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Network geometry and the urban railway system: the potential benefits to geographers of harnessing inputs from “naive” outsiders

发布时间：2013-12-515:55:34来源：作者：Gabriel Dupuy

Gabriel Dupuy

University Paris Panthéon Sorbonne, CRIA-UMR 8504 Géographie Cités, 191 rue Saint-Jacques, 75 005 Paris, France

** Highlights**

•The “naivety” of hard scientists has generated new models to explain the geometry of urban railway systems.

•Experts, especially geographers, have not always been receptive to models presented by “naive” amateurs.

•The experts could open up to and harness the benefits of “naive interdisciplinarity”.

**Keywords**

Edgar Morin; Geography; Geometry; Interdisciplinarity; Networks; Urban railway

**Abstract**

This paper considers a form of scientific interdisciplinarity that brings the experts in one discipline or field into play with uninitiated outsiders from other, unrelated, disciplines – what Edgar Morin might call “naive interdisciplinarity”. The discipline here is network geography and the field the urban railway system (URS), which has benefitted from some significant contributions from “naive” outsiders over the past 50 years, such as graphs, fractals and the scale-free network; and which might be able to continue to do so with the promising new amoeboid model. How have those ground-breaking tools developed by mathematicians, physicists and biologists managed to find their way into the mainly geography-based approach of URS experts? After seeking to grasp what has given rise to naive interdisciplinarity and why the experts might turn against it, the paper identifies the conditions for them to set aside their objections and facilitate a transfer of knowledge.

**Article Outline**

1. Introduction

2. Insights into the laws of network geometry

3. New approaches to network geometry

4. Geometry and the URS: naive outsiders in the field of geographers

5. From polymers to the URS: contribution of fractal analysis

6. “Family attachment” and the URS

7. Biology to the rescue: the amoeboid model

8. What can limit the scope for interdisciplinarity?

9. Barriers to application

10. Long March or utopian dream?

11. Risks, constraints and benefits of naive interdisciplinarity

Acknowledgements

References

**Figures **

Fig. 1.

Network layout modelled using the fractals approach.

Fig. 2.

Network layout modelled using the preferential attachment approach.

Fig. 3.

Network layout modelled using the evolutionist amoeboid approach.

Fig. 4.

Geometric development of the Shanghai URS. Understanding the geometric form of the URS and the spatial dynamics of line deployment is a constant preoccupation among urban planning and transportation experts (Wang and Yang, 2009): how, for example, has Shanghai managed to equip itself with such an extensive railway system in less than 20 years?

Fig. 5.

The Paris regional railway system. Benguigui and Daoud (1991) showed the network’s fractal geometry by counting the number of stations within a series of concentric circles centring on Notre Dame cathedral.

Fig. 6.

Family network model. Network topology and geometry in the evolutionary family network are, as in the BA model, the product of preferential attachment. However, it is no longer single nodes that are incorporated into the network (M = 1) but also nodes already interlinked in a “family-like” manner (M = 2, M = 4, M = 8). Lines and loops are therefore attached to the network representing the actual layout of the central Tokyo URS.

Fig. 7.

Cytoplasmic network generation. An amoeboid cell positioned in P extends towards food sources P1, P2, P3 and P4 (aA) through the multiplication and selective disappearance of pseudopodia (aB and aC) with a figure of equilibrium (aD). Its movements ultimately produce a pattern resembling that of a real network (b). Nakagaki’s team uses this to reproduce the layout of the Tokyo regional rail network (Adamatzky, 2008).

Fig. 8.

A global URS typology, from an expert’s point of view. Lauriot (1996) singled out geometric metro-system types corresponding to different conceptions of urban service. The “Asian” version begins with a single line serving the city centre. That line is then cut in two places by an inner circle line, and other changes occur when those two lines are, in turn, cut by radial lines.

**Tables **

Table 1. URS geometry: new approaches since the 1990s.

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