Mental Models

Small, steady growth adds up to large results over time. Each period's gain becomes part of the base for the next period, so the gains themselves earn gains. The rate of return matters, but how long you let it run, and whether you leave it alone, usually matters more.

The Rule of 72

Divide 72 by the annual return to get the years it takes to double. At 8%, money doubles in about 9 years. At 12%, it takes about 6. Over several decades, a difference of a few percentage points adds up to a lot of money.

The Formula

P = starting amount, r = annual rate, n = times compounded per year, t = years.

Start with how common something is (the base rate), then adjust as evidence comes in. Instead of switching between "true" and "false," hold a level of confidence and move it by an amount that matches the evidence.

The method is named after Thomas Bayes (1701-1761). It treats a belief as a probability that gets refined with each new piece of information.

Bayes' Theorem

The chance of A given you saw B equals how often B shows up when A is true, times how common A is, divided by how common B is overall.

Draw a decision as branching paths. Squares are choices you control; circles are outcomes you don't. Put a probability and a value on each outcome, and you can compare options on paper instead of by gut.

The tree makes you write down your assumptions: which outcomes are possible, how likely each is, and what each is worth to you. That shows where you're guessing and where more information would help.

Instead of asking "How do I succeed?", ask "What would guarantee failure?" Then avoid those things. Problems that are hard to solve directly are often easier when you approach them from the opposite direction.

The mathematician Carl Jacobi advised "Invert, always invert" (man muss immer umkehren). If you can't prove something is true, try proving it false, and if you can't work out what will succeed, start by listing what won't.

"All I want to know is where I'm going to die, so I'll never go there." Charlie Munger

"Show me the incentive and I will show you the outcome." (Charlie Munger)

People respond to incentives, often without noticing that they are doing it. Most of us accept this in principle but still underestimate how strong the effect is. Incentives shape what people do, and over time they also shape what people see and believe, so even honest people can talk themselves into bad behavior when the incentives point that way.

Upton Sinclair described it this way: "It is difficult to get a man to understand something when his salary depends upon his not understanding it."

When we're unsure what to do, we tend to copy other people, and often that's sensible. A packed restaurant next to an empty one does tell you something. It stops working when the crowd knows no more than you do, or when everyone is just copying everyone else.

Copying others was a useful shortcut for most of human history, but the same instinct also leaves us open to bubbles, panics and consensus that isn't real.

Once we take a position, especially in public, we feel pressure to stay consistent with it, even after the facts change. Wanting to look consistent, to others and to ourselves, gets in the way of adapting.

This isn't entirely irrational, since people who change positions constantly are hard to trust. But the same pull can keep us in failing projects, bad relationships and arguments we no longer believe.

When the facts clash with our beliefs, self-image or past actions, we feel an unpleasant tension called cognitive dissonance. To ease it, we often reject or reinterpret the facts instead of changing our minds.

Leon Festinger, who coined the term, studied a group that predicted the world would end on December 21, 1954. When the day passed, many members didn't give up. They decided their faith had saved the world and started recruiting harder. He wrote it up in When Prophecy Fails (1956).

We judge how likely something is by how easily examples come to mind, not by how often it actually happens. Vivid, recent, emotional and heavily covered events feel more common than they are.

Amos Tversky and Daniel Kahneman showed this in 1973. They asked whether more English words start with K or have K as the third letter. Most people say "start with K," because those are easier to recall, but typical text contains about twice as many words with K third. In other words, people treat how easy something is to remember as a sign of how likely it is.

The real cost of anything is what you give up to get it: the value of the next best alternative. When you choose one option, you give up the others.

Most people understand this but don't apply it. We tend to look at the price tag and forget what else the money, time or attention could have been used for. The option you passed on is easy to overlook because you never see it, but it is still part of the cost.

Even if you are better than someone at everything (absolute advantage), you should still focus on what you are relatively best at and trade for the rest (comparative advantage). What matters is how your abilities compare to each other, rather than who is better outright.

David Ricardo set this out in 1817 to explain why trade helps both sides even when one side is better at everything. The stronger party gets more value by spending their time where their lead is largest.

Each extra unit of something is worth less than the one before. When you're hungry, the first slice of pizza is great, but by the eighth slice you'd rather stop. This is diminishing marginal utility, and it applies to money, possessions, work and most other things.

It explains why people don't work unlimited hours for more money, why variety has value, and why there is such a thing as enough. Beyond that point, more of the same adds little and can even make things worse.

When a resource is shared and nobody limits its use, people acting in their own interest will use it up, even though everyone loses in the end. This happens because each person keeps the full gain from taking more, while the cost is spread across everyone.

Garrett Hardin named it in a 1968 essay, borrowing an example William Forster Lloyd used in 1833: a pasture open to all. Each herder gets the full gain from adding a cow but bears only a share of the overgrazing. Nobody has to behave badly for this to happen, because the setup makes overuse the sensible choice for each individual.

When you hire someone (the agent) to act for you (the principal), their interests are not quite the same as yours. They know things you don't, they're paid in ways you may not see, and you bear the outcome more than they do. That gives them room to benefit at your expense, usually legally and often without meaning to.

You can't be an expert in everything, so you hire doctors, lawyers, financial advisors, contractors and real estate agents. Each knows more than you about their field and is paid in a way that may not match what you want.

Individuals in a population vary. Some variants survive and reproduce better than others, so over generations they become more common. No one plans the result. Many variations get tried, the ones that work get passed on, and the rest die out.

The logic isn't limited to biology. Anything that has variation, some kind of selection, and a way of passing traits on will change in the same way over time. That applies to products and ideas as well as genes.

"Now, here, you see, it takes all the running you can do, to keep in the same place." The Red Queen, in Lewis Carroll's Through the Looking-Glass

In a competitive environment you have to keep improving just to hold your position. An improvement that would put you ahead in a static world only keeps you even in one where competitors improve too.

Biologist Leigh Van Valen applied the idea to evolution in 1973. He found that a group of species doesn't get less likely to go extinct the longer it has existed, because predators, prey and competitors keep evolving alongside it.

An ecosystem is a network of species that depend on each other. Each one occupies a niche: what it eats, what eats it, where it lives and how it reproduces. Competition is strongest between species in the same niche, so species often survive by moving into an unoccupied niche or away from their rivals.

Markets and careers work the same way. Some niches are crowded and some are nearly empty, so it matters whether there is room for what you do as well as how good you are at it.

A system can absorb stress for a long time and then change state all at once. At sea level, water at 99°C is hot water. At 100°C it starts to boil, so a one degree change produces a completely different behavior.

The term "critical mass" comes from nuclear physics: the smallest amount of fissile material that can sustain a chain reaction. Below that amount the reaction dies out, and above it the reaction keeps itself going. Social scientists use the term tipping point for the same pattern, where inputs build up for a long time while the system looks stable, and then it shifts fairly quickly.

A system's output feeds back in as input. Positive (reinforcing) feedback amplifies change: a snowball rolling downhill picks up snow, gets heavier and rolls faster. Negative (balancing) feedback resists change: a thermostat turns the heat on when the room is cold and off when it warms up.

Loops explain why small causes can have large effects, why some problems correct themselves, and why systems often respond to an intervention in ways nobody expected.

Systems tend to settle where opposing forces balance and there is no net change. A market clears when supply meets demand. A room settles at the thermostat setting. If you disturb the balance, those forces often push the system back.

Equilibrium doesn't mean nothing is happening. Water behind a dam is in equilibrium even though very large forces are acting on it. The useful questions are which forces are in balance, what could upset them, and what would happen if they did.

Build more capacity than you expect to need. Bridges are designed for loads well above anything they should see. Twin-engine airliners are certified to fly and land on one engine. The difference between what you need and what you have is the margin of safety, and it is there to cover bad estimates, bad luck and things nobody thought of.

Benjamin Graham put the idea at the center of value investing in The Intelligent Investor: only buy when the price is well below your estimate of the company's value. Your estimate will usually be off in ways you can't see, and buying at a discount leaves room for that error.

Every system has a limit past which it stops working. Near that limit, performance often doesn't fade gradually. It tends to hold up and then collapse, so it is worth knowing roughly where that point is before you get close to it.

A breakpoint is similar to a tipping point. The difference is that a tipping point moves a system into a new state, while a breakpoint moves it into failure, and there is often little warning before it happens.

Anything that can fail will eventually fail, so reliable systems are designed on that assumption and have a backup ready to take over when the primary fails. The aim is to stop one failure from taking down everything else, since preventing every failure isn't realistic.

The human body is built the same way. You have two kidneys and two lungs, and you can live with one of each.