In thinking about progress, I was immediately attracted to the process of analyzing the progress we have made in order to predict the behavior of things to come.

In mathematics, this process is called induction. The basic outline of induction is this: To prove that a property holds for all values, first show it holds for a base case (the smallest value the property can be applied to). Next, assume it holds up to an arbitrary value n. The final step is to prove that it holds for n+1. If you can do this, you can show that the property holds for any valid value.

Similarly, we can look at the common elements of the past and see which remain as we progress through time. By an inductive analysis, we can make strong cases for what elements we will see in the future.

This piece represents the process of induction and its strong ties to progress in the natural world.