all articles
Freedom of Model Building
How do scientists decide which model to use when several can fit the same data? This post follows that question through the assumptions and creative choices behind scientific models, and looks at how physical reasoning and experiments help us decide which ones deserve our confidence.
Bertrand's Paradox
What’s the probability that a random chord in a circle is longer than the side of an inscribed triangle? Surprisingly, the answer is 1/4… or 1/3… or 1/2. All are correct. Bertrand’s Paradox reveals why “random” is not a mathematical concept until you define the underlying probability measure — and why hidden modeling assumptions shape every simulation you run.
Modified Coupon Collector's Problem
This article explores the coupon collector's problem, analyzing the expected number of trials and probabilities to collect all or a fraction of distinct items, with extensions to modified scenarios and connections to combinatorics, simulations, and the philosophical Ship of Theseus
Logistic Map
This article explores the logistic map, a nonlinear difference equation capturing dynamic behaviors, including chaos, with insights into bifurcation and complex systems modeling
Logistic Growth Model
This article introduces the logistic growth model, exploring population dynamics with a carrying capacity, and compares it to a modified version with an optimal growth ratio using mathematical modeling and simulations