Curated and summarized from Farnam Street — original framework by Shane Parrish.
Sampling
Sample size is about how much of the world you’re looking at. It’s the number of data points you’re using to draw conclusions. Like trying to guess the average height of people in a city by measuring a few folks on the street. The more people you measure, the more confident you can estimate.
One of the biggest mistakes we can make is drawing conclusions from too small a sample size— like trying to guess a puzzle picture from only a few pieces. In most instances, increasing our sample size gives us valuable information that lets us see our situation in a new light. The catch is that large sample sizes are expensive. It takes time and money to collect all that data. So practitioners and researchers are always balancing the need for precision with the constraints of budget and deadline. They’ll often settle for the smallest sample size that can still give them a statistically significant result.
Using this model means exploring what isn’t obvious and knowing how easy it is to corrupt our samples with bias.
The next time you hear a statistic, think about the sample size. It’ll give you a clue about how seriously to take it. Remember: the larger the sample, the closer to the truth.
Randomness
Randomness is the chaos that underlies the cosmos. It’s the unpredictable, the uncontrollable, the stuff that doesn’t follow any discernible pattern.
Randomness is what makes life surprising. It’s why you can’t predict the future with certainty. You might make plans, but there’s always the possibility of a random event throwing a wrench in the works. A flat tire, a chance encounter, a sudden inspiration. Randomness is the spice that keeps things interesting.
The tricky thing about randomness is that humans are terrible at recognizing it. We see patterns where there are none. We attribute meaning to coincidence. We think we can beat the odds. But true randomness is immune to our predictions and superstitions. It doesn’t care about our theories or desires
Regression To The Mean
Regression to the mean is the universe’s way of saying “not so fast.” It’s the tendency for extreme outcomes to be followed by more average ones. Extreme results are rarely repeated.
The next time you see something extraordinary, enjoy it. But remember, it probably won’t last. Sooner or later, regression to the mean will come calling, pulling the exceptional back to the ordinary. That’s the way the universe keeps things in check.
Multiply by Zero
Multiplying by zero is the mathematical version of the Midas touch in reverse. Everything it touches turns to nothing. No matter how big or small a number is, when you multiply it by zero, you get zero. It’s the ultimate reset button.
Multiplying by zero shows that we must be mindful of the zeros that will negate our other efforts. Just as in engineering, where one faulty component can make an entire system fail, not being reliable can have the same effect in life.
When you multiply by zero, everything else becomes irrelevant.
Equivalence
Equivalence is the art of making things interchangeable. It’s the idea that two things can be swapped out without changing the essence of what they’re a part of. Like swapping a red Lego brick for a blue one. The color changes, but the structure remains the same.
Being equal doesn’t mean being the same. Different inputs can produce identical results, and there is more than one way to solve most problems.
Equivalence lets us simplify complex systems. We can focus on the essentials instead of getting bogged down in details. We can see the forest for the trees. And we can make changes without fear of breaking the fundamental structure.
Of course, equivalence has its limits. Not everything is interchangeable. You can’t swap out a car’s engine for a hamster wheel and expect the car to run. The art is in knowing where equivalence applies and where it doesn’t. It’s in recognizing the essential differences that matter, and the superficial differences that don’t.
The next time you face a complex problem, try thinking about equivalence. Look for the underlying patterns. See if there are components you can swap out or simplify. You might just find a solution that’s been hiding in plain sight all along.
Surface Area
Surface area is what determines how much an object interacts with its environment. The more surface area the more contact. Surface area can be good and bad. Sometimes, keeping it small is favorable, and sometimes, increasing our exposure is beneficial.
Surface area teaches us that increasing cognitive diversity can give us fresh ideas and help us innovate. However, the model also reminds us that in many ways, the more we expose ourselves, the more vulnerable we are. Different situations require different surface areas.
Global and Local Maxima
Global and local maxima as a model can be used differently to help us make the changes we need for success. It encourages us to see achieving our goals not as a steady upward trajectory but as a path full of peaks and valleys. Understanding that sometimes we have to go down to climb even higher helps us make short-term sacrifices to play the long game. In engineering, you might be trying to maximize efficiency. In life, you might be trying to maximize happiness. But in all these cases, getting stuck on a local maximum is easy. You find a pretty good solution, and you stop looking for a better one.
The next time you’re trying to optimize something, remember the concept of global and local maxima. Don’t just settle for the first peak you find. Keep exploring. Keep searching for that global maximum. It might be a tough climb, but the view from the top is worth it.
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