How many times can you cut a stick of butter in half?

When I was first learning fractions, my grandfather asked me a fairly simple question, “How many times can you cut a stick of butter in half?”

Knowing that somehow this was a trick question, I paused and hesitantly said, “Once.”

He further explained, “I want you to really think about this. You have a stick of butter. You cut it in half, and you have two halves. Take one of those halves, cut it in half, and you have two smaller halves or quarters. Take one of the quarters and cut it in half, and you have two even smaller halves or eighths. You can take one of those eighths and cut it in half. Now, really think about this. How many times can you cut a stick of butter in half?”

At such a young age, this was blowing my mind. I shrugged and answered, “A lot.”

He pushed on, “I want you to really think about this. In theory, you can cut that stick of butter in half forever, but in reality, you can only cut that stick up butter in half until you get to a point where the butter is as wide as the knife.”

That lesson has stuck with me over the years and become an illustration of how constant improvement works. In theory, you can always get a half step closer to perfection, yet never fully reach it; but in reality, you can only keep improving as long as your tools are sharper than the needed gains.