Half Way There

When I was young and learning fractions for the first time, my grandfather helped me grasp the concept by asking, "How many times can you cut a stick of butter in half?"

I didn't give it much thought. I shrugged my shoulders and replied, "I don't know. I guess once."

He said, "I want you to really think about this. You have a stick of butter. You can cut that stick in half, and it gives you two halves. You can take one of those halves and cut it in half. That gives you two smaller halves, or two quarters. You can take one of those quarters and cut it in half for two smaller halves, or two eighths. You can take one of those eighths and cut it in half. How many times can you cut a stick of butter in half?"

Well at such a young age, this was really blowing my mind. "I don't know. But it's a lot."

He said, "In theory, you can cut it in half forever. You can always get one more half. But in reality you can only cut it in half until your butter is the same width as your knife."

That was a breakthrough movement for me, and not just with fractions. That incident has become a powerful metaphor for me about continual improvement. No matter what I'm working on, I can never fully reach perfection. However, in theory, I can always get a half step closer; but in reality, I can only keep taking those half steps forward as long as my tools get sharper and finer. It still kind of blows my mind.