The paper approaches this divide from a cognitive science angle, looking at how we categorize things instinctively, which is based not so much on a rigorous Venn-diagram sort of thinking (This is bird, this is not a bird) as an exemplar-centered way of thinking:
Rosch and her co-workers discovered that, in many cases, all members of a category are not 'equal'. For example, when asked to give an example of a bird, subjects tend to name robins and sparrows as examples far more often than they mention turkeys or penguins or ducks. [...] Lakoff (1987) later discussed this in terms of a radial structure for some categories. He noted that peripheral members of different arms of a radially-organized categories may have nothing in common, except different chains of resemblance to some common prototype.It goes on to talk about "schemata" as an intermediary step in cognition between perception and understanding: schematic distinctions like "near and far" and "center and periphery" are models we use to process sensory information. The take-home is that in many cases we don't instinctively form categories and then file experienced objects within them; instead we form categories around exemplars, so that things are more or less "bird-like." Our organization of the world from experience has soft edges.
Getting to (to me) the meat of the paper, a distinction is made between two scales of spatial understanding:
Downs and Stea (1977, p. 197) distinguished perceptual space, studied by psychologists such as Jean Piaget and his colleagues and followers (Piaget and Inhelder, 1956), from "transperceptual" space that geographers deal with, and that we are focusing on in this paper. They claimed that "the two scales of space are quite distinct" (p. 197) in the ways people perceive and think about them. Later in the book, Downs and Stea (p. 199) contrasted the terms "small-scale perceptual space" and "large-scale geographic space." At about the same time, Kuipers (1978, p. 129) defined large-scale space as "space whose structure cannot be observed from a single viewpoint," and by implication defined small-scale space as the complement of this. The large-scale vs. small-scale distinction of Kuipers does not quite correspond to a geographic vs. non-geographic contrast, since as Kuipers pointed out, a high mountain viewpoint or an aircraft permits direct visual perception of fairly large areas. Nevertheless, we will follow Kuipers, and use the term large-scale space as he defined it, and small-scale space to refer to subsets of space that are visible from a single point.Seems sensible enough, though it's a little confusing to a cartographer to have "large-scale" and "small-scale" reversed in meaning. The next bit goes into more detail about how we learn about small-scale space using sensory data with a lot of built-in cognitive processing, which is contrasted against "objective" Euclidean models of space which were originally formulated to make sense of large-scale space.
The argument (before the paper veers off towards its target audience of GIS-makers) is basically that the Euclidean model is not how we think about space in general, and it would be good to design geographic systems that take into account our innate spatial reasoning, which is grounded in the more fluid, less rigorous, and very relativistic way we innately create categories.
My problem with the paper is that it proposes a duality where I think there's a third player, and that's communal understanding. We all perceive our own peculiar space, things looming large and small in importance depending on our own specific background and our own specific immediate needs and goals.
I can tell you more about the details of the road, sidewalk, stairs and hallway between the parking lot and the door to my office than you probably want to know; this knowledge looms large in my internal geographic framework for my neighborhood. There are others who share my general daily pattern; they park in the same lot, enter the building and go up at least some of the same stairs. But most of them go to different offices, and all of them bring different judgmental frameworks (I hate ice and am annoyed by the seriously decayed roadway and sidewalk in front of our building. Others may find the sidewalk charming and enjoy the slippy sensation of ice underfoot). Nevertheless, there is a commonality to our geographic understanding: if there were a notable event in the street (a sinkhole swallowing up an entire delivery truck), we would be able to ask specific questions to one another about the space in which it happened. If I had to tell someone where I parked, it would be easier to do with someone who is in this group because we can all visualize how the parking lot is laid out.
This collective understanding is different than the individual cognitive framework I have developed, and it is different from a detailed numerical-Euclidean survey. A friend of mine habitually counts stairs, and so for her, a part of the description that looms large is the specific number of steps on each course of the stairwell. The common geography would say that there is one set of concrete steps outside, and to get to the third floor there are four sets of stairs with a landing between. (On the other hand, it should be said that there is no single common geography. My friend's detailed knowledge would fall into the common geography of blind visitors to the building, for example)
The averaging of all our experiences, the least-common-denominator quality of our knowledge, forms a useful and necessary basis for all our common local geography. It is the organization of this knowledge that allows maps to be made and used, and this is where Euclidean geometry has been extremely useful; it acts as a "neutral" meeting ground. We can all agree that the sidewalk here is 12 feet wide (once we agree that a foot is as long as this ruler in my hand).
The distinction between "large-scale" (i.e. large area) geographic space and small-scale experiential space is a false one. The reason geographic space (say a map of a state or a nation) is rendered in a Euclidean way is that it makes discussions open. This flies against the whole body of critical cartography, which posits that the Cartesian/Euclidean/Ptolemaic grid is an exercise of power. Power is exercised through that grid, yes, but this is possible because it allows sharing of information across large networks of people without extensive initiation.
So much of our theory is based on "creators" and "users." I don't think we really know how to talk about commonality except as a collections of individuals. I would think it would at least be an interesting exercise to start with commonality and see where that leads us...