Spreading Out Across Expanding Idea Space

Over nearly two centuries, US inventions have become increasingly dissimilar: not just fewer head-to-head collisions between inventors, but growing distance between neighboring inventions. We document this secular decline in similarity using validated neural language models applied to the full text of claims in over 11 million US patents (1836–2023), corroborated by a 98% decline in patent interference rates, a measure of independent simultaneous invention. Measuring this correctly requires validation, since different representations of the same patent text can yield opposite conclusions about whether inventions are converging or spreading out. Our validation framework, the first systematic comparison for patent text, selects among these representations. We develop a spatial competition model in which inventors choose locations in idea space. The model explains spreading out and connects it to several independently documented patterns — rising R&D investment per inventor, increasing patent values, weakening knowledge spillovers, and declining research productivity. The mechanism is spatial; as inventors spread out to capture new territory, inventions become more valuable but also more costly for others to absorb. In doing so, the model turns spillover intensity, innovation step size, and research productivity from fixed primitives into outcomes of inventor positioning. A calibrated decomposition attributes roughly 40% of the long-run decline in US research productivity to these spatial forces, alongside traditional explanations such as fishing out and the burden of knowledge. Where inventors stand relative to each other in idea space matters as much for growth as how many of them there are.