Charles Yang

Everyone knows counting can continue forever, but of course no one actually counts forever. There must be a tipping point at which we figure out the rules for counting in our language. It has been known for decades that, strikingly, this number is around 72 for children learning English. Indeed, it is difficult to find children who can only count to, say, 75, without continuing on. By contrast, Chinese-Learning children reliably take off after counting to only about 40, usually a full year ahead of their American peers.

Learning to count is a typical example of children’s linguistic and cognitive development. While every child is unique, it is also important to recognize the systematic regularity across individuals. All children learn the rules of their language; they even make the same mistakes along the way. Every three year old will occasionally say “I goed home” instead of “I went home”, but all of them grow to know that when a new verb such as “google” enters into English, its past tense form (“googled”) is immediately available. To learn a language is to derive the rules for infinitely varied expressions from finite experience. To count to infinity is the same process: children must discover the pattern for infinite numbers from a finite sample: 72 to be precise.

Ever since my days as a computer science student at MIT, I have been fascinated by the regularity, uniformity, and apparent ease with which children learn languages. Such an accomplishment is only possible if the child’s mind is a machine, one capable of robustly detecting the patterns of language. And if the mind is indeed like a machine, we should be able to develop simple and mathematically precise principles to understand it. To figure out the machinery of child language learning has been the primary focus of my research, which integrates methods and insights from linguistics, computer science, psychology, and neuroscience. These days I am a Professor of Linguistics and Computer Science at the University of Pennsylvania where, as the Director of the Cognitive Science Program, I have also enjoyed helping hundreds of students develop their own interdisciplinary coursework and research. I have written several books, including most recently The Price of Linguistic Productivity: How Children Learn to Break the Rules of Language (2016 MIT Press), which won the Linguistic Society of America’s Leonard Bloomfield Award.

The Guggenheim Fellowship will support a new line of research exploring how children learn to count and how they develop the conceptual understanding of numbers. It turns out that the tipping points of 72 for English, and 40 for Chinese, are predicted by a simple mathematical principle that I have established for child language learning: the Chinese advantage can be precisely characterized by its simpler counting system. I plan to study children’s counting in several additional languages with varying degrees of numerical complexity, including American Sign Language where counting is done by hands but also follows linguistic rules. In particular, I will investigate the hypothesis that learning the rules of number formation in language leads children to understand that there are infinitely many natural numbers, and that the next number is exactly one greater than the previous one (Peano Axioms). This research may provide a concrete account for the relation between language and mathematics, which has intrigued scientists and philosophers for centuries.