Scientific literature, as the major medium that carries knowledge between scientists, exhibits explosive growth in the last century. Despite the frequent use of many tangible measures, to quantify the influence of literature from different perspectives, it remains unclear how knowledge is embodied and measured among tremendous scientific productivity, as knowledge underlying scientific literature is abstract and difficult to concretize. In this regard, there has laid a vacancy in the theoretical embodiment of knowledge for their evaluation and excavation. Here, for the first time, we quantify the knowledge from the perspective of information structurization and define a new measure of knowledge quantification index (KQI) that leverages the extent of disorder difference caused by hierarchical structure in the citation network to represent knowledge production in the literature. Built upon 214 million articles, published from 1800 to 2021, KQI is demonstrated for mining influential classics and laureates that are omitted by traditional metrics, thanks to in-depth utilization of structure. Due to the additivity of entropy and the interconnectivity of the network, KQI assembles numerous scientific impact metrics into one and gains interpretability and resistance to manipulation. In addition, KQI explores a new perspective regarding knowledge measurement through entropy and structure, utilizing structure rather than semantics to avoid ambiguity and attain applicability.

No abstract

No abstract

No abstract

ChatGPT and GPT-4 have raised debates regarding the progress of knowledge in large language models 1-3. The notion of "knowledge explosion" has been controversial in various variations since the 19th century 4-8. Despite numerous indications to the contrary 9-11, conclusive evidence on knowledge growth is lacking 12. Here, we evaluated knowledge as a collective thinking structure within citation networks by analyzing large-scale datasets containing 213 million publications (1800–2020) and 7.6 million patents (1976–2020). We found that knowledge did not explode but grew linearly over time in naturally formed citation networks that expanded exponentially. Our theoretical analysis established that the knowledge never exceeds the size of the network, revealing the limitation of knowledge development. Moreover, our results showed that the knowledge expansion rate shifted at certain inflection points, implying quantitative-driven qualitative changes. Leaps near inflection points may instigate a "knowledge explosion" delusion, allowing us to reconcile the spreading of the misconception. Inflection points in knowledge growth exhibited similar characteristics to the emergent ability of artificial intelligence 13, furnishing fresh insights into the singularities and emergence in complex systems. Overall, our findings reveal a slow pace of knowledge compared to data, reacquainting us with the progress of knowledge over time.