Thread by @ScottHYoung

Some useful mental models worth knowing:

Efficient markets (and the efficient market hypothesis): Prices adjust until quantity supplied = quantity demanded, and that this can result in an "efficient" distribution where nobody can be made better off without making somebody worse off. Applies to a lot more than econ.

Evolution by natural selection: Random variation + faithful copying result in an increasing number of those instances which are better at surviving/copying themselves. Applies to biological life, but works analogously with culture, ideas and possibly more.

Exponential growth: Anything which increases/improves proportional to its current quantity/quality will be a type of exponential growth. It grows way faster than you think.

Progressive training: Anything you want to improve can be improved slowly by taking where you are now and adding one. Can you do 10 pushups? Try 11. Then 12. And so on.

Social signaling: People say and do things not only for instrumental reasons, but to show other people the kind of person they are. Whenever people say they care about X, but won't pay to make it happen, they may just be trying to signal that they care about X.

Classical conditioning: Pair X with Y and most animals (including humans) will learn to expect Y when they see X. You can use this to your advantage--creating new habits. But others can use it against you--conditioning you to buy/pay attention to stuff through habit.

Reinforcement learning: The follow-on to classical conditioning. Pair X with a reward and X will increase. Pair X with punishment and it will decrease. Also can be used for good or manipulation, depending on who's applying it.

Chunking: You can only keep a few ideas in your mind at a time. Better thinking comes from binding small ideas into larger patterns you can recognize with less effort. That you read this sentence without spelling out each letter is an example of this.

Normal distribution: Any process that comes from a bunch of little things averaging each other out will tend to result in a normal distribution. Most things will be near the center, with exponentially less further and further out.

Modular mind hypothesis: Even though you feel singular, you're actually many, all voting on what you should do next. Different moods, contexts and habits can preferentially activate your sub-selves and make decisions you'd disagree with later.

Pareto's Principle (80/20 Rule): For a surprising number of domains a small # of the inputs creates a large # of the outputs. 80% of mistakes are caused by 20% of the people. 80% of the land is owned by 20%. Note: it's not always 80/20, but the inequality can still hold.

Leverage: Borrowing money can magnify your % return. Put 10% down and get a 5% return? That's now a 50% return. But it also magnifies your losses--a 5% loss wipes out half your investment. Tread carefully.

Chaos: Small changes in initial conditions can create wildly divergent end results. Prediction, even for toy models, may be impossible:

Feedback: When a system's output is fed back into its input. Positive feedback occurs when this is a + sign, and it becomes wildly unstable (think mic next to speakers screeching). Negative feedback occurs when this is a - sign, and dampens the output.

Dimensionality: A dimension, mathematically, refers to how many independent numbers you need to measure something. On a string, just one (distance). On land, just two (lat. and long.). Applies to "abstract" dimensions as well: how many to describe your performance?

Regression to the mean: Sick people usually get better. Great victories usually fade. Great successes have lousy sequels. The biggest outliers were pushed out by being lucky, since luck is random it means that we should expect them to return closer to the average.

Resonance: Systems have a resonant frequency. Oscillate at that frequency and small wiggles will become huge waves. Too fast or too slow and they'll cancel out. Find the right sweet spot so that your small inputs don't get cancelled out.

Prisoner's Dilemma: Don't snitch and you both get a light sentence. Snitch and you go free while your partner stays in jail. Regardless of how your partner chooses, you're better of snitching. Except, your partner knows this too. You both snitch and lose the game.

Gestalt: We notice contrast, separating forms into figure and ground. This applies to vision, but also to more abstract ideas. Effect + side effects. Principle cause + unintended consequences. Narrative + complicating details.

Crystallization: A small local pattern can make it easier for the rest of a material to crystallize onto that surface. Different seeds can lead to different ending patterns (graphite vs diamond), even of the same substance. No seed, & patterns that ought to grow can't.

Superposition: A complex pattern can be broken down into different components and added back together to make analysis tractable. Sound waves into frequencies. Particles into energies. Paintings into layers of glazes.

Survivorship Bias: If you can only easily look at winners, you may falsely assume some of their traits led them to win, even if those were also quite common amongst the losers. The lessons of history are tainted by being only told by the victors.

Huffman Coding: The ease of expressing an idea is proportional to its frequency. Common ideas take fewer words. Rare or original ideas take more. This is probably efficient, but it also makes it harder to say something novel in a tweet.

Coase Theory of the Firm: Companies form when transaction costs make it easier to have an employee than a contractor. Thus the ease/difficulty of working with strangers naturally determines the scale of our organizational units.

Nash Equilibrium: You make decisions based on how others react. But they make decisions based on how you react. Nash equilibria are stable points where nobody changes their choice. Prisoner's Dilemma is a type, but NE are more general, applying to all sorts of situations.

Caching: Memorize the answer to past questions, so you can answer them exactly rather than need to recalculate them. Computers use caching to save on processing. Your brain is probably mostly cached answers, which is why habit and routines both help and prevent original thought.

Paradigm: A way of viewing all situations, often from extension from a focal example where that way of viewing things works. Newtonian gravity = apples + planets, but not black holes or precession of Mercury. Often invisible, it takes fraying at the edges for them to unravel.

Meta: Making something "about" itself, or alternatively, moving up a layer of abstraction. Metacognition = thoughts about thinking. Discovering the meta layer often resolves contradictions in the object layer (if at the price of sometimes making things more confusing!)

Pointers: In computers, a pointer is an object that, instead of storing data meant to mean something directly, it stores an address that "points" to other data. Pointers can point to other pointers. Our language is full of pointers, even though we often pretend like it isn't.

Sunk cost: Past investments have no bearing on future decisions. Only consider whether further investments will be worthwhile. Useful both as a decision tool, and as a mechanism to enforce behavior change knowing that you'll probably irrationally defend your own sunk costs.

Marginal cost and benefit: Many things experience diminishing returns (i.e. you get less benefit as you do more of them). The correct amount to do is when the added benefit of doing it once more equals the cost. Less and you miss on gain. More and you're wasting resources.

Simpson's Paradox: It's possible for a pattern to completely reverse when you analyze it by parts. Medical treatment A may work better than B when you consider average success rate, but when you break down patients into groups, B may work better for each group.

Bayes' Rule: A test for a rare disease (1 in 10,000) will say you have it if you actually do with 99% certainty, and say you don't if you actually don't with 99% certainty. You get a positive result. What % do you have the disease? (Hint: It's actually a lot less than 99%!)

Hedging: Suppose you make a decision with some risk. You can reduce the risk if you make another risky decision that tends to have an opposite effect of your first one. Most people do the opposite. e.g. Work and own stock in same company. Company goes under, you lose job & stock.

Comparative advantage: Two people (or nations) are better off specializing, even if one person is strictly better at all things. Even if you're a great programmer, if you're an *even* better entrepreneur, you shouldn't do your own programming for your company.

Global and local minima/maxima: Is your current approach the best possible? Or is it just the best you can get without getting worse first? Our heuristic for improving is usually "go in the direction of better" except this can only guarantee local, not global maxima.

Permutations: They grow waaay faster than you think. You've seen every card in a 52-card deck many times before. Shuffle thoroughly and nobody in the world has ever seen that order before. Simple ideas are common. Complex ones permuting parts have never been thought before.

Fractals: Patterns often exhibit self-similarity at different scales. Life is inherently fractal. They are the physical manifestation of recursive algorithms, procedures that reference themselves from within.

Coase Theorem: You want to play violin all night, your neighbors want you to shut up, who should win? If you can bargain, (e.g. you pay them $50 to keep playing) you'll reach an efficient outcome. Can't? Then permit the side who would pay more if you could bargain.

Friends' paradox: Does it feel like everyone has more friends than you? That's probably because they do! The average # of friends of your friends is usually > your # of friends. Those with more friends also show up more often in others' friends lists, thus biasing est. upwards.

Pigeonholing: It's mathematically certain that if nobody has over 1 million hairs on their head, that at least two people will have *exactly* the same # of hairs in a city over 1M ppl. By same logic, if pops of M and F are equal, avg # of hetero sex partners must be identical.

Dark matter: Sometimes we can deduce something must exist because of its gravitational influence on things nearby. True for astrophysics, but @SamoBurja extends this mental model to lost knowledge of ancient cultures, showing it's an analogy with legs:

Entropy: Systems tend towards disorder, because statistically, ordered states are rarer than disordered ones. Only true for closed systems as life creates order by converting high-entropy light to low-energy infrared. What entropy are you "pumping out" to make your life sane?

P≠NP: The (still unproven, but almost certainly true) conjecture that for many problems its easier to check if an answer is right than to generate the answer itself. Creativity > comprehension and its easier to understand/critique than to create.

Mutation vs Complexity: Higher mutation rates limit the complexity of organisms. If your mutation rate gets too high, the number of bits of data you can faithfully preserve shrinks. Applies to evolution, but also to your habits: more noise => less stability.

Schelling Point: You and a friend have to meet in NYC, but you can't communicate ahead of time, where do you go? Grand Central is a good pick because others would think it is. Social behavior organizes around salient points, even when those are arbitrary.

Rot: Large, complicated systems tend to degrade over time, as self-repair mechanisms under- or over-correct problems. Human bodies age and die. But so do companies, software platforms, religions and cultures. There's a reason we breed new life rather than exist as immortals.

Fourier Transform: Sometimes it makes more sense to think of something as being built out of oscillations than components. Sound better heard by pitch than by air pressure. JPEG compression works by thinking of images as oscillations rather than pixels.