https://signal-and-syntax.com/tags/probability/Recent content in Probability on Signal & SyntaxHugoen-usWed, 24 Dec 2025 12:00:00 -0800https://signal-and-syntax.com/posts/temperature-top-p-creativity-knobs/Wed, 24 Dec 2025 12:00:00 -0800https://signal-and-syntax.com/posts/temperature-top-p-creativity-knobs/Every API call to ChatGPT , Claude , or any other LLM includes two parameters most people either ignore or tweak randomly: temperature and top-p. The defaults work fine for casual use, so why bother understanding them? Because these two numbers fundamentally control how your model thinks. The temperature value determines whether the model plays it safe or takes creative risks while the top-p value decides how many options the model even considers.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/how-large-language-models-read-code/Mon, 06 Oct 2025 09:00:00 -0700https://signal-and-syntax.com/posts/how-large-language-models-read-code/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. The difference may seem subtle, but it has vast consequences.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/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.