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No Coincidence, George: Capacity-Limits as the Curse of Compositionality

In one of the most influential articles in cognitive science, George Miller (1956) describes his “persecution” by similarities in three cognitive capacity-limits: the number of items that can be held in short-term memory, the number of stimuli that can be ordinally ranked, and the number of items in a visual display that can be quickly and accurately reported. Although Miller wondered whether these limits owe to a common source, he ultimately concluded that the likeness was coincidental. Here, we challenge that conclusion. Cognitive systems face a tradeoff between maximizing the number of possibilities they can represent (maximizing entropy), and precisely fitting the data observed thus far (minimizing energy). Equipping a cognitive system with an inductive bias to maximize entropy on different timescales enables one of the hallmarks of cognitive function— efficient generalization— but leads to the limits in information processing that haunted Miller.