Imagine you have a “depth-finding” boat and you need to locate the deepest point in a large lake. For our purposes, the lake is divided into squares.
Let’s also say you have limited time and fuel, so you can’t afford to scan the entire lake today.
One approach is to measure the depth of one square, then check if any adjacent squares are deeper. You keep moving from square to square until all surrounding squares are shallower than your current square, at which point you’ve identified a local deepest point (a square deeper or equal to all its neighbours). This is a pretty good algorithm for getting a quick, “probably good enough” answer, especially if the lake is simplistic
However, if the lake’s bottom is complex, that locally deepest square may not actually be the deepest point in the lake. There could be lake features that hide deeper areas elsewhere. It’s entirely possible there’s a deeper spot, but this algorithm can’t determine whether it exists. And so it short circuits to an answer.
This serves as a useful mental model for understanding some of the limitations LLMs face today. With unlimited resources and time, the answer could be much more precise, but it doesn’t have that luxury and so it valiantly tries for good enough.
This is adapted from a more detailed explanation using Lake Tahoe as an example in The AI Conundrum.