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All animals learn. But only human beings create scientific theories, mathematics, literature, moral systems, and complex technology. And only humans have the capacity to acquire such culturally constructed knowledge in the normal course of immersion in the adult world.

There are many reasons for the differences between the minds of humans and other animals. We have bigger brains, and hence more powerful information processors; sometimes differences in the power of a processor can create what look like qualitative differences in kind. And of course human beings also have language–the main medium for the cultural transmission of acquired knowledge. Comparative studies of humans and other primates suggest that we differ from them as well in our substantive cognitive abilities– for example, our capacity for causal analysis and our capacity to reason about the mental states of others. Each of these factors doubtless contributes to our prodigious ability to learn.

But in my view another factor is even more important: our uniquely human ability to ‘bootstrap.’ Many psychologists, historians, and philosophers of science have appealed to the metaphor of bootstrapping in order to explain learning of a particularly difficult sort– those cases in which the endpoint of the process transcends in some qualitative way the starting point. The choice of metaphor may seem puzzling–it is self-evidently impossible to pull oneself up by one’s own bootstrap. After all, the process I describe below is not impossible, but I keep the term because of its historical credentials and because it seeks to explain cases of learning that many have argued are impossible.

Sometimes learning requires the creation of new representational resources that are more powerful than those present at the outset. Early in the cultural history of mathematics, for instance, the concept of the number included only positive integers: with subsequent development the concept came to encompass zero, rational numbers (fractions), negative numbers, irrational numbers like pi, and so on. . . .