Flow mapping vs movement mapping: a theoretical and cartographic demonstration of their significance at a world scale
Résumé
We observed that mapping flow is to vary the size of a straight directed link between origin (i) and destination (j) places, proportionally to a flow matrix value (Fij). According to Bertin's (1967), this practice reflects the exact application of the visual variable 'size' on the flow feature. Every other aesthetics and semiotic principles - as colored or curvilinear features - can be taken into account without fundamental consequences. This is very popular since earlier flow maps. It even seems to be the unique way to map flow, but is it relevant? Is it obvious that flow mapping raises one dimension of the features while the human eye may perceive several? Assuming that first hypothesis is exact means in fact that the human eye will perceive only one feature's dimension: its width (Fij). Is it really the case? We raise a reasonable doubt about the relevance of this assumption and will examine it in this paper. Our aim is to demonstrate the legitimacy of the conventional approach of flow mapping which leads to the first hypothesis. To do this, we will place us in the theoretical framework defined by Grasland (2009) leading to a joint (analysis of positions and flow. However, the present proposed perspective differs as the analysis is focused on the perceived information on a flow map. Therefore, we'll assume also Bertin's (1967) and Tobler's (1987) cartographic principles for mapping statistical flow data. We will then examine the corresponding cartographic process from two cognitive perspectives, regarding both semiotic and semantic aspects of the feature's flow map. We will explore a set of four assumptions (fig. 1). The fig. 1 describes through assumptions n°1 to n°4 what human eye perceived on a flow map and what it means. Firstly: the eye perceives only the feature's width (ass. n°1). The second assumption suggests the possibility of the perception of the feature's visual area, i.e regarding the amount of color (ass. n°2). It will lead us in a third assumption to the perceived geometric feature's area, that is to say the arithmetic product of the feature's width and length (ass. n°3). This theoretical semantic switching is not trivial; it corresponds to the perception of a new dimension: the cartographic distance, derived from the formal 'graphic distance' (Müller, 1979; Tobler, 1997; L'hostis, 2003), that is equal to the feature's length (Lij) perceived on the map. This effective joint perception of (Lij) and (Fij) leads us to introduce geographic space in flow mapping process, considering Tobler's (1969) first law of geography. This seems in other words to integrate the fact that flow values (Fij) are projected over a geographical area, consisting of (i,j) places that are more or less distant (Dij) or close in the reality... The places' remoteness influences the significance of the perceived flow value as well as in a flow map (but not in a plan as a spatialized graph which has no geographic properties). Assuming the fourth hypothesis (ass. n°4) is exact involves us carrying out a map of movement (Mij) rather than a map of flow (Fij). We demonstrate on selected bilateral international trade flows from Chelem database that if the cartographic construction of (Fij) and (Mij) is the same and unique (ass. n°1 and n°4 are equals), they differ only in their interpretation (Fij) C (Mij) for one main raison: at a world scale, flow mapping can only be an approximation of the geographical movement (fig. 2), as was done earlier by Minard (1862).