by Michael C. Corballis
Recursion is a concept most commonly encountered in programming. It’s a little tricky to understand; you could describe it as “self-nesting”. One example might be a Photoshopped image of a man holding a photograph of him holding the photograph of him holding the photograph…
In programming, a recursive routine is one that calls itself with different parameters; the routine calls itself to do a calculation that calls itself to do a calculation that calls itself… In the case of programming, the routine must have some way of determining when it has drilled deep enough down through enough recursive layers to reach the bottom; otherwise, it will keep recursing until it runs out of memory to hold all the intermediate states.
But it this book is about the use of recursion inside the human mind. That shows up most obviously in language, in phrases like this:
The butcher who gave the meat to the dog that chased the cat that had killed the mouse that had eaten the grain that the butcher’s wife had bought from the shop two doors down from the butcher’s shop.
It’s quite a mouthful, but although you can’t hold the whole thing in your head, you can easily see the nesting structure. That’s linguistic recursion.
We also use recursion when we carry out certain social calculations, such as this:
I would like to tell Jane that I saw Tom kissing Mary, but Tom knows that I saw him kissing Mary, so if Jane yells at Tom about kissing Mary, Tom will be mad at me.
It is interesting to ask how many levels of recursion the human mind can handle. This issue has been researched and the result is that we can all easily handle three levels of recursion; four levels is a little difficult; and five levels is about as much as most people can handle. As always, there are exceptions to these generalizations.
Mr. Corballis maintains that recursion is something that humans are especially good at, a talent that puts them far ahead of most other mammals. There are some examples of mammals demonstrating a little ability to handle recursion one level deep, but that’s as far as they can go.
At the most fundamental level, mental recursion is the ability to assess a situation from a different point of reference. It is based on a neural structure called mirror neurons. These structures are what make you flinch when you see another person hit his thumb with a hammer. They are quite complex in structure and very powerful in implication. When you see another person hit his thumb with a hammer, you create a mental homonculous inside your head, a kind of simulation based on your own person. When the other guy lifts the hammer, the mental homonculous lifts its hammer, and, because it’s based on your own body, you “feel” your imaginary arm lift the hammer. When the guy hits his thumb with the hammer, your mental homonculous feels pain — the same pain that you would feel if you hit your thumb with the hammer. You can say, “I feel your pain” with perfect honesty. You really are feeling the same kind of pain, although not with as much intensity.
At the higher emotional level, we call this ‘empathy’, but in fact it operates at many different levels. When we learn how to throw a ball by watching somebody else throw a ball, we’re using mirror neurons. We learn to speak by listening to other people speak and mimicking their actions — through use of mirror neurons. These mirror neurons are everywhere in our brains and they allow us to understand the world more perceptively than would be the case with normal direct sensation.
This is the neural basis of recursion. Our brains say, in effect, “If I hit my thumb with a hammer the way he did, I would feel pain.” We have our mental model of ourselves, and we can plug into that mental model what we see happening to others.
What makes it so powerful is our ability to apply this process in nested fashion. We can think thoughts like this:
He thinks that I think that he is not as smart as I am, so he will try to trip me up to show that he’s smarter than I am.
This entails me putting myself in his shoes, putting himself back in my shoes.
Sadly, Mr. Corballis does not address mirror neurons in anywhere near the depth I have just described them. He acknowledges their role, but doesn’t say much more. Instead, his book is an extensive examination of human mental recursion from many different angles. It describes recursion very well, but does little to explain it.
Mr. Corballis is an excellent writer; his prose is crisp and clear, and he has a wonderful sense of humor. I wish I could write as well as he does.