Scaling of Atypical Knowledge Combinations in American Metropolitan Areas from 1836 to 2010

abstract

Cities are epicenters for invention. Scaling analyses have verified the productivity of cities and demonstrate a superlinear relationship between cities’ population size and invention performance. However, little is known about what kinds of inventions correlate with city size. Is the productivity of cities only limited to invention quantity? I shift the focus on the quality of idea creation by investigating how cities influence the art of knowledge combinations. Atypical combinations introduce novel and unexpected linkages between knowledge domains. They express creativity in inventions and are particularly important for technological breakthroughs. My study of 174 years of invention history in metropolitan areas in the US reveals a superlinear scaling of atypical combinations with population size. The observed scaling grows over time indicating a geographic shift toward cities since the early twentieth century. The productivity of large cities is thus not only restricted to quantity but also includes quality in invention processes.

Key words:

• cities
• invention
• historic patent data
• scaling analysis
• atypical knowledge combinations

Acknowledgments

I would like to thank Tom Broekel for very helpful comments and fruitful discussions. Special thanks also to Pierre-Alexandre Balland, David Rigby, Kerstin Schäfer, and Timo Kleiner for additional comments. The author used R for numerical simulations and data visualizations. Especially the EconGeo package by Balland (2017) was helpful. It also provides the z-score function to compute the z-scores.

Notes

¹ I used Wikipedia because it offers data for the entire 174 years of observation. I compared the population size for the most recent years with official data sources, such as www.census.gov, finding no differences.

² As a robustness check, I also used the CPC class level (three digits) showing that results are independent of the technological resolution (see Appendix B).

³ I also applied a twenty-year rolling window approach in which the history of knowledge combination washes out over time; see Figure A1 in Appendix A. The cumulative and the rolling window approach correlated on average at a high level, with 0.9 < R < 1.

Additional information

Funding

This work was supported by The Ministry of Science and Culture of Lower Saxony [76ZN 1503].