Geometric Signatures of Scientific Revolutions
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A companion to the paper

Geometric Signatures of Conceptual Reorganization: A Counterfactual Embedding Framework for Detecting Scientific Revolutions

We represent the text of scientific papers as numerical vectors, called embeddings, that allow us to compare their semantic similarity.

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How the comparison works
Observed and counterfactual geometry through timeTwo labeled point clouds compare the observed field with the same retained papers after the target papers are removed. An arrow labeled delta of t connects the observed and ablated centroids. The comparison is repeated across rolling time windows.Observed field at time tTarget concept includedRemovetarget papersCounterfactual field at time tTarget concept removed

Observed field at time t

Target concept included

Remove target papers

Counterfactual field at time t

Target concept removed
Observed centroidAblated centroid

Repeat across rolling time windows

t − 1tt + 1
Within successive time windows, we compare the organization of these representations with and without the papers associated with a selected concept. This lets us examine how that concept's contribution to the field changes over time. The crosses mark average positions (centroids), and the arrow shows their difference, Δ(t). The positions shown here are illustrative.

01 / The premise

Can we detect conceptual reorganization in scientific literature?

Scientific advances can change how ideas relate to one another. We developed a method to investigate these changes using scientific papers from physics, mathematics, and machine learning.

02 / Key findings

What we found.

Across five historical case studies, we find different patterns of conceptual reorganization, with special relativity providing the clearest benchmark. The results also show why identifying the papers associated with each concept matters: assignment errors can produce an apparent signal.

The paper presents the method and case-study results. The supplementary material provides additional figures, robustness checks, and source data.

Read the complete argument in the manuscript

03 / Supplementary analyses

Supplementary material

Additional robustness checks, assignment figures, null tests, and source data are collected in one supplementary section.

Open supplementary material