Standing mathematics · living · standard
Probability as a number between 0 and 1
A probability may be written from 0 to 1 or 0% to 100%. Frequentist and Bayesian readings are not identical. This walk uses both carefully and does not collapse them.
Sources
A forecast is a claim. So is a pattern. Here is where the claims rest.
Jacob Bernoulli and later probability · 1713– · primary
Law of large numbers
Sample proportions tend to settle near a true probability under the right conditions. A short run need not look balanced. Independent trials do not remember.
Probability and computing · living · standard
Randomness, streaks, and computer simulation
Random-looking sequences contain clumps. This app’s live draws use a cryptographic browser source when available. Automated tests use a seed. Computer output is simulated, not a proof of physical randomness.
Statistics and cognitive science · living · survey
Pattern seeking and coincidence
Minds notice structure. Multiple opportunities make coincidences common. A pattern is a hypothesis to test with comparison, base rates, and questions asked before looking.
National weather services · living · standard
Probability of precipitation
Public rain chances are conditioned on place, time window, model, and current evidence. Definitions vary. The 30%-of-the-area shortcut is not a universal law.
Gregor Mendel · 1866 · primary
Experiments on Plant Hybridization
Pea seed color is a classic simple trait. The fractions belong to that model. They do not describe a whole person.
Modern genetics · living · standard
Many genes, development, and environment
Most human traits are not one-gene Punnett squares. Inheritance is not destiny. Family is not reducible to genetics.
Rutherford, Soddy, and nuclear physics · 1902– · primary
Half-life as ensemble behavior
Half-life describes a large group. The next individual decay is not announced. This app’s field is a labeled simulation, not a procedure.
Thomas Bayes, Pierre-Simon Laplace, later statistics · 1763– · primary
Updating a belief with new evidence
Prior, likelihood, posterior. A good prediction is allowed to change. Calibration asks whether 30% days behave like 30% days.
Edward N. Lorenz · 1963 · primary
Deterministic nonperiodic flow
A tiny change in starting numbers grew into a different later weather in a deterministic model. Chaos is not a synonym for randomness.
Dynamical systems · living · standard
Sensitive dependence on initial conditions
Nearby starts can separate in some nonlinear systems. Small differences do not always grow. A poetic butterfly must still tell the truth.
Decision science · living · standard
Risk is more than likelihood
Chance, consequence, uncertainty, time, and values. Probability informs a choice. It does not make the choice. Expected value is a long-run model average, not a moral score.