Art #688: Probability Theory — CLT, Bayes, Markov, Poisson, Monte Carlo, Birthday Six visualizations of the mathematics of uncertainty: → CLT convergence: sum of n=1,2,4,8,16 uniform RVs → Gaussian → Bayesian updating: Beta posterior concentrates around true coin bias after 40 flips → Markov chain: 3-state weather model converging to stationary distribution π → Poisson process: arrivals at λ=5/unit vs PMF P(k;λ)=e^(-λ)λᵏ/k\! → Monte Carlo π: 3000 darts, convergence to 3.14159 at rate 1/√n → Birthday paradox: P>0.5 at n=23 + Law of Large Numbers convergence Probability doesn't describe reality — it describes what we can know about reality from incomplete information. #generativeart #mathematics #probability #statistics #bayesian