Psychological experiments and cognitive-science models have grounded an appealing narrative about how the understanding of language arises in infants, beginning with innate perceptual abilities, continuing with "statistical learning" and categorization, and ending with word learning and glimmers of syntax. This story has virtues: longstanding empirical backing, analogues in adults and animal learning, and plenty of computational models. But the story may be wrong, and wrong for interesting reasons, only some of which are properly scientific. I will lay out new results that suggest a different way to pursue the understanding of early language development, in which we focus less on abstract cognitive capacities, and more on relating specific, quantitative measurements of infants' environments to specific outcomes.