When you type “I love programming” into ChatGPT, you might assume the model reads three words. It doesn’t. It reads somewhere between three and seven tokens, depending on how the text is split.

When you ask Claude to count the letters in the word “strawberry,” it often gets it wrong. The reason is simple. Claude never saw the word “strawberry” as a complete unit. It saw tokens like "str", "aw", "berry" and tried to reason about letters it couldn’t directly access.

And when early GPT-3 users discovered that typing “SolidGoldMagikarp” caused the model to behave erratically - generating nonsense, refusing requests, or producing bizarre outputs - the culprit wasn’t the model’s training. It was a glitch token: a tokenization artifact that never appeared in training data, leaving the model with no learned representation for how to handle it ( Rumbelow & Watkins, 2023 ).

“To a language model, text isn’t a stream of words. It’s a sequence of tokens. The way those tokens are created determines what the model can and cannot understand.”

When you have a long conversation with a large language model (LLM) such as ChatGPT or Claude , it feels like the model remembers everything you’ve discussed. It references earlier points, maintains consistent context, and seems to “know” what you talked about pages ago.

But here’s the uncomfortable truth: the model doesn’t remember anything. It’s not storing your conversation in memory the way a database would. Instead, it’s rereading the entire conversation from the beginning every single time you send a message.

“A context window isn’t memory. It’s a performance where the model rereads its lines before every response.”

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.”

When you interact with a large language model (LLM) such as ChatGPT or Claude , the model seems to respond instantly relative to the question’s degree of difficulty. What’s easy to forget is that every word it predicts comes from a long history of learning where billions of gradient steps have slowly sculpted its understanding of language.

Large language models don’t memorize text. They optimize it. Behind that optimization lies calculus. I’m not referring to the calculus you did with pencil and paper. I’m talking about a sprawling, automated version that computes millions of derivatives per second.

At its heart, every LLM is a feedback system. It starts with random guesses, measures how wrong it was, and then adjusts itself to be slightly less wrong. The word “slightly” in this context is the essence of calculus.

“Each gradient step represents a measurable reduction in error, guiding the model toward a more stable understanding of language.”