Law of the iterated logarithm

The law of the iterated logarithm (LIL) is a fancy term that explains something important about numbers that keep changing over time.

Imagine you have a toy car, and you want to know how far it can move every time you push it. Sometimes it might move a little, and other times it might move a lot. The LIL helps us understand how much it's likely to move over time by looking at how the car's movement changes over and over again.

Here's the complicated part: The LIL says that as you keep looking at the car's movement over longer and longer stretches of time, you'll eventually be able to predict exactly how far it will move on average. This prediction will get more and more accurate the longer you watch the car move.

This might sound confusing, but it's actually really important for things like stock prices or weather patterns. If we can use the LIL to better understand how these numbers change over time, we can make better predictions about what they'll do in the future.

So, in summary, the law of the iterated logarithm explains how we can use patterns in numbers that change over time to make better predictions about what they'll do in the future.