Fall 2005

Why Ask Why?: An Interview with Alison Gopnik

The origin of the idea of chance in children

Courtney Stephens and Alison Gopnik

In 1975, five years before his death, the psycholo­gist Jean Piaget published together with Bärbel Inhelder The Origin of the Idea of Chance in Children, the first major work in developmental psychology to discuss prediction, probability, and randomness as tenets of intelligence.[1] In it, Piaget posited a multi-stage developmental process that turned four- and five-year-old determinists into twelve-year-old probabilists. During the first stage, before the age of seven or eight, a child cannot distinguish the possible from the necessary, so that there is essentially no conceptual room between what could be and what is. In the second stage, from eight to eleven, children begin to detect the presence of fortuitous combinations and arrangements in the outcomes of events. This intuition starts to complicate their former conviction that the world runs along a set order in chained reaction. By age twelve and onward, the idea of a fixed design has been essentially replaced by a footing in probability, as children come to understand that chance phenomena cannot always be modeled, whereas mechanical causality is an intrinsically traceable process. At this final stage, the young person understands that most things that occur in their world are a synthesis of fortuitous distribution, random mixture, and construction. For Piaget this understanding was the climax of an instinctive maturation process that both conveyed a crisp, coherent vision of human development and also echoed the linearity of civilizing progress. Since its time of publication, Piaget’s schema has been found to greatly underestimate and simplify children’s comprehension of chance. Alison Gopnik is a professor at the University of California, Berkeley, who studies related questions of early causal understanding. Borrowing from artificial intelligence models such as Causal Bayes Nets,[2] Gopnik and her contemporaries have found intricate and more generous ways of modeling child intelligence as it relates to chance.[3] Her research on early theory formation is based on the idea that children are not merely undergoing a blind and innate growth process, but are actively and scientifically inquiring into chance and similar ideas starting from a much younger age than Piaget imagined.[4] Courtney Stephens spoke with Gopnik by phone in June 2005.

Cabinet: In Piaget’s work from the 1970s, he likens the way children develop causal understanding to a larger narrative of progress in which the child’s mind stands for the uncivilized, pre-modern mind and a more complex grasp of chance and probability signals the departure to the modern, scientific mind. Has that idea continued to inform the direction of this kind of research?

Alison Gopnik: I think that idea is exactly the perspective that has changed over the last thirty years. The conventional wisdom indeed was exactly that there existed these primitive modes of thought that were shared by women, people in far-off places, and children—that was one end of the spectrum of thought, and at the other end were scientists who were, of course, the peak of rationality and sophistication and reasoning, with statistics being one of the most recent accomplishments in the sciences. What’s happened over the last thirty years is that we’ve increasingly realized that even the very youngest children are already, at least unconsciously, doing some of the same kinds of computations and calculations and kinds of reasoning that even the most sophisticated scientists are doing. So the old great chain of thinking from the primitive to the sophisticated doesn’t seem to be right any more. There probably is a difference in how explicit, how conscious, we are in our reasoning process. So we think that much of what children are doing they’re doing unconsciously, while what scientists are doing they’re doing more self-reflectively and thoughtfully. But the actual ways of thinking, the ways of reasoning, seem to be quite similar.

Could you talk about chance and what these broad stages of causal development are?

We know that even the very youngest children, as young as two months old, already pay attention to differences in the probability of events. Certainly by eight months they’re sensitive to the difference between whether a result follows something all the time, or only follows it some of the time. They seem to be able to discriminate between something leading to something else with varying likelihood. By the time they’re two-and-a-half, we know that they can translate that kind of information into conjectures about causation. So if they see one thing following another all the time but something else that only follows in a particular context, say when a third article is present, then they can translate that into a set of causal information. And we know by the time they’re four years old, they really grasp probability—for example, if you show them a machine where placing different colored blocks on it makes it light up two-thirds of the time for one color block and one-third of the time with the other, they’ll say that the block that made it light up two-thirds of the time is stronger, has more special stuff in it, makes it go better than the one that only does it one-third of the time.[5]

Do the youngest children seem to start with a fixed philosophy on chance?

It’s a complicated story. We don’t know for sure whether children are objectivists or subjectivists about probability. In philosophy, there are two classical approaches to thinking about probability. One is to think that there’s actually something intrinsically chancy or random going on in the world, which is the idea of objective probability. This holds that some things just are intrinsically probabilistic, intrinsically random. The other idea is that things in the world really are not random, they really are not chancy, but that they’ll always look chancy to us observers because there are so many other factors involved. That’s the notion of subjective probability, the idea that it’s just the way our minds are, that even if things are indeed deterministic in the world we can never see them that way, there will always be too many intruding factors that are going to make things look random. So, if we want to find out about the world, we’ll have to think in terms of probabilities, not because that’s necessarily the way the world works, but because that’s the way minds work when they go out into the world. We don’t know whether children are objective probabilists, or whether they are more subjective probabilists; whether chance is, to them, a fact of how things work, or whether they think that the world is simply far too complicated and noisy and so you have to use probability.

Piaget seemed to think that children would always assume hidden factors, even when things appeared random.

There’s some evidence for that. Laura Schultz and I have done work where three-year-olds were presented with a mechanical device, and it only worked part of the time, not all the time. Then she showed them something that was hidden in the device. The children assumed a relationship between failure and the hidden object. In fact, they seemed to be looking for hidden causes as though they were determinists. But the important thing was that they weren’t confused about probabilities; they were subjective probabilists. But, of course, that example was an example of a physical machine, which you usually expect to be deterministic. When we told them that some of the machines simply worked better, that they had more special stuff, they did understand that more or less special stuff would translate to correlative functionality. They seemed to be more willing to treat probabilities objectively in that case. A very crucial area that we don’t really know the answer about is the psychological case. When you have a machine, everyone will expect them to function deterministically, including philosophers. But what about watching two people interact? Some people have suggested that children might think about people genuinely interacting probabilistically, that it might be a sign of what makes people different from other things, that you can’t just manipulate people all the time. The psychologist John Watson has suggested that that might be how we actually identify people. But an interesting alternative suggestion is that maybe that’s part of why we think that people have minds inside of them, that we actually see them behaving probabilistically, when as children we are more deterministic. We think, “This person is behaving unpredictably, there must be something going on in their head.”

This really torments our solipsism.

Yes, exactly.

Is there any precedent for the miraculous in early childhood or is that more or less an acquired concept?

Well, there’s some very interesting research that’s been done on children’s understanding of things like magic. It’s a little hard to tell what they think. By the time they’re three or four, they have a concept of magic, but they treat it as a way of bracketing off things that don’t fit their causal understandings of the world. The traditional wisdom was, “Oh, the primitives, the children, women, they don’t understand the causal connections between things; so they just think that something is similar to something else and simply link the two through magic.” Another way of thinking about it, which seems to be closer to the way children think, is that they have a great deal of causal knowledge as far as physics, biology, and psychology go; they know all about how growth and inheritance work, how everyday physical events and psychology work. And when they come across something that doesn’t fit what they know, not unlike adults, they say, “Well okay, there’s evidence for this, I don’t understand it, it doesn’t fit into my causal framework, and I have this category that I’m going to call magic, which are things that seem to be true, seem to be happening, but don’t fit what I think about the causal nature of the world.”[6]

And what about false belief, when children have to undergo the process of being wrong, of having their causal inferences completely rejected. In one of your papers, you give children a candy box, but it’s filled with pencils and they seem to retroactively revise their expectations.

Yes, well, the interesting thing is from the time children are very little they are revising and changing their beliefs in the light of new evidence, but they don’t seem to know that’s what they’re doing. In that experiment, we showed the children the candy box full of pencils; the children then changed their minds about what could possibly be inside, but they didn’t realize they’d changed their minds. This is what psychologists call meta-knowledge, knowledge about knowledge, which seems to be something that is slightly delayed relative to functioning.

Does surprise, which most children love so much, factor into this learning process?

We know that surprise and interest are emotions that seem to motivate children from the time they’re little babies. There is a revolutionary technique called habituation in which you show the baby something it doesn’t expect, and even tiny babies, two-month-olds, will look very long at things that are unexpected and novel, seemingly very motivated to find out what’s going on. They seem to have these kinds of emotions of surprise and curiosity and intense interest. By the time they’re two or three years old, those emotions are probably the most overwhelming, driving motivation they have—so much so that they put themselves at mortal peril for the sake of figuring out the causal structure of the world. Parents have given this the technical term “getting into everything.” So in fact surprise and curiosity seem to not only be there from the time they’re born, but they seem in some ways to be the overwhelming motivation and emotion for babies and certainly for preschoolers through school-age period. They’re looking out in the world, trying to find causal and other kinds of patterns, looking for violations of those patterns, trying to makes sense out of these violations.

And this peaks in the why-question cycle.

Right, Henry Wellman did these wonderful studies where he looked at childrens’ spontaneous language.[7] It turns out there’s a database that has all these recordings of children just talking to their parents, going back to the time they begin speaking. So you can go back and search the database for what children are talking about in everyday conversation. It turns out that as young as you can test them, they’re talking about why things happen. By the time they’re two or three, they’re asking why questions all the time. And they’re giving explanations, they’re giving causes all the time. They’re using grown-ups to find out. They’re doing scientific research long before they get near a school.

And does emotion react to or compliment these cognitive developments?

Well, these cognitive emotions, as it were, seem to be very powerful and strong, even in very young children. It’s funny—it’s again part of this great chain of thinking where there’s reason, which is this hard, cold thing that adults do, and then there’s emotion and magic which is what children and women do. But after all, curiosity and joy in figuring things out are just as powerful emotions as love or desire or any other kind of emotion, and in fact those emotions seem to be in children from very early on. They seem to be driving forces for figuring out what’s going on in the world in the way that lust is a driving force for reproducing. I wrote a paper once called “The Explanation Is Orgasm,” where I argued that the wonderful emotion of “a-ha!” and figuring out how the world works was to cognition as orgasm is to reproduction, a way nature has of telling you “Okay! Keep going! You’re on the right track! You’re headed for the truth! You got it!” Now, in both cases, if you had to wait to find out whether you were right or not, it would be too late. You don’t want to wait to see if these things will turn out well in the long run—whether I’m going to reproduce or get to the moon; nature instead thinks to say, “This is great! Just keep at it. This feels wonderful! You got it!” and then, of course, it turns out that this helps you get to the moon or cure cancer or make fire or hunt mastodons or all those other things. Children are the blue-sky R & D branch of the human species. They’re the ones who don’t have to do any marketing or management or put anything to any kind of applied use—they just get to sit there, blissfully calculating, figuring out what reality looks like and why it does what it does. And this impulse for knowledge, whatever form it takes, seems to be the real triumph over chaos and randomness. So it’s sort of comforting that our search for order is not necessarily a mechanism of adult culture, but a very fundamental nature of the mind.

We regret that this article originally failed to credit Bärbel Inhelder as the co-author of The Origin of the Idea of Chance in Children.
  1. Jean Piaget and Bärbel Inhelder, The Origin of the Idea of Chance in Children, trans. Lowell Leake Jr., Paul Burrell and Harold D. Fishbein (New York: Norton, 1975).
  2. Bayes Nets are probabilistic graphical models that are used specifically to represent uncertainty and complexity. For more information about Bayes Nets, see http://www.cs.ubc.ca/~murphyk/Bayes/bnintro.html.
  3. Alison Gopnik et al, “A theory of causal learning in children: Causal maps and Bayes Nets,” Psychological Review, vol. 111, no. 1, (2004), pp. 1–31.
  4. For papers that elucidate Gopnik’s “theory theory,” see Gopnik, “The theory theory as an alternative to the innateness hypothesis,” in L. Antony and N. Hornstein, eds., Chomsky and his Critics (Oxford: Blackwells, 2003).
  5. See Alison Gopnik & Laura Schulz, “Mechanisms of theory-formation in young children,” Trends in Cognitive Science, vol. 8, no. 8, (2004), pp. 371–377.
  6. Vivian Gussin Paley, a former kindergarten teacher, has done innovative writing on children and magic, among other subjects. See her A Child’s Work: The Importance of Fantasy Play (Chicago: University of Chicago Press, 2004).
  7. See Karen Bartsch and Henry M. Wellman, Children Talk about the Mind (Oxford: Oxford University Press, 1995).

Alison Gopnik is professor of psychology at the University of California at Berkeley. In addition to over 100 academic articles, she has written for the New York Times, the New York Review of Books, the Guardian, and the Times Literary Supplement. She is also the author of The Scientist in the Crib: What Early Learning Tells Us about the Mind (HarperCollins, 1999) and the forthcoming How Children Change the World: The New Science of Discovery, Imagination and Transformation (Houghton Mifflin).

Courtney Stephens is an assistant editor at Cabinet.

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