Filling holes in science draws collective attention, but most higher-order holes remain unexplored

Abstract

Much scientific discovery involves filling holes between ideas and arguments that unleash techno-scientific advance. Representing knowledge as high-dimensional concept embeddings, we use persistent homology to detect holes of increasing order, from gaps between disconnected ideas to higher-order cavities, and identify the research works that fill them. We find two empirical asymmetries. Researchers who fill anticipated holes are poised to draw collective attention by staging outsized novelty and foresight, indicating that bridging holes anticipates where science will converge, most strongly in empirical fields and least in formal and design fields. Yet as knowledge grows, higher-order holes explode while the fraction science fills collapses, leaving most higher-order combinations unexplored. These results call for a richer science of holes, and mark a frontier where contemporary AI might help fill the high-dimensional gaps human science opens.