4 "Simulation" Posts

While researching why car insurance rates are so extremely high in Las Vegas, I started thinking about the three-second rule and its validity. As I’ve always heard, the three-second rule refers to how far you should be behind a car in traffic. The idea is that you pick out a fixed roadside marker and you are supposed to pass that marker at least three seconds after the car in front of you. That rule is simple enough, yet deceptively deep once you unpack the physics.

“Three seconds is a rule of thumb. Physics reveals the truth.”

Every summer, it feels like a small miracle when the pool finally warms up enough to swim. In Nevada, where the air temperature can sit above 100°F (38°C) for weeks, you’d expect the water to keep pace. Yet, somehow, it takes forever to warm, and only a few cool nights can undo all that progress.

The same phenomenon shows up in a stick of butter. Butter melts quickly, while margarine stays stubbornly firm even under the same heat. That’s not coincidence; it’s thermodynamics.

The butter versus margarine comparison is a staple example in nutrition science. It shows how the proportions of fat, water, and solids affect how much energy it takes to change temperature. Butter, with more fat and less water, heats up and melts quickly. Margarine, full of water and unsaturated oils, absorbs more energy before softening because water’s specific heat is much higher.

“A pool in the desert and a stick of margarine in the kitchen both tell the same story: water resists change.”

You know the story: drop a cookie on the kitchen floor, swoop in before five seconds are up, and declare it safe. It is comforting. It is also wrong.

“Germs don’t wait five seconds. They start the party the instant your food hits the floor.”

The truth is much more interesting than the myth. Germs do transfer gradually, but they are especially fast at the beginning. That means if you want to know whether your floor-cookie is still edible, you need to think in curves, not in timers. And curves are something we can model.

Every week your calendar fills with more meeting invites than you can reasonably handle. Which ones are worth the time and energy, and which should you politely decline? What if there was a way to quantify that choice?

“Your calendar is a knapsack. Every meeting takes space, but only some add enough value to justify carrying them.”

The good news: math can help. By modeling your schedule as a 0/1 knapsack problem with two constraints , you can treat meetings like items with value, time cost, and energy cost. Classic optimization techniques then help decide which meetings to attend. In this post, we’ll walk through framing the problem, prompting AI to scaffold the code, and running a simulation to visualize your optimal “meeting diet.”