Probability, Risk & Uncertainty

Watch

• How statistics can be misleading - Mark Liddell ↗TED-Ed
• 3 game theory tactics, explained ↗Big Think
• Bayes theorem, the geometry of changing beliefs ↗3Blue1Brown
• The Uncertainty Principle: What Does It Mean, How Does It Work? ↗Sabine Hossenfelder

Read

• Against the Gods: The Remarkable Story of Risk ↗A compelling historical narrative illuminating humanity's evolving understanding and management of risk, from ancient divination to modern finance.Peter L. Bernstein
• Thinking, Fast and Slow ↗Essential reading for understanding the cognitive biases that distort human judgment of probability and risk, offering insights into both individual and market irrationality.Daniel Kahneman
• The Black Swan: The Impact of the Highly Improbable ↗A provocative challenge to conventional risk models, arguing that rare, unpredictable events disproportionately shape history and markets, demanding a re-evaluation of forecasting.Nassim Nicholas Taleb
• Prospect Theory: An Analysis of Decision under RiskThe seminal paper that introduced prospect theory, revolutionising our understanding of how individuals make decisions under uncertainty by demonstrating systematic deviations from rational choice.Daniel Kahneman and Amos Tversky
• Probability Theory: The Logic of Science ↗A profound and rigorous exposition of probability as extended logic, advocating for a Bayesian approach to inference and challenging frequentist orthodoxy.E.T. Jaynes

Voices to follow

• Nassim Nicholas Taleb ↗His work on 'black swan' events and the fragility of systems has profoundly influenced thinking on risk management and decision-making under extreme uncertainty.Essayist, mathematical statistician, former options trader
• Gerd Gigerenzer ↗He champions ecological rationality, arguing for the power of simple heuristics in navigating complex probabilistic environments and improving risk communication.Psychologist, Director at the Max Planck Institute for Human Development
• Nate Silver ↗His rigorous application of statistical models to real-world phenomena, from sports to politics, offers a masterclass in probabilistic forecasting and the communication of uncertainty.Statistician, author, founder of FiveThirtyEight
• David Spiegelhalter ↗A leading voice in demystifying statistics and risk, he provides invaluable frameworks for understanding and communicating uncertainty in public discourse.Statistician, Winton Professor for the Public Understanding of Risk at the University of Cambridge

Glossary

• Certain EventA certain event is something that will definitely happen, no matter what. Its probability is 1 or 100%. For example, it's a certain event that the sun will rise tomorrow (from Earth's perspective).
• EventAn event is a specific result or a group of results that you are interested in from an experiment. It's a collection of one or more outcomes. For example, when rolling a dice, getting an "even number" (which includes 2, 4, or 6) is an event.
• Impossible EventAn impossible event is something that can never happen. Its probability is 0 or 0%. For example, it's an impossible event to roll a 7 on a standard six-sided dice.
• LikelihoodLikelihood describes how probable or likely something is to happen. It's a way of talking about the chance of an event occurring, often using words like "likely," "unlikely," or "certain." For example, it's highly likely that you will have homework tonight, but it's unlikely that it will snow in Mumbai in July.
• OutcomeAn outcome is one possible result of an action or experiment. It's what actually happens when you do something. For example, when you roll a standard six-sided dice, getting a '3' is one possible outcome.
• ProbabilityProbability is a number that tells you how likely something is to happen. It's usually shown as a fraction, decimal, or percentage between 0 (impossible) and 1 (certain). For example, the probability of flipping a fair coin and getting heads is 1/2 or 50%, because there are two equally likely sides.
• Random ExperimentA random experiment is an action or process where you know all the possible outcomes, but you can't predict exactly which outcome will happen each time. For example, flipping a coin is a random experiment because you know it will be heads or tails, but you don't know which one it will be before you flip it.
• RiskRisk is the chance that something bad or unwanted will happen, and it often involves a negative consequence. It's about the possibility of loss, injury, or other harm. For example, if you don't study for a test, there's a risk that you might fail it.
• Sample SpaceThe sample space is the list of ALL the possible outcomes that could happen in an experiment. It shows everything that could possibly occur. For example, when flipping a coin, the sample space is {Heads, Tails}. When rolling a standard dice, it's {1, 2, 3, 4, 5, 6}.
• UncertaintyUncertainty means not knowing for sure what will happen in the future. It's the state of having limited knowledge about future events or outcomes. For example, there's uncertainty about what the weather will be like next week, even with a forecast.

Threads 18

Where this connects to other fields, and why it's worth knowing.

• Does God Exist? Philosophy

  Pascal said: bet that God exists. If you're right, the reward is infinite; if you're wrong, you lose almost nothing. Even if the odds are tiny, a tiny chance times an infinite payoff still wins the bet. That weird 'multiply the payoff by the odds' move is exactly how casinos and insurance companies price everything today.

• Natural Hazards and Disaster Geography Geography

  Insurance exists because people needed to put a price on rare disasters, the once-in-a-century flood or quake. Figuring out the odds of those freak events forced people to invent the math of 'tail risk,' the rare-but-huge stuff. Now climate change is making those disasters so frequent that the math breaks and some places can't be insured at all.

• Political Philosophy Philosophy

  Philosopher John Rawls asked: design the rules of society before you know who you'll be, rich or poor, healthy or sick, behind a 'veil of ignorance.' You'd build a fair world because you might land at the bottom. That's really just buying insurance: you protect against every version of yourself, because you don't know which one you'll get.

• Planetary Boundaries Environment

  Why build a fence far back from a cliff edge instead of right at it? Because thick fog hides exactly where the edge really is. Scientists set 'planetary boundaries' the same way, giving Earth a wide safety margin, not because we'll fall at the line, but because nobody knows precisely where the true danger point sits.

• Cyber & Critical Infrastructure Global Risks

  Insurance works because car crashes are independent; yours doesn't cause your neighbor's, so payouts average out. Cyberattacks break that. One computer worm can hit millions of customers on the same day at once. When everyone fails together, the 'safety in numbers' that insurance depends on collapses, which is why cyber is so hard to insure.

• Climate Migration and Habitability Geography

  The first people to flee a climate danger zone aren't residents; they're insurance companies. Their number-crunchers quietly raise prices or refuse to cover flood-prone areas, pulling money out before a single family packs up. So the cold math of risk is the earliest warning sign that a place is becoming unlivable.

• Extreme Weather Environment

  The first group to give up on a flooding coastline isn't the government, it's the insurance company. When they decide a place is too risky to insure, the math nerds who calculate risk have basically declared it unlivable, long before anyone official says so.

• The Trolley Problem Philosophy

  The trolley problem asks if you'd sacrifice one life to save five. Governments actually answer this in spreadsheets, putting a dollar price on a human life. That number decides how many deaths a safety rule is allowed to prevent.

• Stoicism Philosophy

  A smart gambler judges a bet by whether it was a good call, not by whether it happened to win. Ancient Stoics did the same with life: imagine what could go wrong, then focus on deciding well, not on the result. Both are really the art of choosing when you can't know the outcome.

• Work, Automation & the Gig Economy Economics

  A regular job hands the boss the risk: you get the same paycheck and sick pay even in a slow week. Gig work like driving or delivery flips that, so a bad week is your problem alone. What gets sold to you as 'be your own boss, work when you want' is really the company handing you all the uncertainty it used to absorb.

• The Search for Alien Life Science

  There's a famous equation that guesses how many alien civilizations might be out there by multiplying a bunch of maybes together. If life is common, though, the silent sky becomes a warning: something keeps wiping civilizations out, a 'Great Filter,' and it might be a disaster still ahead of us, not behind.

• AI in Medicine Health

  Imagine a test that's 99% accurate for a disease only 1 in 10,000 people have. Run it on everyone and most "positive" results are false alarms. AI diagnostics do this at massive scale, tripping over the same math trap as always.

• Nuclear Energy Technology

  No private insurance company will cover a full nuclear meltdown, because the worst case is too catastrophic to price. So nuclear power only exists because governments agree to absorb that giant risk. That refusal to insure is the honest measure of how dangerous a meltdown really is.

• Startup Funding Business

  Startup investing isn't a bell curve where most bets land near average. It's a world where one giant 100x winner pays for ninety-nine total flops. So the usual advice to "spread out to stay safe" is backwards here; you're hunting for the rare monster win.

• Genetic Engineering & CRISPR Health

  Insurance works because nobody knows exactly who'll get sick, so everyone chips in and shares the risk. But once companies can read your DNA, they can price you by your personal odds. That knowledge quietly breaks the shared gamble that makes insurance possible.

• Catastrophic & Existential Risk Global Challenges

  Extreme risks expose the difference between a precise-looking number and a well-supported probability. Probability provides tools for expressing assumptions; catastrophic-risk cases test where those tools become fragile.

  Sources: Probing the Improbable ↗ · Introduction ↗

• Personal Finance & Money Skills Economics

  Investor.gov explains that spreading investments across and within asset classes can reduce concentration risk. This connects personal finance to uncertainty: outcomes depend on how assets move together, and diversification does not guarantee against loss. Risk tolerance also concerns the losses a person can withstand, not just a probability calculation.

  Sources: SEC Investor.gov — Asset allocation ↗

• Space Exploration & the New Space Age Science

  NASA’s probabilistic risk assessment guidance connects possible failure scenarios, their likelihoods and their consequences. Space missions make uncertainty tangible: engineers must distinguish a component failure from a mission-level outcome and examine assumptions behind estimates, rather than treating a single risk number as certainty.

  Sources: NASA — Probabilistic Risk Assessment procedural requirements (historical edition) ↗