That and also why start with multiplication? String concatenation, addition, list concatenation all make more intuitive sense to a working programmer.

What's a straightforward way to combine a bunch of numbers? Just keep multiplying them to get a resulting volume in an ever-higher dimensional space.

The working programmer might be interested in the series on ropes on the Xi Editor website[1] as a practical application, as it motivates the concept as it goes. (Alternatively, if you’ve taken an algorithms class you have probably encountered the idea of computing things over an interval of an array by storing them in for each node of a tree that flattens to that array, such as a search tree or interval tree.)

[1] https://xi-editor.io/docs/rope_science_00.html