The book Wait, I Want to Tell You A Story by Tom Williams is a perfect opportunity to explore recursion. In the story one animal wants to prevent himself from being eaten by telling his predator a story about another animal who attempts to do the same thing, and so on and so on. The story also seemed to me like a good time to talk about math and the order of operation. Things in brackets are like the little stories that must be completed before you can eat the storyteller.
There is a book Zoom by Istvan Banyai that has no words, only pictures and each picture shows how the picture previous is but a tiny part of a larger picture. I don’t have the book in front of me so I can’t remember exactly how it goes but one scene might turn out to be the scene through the window of a different room, and then zoomed out again you see that the window is part of a picture on the cover of a magazine in the next scene, which is being read by someone who is part of a television scene being watched by someone else. Is that recursion, I wondered? Are the scenes inside one another like those of Tom Williams? They are both about something inside something inside something and so on, but what it means to be inside is slightly different. The “where” is different. One of them is about physical things (though the book takes them beyond the possible – no picture could have so much detail that if you zoomed in you could see such a world inside it) and the other is about stories. Where are stories located? Where do they exist?
There is an Elephant and Piggie Book by Mo Willems called I Broke My Trunk. In it Elephant is telling Piggie a fantastic story about all the feats he did with his trunk and Piggie waits excitedly wondering which of these feats is going to explain the broken trunk. Eventually Piggie is surprised to hear that the trunk was broken while Elephant tripped running to tell Piggie the story of those feats. There’s a shift of frames, a zooming out. The story of the feats isn’t the story of him breaking his trunk, its the story inside the story of him breaking his trunk. I think the humor comes partly from this shift in framework.
Do stories exist outside of being told? Where do stories exist anyway? I made up a little graphic about stories within stories, and then I think suddenly that none of those stories really exist within each other. The illustration is not of how the stories exist but rather how they fit together in the landscape of my imagination.
Thinking about recursion also makes me think about limits. What are the limits to what we can draw? Could you draw a picture of someone watching television where inside the television someone is reading, and you can see the picture on the book? There’s a basic physical limit to how small a drawn line can get, and thus how much of a picture a person can fit into a small space. A recursive picture on a wall could probably hold more layers than a recursive picture on a single sheet of paper. The Zoom book works by having separate pictures on different pages, so although the pictures suggest they fit together they don’t really. The one picture isn’t really inside the other, except inside the viewers imagination.
Do computers allow us to get around the physical limits? A scale of the universe webpage can help us see scale in a way that is challenging outside of the computer. Yet at the same time it doesn’t, because suddenly everything is the size of a computer screen and when you scroll out the tiny things cease to exist on the screen anymore than they exist on the later pages of the Zoom book. What are these images anyway? An orange circle that represents a dwarf star is still just an orange circle. Yet they can become something within our imaginations. They can help to shape the scale of our imaginary landscapes.
If physical illustrations pose a problem because of the thickness of a line (whether on computer or paper) are there limits to how many recursions work in a story? How many stories within stories can we tolerate before we just become confused? In some ways stories within stories are like the Zoom book not really within one another but put together in the landscape of our imaginations. They aren’t really inside of one another, they’re just a jumble of words strung together to make stories and the stories are linked, but we have to create the shape of them. We have to imagine them and too many recursions gets too confusing to keep clear in my mind.