https://signal-and-syntax.com/categories/applied-modeling-and-simulation/Recent content in Applied Modeling and Simulation on Signal & SyntaxHugoen-usWed, 01 Apr 2026 06:00:00 -0700https://signal-and-syntax.com/posts/minimal-transformer/Wed, 01 Apr 2026 06:00:00 -0700https://signal-and-syntax.com/posts/minimal-transformer/In 2017, Vaswani et al. published “Attention Is All You Need,” a paper that quietly rearranged the entire landscape of machine learning. It introduced the Transformer architecture — a design that has since become the backbone of every major language model you’ve heard of: GPT, BERT, Claude, Gemini, and dozens of others. The paper’s title was a provocation. Attention mechanisms already existed. The claim was that you could throw out recurrence entirely and let attention carry the whole load.https://signal-and-syntax.com/posts/edmund-fitzgerald/Sun, 30 Nov 2025 06:00:00 -0700https://signal-and-syntax.com/posts/edmund-fitzgerald/Originally appearing on his 1976 album, Summertime Dream, “The Wreck of the Edmund Fitzgerald” is a powerful ballad written and performed by folk singer Gordon Lightfoot . In 1976, the song hit No. 1 in Canada on the RPM chart, and No. 2 in the United States on the Billboard Hot 100. The lyrics are a masterpiece, but there was one specific line that always stood out to me: “The lake, it is said, never gives up her dead.https://signal-and-syntax.com/posts/birthday-paradox/Fri, 28 Nov 2025 06:00:00 -0700https://signal-and-syntax.com/posts/birthday-paradox/You generate a UUID. It’s 128 bits total, with 122 bits of randomness ( Davis et al., 2024 ). That’s 340 undecillion possible values. Collision-proof, right? Your system generates a million IDs per second. Still safe? What about a billion? As I like to say, common sense and intuition are the enemies of science. Common sense tells you that with 340,000,000,000,000,000,000,000,000,000,000,000,000 possible values, you’d need to generate at least trillions before worrying about duplicates.https://signal-and-syntax.com/posts/safe-distance-in-traffic/Thu, 23 Oct 2025 09:00:00 -0700https://signal-and-syntax.com/posts/safe-distance-in-traffic/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.https://signal-and-syntax.com/posts/thermo-water-energy-balance/Sun, 12 Oct 2025 09:00:00 -0700https://signal-and-syntax.com/posts/thermo-water-energy-balance/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.https://signal-and-syntax.com/posts/five-second-rule/Thu, 04 Sep 2025 06:00:00 -0700https://signal-and-syntax.com/posts/five-second-rule/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 ( Dawson et al., 2007 ; Miranda & Schaffner, 2016 ). 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.https://signal-and-syntax.com/posts/meeting-diet/Thu, 28 Aug 2025 05:00:00 -0700https://signal-and-syntax.com/posts/meeting-diet/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? The good news: math can help. By modeling your schedule as a 0/1 knapsack problem with two constraints ( Kellerer et al., 2004 ), you can treat meetings like items with value, time cost, and energy cost.https://signal-and-syntax.com/posts/three-d-packing/Wed, 20 Aug 2025 09:00:00 -0700https://signal-and-syntax.com/posts/three-d-packing/My first full-time programming job was for Holiday on Ice, an international ice show. While I focused mainly on back office systems such as accounting, itinerary, and box office reporting, I knew that one of the biggest technical challenges faced by the show’s crew was efficiently loading trucks for the next city. One day, the controller asked me if I could code a system that took, as input, the trucks’ 3D dimensions and the 3D dimensions (and weight) of every object to be packed.https://signal-and-syntax.com/posts/rain-paradox/Mon, 18 Aug 2025 09:00:00 -0700https://signal-and-syntax.com/posts/rain-paradox/Early in my programming career, I came across a coding challenge that stuck with me for many years: At the time, I didn’t have the skillset or tools to simulate the problem properly. It became one of the first exercises that nudged me toward a lifelong fascination with modeling the real world through code. The problem wasn’t about recursion or memory management. It was about getting wet, and how fast you move through falling rain.