Mathematics is much more than the manipulation of numbers. At its best, it involves simple, clear examples of thought so apt to the world we live in that those examples provide guidance for our thinking about problems we meet subsequently. We call such examples, capable of heuristic use, POWERFUL IDEAS, after Papert (1980). This article documents a child's introduction to a specific powerful idea in a computer environment. We trace his extensions of that idea to other problem areas, the first similar to his initial experience and the second more remote from it.