增长、创新、规模标度及城市节奏

Growth, Innovation, Scaling and the Pace of Life in Cities

一直以来，城市被认为是社会创新和创富的最有力引擎，然而城市也同时是犯罪、污染和疾病的主要来源地。城市化这一不可阻挡的世界趋势向人们提出了一项紧迫挑战：需要构建出一套关于城市组织及可持续发展的定量预测理论。本文所提供的经验证据表明，城市化与经济发展和知识创新联系过程具有普遍性，不仅仅适合于属于同一城市体系的城市，而且不同国家、不同阶段也遵循这一规律。城市的许多不同属性，从专利产出、个人收入到电缆长度等，都显示出是人口规模的幂律函数，其规模标度指数G在整体上分成了几类。反映财富创造和创新属性的β≈1．2〉1（收益递增），而代表基础设施属性的β≈0．8〈1（规模经济）。本文预测，城市中社会生活节奏会随着人口规模的加大而加快，这和已有数据相吻合。文中还讨论了城市如何与生物有机体相似或相异，后者的β〈1。最后，通过推导增长方程定量探讨了这些标度关系的可能后果，结果显现：由创新驱动增长和规模经济驱动增长之间有巨大差异。这种差异表明，伴随人口增长，主要的创新周期必须持续加速运行，这样才能维持城市增长，从而避免停滞及垮塌。

Humanity has just crossed a major landmark in its history with the majority of people now living in cities. Cities have long been known to be society＇s predominant engine of innovation and wealth creation, yet they are also its main source of crime, pollution and disease. The inexorable trend toward urbanization worldwide presents an urgent challenge for developing a predictive, quantitative theory of urban organization and sustainable development. Here we present empirical evidence indicating that the processes relating urbanization to economic development and knowledge creation are very general, being shared by all cities belonging to the same urban system and sustained across different nations and times. Many diverse properties of cities from patent production and personal income to electrical cable length are shown to be power law functions of population size with scaling exponents, fl, that fall into distinct universality classes. Quantities reflecting wealth creation and innovation have β≈1.2〈1 （ increasing returns）, whereas those accounting for infrastructure displayβ≈0.8〈1 （economies of scale） . We predict that the pace of social life in the city increases with population size, in quantitative agreement with data, and we discuss how cities are similar to, and differ from, biological organisms, for which β〈1. Finally, we explore possible consequences of these scaling relations by deriving growth equations, which quantify the dramatic difference between growth fueled by innovation versus that driven by economies of scale. This difference suggests that, as population grows, major innovation cycles must be generated at a continually accelerating rate to sustain growth and avoid stagnation or collapse.