Babies are just gurgling, screaming, dribbling, vomiting, defecating blobs of flesh and bone. Toddlers are not much more interesting, while small children in general are thick and ignorant.

Not an unusual portrait of babies and toddlers but, it turns out,one that does them something of an injustice. We know this in part through the research of Alison Gopnik, professor of cognitive science in the University of California at Berkeley and author of among other books, The Philosophical Baby.

Her experimental work — and the work of others — has shown that babies are intensely conscious creatures, and that babies and toddlers have a basic understanding of the laws of physics and develop an early sense of morality. They’re also reasonably adept statisticians.

Here’s a description of one experiment conducted by Professor Gopnik. It involved a so-called blicket detector. A blicket detector is a box which lights up and plays music when certain objects are put on top of it. Kids love it. What Gopnik and her collaborators did was place one of two blocks on the blicket detector. The two blocks had different colours, one red, the other blue. They arranged it so that, for example, if the red block was put on the blicket detector three times it would light up twice, while if the blue block was put on the blicket detector six times, it would still only light up twice.

Then toddlers— aged just 24 months — were given a choice. They had to select a red or blue block to place on the blicket detector. And, showing a rudimentary grasp of statistics, they tended to choose the red block.

Toddlers, Gopnik believes, also read the minds of others much earlier than it was once thought. Understanding that other people have a perspective different from one’s own is a basic stage of development. To demonstrate how early this happens, an experimenter, in front of a toddler, screwed up her face and said “yuk” when shown crisps and smiled and “mmmm” when shown raw broccoli. She then asked toddlers for some food. Fourteen-month-old toddlers usually gave the experimenter crisps — which they would have chosen for themselves. But 18-month-old toddlers would give the experimenter the raw broccoli; they understood that the adult had different desires to their own. And they wanted to make that adult happy.

Given her background, it was perhaps not a great surprise that Alison Gopnik became a scholar. She and her five siblings grew up in a Philadelphia household where intellectual enthusiasm was, as she puts it, “idiosyncratically intense”. On camping holidays, this rather weird high-culture family read 18th-century novels out loud to each other and when the children put on a play they chose the 18th century The School for Scandal by Sheridan. They moved for a period to Montreal, where her father was an English professor at McGill University and her mother, a linguistics professor. Her younger siblings include the head of the National Academy of Sciences ocean studies board; a Near Eastern archaeologist; and the Washington Post art critic. Her brother, Adam Gopnik, is a renowned New Yorker writer.

Gopnik describes her family as “proud — and, indeed, practically religious — atheists”. Her grandfather came from a shtetl in Ukraine and, after moving to Philadelphia, set up a deli, specialising in smoked fish. Her great-grandfather on her mother’s side was the first rabbi to return to Portugal since the inquisition. In more up-to-date family news, her son has recently opened a successful Jewish deli in Berkeley. As she told the JC, “In spite of secularisation, the twin Jewish traditions of study and intellectual life, and smoked brisket and chicken soup, have been entwined in my life.”

David Edmonds is the host of the BBC’s Big Idea on which Alison Gopnik has been a guest.