Biological systems often detect species-specific signals in the environment. In humans, speech and language are species-specific signals of fundamental biological importance. To detect the linguistic signal, human brains must form hierarchical representations from a sequence of perceptual inputs distributed in time. What mechanism underlies this ability? One hypothesis is that the brain repurposed an available neurobiological mechanism when hierarchical linguistic representation became an efficient solution to a computational problem posed to the organism. Under such an account, a single mechanism must have the capacity to perform multiple, functionally related computations, e.g., detect the linguistic signal and perform other cognitive functions, while, ideally, oscillating like the human brain. We show that a computational model of analogy, built for an entirely different purpose-learning relational reasoning-processes sentences, represents their meaning, and, crucially, exhibits oscillatory activation patterns resembling cortical signals elicited by the same stimuli. Such redundancy in the cortical and machine signals is indicative of formal and mechanistic alignment between representational structure building and "cortical" oscillations. By inductive inference, this synergy suggests that the cortical signal reflects structure generation, just as the machine signal does. A single mechanism-using time to encode information across a layered network-generates the kind of (de)compositional representational hierarchy that is crucial for human language and offers a mechanistic linking hypothesis between linguistic representation and cortical computation.