice is denied or diminished, no amount of talent is going to get you there.

Thus, if you have the time and opportunity to devote to practice, you’ve crossed the first hurdle. The second is understanding the characteristics of the type of practice which will push you ahead.

The best type of practice does two things:

1. It helps us to acquire the skills that speed up/automate processes and feedback (see how Brazil develops its soccer players, for example.)
2. It pushes us to the edge of our competence and forces us to focus. This is where the learning happens

***

Let's explain the first point in greater detail, using an example of a specific process happening in the brains of experts.

We all do something called chunking. You probably don’t realize you’re doing it, but you do it all the time. Say I asked you to read the line below once and then, without looking back at the page, repeat the letters back to me.

HOCBTELAKGD

The average person will find this difficult to do. Generally speaking, our mind can only keep track of about seven things at once, and I asked you to try and recall eleven. Now watch what happens when I rearrange the letters.

THE BLACK DOG

These are the exact same letters, but sensibly grouped in a way that your mind can understand: This is chunking.

Now, instead of trying to remember eleven letters you are remembering three words (which is still eleven letters). Even if you were able to recall the letters the way they were presented in the first example, think of how much quicker you could recall them in the second one.

This is one way that experts become so good. They learn how to chunk processes specific to their area of expertise. This helps them to use a sort of autopilot, allowing them to elevate their minds to a higher level. That's why you'll hear a great pianist talking about trying to use the instrument to “paint an emotion in the listeners' minds” while you or I would struggle to eke out a few notes.

As Janet Starkes, professor emerita of kinesiology at McMaster Univeristy, noted in Bounce,

The exploitation of advance information results in the time paradox where skilled performers seem to have all the time in the world. Recognition of familiar scenarios and the chunking of perceptual information into meaningful wholes and patterns speeds up processes.

This chunking and pattern recognition not only enables the expert to perform faster, it also helps them to make better decisions.

Unfortunately, figuring out how to best recognize, process, and use this information isn’t something that can be learned from a book or a classroom, it comes from experience. This may seem like common sense but it won’t happen just by putting in the time: You have to focus to find these patterns.

This is why (as dozens of studies have shown) length of time in many occupations is only weakly related to performance. Mere experience, if it is not matched by deep concentration, does not translate into excellence.

Put another way, someone with 20 years of experience, might be repeating one year of experience 20 times.

Let’s look at a great example from the book to illustrate this point.

***

Take a look at the anagrams in List A and try to solve them. Then do the same for list B.

Both lists are the same words. The only difference is that one list was more difficult to solve. When researchers asked participants to list off words like those in List A, that were easy, the participants had problems recalling them. Their recall soared when asked to list words from more difficult anagrams like those is List B.

To figure out words like those in list B it takes more time, concentration, and effort: You are engaging much more of your brain. This means that if you want to remember something or maintain your focus, make it hard.

This example, taken from the work of psychologist S. W. Tyler, neatly emphasized the power of practice when it is challenging rather than nice and easy. “When most people practice they focus on the things they can do effortlessly,' Ericsson has said. ‘Expert practice is different. It entails considerable, specific, and sustained efforts to do something you can’t do well – or even at all. Research across domains shows that it is only by working at what you can’t do that you turn into the expert you want to become.

This isn't to say that a certain amount of time and effort don’t go into maintaining a certain skill. But if you want to grow, you need to strain. In other words, you must eat a lot of broccoli; and since most people won't stomach it, they will never develop a high fluency in their discipline.

…world-class performance comes by striving for a target just out of reach, but with a vivid awareness of how the gap might be breached. Over time, through constant repetition and deep concentration, the gap will disappear, only for a new target to be created, just out of reach once again.

It is worth mentioning that this type of deliberate practice can only happen if the individual has made a conscious decision to devote themselves: We can’t make these decisions for other people. We have to go “all in”; no substitute will do.

It is only possible to clock up meaningful practice if an individual has made an independent decision to devote himself to whatever field of expertise. He has to care about what he is doing, not because a parent or a teacher says so, but for its own sake. Psychologists call this ‘internal motivation,’ and it is often lacking in children who start too young and are pushed too hard. They are, therefore, on the road not to excellence but to burnout.

In theory we can all be that wide receiver picking the ball from the air, or that musician who speaks to us through their instrument. 10,000 hours of hard, correct work is all it takes.

But as they say, “In theory, reality and theory are the same. In reality, they're not.”

If you want to make it there, the road is bumpy. It has to be. Only a difficult road will cause you to grow and learn. And you have to personally want to travel this road, because it will be long and if you can’t motivate yourself you’ll never get where you need to be.

And as much as we shy away from reality, we can't also forget the roles of luck and genes in making it to the absolute “top” of a profession. The recent scholarship has been extremely egalitarian, emphasizing the necessary hard work that goes into creating high level performance.

But that doesn't mean that different folks don't have different biology — Is there a world in which Woody Allen could have played in the NFL? — and it doesn't mean that for every Daniel-Day Lewis, there aren't a few hundred other actors who are extremely talented but for whom life got in the way.

Top 0.01% success is a multiplicative system: Everything's gotta go right. The world is too competitive to allow for anything else. The magical mix of luck, genes, and correct practice probably differ widely depending on the field.

So in your quest for success, realize that you'll have to do deep, hard work for many years, you may need the right parents (to an extent) and you'll need a whole lot of luck.

On a lighter note, even if you just work on the first one, the only one within your control, we suspect you won't be disappointed with the result.

***

Still Interested? Pick up the Bounce. It has more information on how to reach the top and how not to choke when you get there.

## Bloomberg to the Ivy League: Consider the Other Side

Recently, Charlie Munger commented that when he reads the New York Times, he pays special attention to Paul Krugman—with whom he very often disagrees—in order to expose himself to opposing political and economic viewpoints. His methodology is akin to that of Charles Darwin, who described, in his autobiography, his tendency to immediately note observations that seemed contrary to his prior beliefs.

Munger is not the only one. Malcolm Gladwell, in his recent AMA, wrote:

A lot of people wondered why I went on Glenn Beck's show. I don't agree with a lot of what he says. But I was curious to meet him. And my basic position in the world is that the most interesting thing you can do is to talk to someone who you think is different from you and try and find common ground. And what happened? We did. We actually had a great conversation. Unlike most of the people who interviewed me for David and Goliath, he had read the whole book and thought about it a lot. My lesson from the experience: If you never leave the small comfortable ideological circle that you belong to, you'll never develop as a human being.

You can't really have an informed opinion if you can't state the other side of the argument better than the smartest person who holds the opposite view.

***

On May 29, former New York Mayor and Chairman of Bloomberg LP, Michael Bloomberg, gave the commencement address at Harvard. The gist of his speech was that liberal ideology has so pervaded high level American education that conservative voices are being silenced by popular fervor. His speech made some excellent points about the nature of free thought.

Modern Day McCarthyism

There is an idea floating around college campuses—including here at Harvard—that scholars should be funded only if their work conforms to a particular view of justice. There's a word for that idea: censorship. And it is just a modern-day form of McCarthyism.

Liberal Monopoly

In the 2012 presidential race, according to Federal Election Commission data, 96% of all campaign contributions from Ivy League faculty and employees went to Barack Obama.

Ninety-six percent. There was more disagreement among the old Soviet Politburo than there is among Ivy League donors.

That statistic should give us pause—and I say that as someone who endorsed President Obama for re-election—because let me tell you, neither party has a monopoly on truth or God on its side.

Role of Universities

The role of universities is not to promote an ideology. It is to provide scholars and students with a neutral forum for researching and debating issues—without tipping the scales in one direction, or repressing unpopular views.

Requiring scholars—and commencement speakers, for that matter—to conform to certain political standards undermines the whole purpose of a university.

… As a former chairman of Johns Hopkins, I strongly believe that a university's obligation is not to teach students what to think but to teach students how to think. And that requires listening to the other side, weighing arguments without prejudging them, and determining whether the other side might actually make some fair points.

Always remember, you must consider your own ideologies as intensely as you consider those held by others.

## Complexity and the Ten-Thousand-Hour Rule

Herbert Simon and William Chase, in a paper from forty years ago, drew one of the most famous conclusions in the study of expertise:

There are no instant experts in chess—certainly no instant masters or grandmasters. There appears not to be on record any case (including Bobby Fischer) where a person reached grandmaster level with less than about a decade's intense preoccupation with the game. We would estimate, very roughly, that a master has spent perhaps 10,000 to 50,000 hours staring at chess positions …

That's the famous ten-thousand-hour rule.

Malcolm Gladwell takes this up in the New Yorker:

This is the scholarly tradition I was referring to in my book “Outliers,” when I wrote about the “ten-thousand-hour rule.” No one succeeds at a high level without innate talent, I wrote: “achievement is talent plus preparation.” But the ten-thousand-hour research reminds us that “the closer psychologists look at the careers of the gifted, the smaller the role innate talent seems to play and the bigger the role preparation seems to play.” In cognitively demanding fields, there are no naturals. Nobody walks into an operating room, straight out of a surgical rotation, and does world-class neurosurgery. And second—and more crucially for the theme of Outliers—the amount of practice necessary for exceptional performance is so extensive that people who end up on top need help. They invariably have access to lucky breaks or privileges or conditions that make all those years of practice possible. As examples, I focussed on the countless hours the Beatles spent playing strip clubs in Hamburg and the privileged, early access Bill Gates and Bill Joy got to computers in the nineteen-seventies. “He has talent by the truckload,” I wrote of Joy. “But that’s not the only consideration. It never is.”

The key point of The Sports Gene, a new book by David Epstein, is that the ten-thousand-hour idea must be understood as an average.

[B]oth he and I discuss the same study by the psychologist K. Anders Ericsson that looked at students studying violin at the elite Music Academy of West Berlin. I was interested in the general finding, which was that the best violinists, on average and over time, practiced much more than the good ones. In other words, within a group of talented people, what separated the best from the rest was how long and how intently they worked (see deliberate practice). Epstein points out, however, that there is a fair amount of variation behind that number—suggesting that some violinists may use their practice time so efficiently that they reach a high degree of excellence more quickly. It’s an important point. There are seventy-three great composers who took at least ten years to flourish. But there is much to be learned as well from Shostakovich, Paganini, and Satie.

The point of Simon and Chase’s paper years ago was that cognitively complex activities take many years to master because they require that a very long list of situations and possibilities and scenarios be experienced and processed. There’s a reason the Beatles didn’t give us “The White Album” when they were teen-agers. And if the surgeon who wants to fuse your spinal cord did some newfangled online accelerated residency, you should probably tell him no. It does not invalidate the ten-thousand-hour principle, however, to point out that in instances where there are not a long list of situations and scenarios and possibilities to master—like jumping really high, running as fast as you can in a straight line, or directing a sharp object at a large, round piece of cork—expertise can be attained a whole lot more quickly. What Simon and Chase wrote forty years ago remains true today. In cognitively demanding fields, there are no naturals.

So maybe being ‘a natural' means you're on the lower end of the average.

(Update: I'm not sure how to think about this stuff. What I do believe is something along the lines of: (1) We're born with different innate talent or physical attributes that sometimes no amount of “hard work” can overcome; (2) having a growth mindset and a little bit of grit makes a big difference (call this tenacity for short, it helps but it's not everything); and (3) deliberate practice makes a difference but it won't, for instance, make you taller. In short, you can tilt the odds in your favor and how many hours that takes may be a function of what you're born with. )

## What’s on Malcolm Gladwell’s Bookshelf

What we're reading says a lot about who we are – or who we want to be. In a new feature in the Globe and Mail, Jane Mount asks 100 writers, artists, and foodies to describe the books that inspire them.

I wanted to highlight Malcolm Galdwell's and Jennifer Egan's.

I’m in the middle of writing my new book, which is about power. I’m very interested in the strategies we use to keep people who are powerless in check. And the ways in which the powerless fight back. So I started reading about crime. I’ve probably acquired 150 books for this project. I haven’t read all of them, and I won’t. Some of them I’ll just look at. But that’s the fun part. It’s an excuse to go on Amazon. The problem is, of course, that eventually you have to stop yourself. Otherwise you’ll collect books forever. But these books are markers for the ideas that I’m interested in. That’s why it’s so important to have physical books. When I see my bookshelf expanding, it gives me the illusion that my brain is expanding, too.

Texas Tough: The Rise of America's Prison Empire

Texas Tough, a sweeping history of American imprisonment from the days of slavery to the present, explains how a plantation-based penal system once dismissed as barbaric became a template for the nation.

On the Rock 2008: Twenty-Five Years in Alcatraz : the Prison Story of Alvin Karpis

Anyone interested in reading about old school gangsters — as opposed to this generation's wannabe “gangstas” — and prison life in general, will find this the best book you've probably never heard of.

Armed Robbers In Action: Stickups and Street Culture

By analyzing the criminals' candid perspectives on their actions and their social environment, the authors provide a fuller understanding of armed robbery. They conclude with an insightful discussion of the implications of their findings for crime prevention policy.

The Illusion of Free Markets: Punishment and the Myth of Natural Order

The Illusion of Free Markets argues that our faith in “free markets” has severely distorted American politics and punishment practices.

Popular Crime: Reflections on the Celebration of Violence

With Popular Crime, James takes readers on an epic journey from Lizzie Borden to the Lindbergh baby, from the Black Dahlia to O. J. Simpson, explaining how crimes have been committed, investigated, prosecuted and written about, and how that has profoundly influenced our culture over the last few centuries—even if we haven’t always taken notice.

The Business of Crime: Italians and Syndicate Crime in the United States

A definitive history of organized crime in America.

Ride the Razor's Edge

The story tracks the deeds and misdeeds of Cole Younger and his brothers James, John, and Bob, and tells the story of a troubled state during the late 1800s. From their Civil War battles against the Union with William Quantrill and his band of guerrillas, to the raid in Lawrence, Kansas, to their first bank robbery in Liberty, Missouri, the Youngers were both heroes and foes of their state.

Black Mafia

But They All Come Back: Facing The Challenges Of Prisoner Reentry

[D]escribes the new realities of punishment in America and explores the nexus of returning prisoners with seven policy domains: public safety, families and children, work, housing, public health, civic identity, and community capacity. Travis proposes a new architecture for our criminal justice system, organized around five principles of reentry, that will encourage change and spur innovation. It is a Herculean synthesis and an invaluable resource for anyone interested in prisoner reentry and social justice.

American Mafia: A History of Its Rise to Power

Organized crime—the Italian American kind—has long been a source of popular entertainment and legend. Now Thomas Reppetto provides a balanced history of the Mafia's rise—from the 1880s to the post-WWII era—that is as exciting and readable as it is authoritative.

* * *

I found Jennifer Egan's bookshelf a little more interesting.

Emma has always been my favourite Jane Austen novel. A lot of people tend to like Emma – she’s such a winningly flawed person. One thing that surprises me about Austen is that her characters are very inflexible; nobody changes that much. Emma might be the slight exception, but she still stays Emma in the end, even if she’s a little bit wiser. You could almost say that Austen deals in types, which normally is a very dangerous practice and doesn’t lead to anything interesting. Yet her work is stupendous. Her novels work themselves out with a tremendous clarity that feels mathematical or geometric. It’s very spare; there’s nothing extra. Her books shouldn’t work, but they do, and better than almost anyone else’s.

Don Quixote

Don Quixote has become so entranced reading tales of chivalry that he decides to turn knight errant himself. In the company of his faithful squire, Sancho Panza, these exploits blossom in all sorts of wonderful ways. While Quixote's fancy often leads him astray—he tilts at windmills, imagining them to be giants—Sancho acquires cunning and a certain sagacity. Sane madman and wise fool, they roam the world together-and together they have haunted readers' imaginations for nearly four hundred years

The Image: A Guide to Pseudo-Events in America

First published in 1962, this wonderfully provocative book introduced the notion of “pseudo-events” — events such as press conferences and presidential debates, which are manufactured solely in order to be reported — and the contemporary definition of celebrity as “a person who is known for his well-knownness.”

Don Juan

Byron’s exuberant masterpiece tells of the adventures of Don Juan, beginning with his illicit love affair at the age of sixteen in his native Spain and his subsequent exile to Italy. Following a dramatic shipwreck, his exploits take him to Greece, where he is sold as a slave, and to Russia, where he becomes a favorite of the Empress Catherine who sends him on to England.

The Golden Notebook

Anna is a writer, author of one very successful novel, who now keeps four notebooks. In one, with a black cover, she reviews the African experience of her earlier years. In a red one she records her political life, her disillusionment with communism. In a yellow one she writes a novel in which the heroine relives part of her own experience. And in a blue one she keeps a personal diary. Finally, in love with an American writer and threatened with insanity, Anna resolves to bring the threads of all four books together in a golden notebook.

Good Morning, Midnight

No one who reads Good Morning, Midnight will ever forget it.

Emma

Sparkling comedy of provincial manners concerns a well-intentioned young heiress and her matchmaking schemes that result in comic confusion for the inhabitants of a 19th-century English village. Droll characterizations of the well-intentioned heroine, her hypochondriacal father, plus many other finely drawn personalities make this sparkling satire of provincial life one of Jane Austen's finest novels.

Middlemarch

[A] complex look at English provincial life at a crucial historical moment, and, at the same time, dramatizes and explores some of the most potent myths of Victorian literature.

The Life and Opinions of Tristram Shandy, Gentleman

A forerunner of psychological fiction, and considered a landmark work for its innovative use of narrative devices, Sterne's topsy-turvy novel was both celebrated and vilified when first published. Originally released in nine separate volumes, it is in effect an exercise about the difficulties of writing. Impossible to categorize, it remains a beguiling milestone in the history of literature.

Germinal

Germinal is generally considered the greatest of Emile Zola's twenty novel Rougon-Macquart cycle. Of these, Germinal is the most concerned with the daily life of the working poor. Set in the mid 1860's, the novel's protaganist Etienne Lantier is hungry and homeless, wandering the French countryside, looking for work. He stumbles upon village 240, the home of a coal mine, La Voreteux. He quickly gets a job in the depths of the mine, experiencing the backbreaking work of toiling hundreds of feet below the earth. He is befriended by a local family and they all lament the constant work required to earn just enough to slowly starve. Fired up by Marxist ideology, he convinces the miners to strike for a pay raise. The remainder of the novel tells the story of the strike and its effect on the workers, managers, owners and shareholders.

Invisible Man

The nameless narrator of the novel describes growing up in a black community in the South, attending a Negro college from which he is expelled, moving to New York and becoming the chief spokesman of the Harlem branch of “the Brotherhood”, and retreating amid violence and confusion to the basement lair of the Invisible Man he imagines himself to be.

Underworld

Underworld is a story of men and women together and apart, seen in deep, clear detail and in stadium-sized panoramas, shadowed throughout by the overarching conflict of the Cold War. It is a novel that accepts every challenge of these extraordinary times.

The Transit of Venus

It tells the story of two orphan sisters, Caroline and Grace Bell, as they leave Australia to start a new life in post-war England. What happens to these young women–seduction and abandonment, marriage and widowhood, love and betrayal–becomes as moving and wonderful and yet as predestined as the transits of the planets themselves.

The House of Mirth

Wharton's first literary success, set amid fashionable New York society, reveals the hypocrisy and destructive effects of the city's social circle on the character of Lily Bart. Impoverished but well-born, Lily must secure her future by acquiring a wealthy husband; but her downfall — initiated by a romantic indiscretion — results in gambling debts and social disasters.

 Still curious? Check out My Ideal Bookshelf.

Source

## The Difference Between a Puzzle and a Mystery?

An eloquent explanation on the difference between mysteries and puzzles by Gregory Treverton:

There's a reason millions of people try to solve crossword puzzles each day. Amid the well-ordered combat between a puzzler's mind and the blank boxes waiting to be filled, there is satisfaction along with frustration. Even when you can't find the right answer, you know it exists. Puzzles can be solved; they have answers.

But a mystery offers no such comfort. It poses a question that has no definitive answer because the answer is contingent; it depends on a future interaction of many factors, known and unknown. A mystery cannot be answered; it can only be framed, by identifying the critical factors and applying some sense of how they have interacted in the past and might interact in the future. A mystery is an attempt to define ambiguities.

We may like puzzles better, but the world increasingly offers mysteries.

In a 2007 New Yorker article “Open Secrets,” written by Malcolm Gladwell expands on the distinction:

The problem of what would happen in Iraq after the toppling of Saddam Hussein was, by contrast, a mystery. It wasn't a question that had a simple, factual answer. Mysteries require judgments and the assessment of uncertainty, and the hard part is not that we have too little information but that we have too much.

Gladwell goes on to show how understanding the difference between puzzles and mysteries can lead us to interpret the same facts differently. “If you sat through the trial of Jeffrey Skilling,” Gladwell writes, “you'd think that the Enron scandal was a puzzle.” But Enron wasn't really a puzzle it was a mystery.

In his book, Boombustology, Vikram Mansharamani sums up the Enron situation:

…the truth about Enron's transactions was openly reveled in public filings and all it took was a diligent Wall Street Journal reporter to unveil the issues at hand. The needed capability was not the ability to find particular information, but rather the skill to assemble disparate data point into a clear image of the whole. The problem is not one of inadequate information, but instead one of too much information overwhelming the processing capabilities…