Figuring Out

Abstract

The paper focusses on the spread of Hindu-Arabic arithmetic among European practitioners. The analysis is based on an original database recording detailed information on over 1200 practical arithmetic manuals, both manuscript and printed. This database provides the most detailed reconstruction available of the European tradition of practical arithmetic from the late 13th to the end of the 16th century. The paper argues that studying this spread makes it possible to open a perspective on a progressive transmission of ‘useful knowledge’ from the ‘commercial revolution’ to the ‘little divergence’. Focussing on the transmission of practical arithmetic allows to stress the role of skills and human capital in pre-modern European economic development. Moreover, it allows to reconstruct a progressive transmission, from the Mediterranean to the Atlantic, of a ‘practical knowledge’ which eventually contributed to major developments in European ‘theoretical knowledge’.

L’economia della conoscenza: innovazione, produttività e crescita economica nei secoli XIII-XVIII / The knowledge economy: innovation, productivity and economic growth, 13th to 18th century

“…Interestingly, practical arithmetic spread progressively from the south to the north of Europe not following the main routes of international trade, but through an inland network based on proximity. The key channels for this transmission were master-pupil relationships and the migration of skilled people (Danna 2021;. The foundation of practical arithmetic schools also followed this path.…”

“…Following its origins in the 13 th -century Mediterranean, practical arithmetic spread to the rest of the European continent. The evidence extant on the publication of practical arithmetic manuals shows that the spread of this mathematics followed a south-to-north axis, with northern European countries adopting this mathematical knowledge well into the 16 th century (Danna 2021;. This evidence suggests that there may also have been a continuity in the diffusion of advanced business methods between the commercial revolution and the little divergence.…”

The spread of Hindu-Arabic numerals among practitioners in Italy and England (13th-16th c.): two moments of a European innovation cycle?

“…Following its origins in the 13 th -century Mediterranean, practical arithmetic spread to the rest of the European continent. The evidence extant on the publication of practical arithmetic manuals shows that the spread of this mathematics followed a south-to-north axis, with northern European countries adopting this mathematical knowledge well into the 16 th century (Danna 2021;2022). This evidence suggests that there may also have been a continuity in the diffusion of advanced business methods between the commercial revolution and the little divergence.…”

“…Interestingly, practical arithmetic spread progressively from the south to the north of Europe not following the main routes of international trade, but through an inland network based on proximity. The key channels for this transmission were master-pupil relationships and the migration of skilled people (Danna 2021;2022). The foundation of practical arithmetic schools also followed this path.…”

“…It has been argued that it is possible to identify a continuous spread of Hindu-Arabic numerals from the commercial revolution of the 13 th century to the little divergence of England and the Low Countries (Danna 2022;2021). In this paper, I expand on this hypothesis by investigating the diffusion of advanced commercial practices and of other forms of practical knowledge in the initial and final contexts of this process.…”