  Language is hierarchically organized: words are built into phrases,
sentences, and paragraphs to represent complex ideas. Here we ask whether the
organization of language in written text displays the fractal hierarchical
architecture common in systems optimized for efficient information
transmission. We test the hypothesis that the expositional structure of
scientific research articles displays Rentian scaling, and that the exponent of
the scaling law changes as the article's information transmission capacity
changes. Using 32 scientific manuscripts - each containing between three and 26
iterations of revision - we construct semantic networks in which nodes
represented unique words in each manuscript, and edges connect nodes if two
words appeared within the same 5-word window. We show that these semantic
networks display clear Rentian scaling, and that the Rent exponent varies over
the publication life cycle, from the first draft to the final revision.
Furthermore, we observe that manuscripts fell into three clusters in terms of
how the scaling exponents changed across drafts: exponents rising over time,
falling over time, and remaining relatively stable over time. This change in
exponent reflects the evolution in semantic network structure over the
manuscript revision process, highlighting a balance between network complexity,
which increases the exponent, and network efficiency, which decreases the
exponent. Lastly, the final value of the Rent exponent is negatively correlated
with the number of authors. Taken together, our results suggest that semantic
networks reflecting the structure of exposition in scientific research articles
display striking hierarchical architecture that arbitrates tradeoffs between
competing constraints on network organization, and that this arbitration is
navigated differently depending on the social environment characteristic of the
collaboration.
