CMP Review 2025-05-22

May 22, 2025

In 1782 Pierre-Simon Laplace published a paper describing an integral that can be used to transform one function into another. His focus was on probability theory, but his transform was picked up in 1893 by Oliver Heaviside who saw that it could be used to solve differential equations encountered in electrical engineering. Thanks to Heaviside, the Laplace transform is part of the standard curriculum for modern engineers.

I got caught up in this story when my eldest son was taking his last pure math class in college. I was following along with him so I could answer his questions and support his learning. It was hard for me to grasp but something intrigued me about it. An 11-year-old was around and overheard the many and incidental conversations around the house about the Laplace transform.

This 11-year-old was my youngest son, and he wanted to know what it was all about. But I explained to him that math is sequential. I said that there were many, many things he had to learn first. But that someday, if he worked very hard, I might be able to share with him what I know about the Laplace transform — if he hadn’t graduated from homeschool by then.

Lesson after lesson, hour after hour, week after week, this boy worked. Years passed and he became a teenager and then a young man. He never tired, he never grew weary, because math was his favorite subject. His interest never lagged.

Finally, he completed every prerequisite. He reached his goal and calculated his first Laplace transform last week. Not with a sketchy understanding but with a firm grasp based on a solid foundation.

Some experts out there issue stern warnings about Charlotte Mason. They say she was an idealist and that her ideas will not work in the real world. It will only lead parents to frustration. Love of knowledge is not enough motivation for a child to learn, they say. Some other motivation must be called into play. Rewards. Marks. Prizes. That’s the way things work. Charlotte Mason, they say, is just telling a fairy tale.

In one sense they are right. Charlotte Mason did tell me a fairy tale. I believed it. And it came true.

@artmiddlekauff