Rejoinder to Hillier and Penn

Some questions about space syntaxöa well-known technique of urban analysis developed over the past decades by Bill Hillier et alöwere raised by Ratti in this journal. Hillier and Penn produced a detailed rejoinder, rebutting most of the criticisms and restating the assumptions made by the technique. However, their arguments, if accepted, lead to paradoxical consequences. DOI:10.1068/b3019b Figure 1. Are they the same or not? There is an elemental difference between the two patterns (say a 0.01 degree, or arbitrarily small variation in their skew), which is not perceptible to the eye. Hillier and Penn argue that this would lead to a radical transformation in terms of pedestrian movement in hypothetical cities based on the two patterns above. (B) The two grids are geometrically the same. Movement patterns in two hypothetical cities based on the two patterns of figure 1 are the same. The troubled reader is invited to trust his or her visual intuition. She or he should also know that there is an elemental difference between the two patterns (say a 0.01 degree, or some arbitrarily small variation in their skew), which is not perceptible to the eye. Answer (A) contains quotes from Hillier and Penn (page 502) and summarizes their argument; answer (B) is my choice. 3 Absurdum alterum (second section in Hillier and Penn, 2004) The second section in Hillier and Penn is a response to my questions about the most common archetypal city pattern: a regular grid. There, the axial analysis becomes useless, as it outputs uniform values for all streets. How to deal with such simple evidence? Hillier and Penn state: ``in spite of the fact that, theoretically, a pure orthogonal grid yields standardised values for axial lines, in practice such grids do not occur'' (page 503). The above answer seems a rather facile way to settle the issue. Even if infinite regular grids do not exist in the real world, they certainly can be thought of and subjected to what physicists would term Gedankenexperiment. If the experiment yields different results from those obtained in reality, it is then necessary to understand the cause. In our case, this would mean asking the following questions: what are the applicability limits of space syntax? If these uniformly gridded configurations do not occur in the real world because they are always connected to an outside world (such as Manhattan to Brooklyn), what is the extent of this world that we should consider? How does space syntax deal with boundary conditions? These questions, clearly set out in my previous paper, do not find a clear answer in Hillier and Penn's rejoinder. A very interesting point arises in Hillier and Penn's discussion of regular grids. In my initial paper, as an aside, I made the following observation about the axial analysis and the city of Manhattan: `̀ The first concern of the newcomer to axial analysis would probably be related to its topological representation of the city, which discards all metric information. The difficulty in accepting this becomes clear when considering pedestrian decisionmaking rather than urban configuration. Convincing a pedestrian that his urban movement strategy is not based on metric but on topological distance might prove as difficult as convincing a New Yorker living on Fifth Avenue, between 111th and 112th Streets, that going to Central Park North round the corner (two changes of direction in the axial map) or to Columbus Circle (a few miles away, but still two changes of direction) is the same'' (page 490). Hillier and Penn promptly jump on this point to state that my observations `̀ betray a misapprehension of what it is that space syntax seeks to predict. Space syntax in itself says nothing about `pedestrian choice making', but deals only with observed flows and thus only with aggregate statistical effects in different alignments in the grid'' (page 504). Their assumption is very interesting: it implies that a NewYork pedestrian's decisionmaking might be based on metric distance (or on some other nontopological measure), but that global patterns of pedestrian movement can be predicted using topological measures, such as the axial map analysis. This assumption, however, leads to a paradox, as demonstrated by the following reductio ad absurdum. Take the map presented in figure 2(a), which represents a five-by-five street portion of New York City. Individual patterns of pedestrian movement will respond, say, to the metric structure of the city (or to some other nontopological measure). All these individual patterns add up and lead to an aggregated pedestrian movement diagram, which can be determined, according to space syntax, by a topological analysis of the axial map. Now imagine deforming the grid by inserting a large unbuilt area between 2 C Ratti