Mental Models

Introduction

As Douglas Hofstadter would have it, analogies are the "fuel and fire of thinking" — A is to B as C is to D. We are continuously creating analogies as we pass through life observing similarities between seemingly unrelated events. As we encounter new things in the world, our past experiences shape our approach.

Similarly, when we encounter a new idea, the best way we can begin evaluating its potential is to view it in terms of some other mental construct we already understand. We need a pool of ideas to draw insight from, and the more toys we have in the pool, the better the party.

The motivation behind the study of mental models is that our thought processes do not always produce good results. Our naked cognition doesn't always work in the intended way: the idea pool is empty or in bad keep. For various reasons we simply fail to understand, we miss the answers, we make mistakes. Fortunately, just as we have learned to build tools to extend the abilities of our physical bodies, so, too, have we learned to work with ideas to increase the reach of our mercurial minds.

Tools for thought come in many shapes. Over time, as we have mastered the natural domains with which we interact every day, we have come across various kinds of useful ideas. These thinking tools, these concepts and principles and representations, are in a sense common and shared by all humans. The Great Mental Models collection presented here is a library of standard ideas and analogies that can be applied in a variety of contexts.

The argument goes that an awareness of mental models, and a basic understanding of how and where to apply them, may improve our thinking, may help us make the most of our cognitive abilities. Mental models capture the essence of some useful notion in a way that may have broader utility.

The selection process for this collection — again, based on the FS blog post — is somewhat arbitrary. It doesn't really matter what is or isn't a valid mental model. The items listed below do not all function in the same way, or meet any particular purpose, but rather each one aims to provide some kind of valuable insight. The point is that an awareness of these concepts can help us avoid pitfalls in our thinking and may aid our understanding. Mental models are a particularly nutritious kind of food for thought.

More broadly, there's two additional reasons to be interested in mental models. Firstly, mental models are the foundation of all digital tools. As users we manipulate the internal state of software systems through some kind of a user interface, which has to match our expectations, or otherwise we easily get confused. It is essential that the representation presented to us is compatible with our mental models of not just the system, but the original problem domain. Furthermore, the very best systems open up entirely new mental models for the user to explore. Great tools enable us to work in entirely new application areas and to make use of new capabilities, find new ways of doing things with a computer — and new things to do.

Secondly, mental models give us a flavour of the subtlety of human cognition and the analogy process. Mental models feature all kinds of fascinating concepts and representations that each would, for example, present a challenge to simulate or reproduce in AI systems. In a sense, mental models are some of our best representations for intangible things that we still consider to be real. A solid understanding of mental models and their relation with human cognition should prove a useful stepping stone on the path to building artificial minds.

Mental models are all those invisible constructs with which we try to make sense of the world. They help us make new connections and find new opportunities, and they help us decide what is relevant and salient. Mental models simplify complexity and point us in the direction of better reasoning and better thinking.

Mental Models

The collection here is grouped into several categories. We begin by looking at the human mind with its numerous heuristics and biases, followed by a brief review of human nature from feelings and instincts to other colourful facets of our fateful condition. Next up is abstract thinking, a powerful set of ideas with which we try to balance out the immediacy of our minds.

We then turn to the phenomena of the natural world. We'll first look at physics, chemistry, and biology, and then slowly turn our attention to man-made systems and mathematical wonders. We conclude the survey with some examples drawn from economics, and the art of war.

Again, all this is based on the excellent Farnam Street compilation. I've shuffled and structured the entries in a way that I find more accessible. Each entry is described by a succinct statement or two, in lieu of a deeper explanation.

This is by no means an exhaustive list of mental models, that's not the point at all. This is merely a beginner's guide, more of a highlights tour. Do check out Farnam Street for more details, including the Great Mental Models books in which they dedicate a full chapter to each model.

Human Judgement

• Representativeness Heuristic: We fail to account for base rates, we think in stereotypes

• False Conjunction: Extra detail makes an untruth more believable, makes a story (falsely) seem more probable

• Availability Heuristic: We recall the important, the frequent, and the recent

• First Conclusion Bias: We settle for the first plausible answer

• Overgeneralisation: We form categories even from hopelessly small samples

• Commitment / Consistency Bias: We are not great at changing our mind or habits

• Hindsight Bias: We convince ourselves that we knew something all along

• Confirmation / Falsification Bias: We believe what we want to see, choose to see

Human Nature

• Trust: We choose to trust others outside our family

• Denial: We cope and survive through “behavioural inertia”

• Envy, Jealousy: We compare our share with those of others

• Love, Hate: We are blinded by our passion for ideas, things and people

• Stress: We rely on our instincts, when low on energy, which amplifies our biases

• Incentive Bias: We are controlled by our desires

• Pavlovian Association: We learn to respond to indirect incentives

• Safety in Numbers: We are team players and socially conditioned

• Sense of Justice : We are careful arbiters of fairness and propriety

• Curiosity Instinct: We ask questions and find answers

• Narrative Instinct: We tell stories to construct and seek meaning

• Language Instinct: We are hardwired to receive and transmit meaning

• Fundamental Attribution Error: We are surprised by how “inconsistently” others behave

• Boredom Syndrome: We act, even when actions are not needed

• Relative Satisfaction/Misery: We are happy relative to our past self or our peers

Abstract Thinking

• Circle of Competence: Knowing the limits of our knowledge helps us make better meta-decisions

• First Principles: Reverse-engineer complexity by breaking things down, build new results up from essentials

• Thought Experiments: Using imagination to examine ideas on the outset; "What if...?"

• Second-order Thinking: Causes have causes, effects have effects

• Probabilistic Thinking: Estimation methods for identifying likely outcomes

Fat-tailed processes: Abnormal black swan events are surprisingly common

Bayesian updating: Using data to update beliefs

• Inversion: Flip the problem around and think backwards

• Occam’s Razor: Simpler explanations are more likely to be true, parsimony

• Hanlon’s Razor: Assume the least amount of intent in events

“Don’t attribute to malice what can be explained by stupidity”

Physics & Chemistry

• Thermodynamics: Energy cannot be created or destroyed

• Inertia: Things in motion continue where they are going

• Friction / Viscosity: Resistance at the interface drains momentum

• Relativity: It is difficult observe the system you are in

• Leverage: Great output from a small input

• Velocity: Motion has a direction, a vector nature

• Reciprocity: Actions have consequences in equal measure

• Activation Energy: The reaction starts only when a critical limit is reached

• Catalysts: The extra ingredient that makes the soup work

• Alloying: Combinations can be more than the sum of their components and properties

Biology

• Natural Selection and Extinction: As conditions change, the fittest survive

• Adaptation, The Red Queen Principle: Have to keep running to stay in the game

• Ecosystems: Life is diverse, there are many interdependent ways of playing the game

• Niches: Competition for resources leads to specialisation

• Self-Preservation Instinct: The real game is to keep on playing the game

• Replication: Life is built on high-fidelity copying

• Laziness: Efficient energy use is a competitive advantage

• Cooperation: From mutual benefit to ever greater levels of organisation

• Hierarchical Organisation: Yearning for authority, leadership, and structure

• Incentives: Reward to get more of the same, to keep playing the game

Systems

• Feedback Loops: Cyclic structures lead to complex flows

• Bottlenecks, Constraints: Limitations on flow change the dynamics of the system

• Homeostasis, Equilibrium: Self-regulation keeps control values within acceptable range

• Scale: Some processes and behaviours are sensitive to scale

• Law of Diminishing Returns: Positive trends often fade away in terms of incremental value

• Churn: To be keep the game alive, what is lost must be replaced

• Irreducibility: There are fundamental limits to scalability and leverage

• Cumulative Advantage (Preferential Attachment): Leaders reap the rewards; network effect, momentum

• Margin of Safety, Backups: Over-resource, over-allocate to allow for error and decay

• Criticality: Moments before a phase shift are loaded with expectation

• Algorithms: Processes can be thought of in terms of discrete steps

• Emergence: Higher-level behaviour from the interaction of lower level elements

Numeracy

• Distribution: Processes produce values in a characteristic pattern

• Compounding: A regular multiplier manifests as interest on interest

• Law of Large Numbers: With more event instances, results converge to the expectation

• Multiplying by Zero: In a product of many components, the critical value dominates

• Algebraic Equivalence: Symbolic manipulation opens the door to numeric analogy

• Fooled by Randomness : We tend to pick up patterns in a non-sequential, unordered world

• Regression to the Mean: Long deviations from the average normally tend to disappear

• Surface Area: More surface area, more exposure to the environment

• Global and Local Maxima: Some peaks are higher than others, but it’s hard to see up close

Economics

• Creative Destruction: Out with the old, in with the new

• Opportunity Cost: Doing one thing means not being able to do another

• Comparative Advantage: Trading is beneficial, even if one party is better at everything

• Specialisation (Pin Factory): The system benefits when everyone doesn’t do everything

• Seizing the Middle: There are more moves to be made from the middle of the board

• Trademarks, Patents, Copyright: Limits on free distribution protect the creative establishment

• Double-Entry Bookkeeping: Every transaction has two parties; error detection by invariance

• Bribery: Removing the enforcer may be easier than playing by the rules

• Arbitrage: Two markets price the same thing in profitably different ways

• Utility (Marginal, Diminishing, Increasing): Usefulness of additional units tends to vary with scale

• Supply and Demand: Limited supply leads to competition and price discovery

• Scarcity : Constrained supply leads to fierce competition and high prices

• Mr. Market : The market is like a moody neighbour, with his ups and downs

War

• Two-Front War: Splitting resources weakens the overall position

• Seeing the Front: First-hand experience of trenches helps with decisions higher up

• Asymmetric Warfare: Each side plays by their own rules; underdogs are unpredictable

• Counterinsurgency: Asymmetry requires a deliberate strategy from the overdogs

• Mutually Assured Destruction: As opponents get stronger the less likely they are to engage

Reflections

“The best language [today] seems to be more colorless and glib than some of the language of [centuries past]. There's a vividness, a willingness to use metaphor and literary flourishes that you are less likely to see today. [..] It may be that because we have so many technical terms available to us, that we don't reach for the metaphor and that will drain prose of some of its vitality, even though it kind of makes it [easier] to convey abstract ideas." — Steven Pinker on contemporary language, during a Q&A for a talk based on his book The Sense of Style (2014)

"All models are wrong, but some are useful." — Statistics lore, popularised by George Box