Here, according to the Spelke lab, are some of the things that babies know, generally before the age of 1:

They know what an object is: a discrete physical unit in which all sides move roughly as one, and with some independence from other objects.

“If I reach for a corner of a book and grasp it, I expect the rest of the book to come with me, but not a chunk of the table,” said Phil Kellman, Dr. Spelke’s first graduate student, now at the University of California, Los Angeles.

A baby has the same expectation. If you show the baby a trick sequence in which a rod that appears to be solid moves back and forth behind another object, the baby will gape in astonishment when that object is removed and the rod turns out to be two fragments.

“The visual system comes equipped to partition a scene into functional units we need to know about for survival,” Dr. Kellman said. Wondering whether your bag of four oranges puts you over the limit for the supermarket express lane? A baby would say, “You pick up the bag, the parts hang together, that makes it one item, so please get in line.”

Babies know, too, that objects can’t go through solid boundaries or occupy the same position as other objects, and that objects generally travel through space in a continuous trajectory. If you claimed to have invented a transporter device like the one in “Star Trek,” a baby would scoff.

Babies are born accountants. They can estimate quantities and distinguish between more and less. Show infants arrays of, say, 4 or 12 dots and they will match each number to an accompanying sound, looking longer at the 4 dots when they hear 4 sounds than when they hear 12 sounds, even if each of the 4 sounds is played comparatively longer. Babies also can perform a kind of addition and subtraction, anticipating the relative abundance of groups of dots that are being pushed together or pulled apart, and looking longer when the wrong number of dots appears.

Babies are born Euclideans. Infants and toddlers use geometric clues to orient themselves in three-dimensional space, navigate through rooms and locate hidden treasures. Is the room square or rectangular? Did the nice cardigan lady put the Slinky in a corner whose left wall is long or short?

At the same time, the Spelke lab discovered, young children are quite bad at using landmarks or décor to find their way. Not until age 5 or 6 do they begin augmenting search strategies with cues like “She hid my toy in a corner whose left wall is red rather than white.”

“That was a deep surprise to me,” Dr. Spelke said. “My intuition was, a little kid would never make the mistake of ignoring information like the color of a wall.” Nowadays, she continued, “I don’t place much faith in my intuitions, except as a starting place for designing experiments.”

These core mental modules — object representation, approximate number sense and geometric navigation — are all ancient systems shared at least in part with other animals; for example, rats also navigate through a maze by way of shape but not color. The modules amount to baby’s first crib sheet to the physical world.

“The job of the baby,” Dr. Spelke said, “is to learn.”