A library for thoughtful decisions
An independent collection inspired by Charlie Munger’s approach to learning across disciplines. Explore connections between mathematics, science, human behavior, and judgment.
This is not a prescribed list by Munger. Scientific concepts are explained in their original disciplines; a useful business analogy does not establish an identical mechanism.
65 entries
When each period’s gain is added to the base for the next period, growth compounds. Starting with an amount P and a constant rate r, the amount after n periods is P(1+r)^n.
Use and limitsPositive exponential growth has no mathematical inflection point. Learning and relationships do not automatically follow this formula.
Counting methods describe possible arrangements; probability assigns likelihoods under a stated model. For mutually independent events, their joint probability is the product of their probabilities.
Use and limitsThree mutually independent 80% events all occur with probability 51.2%. Without independence, use conditional probabilities.
Further readingFor evidence E with P(E) > 0, Bayes’ theorem relates a hypothesis’s posterior probability to its prior probability and the likelihood of that evidence: P(H given E) = P(E given H)P(H)/P(E).
Use and limitsCheck base rates and evidence quality; a precise calculation can still rely on poor assumptions.
Further readingThomas Bayes, “An Essay towards Solving a Problem in the Doctrine of Chances” (1763).
For independent, identically distributed observations with a finite mean, the sample average converges to the expected value as sample size increases.
Use and limitsIt does not predict the next outcome or make a losing bet profitable through repetition.
Further readingHossein Pishro-Nik, Introduction to Probability, Statistics, and Random Processes, §7.1.1
Normal and power-law models describe different patterns of variation. A power-law tail can assign much greater probability to extreme values than a normal model.
Use and limitsSelect a model from evidence and diagnostics, not from an appealing story about outliers.
Further readingClauset, Shalizi & Newman, Power-law distributions in empirical data
For a repeated binary bet with net odds b and win probability p, the unconstrained Kelly fraction is f* = p − (1−p)/b. It maximizes expected logarithmic wealth under the model’s assumptions.
Use and limitsUnknown probabilities, correlated bets, and drawdowns matter. This formula does not prescribe how much of a life or career to risk.
Further readingJ. L. Kelly Jr. (1956), A New Interpretation of Information Rate — publisher record
A phase transition changes a material’s phase. In a fluid, the critical point is where the liquid–gas phase boundary ends.
Use and limitsBoiling water at ordinary pressure is a phase transition, not the water critical point. Business thresholds are analogies.
Further readingThe total entropy of an isolated system does not decrease. Local decreases are possible when accompanied by compensating changes in the surroundings.
Use and limitsOrganizational disorder is a metaphor; thermodynamics does not prove that teams inevitably deteriorate.
Further readingWhen two bodies interact, the force one exerts on the other is equal in magnitude and opposite in direction to the force it receives.
Use and limitsThe forces act on different bodies. Social reactions need not be equal and opposite in a physical sense.
Further readingEnergy can be transferred or transformed. In an isolated system, the total energy remains constant.
Use and limitsEconomic value is not physical energy, so this law does not imply that wealth creation is zero-sum.
Further readingOpenStax, University Physics Volume 2 — thermodynamics chapters
In an inertial reference frame, an object maintains constant velocity unless acted on by a net external force.
Use and limitsOrganizational inertia is an analogy; habits and institutional constraints need their own explanations.
Further readingOpenStax, University Physics Volume 1, §5.2 Newton’s First Law
An oscillating system can respond strongly to periodic forcing near one of its natural frequencies; damping influences the response.
Use and limitsCoordinated teamwork is only a metaphorical comparison, not evidence of physical resonance.
Further readingOpenStax, University Physics Volume 1 — index entry for standing waves and resonance
In an autocatalytic reaction, a reaction product or intermediate acts as a catalyst for the reaction.
Use and limitsThis is a specific chemical mechanism. A self-reinforcing business process is analogous, not necessarily autocatalytic in the chemical sense.
Further readingA chemical equilibrium involves equal forward and reverse reaction rates. Changing conditions can shift the equilibrium composition in a direction that partially counteracts the disturbance.
Use and limitsEquilibrium is dynamic. The principle does not prove that markets or organizations always restore their previous state.
Further readingActivation energy characterizes the energy barrier associated with a reaction pathway and helps explain how reaction rates depend on temperature.
Use and limitsCrossing a barrier does not mean every reaction releases energy or is thermodynamically favorable.
Further readingA material’s properties depend in part on its composition, bonding, and arrangement across relevant length scales.
Use and limitsTemperature, processing, and environment also matter; “structure determines everything” is too strong.
Further readingOpenStax, Chemistry 2e.
Heritable differences that affect survival and reproduction can change the frequencies of traits in a population across generations.
Use and limitsSelection has no foresight and does not imply moral superiority or inevitable progress.
Further readingCharles Darwin (1859), On the Origin of Species — first edition
A species’ niche concerns the conditions and resources under which it can persist and its relationships with other organisms.
Use and limitsA business niche is an analogy; commercial opportunities require evidence about customers and competition.
Further readingEvolutionary success is relative to a changing environment that includes other evolving organisms. Maintaining a relative position may require continued adaptation.
Use and limitsIts application to business is an analogy, not a biological proof that constant expansion is necessary.
Further readingLeigh Van Valen, “A New Evolutionary Law” (1973).
Symbiosis describes close, persistent relationships between different species. Depending on usage, it includes mutualism, commensalism, and parasitism.
Use and limitsDo not equate all symbiosis with mutual benefit; specify who benefits and who bears costs.
Further readingA system’s outputs can influence its future behavior. Reinforcing feedback amplifies change; balancing feedback counteracts it.
Use and limitsTrace the actual connections and delays. Positive feedback does not mean beneficial feedback.
Further readingInteracting agents that respond to experience or changing conditions can generate system-level patterns that evolve over time.
Use and limitsNonlinearity and adaptation can limit prediction; describing a system as complex does not explain its specific behavior.
Further readingJohn H. Holland, Hidden Order: How Adaptation Builds Complexity (1995).
Rewards, penalties, and rules influence what people choose to do. A measure used for rewards can redirect effort toward improving that measure.
Use and limitsCheck for gaming, neglected tasks, and effects on intrinsic motivation rather than assuming more reward is always better.
Further readingSteven Kerr (1975), On the Folly of Rewarding A, While Hoping for B
The opportunity cost of a choice is the value of the best feasible alternative that must be forgone.
Use and limitsCompare realistic alternatives, not every imaginable benefit; time and other scarce resources also count.
Further readingOpenStax, Principles of Economics 3e, Chapter 2: Choice in a World of Scarcity
Under a common preference assumption, each additional unit consumed provides less extra satisfaction than the previous unit, other things equal.
Use and limitsThis is an assumption used in models, not a universal income threshold for happiness.
Further readingWilliam Stanley Jevons, The Theory of Political Economy (1871).
An actor has a comparative advantage in an activity when its opportunity cost is lower than another actor’s, even if its absolute productivity is lower.
Use and limitsPotential gains from specialization do not imply equal gains or eliminate adjustment costs.
Further readingDavid Ricardo, On the Principles of Political Economy and Taxation (1817), chapter 7.
When users share a resource and each bears only part of the cost of extraction, individually attractive choices can lead to overuse.
Use and limitsOveruse is not inevitable. Community rules, monitoring, and other institutions can support collective management.
Further readingElinor Ostrom (2009), Beyond Markets and States — Nobel lecture
A principal delegates action to an agent whose information or objectives may differ, creating problems of incentives, monitoring, and accountability.
Use and limitsContracts cannot foresee everything; consider measurement costs, trust, and unintended incentives.
Further readingRewards and penalties can strongly influence behavior.
Use and limitsCheck what conduct a rule actually rewards, not merely what it intends.
Further readingB. F. Skinner, The Behavior of Organisms (1938).
Affection or dislike can color judgments about people and their claims.
Use and limitsAssess the evidence separately from feelings about its source.
Further readingMunger, Poor Charlie’s Almanack, “The Psychology of Human Misjudgment”.
People may resist information that conflicts with an existing commitment.
Use and limitsAllow explicit revisions when evidence changes.
Further readingLeon Festinger, A Theory of Cognitive Dissonance (1957).
Other people’s behavior can influence what seems appropriate or credible.
Use and limitsPopularity can provide information, but cannot replace evidence.
Further readingRobert B. Cialdini, Influence (1984).
A comparison point can change how an option is perceived.
Use and limitsEvaluate absolute terms as well as relative differences.
Further readingMunger, Poor Charlie’s Almanack, “The Psychology of Human Misjudgment”.
Curiosity can motivate exploration and the search for explanations.
Use and limitsFollow questions with evidence checks rather than collecting novelty alone.
Further readingMunger, Poor Charlie’s Almanack, “The Psychology of Human Misjudgment”.
Stress can change attention, memory, and decision-making.
Use and limitsEffects depend on intensity, duration, and task; avoid one universal rule.
Further readingMunger, Poor Charlie’s Almanack, “The Psychology of Human Misjudgment”.
Optimism concerns expected outcomes; confidence concerns certainty or perceived ability.
Use and limitsCompare forecasts with outcomes and relevant base rates.
Further readingPopper proposed that scientific claims should expose themselves to possible refutation by making claims that could conflict with observations.
Use and limitsA failed test also raises questions about measurement and auxiliary assumptions; one anomaly is not always decisive.
Further readingKarl Popper, The Logic of Scientific Discovery (English edition, 1959).
When explanations account for the evidence comparably well, prefer one that introduces fewer unnecessary assumptions.
Use and limitsSimplicity is a guide, not proof. A simpler explanation can still be wrong.
Further readingStanford Encyclopedia of Philosophy, “Simplicity.”
A conclusion about what ought to be done does not follow from purely descriptive premises without some normative premise.
Use and limitsState the values linking evidence to a recommendation rather than presenting a value judgment as a fact.
Further readingDeduction concerns conclusions that follow necessarily from premises when the argument is valid. Induction extends beyond observed cases and yields defeasible conclusions.
Use and limitsValid reasoning does not make false premises true; repeated observations do not logically prove every future case.
Further readingRecognize that one’s knowledge and reasoning can be incomplete or mistaken, while remaining willing to form and defend evidence-based judgments.
Use and limitsHumility means calibrating confidence, not treating all claims as equally plausible.
Further readingLeary et al. (2017), Cognitive and Interpersonal Features of Intellectual Humility
Compare past and present situations to identify possible mechanisms, recurring tensions, and important differences.
Use and limitsUse analogies to generate questions. Differences in institutions, incentives, and circumstances can make a past outcome a poor guide to the present.
Further readingRichard E. Neustadt and Ernest R. May, Thinking in Time (1986).
An outcome can arise from interacting causes and contingencies. Knowing the result can make one explanation seem more inevitable than it was.
Use and limitsCompare alternative causal accounts and distinguish necessary conditions from contributing factors.
Further readingFischhoff, Hindsight not equal to foresight — reprint of the 1975 paper
Past choices can shape current options through switching costs, accumulated skills, complementary investments, or self-reinforcing adoption.
Use and limitsHistory matters, but persistence alone does not prove inefficiency or impossibility of change.
Further readingPaul A. David, “Clio and the Economics of QWERTY” (1985).
When repeated measurements are imperfectly correlated, unusually extreme observations tend to be followed by observations closer to the mean.
Use and limitsThis is a statistical selection effect, not a force that reverses every trend or proves an intervention worked.
Further readingFrancis Galton, “Regression towards Mediocrity in Hereditary Stature” (1886).
Two variables can move together because one affects the other, because of a common cause, or because of selection and other processes.
Use and limitsA causal claim requires assumptions and a design that addresses alternative explanations.
Further readingJudea Pearl, Causality (2000).
An analysis can be misleading when it includes only cases that survived a selection process and omits failures or other excluded cases.
Use and limitsDefine the original population and the selection process before generalizing from visible successes.
Interpreting evidence requires both its diagnostic value and the prior frequency of the condition being considered.
Use and limitsA positive test is not the same as a high probability of the condition; account for false positives and prevalence.
Further readingTversky and Kahneman, “Evidential Impact of Base Rates” (1982).
An association observed within separate groups can reverse when the groups are combined because their composition and weights differ.
Use and limitsNeither the grouped nor aggregated result is automatically the causal answer; use subject-matter knowledge and a causal model.
Further readingE. H. Simpson (1951), The Interpretation of Interaction in Contingency Tables
Divide a problem into smaller instances, solve those instances, and combine their solutions, often recursively.
Use and limitsThe decomposition and combination must preserve correctness; coordination overhead affects efficiency.
Further readingThomas H. Cormen et al., Introduction to Algorithms.
Represent the features relevant to a task while hiding details that need not be considered at that level.
Use and limitsCheck what information the abstraction omits and when those omissions become important.
Further readingBarbara Liskov and Stephen Zilles, “Programming with Abstract Data Types” (1974).
Unreliable inputs, inappropriate assumptions, or unsuitable objectives can produce misleading outputs even when computation is correct.
Use and limitsCheck provenance, measurement, missingness, and whether the model fits the question; “garbage in, garbage out” is a maxim.
Analyze how an algorithm’s resource requirements change with input size, under a stated model of computation.
Use and limitsAsymptotic bounds do not determine every practical runtime; constants, data structure, and hardware also matter.
Further readingThomas H. Cormen et al., Introduction to Algorithms.
Fault-tolerant systems aim to maintain specified functions despite component faults, sometimes using redundant components, detection, and recovery.
Use and limitsRedundancy is not enough if backups share a failure mode or cannot take over when needed.
Further readingJohn von Neumann, “Probabilistic Logics and the Synthesis of Reliable Organisms from Unreliable Components” (1956).
A safety margin provides capacity beyond an expected requirement; redundancy provides additional components or paths that can maintain a function if one fails.
Use and limitsThey address different risks. Shared dependencies can defeat apparently independent backups.
System performance can be limited by a constraint. Identify it, improve its use, align other activities, increase its capacity where appropriate, and reassess.
Use and limitsImproving a nonconstraining activity may not improve total output; the constraint can move.
Further readingGoldratt Research Labs, Introduction to the Theory of Constraints
Feedback control uses measured output to adjust an input. A PID controller combines proportional, integral, and derivative responses to control error.
Use and limitsA periodic management review is a feedback loop, but not automatically a PID controller.
Further readingDesign components with clear responsibilities and interfaces so that changes inside one component have limited effects on others.
Use and limitsDependencies cannot always be eliminated; interfaces and integration require deliberate design.
Further readingDavid L. Parnas, “On the Criteria To Be Used in Decomposing Systems into Modules” (1972).
Ties connecting otherwise separate social circles can provide access to information that close, overlapping networks do not supply.
Use and limitsWeak ties are not always more valuable; the task, trust required, and network structure matter.
Further readingBourdieu distinguishes embodied dispositions and knowledge, cultural objects, and institutional credentials that can have value within a social field.
Use and limitsThis explains forms of social advantage, not a ranking of people’s inherent worth or a guarantee of career success.
Further readingGiddens examines how social practices draw on rules and resources while also reproducing or changing those structures.
Use and limitsStructure and agency are interrelated; this is not simply a claim that individuals can redesign any institution at will.
Further readingAnthony Giddens, The Constitution of Society — publisher edition
A narrative selects events, causal links, and perspectives that shape how an audience understands a situation.
Use and limitsA coherent story can omit evidence; compare alternative accounts and separate persuasion from verification.
Further readingJerome Bruner, “The Narrative Construction of Reality” (1991).
Aristotle distinguishes persuasion through the speaker’s character, the audience’s emotions, and the argument presented.
Use and limitsThese describe means of persuasion; neither confidence nor emotional impact proves a claim true.
Further readingWriting makes claims, assumptions, and transitions visible, allowing an argument’s gaps or ambiguities to be examined.
Use and limitsClear prose can still express a false claim; clarity and truth require separate checks.
Further readingGeorge Orwell, “Politics and the English Language” (1946).
A metaphor interprets one domain in terms of another, highlighting some relationships while obscuring others.
Use and limitsIdentify where the comparison breaks down; an illuminating metaphor is not evidence of an identical mechanism.
Further readingGeorge Lakoff and Mark Johnson, Metaphors We Live By (1980).