8 "Applied Modeling and Simulation" Posts

Real-world problems explored through mathematics, modeling, simulation, and code. These posts use specific problems as a way to develop broader techniques for reasoning about complex systems.

The Wreck of the Edmund Fitzgerald: Modeling Decomposition in Extreme Environments

How cold, pressure, and buoyancy explain why Lake Superior may never give up her dead
What You'll Learn
  • Why bodies normally resurface after a drowning
  • How cold water dramatically slows decomposition
  • How water pressure compresses decomposition gases at depth
  • How temperature, pressure, and buoyancy interact in Lake Superior
  • How Python can model whether a body will ever surface
  • Why the Edmund Fitzgerald’s depth creates an extreme preservation environment

The Birthday Paradox in Production: When Random IDs Collide

Why collision risk grows faster than intuition suggests, and what that means for IDs, hashes, and distributed systems
What You'll Learn
  • Why collisions happen long before an ID space is full
  • Why collision risk grows much faster than intuition suggests
  • How the birthday paradox applies to computer systems
  • How to calculate the probability of an ID collision
  • Why the square root of the ID space determines the danger zone
  • How 32-bit, 64-bit, and UUID v4 IDs compare
  • How generation rate changes the time until collisions become likely
  • How to choose an acceptable collision risk for a real system
  • How Monte Carlo simulation can validate collision calculations
  • How to predict when an ID strategy needs to be replaced

Rethinking the Three-Second Traffic Rule: When Physics Says It’s Not Enough

Using kinematics and Python to test when a familiar following-distance rule stops being safe
What You'll Learn
  • Why a three-second following gap can be adequate in some situations but dangerously short in others
  • How reaction time and braking distance combine to determine the minimum safe following gap
  • Why higher speeds require more than a fixed three-second buffer when the lead car stops instantly
  • How dry, wet, and icy roads change the amount of time a following driver needs to stop
  • How kinematics can turn a familiar driving rule into a mathematical model
  • How Python can simulate and visualize safe following times across speeds and road conditions