A Comprehensive History of Mathematics Through Ages
A comprehensive history of mathematics from Babylonian arithmetic and Euclid's geometry through calculus, non-Euclidean geometry, Cantor's...
Welcome to the complete index of every article in our How It Works collection on When Notes Fly. This page lists every article in the section, organized alphabetically for easy reference. Each piece is researched, written by hand, and grounded in academic sources, professional practice, or empirical data. Whether you are diving into How It Works for the first time or returning to find a specific article, the index below gives you direct access to the full collection within Explainers.
If you are new to How It Works, we recommend starting with the foundational explainers and definitions before moving on to specific case studies, applied frameworks, and deeper analytical pieces. Articles are written for thoughtful readers who want substance over summary, with clear explanations of how ideas connect, where they come from, and why they matter. Use this index as a navigational map: skim the titles, read the short summaries, and click through to the pieces that draw your interest. Each article also links to related material so you can follow a thread of ideas across our entire Explainers library.
Most articles in this collection run between 1,500 and 3,000 words. We aim for the kind of explainer that holds up six months later: enough mechanism to be useful, enough nuance to be honest, and enough citation that you can verify the claims yourself. Where the research disagrees or the evidence is thin, we say so. Where a claim is well-established, we say that too. The goal is for you to leave with a working model you can apply, not a vibe you'll forget by Tuesday.
Bookmark this index — it gets fresh entries weekly. New articles are added at the top of the chronological feed and integrated into this alphabetical archive. If you can't find what you are looking for, try the broader Explainers archive for related ideas across all of Explainers, or browse our homepage for the latest writing.
A comprehensive history of mathematics from Babylonian arithmetic and Euclid's geometry through calculus, non-Euclidean geometry, Cantor's...
Alcohol affects nearly every neurotransmitter system in the brain. Understanding the neuroscience of alcohol — from the first drink to dependency —...
Algorithms explained in plain English: what they are, how sorting and search algorithms work, Big O notation simplified, recommendation systems,...
Electric vs petrol cars — 5-year total cost of ownership, charging vs fuel, depreciation, full lifecycle environmental impact, and when EVs make...
Asymmetric information occurs when one party in a transaction knows more than the other. Learn Akerlof's lemons market, adverse selection, moral...
Learn how blockchain works, including distributed ledgers, consensus mechanisms like Proof of Work and Proof of Stake, smart contracts, real-world...
A clear explanation of what central banks are, how monetary policy works, what quantitative easing does, and how the Federal Reserve navigated the...
A comprehensive guide to child development: Piaget's cognitive stages, Vygotsky's ZPD, attachment theory, language acquisition, theory of mind,...
How does climate change actually work? Understand the greenhouse effect, CO2 emissions, climate feedback loops, and why scientists are so confident...
Cognitive science unites psychology, neuroscience, linguistics, philosophy, and computer science to understand how minds work.
What causes recessions? Understand the economic mechanisms behind downturns, from demand shocks and credit crunches to the role of central banks in...
What does sleep deprivation actually do to your body and brain? From impaired cognition and immune suppression to Alzheimer's risk and emotional...
A thorough explanation of Einstein's general theory of relativity: from the equivalence principle to curved spacetime, gravitational waves, black...
What is entropy? Explore Boltzmann's statistical mechanics, the second law of thermodynamics, Shannon's information theory, and why entropy gives...
Epidemiology is the science of how diseases spread, who gets them, and why. Learn about John Snow's cholera map, study designs, the Bradford Hill...
What is carbon pricing: how carbon taxes and cap-and-trade systems work, the social cost of carbon, the BC carbon tax evidence, EU ETS, carbon...
Understand how compound interest works, including the formula, the Rule of 72, real examples over 10 to 30 years, and why starting early makes an...
Dark matter and dark energy together make up 95% of the universe, yet neither has been directly detected.
Why is there something it's like to be you? Consciousness remains the deepest unsolved problem in science.
Cosmology is the scientific study of the universe as a whole — its origin in the Big Bang, its large-scale structure, the mysteries of dark matter...
John Ioannidis's 2005 mathematical argument, the replication crisis in psychology and cancer biology, p-hacking, publication bias, and what good...
The human microbiome consists of trillions of microorganisms living in and on the body. Explore the science of gut bacteria, immune crosstalk, the...
Housing costs have outrun incomes for decades. The cause is not mysterious: zoning restrictions, NIMBYism, and political economy that...
What does the science actually say about recovering faster from illness? Understand the biology of healing — fever, rest, nutrition, hydration, and...
Supply and demand is the most fundamental framework in economics. Here is how it works, what price elasticity means, when markets fail, and what...
Gene therapy delivers functional DNA into cells to treat or cure genetic disease. From Jesse Gelsinger's death in 1999 to CRISPR-based cures for...
What is the gut microbiome and what does it actually do? Understand the science of gut bacteria, the gut-brain axis, how diet shapes the...
How does gravity actually work? Explore Newton's law of gravitation, Einstein's general relativity, gravitational waves, and the unsolved mystery...
How does artificial intelligence actually learn? Understand neural networks, gradient descent, backpropagation, and why modern AI systems can...
The aging brain is not just a slower version of the young brain. It processes differently, loses some capacities, gains others, and remains...
How do antibiotics work? Understand the mechanisms of different antibiotic classes, why antibiotic resistance is a global health crisis, and what...
Pattern recognition overgeneralizes from few examples to broad rules. Cultural learning transmits biases. Emotions attach value creating preferences.
How does CRISPR gene editing work? From bacterial immune systems to Nobel Prizes, base editing, and the first approved CRISPR therapy for sickle...
Cancer is not one disease but two hundred, united by a common logic: cells that break free from the constraints evolution built to stop them.
Variation creates diversity. Selection preserves what works and eliminates failures. Retention passes successful adaptations forward over time.
How does cryptocurrency actually work? Understand blockchain technology, Bitcoin's proof-of-work, wallets, smart contracts, and why crypto is both...
Culture evolves through transmission from parents, innovation when someone tries new behavior, and selection when successful behaviors spread.
Frameworks reduce bias by structuring choices. They make criteria explicit. Consistency improves through repeatable processes despite limitations.
How does democracy actually work? Understand electoral systems, checks and balances, political parties, voting mechanisms, and why democracies...
Learn how the stock market works, from exchanges and market makers to bid-ask spreads, price movements, and how to start investing as a beginner.
How epigenetics works: DNA methylation, histone modification, epigenetic clocks, and whether stress and trauma can be passed to future generations...
Evolutionary psychology asks whether humans are general-purpose learners or have Pleistocene-shaped psychological adaptations.
Reinforcing loops amplify changesviral growth and panic spirals. Balancing loops stabilize systems through homeostasis and resistance.
Learn how GPS works, including satellite triangulation, atomic clocks, signal timing, accuracy limits, assisted GPS in phones, and GLONASS and...
How do financial markets actually work? Understand stocks, bonds, derivatives, market mechanisms, price discovery, and why markets sometimes crash.
How does CRISPR actually edit genes? Understand the science of genetic engineering, from restriction enzymes and recombinant DNA to CRISPR-Cas9,...
Incentives direct attention and effort toward rewarded behaviors. They signal importance and create competition.
How does inequality affect health? Explore the Whitehall Studies, allostatic load, the Spirit Level thesis, ACEs, and what interventions actually...
Learn how inflation works, including CPI vs PPI, demand-pull vs cost-push causes, how central banks fight inflation with interest rates, and what...
Metrics create visibility making performance transparent. Accountability follows visibility.
Inflation is the gradual loss of purchasing power as prices rise over time. Learn the causes of inflation, how central banks fight it, and why some...
A deep look at how humans acquire language — from nativist theories and the critical period hypothesis to statistical learning, word learning,...
Brain learning: neurons fire together during experience, synapses strengthen with repetition through long-term potentiation, wiring pathways...
Formal hierarchies route decisions upward. Informal influence involves politics and relationships.
How does propaganda actually work? Understand the psychological techniques behind mass persuasion — from World War I posters to social media...
Learn how sleep works, including sleep stages NREM and REM, the circadian rhythm, adenosine and sleep pressure, sleep cycles, and what disrupts...
Stress isn't just psychological. Chronic stress produces measurable physical damage to the heart, immune system, brain, and gut.
Technology adoption curve: innovators 2.5%, early adopters 13.5%, early majority 34%, late majority 34%, laggards 16% follow predictable patterns.
Vaccines teach the immune system to recognize and fight pathogens before real infection occurs.
Pain is not simply damage detected by the body — it is a construction of the brain. Understand nociception, the gate control theory, phantom limb...
How does the immune system actually recognize and fight infections? Understand innate and adaptive immunity, T cells and B cells, antibodies,...
The immune system can remember pathogens it has encountered before and respond faster and stronger on re-exposure.
Learn how the immune system works, from innate and adaptive immunity to T cells, B cells, antibodies, how vaccines work, and why autoimmune...
How the internet actually works: TCP/IP, DNS, HTTP/HTTPS, packets, routers, and exactly what happens when you type a URL. Clear, accurate, no jargon.
Learn how the internet works, from TCP/IP and DNS to packets, ISPs, backbone networks, CDNs, and what actually happens when you type a URL into...
Nuclear weapons derive their power from the physics of fission and fusion. This explainer covers how nuclear weapons work, the Manhattan Project,...
The scientific method is not a checklist — it is a set of interlocking practices designed to minimize self-deception.
Adolescent behavior is not irrational — it's the product of a brain in a specific developmental phase.
The Big Bang is the best-supported scientific account of the universe's origin — but it raises as many questions as it answers.
A guide to information theory — how Shannon defined information, what entropy measures, how data compression and error correction work, and how...
Leontief's input-output model explains how industries depend on each other — and why supply chain disruptions, COVID shocks, and climate policy...
A rigorous introduction to quantum mechanics: wave-particle duality, the uncertainty principle, entanglement, Schrodinger's equation,...
How the brain processes language: from Broca and Wernicke's classic discoveries to modern dual-stream models, language acquisition, reading...
Learn how memory works, including encoding, storage, retrieval, short-term vs long-term memory, the hippocampus, memory consolidation during...
Molecular biology explains how genetic information flows from DNA to RNA to protein. Explore the central dogma, CRISPR, PCR, gene regulation, and...
Falling in love activates the same brain circuits as cocaine addiction. The neuroscience of romantic love — dopamine, oxytocin, attachment bonds,...
Science debunks the biggest nutrition myths: fat doesn't make you fat, breakfast isn't mandatory, dietary cholesterol guidelines reversed, detox...
Plate tectonics explained: from Wegener's rejected continental drift hypothesis to seafloor spreading, magnetic reversals, and modern...
Personalized medicine tailors treatment to your individual genetic profile. From cancer targeted therapies to pharmacogenomics, learn how genomics...
Price elasticity of demand explained: elastic vs inelastic demand with real examples, cross-price elasticity, income elasticity, and how...
A science-based guide to psychedelic-assisted therapy: how psilocybin, MDMA, and ketamine are being used clinically, what the research shows, and...
Public health is the science of protecting and improving health at the population level. From John Snow's cholera map to COVID-19 vaccines, explore...
How do social media algorithms actually decide what you see? Understand the ranking systems behind TikTok, Instagram, Facebook, and YouTube — and...
Social media platforms are engineered to exploit fundamental brain systems. What neuroscience and psychology actually know about how social media...
The United States has lower social mobility than most rich democracies. This is a detailed account of what the research shows: how mobility is...
Oil is not just an energy commodity — it is the hidden variable in most major geopolitical conflicts of the last century.
What is the Anthropocene: the geological epoch defined by human planetary impact, the Great Acceleration, planetary boundaries, the sixth mass...
Supply and demand explained clearly: equilibrium, elasticity, price floors and ceilings, and how markets actually set prices for housing, oil,...
How taxes work explained: progressive income taxes, capital gains, corporate tax incidence, wealth taxes, the Laffer curve, and why billionaires...
From Hippocratic humors to CRISPR gene editing, the history of medicine spans 2,500 years of revolution.
A comprehensive guide to the immune system — innate and adaptive immunity, B and T cells, vaccines and memory, autoimmunity, cancer immunology,...
Learn how machine learning works, from training data and feature selection to supervised learning, neural networks, overfitting, and how models...
The labor theory of value is Marx's foundational economic concept. Understand its origins in Ricardo, Marx's development of it, the transformation...
How does evolution actually work? Understand natural selection, genetic mutation, speciation, sexual selection, and the evidence that has made...
How does the brain make decisions? Explore the neuroscience of choice: somatic markers, dopamine reward, the prefrontal cortex, and why emotion is...
US obesity tripled in four decades, reaching 42% by 2020. Explore the biology of why energy regulation fails, the role of the food environment,...
What is actually happening in your muscles, heart, lungs, brain, and cells when you exercise?
The placebo effect is not just 'in your head' — it produces real neurobiological changes. Understand the science of expectation, nocebo effects,...
Where does money actually come from? Understand how commercial banks create money through lending, how central banks control the money supply, and...
Fasting triggers a cascade of metabolic changes — from insulin drops to autophagy to ketosis.
How does nuclear energy work? Understand nuclear fission, chain reactions, reactor designs, safety systems, and why nuclear power is central to the...
The full science of what exercise does to your body and brain: BDNF and neurogenesis, VO2max and longevity, muscle as endocrine organ, depression...
Nick Bostrom's simulation argument explained: the trilemma, the physics objections, the consciousness problem, and what it would mean if our...
A thorough guide to the welfare state — its Bismarckian origins, Esping-Andersen's three worlds typology, the Beveridge Report, Nordic...
Trauma doesn't just leave psychological scars — it physically rewires the brain, dysregulates the nervous system, and alters gene expression.
A deep look at the neuroscience of addiction, the dopamine system, how tolerance works, what the opioid crisis reveals about pharmaceutical...
Black holes are regions of spacetime where gravity is so extreme that nothing — not even light — can escape.
How does the greenhouse effect warm the planet, what are climate tipping points, and what does the IPCC actually say?
Comparative advantage explains why trade benefits both parties even when one country can produce everything more efficiently.
Why does inequality grow? Understand Piketty's r > g thesis, the mechanisms of wealth concentration, what the research shows about inequality's...
A comprehensive guide to genetics and DNA: from Mendel's pea plant experiments and the discovery of the double helix to CRISPR gene editing and...
Long COVID affects an estimated 10-30% of COVID-infected individuals with symptoms lasting months.
How do pandemics spread? Understand R0, transmission routes, the SIR model, how viruses evolve, and why some outbreaks become pandemics while...
How does urban planning work? Explore zoning laws, housing scarcity, Jane Jacobs vs Le Corbusier, Robert Moses, transit-oriented development, and...
Why we age explained: the 12 hallmarks of aging, telomeres, epigenetic clocks, sirtuins, rapamycin, caloric restriction, and what longevity science...
Sugar activates the same dopamine pathways as cocaine. Understanding the neuroscience of sugar addiction — and what's hype versus real — can help...
Chronic low-grade inflammation underlies heart disease, diabetes, Alzheimer's, cancer, and depression.
Meditation produces measurable changes in brain structure, immune function, gene expression, and stress hormones.
Psychedelics are not random noise in the brain — they are precise pharmacological tools with a defined mechanism: 5-HT2A receptor agonism that...
Cognitive science is the interdisciplinary study of the mind and intelligence, drawing on psychology, neuroscience, computer science, linguistics, philosophy, and anthropology. Explore its origins, key theories, and ongoing debates.
Dark matter and dark energy make up 95% of the universe, yet neither has been directly detected.
Emergence is how complex properties arise from simple rules — from starling murmurations to consciousness to market prices.
Gerrymandering is the manipulation of electoral district boundaries to favor one party or group.
A comprehensive introduction to macroeconomics: GDP measurement, the business cycle, Keynesian economics, monetarism, the 2008 financial crisis,...
Microeconomics studies individual decisions and markets; macroeconomics studies national and global economies.
Nuclear energy releases the binding energy of atomic nuclei through fission. From Einstein's E=mc2 and Fermi's first reactor to Three Mile Island,...
What is nuclear fusion: how it differs from fission, the NIF ignition breakthrough in 2022, ITER, tokamaks, private fusion companies, fusion fuel...
Pharmacology explained: how drugs move through the body, bind to receptors, and produce effects.
What drives population growth and decline? Explore Malthus, the demographic transition, falling birth rates, population aging, the 8 billion...
Public choice theory applies economic reasoning to political actors. Politicians, voters, and bureaucrats pursue self-interest, not the common good.
Regenerative agriculture explained: soil biology, carbon sequestration evidence, holistic grazing, agroforestry, and the economic challenges of...
Renewable energy is electricity and heat generated from sources that replenish naturally. Learn how solar, wind, hydropower, and storage work, why...
Statistics is the science of collecting, analyzing, and drawing conclusions from data under uncertainty.
The gig economy explained with real data: how large it actually is, what gig workers earn, the benefits gap, which platforms dominate, and who it actually works for.
The labor market determines wages, employment, and who works where. Learn supply and demand for labor, unemployment types, monopsony, and AI's impact.
The opioid crisis killed over 500,000 Americans between 1999 and 2019. Understand the three waves, the neuroscience of addiction, Purdue Pharma's...
Near-death experiences are reported by millions worldwide and are strikingly consistent across cultures.
What actually strengthens your immune system? Separate science from marketing hype — understand what sleep, exercise, nutrition, stress, and...
What does longevity research actually support? Understand Blue Zones, the hallmarks of aging, caloric restriction, exercise, sleep, and why most...
The science behind why cities generate disproportionate economic output: urban scaling laws, agglomeration economics, knowledge spillovers, and...
Why do 95 percent of dieters regain the weight within five years? Discover the metabolic, hormonal, and behavioral science behind diet failure,...
Why do 95% of diets lead to weight regain? Understand the biology of metabolic adaptation, hunger hormones, set point theory, and what the research...
Why do we age and die? Explore the biological mechanisms of aging — from telomeres and DNA damage to senescent cells and the hallmarks of aging —...
The runner's high is real — but it's not caused by endorphins the way most people think. The neuroscience behind why exercise feels good reveals a...
Exercise doesn't just improve fitness — it reshapes the brain. Understand the neuroscience of how physical activity boosts mood, sharpens memory,...
Why do humans cooperate at unprecedented scales? The science of kin selection, reciprocal altruism, Axelrod's tournaments, altruistic punishment,...
The sky is blue because of Rayleigh scattering — smaller wavelengths of light scatter more in the atmosphere.
Loneliness is a public health crisis. Chronic social isolation increases mortality risk equivalent to smoking 15 cigarettes a day.
Music can give you chills, make you cry, or fill you with inexplicable joy. Neuroscience is beginning to explain why — and the answers involve...
A steel ship weighs thousands of tons yet floats easily. A small pebble sinks. Why? Archimedes' principle and buoyancy explain how shape — not...
Sleep-deprived people are the worst judges of their own impairment. The Penn chronobiology study, the glymphatic system, and the neuroscience that...
Sleep is not rest — it is active biological maintenance. Discover what the latest neuroscience reveals about sleep stages, brain waste clearance,...
Smartphone compulsion isn't a character flaw — it's the product of deliberate design. Here's the neuroscience and behavioral engineering behind why...
Thomas Piketty's r>g thesis, Robert Merton's Matthew effect, Raj Chetty's mobility data, and the Gini coefficient's trajectory explain why wealth...