Below is list of useful tools and ideas you can use to improve your thinking skills. (You may have also heard these referred to as “mental models”.) They can help you make better decisions, organize your thoughts, generate new ideas, and attack problems from different angles.
I will continue to update the list with new tools, descriptions, useful links, and more, so check back often! In particular, I think this list is useful to reference whenever you’re thinking through a problem / decision, just as you might dig around in your toolbox whenever you need to fix something that’s broken.
(Note, the current list is very incomplete and mostly just a quick brain dump lacking any real organization. I will be improving this in the near future.)
People tend to be comfortable reasoning about “normal” size numbers: 1, 2, 3, 4, even 100, or 1,000. But, people have a harder time wrapping their head around very large or very small numbers: 1 billion or 1 millionth (1 / 1 million). Getting more comfortable with very small or large numbers can help you better reason about real things like large amounts of money, people, etc. or low probability events like winning the lottery, getting some disease, etc.
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People are generally very comfortable with linear growth (e.g. constant or additive growth, \(y=x\), counting, etc.). But, many people have poor to no understanding of exponential growth (e.g. percentage-based growth, \(y = 1.01^x\), interest rates, etc.) and as a result compounding / compound interest. Understanding exponential growth has many real-world benefits such as helping you build wealth, develop better habits, and more. Indeed, Einstein is reported to have said: “Compound interest is the eighth wonder of the world. He who understands it, earns it. He who doesn’t, pays it.” Don’t be the one who pays it!
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People tend to think in black and white, true and false; but the real world is much more uncertain, more gray. Thinking probabilistically can help you be more comfortable with uncertainty. It can help you minimize risk, while helping you take calculated risks when it’s appropriate. And, it can help you take actions that are the likeliest to help you reach your goals, even if the outcome of those particular actions is uncertain.
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A “Back of the Envelope” calculation is a quick / rough estimate of some quantitative value. The name comes from the idea of quickly doing this type of calculation literally on an envelope. The goal is to get to a close, but not perfect, answer to some question. In practice, going through such an exercise can get you a much more accurate answer than your initial uninformed guess in much less time than would be required to determine / calculate the truly accurate value (if it’s even possible to get that true value).
An example might be: How much money do you spend on food in a year?
Right away you can probably say it’s more than $100 and less than $100,000, but a quick “back of the envelope” will let you do even better. Say you buy groceries once a week and spend about $100 each time. That would be \($100 \times 52 \operatorname{weeks} = $5,200\). Let’s say you also spend $100 a month eating out. That would be \($100 \times 12 \operatorname{months} = $1,200\). Add those two together and you get: \($5,200 + $1,200 = $6,400\). While likely not exactly right, if your assumptions were reasonable, that would be a pretty good estimate of the true value in just a single paragraph (far quicker than going through every receipt to figure out the exact value!).
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The normal distribution, also sometimes called a bell curve, is probably the most common statistical distribution, hence it being called “normal”. It’s characteristic bell-like shape indicates most data is near the center (median) or average (mean) with more extreme data points becoming increasingly less and less likely. Many real life / natural phenomena are approximately normally distributed such as human height, IQ (technically it was designed to be normally distributed), etc. Understanding and being able to identify real life situations that are approximately normally distributed can help you better reason about how common / rare certain things are, e.g. most ____ are about average; very few ____ are much larger / better or much smaller / worse.
Surface area is the geometric area of the outside of a shape / object. It’s not necessarily important that you know how to calculate a surface area. Rather, you should understand that surface area equals “exposure” to the outside world. In some situations this is good, such as maximizing the number of places a customer might find out about you if you’re a marketer. In others it can be bad, such as having many points of possible failure in a process. In practice, you should increase your “surface area” only when there is a likely benefit or a true need to do so.
Correlation
Correlation ≠ Causation
Supply & Demand
Monopoly & Monopsony
Opportunity Costs
Sunk Costs
Time is Money / the Most Valuable Resource
Comparative Advantage
Discounting
Utility Functions
Diminishing Utility
Marginal Utility
Pareto Principle / 80/20 Rule
Specialization
Economies of Scale
Inflation
Nash Equilibrium / Game Theory / Prisoner’s Dilemma
Overfitting / Underfitting
Law of Large Numbers
Narrow vs. General AI
“Superhuman” Performance
Automation / “Don’t Repeat Yourself”
Your Data is Valuable
All Models are Wrong, but Some are Useful
Normal Variation
Trends / Trend Changes
Statistically Significant vs. Meaningful Differences
Global and Local Maxima / Minima
The Map is Not the Territory
Thinking from First Principles
Second+ Order Thinking
Working Backwards from the Goal
Occam’s Razor
Maslow’s Hierarchy of Needs
Momentum
Friction
Direction
Leverage
Activation Energy / Catalysts
Niches
Self-Preservation
Tendency to Minimize Energy Output (Mental & Physical)
Synergy
Feedback Loops
Bottlenecks
Scale
Churn