Uncertainty propagation

Imagine you have a toy car that you want to push across the room. You know that the car is going to move, but you don't know exactly how far it's going to go. Maybe you'll push it harder than last time, or maybe there's a bump in the carpet that will slow it down. That's what we call uncertainty - we can't be sure exactly what will happen.

Now let's say you have a tool that you can use to measure how far the car moves. Maybe it's a ruler or a tape measure. You can use this tool to make a guess about how far the car will go, but your guess also has some uncertainty. Maybe you accidentally measured the wrong distance or the tool isn't very precise.

Uncertainty propagation is a way of figuring out how much uncertainty will be in something based on all the uncertain things that contribute to it. In our example, the distance the car moves has uncertainty because of how hard you push it and the bumpy carpet, and the measurement tool has uncertainty because of how accurately you can measure. Uncertainty propagation helps us figure out how much uncertainty there will be in the result - how far the car actually moved - based on all these different factors.

This can be really important in a lot of areas of science and engineering, like calculating how much weight a bridge can support or predicting the weather. We can use uncertainty propagation to figure out how confident we can be in our calculations and make decisions based on that confidence.