Does 2x bigger mean 2x better?

Piotr Migdał (ICFO, Castelldefels (Barcelona), Spain), http://migdal.wikidot.com/en

Summary

• Scaling, power laws $x = c y^\beta$
• Scaling in nature
  • Walking speed, jump height, why only small animals can walk on the ceiling
  • Kleiber's law: relations between: body weight, metabolic rate, lifespan, heart rate
• Cities
  • GDP, patents, crime, infrastructure vs population
  • Virtues (e.g. supercreative workers) and vices (e.g. crimes) scale superlinearly
• Efficiency of universities and research groups
  • The bigger institute, the higher % of supportive workers
  • Research group efficiency grows rapidly up to a critical size
• Group problem solving

Further reading

• Metabolic rate and Kleiber's Law
• Resting heart rate and life expectancy in mammal (plot)
• P.W. Anderson, More Is Different Science (1972) vs http://xkcd.com/435/
• L. Bettencourt, G. West, A unified theory of urban living, Nature (2010), paywall :/
• L. Bettencourt et al., Growth, innovation, scaling, and the pace of life in cities, PNAS (2007)
• L. Bettencourt et al, Urban scaling and its deviations: revealing the structure of wealth, innovation and crime across cities, PloS one (2010)
• Cosma Rohilla Shalizi, Scaling and Hierarchy in Urban Economies, arXiv:1102.410 [stat.AP]
• B. Jamtveit, E. Jettestuena, J. Mathiesena, Scaling properties of European research units, PNAS (2009)
• J. Mathiesena, B. Jamtveit, K. Sneppen, Organizational structure and communication networks in a university environment, arXiv:1006.4652, PRE (2010)
• R. Kenna, B. Berche, Critical mass and the dependency of research quality on group size, arXiv:1006.0928, Scientometrics (2010)
• R. Kenna, B. Berche, The extensive nature of group quality, arXiv:1004.3155, Europhysics Letters (2010)
• P. Migdał, M. Denkiewicz, J. Rączaszek-Leonardi, D. Plewczynski, Information-sharing and aggregation models for interacting minds, arXiv:1109.2044 (shameless self-advertisement)