preprints.org > environmental and earth sciences > geography > doi: 10.20944/preprints201901.0173.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 16 January 2019 / Approved: 17 January 2019 / Online: 17 January 2019 (03:30:08 CET)

As noted in the introductory quotation, an ideal map was long ago seen as the map of the map, the map of the map, of the map, and so on endlessly. This recursive perspective on maps, however, has received little attention in cartography. Cartography, as a scientific discipline, is essentially founded on Euclidean geometry and Gaussian statistics, which deal with respectively regular shapes, and more or less similar things. It is commonly accepted that geographic features – such as rivers, cities, streets and building – are not regular and that the Earth’s surface is full of fractal or scaling or living phenomena with far more small things than large ones at different levels of scale. This paper argues for a new paradigm in mapping, based on fractal or living geometry and Paretian statistics, and – more critically – on the new conception of space, conceived and developed by Christopher Alexander, that space is neither lifeless nor neutral, but a living structure capable of being more living or less living. The fractal geometry is not limited to Benoit Mandelbrot’s framework, but is extended towards Christopher Alexander’s living geometry and based upon the third definition of fractal: A set or pattern is fractal if the scaling of far more small things than large ones recurs multiple times. Paretian statistics deals with far more small things than large ones, so it differs fundamentally from Gaussian statistics, which deals with more or less similar things. Under the new paradigm, I make several claims about maps and mapping: (1) Topology of geometrically coherent things – in addition to that of geometric primitives – enables us to see a scaling or fractal or living structure; (2) Under the third definition, all geographic features are fractal or living, given the right perspective and scope; (3) Exactitude is not truth – to paraphrase Henri Matisse – but the living structure is; and (4) Töpfer’s law is not universal, but scaling law is. All these assertions are supported by evidence, drawn from a series of previous studies. This paper demands a monumental shift in perspective and thinking from what we are used to on the legacy of cartography and GIS.

third definition of fractal; fractal or living geometry; wholeness; head/tail breaks (ht-index); scaling law

Environmental and Earth Sciences, Geography

* All users must log in before leaving a comment