Fractals and Vectors

My sister and I have always been fascinated by physics. And between my college physics courses and her reading books by people like Carl Sagan and Stephen Hawking, we can usually come up with a reasonably scientific explanation for most physical phenomena. But every once in a while we come across something that defies explanation (to us, anyway). And when that happens, we always have the same response: “It’s fractals and vectors!” Anything we describe as “fractals and vectors” is beyond our comprehension.


Ryan has been studying physics in his own baby way of late. He’s discovered that balls rolls down a ramp but blocks don’t. He’s discovered that balls and things with wheels can be rolled back and forth between people. And just this morning he discovered that if he throws one of his stacking rings at the floor hard enough, it bounces. He spent twenty minutes throwing rings at the floor and curiously watching them bounce. Sometimes they would bounce directly back at him. Sometimes they would bounce away from him. Sometimes they would land on their sides and roll a few inches or even a few feet. And each time, he would pick the ring up, study it intently for a moment, wave it in the air a few times, and then bounce it off the floor once again. His curiosity was mixed with puzzlement. I could imagine him wondering, “Why does it sometimes come back and sometimes roll away?” And they I could imagine him deciding, “Oh! It must be because of fractals and vectors!”

At this stage in his life, everything must seem like fractals and vectors to him. He can’t possibly understand yet that round things roll and square things don’t. He hasn’t made the connection that sometimes he slips on the floor because he’s wearing socks and sometimes he sticks because his feet are bare. He hasn’t figured out that gravity is what makes him fall on his bottom when he lets go of the furniture, or what makes his toys fall on the floor when he lets go of them. He doesn’t have any idea why grabbing onto a book that’s sitting on the couch doesn’t stop him from falling over but grabbing onto the couch itself does. So many things that are easily explainable by an adult are a complete mystery to him.

And yet, I can tell that he’s slowly putting the pieces of the puzzle together. He’s no longer surprised that blocks don’t roll down the slide, or that the ball bounces off the wall when he pushes it, or that when he drops his toys they fall to the floor. He doesn’t understand why quite yet, but he does understand that things behave in repetitive, predictable ways. And that’s the beginning of understanding why they do what they do. For now, it’s enough. It’s fractals and vectors!