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A new paradigm in cartography
Traditional cartography has essentially been based on Euclidean geometry, Gaussian statistics, Newtonian absolute space, Leibnizian relational space and a Cartesian worldview. The implications of these foundations for cartography mean that cartography has long been concerned with depicting the underlying structures or patterns of geographical space through scientific abstraction, with an excessive focus on Tobler's law and precision. This is useful for measuring and analyzing geographic objects at local scales, but it is useless for developing new insights with respect to spatial heterogeneity or scaling laws (Jiang 2019: 10, 14, 16; Jiang 2022; 31).
The original definition of cartography is that cartography is the art, science and technology of making maps (Jiang 2019: 17). A map, according to Korzybski (1933), is not the territory, but rather a depiction of the structure of the territory. A map, also according to Korzybski, is a map of the area. In other words, cartography strives for a true representation of reality through maps. However, as Jiang (2022:37-38) argues, Euclidean geometry falls under the Cartesian worldview, which focuses on the fragmented pieces of reality (or structure), rather than a collection of pieces - and a geographical space is represented as a collection of geometric primitives such as points, polygons and lines. As a consequence, geographical objects look regular and similar. But reality is, as Jiang (2019:10,12) argues, not regular, and reality consists of a whole rather than fragmented pieces. This whole, according to Jiang (2019:13), consists of much more small things than large things. This scaling hierarchy cannot be described using Euclidean geometry, but it can be described using fractal or living geometry.
The new paradigm in Cartography advocated by Jiang (2019) is a major change that involves shifting the focus from the Cartesian to the organic worldview (Jiang 2022), from the Newtonian and Leibnizian to the third view of space (Jiang 2022:31-32), from Euclidean to fractal geometry (Jiang 2019:12) and from Gaussian statistics to Paretian statistics (Jiang 2019:14). With this shift in perspective, we can, according to Jiang (2019:14), see that much of reality is living structures - and such a perspective helps us answer the question of how complex a set or pattern is. Which means that maps can and should reflect the underlying complex, scaling or living structure of the earth's surface rather than reflecting the sizes and directions of geographical objects (Jiang 2019:12). Key concepts of the new paradigm of cartography are presented below.
Organic worldview & the third view of space
Living structures
Head/tailbreaks
The organic worldview sees the earth's surface as a collection of fractals that together form a whole, which also includes people. The perspective is based on the third view of space where space is a more or less living structure. Which is appropriate as there is a recursive scaling hierarchy in the form of many more small things than large things, in this whole (Jiang 2019:13; Jiang 2022:37-38).
The third view of space, of a more or less living structure, is underpinned by Tobler's law and the law of scaling where Tobler's law represents "more or less similar things" on a local scale, and where the law of scaling represents "much more small than large things" on a global scale (Jiang 2022: 31-32).
From such a perspective, a map can reveal deeper knowledge about geographical areas rather than merely describing them. This reflection is based on the fact that the main concern of cartography shifts from focusing on accuracy and "how far something is" to focusing on how "complex" something is. Which reveals topological (popular or unpopular) and/or semantic (meaningful or meaningless) geographical phenomena, rather than merely describing geometric properties of these geographical phenomena (Jiang 2019: 12; Jiang 2020 & Slocum: 8).
Tobler's law (secondary) and the law of scaling (primary) are two laws of geography that are fundamental to the concept of living structure. These two laws of geography emphasize that the Earth's surface is unbalanced and heterogeneous. The new geography of living structures aims to understand the complexity of the Earth's surface, but also to illustrate the Earth's surface as a living structure (Jiang 2022: 32; Jiang 2020 & Slocum: 7-8).
But what exactly is meant by a living structure? To explain the concept of living structures, there is a point to reconnect with Tobler's law and the law of scaling. Tobler's law is about more or less similar things at each scale, while the law of scaling is about more small things than large ones across scales. By things Jiang (2022:34) means those things that collectively constitute a living structure.
All geographical features are living structures with the right perspective. But a basic idea is that a living structure has an inherent scaling hierarchy of many more small things than large ones that together form a whole. An example of such a living structure is the street network, which consists of more small streets than large ones (Jiang 2022:35). Another example of a living structure is the urban system, which consists of more small (streets, parks, buildings) things than large ones. Together, the city's smaller elements support the city's larger ones, forming a dynamic and vibrant city.
Inherent in the new paradigm of cartography, space is more or less living - a living structure in which the phenomenon of many more small than large is universally recursive. This means that space possesses an inherent disproportionate hierarchy. The purpose of a map is to represent the territory, which means that a map should also represent this underlying hierarchical structure. To do so, new data classification methods are required as Gaussian methods rather represent more or less similar things. According to Jiang & Slocum (2020:8-9), head/tail breaks are a better method for visualizing the hierarchy of the territory and the method can be used for mapping in general and for data classification and map generalization in particular.
In a head/tailbreak process, data values are ranked according to size. The classification is done by averaging all data values and then dividing the data into two groups where one group is larger than the average, and where the other is smaller than the average. The group that is larger than the mean is called the head and the group that is smaller than the mean is called the tail (Jiang & Slocum 2020:9). This process is recursive, but the iteration process ends according to Jiang & Slocum (2020:9) when the percentage of the head is less than the tail, more specifically closer to 40%.
In the head/tailbreak method, the data is treated as a whole, and the mean of the whole is used to divide the whole into sub-wholes. These sub-units are firstly a part of the whole, and secondly the sub-units are a whole of themselves - with containing sub-units (Jiang 2022:36). In this method, the data speaks for itself and reveals the inherent hierarchy of the space. In this way, what Jiang (2022:35) argues for, the recurring notion of far more small than large, is made visible, which also makes the living structure of the space visible.
References:
Jiang B. (2019), New paradigm in mapping: A critique on Cartography and GIS, Cartographica, 54(3), 183–205. Reprinted as the cover story in the magazine Coordinates, October issue, 9–21.
Jiang B. and Slocum T. (2020), A map is a living structure with the recurring notion of far more smalls than larges, ISPRS International Journal of Geo-Information, 9(6), 388. Reprinted as the cover story in the magazine Coordinates, August issue, 6–17, 2020.
Jiang B. (2022), Geography as a science of the Earth’s surface founded on the third view of space, Annals of GIS, 28(1), 31–43.
Korzybski, A. (1933) On Structure, In Science and Sanity: An Introduction to Non-Aristotelian Systems and General Semantics, 5th ed.; Korzybski, A., Ed.; Institute of General Semantics: Brooklyn, NY, USA, 1933; s. 54–65.
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