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A mathematical model for the process of accumulation of scientific knowledge in the early modern period

Maryam Zamani
Hassan El-Hajj
Malte Vogl
Holger Kantz
Matteo Valleriani

August 25 , 2023

In the present work, we model the diffusion of scientific knowledge embodied in the textbooks of the Sphaera corpus. This corpus consists of more than 350 different editions of textbooks used for teaching astronomy in European universities during the early modern period. Connections between the editions are based on mutual semantic knowledge and are arranged in a multiplex network of four layers, with each layer representing a different semantic relation. The modeling aims for a better understanding (and possible prediction) of the process of knowledge accumulation in the various editions. We consider semantic text-parts as knowledge units transferred between the editions, and show how these units spread using both an SI model and its modified version, the Bass model. Both models include a parameter representing the rate of transfer, which is interpreted as the mechanism underlying the process of knowledge accumulation; the Bass model has an extra parameter that represents the rate of external influence and stands out as the “resistance to adoption from” and “resistance to be influenced by” other knowledge systems. The modeling has helped us to chart the path and mechanisms of knowledge transformation in the early modern period. Networks are identified by adding further layers whose graphs express socioeconomic relationships and conditional sub-networks. The comparison between the model and these layers enables us to conclude that the accumulation of knowledge was highly dependent on the institutional embedding of scientific production because the diffusion of knowledge was mostly determined by the economic constraints of early modern printers and publishers. It further suggests that geographic proximity played a role—although secondary—in the diffusion of knowledge but only under the condition that the book producers involved were still living. The transformation of early modern scientific knowledge is, therefore, highly dependent on the institutional and economic contexts of the book producers.