The Recurring Case of 'Recursion': a pattern for making sense of the world

Some call it "self-similarity." Others define it vaguely as "wheels within wheels" or refer to the image of nesting Russian dolls. For such a fundamental concept, recursion is strangely less famous and more often overlooked than it deserves to be. With help from a cognitive scientist, a language expert, and a physicist, Paul Kennedy tries to remedy this state of affairs, without getting himself tied up in knots within knots within knots…

People are fascinated to see the same thing on multiple levels, says author

Recursion is a pattern found anywhere, from the branches of trees to the branches of mathematics, even in broccoli florets. (Dan Kitwood/Getty Images)
Listen to the full episode53:59

** This episode was originally published on June 20, 2019.

It runs across cultures, through science, mathematics and art. It's as common as the branches on a tree or the layers of a Russian doll — but it's also vital to the way humans think and communicate: it's 'recursion', or what some scientists call 'self-similarity.'

"It's important because some people think it defines our species," says Michael Corballis, of the University of Auckland.

"One has to be a little bit in awe of how it evolved," Corballis adds.

He sees the recursive process as key to our journey from simple organisms to complex creatures with infinite possible thoughts.

Recursion involves nesting a structure within another structure, or embedding one sequence inside another, whether it's a sequence of words, events, or physical objects.

A spiral staircase in Nantes, France represents recursion — a sequence inside a sequence inside a sequence... (Loic Venance/AFP/Getty Images)

It's one way to describe how almost any type of progress or evolution occurs.

"You start with a primitive creature not much more than a molecule in a mud swamp... and you've invented this extraordinarily complicated organism that's capable of bringing the world into its own head and manipulating it."

Corballis argues the amazing results of recursion — and the difficulty understanding how it works — leads some people to attribute our existence to a deity.

Beneficent spiral

Research at Newcastle University points to a possible source for a particular recursive ability in the human mind: our skill at conceiving of the minds of others.

"What we suggest is that the hemispheres of the brain, as they become very different from one another in function, and take on different jobs … in a sense, we get the hemispheres acting as parallel mirrors," says Rachael Bailes, a cognitive scientist who studies evolutionary linguistics.

"If my left hemisphere can represent my right hemisphere, it can also represent yours," Bailes adds. "That's when things take off in this beneficent spiral of representing others."

Cognitive scientist Rachael Bailes points out how a simple desire to refer to a nearby laptop could prompt complex, recursive descriptions. 1:06

Bailes suggests the prompt for this development in our evolution might be tool use, which led to humans becoming more right-handed or left-handed, unlike other primates.

Recursive predictability

Geoffrey West is a theoretical physicist and the author of Scale: the Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life in Organisms, Cities, Economies, and Companies. He believes that recursion is ubiquitous across natural and human society.

He points out how details such as the length of a creature's aorta, the number of offspring it produces, and its lifespan — and many other aspects of its internal structure — follow a set of rules with predictable results.

Artist Yayoi Kusama's infinity mirrored room called, Let's Survive Forever. (Yayoi Kusama/Maris Hutchinson, EPW Studio/AGO)

"Despite the fact that the whale lives in the ocean and a giraffe has a long neck and mice scurry around… they are [to a great extent] scaled versions of one another," says West.

He explains that the networks on which living creatures are based all need to solve the same problems of filling space and using energy efficiently.

"The structure that most reflects that is in fact this recursive, self-similar structure," West says. "It's no accident that almost all the networks that sustain life have this self-similar property."

Source of delight

Aside from its importance in biology, art, music, computing, and more, recursion is also important as a source of delight.

Douglas Hofstadter, author of Gödel, Escher, Bach: An Eternal Golden Braid, notes the long-standing popularity of toys such as Russian dolls, which bring joy to children by hiding smaller versions of an object inside larger ones.

"Any kind of struck or nested inside another structure is something that humans have always found amusing," Hofstadter says.

"It's not something that I think would amuse a dog. I don't think a dog would be particularly amused by Russian dolls but children are. There's something about the human makeup that finds it charming and fascinating to see the same thing on multiple levels."

Guests in this episode:

  • Rachael Bailes teaches cognition and evolutionary linguistics at Newcastle University. Her work includes studying mirror neurons and 'meta-representation' in human brains.

  • Michael Corballis researches language and the brain at the University of Auckland. He is the author of The Recursive Mind: The Origins of Human Language, Thought, and Civilization.

  • Douglas Hofstadter directs the Center for Research on Concepts and Cognition at at Indiana University. His first book was Gödel, Escher, Bach: an Eternal Golden Braid, published in 1979. More recent work includes I Am a Strange Loop.

  • Geoffrey West is the author of Scale: The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life in Organisms, Cities, Economies, and Companies. He is a former president of the Santa Fe Institute.

** The episode was produced by Mark Dance, with help from Tom Howell.