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

Recent research suggests that scientific discovery often involves bridging conceptual gaps, or 'holes,' between existing ideas. While filling anticipated lower-order holes garners significant attention and indicates where scientific convergence is likely, the vast majority of more complex, higher-order conceptual gaps remain unexplored despite the growth of knowledge. This highlights a strategic imbalance in how research attention is allocated.

Why it matters

This analysis reveals a fundamental dynamic in research and development: while filling immediate, identifiable knowledge gaps is crucial for progress and recognition, the neglect of more complex, higher-order 'holes' represents a significant missed opportunity. Understanding this imbalance is vital for guiding future research funding, innovation strategies, and fostering truly transformative breakthroughs.

Key insights

• Scientific discovery is conceptualized as filling 'holes' between ideas and arguments.
• Using persistent homology, the study identifies holes of increasing complexity, from simple gaps to higher-order cavities.
• Researchers who fill anticipated lower-order holes tend to attract collective attention due to their perceived novelty and foresight.
• Bridging these lower-order holes indicates potential areas of scientific convergence, particularly in empirical fields.
• Despite knowledge expansion, the number of higher-order holes grows rapidly, while the proportion of these complex gaps being filled decreases significantly.

Source

arXiv — Computers and Society — https://arxiv.org/abs/2608.28822