3 "Probability" Posts

How Large Language Models (LLMs) Read Code: Seeing Patterns Instead of Logic

Oct 6, 2025 • Categories: AI & The Mathematics of Language, • Tags: #AI, #LLMs, #probability, #tokenization

Developers are accustomed to thinking about code in terms of syntax and semantics, the how and the why. Syntax defines what is legal; semantics defines what it means. A compiler enforces syntax with ruthless precision and interprets semantics through symbol tables and execution logic. But a Large Language Model (LLM), reads code the way a seasoned engineer reads poetry, recognizing rhythm, pattern, and context more than explicit rules.

“When an AI system ‘understands’ code, it is not executing logic; it is modeling probability.”

The Five-Second Rule Explored with Math & Python

Sep 4, 2025 • Categories: Applied Modeling & Simulation, • Tags: #physics, #Python, #probability, #simulation

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.

Should You Walk or Run in the Rain? The Puzzle That Sparked a Passion

Aug 18, 2025 • Categories: Applied Modeling & Simulation, • Tags: #modeling, #physics, #probability, #Python

To walk or to run. That is the question. Early in my programming career, I came across a coding challenge that stuck with me for many years: “If it’s raining, will you stay drier by walking or running through it?” 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.