which way? perceptual surveying as a tool for schematic map making

Which Way?Perceptual Surveying as a tool

for Schematic Map Making

Chester Harvey

Submitted in Partial Fulfillment of the Requirements for the Degree of Bachelor of Arts

Department of GeographyMiddlebury College

Middlebury, VermontMay, 2009

ii Which Way? Perceptual Surveying as a Tool for Schematic Map Making

i

Table of contents

Acknowledgments ........................................................................................................ii

Preface .....................................................................................................................................v

chapter 1: cognition to cartography ......................................................1chapter 2: Spatial cognition in Review .................................................13 Cognitive Maps ...........................................................................................15 Spatial Heuristics .......................................................................................20 Measuring Directional Judgments .............................................32chapter 3: The Perceptual Survey ...............................................................39 Survey .................................................................................................................40

Data Management, preliminary Analysis, and development of working visualizations ..........................................................................46chapter 4: a New Map of Middlebury .....................................................50 Site Analysis ...................................................................................................53 The New Map ...............................................................................................72 Schematization Tools .............................................................................72chapter 5: Beyond the case Study .............................................................76

Appendix 1: Full Page Figures ..............................................................................81Appendix 2: Survey Data ..........................................................................................121

Bibliography........................................................................................................................133

ii Which Way? Perceptual Surveying as a Tool for Schematic Map Making

acknowledgments

To my advisor, Professor Anne Kelly Knowles, who has been perpetually encouraging me as a mentor and friend: I am grateful for your enthusiasm when I came to you with ambitious goals, and for your understanding when we both realized they were a little too ambitious. You were flexible but rigorous, and could always suggest a new direction for inquiry. Thank you.

Abel LillyMarty Sasha

Thank you for being such good friends throughout the adventure of thesis writing. For dragging me on bike rides and to Pub Night when you thought I needed a break – you were always right – and for supporting me through late nights from as far away as Chile, Tanzania, and Vietnam. I will be eternally grateful for your friendship.

To my parents, who thought writing a thesis was “probably a good idea:” thank you for letting me borrow the handle of your tape dispenser, for letting me write Chapter 2 on Thanksgiving, and for encouraging me always to ask questions. Finding the answers has always been great fun!

iii

Thank you to all of my friends who agreed to participate as subjects in my study, and who subsequently encouraged me to “just get done with it” so they could see how well they did:

Bonnie HemphillChristian Woodard

Pier LaFargeKyle AldenLeah BevisAlex Yule

Miriam JohnstonHeather Pangle

Anne WillbornSasha SwerdloffAnders Meyer

Nate BlumenshineCaitlyn OlsonPeter SpyrouToral Patel

Natty Smith

Abel FillionChristine BachmanNicole Grohoski

Philip PicotteHannah Day

Nick SpenglerChris Hassig

Finally, thank you to the faculty of the Middlebury College Geography Department for supporting me throughout my undergraduate journey. I will always feel at home in the sandbox.

Anne KnowlesPeter Nelson

Jonathan SchroederGuntram Herb

Timi MayerJeff HowarthBill Hegman

iv Which Way? Perceptual Surveying as a Tool for Schematic Map Making

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◄ The new, perceptual schematic map of Middlebury, designed with evidence from a perceptual survey.

v

Preface

This thesis is rooted in a question we ask, often subconsciously, hundreds of times each day: which way is it from here to there? While the answer can be concrete – locations can be defined and the vectors between them measured – it can also be highly theoretical. In the context of everyday experience, location is not described by coordinates but by the relative position of other features. If I ask you, “which way to the store?” and you cannot see the store, you must make a judgment based on what you can see and assumptions about what lies beyond. But how do you know what fills that unseen space? How do you know if your judgment is correct? Is the precision of your judgments even all that important, so long as your general sense of direction is correct? Is it more useful to conceptualize simplified landscape geometry than to include every detail?

I was fascinated by the likelihood for spatial error in both perception of the landscape we can see and memory of the parts we cannot. Instead of treating this error as a hurdle to overcome, I was eager to explore methods for embracing it and using it to our advantage, particularly in the discipline of cartography. What if map geometry could be shaped by the perceptions people have of a place – how they understand it? Would it be a better map? This thesis demonstrates that people’s perceptions of landscape geometry can be measured in the field, that these perceptions are simplified geometrically, and that the simplifications can be used as evidence for making a perceptual map. In theory, this map shows us how people think things are located and oriented in relation to each other. It is a graphic answer to the initial Which Way? question, accounting for the aggregate spatial perceptions of twenty-three volunteers. The following chapters will describe how I went about making this map and the role my approach might play in making better tools for navigating the world.

vi Which Way? Perceptual Surveying as a Tool for Schematic Map Making

We shall not cease from explorationAnd the end of all our exploringWill be to arrive where we startedAnd know the place for the first time.

T. S. Elliot, Four Quartets

1Chapter 1 Cognition to Cartography

1 cognition to cartography

The modern urban landscape is a complex mosaic of infrastructure: buildings, streets, sidewalks, plazas, parks, rail lines, waterways, and bridges. Interwoven transportation networks are a principal feature of the urban fabric. Almost every place we go can be addressed relative to a street or highway. Locations are framed by the geometry of the networks along which we travel to get to them. Streets are the vantage point for most of our images of cities; they are the matrix which binds places in the city together, and which connects the city to the surrounding countryside.

While the streets in iconic downtown New York are neatly and rationally arranged, most places are not so cleanly laid out by planners and architects. Instead, cowpaths have been widened into roads and paved into streets that accommodate topography, property boundaries, or even political disputes. Nonetheless, people familiar with these areas have little trouble getting from place to place. In order to efficiently navigate complex networks, cognitive psychologists suggest, people simplify street geometry in their mental maps (Tversky 1992, 131). We conceive of streets as straight lines, even if they are somewhat curved. We imagine intersections to be right angles, even if they are not. Somehow this does not interfere with our ability to navigate effectively. In fact, because we are not concerned with the details of every twist and turn, it increases our efficiency as users of the urban landscape.

What allows such simplification is that streets are a functional network. At a conceptual level, this network consists of only two things: nodes – any address – and links, the segments of streets between nodes. Links in series make up whole streets, and nodes connecting more than two links constitute an intersection. The most important characteristic of a street network is that it restricts movement as

New York - regular grid

Boston - grid spliced with cowpaths

(ESR

I 200

8)

▼ Nodes in a functional network are connected by links. A node connecting more than two links is an intersection.

2 Which Way? Perceptual Surveying as a Tool for Schematic Map Making

much as it facilitates it. While cars and pedestrians are free to travel along streets, they are seldom able to traverse through open space between them. Because of this, the precise shape and position of streets and intersections is relatively unimportant to the typical user. They are merely concerned with which series of streets they should take to reach their destination and the topological relationships between the links and nodes. The work required for precise navigation is already done and communicated by the infrastructure itself. Street lines, signs, and signals ensure that we travel in the right direction and know exactly where intersections and our destinations are located. Train and airline networks are similarly functional, yet even further simplified. To most users, the route is entirely unimportant. Only a schematic understanding of nodal stations or airports and the rail lines or flights linking them is important for trip planning.

Because our minds conceive of transportation networks schematically, it makes sense to represent them using schematic maps. A relatively unstudied cartographic genre, schematic maps are probably best known in the context of subway maps (Waldorf 1979, 12). While the Romans can be credited with schematizing maps of road networks as early as the third century – the Peutinger Table is the earliest extant example – modern schematic maps have been popularized only within the past eight decades (MacEachren & Johnson 1987, 148; Talbert and Elliot 2008). Harry Beck, an engineering draftsmen, drew the first schematic map of the London Tube in 1931. Little did Beck know that his design, published for the public in 1933, would become the most widely recognizable example of schematic mapping, or that he would effectively father this genre of cartography. The Tube map’s geometric style has become the standard for

▲ The typical airline route map shows flights between cities as simplified arcs. Customers do not need to know the exact flight path, only that a flight travels to their intended destination.

► The modern street is a tool for moving between nodes with minimal navigational effort. With curbs, lines, signs, and bordering infrastructure keeping you on the roadway, it would be difficult to follow the wrong path to the next intersection.


◄ The Roman Peutinger Table is credited as the first example of a schematic map. Scholars believe early editions of the table may date as far back as AD 300 (Talbert and Elliot 2008, 200). This copy was made around the year1200. Routes between cities are represented by straight lines and the shapes of landmasses are vastly distorted to accommodate this linearization.

◄ A schematized London Tube map was first drawn by Harry Beck in 1931. The map was initially controversial because it inflated the size of the central city relative to outlying areas, but was published in 1933 as the official Tube Map and has been popular among the public ever since. Subway maps all over the world have been drawn in a similar style, and the London Tube still uses an updated version of the original design.

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The service betweenWoodford - Hainault operatesuntil approximately 2400. There is major escalator work at Bank andMonument stations. Pleasesee information below.

No special arrangements.

There is step free interchange between Canary Wharf Underground and DLR stations and Heron Quays DLR station at street level.

District Cannon Street open until2100 Mondays to Fridays. Open Saturdays 0730 to 1930.Closed Sundays. Earl’s Court - Kensington (Olympia) 0700 to2345 Mondays to Saturdays,0800 to 2345 Sundays.Turnham Green is also servedby Piccadilly line trains earlymornings and late evenings.Blackfriars Underground stationis closed until late 2011The East London line is closed.Use replacement buses or alternative Tube, bus and DLRroutes via zone 2.

East London

Jubilee

Overground

Hammersmith& City

No service Whitechapel - Barking early morning or late evening Mondays to Saturdays or all day Sundays.

Northern Except during weekday peakhours, all trains to/fromMorden run via Bank - for theCharing Cross branch, changeat Kennington. For journeysto and from Mill Hill East atoff-peak times, change atFinchley Central. On Sundaysbetween 1300 and 1700,Camden Town is open for interchange and exit only. There is major escalator workat Bank and Monumentstations. Please seeinformation below.

Metropolitan For Chesham, change at Chalfont & Latimer on most trains.

Piccadilly No service Uxbridge - Rayners Lane in the early mornings. Heathrow Terminal 4 station open Mondays to Saturdays until 2345 only. Sundays until 2315. Trains via Terminal 4 may stop there for up to 8 minutes before continuing to Terminals 1, 2, 3. Turnham Green is served by Piccadilly line trains early mornings and late evenings. Avoid the crowds at Covent Garden station by taking a short walk there from nearby Holborn (9 minutes), Leicester Square (6 minutes) or Charing Cross (11 minutes walk). Hounslow West is step-free for wheelchair users only.

Victoria

Waterloo & City Mondays - Fridays 0615-2148. Saturdays 0800-1830.Closed Sundays andpublic holidays.



No special arrangements.DLR

Transport for London

Major escalator work is taking place at Bank and Monument stations. Avoid interchange between lines or use nearby alternative stations wherever possible. Please check before you travel.This diagram is an evolution of the original design conceived in 1931 by Harry Beck · 03.09

Correct at time of going to print, March 2009

East London line is closed for major line extension work to become part of the London Overground network

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Tube Map

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until late 2011

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information

▲ The modern London Tube Map still uses the same schematic designed by Harry Beck in 1931. The map has been updated to include new lines, and fare regions are denoted with gray bands in the same schematic style. The original cartographer is credited in the lower right corner.

► A geographically accurate version of the London Tube

Map is more difficult to follow and takes considerably more

space to display. This detail shows only the central portion

of the system.

(Transport for London 2009)

(Cla

rke

2000

)


mapping subway systems and has similarly inspired maps of all sorts of functional networks.

The premise of Beck’s design was that from beneath the city, where movement was constrained to the rail network, the geographic position of stations and the paths of the lines were unimportant. The map shows no surface features except a highly abstracted River Thames, which divides the city into two functional regions and provides a simple reference with which travelers can orient the map. Stations are reduced to ticks or squares, and their relative positions are substantially distorted to allow straightening of the lines connecting them. At first, Beck’s map received criticism from the Tube authorities for being geographically inaccurate (BBC 2002). To increase clarity in the city’s dense core it shows this area relatively larger than outer areas. Moreover, the abstraction and geographic dislocation of stations sometimes makes it unclear whether the Tube is a reasonable transportation choice at all. Someone unfamiliar with London might take the Tube from Bank to Mansion House, a ‘distance’ of six stops with one line change. While this looks like the best way of traversing this distance on the map, someone more acquainted with the city would probably just walk 50 meters between the stations aboveground. Even with these anomalies, the Tube Map has proved popular among the general public because it is so easy to read – much easier than a geographically accurate map of the underground system. The efficiency gained through the graphic clarity of schematic maps seems to outweigh the difficulty of relating them to real geographic space where the schematization ends, either aboveground or beyond the extents of the map.

While schematic maps are esteemed as highly effective, they are few and far between. This is chiefly because they are difficult to make. Modern tools for surveying – including satellite positioning and imaging – have provided a glut of precise geographic information, much of which is free and publicly accessible. Drawing national borders that are accurate to the nearest meter is as easy as a few clicks in a geographic information system (GIS), so unless someone is a cartographer trained in generalization techniques, they are likely to produce an overprecise map. Moreover, a precision paradigm fueled by geoscience has reinforced this trend. A century ago, when cartographers were considered craftsmen more than scientists, imprecision in maps was more common and more accepted as a feature of their design. Cartographers considered what level of

Mark MonmonierHow to Lie With MapsSecond Editionp.177Chicago: University of Chicago Press

▼ Modern GIS systems make cartography quick and easy, but have made overprecise maps ubiquitous. The top map, made using

a publicly accessible census dataset, has state boundaries that are far too detailed

for its scale. Note the muddle of coastal inlets along the eastern seaboard. Mark Monmonier’s map of the United States

(bottom), with generalized state boundaries, is more appropriate for its scale.

(adapted from Monmonier 1996, 177)

(ESRI 2008)


precision was necessary for a map to function properly, and worked with evidence that would be considered crude by modern standards – transit surveys, drawings, notes, and their own observations of a place – to draw maps that adequately met these needs. Nowadays, most maps are made on computers using GIS and graphics software. Geographic evidence, even a simple regional boundary, is referred to as ‘data.’ Maps are assembled rather than drawn. This process is quick and inexpensive, and it satisfies the scientific craving for greater precision and presentation of as much information as possible on a single page. Increased precision and detail are considered “hallmarks of cartographic progress” by map historians (Monmonier 1985, 7).

In contrast, production of a schematic map requires a liberal dose of time and creative thinking to achieve an end that is, ironically, simpler than it began. The adage goes, if I had more time, I would have written a shorter letter.1 A similar statement can be made for cartography. A map is not complete until, while maintaining its purpose, nothing else can be removed from the page.2 For the most part, this is achieved through traditional processes of feature selection and generalization. Depending on the scale and application of a particular map, it may not be necessary to show every point, line, or shape for which the cartographer has data, or perhaps they can be symbolized more efficiently. Street networks are generalized by removing less trafficked or smaller streets, or simplifying their paths by removing vertices. This maintains the geographic precision of the remaining vertices, and the geographic accuracy of the map as a whole. While researchers have long tried to develop automated techniques for generalization, some of the most recent being quite sophisticated, almost all generalization for professionally designed maps is still accomplished by hand (Roth 2008).

A more drastic type of generalization involves simplifying the map geometry itself to make a schematization. Doing this requires treating the position and orientation of map features as attributes that can be manipulated and abstracted, something that mainstream GIS software is not designed to do. While a small

1. Blaise Pascal, Lettres provinciales; Thoreau; Marcus T. Cicero; Twain; Karl Friedrich Gauss; Nietzsche

2. Adapted from a quote by French author, Antoine de Saint-Exupery, who wrote, “Perfection in anything at all is attained not when nothing more can be added, but when nothing more can be taken away.” Adaptation was presented by Dennis McClendon in his talk, “Highly Stylized Maps,” at the 2008 Annual Meeting of the North American Cartographic Information Society, Missoula, MT.

Factory Point, Vermont, Later called ManchesterAtlas of Bennington County, Vermont, 1869, F.W. BeersPortion of the Equinox, Vermont, USGS 15-minute quadrangle, 1894Mark S. Monmonier (1985)Technological Transition in CartographyMadison: The University of Wisconsin Pressp. 6-7

Factory Point, Vermont, Later called ManchesterAtlas of Bennington County, Vermont, 1869, F.W. BeersPortion of the Equinox, Vermont, USGS 15-minute quadrangle, 1894Mark S. Monmonier (1985)Technological Transition in CartographyMadison: The University of Wisconsin Pressp. 6-7

From Scalemaster poster; Roth, Stryker, Brewer

▲ The precision of topographic maps has increased with the development of mapping technology, but they are no better at describing the connectivity of functional networks.

▼ Traditional cartographic generalization techniques include eliminating (top) and simplifying (bottom) features.

(adapted from Roth 2008)

(Mon

mon

ier 1

985,

6-7

)

1869 - F. W. Beers Atlas of Bennington County, VT

1894 - USGS Quadrangle, Equinox, VT


amount of recent research has focused on developing algorithms and models for creating schematic maps with GIS interfaces, most are still created by hand or with computerized design programs that make the drawing process more efficient. Elroi (1988) identifies a few ways schematic maps might be constructed. The most basic, which he terms manual graphic, involves drawing the schematization with paper and pen through an iterative process of adjusting relative distances and orientations with a geographically accurate map as reference. While certain guidelines are followed to preserve stylistic consistency throughout the map, its form is guided primarily by the cartographer’s graphic sensibility and familiarity with the mapped area. The largest obstacle to this process is the time required to complete it satisfactorily. Elroi (1988) notes that when the Paris subway map was schematized in the 1970s it took over 300 hours to complete.

Another technique, interactive use of CAD, requires a similar degree of human attention, but the process is speeded up by using software to perform initial simplifications and draft the network more efficiently. While the cartographer is still responsible for most design decisions, the workflow is greatly accelerated. This technique most resembles the one I describe in Chapter 4 as part of my own schematization process.

Because Elroi considers these manual and semi-manual techniques too laborious for efficient schematization, including potential on-the-fly schematization in GIS software, his research is aimed at designing fully automated techniques. The most important characteristic of a schematic map, he notes, is that topology is maintained. While distances and directions may be abstracted, topological consistency gives them functional compatibility with the real world. Because GIS software has built-in features for detecting topological errors, it is theoretically ideally suited to perform schematization tasks.

That little progress has been made in this area over the past two decades demonstrates that producing effective schematic maps with GIS software has been more challenging than initially hoped. While the bulk of a schematization process can be accomplished by following basic, logical rules, my sense is that researchers encountered a limit to these rules where complex design decisions – whether the orientation of a road running north-northwest should be simplified as vertical or diagonal, or how a complex series of intersections should be laid out – require human judgments to ensure the legibility of the map. These decisions

Functionally identical but graphically dissimilar computer generated schematic maps.Topology is maintained (relative position of nodes is identical).

Cabello et al 2001, p. 7

Functionally identical but graphically dissimilar computer generated schematic maps.Topology is maintained (relative position of nodes is identical).

Cabello et al 2001, p. 7

(Cab

ello

200

1, 3

4)

▼ These two schematic maps, produced algorithmically, show the same nodes

connected by two different link networks. They are functionally identical but visibly different. Developing algorithms that can

judge which of many variations is more understandable for a specific application

presents an enormous challenge for researchers.


require not only a personal knowledge of the mapped network, but of how people conceptualize the network while using it.

Nonetheless, guidelines for schematization can be useful, both for understanding what defines a schematization, and as a basis for beginning the map making process. Waldorf (1979, 81-92) identifies four basic characteristics of a schematization:

Features which are not functionally relevant are eliminated.1. Other networks (or portions of networks) that are not 2. functionally relevant are eliminated. Ideally, only one functional network is mapped at a time.Geometric structure of the network, except topological 3. accuracy, is relaxed.Routes and junctures are symbolized abstractly.4.

Elroi proposed three graphic operations that could be used to produce a map which adheres to these characteristics and has a style similar to that of the London Tube Map:

“ 1. Simplify lines to their most elementary shapes2. Re-orient lines to conform to a regular grid, such that they all

run horizontally, vertically, or at a forty-five degree diagonal3. Expand scale in congested areas at the expense of scale in

areas of lesser node density” (Elroi 1988)

While at its most basic level, a schematic map is any which distorts the relative position and shape of features to accommodate a simplified graphic style, these characteristics help identify what is truly meant to be a schematic depiction, and what has merely been distorted as an effect of scale or feature simplification.

The process for drawing a schematic map is similar to that involved with constructing a cognitive map (Waldorf 1979, 12). Moreover, the two types are interpreted and translated into instructions for movement in much the same way (MacEachren & Johnson 1987, 147). To build and use a cognitive model of a street network requires a number of processes: perception of our surroundings,

▲ Waldorf’s schematization process involves (1) eliminating all features except roadways, (2) eliminating all roadways other than interstate highways, and (3, 4) relaxing the roadway geometry, abstracting its symbolization, and simplifying its paths and intersection angles.

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identification of ground features, filtration of select features, rationalization of their spatial arrangement, and finally, recollection of this arrangement throughout the navigation process (Elroi 1988). In many ways, these steps are analogous to those involved with the drawing of any map. A cartographer needs to gather evidence from the world, identify specific features or phenomena he wishes to map, and arrange them intelligibly for a reader. Rationalizing the arrangement of features, however, is unique to the creation of schematic maps. In this way, they are well suited for representing cognitive map structures, or for accepting evidence

▲ The whole U.S. interstate highway system can be schematized and still be relatively usable as a tool for navigation. This map adheres to Elroi’s graphic operations for production of a schematic map. (1) Interstate routes are simplified to straight lines. (2) The lines are reoriented to conform to a grid. (3) Scale is expanded in urban areas, such the northeast, to limit node density.

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from spatial cognition tests as an influence on their design.Schematic maps also correspond to the way we verbalize route navigation

(MacEachren 1987, 147; Elroi 1988). We do not typically specify our exact heading at points along a street, or the exact angle we turn at an intersection. Instead, we describe our movement by naming the nodes or links we traverse: “go from Springfield to Manchester by taking I-90 to I-494 to I-93.” Turns are conceptually simplified to right angles: left or right. Schematic maps, constructed from nodes and links intersecting at simplified angles, are efficient for diagramming these instructions. They are an ideal vehicle for representing how our street systems operate and how we think about them.

Because schematizations are so compatible with the way we represent space conceptually, I wanted to examine how evidence of spatial perception could be used to influence the schematization process. Traditional methods for creating schematic maps do not incorporate any empirical evidence for how the positions and orientations of features should be abstracted. These decisions are left entirely to the cartographer, or in the case of an automated strategy, an algorithmic process. My research has been framed around two principle questions. First, can a simple, efficient, and accurate method be designed for surveying people’s perceptions of spatial relationships and orientations? In general, I have concluded that this is feasible, although there are certain concessions involved with my solution. The most obvious is the large amount of time needed to complete such a survey, a factor that significantly restricts the number of individuals who can be sampled. On the other hand, such a process allows great depth of knowledge and deliberation to be conveyed by subjects throughout the survey. There is no ideal way to understand how an aggregate population conceptualizes space. It is a highly individual process.

Second, I asked whether I could effectively use the results of this survey to create a schematized map that better matched peoples’ cognitive maps of a street network. Ideally, people would find this map more familiar – they would be able to better orient themselves within it, and use it more efficiently as an aid for navigation. However, I had no efficient way of directly measuring the effectiveness of a map. Therefore, I judged my success in answering this question by comparing a map drawn based on survey results to a hypothesis schematization drawn based only the guidelines established by Waldorf (1979) and Elroi (1988). Where the two


disagreed, the survey was assumed responsible for distorting the new map so it better fit a collective perception of the network’s geometry.

In summary, schematic maps are an efficient way of representing functional networks, especially transportation systems, so they can be easily understood by readers. Although functional networks share many features with our cognitive maps, no researcher has yet developed a technique for using spatial cognition as a source of evidence for the creation of schematic maps. The following chapters will make the argument that not only is this process feasible, but that it may support development of a new variety of empirically based schematic map design. While my case example, mapping the street network of Middlebury, Vermont, was accomplished using a manual process, my conclusions could potentially be incorporated into automated systems for more efficient production. If researchers can gain insights on the input variables needed to produce easily understandable schematic maps algorithmically, and produce better mechanisms for automating the drawing process, this genre of maps could be a popular, everyday option for visualizing functional networks of all sorts.


At every instant, there is more than the eye can see, more than the ear can hear, a setting or a view waiting to be explored. Nothing is experienced by itself, but always in relation to its surroundings, the sequences of events leading up to it, the memory of past experiences.

Kevin Lynch, The Image of a City

(Lynch 1960, 1)

13Chapter 2 Spatial Cognition in Review

2 Spatial cognition in Review

Geographers and psychologists have invested substantial effort in studying how people understand the geometric structure of space and use this understanding to orient themselves within it. Collecting spatial knowledge and relating it to the perceived world is one of the most elemental cognitive processes and an intuitive ability we draw on every day. Yet from a theoretical perspective, it is highly complex. Say you want to go to a coffee shop a few blocks away. To navigate there you must first make a judgment about the shop’s position relative to your own. If there are no buildings blocking your view of the shop, this judgment may be relatively simple. By looking at it you can “dead reckon” the direction you should walk to get there. But in the vast majority of circumstances, your destination will be hidden behind buildings, hills, trees, or other features of the landscape. Determining the direction to the shop will require that you align your current perspective with whatever prior knowledge you possess of the area’s spatial geometry and landmarks – your cognitive map – to make a judgment about the shop’s location relative to your own.

The cognitive map, whatever form it takes, is fundamentally a tool for way-finding (Sholl 1996, 158). As mobile beings, it is necessary for us to be oriented to our surroundings no matter our own position – to “have a general frame of reference from which an individual can act” (Lynch 1960, 125). It would be unusual and inefficient for us to carry, everywhere we go, a physical map that shows us what lies on the other side of a building or hill. Instead, we stitch together our past perceptions of the world to create a mental model of familiar environs. These images, as Kevin Lynch terms them, become the basis not just for wayfinding, but for our general understanding of spatial structure. According to Reginald Golledge and Robert Stimson (1997, 45), studies of wayfinding have

▲ If a destination can be seen it is easy to know which direction you should move to get there. However, navigating to a hidden destination requires spatial knowledge of its location relative to your own (dashed line), and of the most appropriate series of pathways to get there (solid arrow).

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showed that “it was not what was physically or objectively there but what was perceived, remembered, or recalled to be there that was a critical factor in invoking decision rules and making choices.” It is worthwhile to study how we perceive the environment because it is often the most important source of information used for spatial decision-making of any sort, including that which informs architectural design and planning (Robinson and Petchenik 1976, 89).

Past research on spatial cognition suggests that people make significant errors in both how they perceive and remember spatial knowledge, resulting in distorted interpretations of the landscape geometry they use to make navigational decisions. Perhaps you assume that the coffee shop is “straight ahead,” when in fact the street curves substantially before reaching it. Such errors are not viewed by psychologists as a fault with cognitive processes, but as clues to the way our cognitive systems operate (Tversky 1992). That we mentally distort the shape of space has led researchers to investigate the potential for systematic distortion: patterns in the way we erroneously perceive the world around us. Indeed, a number of these patterns have been identified and termed “spatial heuristics.”

This chapter will examine the role heuristics play in distorting judgments made in a navigational context, and will provide a framework for interpreting the results of a perceptual survey and the designing of a schematic map in Chapter 4. I have identified four heuristics which are repeatedly evidenced in geography and psychology literature – rotation, alignment, normalization, and regionalization – and my discussion will be focused around them. However, it will first be helpful to review the theoretical structure of cognitive maps on which they operate. To this end, I will offer a brief summary of the predominant cognitive map models.

Once we are familiar with models for the storage and distortion of spatial information, we can begin to consider how this information should best be communicated to researchers studying the effects of spatial heuristics on behavior. In the third section of this chapter, I will discuss different methods used by psychologists and geographers to record directional judgments. I conclude by suggesting that further research should move out of the laboratory to test for systematic distortions of judgments in real-world environments. This will provide the theoretical context for my own investigation of directional distortion in Chapter 3.

▲ Gradually curving pathways tend to be

mentally straightened.


cognitive Maps

The cognitive map, or mental map as it is known more colloquially, is an umbrella term for the vehicle we use to store and understand spatial knowledge. The term implies the image of a planimetric map which we can “see” in our mind’s eye. Many people describe just such a direct visualization of space when they are making judgments of location and navigating to them. However, there is growing evidence that the structure of cognitive maps is not entirely analogous with that of cartographic maps. Cognitive maps do not use variable symbology to represent different types of features, nor do they maintain a constant scale or have a defined extent. They are a patchwork of spatial information gleaned from numerous sources: sensory perception and spatial memory from a variety of locations, verbal descriptions, and the cartographic maps that are now published for nearly every place and at every scale (Kulhavy and Stock 1996).

While literature on the structure of cognitive maps is vast, no dominant model has yet been established. This is partly because research methods are still so speculative. Although cognitive psychologists have worked hard to make their work a scientific discipline, it is impossible to know exactly how people interpret space – how they perceive, store information, and make judgments about the world around them. It is difficult to communicate these processes because they happen so intuitively. Neurologists have thus far gleaned little understanding of the brain functions associated with them. We cannot project a person’s cognitive map on the wall for all to see and interpret, so we must trust our subjects to represent and interpret them for us.

In this brief discussion of cognitive maps I will describe two leading models for their internal structure: the map image, and the spatial database. Both have been widely discussed in the context of heuristic distortion, but they offer entirely different frameworks for spatial logic. Whereas the map image is focused on the visualization of surface shapes, the spatial database uses a more abstract network of relations for spatial judgment. Users of both systems may arrive at similar conclusions and may be effected by similar heuristic distortions. There is also reason to believe that many people employ both systems and use one, the other, or both depending on the scale at which they are making judgments or their


familiarity with the locale. Spatial heuristics act on both cognitive map models, although as we will see later, a certain model may especially promote certain heuristic tendencies.

Map Images

The cognitive map metaphor was first used by Edward Tolman (1948) to describe spatial knowledge demonstrated by rats running through mazes. Tolman noticed that rats learned to generalize the overall spatial relationship between the start and end – from one side to the other – even when the walls of the mazes were changed between tests. The navigational decisions they made were aligned with the tendency to move in this overall direction. From this he concluded that the rats were able to conceive, if only schematically, of the mazes from an overhead perspective, and interpret an “as the crow flies” path between its start and end (Golledge and Stimson 1997, 224). He went on to suggest that humans do the same. Seeing the straight-line direction to a non-visible destination in our mind’s eye, we can make judgments about which paths to take to get there most efficiently.

Early behavioral geographers interpreted cognitive maps as literal ‘images’ of the landscape from above. Lynch (1960, 4) explains the mental image of a city as a “generalized mental picture of the exterior physical world that is held by the individual.” A clearer image, he notes, is obviously more helpful for navigation. But even the most simplified forms are nonetheless useful and functional in most circumstances. Lynch describes such generalization as decomposition of the landscape into five types of recognizable features: paths, edges, nodes, districts, and landmarks. These features are arranged in a mental map that does not necessarily account for exact distances or directions between them, but is good at recording topological relations such as connectivity and adjacency to the back, front, or sides. Within this topological structure we can easily locate features contextually and make inferences about the location of features we do not know explicitly.

Cognitive maps can help one infer unknown locations. Just like a physical map, spatial knowledge cannot be based on precise information at every point. Cartographers use interpolation to derive estimates of location and attribute information from a limited sample of known points. We do the same for cognitive

▲ Tolman (1948) demonstrated that rats learned to generalize the

relationship between the start and end of a maze, making their passage through it dramatically

more efficient. He concluded that they could conceive of space from an overhead perspective - a

cognitive map.


maps, using knowledge from the perspective of certain locations. However, because we perform these interpolations without mathematical methods, there is incredible potential for variability in judgment (Tversky 1992, 131). Not only can people make inferences using different information from different perspectives, they can also use different processes ranging from systematic deduction to pure speculation. Moreover, the way spatial information is stored may effect the outcome of locational inference.

Raymond Kulhavy and William Stock (1996, 123) argue that a “map image” is the most efficient model for making spatial inferences because it preserves structural relationships across a two dimensional surface. The “space” of mental imagery is analogous to the space in which we perceive the world, and there is evidence for overlap in the neurological systems used to process each. Kulhavy and Stock contrast the image model with a descriptive model founded in language. From a neurological perspective, depiction, and descriptions are processed differently and there is limited potential for precise translation between them (Kulhavy and Stock 1996, 128). As the saying goes, “a picture is worth a thousand words.” It would be incredibly inefficient to code spatial knowledge using conventional syntax. Places that are described with language, such as those in novels, are often imagined wildly differently by various readers. When J. R.

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◄ ▲ Lynch derived city images from sketch maps, interviews, and field trips with subjects from Boston, Jersey City, and Los Angeles. He sorted landscape features into five categories: paths, edges, nodes, districts, and landmarks. At left is his city image of Boston “as seen in the field.”

▲ Cartographers use mathematical interpolation to predict values that have not been directly surveyed. Likewise, we mentally interpolate positions of non-visible features as we navigate.

(Lynch 1960, 18-19)


R. Tolkien wanted his readers to have precise knowledge of Middle Earth he preceded his manuscript with a map. Whether cartographic or cognitive, maps are a much more efficient way of storing and interpreting spatial information than text.

A number of authors who assess the mental image model make distinctions between three types of knowledge recorded by it (Thorndyke 1981; Golledge and Stimson 1997; Tversky et al.1999). Landmark knowledge is the least developed. It refers to awareness of certain landmarks whose relative positions can be dead reckoned from each other or are entirely unknown. The locations of lower-level features are coded with respect to their closest landmark. You might know that the coffee shop is in a certain tall building, but the location of that building is unknown without seeing it directly. Procedural knowledge, on the other hand, is acquired by moving through space along a consistent path. You remember the series of turns required to get the coffee shop. However, even if you have great familiarity with a linear, procedural landscape, you may have very little understanding of the shape of land on either side – how the shop is situated among surrounding buildings. This most developed form of spatial knowledge is called survey knowledge. A survey perspective requires that we make a clear distinction between our own orientation and that of the world around us by using a broader reference frame. It also requires a level of comfort with symbolic abstraction – a road may simply take the form of a line in the mind’s eye (Thorndyke 1981, 140, 144-5,).

The precision of survey knowledge can vary substantially while maintaining its usefulness (Thorndyke 1981, 143). We may have precise knowledge of an area with which we are intimately familiar, and be able to imagine and recount every nuance of its shape. On the other hand, we may have highly schematic knowledge of the same area and be able to navigate it just as proficiently. For the most part, we travel along established paths that are easily followed between junctions where we are presented with limited options for successive directions of travel. Moreover, most adults have an intuitive tendency to account for Euclidean rules and “mental trigonometry” during spatial inference, so they can efficiently construct a usable image of spatial geometry for areas with which they are relatively unfamiliar (Golledge 1999, 15). At a local scale, where our spatial cognition is most useful on a regular basis, our mental maps can be highly

► It is much more concise and

understandable to describe a route with a map than

with prose. To walk from the black to

the white building: (1) turn right (2) walk south (3) turn left (4) walk east (5) turn right (6) walk south (7) turn left

◄ Three levels of spatial knowledge can be recorded by a map image. Landmark knowledge records positions relative to a landmark feature. Procedural knowledge records the specific route necessary to move from one point to another. The most advanced form, survey knowledge, includes surrounding features from which a route is derived by the user on the fly.

Landmark

Procedural

Survey


generalized before they result in significant navigational error.

Spatial Databases

Golledge and Spector (1978) suggest that cognitive maps might be further simplified if they contained only a few landmarks and the bulk of spatial knowledge was stored in associated mental databases of proximal features. This model, dubbed the anchor point theory, is similar to the structure of a modern vector-based GIS. Geographic locations of symbolized features are stored separately from lists of attribute information. A database of buildings might store a central point location for each one, and then list the tenants occupying the storefronts around its perimeter. Their positions within the structure go unspecified because they are superfluous for the analysis the database was designed to facilitate, or because other tools for specifying more precise location, such as signs or building directories, already exist on-site. People may associate a location with a landmark stored in their survey knowledge, and its exact position will be obvious once they are nearby. Such a model straddles the boundary between map image and spatial database.

In the same year, Stevens and Coupe (1978) presented evidence for a cognitive map model that completely discarded the map image in favor of a hierarchical database structure linked to the basic understanding of a global reference frame. Instead of explicitly storing the relative locations of most features on a planar surface, they proposed that we remember locations using a structure of nested geographic regions: cities fit within counties, which fit within states, which fit within countries, which fit within continents. We can deduce the location of a given feature based on the relative position of its superordinate region. If California is west of Massachusetts, then San Francisco must be west of Boston.

This model is founded on the argument that we cannot possibly store detailed relational information about every pair of familiar points within a single, all encompassing reference frame. The result would be an unwieldy network of connectivity – extremely difficult to query, and inefficient to store. Instead, we catalogue feature positions based on their encompassing regions. Imagine you are confronted by a paper map of New York and you are asked to point out the location of an unfamiliar coffee shop. If you search the map surface, finding the shop is likely to take quite a long time, like searching for the eponymous hero of

USA

MA

CA

Boston

SanFrancisco

▼ A hierarchical database model sorts landscape features into nested geographic regions whose shape is greatly simplified conceptually. Because California is west of Massachusetts, San Francisco must be west of Boston.


Where’s Waldo. However, if you consult the index, which tells you the shop is in Greenwich Village, you will likely find it much more quickly. Moreover, you may not need to find its specific location at all if you deem the position of the district sufficient for making the necessary relational inference – the shop is south of your current position in the Upper West Side. The index is the equivalent of a database structure for spatial knowledge. It is related to and may sometimes be used with a map image, but may be sufficient on its own.

Cognitive maps have been described in further detail by many authors. For the purposes of this study, however, only a basic understanding of these two models is essential for interpreting how spatial heuristics effect their structure. Robinson and Petchenik (1976, 89) write that “mapping represents a way of thinking about space, not just dealing with it directly.” This statement was included in a discussion of cartographic maps, but as we have seen, the differences between these and mental images are sometimes few. A cognitive map can be entirely abstract, even leaving behind spatial geometry in favor of a relational database structure. They may take a variety of forms, and are not necessarily map-like. But for whatever reason, the cognitive map metaphor provides an easily understood vehicle for discussing our mental representations of spatial relations.

Spatial heuristics

Heuristics are cognitive systems for producing a conclusion based on a number of inputs. They may function deliberately, such as the diagnostic heuristics used by physicians, or intuitively, as is the case with the spatial heuristics identified here. The purpose of heuristics is to simplify how we process recurring cognitive operations by using preconceived, formulaic strategies. For the most part, they are wonderfully effective and efficient tools. But like any simplification, they can introduce significant error in an anomalous scenario. Studies of spatial cognition show that many people remember road intersections as right angles, even the minority which actually form acute or obtuse angles. This indicates the existence of a normalizing heuristic which acts upon our perceptions of landscape geometry. It is much simpler to presume all intersections are orthogonal in structure than to note the exact angles of each. The distortion this produces

▲ It is much easier to locate a feature on a reference map if you know it is contained within a specific region. If you are familiar with the arrangement of neighborhoods in New York City, it will be easier for you to navigate to specific points within them. At the very least, you will know the general direction you should move to get from one to another.

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may result in a cognitive map which is geometrically impossible over a broad area, but remains highly functional for localized navigation. This is thought to be why people can successfully navigate through a complex street network, but have difficulty drawing a map of their route (Lynch 1960).

While heuristics have been documented by a variety of researchers, the rotation and alignment heuristics are the only two which affect directional judgments and have been formally identified in spatial cognition literature. However, the normalization and regionalization heuristics have been demonstrated by a similarly large body of scholarship. I suggest them as useful classifications for distortions that are based on rectilinear and regionally organized conceptions of space.

Rotation

The rotation heuristic was first identified in a 1981 paper by Barbara Tversky, although evidence for it has been gathered by a variety of studies since the 1960s. She and other cognitive psychologists argue that every figure has a natural axis of orientation. Irvin Rock (1974) and Lila Braine (1978) suggest that the assignment of an orientation to a figure is fundamental to the process of perception, and that vertical is the preferred axis for this orientation. Contemporary linguistics uses verticality as a metaphor for a host of spatial configurations. We say we are going “up” when we are ascending even a slight grade, moving toward a place of particular importance, or when we are going north (Shepard and Hurwitz 1984). This is likely due in part to the modern cartographic standard of northern orientation toward the top of the page. A nearly ubiquitous reference frame, it has carried over into our mental image of the world. As an effect, we tend to rotate figures in our spatial memory so that their natural axes are oriented upward or northward.

Tversky (1981) demonstrated this tendency for uprighting by testing subjects’ memory for figures with dominant axes that were skewed, sometimes dramatically, from north-south orientation. She preformed these tests using familiar geographic figures at two scales, cities and continents, and also with abstract non-geographic figures that subjects were asked to study and recall from memory. Subjects exhibited mental uprighting tendencies in all scenarios, recalling the San Francisco Peninsula as having north-south orientation when its major axis actually runs

RegionalizationNormalizationAlignmentRotationfeatures rotatated to

align with other featuresfeature intersections

squaredfeatures rotatated to

align with cardinal axesareas divided into simplified regions, often normalized

►▼ Street intersections are often simplified to right

angles in cognitive maps. While this may result in geometric

impossibility over a broad area, it greatly reduces the amount

of spatial information stored in memory. The simplified

intersections on the map below could never fit together

while maintaining the shape of connecting streets, but it would be inefficient to store the exact angle of every intersection and

the exact shape of the streets connecting them is largely

irrelevant for navigation.

◄ According to the rotation heuristic, features will be mentally rotated so they have upright orientations.


northwest. Similarly, subjects uprighted the shape of South America so that its central axis ran northward, and rotated the long axes of abstract shapes so they were parallel with the sides of a rectangular page. According to Tversky (1981), Ian Moar (1979) found similar evidence for rotation of island geometry through his work in Britain. Subjects assumed that the central axis of the island was oriented northward although it is tilted considerably to the northwest.

Rotation also effects spatial knowledge of local geographical features. When Tversky (1981) asked subjects to draw familiar street networks they rotated the axes of major arteries to conform to cardinal directions. Lynch (1960) had similar findings. In his study of perceived structure of American cities, Lynch (1960, 57) noted that when asked to draw a map of Los Angeles, local residents had difficulty reconciling the discrepancy in angle between the street system, cardinal directions, and the Pacific shoreline. Although the rigidly gridiron structure of the city streets was convenient for people orienting themselves locally, it made orientation difficult in a broader context. When subjects mentally rotated the grid structure so it was falsely aligned north-south and east-west, they ran into difficulty trying to join it with streets outside the city center that actually were aligned with the cardinal directions.

D. C. D. Pocock’s (1973) study of maps drawn from memory demonstrates a similar tendency. All sixty-two subjects in his study were undergraduate geography majors, and the street intersections they were asked to map were near the geography building. They should have been well aware of the study area’s spatial structure. Their drawings, however, indicated consistent distortions due to a rotation heuristic. Streets which actually approached the intersections from the southwest or northeast were drawn with entirely north-south orientation.

There is also evidence that mental uprighting is a precondition for broader interpretation of landscape geometry in cognitive maps. People often rotate a paper map in their hands so its orientation is consistent with their headings. When recalling spatial knowledge it makes sense that they would similarly align features with a global reference frame to help relate geometry perceived from a variety of perspectives. Shepard and Hurwitz (1984) demonstrated that people mentally rotate figures to help them distinguish between right and left hand turns. Figures that were already aligned with cardinal directions, and thus required less mental rotation, allowed subjects to interpret the orientation of associated figures more

▼ D. C. D. Pocock (1973) asked students to draw Charley’s Cross (left). His subjects drew intersections that were rotated and normalized.

(Pocock 1973, 254)

▲▼ Tversky (1981) demonstrated that people mentally rotate the axis of the San Francisco Peninsula to run predominantly northward while it actually points to the northwest. Tversky’s subjects also uprighted the axis of South America, while Moar (1979) found that Britons uprighted Britain.


quickly. Clearly the rotation heuristic effects both how we remember and how we make judgments based on the memory of spatial information.

Alignment

The alignment heuristic was also first identified in Tversky’s 1981 paper, and has similarly been supported by the work of other researchers. Alignment refers to the propensity for grouping figures as straight, orderly arrays even if, in reality, connecting them would form a non-linear or jumbled pattern. A good example is the tendency for coastal cities to be artificially aligned with a prominent linear edge: the shoreline (Moar and Bower 1983). American cities along the Atlantic seaboard are often conceptualized as being stacked directly above one another. However, if you were to draw a straight line between Boston and Miami, every other major coastal city would lie significantly west of this axis. The coastline is concave, and its shape is far more complex than many imagine it to be. This effect is similar to the mental straightening of landscape features such as roads, rivers, and borders described by other authors, so for the purposes of this study I will interpret the two as descriptions of the same distortion heuristic.

Although it can be difficult to distinguish between the effects of rotation and alignment, there is a subtle but important theoretical difference between them. Rotation takes place when a feature is related to an abstract reference frame, such as the cardinal points, which cannot be perceived on the ground. Alignment is due to the relation of tangible features to each other. Tversky (1981) offers the example of orienting El Camino Real, an arterial street south of San Francisco, along a north-south axis. Is this an effect of rotating the street itself, or is it the result of aligning it to be parallel with the similarly rotated axis of San Francisco Bay? Which heuristic is responsible for the distortion is likely a function of how familiar a given person is with either feature – which would they draw first if asked to make sketch map of the area, or which requires fewer relational steps. Functionally, the sequence is a moot point. Spatial heuristics are closely related to each other and will operate together to effect our images of landscape geometry.

Tversky (1981) studied the effects of alignment by asking subjects to assess the relative positions of the four continents bordering the Atlantic Ocean: North and South America, Europe, and Africa. These continents approximate the form of a quadrilateral array, with North America to the west of Europe, and north

► Cities along the east coast of the U.S. are often conceptualized as being aligned and rotated to stack vertically on top of one another. However, a line drawn between Boston and Miami demonstrates that the coast is substantially concave and the axis leans to the northeast.

► Teversky (1981) notes that El Camino Real, a street on the San Francisco Peninsula, is often mentally uprighted. Is this an effect of rotation, or alignment with the nearby San Francisco Bay?


of South America. However, subjects conceived of these loose relationships as being much more exact. They were significantly more likely to choose a contrived map showing South America aligned directly below North America as an accurate representation compared with a real one showing South America offset to the east. That New York and Boston share a time zone with much of South America’s Pacific coast is not widely recognized.

Similarly, Tversky’s subjects speculated that Europe was aligned precisely to the east of North America when in reality, the bulk of the European continent is more northerly. Southern European cities, such as Madrid and Rome, share latitudes with northern U.S. cities. Savannah and Miami, on the other hand, are due west of northern Africa. Tversky recognizes that a regionalization framework of “northerness” versus “southerness” may play a role in this simplification. However, it cannot be ignored that the neatly aligned array conceptualized by her subjects was far from an accurate description of the continental arrangement.

Pocock (1973) demonstrated the alignment heuristic at a more local scale, and in the context of straightening a linear feature. One of the intersections he asked subjects to draw had a long, curved street extending from it. This curvature was largely ignored; most people drew the street as a single, straight line. This is a curious effect, especially considering that from street level one would not be able to see from end to end of a curved street, a clear indication of its curvature at the time of perception. It would seem that the street’s alignment along a straight course is an effect of how the street is stored in memory, or how it is retrieved and judged when related to other nearby features.

The same effect of straightening a large, sweeping curve is demonstrated by Lynch (1960) in his discussion of the street geometry of Boston, a city that is known for having anything but a rectilinear spatial structure. Lynch suggests that the directionality inherent in streets, or ‘paths’ as he refers to them more broadly, might have the propensity to be aligned with “some larger system” (Lynch 1960, 55-6). He notes that people often miss the subtle curve in Massachusetts Avenue at Falmouth Street, and assume it is straight along its entirety. Among those he interviewed, this often confused their entire image of downtown Boston as it was constructed from this primary feature. Atlantic Avenue, which turns almost entirely around as it circles the north end, but is straight in certain portions, was also difficult for people to reconcile with their mental images of the city structure.

▲► Subjects in Tversky’s (1981)

study thought South America

should be aligned vertically with

North America, and Northern Europe

should be aligned horizontally with the northern U.S.

▼ In their drawings (right), subjects straightened the path of a street to align with its trajectory as it left the intersection (left).

(Pocock 1973, 254)

Falmouth St.

Mas

sach

uset

ts

Ave

.

(adapeted from Lynch 1960, 56)

◄ Lynch (1960, notes that his subjects rarely acknowledged the curve in Massechuetts Avenue at Falmouth Street, a mistake that confused their entire city image of Boston.


Dirk De Jonge (1962) found similar evidence of straightening central routes in his study of towns and cities in Holland (as described by Canter 1977, 56). Bends in the midsections of roads seem to be largely overlooked.

Subjects in Stanley Milgram and Denise Jodelet’s (1976) study revealed that Parisians simplified and straightened the shape of the Seine River, one of the city’s most distinctive geographical features. The Alma bend quickly redirects the course of the river from northwest to southwest, but this tight curve was not reflected in the drawn maps of city residents, who instead interpreted the Seine as arcing gently through the city. Milgram and Jodelet argue that this is based on how residents experience the river from vantage points along its bank. When one walks or drives through the city, the bend is never readily apparent. It has too great a radius to be distinguishable from alongside, so it is conceptually aligned with more graceful curvature upriver (as described by Chase and Chi 1981, 127).

The orientation of maps drawn by subjects in K. Clayton and M. W. Woodyard’s (1981) study also revealed an important feature of the alignment principle. Most of the subjects drew their maps in a consistent orientation, although no particular one was specified by the instructions. Each session began with the drawing of a specific feature, and subjects proceeded to align the remainder of their drawing with it. This is similar to the effect noted by Pocock (1973) in his study of drawn intersections. Subjects were given a reference figure to help them begin their drawings and to aid in later comparison. There was a strong tendency to simply extended angles in this figure as straight lines, so a street that had a dominant direction of north-south over its length but exited the intersection on a diagonal was remembered as having an entirely diagonal orientation. Pocock suggests that people artificially align to their initial orientation in a given circumstance.

Lynch (1960) describes perceived alignment among an indigenous population, demonstrating that the heuristic is not merely a function of cultural expectations or the cardinal reference system adopted by Westerners. The people of the island Tikopia, according to Raymond Firth’s 1936 account, use a spatial reference system related to the dominant ‘edge’ in their landscape: the shoreline. They defined the location of houses and villages lining the shore simply by referring to the “next” or the one beyond that, as if the entire settlement were one-dimensional. It is highly unlikely that the shoreline was entirely straight, or that

► Lynch (1960) describes an indigenous system for defining village location that makes use of a conceptually linearized shoreline. Only the order of villages up and down the coast is important for navigation between them.

▲ Subjects in Milgram and Jodelet’s (1976) study simplified the shape of the Seine River so that it arched gracefully through Paris (dashed line). They largely ignored the abrupt turn of the river at the Alama Bridge (as described by Chase and Chi 1981, 127).

Alama Bridge

(adapted from Chase and Chi 1981, 127)


the houses were placed in a perfect row, but there was no need to describe their positions with any greater precision. Like any heuristic, the alignment principle is an efficient way of simplifying the spatial structure when no greater amount of information is relevant on an everyday basis.

Normalization

Within geography and psychology literature the normalization heuristic has not been formally identified, but evidence for it is documented by myriad authors. It can be described as the propensity to normalize mental images by constructing them from parallels and perpendiculars. It contrasts with rotation and alignment in that it applies to multipart networks rather than distinct paths, edges, or axes. Normalization has been largely studied with respect to the configuration of transportation networks, because they are the dominant network features in the modern landscape and are familiar to the average person who travels along them on a daily basis.

Intersections are of particular interest because they are a convenient point for comparing the relative orientation of multiple paths from a curbside perspective. Moar and Bower (1983) studied subjects’ memory for intersections to determine whether they were internally consistent with Euclidean properties of space such as non-intersecting parallels and triangles whose internal angles sum to 180 degrees. Subjects imagined themselves standing in the middle of familiar intersections in Cambridge, England, and were asked to draw arrows indicating the direction, ‘as the crow flies,’ to two adjoining intersections forming a triangle. In nearly all scenarios, judgments of angles were biased toward 90 degrees – people assumed that the intersections were more orthogonal than they were. As a result, the sum of judged angles within a given triangle was significantly greater than 180 degrees. When considering the relationship of intersections from a specific perspective, subjects did not account for the Euclidian geometry of the triad as a whole.

Pocock (1973) demonstrated a similar effect among subjects asked to draw a familiar four-way intersection. Not only did they artificially rotate their drawings of Charley’s Cross to conform with the cardinal directions and straighten the exiting roads, they normalized the intersection angles. While the streets actually met each other at an acute angle, much like the blades of partially opened scissors, subjects routinely drew them crossing at 90 degrees. Canter (1977, 54) notes that

RegionalizationNormalizationAlignmentRotationfeatures rotatated to

align with other featuresfeature intersections

squaredfeatures rotatated to

align with cardinal axesareas divided into simplified regions, often normalized

▼ Drawings of Charley’s Cross from Pocock’s (1973) study also reveal normalization.

(Pocock 1973, 254)

► Normalization is the tendency for features to be mentally aligned with a grid and their intersections simplified as right angles.

▼ Moar and Bower (1983) asked subjects to estimate relative direction to adjacent intersections around a triangular block. Judgments were regularly biased toward 90 degrees and the sum of the angles was substantially greater than 180 degrees.

(Moar and Bower 1983, 109)


Goodchild (1974) found similar evidence that “road junctions tend to be drawn as right angles.”

Studies show that angles measuring from 60 to 120 degrees at intersections are interpreted or remembered as right angles. Clayton and Woodyard (1981) describe how campus map drawers at Vanderbilt University are often confused by the 60 degree intersection of major streets adjacent to campus. They are inclined to conceptualize them as right angles, and although they recognize that their maps look erroneous and their geometry is nonsensical, they do not recognize that the schematized intersections are at fault. Clayton and Woodyard note that “within a region, their knowledge is [topologically] valid, but across regions [it] is not” (1981, 156).

Bryne’s (1979) study of memory for intersections among residents of Cambridge, England indicated a similar tendency to normalize angles. He tested subjects at intersections measuring 60-70 and 110-120 degrees, and found that the majority were remembered as right angles. More importantly, he notes that 60-70 degree angles were as often remembered acute as they were obtuse, and visa-versa for those that were 110-120 degrees. This indicates that people store very little detailed knowledge about the shape of intersections – perhaps no more than the number of streets converging at them. Instead we apply prescriptive knowledge of a normative intersection geometry in multiple locations throughout the landscape. This substantiates the theory that we use a topologically structured “network-map” rather than an angle and distance-specific “vector-map” as the basis for our city images (Byrne 1979, 153).

If we assume all street intersections to be right angles, it is logical for us to assume that streets form a rectilinear network – a gridiron pattern. Chase and Chi (1981) found that subjects created just such an artificially rectilinear mental map of the streets bounding the Carnegie-Mellon campus in Pittsburgh. The eastern end is bordered by four straight segments connected by two obtuse and one right angle bend. The study tested subjects both with and without architectural background, a variable that was intended to provide insight on how familiarity with spatial thinking affected spatial memory. The architects routinely drew the streets correctly, while non-architects reduced the schema to three street segments with two right angle bends, converting the shape of the enclosed space from pentagonal to rectangular. There was such an inclination to normalize exterior

60 - 70° junctions

110 - 120° junctions

80

60

30 40 50 60 70 80 90 100 110 120 130 140 150

40

20

Freq

uen

cy

Estimated Angle

Bryne 1979p. 152

▼ Judgments of intersection angles in Byrne’s (1979) study demonstrate that both acute and obtuse junctions are likely to be normalized to right angles.

(adapted from Byrne 1979, 152)

(Chase and Chi 1981, 126)

◄ Chase and Chi (1981) had architects and non-architects draw sketch maps of streets adjoining the Carnegie-Mellon Campus. Architects were much less likely to straighten streets and normalize intersections.


angles that the geometric reality of the interior space was jeopardized.Bostonians similarly interpret the shape of Boston Common as artificially

rectilinear (Lynch 1960, 21). Each corner of the park is framed by a right angle intersection, but there are five of them. What would logically be interpreted as a square based on its corner angles its actually more pentagonal. This geometric impossibility is accommodated by the fact that three of its bordering streets are curved. Lynch reports that they are straightened in Bostonian’s city images, evidence of an alignment effect among consecutive intersections on a given street.

Conceptions of the park’s geometry are further confused by the intersections of three arterial streets alongside it. Boylston and Tremont Streets are experienced as parallel on the opposite side of the city (Lynch 1960, 22). Both originate as perpendiculars from Massachusetts Avenue, but cross at the southern end of the Common. Tremont then proceeds to cross Beacon Street, another perpendicular from Mass. Ave., at the Common’s eastern end. That three conceptually parallel streets form three intersecting sides of the park compounds the difficulty of visualizing its true shape. Parallel and perpendicular geometry was so dominant in the minds of Lynch’s subjects that they almost entirely overlooked the street curvature that made these intersections geometrically possible.

Arterial streets in Nashville radiate from the center of town, much like the avenues and boulevards extending from Paris’s Arc de Triomphe or Place de la Republique. Clayton and Woodyard (1981, 156) emphasize the difficulty of visitors and newcomers who are used to more conventional, gridded street patterns in navigating the city. For better or worse, the grid has become a nearly ubiquitous urban form, especially in the United States, and city goers have come to expect its regularity.

In Los Angeles, a city with predominantly gridiron street geometry in its downtown area, people are surprised when they find variation from this structure outside the city or in the freeways that snake through it. Thorndyke (1981) notes that those who are new to the city schematize the entire metropolitan area to fit with the regularity of the grid. When asked to draw a map of the area they are confused by the intersection of streets they assumed were parallel based on a perspective from a different part of the city. This points to two effects of everyday spatial cognition. First, assumed parallelism plays an important role in how people conceive of spatial geometry over broad areas. Second, people have relatively

► Lynch (1960, 21) notes that Bostonians interpret Boston Commons as a five sided rectangle. They normalize the intersections of the surrounding streets, yet are aware that there are five of them.

► Los Angeles has a patchwork of grid systems and freeways that snake through the city. Thorndyke (1981) notes that residents are often confused about how grid systems in various parts of the city align with one another.

(Lynch 1960, 21)

Mas

s

A

ve.

BeaconBoylston

Tremont

► Beacon, Boylston, and Tremont streets are conceptualized as parallel because they all intersect Massachusetts Ave. perpendicularly. Yet they intersect at right angles near Boston Common.

(adapted from Lynch 1960, 56)

(ESRI 2008)


consistent and usable knowledge of regional network topology, but this geometric consistency breaks down across regions and it its difficult to form a topologically accurate map of an entire city (Clayton and Woodyard 1981, 156).

One reason for this regionalized understanding may be the way we experience the world around us from point perspectives. It is clear that the perception process is a highly complex exchange between the observer and the environment around him, and that the geometry of both may effect how he remembers the structure of the world from each perspective he takes. According to Lynch (1960, 131), “what he sees is based on exterior form, but how he interprets and organizes this, and how he directs his attention, in its turn affects what he sees.”

The sorting of visual space relative to the form of the human body is the most convincing evidence we have for a natural disposition toward normalized perception of geometry, especially at a local scale. The body’s axial nature makes a convenient reference frame for relating to the space directly around it (Tuan 1977; Tversky 1999). We interpret the location of objects in this space relative to the three axes of the body: up-down, front-behind, and right-left. For instance, we might describe two objects as being “in front” and “to the right,” a configuration that implies an angle of 90 degrees between them. In fact, this angle may be substantially greater or lesser, but we would still use similar terms to describe their positions. That we tend to describe these relationships only in terms that imply right angles is an indication that we are naturally included toward normalized perception. The normalization heuristic effects not only the way we store spatial information, but how we perceive it (Tuan 1977, 36).

Regionalization

This fourth spatial heuristic refers to distortion of spatial knowledge as an effect of coding places in terms of the regional areas encompassing them. The origin of these regions may be natural (plains, desert, mountains), cultural (downtown, uptown, suburban), political (counties, states, countries), or they may be constructed on the basis of a reference system (north, south, east, west). Once we have established the location of regions, we can make inferences about the relative location of points of interest contained within them. People can much more quickly identify one city as north, south, east, or west of another if they are in separate regions than if they are in the same one (Tversky 1999, 518; Wilton

▲ The three perpendicular axes of the human body are a convenient way to define relative location and are the likely basis for normalization tendencies. Even if objects do not perfectly align with our orientation, we can usually sort them into front, back, left, right, up, or down spaces.


1979; Maki 1981). This efficiency, however, is often traded for a substantial loss in accuracy.

The validity of this regional schema breaks down when place locations do not conform with the overall location, perhaps better described as the centroid, of their superordinate region. Moreover, the shape of perceived regions is often highly simplified. As a result, regionalization can substantially distort perceptions of relative positions. Vermont and New Hampshire, for instance, might be abstractly conceptualized as side-by-side rectangles. A person unfamiliar with the actual shape of their mutual boundary might readily assume that Hanover, New Hampshire is more easterly than St. Johnsbury, Vermont. Although correct that New Hampshire lies east of Vermont, he would have overlooked the complexity of their mutual border, a characteristic that allows Hanover to be south-southwest of St. Johnsbury. As Tversky (1991, 133) notes, “people infer the direction of entities in a category from the overall direction of the category, thereby distorting the direction of cities in a state in the overall direction of the state.”

We conceptualize space in terms of regions in all sorts of settings, and at all sorts of scales. Continents may be the largest unit of terrestrial regionalization, while the rooms of a house are the most local. Lynch (1960, 47) describes regions, which he terms “districts,” as one of five elemental features of the urban landscape. Districts are areas of the city “which the observer mentally enters ‘inside of,’ and which are recognizable as having some common, identifying character.” Based on the findings of his study, Boston has fourteen distinct districts which are not planimetrically arrayed in any formal structure. Yet from within any district, Bostonians could easily identify the general direction of those surrounding it (Lynch 1960, 66).

Although the boundaries of urban districts can usually be identified by linear elements – streets, rivers, elevated highways – the exact shape and location of these boundaries are not typically solidified in the mind’s eye, no doubt partially an effect of the alignment and normalization heuristics (Lynch 1960, 67). Our conceptualization of districts, similar to that of roadways, might be better described as a functional network of amorphous spaces whose relationship to each other we can identify, but whose geometry it is difficult to resolve precisely. Such rough definitions of regional boundaries and shapes are well demonstrated by Lynch’s maps of city districts, which have rounded corners and highly generalized

St. Johnbury

Hanover

St. Johnbury

Hanover

St. Johnbury

Hanover

St. Johnbury

Hanover

► Regionalization refers to the tendancy to simplify the shape and relative orientation of regional areas. A person unfamiliar with the geography of Vermont and New Hampshire might simplify them as rectangular regions situated east and west of each other, and might wrongly assume that St. Johnsbury, Vermont is west of Hanover, New Hampshire.

▼ Lynch (1960) recognizes fourteen distinct regions, or “districts,” in the city of Boston. These regions have generalized shapes and somewhat fuzzy boundaries, but Bostonians can easily distinguish between them and point out where they are located relative to one another.

(Lynch 1960, 69)


form. We think much less about where one region ends and another begins than about where each region generally is.

Stevens and Coupe’s (1978) groundbreaking study on regional distortion in cognitive maps proposed a more complex nesting schema to describe how we associate regions at a variety of scales. Their hierarchical database cognitive map model is based on evidence of regionalized heuristic distortions. Noting that we tend to organize known locations within a structure of nested superordinate regions, they suggest that we make judgments of relative position only between two regions at the same hierarchical level – state to state or country to country – or between two points in the same region. Stevens and Coupe’s testing of this hypothesis famously revealed that subjects erroneously judged Reno to be east of San Diego because Nevada is generally east of California. Had they tested an intra-regional control, perhaps the direction from San Diego to Sacramento, they would have expected considerably more accurate judgments. Furthermore, they note that the size of the unit used to make these judgments, and therefore their potential accuracy, does not seem to be a function of familiarity with a given area. Residents of San Diego made similarly poor judgments of the direction to Reno as they did between more distant pairs of cities (Stevens and Coupe 1978, 425).

Spatial heuristics work together to effect our judgments of spatial geometry. When axes are rotated to the north and aligned with each other the result is an upright, straight-line figure. The addition of a normal, grid-like structure and of regional classification is eerily similar to many dominant forms in the modern landscape: tall buildings with rectilinear facades, rectangular vehicles, rooms with straight and vertical walls. Manhattan Island is the prototypical example of planimetrically “normal” geometry. Its streets are arranged in a grid running north-south and east-west through districts that are neatly organized. That the island is not actually oriented north-south, and that some of its streets do not fit the grid pattern, or than its districts – Midtown, East Side, West Side, Central Park, Harlem – have jagged and blurry boundaries is of relatively little concern. Researchers speculate that it is more efficient to remember a vague and distorted city structure, and repeatedly demonstrate this tendency as evidence of heuristic simplification.

Reno

San Diego

Sacramento

▼ Stevens and Coupe (1978) suggest that spatial relationships between regions are stored used a hierarchical database model. They use a flowchart to describe the relationship between nested cities, states, and countries.

►▼ Stevens and Coupe (1978) demonstrated San Diegans inappropriately regionalized the relationship between California and Nevada, assuming that they were simply east and west of each other. Judgments of the direction from San Diego to Reno (below) were skewed dramatically to the east, while the actual direction (solid arrow) is to the northwest.

(Stevens and Coupe 1978, 435)

(Stevens and Coupe 1978, 425)


Measuring Directional Judgments

So far I have discussed the prevalent models for cognitive maps and how the spatial information stored in them can be distorted according to heuristic rules. Because we cannot directly measure these cognitive processes, evidence for them must be derived from external behavior (Robinson and Petchenik 1976, 86). Psychologists and geographers have designed a variety of experiments to measure behavior so it can be interpreted as data and compared to the behavior of others. For the most part, previous investigations of spatial knowledge have taken place in laboratory settings. I contend that an integral component of research methodology is the environment in which judgments are made. We can better understand how and why people make spatial judgments by shifting investigation into the real world, and by structuring experiments to mimic everyday methods of indicating spatial relations. This is the theoretical foundation for the survey procedure I present in the following chapter. To guide its design I investigated methods for recording the perception of angles, relative directions, and figure orientations that contribute to directional inference.

The most common method for recording spatial knowledge in psychological research has been asking subjects to draw their perceived environment. Studies using this method can be divided generally into two categories: those which ask subjects to draw a map (Lynch 1960; Canter 1977; Golledge and Stimson 1997; Kitchen 1997; Haber et al. 1993; Byrne 1979) and those which ask them to indicate relative direction or location with a computer program, technical instrument, or by drawing diagrams on a survey form (Moar and Bower 1983; Tversky 1981; Kitchen 1997; Hintzman et al. 1981). Both are typically performed remote from the environment in question, requiring subjects to employ only their memory of spatial configurations to complete the tasks. For studies specifically concerned with the structure of knowledge, this experimental model makes sense. It reduces the likelihood of external factors affecting the judgment process. However, external influences are an important part of how we make judgments on an everyday basis. Researchers wishing to study wayfinding or other activity related to a specific environment are better served by investigating behavior in that environment rather than in a white-walled psychology laboratory.

In a number of studies, subjects have been asked to imagine themselves in a


certain place and then use this imagined orientation to make spatial judgments. Robert Kitchen (1997) asked people to draw the direction to objects around them relative to a line indicating their current heading. Douglas Hintzman and his associates (1981) did the same using an electronic “drawing” device. Moar and Bower (1983) conducted research on perceived directions from one intersection to another in a neighborhood only blocks from their laboratory, yet they chose to stay inside and asked subjects to draw the relative positions on paper. These studies suggest researchers are reluctant to break from a strictly scientific method and study the environment in situ.

Sketch mapping has often been thought of as a reliable and consistent way of communicating spatial knowledge. Sketch maps can be easily compared, measured, and stored. They can also be made just about anywhere with simple materials. Most adults, and many children for that matter, can easily relate to a sketch map of an area, and will be able to create at least a crude map themselves if asked to do so. Byrne (1979, 147), however, describes two fundamental disadvantages of sketching compared to other methods of recording spatial knowledge. First, drawing a map which accurately conveys a map image in the mind’s eye requires some technical skill. Although nearly everyone can put pen to paper, it is difficult for some to draw straight lines or compose realistically proportioned arrangements without measurement tools. What may have merely been technical errors can be easily interpreted as a characteristic of someone’s spatial knowledge. Secondly, commonsense Euclidean geometry is much more apparent on a map of a broad area. Through the process of mapping, subjects may be able to correct for geometric error that would otherwise have gone unnoticed. A good example is Moar and Bower’s (1983) investigation of directional relationships between intersections. Had they asked subjects to draw a map of the triad as a whole, the figure would have necessarily been drawn much more accurately. Instead, they asked them to make independent judgments from each intersection, and the aggregate angles summed to more than 180 degrees. Byrne’s (1979) test used a similar methodology so the results would not be skewed by known geometry at a broader scale.

Lynch (1960) asked residents of the cities he studied to draw sketch maps of their neighborhoods and the city as a whole, and he used these maps to help identify major features that anchored their city images. But he also conducted

(Moar and Bower 1983, 109)


interviews and walked around the cities with a portion of his subjects so they could describe first-hand, from a street-level perspective, what they found most significant about the structure of the urban environment. Although Lynch’s study included no quantitative measurement and did not even pretend to be a controlled psychological experiment, its success in revealing perceived urban form demonstrates the value of bringing studies of spatial cognition outside into the environments where spatial knowledge forms and where cognitive processes normally take place.

Environmental psychologists separate themselves from cognitive psychologists and break away from the laboratory and work directly within the spaces they study. Proshansky (1981, 7) writes that “the root of the problem of how psychologists think and do research at the individual level of analysis is the experimental-laboratory model and the assumptions underlying its use.” Although psychologists have made great strides to move in an environmental direction, the bulk of spatial cognition research was conducted decades ago and has not yet been adapted with this philosophy in mind. Doing so provides substantial opportunities for new research, especially among behavioral geographers who, by definition, are interested in how people live, work, and otherwise interact with the real-world spaces around them.

If we are going to study behavior in real-world environments, we must next ask what method we should use to record this behavior. Lynch’s (1960) interview methodology was clearly quite effective for providing a generalized critique of urban structure. But if we are interested in more precise analysis of systematic distortions in judged relations it would be helpful to use a quantifiable technique that allows for direct comparison between subjects and statistical analysis.

Lyn Haber and her coauthors (1993) tested nine methods for indicating relative direction among blind adults, including pointing, positioning of a dial, drawing, and verbal description. In their trials, the most accurate methods for indicating direction were those using body parts (pointed finger, nose, or facing of chest) or extension implements (a short or long stick). Drawing an angle on a piece of paper, turning a dial to point in the desired direction, and verbal descriptions using clock face directions were significantly less accurate, although this may have been influenced by the subjects’ inability to visually align a pointer with a desired target. Studies undertaken with sighted adults resulted in similar findings,


although with a much higher degree of accuracy – about 2 degrees error instead of 7.5 degrees for the pointing method (Haber et al. 1993, 35, 41). This indicates that there is an element of hand-eye coordination associated with the accuracy of pointing. We can sight along our outstretched arm to better refine our indicated direction.

New insight on spatial judgment can be gained by changing both the setting and the method used for investigation. First, shifting from the cognitive psychology laboratory to the real-world landscape already embraced by environmental psychologists will help us understand how spatial knowledge and perception jointly influence spatial judgments. If researchers are correct that we abstract our knowledge of environmental structure based on heuristic influences, we cannot expect people to interpret an imaginary environment in the same way

The Boston image as derived from verbal interviews

The Boston image as derived from sketch maps

The visual form of Boston as seen in the field

Lynch gathered evidence on subjects’ images of Boston by asking them to sketch the city, interviewing them about their daily interactions (emotional and physical) with the city, and going into the city with them on a field trip so they could point out places most important to them. Lynch created city images based on each of these methods, and the diversity of their forms is a testament to the influence of a sampling method on a study’s results.

(all maps from Lynch 1960, 146-7)


they would a real one. The argument that this inability merely leads to judgmental distortion fails to account for everyday behavior. People do not typically make these judgments remotely, but from where they are, in the moment, drawing on their sensory perceptions of space around them. Furthermore, judgments should be measured using a methodology that is inherent to the behavior of wayfinding, such as pointing with an outstretched arm. These circumstances surely influence peoples’ judgments. Why should our investigations not replicate these conditions as closely as possible?

The way we perceive, store knowledge of, and make judgments about the geometry of the world around us is theoretically complex, yet intrinsic in our day-to-day functionality. Throughout our lives we gather an immense amount of spatial information in our cognitive maps, a large portion of which is likely distorted by spatial heuristics. As we navigate the world we draw on this knowledge, distortions included, to help make directional judgments and decide exactly where to go.

Advances in spatial cognition research should fill the environmental shortfall by studying the way people make judgments of relative location in real-world situations. Perception not only plays a role in forming cognitive maps, but in aligning them with our current position. The perceived environment should not be excluded from our consideration because it is an unwieldy variable to isolate using the scientific method. The difficulty of isolating it gives us even greater reason to study it – to try to understand what aspects of the first-hand world affect our judgments of direction and cause distortion in these judgments. If moving this investigation outside the laboratory means sacrificing a portion of its scientific purity, then so be it. Lynch’s Image of the City had no basis in the scientific method, but it was systematic, and it has been more influential for the work of geographers, planners, and architects than any scholarship in the formal spatial cognition literature.

In Cognition in the Wild, Hutchins (1995, xiv) notes that “pure research on the nature of real cognitive practices is needed … because it is in real practice that culture is produced and reproduced.” Awareness of spatial geometry, and perceived geometry in particular, is useful for tasks that permeate nearly every aspect of our everyday activity, from designing buildings and planning highways to deciding how to get to the nearest coffee shop. While cognitive maps remain the


most frequently used tool for achieving any of these tasks, cartographic maps are a useful reference for spatial geometry in less familiar places.

The challenge for cartographers is to learn from research in spatial cognition to design more efficient maps (Lloyd 1999, 525). The following chapters describe my solution: a survey procedure for gathering spatial cognition data in the field, and a process for assessing this data and using it to draw a schematic map.


▲ This aerial photo shows the Middlebury College campus and the Champlain Valley to its west. The convergence the four arterial streets on the west side of Otter Creek − South Street, Main Street, College Street, and Weybridge Street − is clear in the center foreground. The downtown bend in the Creek is noticeable in the lower left.

(courtesy of the photographer, Bill Hegman, Middlebury College Department of Geography)

39Chapter 3 The Perceptual Survey

3 The Perceptual Survey

To gather spatial cognition evidence I developed a procedure for measuring directional judgments in the field. This chapter describes a case application of this procedure in the town of Middlebury, Vermont. While the process was designed to be replicable for use in other study areas, it should be understood as a pilot, and will necessarily be improved upon in future applications with refinements in technical approach, sample size of test subjects and sites, and other aspects to accommodate a given study area.

The procedure consisted of two phases: surveying and data management/ preliminary analysis. The survey phase, in which data was collected from the field, was conceptually straightforward but the most time-consuming and technically complex of the two. It involved bringing subjects who were familiar with the study area to a variety of sites throughout it. At each site, subjects were asked to make judgments of the direction to designated landmarks by pointing to them, and these judgments were recorded using a specialized compass. Raw data from this survey required significant processing to account for magnetic declination and convert between various polar coordinate systems. Storing, processing, and later visualizing polar data required substantially more time and effort than originally anticipated. While the bulk of data analysis was accomplished during the map design process, some preliminary statistical analysis was included in the data management phase to determine which results should have the greatest influence on the design of a new, perceptual schematic map of Middlebury.

As a result of the emphasis placed on testing subjects in the field, an untold number of uncontrolled variables – influences on judgments – were inevitably introduced. While the testing procedure I used is certainly replicable, I do not intend it to be seen as a conventional scientific experiment. Cartography is an


unusual blend of science and art, and insomuch as this procedure is intended to inform the cartographic process it requires that those using it have an awareness of its weaknesses. Only a limited number of subjects were tested, and the variability of their perspectives is evident. The results are not intended to provide truths, but rather reveal patterns in how subjects perceived the geometry of the land around them.

Survey

Setting

Middlebury is a small town in Vermont’s Champlain Valley, an agricultural corridor which spans the state’s western side. From within town, the foothills of Vermont’s Green Mountains are visible to the east, and on clear days New York’s Adirondacks, which lie just across Lake Champlain, can be seen to the west. While most of the town’s thirty-nine square miles are farmland, a village in its northwest corner is home to most of the town’s 8,000 residents and about 2,300 undergraduate students at Middlebury College. The college campus lies just west of downtown to the south and west of Otter Creek. This substantial river simultaneously divides the town into two halves and unites it around an important crossing point. Only one downtown bridge has ever provided a crossing over the creek. This restriction has shaped the town’s traffic and development patterns. The bridge is a traffic funnel, a landmark in the street network which functions like the knot of a bow tie, cinching together the streets that fan out on either side of town.

Middlebury’s streets are known for being anything but organized or rectilinear. Like the cow paths of Boston’s North End or Manhattan’s Financial District, Middlebury’s streets have developed vernacularly over 250 years of use. Right-angle intersections are unusual. While each of the four state and federal highways that converge downtown have directional designations, none of them runs cardinally aligned for any notable distance. It takes time for new residents to understand Middlebury’s traffic network and navigate it efficiently, but as in any initially confusing place, this learning curve is soon accomplished.

The combination of prior knowledge and sensory perception required to navigate Middlebury made it an ideal site for my field research. Because the streets to not follow a consistent pattern, subjects could not use regular geometry (e.g.

Middlebury College

Downtown

to N

ew York

to New York

to Rutland and Boston

to B

urlin

gton

Middlebury

Boston

Burlington

Manchester

▲ Middlebury is located in Vermont’s Champlain Valley

▼► Middlebury College occupies most of the western side of town, while the commercial downtown spans both sides of the bridge.


(Mid

dleb

ury

Colle

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four blocks over, five blocks up) to logically deduce location. The variability of the road network and built environment allowed me to select testing sites where subjects would encounter a variety of landscape features – streets, buildings, rivers – oriented in a variety of directions. The small size of the town also allowed subjects to visit a variety of environments in a relatively short time, including open areas, residential neighborhoods, downtown business districts, commercial areas, hills that overlooked the town, and low areas by the creek.

The Tour

In order to test subjects from a variety of locations around Middlebury, a four-mile tour route was designed to connect fourteen study sites. Each site was designed to provide insights on how subjects would be affected by certain nearby features of the landscape, including the orientation of street intersections and adjacent building facades. Sites were selected on the College campus, downtown, in outlying residential areas, along major highways and small side streets, in areas where subjects walked everyday, and in places most had visited only infrequently. All sites were positioned adjacent to roadways, and subjects were told that their understanding of the town’s street network was the study’s primary focus.

To ensure that subjects were drawing from their person memory rather than a short-term image of the town’s geography, no maps of the area were shown to subjects during the tour. Although some subjects had worked with maps and orthoimagery of Middlebury in classes or for other purposes, they were asked not to study any maps of the area in preparation for the tour. Other than this, no effort was made to standardize subjects’ familiarity with Middlebury geography. Each was simply taken as a representative sample of the student population, and it was assumed that the results of those whose judgments were particularly adept would be balanced by the results of those who were not.

At each site, subjects were asked if they recognized where they were. In a few cases they were hesitant, and I pointed out some recognizable landmarks (“the hospital is over there,” or “that steeple is the Congregational Church”). In each of these cases, the hesitant subjects affirmed that they now understood their location and could confidently proceed with the testing.

Groups of two to four subjects were scheduled to take the tour together. As a group arrived at each site, the directional judgments of individual subjects were


tested one at a time. Other subjects were asked to stand at a distance and with their backs turned so their judgments would remain uninfluenced by their peers.

While some tour groups walked the entire route, most drove from site to site. Both walkers and drivers followed the same route, and I observed that walkers were no more confident in their positions when they arrived at sites than were drivers. In both scenarios subjects were very social while moving between sites and were relatively unaware of the route they had taken between them. When arriving at a site, both walkers and drivers generally took a moment to look around and orient themselves before expressing confidence in their location. Given this similarity, I did not find a reason to discriminate between walkers and drivers in my analysis.

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Carol’s Co�ee Shop

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◄ The tour route was approximately four miles long and ran counterclockwise around town to visit fourteen test sites on the College campus, downtown, and on slightly outlying side streets.


At each site, subjects were asked to make two directional judgments: to a stationary landmark, Carol’s Coffee Shop, and a compass direction, North. These two types of judgments were included to test for the differences in how subjects oriented themselves within local and global reference frames. Originally I intended to have subjects judge direction to more than one landmark in Middlebury. However, preliminary testing demonstrated that the most time consuming portion of the testing procedure, even more than travel between sites, was that devoted to making judgments. Each additional landmark to which subjects were asked to point would have added significant time to each tour. As it was, visiting fourteen sites and asking subjects to make two judgments at each took three subjects about an hour and a half to complete by car, and an additional hour by foot.

Carol’s was chosen as a local landmark because it is near the center of town and because its location was well known to Middlebury College students. All of the subjects confidently knew the location of the shop. Additionally, Carol’s has only one public entrance so its location could be refined and easily understood as this doorway if subjects asked for greater specificity. Typically I did not include this detail because the shop’s entire floor plan was so small as to account for substantially less than one degree on the horizon from every site at which a direction to Carol’s was judged. At Site 6 the shop’s entrance was clearly visible and subjects were asked only to judge the direction of north.

North was chosen as a global landmark because it is commonly associated with the top of a reference frame. There is also no clearly identifiable feature visible from every site which signifies the direction of north. If subjects had been asked to point east or west, for instance, they would likely have simply pointed to the Green or Adirondack Mountains.

Vermont winter weather is variable and presented a few challenges throughout the testing process. Tours were not led if temperatures were extremely cold: less than 0°F. Tours were also canceled if it was actively snowing, as visibility was considered a requirement for subjects to orient themselves at each site. The vast majority of tours were led on clear days, when visibility was upward of 20 miles – the Green Mountains were typically visible from College Hill. Tours were always conducted during daylight hours, and the position of the sun was always visible although tours were led at various times during the day.

▲ North judgments were designed to test distortion of street orientation

relative to the outside world (top). Carol’s judgments were designed to test distortion of street orientations relative

to other streets and other features within the town (bottom).

North Judgmentsdistortion relative to global reference frame

Carol’s Judgmentsdistortion relative to local reference frames

▲ The entrance to Carol’s Coffee Shop on Merchant’s Row


Measurement Instrument

Directional judgments were measured using a customized version of the Suunto KB-20, a high-precision compass designed for sighting bearings while orienteering. The compass featured a platter-style compass rose visible from the top, and a lens on the front through which the bearing of the compass’s central axis could be read with one degree gradations. According to Suunto, the compass was accurate to half a degree. I customized the compass by covering the top so subjects could not read bearings during the testing process, and adding a post and notch along which subjects could sight to ensure the instrument was aligned with their judged direction. I then mounted the compass backward on an ergonomic, plastic handle so the compass platter would remain level when held at arm’s length. Subjects were asked to hold the instrument so their outstretched arms pointed in their judged direction. This position was designed to feel natural and to be representative of the gesture typically used to point at distant objects. Subjects were asked to use their dominant hand to hold the instrument. When they indicated that they were pointing in the desired direction, I recorded this bearing by looking through the lens on the compass’s front.

Subjects

Subjects consisted of twenty-three Middlebury College students and recent graduates in their early to mid twenties. All subjects had lived in Middlebury for three to six years (summers not included). There were eleven women and twelve men.

Throughout each tour I had the opportunity to informally interview subjects about their navigational experience. Some subjects grew up in large cities and felt very comfortable navigating streets surrounded by tall buildings, while others were more familiar with and comfortable in open, rural environments. A few subjects had spent significant time orienteering with topographic maps and compasses. Some had navigated boats with charts and global position system (GPS) units. Some had made their own maps using GIS software. Still others had never navigated anything more than a car, and some were not even proficient map readers. All had successfully navigated by foot countless times to class, their dorms, the dining hall, and to various shops, including Carol’s, in downtown Middlebury. Interestingly, only some were quick to agree that these were examples

▲ The testing instrument was a modified sighting compass mounted backward on a plastic handle. Subject’s held the compass in their outstretched hand and sighted across its top to indicate their desired directional judgment. The compass face was covered so they could not see their judged bearing. The tester could look into the lens on the front of the compass to read and record the bearing.


of successful navigation or any sort of directional aptitude. Subjects commonly responded, “I just go there,” with very little consideration for how their arrival was achieved.

Many subjects felt confident about their sense of direction. Some were extremely confident, and took time at each site to refine their judgments with an exacting precision. Still others had no confidence in their sense of direction, noted repeatedly that they were going to fail, and then made hasty yet relatively accurate judgments. Although this study was not intended to examine the relationship between perceived sense of direction and judgment accuracy, the survey results indicate that the two had very little effect on each other. For this reason, I am confident that my inability to control for this variable among subjects influenced my results very little.

Subjects were recruited using an email advertisement sent to personal friends and classmates at the beginning of January 2009. Tours were led by arrangement until the end of that month, with the original goal of leading thirty subjects. No attempt was made to randomize selection of subjects because of the time consuming nature of the study and the relatively short time allocated for scheduling tours. No compensation was offered other than the disclosure of results for comparison with friends. Subjects were encouraged to schedule the tour with friends so they could be social while moving from site to site and so they could compare their results upon completion. Although there was no officially staged competition involved with the study, competition for the greatest judgment accuracy was encouraged to motivate good directional judgments and to sustain morale throughout the tour. This unofficial competition also increased interest in participation as students signed up to see if they could make better judgments than their friends. In general, subjects had fun participating and were interested to learn more about the study following their tour.

Data management, preliminary analysis, and development of working visualizations

Data collected using the survey procedure was stored and manipulated in an Excel spreadsheet. Formulas were used to correct for magnetic declination and to complete other data transformation processes. Because the compass instrument


was marked with one degree gradations, all data and processing inputs were stored with equivalent precision. The National Oceanic and Atmospheric Administration reports magnetic declination for Middlebury, Vermont to be 14 degrees, 39 minutes west (NOAA 2009). This was rounded for data processing to 15 degrees west. All data was rotated 180 degrees to account for the compass being mounted backward on the handle. To allow for mapping and other visualization of the data, the polar coordinate system used by compasses, where due north is 0 degrees and the scale increases clockwise, was converted to the coordinate system used by GIS and computer aided design (CAD) software, where due east is 0 degrees and the scale increases counterclockwise. The differences between judgments and the correct directions (to both Carol’s and north) from each point were also calculated for the purpose of statistical analysis. Because directional data is circular – one degree larger than 359 degrees is 0 degrees – these calculations required a complicated series of conditional statements in the spreadsheet formulas to maintain each datum in an appropriate range. In the case of future research on an expanded scale, development of a database which more efficiently interprets polar data would be prudent.

Preliminary data analysis consisted of performing T-tests to indicate which subsets of judgment data should be considered statistically significant and should therefore influence the schematization process for the new map most heavily (Appendix 1, Figure 5: Statistical Results). Sets of Carol’s and North judgments from each of the fourteen sites were analyzed individually. Because only north judgments were made at Site 6, there were twenty seven sets overall. Judgments were converted to a difference (in degrees) from the actual direction appropriate for each set – the angle of a perfect judgment to either Carol’s or north. A T-test was preformed on each set to indicate whether the average of these differences varied significantly from the actual direction. The means of seven sets of Carol’s judgments and five sets of north judgments varied significantly from the actual bearing,1 and were therefore considered primary influences on the schematization process described in the following chapter.

Two types of working maps were made to help visualize the results during the schematization process. Polar histogram maps were made for both Carol’s and

1. p < 0.05

magnetic north

15˚

0˚

0˚

◄ Magnetic declination for Middlebury on January 1, 2009 was 14 degrees, 39 minutes west. This was rounded to 15 degrees west for data analysis.

▲ Compasses measure angles using a polar coordinate system where due north is 0 degrees and the scale increases clockwise. CAD and GIS systems use a different polar coordinate system, where 0 degrees is due east and the scale increases counterclockwise.

0˚: actual bearing to Carol’s or north (T-Test test value)

mean judgment

individual judgment

▲ T-tests were used to compute the statistical significance of the difference between mean judgments of each judgment set and the respective actual bearings to Carol’s or north. Before the tests were performed, each judgment was converted to a difference (or error) from this actual bearing so every test could use a test value of 0.


north results to show the distribution of judgments made at each site (Appendix 1, figures 6: Carol’s Judgment Histogram Map; Appendix 1, Figure 7: and North Judgment Histogram Map). Similar to the construction of a typical histogram, judgments were sorted into bins, each with an arc range of five degrees. However, instead of drawing rectangular bins lined up next to each other, the bins were drawn as wedges oriented to correspond with their respective arc ranges. The length of the wedges was increased proportionally to reflect the number of judgments in each bin. These diagrams allowed the aggregate results from each site to be easily interpreted and visually compared with the orientations of nearby landscape features such as streets and buildings. They also showed how judgments from each set were distributed; many were multimodal. The average judgments from each set were also indicated to allow for easy assessment of skewing and the relationship between the mean and actual direction of Carol’s or north. Because no software was available to construct polar histograms automatically, AutoCAD was used to draw each histogram manually. Future research with a greater number of test sites would certainly benefit from a customized computer program for drawing these figures.

Another map was made to demonstrate how subjects interpreted their own position at each site relative to Carol’s (Appendix 1, Figure 8: Hypothetical Site Position Map). With the position of Carol’s fixed, and the linear distance between Carol’s and each site held constant, hypothetical site positions were marked along an arc to indicate where each subject would have needed to stand for their judgments to be correct. A very accurate judgment would mean a hypothetical site only a few meters from the actual location, while a very inaccurate one could mean a displacement of many hundreds of meters. The span of hypothetical positions showed the range of judgments recorded at each site and clearly demonstrated how subjects perceived the absolute and topological relationships of sites to one another. The map was made by calculating Cartesian coordinates for each hypothetical site relative to the location of Carol’s using trigonometric functions in a spreadsheet. These coordinates were converted to point features in a GIS using a custom coordinate system with its origin located at Carol’s.

A third visualization was made to help compare the accuracy of individual judgments made by each person at each site (Appendix 1, Figure 9: Individual Error in Judgments to Carols; Appendix 1, Figure 10: Individual Error in

test site

average judgment actual bearingto Carol’s

300-30

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► Polar histograms were created for

each judgment set by drawing

five degree bins as wedges spanning

their representative angles. The length

of each wedge corresponds to

the number (or frequency) of

judgments falling within it. Wedges

containing a greater number

of judgments are inherently

emphasized because a wedge’s width increases as

it is lengthened. The angle of the

average judgment in each set is

represented by a diamond.

▲ A hypothetical test site is the position from which a Carol’s judgment would have needed to have been made for it to be accurate, the position of Carol’s and the distance from Carol’s to the test site held constant.


Judgments to North). Judgment error, the difference between a judgment and the actual direction to Carol’s or north, was calculated and represented proportionally by the area of a circle – one for each judgment. Larger diameters indicated greater error. The circles were colored green and blue to indicate error in the clockwise and counterclockwise directions, and greater color saturation was used to reinforce the visual presence of high-error circles. Proportionally sized unfilled rings around the same centers showed each judgment’s difference from the mean, also colored by direction. The circles and rings were arranged in a grid with rows for each subject and columns for each site. By looking across these rows or columns consistency in error can easily be detected. A bubble plot was used to initially scale and shade the circles. Other graphic elements were added using illustration software.

These graphics were used as the primary means for result interpretation while drawing the perceptual schematic map of Middlebury.

Sites

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Bonnie

Christian

Pier

Kyle

Leah

Alex

Miriam

Heather

Anne

Sasha

Anders

Nate

Caitlyn

Peter

Toral

Natty

Abel

Christine

Nicole

Philip

Hannah

Nick

Chris

Bonnie

Christian

Pier

Kyle

Leah

Alex

Miriam

Heather

Anne

Sasha

Anders

Nate

Caitlyn

Peter

Toral

Natty

Abel

Christine

Nicole

Philip

Hannah

Nick

Chris

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error from actual bearing error from mean judgment

clockwise west


east

Judgments to Carol’s Judgments to Northlarger circles denote greater errorlarger circles denote greater error

▼ Errors in Carol’s judgments of selected test subjects. Errors for all subjects are printed in Appendix 1, Figure 9: Individual Error in Judgments to Carol’s. Error in north judgments is printed in Appendix 1, Figure 10: Individual Error in Judgments of North.

Sites

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Bonnie

Christian

Pier

Kyle

Leah

Alex

Miriam

Heather

Anne

Sasha

Anders

Nate

Caitlyn

Peter

Toral

Natty

Abel

Christine

Nicole

Philip

Hannah

Nick

Chris

Bonnie

Christian

Pier

Kyle

Leah

Alex

Miriam

Heather

Anne

Sasha

Anders

Nate

Caitlyn

Peter

Toral

Natty

Abel

Christine

Nicole

Philip

Hannah

Nick

Chris

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clockwise west


east



4 a New Map of Middlebury

The goals of performing a perceptual survey were twofold. The survey results were intended to provide empirical evidence for producing a new, schematized map of Middlebury. This map would serve as a test case for evaluating the usefulness of survey evidence for the schematization process. In addition, I hoped the results would reveal the propensity of certain types or arrangements of features to conform to heuristic simplifications. Do the survey results demonstrate that people tend to rotate large buildings or arterial streets so they are oriented cardinally? Are irregularly shaped blocks normalized as being rectilinear in people’s mental maps? If so, then evidence for these schematization tendencies may be applied to schematic mapping of other areas without having to implement an entire perceptual survey. This chapter will report on how these goals were accomplished, and the degree to which the perceptual survey was successful at providing useful evidence for them.

Production of the schematized map of Middlebury was the primary focus of data analysis. To accomplish this, survey results were compared to two maps of the town: a planimetrically accurate map of the town’s street network – the real map (Appendix 1, Figure 2: Street Map of Middlebury) – and a schematization of this network – the hypothesis map (Appendix 1, Figure 11: Hypothesis Map) – based on my personal understanding of the town’s geometry, Waldorf ’s (1979) four characteristics of schematic maps, and Elroi’s (1988) three graphic operations for drawing schematic maps as outlined in Chapter 1. The hypothesis map was designed to represent what any cartographer might produce if commissioned to make a schematic map of Middlebury without any input other than a copy of the real map. To reduce the complexity of the schematization process, both maps included only arterial streets, major side streets, and the Otter Creek. During

51Chapter 4 A New Map of Middlebury

the schematization process the new map was kept similarly stark, although a few landmarks and labels were added in a final version to help readers orient themselves.

Production of the Hypothesis Map was a multistage process, and is worth a brief description. Schematization is a complex art, and becomes more difficult as more features are added. Middlebury’s downtown, in its simplest form, can be conceptualized as a bow-tie with a river running through it. If arterial streets are further resolved, Main Street crosses the river perpendicularly and divides into four radial streets extending to the west. The east side is similar, but there are only three radii. The scene is quickly complicated when side streets are added. Because the street geometry only fits together perfectly as the real map is more closely approximated, the more detail that is added the less schematic the map can afford to be. Once the intersections on the west side of the river are drawn more realistically, the bridge must cross the river on a diagonal. The river, then, must be bent so it flows perpendicular to the bridge. The possibilities for such refinement are endless. Therefore, the Hypothesis Map was limited to show the bare minimum of side streets for the map to be useful as a navigational aid.

In comparison, the procedure for producing the new map was straightforward. The hypothesis map was considered a graphic null hypothesis: if results from the perceptual survey didn’t suggest that it was wrong, it went unchanged. In many cases the survey results supported schematizations already made in the hypothesis map – Washington Street exited town due east, and Weybridge Street ran due north – so these configurations were retained. The real map was consulted to help analyze results and confirm that schematizations were not too abstract, but was otherwise set aside throughout the process.

The degree to which survey results from a specific set of results were considered a valid description of subjects’ aggregate judgments was based on the T-tests described in the previous chapter. Sets whose judgment means were statistically different from their actual bearings were considered primary influences on the new map.

Non-statistically significant judgments were not entirely ignored. Many of these judgment sets had tight distributions, but their means were too accurate to be significantly different from the correct bearing. It was valuable to know where these accuracies were located, and where they were not. Even sets with variable

▲ At its most basic level, Middlebury’s street network can be described as a bow tie of fanning streets held together by a central knot: the bridge. The more detail added to the map, the less generalized it can afford to be.


distributions often contained clusters of judgments showing that multiple subjects aligned their judgments similarly. These, too, were useful as supporting evidence for schematizations prompted by primary influence sets.

While Carol’s and north judgments indicated two different types of orientation – local versus global – they often supported similar schematization conclusions. Carol’s was largely considered to be an indicator of the general location of downtown, although at some of the closer test sites subjects were able to demonstrate their ability (or inability) to position it more precisely within the downtown street network. The distributions of Carol’s judgments were less variable and more accurate than north judgments. This is understandable given that its position is less abstract. Overall, however, both Carol’s and north judgments were impressively accurate and consistent between subjects (Appendix 1, Figure 9: Individual Error of Judgments to Carol’s; Appendix 1, Figure 10: Individual Error in Judgments of North).

Analysis of results was initially performed for each site on an individual basis. The overall trends of Carol’s and north judgments were compared and used to interpret how subjects perceived their location at each site and the orientations of nearby features. Trends from individual sites were then compared to each other, most importantly to neighboring sites, to assess how subjects understood the local geometry of the street network – the rectilinearity of blocks or the alignment of streets fanning outward from a single location. Results were analyzed in the context of each site’s physical characteristics and notes on subjects’ deliberations during the survey procedure. Alterations to the hypothesis map influenced by this analysis were ultimately assessed collectively to resolve any conflicting schematizations of intersection geometry or street orientation. Examples of heuristic simplifications identified at specific sites were then used to produce six guidelines that could be applied for the production of perceptual schematic maps in other areas.

The hypothesis map was largely supported by the survey results (Appendix 1, Figure 12: New and Hypothesis Maps). The geometry of the new map is similar to it with two major exceptions: the trajectories of Main Street and South Street are pulled northward toward College Street, and the orientations of North Pleasant Street and Seymour Street are rotated to the northeast as they leave town. Schematization was supported in other areas of town, but these


changes already matched the hypothesis so no apparent alterations were made. While the results were largely consistent, with clusters of similar judgments in nearly every set, this may also have been their greatest weakness. The survey had a relatively small number of participants, and all were students at the college. As a result, they developed their familiarity with the town from the perspective of the college campus. Because the geometry of the new map is largely an artifact of their judgments, it should be considered a perceptual map by and for Middlebury College students. If I intended the map to be useful for a broader audience, it would be prudent to repeat the survey with a larger sample and include residents from other parts of Middlebury.

Site analyses

Site 1 – College Street at Adirondack Circle

Adirondack Circle, where the tour began, is a popular meeting place on College Street just before it leaves the west side of campus and becomes Route 125. The car turnaround sits on the ridgeline running roughly north-south across western campus, and has a good view of the Champlain Valley and Adirondacks to the west. A few downtown buildings can be seen to the east by looking down College Street, but the view in this direction is largely blocked by campus buildings and foliage. Site 1 was located in the traffic island at the center of the turnaround.

While College Street runs roughly east-west through campus, its centerline is actually about seven degrees to the northeast. Nearby campus buildings parallel the street, so are similarly misaligned with the cardinal directions. With few exceptions,

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▼ Panorama from Site 1

▲ Site 1 north judgment histogram

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no straight road segment or building façade on campus is oriented perfectly north, south, east, or west. This was a point of confusion for many subjects. While College Street was popularly assumed to run perfectly east-west, the Ross buildings and Bicentennial Hall were popularly interpreted as giant ‘north arrows’ on campus; they were some of the most frequently noted features influencing both Carol’s and north judgments. Many subjects tried to align their Site 1 north judgments with the façades of Ross, Adirondack House, and Forrest Hall.1

Site 1 was chosen to test for these slight, but nonetheless false orientational preconceptions. It was also designed to test subjects from a point that was highly familiar to them. Friends often meet at Adirondack Circle to go to town, and it is the bus stop for the only public transportation into town, so subjects were expected to have a familiarity with its relationship to the downtown area.

The means of neither the Carol’s nor the north results from Site 1 had statistically significant variation from actual bearings, so it was not considered a primary influence for building the new map. However, the results do support my schematization hypothesis by demonstrating the influence of a local rotation heuristic and the lack of a regionalization heuristic for relating the campus to the downtown. The majority of north judgments err slightly to the west and align with nearby buildings, suggesting a mental rotation of these buildings, and therefore College Street, to align with cardinal directions. Meanwhile, the Carol’s judgments demonstrate the lack of a regionalization heuristic arranging the Campus and downtown directly east and west of one another. Many subjects discussed the left-hand turn at the intersection of College and Main Street, and the majority correctly indicated that downtown was slightly northeast of the site. These results solidified my decision to maintain the northeast orientation of Main Street as it crosses Otter Creek and preserve a more accurate spatial relationship between the campus and downtown on the new map.

1. Even when these alignments were explicitly identified, subjects were sometimes unable to point absolutely parallel to a building façade. This indicates that hand-eye coordination and aptitude for judging Euclidian space still contributed to a certain degree of error in judgments. For the purposes of data analysis, however, these effects will be assumed negligible and will not be corrected for artificially.

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▲ Site 1 Carol’s judgment histogram

CAMPUSCAMPUS

TOWNTOWN► More regionalized relationship between

campus and downtown (left), and more realistic

relationship (right). It is worthwhile not to oversimplify this

arrangement.


Site 2 – Old Chapel Road at Old Chapel

Old Stone Row, comprising of Old Chapel and the two dormitories flanking it, is another campus landmark that acts as a false ‘north arrow.’ The buildings align with Old Chapel Road, which intersects College Street at a T intersection at its northern end. The road is tilted about six degrees to the northeast, which, when compounded with the angle of College Street, bounds what is obviously a non-rectangular quadrangle when seen from above. However, just as Bostonians perceive the Common as a five-sided rectangle (Lynch 1960, 21), the Main Quad feels square from ground level.

Site 2, at the northeastern corner of Old Chapel, was designed to test subjects’ sensitivity to this irregular geometry. It was also meant to provide further evidence for how subjects understood the relationship between campus and the downtown, of which the site affords substantial visibility. The Main Library and Twilight Hall, which mark the eastern boundary of campus, are highly visible and many subjects discussed them as reference points for their Carol’s judgments. Some landmark downtown buildings, including the Middlebury Inn and the Town Hall Theater could also be seen from this point. Perhaps more importantly, the Old Chapel cupola could be seen from many later test sites, so the building and Site 2 became popular landmarks used by subjects to orient themselves throughout the tour.

Results from north judgments at Site 2 are generally consistent with the schematization hypothesis. The means of these results are not statistically different from the actual bearing of north – not surprising given the subtle angle of Old Chapel Road and the moderate variability of the judgments – but they reflect a general tendency toward rotating the road cardinally and normalizing its

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Middlebury College Main Quadca. 700

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▲ The College’s Main Quad feels square, but does not have any parallel sides.

north Carol’s


intersection with College Street. This tendency is especially pronounced when compared with the Site 1 north results. Just as judgments at Site 1 are skewed to the west to align with nearby buildings, the bulk of judgments at Site 2 are skewed to the east to align with Old Stone Row and Old Chapel Road. That the skewing occurs in opposite directions suggests judgments were largely influenced by nearby rather than regional features.

The means of Carol’s judgments from Site 2 were statistically different from the actual bearing to the shop, so these results contributed as a primary influence to the new map. While many subjects accurately identified the downtown as being to the northeast, the mean judgment was more eastward; in aggregate, subjects judged that Carol’s was directly between Twilight Hall and the Library. Not only does this demonstrate that subjects did not carefully study visible landmarks – they could see downtown buildings from the site – it shows a tendency toward simplified east-west regionalization of the town and campus that was less apparent at Site 1.

While Site 1 and 2 exhibit similarities in their distributions of judged angles, these similarities are not an artifact of specific individuals making consistent errors. With a few exceptions, error in Carol’s judgments were highly irregular at the individual level (Appendix 1, Figure 9: Individual Error in Judgments to Carol’s). Error was more likely to be consistent at each particular site. North judgments, in contrast, exhibit more consistent (and more sizable) error among individuals (Appendix 1, Figure 10: Individual Error in Judgments of North). Anders and Nate were regularly biased to the east, while most others were predominantly biased to the west. There is also less consistency in error on a site-by-site basis. These differences between the Carol’s and north error profiles may be explained by the difference in specificity of the “thing” they were pointing to. Carol’s represents an easily recognizable, discrete point, while north is an entirely abstract concept defined by earth movement more than any ground feature. The only way for a subject to know the direction to north is to have prior knowledge of a northward feature, such as Burlington, and know along which path you would leave Middlebury to get there. The overall direction of this path is north as defined by their mental map.

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Site 3 – Main Street and Stewart Hill Road

As Main Street exits the southern end of campus it becomes Route 30, the principal route of arrival and departure from Middlebury for those coming from southern New York and the Mid-Atlantic. As an result, this otherwise mundane, ‘backdoor’ entrance to Middlebury is the first direction from which many students experience the town. The street also plays a role in defining the extents of campus. Most academic and residence halls lie northwest of it, while the College’s sprawling performing arts center, athletic building, and sports fields lie to its southeast.

In general, these two sides are reductively conceptualized as north and south of one another. Even the College’s Master Plan breaks the campus into simplified regions (Michael Dennis and Associates 2008, 59). North Campus consists of areas north of College Street, Central Campus lies between College and Main Streets, and South Campus is everything to the southeast of that. It would be exceptionally awkward to denote these areas in any other way. A more accurate description might allude to the wedge shapes formed by the convergence of Weybridge, College, Main, and South Streets. But saying, “I’m going to South-Southwest Campus” would be mouthful and uselessly complex. It is practical, both linguistically and conceptually, that we regionalize the campus and align it with an abstract axis.

While Main Street runs toward downtown along a straight trajectory, topography prevents direct line-of-sight to most downtown buildings. Site 3 was designed to test how well subjects understood the straightness of the street

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▼ Panorama from Site 3▲ Site 3 north judgment histogram

College Street

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► Three areas of the College campus, divided by streets, are conceptually aligned one on top of the other. In reality, the streets are radial, not parallel, and the regions are wedge-shaped.

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between campus and town, and how they aligned it with cardinal directions given that it is both an entrance to campus (an upright, central axis) and a boundary between campus regions (conceptually parallel to College Street).

North judgments from this site indicate that many subjects saw Main Street according to the first model: a mostly upright, central axis. That the seven people who make up the most prominent segment of the distribution pointed only slightly west of the street seems to show that they recognize it does not run exactly north, but this variance is negligible. Another, smaller cluster of judgments on the western extreme indicate the second model: Main Street parallels the east-west running College Street to form the boundary between Central and South Campus. A third cluster aligns vaguely with Old Chapel Road, not visible from the test site, but with which subjects had familiarized themselves only minutes before. Needless to say, no significant conclusions could be made from these results other than to strongly reiterate that from a curbside perspective, street axes are convincing evidence of cardinal orientation.

The Carol’s judgments from Site 3 were more statistically significant and were primary influences on the new map. The results demonstrate that subjects did not accurately remember Main Street as having a straight trajectory toward downtown, but assumed it bent slightly to the east. On average, subjects judged the direction of the shop to be about ten degrees east of its actual bearing. Holding distance constant, subjects indicated that Carol’s was on Pleasant Street. Looked at another way, Site 3 would have to move about 200 meters northwest for the mean judgment to be accurate given the current position of the shop (Appendix 1, Figure 8: Hypothetical Site Position Map). To accommodate this relationship and to better address Main Street’s role as a boundary between Central and South Campus, the new map shows Main Street pulled up to meet this hypothetical position of the test site.

Site 4 – South Street and Porter Field House Road

South Street, although a major town road, is less frequently visited by students. It is a primarily residential street that becomes unpaved about 800 meters south of the test site and begins to follow a more curvilinear path. Athletic students know this section in the context of a popular running route. Virtually no students use the street to travel into town. It is also relatively remote from major landmarks

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such as church spires, large buildings, and ridgelines. The amorphously shaped athletic center and Center for the Arts can be seen down Porter Field House Road, and the lackluster Municipal Building can be glimpsed to the north, but vegetation and topography block any other commonly distinguishing features. Many subjects found themselves relying on the Green Mountain ridgeline to orient their north judgments.

Because it is relatively isolated and unfamiliar, Site 4 was intended to test the effect of the orientation of South Street on Carol’s judgments. It was assumed that students would say, “South Street … it must run north-south,” and would have little error in their north judgments. The hypothesis map shows the street running due south from town as it does in reality. In contrast with these expectations, Carol’s results were substantially more accurate than those for north. There was no significant difference between the mean Carol’s judgments and the actual bearing, an indication that subjects were more familiar than anticipated with South Street’s relationship to town.

Confoundingly, north judgments were extremely variable. No five-degree segment of the distribution contained more than two judgments. The street’s name was, for the most part, ignored by subjects as they discussed their judgments. Instead they referred mostly to vague non-visible features such as “campus” and Bicentennial Hall.

While the judgments were variable in terms of frequency distribution, they had a moderate standard deviation (twenty-six degrees) and a mean that was significantly different from true north, so the results were incorporated into the new map. The mean judgment indicates that South Street, like Main Street, should be pulled in toward campus and drawn with a heading to the northeast. This also

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▼ Site 4 north judgment histogram

► Site 4 Carol’s judgment histogram

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significantly shrinks the area between these two streets and reduces the conceptual area available for South Campus, chiefly the sprawling athletic fields and the golf course. However, it is understandable that this area might be overlooked by students who have little connection with this terrain. While the relative few who play golf may know precisely the size of a fairway compared with the Main Quad – the fairway is much longer – most would not be expected to object, at least in their spatial conception of this area, to its size being dramatically reduced.

Site 5 – Main Street and South Street

The four principal streets on the west side of Otter Creek converge on Main Street at the western end of downtown. That Middlebury’s Municipal Building is located at the center of these intersections is civically appropriate, but the building is ironically inconsequential as a landmark. Most students do not even seem to recognize its existence, let alone acknowledge that it is the seat of local government. Instead, Middlebury Market and Two Brother’s Tavern were the primary landmarks by which subjects oriented themselves during the survey. Site 5 was designed to test whether the alignment of the Municipal Building, when experienced in close proximity, would effect north judgments, or whether subjects would continue to align themselves with Main Street or South Street as they had at previous sites. It was also meant to serve as a segue into town and test how subjects were able to place Carol’s relative to the Main Street once its downtown portion was fully visible.

The Municipal Building’s position actually benefited the study by blocking the view between the intersection of Weybridge and College Streets on one side, and Main and South Streets on the other. This allowed the alignment effects of the two intersections to be studied more independently – the convergence of

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all four streets is not obvious from a curbside perspective. The mean error of Carol’s judgments from Sites 5 and 14 were substantially different from each other,2 indicating that subjects oriented themselves differently on one side of the Municipal Building versus the other. However, neither of their means were significantly different from the actual bearing to Carol’s, so the results did not contribute to the new map.

The mean of north judgments from Site 5 did err significantly from due north, and tended toward alignment with the Municipal Building. Similar to Site 4, subjects were hesitant to believe that South Street was oriented cardinally. The largest cluster of judgments, which contained the mean, pointed ten to fifteen degrees northwest to align with the Municipal Building’s western annex. A smaller cluster of three subjects aligned themselves with the main building by pointing directly at its entrance. Both clusters support the conclusion that Main Street should be rotated slightly clockwise in the new map.

Site 6 – Main Street and Merchant’s Row

The intersection of Main Street and Merchant’s row is perhaps the only place in Middlebury that is truly suggestive of an urban downtown. Both sides of Main Street and the south side of Merchant’s row are lined by multistory buildings, storefronts with display windows, and broad sidewalks. Because the buildings are taller and closer together than in any other area of town, it is also more difficult to see landmarks useful for orientation. The Congregational Church at the far end of Main Street is highly visible, but subjects were cautious about assuming its cardinal orientation. The relative angle of Main Street was confusing, and subjects were unsettled about pointing directly into a wall of storefronts that were so close to

2. Mean Carol’s judgments from Sites 5 and 14 were just shy of statistical difference based on a 0.05 significance convention: p = 0.07, using an independent samples T-test.

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▲ Site 5 North judgment histogram


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them. In general, subjects expressed greater confidence in their judgments from sites that were more open and had larger viewsheds.

Because the Carol’s storefront was clearly visible from this test site, subjects were only asked to make a north judgment. The site was designed to clarify how subjects oriented the downtown portion of Main Street, especially in the context of its T intersection with Merchant’s Row. The mean of the results did not differ significantly from due north, so it did not prompt an adjustment on the new map. However, the results do demonstrate subjects’ orientational confusion in this area of town. The standard deviation of the judgments was a staggering twenty-nine degrees. Subjects clearly rejected any speculation that Main Street should be oriented north-south or east-west, but on average indicated that it leaned sixteen degrees east from its actual angle. This supports my hypothesis that it should be schematized along a forty-five degree diagonal.

Site 7 – Pleasant Street and Cross Street

Cross Street, Pleasant Street, and Court Street bound one of the only clearly rectilinear blocks in the downtown area. It is bounded on four sides by straight streets and has four, roughly right-angle corners. The tour wrapped around three sides of the block, and Sites 7 and 8 were located at its southern corners to test the degree to which subjects judged its long sides to be parallel. Site 7 was also the first opportunity for subjects to make a Carol’s judgment on the eastern side of the river.

This site supplied moderate visibility to popular landmarks, including the Town Hall Theater at the end of Pleasant Street, and campus buildings, which were barely visible across the river. It was also the only site with a direct view of the river, which is a dominant feature downtown but whose path north and south of the bridge was unfamiliar to most subjects. In general, its meanders went

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► Site 7 north judgment histogram

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unaccounted for in their judgments. Most subjects assumed it was more or less straight – that if you crossed it perpendicular to the shoreline you would be aimed at the College – until just downstream of the bridge where a bend is visible from downtown.

The mean of Carol’s judgments from Site 7 were quite accurate and not significantly different from the actual bearing. As they had at Site 5, subjects discussed moving down the street and taking a slight turn, this time to the left – a simple geometric deduction. North judgments were more varied but also not significantly erroneous. Pleasant Street runs almost perfectly north, and a large cluster of judgments aligned correctly with this bearing. However, a substantial number also aligned with their prior Carol’s judgments, an indication that the procedural order may have influenced their north judgments. This is the only site at which Carol’s and north judgments were explicitly similar. I did not attempt to artificially correct for this or any other potential effect of the experimental design.

Site 8 – Court Street and Cross Street

Court Street, which turns into US Route 7 south, is Middlebury’s largest and busiest street. It is also a common route for arrival to town from southern Vermont and Massachusetts, and for going to Middlebury College’s ski area in Ripton. South of downtown, Route 7 is lined with convenience stores and shopping centers, including a T.J. Maxx, the town’s largest grocery store, and the State liquor store. Needless to say, most students know how to navigate from campus to at least one of these destinations.

While Route 7 follows a roughly north-south path through western New England, it is far from cardinally aligned along most of its length in Middlebury. It leaves downtown traveling south-southeast, making the “rectangular block” described earlier more of a wedge in actuality. Site 8 was designed to examine

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whether subjects would mentally rotate the highway, and how this rotation might affect their estimates of the relative position of Carol’s.

Other than its obvious relation to Site 7, which could be seen down Cross Street, very few major landmarks were visible from Site 8 to help subjects orient themselves. Many referenced the position of Chipman Hill, a low hill to the northeast, as an indication of the street’s northern orientation. However, the hill is so uniformly shaped and close to town that it is deceptive as an indicator of northernness. This was especially true at later sites such as 10 and 11, which were even closer alongside it.

Both Carol’s and north results from Site 8 are significant and clearly demonstrate a rotation effect. The mean north judgment was directly aligned with Court Street, suggesting that it should be rotated to parallel Pleasant Street and run directly north-south. The Carol’s judgments were sympathetic to this rotation. The mean judgment bisects the angle between Cross and Court Streets. If this angle were expanded to normalize the angle of Court Street, the new bisector would point directly at Carol’s. These changes are consistent with my schematization hypothesis, which normalizes Pleasant, Cross, and Court Streets to form a truly rectangular block between them.

▼ Panorama from Site 9northCarol’s


Site 9 – Washington Street and High Street

Washington Street is the dominant route out of town to the east. Students are most likely to travel on it to reach the Middlebury Natural Foods Co-op and Shaw’s, the only large supermarket within walking distance of the downtown and the College. While the street itself is straight and relatively small, getting to it requires traversing a large and complicated intersection with Route 7 that can be highly disorienting. Traffic is one-way around the rectangular Courthouse Square, so driving to Washington Street from north of town requires negotiating two left, and one right hand turn, only one of which is signaled. It is little wonder that newcomers often find themselves turning around in circles upon arrival to Middlebury.

Site 9 was positioned about 200 meters northeast of this confusion at Washington Street’s intersection with High Street and Buttolph Drive. There was no reason to believe students would be familiar with either of these side streets – they are both small and residential – but the site provided an interesting case as a four-way intersection. I was especially interested in potential alignment with High Street, which runs almost due north but intersects Washington Street at an acute angle. In my hypothesis map I normalized this intersection to orient High Street due north and Washington Street due east.

The means of both Carol’s and north results were significantly different from their actual bearings at this site, and they encourage a schematization similar to my hypothesis. Subjects pointed almost unanimously south of the actual bearing to Carol’s. If Washington Street were rotated to run due east from the Courthouse Square the mean judgment would be nearly correct. Moreover, the mean north judgment was perpendicular to Washington Street, a further indication that it should be normalized. The case for rotation is slightly weakened by the fact that this mean aligns with only one judgment. The distribution is split between clusters that are aligned with High Street and Buttolph drive. This can be interpreted as evidence for normalizing the trajectories of all three streets.

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Site 10 – North Pleasant Street and Stewart Lane

Route 7 leaves Middlebury to the north along North Pleasant Street. This is the primary route to Burlington, which is the largest nearby city. Students who fly to school typically arrive at the Burlington International Airport, and this is the first direction from which they experience the town. As noted earlier, Pleasant Street runs almost due north at its southern end, but it bends slightly to the east at its northern extreme. The curve is subtle and noticeable mostly because there is no line-of-sight to the prominent Congregational Church from the test site at the Stewart Lane and Elm Street intersection.

Site 10 was designed to test subjects’ understanding of this curve and the orientation of North Pleasant Street as it leaves town. Like Site 9, it also provided an opportunity to study alignment tendencies at a four-way intersection. The hypothesis map shows the street rotated to align cardinally and also schematizes its trajectory to a straight line.

The mean of Carol’s judgments from this site was significantly different from the actual bearing, so it was considered a primary influence on the new map and supported an alteration from the hypothesis map. The majority of judgments erred west along a tight distribution, indicating that if the street were rotated further to the east, the judgments would be largely correct. Straightening the street would also help correct for this error.

While the mean of north judgments was not significantly different from true north and the judgments were highly variable – they had a standard deviation of twenty-nine degrees – the two most prominent judgment clusters support the conclusion that North Pleasant Street should be drawn with a northeast trajectory. Surprisingly, relatively few subjects aligned their north judgments with the street’s orientation, an indication that they recognized the street’s subtle curve as it entered town.

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▼ Panorama from Site 10northCarol’s


Site 11 – Seymour Street and Elm Street

Similar to the Cross Street test sites on the other side of town, Sites 10 and 11 were designed to investigate how subjects conceptualized the relationship between North Pleasant and Seymour Streets. The two are connected by right-angle intersections with Elm Street, and a vaguely rectilinear block is formed between them. I hypothesized that subjects would normalize the shape and orientation of this block by rotating and straightening Seymour Street to parallel the already uprighted North Pleasant Street.

Greg’s meat market and the nearby discount beverage store and pizzeria draw a substantial amount of student traffic to the intersection, so subjects were well acquainted with its position relative to the town. However, most subjects were used to approaching the area from the south via Seymour Street, rather than the east on Elm Street. They were caught off guard when, on their way to the next site, they realized the extent to which Seymour Street curves, a feature they had not recorded in memory.

Their judgments to Carol’s reflect this error. The mean is seventeen degrees west of the actual bearing, and lies just east of the street. Most subjects accounted slightly for the curve – it is visible from the test site – but not nearly enough. The mean is significantly different from the actual bearing, and is accounted for in the new map by substantially straightening Seymour Street and rotating it slightly to the east.

Because the mean of north results from this site does not vary significantly from true north, it is impossible to confidently say whether subjects normalized the orientation of the intermediary block. Two substantial clusters of north judgments err to the east, indicating such a rotation, but a large cluster also points to the west. Because of these inconclusive results, greater weight is placed on the Carol’s judgments and the block is, ironically, schematized on the new map with a more irregular shape than it has in actuality.

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◄ Site 11 Carol’s judgment histogram

◄ Site 11 north judgment histogram

▼ Panorama from Site 10 northCarol’s


Site 12 – Main Street and Seymour Street

The Congregational Church is one of the most distinct landmarks in Middlebury. It sits in a prominent position at the top of Main Street, and its white spire can be seen from most areas downtown. The church’s footprint is aligned almost perfectly with the cardinal directions, so it eastern façade parallels South Pleasant Street, but it is otherwise unaligned with nearby streets. Main and Seymour Streets cross awkwardly in front of the building to meet South Pleasant above. Because of this tangle of street orientations, the church’s potential as a downtown ‘north arrow’ is substantially muddled.

Site 12 was designed to test whether the orientation of the church building would have a greater influence on north judgments than that of the roads around it. It was intentionally positioned at the intersection of Main and Seymour Streets, both of which are not cardinally aligned, where the north-oriented North Pleasant Street would be less visible. The site was also intended to indicate the degree to which subjects could pinpoint the location of Carol’s along Merchants Row. Did they simply know it was on this street, or could they remember its location relative to either end of the block? Conveniently, the Episcopal church and vegetation in the Town Green blocked the view of most of the Merchant’s row from this site. Subjects had the opportunity to point to Carol’s, without seeing it directly, from only about 150 meters away.

The mean of north judgments from this site was not significantly different from due north, nor were there any anomalous clusters aligned with the church building or Seymour Street. The distribution was fairly evenly dispersed between the street orientation and slightly east of the church’s long axis.

The mean of Carol’s judgments, however, was significantly different from the actual bearing with an error of about four degrees to the west and an equal standard deviation. Given the small distance between the sites, this is a surprisingly


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► Site 12 north judgment histogram

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large error and indicates that subjects were not good at distinguishing the position of the Carol’s storefront from that of the intersection of Main Street and Merchant’s Row. Nonetheless, because of the proximity of the test site and the density of downtown streets, little variation in the new map geometry could be made to accommodate these results.

Site 13 – College Street and Weybridge Street

Weybridge Street is the only corridor running north from downtown on the west side of Otter Creek. Like South Street it is residential and doesn’t receive high volumes of traffic other than for commuters from Weybridge and other towns to the northwest. Some student housing borders the street, and the north entrance to the College, with access to an upperclassman parking lot, lies about 800 meters from the intersection where Site 13 was located.

As previously discussed, Site 13 was chosen to study the perceived relationship between the north and south sides of the radial street convergence around the Municipal Building. While this convergence is strikingly obvious from an aerial perspective, the volume of the Municipal Building impedes its visual detection from the ground. The sites were designed to test whether subjects nonetheless perceived these two halves as unified – their judgments would be consistent with geometric possibility – or they viewed the two halves independently by aligning or rotating them independently.

Because Weybridge Street meets College Street at a nearly perpendicular intersection, I hypothesized that subjects would rotate the street to run northward. In fact, while the mean of north judgments from Site 13 is statistically significant, it is substantially east of the street’s trajectory. Moreover, it is aligned almost perfectly with the mean of north judgments from Site 5. This would indicate

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that subjects were aware of the spatial relationship between the two sides of the convergence. However, the mean judgment from Site 13 is unrepresentative of the distribution. Clusters are dispersed on either side, and the largest of these clusters is aligned with Weybridge Street. If this cluster is used for comparison with the Site 5 results, the orientation of the two sides appears to have been conceptualized by subjects quite differently.

The Carol’s judgments, although their mean is not statistically different from the actual bearing, support the latter conclusion. While judgments from Site 5 erred four degrees to the west, those from Site 14 erred four degrees to the east. Examining the results of individual subjects makes it similarly clear that there is little internal consistency between the two sites in either north or Carol’s judgments (Appendix 1, Figure 9: Individual Error in Judgments to Carol’s). Were the Municipal Building not creating a visual barrier, one would assume that judgments would have been more consistent between sites that were only about 100 meters apart.

Because of the modal orientation of the north results, Weybridge street is drawn due north on the new map. This is consistent with the hypothesis schematization, and allows the normalization of the street’s intersection with College Street. However, it dramatically increases the size of North Campus and forces Otter Creek to run more northerly than it does in reality. I assume that the area north of downtown is sufficiently unfamiliar to students that they would be largely oblivious of these changes if asked to identify them.

Site 14 – Shannon Street at Atwater Driveway

The final test site on the tour was located at the bend in Shannon Street, just east of North Campus. While a few student houses line Shannon Street, it is most heavily trafficked to access the dining hall and upperclassman parking just uphill

▼ Panorama from Site 14north Carol’s


to the west. The site looks downhill over the Saint Mary’s School playground and athletic fields, and has a good view of the downtown ‘skyline;’ the Congregational Church, Town Hall Theater, and the Battell Block, in which Carol’s is located, are barely visible. The Green Mountains and Chipman Hill, both clearly visible, were discussed by a number of subjects as having influenced their north judgments from this site.

The space between Shannon, College, and Weybridge Streets is four-sided but is far from rectangular. Site 14 was designed to test whether subjects would schematize the shape of a block by normalizing its corners and aligning its opposite sides with one another. I hypothesized that while College Street would be rotated to align northward – a prediction that was supported by the Site 13 results – Shannon Street would be judged to have a similar orientation along its southern portion. While I did not anticipate any direct evidence to prompt the normalization of the Shannon Street bend, it was drawn this way on the Hypothesis Map to protect its right-angle intersection with Weybridge Street. I regret having not placed an additional test point at this intersection, which may have confirmed this normalization and provided further evidence for rotating the trajectory of Weybridge Street.

The means from neither north nor Carol’s Site 14 judgments were significantly different from their actual bearings, but they still loosely supported the hypothesis map. The tight distribution of Carol’s results was not surprising given the visibility of downtown buildings from the site. The mean judgment erred by seven degrees to the south; if the bend in Shannon Street had been located 100 meters due north, the mean would have been accurate. This provided further evidence for normalization of the bend.

While the mean of north judgments was well aligned with the lower section of Shannon Street, the distribution of these judgments was also broken between two clusters on either side of the mean. The larger of these clusters was aligned with the street, providing at least some evidence that subjects conceptualized it with a north-south trajectory. To this extent, the results support the normalization of the block on the new map, although the slight curvature of the bend and the shallow angle of the northern segment of the street were maintained to allow users to more easily identify with the actual street geometry in this open location.

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◄ Site 14 Carol’s judgment histogram

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The New Map

Based on the survey results, the Hypothesis Map was altered in two significant ways to derive the new map (Appendix 1, Figure 12: New and Hypothesis Maps). North Pleasant Street was rotated to the northeast to better approximate its actual orientation at Site 10. Subjects did not align their north judgments with the trajectory of the street as I had anticipated, and the Carol’s judgments indicated that the site should be positioned more easterly. While the Site 11 north judgments indicated that Seymour Street should be oriented north-south, it was instead kept parallel to North Pleasant Street to maintain the perpendicularity of Elm Street. As the Carol’s judgments were erroneous largely because subjects underestimated the curve of Seymour Street, the street was substantially straightened as it approached town.

The orientations of South Street and Main Street on the west side of the river were the other major alteration on the new map. Carol’s judgments from Site 3, and north judgments from Site 4 indicated that these streets should be pulled to the north so they approached town at a shallower angle. While the north judgments from Site 3 demonstrate that a number of subjects oriented Main Street to the north, this rotation would have conflicted topologically with the angle of South Street so it was not enacted.

Once the schematization was complete, the new map was embellished with labels and perspective models of key landmark buildings identified by subjects throughout the survey (Appendix 1, Figure 14: New Map – Final Edition). The map was designed with the intention that it would be useful for navigating and exploring the town.

Schematization Tools

The survey results demonstrate six notable heuristic tendencies associated with certain arrangements of buildings or streets relative to the test sites. These tendencies may be useful for cartographers as guides for creating schematizations of other areas without performing a full perceptual survey.


Rotation from Street orientation.1. Streets are axial figures and they tend to be mentally rotated to align cardinally. At nearly every test site, the mean or a major cluster of north judgments was aligned with a street. In most places, these alignments were biased toward arterial streets. Among north judgments from Site 3, a large cluster indicated that Main Street should be oriented north-south, while a smaller one was biased toward Stewart Hill Road. Both demonstrate a rotation tendency, but rotation of the larger street was clearly more popular. When possible, arterial streets should be rotated to conform with cardinal directions.

Rotation from building orientation.2. Buildings with large, planar façades promote mental rotation of nearby streets. North judgments from Site 5 best demonstrated this principle because the Municipal Building does not entirely align with the streets surrounding it. On average, subjects aligned their judgments with the annex’s eastern façade, and this mean was significantly different from true north. At a number of other sites, subjects discussed aligning their judgments with buildings, although these cannot be distinguished from street alignment because the buildings and streets were aligned with each other. While building orientation was not as powerful a rotation influence as street orientation, it is nonetheless an important consideration.

Street straightening.3. While straightening is inherent to the style of most schematic maps, it was also encouraged by the survey results. Carol’s results from Site 10 and 11 indicated that subjects did not detect the magnitude of the curves in North Pleasant and Seymour Streets. They were considerably straightened on the new map to demonstrate their perceived trajectories.

Block normalization.4. In three instances, judgments from the corners of non-rectilinear blocks indicated that they should be substantially normalized. In general, the schematization process already promotes these changes by aligning and straightening streets and simplifying intersection angles.

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Geometric disruption because of broken sightlines.5. While people are expected to perceive the relationships of street angles imprecisely – this is why schematization is possible – results from Site 13 and Site 5 demonstrated that this imprecision could be amplified, even over a short distance, because of broken sightlines. If the Municipal Building had not blocked their views of nearby intersections, subjects would likely have better understood the relationship of converging arterial streets in this area. Cartographers making schematizations should embrace this effect, which allows them to treat two nearby areas separated by an obstacle as entirely disjointed from one another.

Location simplification.6. While subjects were always asked to point to the entrance of the Carol’s coffee shop, results from Site 12 demonstrate that many were unsure of its precise location on Merchant’s row. The mean Carol’s judgment, within a very tight distribution, suggested that it was closer to the intersection with Main Street. This indicates that subjects may have had a rudimentary memory for its location, even after having seen the shop relative to Site 6, and simply associated it with the corner of the Battell Block. I would expect this simplification of position – snapping it to a landmark node – to be a popular strategy for remembering location information. In fact, Lynch identifies a similar strategy in his discussion of landmarks in city images (Lynch 1960, 83). People are likely to judge the position of less prominent features relative to those which are more prominent.

Results from the perceptual survey were useful for producing a new, schematized map of Middlebury that accounted for student subjects’ perceptions of street geometry, and for deriving guidelines that may be useful for cartographers to create schematic maps of other places without seeking direct input in the form of a survey. While sites presented unique feature arrangements and other characteristics that influenced judgments, there were also remarkable similarities in the way subjects approached their judgments at each location. These similarities – the heuristic alignment, rotation, normalization, and regionalization affecting street and intersection placement – demonstrate that schematization from a perceptual survey is not only a feasible cartographic technique, but is an

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accurate communication of the way people conceptualize landscape geometry. Schematized maps derived with this process may be useful not only as tools for navigation, but as evidence for studying cognitive maps. While the bulk of cognitive map research has focused on individual conceptions of space, this method may allow researchers to effectively critique the combined spatial perceptions of a sample population. The new map describes the combined effects of spatial heuristics on not one, but twenty-three users of the Middlebury street network. Hopefully students would find the map representative of their mental images of Middlebury geometry, and a useful as an aid for navigating the town.


5 Beyond the case Study

My research supports the proposition that functional networks are simplified in our cognitive maps according to heuristics tendencies. Moreover, it demonstrates that schematic maps, which correspond graphically to these heuristics, are useful for illustrating functional networks and that their form can be guided by peoples’ judgments of spatial relations. By developing a process for collecting and analyzing such judgments, I hoped to create a map which better reflected the way people perceived and understood ground geometry in the town of Middlebury, and derive guidelines for creating similar perceptual schematizations in other areas.

While a survey was successfully implemented and a new map and guidelines were created, my work leaves an important question unanswered. Is a perceptual schematization really a more effective map for navigation? Will Middlebury College Students, the map’s intended audience, relate to the new map more easily than they would a geometrically accurate map, or a schematization that did not incorporate perceptual evidence? Further research might investigate whether it is worth the effort of a survey and schematization process to create a ‘better’ map, and whether such a map is really better at all.

A number of methods could be used to evaluate effectiveness of a perceptual map by different standards. Efficiency of reading the map is important. A test might ask subjects to point to the location of certain businesses and time their responses. The map – geometrically accurate, schematic, or perceptual schematic – which yielded the fastest response times would be considered most efficient to read. The ability to determine an efficient route between points is also important. Subjects might be asked to draw the best route between known points on each type of map, and the routes could be evaluated in terms of overall distance or

77Chapter 5 Beyond the Case Study

travel time. The map which consistently prompted the shortest routes to be drawn would be considered the most useful for navigational planning. The map should also be efficient for real-time navigation in the field. Subjects might be dropped off around town and asked to navigate to various places using each style of map. The map which afforded the fastest or most direct route choices would be considered the most useful for navigation.

While it will be important for further research to assess whether it is worthwhile to invest time and energy into the complicated process of creating a perceptual schematic map, it should also look for ways that the survey and data analysis processes can be undertaken more precisely and in a more structured and streamlined manner. This may initially involve an expanded study to test whether certain characteristics of the test subjects, the natural environment, or individual test sites are substantially influential to judgment results.

The most obvious limitation of my survey method was the small sample of test subjects. While maintaining statistical significance of T-test results, it was infeasible to divide them into sub-samples and investigate judgment variability based on the amount of time spent living in Middlebury, location of residence, experience navigating the town, familiarity with orienteering strategies, or other variables that may have impacted their ability to make accurate directional judgments. To reduce such variability as much as possible I gathered a sample that was relatively homogeneous. All were students at Middlebury College. None had lived in Middlebury before arriving as students, so it was assumed that they had similar experiences acquainting themselves with the town from the perspective of campus. They had all been at Middlebury for between three and six school years. While they had various backgrounds and proficiencies using and making maps, and thought they had both good and bad senses of direction, these variables were expected to average themselves out among the sample and were not considered in the analysis. In short, the new map based on their judgments is merely representative of the average perceptions of twenty-three Middlebury College Students. It cannot be legitimately applied to another audience until further research can demonstrate that other variables do or do not substantially affect judgments. If other variables do have an influence, it would be interesting to use perceptual maps as tools for analyzing differences in judgment accuracy between representative sub-samples. To do this effectively would require an enlarged pool


of subjects and a method for selecting them that is better founded in the scientific method such as stratified random sampling.

A certain amount of environmental variability between tours and specific test sites was also unaccounted for in my research. Investigation of the impacts of these variables on judgment accuracy would be an obvious direction for further study. While the characteristics of subjects can be standardized or randomized, it is much more difficult to control weather, sun angle, or other testing circumstances while subscribing to the in-situ testing model I emphasized. Therefore, it would be beneficial to dedicate a study to observing how these variables affect judgments so they can be accounted for in later surveys.

While all tours followed the same route and were led during daylight hours, they took place in a variety of temperatures and weather conditions. Visibility of the sun was a requirement for a tour to be led, but sun angle fluctuated based on the time of day. Subjects on late afternoon tours may have had a distinct advantage judging the direction of north because the sun was low in the west. However, tours were led min-winter, so the sun set far south of due west. It would be interesting to assess how seasonality affects orientational judgments.

Test sites had a variety of environmental characteristics. Some were downtown amidst tall buildings. Others were in more residential areas where there was greater visibility of the sky and distant landscape features. All test sites were on sidewalks adjacent to streets, but perhaps judgments would have been different had sites been on the other side of the street, in the lane of traffic, or on the street centerline. More test sites, with a greater number of subjects to visit them, would have afforded such comparisons, but at the expense of lengthening an already laborious survey procedure.

Further research might also guide how tests sites are selected for a tour. My sites were chosen based on hypotheses of how subjects would or would not simplify street intersections or trajectories from certain perspectives. All were placed at intersections. The number of sites was based primarily on the length of time I thought subjects would be willing to commit to a tour. Fourteen sites could be visited in an hour and a half with some room for fluctuation. While I can’t definitively say that certain sites were more valuable than others, some provided more concise results to demonstrate that there was or was not a simplification tendency. An investigation of how site characteristics influence judgments might

79Chapter 5 Beyond the Case Study

better guide site placement in future studies, and might allow a smaller number of sites to be visited while achieving similar results.

It would also be worthwhile to investigate the effects of various transportation methods. Some of the subjects walked the tour route, while most were driven from site to site, getting out of the car to make their judgments. Discussions and behavioral observations of the walkers and drivers led me to conclude that there was no substantial difference between their judgments, so the walkers were included in the overall dataset. However, we undoubtedly perceive and navigate the world differently on foot and in a vehicle. These two methods of transportation, and their often distinct functional networks, should likely be assessed independently. Perhaps heuristic simplification affects each differently. Are we more likely to generalize the shape and orientation of a roadway than a walking path? Does speed of travel have an effect on the level of detail our cognitive maps store? Examination of a place where pedestrian and vehicle paths are not adjacent to each other might reveal how we perceive the world differently from one network versus another.

A perceptual survey and schematization procedure may also not be suitable for mapping all places. The case setting of Middlebury was conveniently structured for such an analysis. The town is small and focused around a central feature: the bridge. As a result, it was relatively easy to visit test sites on all sides of town and in a variety of environments. Furthermore, the downtown is hub for a number of highways and arterial streets which are not necessarily oriented cardinally, but were obvious candidates for such heuristic simplification. At most sites even erroneous judgments were relatively consistent among subjects, demonstrating that there were somewhat universal opinions about how streets should be oriented. Mapping a town where the streets are more curvilinear and are there is less consensus about how they should be simplified would require testing many more subjects to produce conclusive results. Moreover, a schematic map might simply be inappropriate as a representation of a network with this degree of geometric complexity.

While perceptual schematic maps may not have universal application, my research demonstrates that they have great potential as a tool for visualizing much of the matrix of transportation networks that frame the modern landscape. Schematizations reflect the simplified structure of our mental maps, so there


is reason to believe that they may be used more efficiently than geographically accurate maps for navigation along these networks. Perceptual schematizations are likely inappropriate for use as general reference maps, or as the base geometry for thematic mapping in a scholarly context, unless as a visualization of spatial perception. They are, however, thematic maps. Their visual variable is the map geometry itself, and its communicates the perceived arrangement of surface features. If their usefulness can be empirically demonstrated, and they can be produced efficiently, they have extensive potential application for functional network mapping. Perhaps the Middlebury Business Association could publish a perceptual schematic map to point out how to get from campus to downtown shops. The town’s bus company could use a similar map to show a downtown route. Or the College’s Cycling Club could publish a map showing popular area routes. For none of these applications is precision representation of the street network a requirement. Moreover, it would likely be distracting. These maps can be stripped of all detail except the basic arrangement of streets and intersections. If they coordinate with our simplified perceptions of the town’s street geometry they will be effective tools for navigation.

81Appendix 1

appendix 1 Full Page Figures

Appendix 1 Full Page Figures


(fold out)

Figure 1 Middlebury From Above

Figure 1 Middlebury From

Above

►▼ The town of Middlebury as seen from above. The Middlebury College campus oc-cupies most of the west side of town, while the commerical downtown straddles the Otter Creek. A single bridge is the only downtown crossing of the creek.

Middlebury College

Downtown

to N

ew York

to New York

to Rutland and Boston

to B

urlin

gton

83Appendix 1 Full Page Figures

(Middlebury College Photographs 2006)



(fold out)

Figure 2 Street Map of Middlebury

Figure 2 Street Map of M

iddlebury

► Six arterial streets radiate from Middlebury’s downtown. These include two state highways, Routes 125 and 30, and a federal highway, Route 7. Side streets shown on this map were considered important for everyday navigation of the town and where included on the perceptual schematic map (Appendix 1, Figure 13).

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Bicentennial Hall

Ross Hall

LaForce Hall

Adirondack House

Forrest Hall

Gi�ord Hall

Mead Chapel

Hepburn Hall

Stewart Hall

MunroeHall

VoterHall

Library

Axinn Center

Old StoneRow

Facilities Building

CentenoHouse Center for

the Arts

Twilight Hall

MiddleburyMarket

Municipal Building

Saint Mary’s School

Public Library

Battell Block

Town HallTheater

Old Court House

MiddleburyInn

CongregationalChurch

EpiscopalChurch

Greg’s MeatMarket

Two BrothersTavern

Figure 3 Landmark Buildings of Middlebury

Figure 3 Landmark Buildings of M

iddlebury

► These landmark buildings were discussed by subjects during the survey. Some, such as Bicentennial Hall and the Congregational Church, are large and easily recognizable. Others are simply well known as destinations around the town.




(fold out)

Figure 4 Tour Route

Figure 4 Tour Route

► The tour route was roughly four miles long and ran counterclockwise around and the through the downtown. Test sites are numbered in the order they were visited on the tour.

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(fold out)

Figure 5 Statistical Results

Figure 5 Statistical Results

► A T-test was preformed on each set of judgments, Carol’s and north, collected at each test site. Prior to the tests an error value - the di� erence between a judgment and the actual bearing to Carol’s or north - was calculated for each judgment. The T-test measured whether the mean of judgment errors from each site was statistically di� erent from the actual direction. A test value of 0, representing the actual bearing to Carol’s or north, was used for each test.

Seven sets of Carol’s judgments and � ve sets of North judgments had means that were signi� cantly di� erent from the actual bearing to Carol’s or north. These sets are bold in the table at right.

Lower Upper

1 1.57 18.108 0.682 -6.27 9.402 9.39 14.282 0.005 3.22 15.573 9.57 9.144 0.000 5.61 13.524 -3.26 13.545 0.261 -9.12 2.605 -0.52 5.559 0.657 -2.93 1.887 -2.61 9.442 0.199 -6.69 1.478 -13.43 12.838 0.000 -18.99 -7.889 -13.17 8.004 0.000 -16.63 -9.71

10 11.22 12.165 0.000 5.96 16.4811 17.04 19.305 0.000 8.70 25.3912 4.09 3.813 0.000 2.44 5.7413 4.17 13.276 0.146 -1.57 9.9114 7.17 14.711 0.029 0.81 13.54

1 -2.13 17.713 0.570 -9.79 5.532 5.83 19.194 0.160 -2.47 14.133 11.83 21.737 0.016 2.43 21.234 -31.13 26.265 0.000 -42.49 -19.775 -14.65 22.376 0.005 -24.33 -4.986 -16.30 29.496 0.015 -29.06 -3.557 -5.52 22.691 0.256 -15.33 4.298 -21.00 21.288 0.000 -30.21 -11.799 -24.91 30.476 0.001 -38.09 -11.7310 -5.65 29.365 0.366 -18.35 7.0511 -5.43 22.209 0.253 -15.04 4.1712 -9.57 23.063 0.059 -19.54 0.4113 -20.13 23.932 0.001 -30.48 -9.7814 -6.91 16.465 0.056 -14.03 0.21

95% Confidence Interval (°)

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standard deviation of error (°)

mean error from actual bearing (°)Site

0˚: actual bearing to Carol’s or north (T-Test test value)

mean judgment

individual judgment


tests with statistical signi� cance (p<.05) are bold



(fold out)

Figure 6 Carol’s Judgment Histogram Map

Figure 6 Carol’s Judgment H

istogram M

ap

► Polar histograms for judgment set was over-laid on a map of the town. The orientation of wedges (bins in a typical histogram) could easily be compared with those of streets and building facades. At right is the polar histogram map for Carol’s judgments. The following page shows the polar histogram map for north judgments.

▼ Polar histograms were created by drawing � ve degree bins as wedges spanning their representative angles. The length of each wedge corresponds to the number (or frequency) of judgments falling within it. Wedges containing a greater number of judgments are inherently emphasized because a wedge’s width increases as it is lengthened. The angle of the average judgment in each set is represented by a diamond.

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Figure 7 North Judgment Histogram Map

Figure 7 North Judgm

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(fold out)

Figure 8 Hypothetical Site Position Map

Figure 8 Hypothetical Site Position M

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►▼ A hypothetical test site is the position from which a Carol’s judgment would have needed to have been made for it to be accurate, the position of Carol’s and the distance from Carol’s to the test site held constant.

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(fold out)

Figure 9 Individual Error in Judgments to Carol’s

Figure 9 Individual Error in Judgments to Carol’s

Sites

1 2 131211109876543 14

Bonnie

Christian

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Leah

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larger circles denote greater error




(fold out)

Figure 10 Individual Error in Judgments of North

Figure 10 Individual Error in Judgments of N

orth

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(fold out)

Figure 11 Hypothesis Map

Figure 11 Hypothesis M

ap

► The hypothesis map was considered a null hypothesis demonstrating how Middlebury would likely be schematized without perceptual survey evidence. Unless results from the survey explicitly prompted a change in the hypothesis map’s geometry, it was carried through onto the new schematic perceptual map.

▼ Initial drafts of the hypothesis map show the evolution of its design. As originally drawn, Main Street crossed a highly simpli� ed Otter Creek running perfectly east-west. It quickly be-came apparent that adding a bend to the creek, lending it a more realistic shape and allowing Main Street to cross it at a diagonal, would make the dense geometry of the downtown much easier to compose and later interpret by a map reader. The paths of the streets and creek were smoothed to prevent interpretation of tight corners as junctures of straight segments in the actual town.

location of test site relative to new street positions


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(fold out)

Figure 12 New and Hypothesis Maps

Figure 12 New

and Hypothesis M

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► The new perceptual map was overlaid on the hypothesis map for easy comparison between them. The most substantial di� erences are the orientations of N. Pleasant, Seymour, Main, and South Streets.

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Figure 13 New Map of Middlebury

Figure 13 New

Map of M

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Bicentennial Hall

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Mead Chapel

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Library

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Town HallTheater

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MiddleburyInn

Greg’s MeatMarket

Center for

the Arts

Figure 14 New Map - Final Edition

Figure 14 New

Map - Final Edition

► Rough building masses were added to the perceptual map to help users orient themselves while using it. Building footprints were rotated to align with the schematized streets, and they were not necessarily drawn to scale. For instance, the footprint of the College’s Library is much larger than it looks from the outside. Its footprint was reduced relative to other build-ings on this map to better � t user’s anticipated perceptions of its size.


121Appendix 2

appendix 2 Survey Data

Appendix 2 Survey Data


(fold out)

123

Figure 1 Raw Survey D

ata

Figure 1 Raw Survey Data

Raw Survey Data

TransportTest Date Mode Carol's North Carol's North Carol's North Carol's North Carol's North Carol's North Carol's North Carol's North Carol's North Carol's North Carol's North Carol's North Carol's North Carol's North

1 Bonnie 246 168 250 184 261 216 202 161 239 158 NA 109 172 170 127 141 63 180 28 185 12 178 25 190 266 163 272 168

2 Christian 269 189 251 194 239 191 176 158 231 195 NA 213 181 191 138 187 69 185 36 205 18 185 27 171 252 171 272 200

3 Pier 277 202 281 222 230 225 224 191 227 191 NA 170 175 195 122 188 62 188 40 232 28 200 31 178 253 203 268 195

4 Kyle 245 184 248 192 247 192 205 173 229 189 NA 192 164 166 138 162 72 150 35 192 8 180 33 178 230 162 272 179

5 Leah 264 181 241 185 225 196 175 89 214 193 NA 174 158 261 138 169 42 145 41 112 3 189 34 235 254 184 289 205

6 Alex 278 194 282 209 252 187 181 172 225 155 NA 157 155 172 168 185 70 182 40 175 10 237 35 194 251 236 279 206

7 Miriam 315 161 286 165 250 167 202 151 234 130 NA 211 170 208 140 188 52 187 74 187 77 170 36 166 269 157 321 172

8 Heather 250 192 245 202 240 169 207 182 235 172 NA 176 156 178 117 163 58 168 54 180 17 159 31 186 232 160 262 178

9 Anne 248 160 255 168 245 165 195 164 229 182 NA 185 158 173 111 170 65 186 52 206 32 184 31 193 225 156 264 174

10 Sasha 291 233 261 225 262 233 208 175 230 184 NA 193 167 196 119 173 65 160 33 187 35 201 33 213 260 200 297 212

11 Anders 257 200 246 197 243 226 200 189 228 202 NA 221 157 233 128 231 74 231 42 230 23 223 32 220 239 213 284 206

12 Nate 255 222 272 248 252 243 207 198 234 232 NA 242 166 212 130 214 78 220 23 231 1 223 32 244 238 213 278 228

13 Caitlyn 259 210 240 214 245 226 212 176 233 172 NA 184 164 172 123 135 58 111 42 156 21 164 36 160 244 150 281 183

14 Peter 270 194 265 200 244 224 201 134 233 183 NA 162 170 191 149 173 56 104 25 125 44 204 36 184 268 171 314 181

15 Toral 289 210 281 230 236 198 210 140 236 202 NA 177 140 192 120 170 58 141 57 213 45 224 25 182 274 191 283 208

16 Natty 248 184 246 192 247 226 204 172 231 187 NA 191 173 186 136 173 68 176 27 195 359 186 37 190 258 186 270 191

17 Abel 242 190 249 198 243 202 188 162 230 177 NA 176 168 165 126 171 67 174 52 195 27 182 29 172 242 154 267 167

18 Christine 276 209 259 188 243 201 217 150 242 158 NA 184 171 193 121 194 68 200 24 196 346 174 37 182 256 148 284 174

19 Nicole 260 187 261 220 247 226 201 177 233 183 NA 166 182 186 141 171 62 142 35 173 25 149 37 162 252 156 272 180

20 Philip 269 190 249 198 244 204 218 154 228 166 NA 157 168 191 130 167 58 170 40 211 26 200 34 162 252 164 271 188

21 Hannah 284 207 273 198 264 208 223 115 227 142 NA 122 165 164 115 148 62 178 35 177 18 178 37 160 270 165 280 184

22 Nick 248 180 255 192 241 225 216 192 228 207 NA 195 170 178 124 155 68 142 37 192 44 174 35 170 244 157 268 175

23 Chris 268 189 247 198 248 207 214 194 225 188 NA 153 177 185 142 174 73 192 30 200 8 196 38 173 248 162 273 172

All values in degrees

Site 1

Adirondack Circle

1/15/2009

1/8/2009

Porter Field Rd & South St

Site 4Site 2 Site 3 Site 12

Seymour St & Main St

Car

Subject

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Pleasant St & Cross St

South St & Main St

Site 8Site 5 Site 13

Main St & Weybridge St

Site 14

Shannon StOld Chapel RdWashington St &

High StElm St &

Seymour St

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Stewart Ln & Route 7

Site 11

Cross St & Route 7

Site 6

Main St & Merchant's Rw

Stewart Hill Rd & Route 30

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1/14/2009

1/16/2009

1/23/2009

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Figure 2 Rotated and Magnetically Corrected Survey D

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Figure 2 Rotated and Magnetically Corrected Survey Data

Survey Data rotated 180° and corrected for magnetic declination (15° W)


1 Bonnie 51 333 55 349 66 21 7 326 44 323 NA 274 337 335 292 306 228 345 193 350 177 343 190 355 71 328 77 333

2 Christian 74 354 56 359 44 356 341 323 36 360 NA 18 346 356 303 352 234 350 201 10 183 350 192 336 57 336 77 5

3 Pier 82 7 86 27 35 30 29 356 32 356 NA 335 340 360 287 353 227 353 205 37 193 5 196 343 58 8 73 360

4 Kyle 50 349 53 357 52 357 10 338 34 354 NA 357 329 331 303 327 237 315 200 357 173 345 198 343 35 327 77 344

5 Leah 69 346 46 350 30 1 340 254 19 358 NA 339 323 66 303 334 207 310 206 277 168 354 199 40 59 349 94 10

6 Alex 83 359 87 14 57 352 346 337 30 320 NA 322 320 337 333 350 235 347 205 340 175 42 200 359 56 41 84 11

7 Miriam 120 326 91 330 55 332 7 316 39 295 NA 16 335 13 305 353 217 352 239 352 242 335 201 331 74 322 126 337

8 Heather 55 357 50 7 45 334 12 347 40 337 NA 341 321 343 282 328 223 333 219 345 182 324 196 351 37 325 67 343

9 Anne 53 325 60 333 50 330 360 329 34 347 NA 350 323 338 276 335 230 351 217 11 197 349 196 358 30 321 69 339

10 Sasha 96 38 66 30 67 38 13 340 35 349 NA 358 332 1 284 338 230 325 198 352 200 6 198 18 65 5 102 17

11 Anders 62 5 51 2 48 31 5 354 33 7 NA 26 322 38 293 36 239 36 207 35 188 28 197 25 44 18 89 11

12 Nate 60 27 77 53 57 48 12 3 39 37 NA 47 331 17 295 19 243 25 188 36 166 28 197 49 43 18 83 33

13 Caitlyn 64 15 45 19 50 31 17 341 38 337 NA 349 329 337 288 300 223 276 207 321 186 329 201 325 49 315 86 348

14 Peter 75 359 70 5 49 29 6 299 38 348 NA 327 335 356 314 338 221 269 190 290 209 9 201 349 73 336 119 346

15 Toral 94 15 86 35 41 3 15 305 41 7 NA 342 305 357 285 335 223 306 222 18 210 29 190 347 79 356 88 13

16 Natty 53 349 51 357 52 31 9 337 36 352 NA 356 338 351 301 338 233 341 192 360 164 351 202 355 63 351 75 356

17 Abel 47 355 54 3 48 7 353 327 35 342 NA 341 333 330 291 336 232 339 217 360 192 347 194 337 47 319 72 332

18 Christine 81 14 64 353 48 6 22 315 47 323 NA 349 336 358 286 359 233 5 189 1 151 339 202 347 61 313 89 339

19 Nicole 65 352 66 25 52 31 6 342 38 348 NA 331 347 351 306 336 227 307 200 338 190 314 202 327 57 321 77 345

20 Philip 74 355 54 3 49 9 23 319 33 331 NA 322 333 356 295 332 223 335 205 16 191 5 199 327 57 329 76 353

21 Hannah 89 12 78 3 69 13 28 280 32 307 NA 287 330 329 280 313 227 343 200 342 183 343 202 325 75 330 85 349

22 Nick 53 345 60 357 46 30 21 357 33 12 NA 360 335 343 289 320 233 307 202 357 209 339 200 335 49 322 73 340

23 Chris 73 354 52 3 53 12 19 359 30 353 NA 318 342 350 307 339 238 357 195 5 173 1 203 338 53 327 78 337


1/14/2009

1/16/2009

1/23/2009

1/23/2009

1/25/2009

1/30/2009

Car

Walk

Car

Car

Car

Car

Car

Cross St & Route 7

Site 6



Washington St & High St

Elm St & Seymour St

Site 10


31 etiS11 etiS


Site 14

Shannon St

Site 12


Car

Subject

Site 9Site 7


South St & Main St

Site 8Site 5


Site 4Site 2 Site 3

Old Chapel Rd

Site 1

Adirondack Circle

1/15/2009

1/8/2009




(fold out)

127

Figure 3 CAD and G

IS Converted Survey Data

Figure 3 CAD and GIS Converted Survey Data

Survey Data converted to CAD and GIS polar coordinate systempreviously rotated 180° and corrected for magnetic declination (15° W)


1 Bonnie 39 117 35 101 24 69 83 124 46 127 NA 176 113 115 158 144 222 105 257 100 273 107 260 95 19 122 13 117

2 Christian 16 96 34 91 46 94 109 127 54 90 NA 72 104 94 147 98 216 100 249 80 267 100 258 114 33 114 13 85

3 Pier 8 83 4 63 55 60 61 94 58 94 NA 115 110 90 163 97 223 97 245 53 257 85 254 107 32 82 17 90

4 Kyle 40 101 37 93 38 93 80 112 56 96 NA 93 121 119 147 123 213 135 250 93 277 105 252 107 55 123 13 106

5 Leah 21 104 44 100 60 89 110 196 71 92 NA 111 127 24 147 116 243 140 244 173 282 96 251 50 31 101 356 80

6 Alex 7 91 3 76 33 98 104 113 60 130 NA 128 130 113 117 100 215 103 245 110 275 48 250 91 34 49 6 79

7 Miriam 330 124 359 120 35 118 83 134 51 155 NA 74 115 77 145 97 233 98 211 98 208 115 249 119 16 128 324 113

8 Heather 35 93 40 83 45 116 78 103 50 113 NA 109 129 107 168 122 227 117 231 105 268 126 254 99 53 125 23 107

9 Anne 37 125 30 117 40 120 90 121 56 103 NA 100 127 112 174 115 220 99 233 79 253 101 254 92 60 129 21 111

10 Sasha 354 52 24 60 23 52 77 110 55 101 NA 92 118 89 166 112 220 125 252 98 250 84 252 72 25 85 348 73

11 Anders 28 85 39 88 42 59 85 96 57 83 NA 64 128 52 157 54 211 54 243 55 262 62 253 65 46 72 1 79

12 Nate 30 63 13 37 33 42 78 87 51 53 NA 43 119 73 155 71 207 65 262 54 284 62 253 41 47 72 7 57

13 Caitlyn 26 75 45 71 40 59 73 109 52 113 NA 101 121 113 162 150 227 174 243 129 264 121 249 125 41 135 4 102

14 Peter 15 91 20 85 41 61 84 151 52 102 NA 123 115 94 136 112 229 181 260 160 241 81 249 101 17 114 331 104

15 Toral 356 75 4 55 49 87 75 145 49 83 NA 108 145 93 165 115 227 144 228 72 240 61 260 103 11 94 2 77

16 Natty 37 101 39 93 38 59 81 113 54 98 NA 94 112 99 149 112 217 109 258 90 286 99 248 95 27 99 15 94

17 Abel 43 95 36 87 42 83 97 123 55 108 NA 109 117 120 159 114 218 111 233 90 258 103 256 113 43 131 18 118

18 Christine 9 76 26 97 42 84 68 135 43 127 NA 101 114 92 164 91 217 85 261 89 299 111 248 103 29 137 1 111

19 Nicole 25 98 24 65 38 59 84 108 52 102 NA 119 103 99 144 114 223 143 250 112 260 136 248 123 33 129 13 105

20 Philip 16 95 36 87 41 81 67 131 57 119 NA 128 117 94 155 118 227 115 245 74 259 85 251 123 33 121 14 97

21 Hannah 1 78 12 87 21 77 62 170 58 143 NA 163 120 121 170 137 223 107 250 108 267 107 248 125 15 120 5 101

22 Nick 37 105 30 93 44 60 69 93 57 78 NA 90 115 107 161 130 217 143 248 93 241 111 250 115 41 128 17 110

23 Chris 17 96 38 87 37 78 71 91 60 97 NA 132 108 100 143 111 212 93 255 85 277 89 247 112 37 123 12 113

66 92 42 84 39 78 81 121 55 105 NA 106 119 96 154 111 221 115 246 96 263 95 252 100 34 110 68 97

21 90 36 90 49 90 78 90 54 90 NA 90 116 90 141 90 208 90 257 90 280 90 256 90 38 90 13 90


1/8/2009

Site 2 Site 3

Old Chapel Rd

Site 1

Adirondack Circle

Site 12


Car

Subject

Site 9Site 7


South St & Main St

Site 8Site 5 Site 13


Site 14

Shannon StWashington St &

High StElm St &

Seymour St

Site 10


Site 11

Cross St & Route 7

Site 6




Site 4

Walk

Car

Car

Car

1/25/2009

1/30/2009

Car

Actual Bearings Measured from Orthophotography

Average

Car

Car

1/15/2009

1/14/2009

1/16/2009

1/23/2009

1/23/2009




(fold out)

129

Figure 4 Judgement Errors

Figure 4 Judgment Errors

Survey Data judgment errors relative to actual bearing of Carol's or north


1 Bonnie 18 27 -1 11 -25 -21 5 34 -8 37 NA 86 -3 25 17 54 14 15 0 10 -7 17 4 5 -19 32 0 27

2 Christian -5 6 -2 1 -3 4 31 37 0 0 NA -18 -12 4 6 8 8 10 -8 -10 -13 10 2 24 -5 24 0 -5

3 Pier -13 -7 -32 -27 6 -30 -17 4 4 4 NA 25 -6 0 22 7 15 7 -12 -37 -23 -5 -2 17 -6 -8 4 0

4 Kyle 19 11 1 3 -11 3 2 22 2 6 NA 3 5 29 6 33 5 45 -7 3 -3 15 -4 17 17 33 0 16

5 Leah 0 14 8 10 11 -1 32 106 17 2 NA 21 11 -66 6 26 35 50 -13 83 2 6 -5 -40 -7 11 -17 -10

6 Alex -14 1 -33 -14 -16 8 26 23 6 40 NA 38 14 23 -24 10 7 13 -12 20 -5 -42 -6 1 -4 -41 -7 -11

7 Miriam -51 34 -37 30 -14 28 5 44 -3 65 NA -16 -1 -13 4 7 25 8 -46 8 -72 25 -7 29 -22 38 -49 23

8 Heather 14 3 4 -7 -4 26 0 13 -4 23 NA 19 13 17 27 32 19 27 -26 15 -12 36 -2 9 15 35 10 17

9 Anne 16 35 -6 27 -9 30 12 31 2 13 NA 10 11 22 33 25 12 9 -24 -11 -27 11 -2 2 22 39 8 21

10 Sasha -27 -38 -12 -30 -26 -38 -1 20 1 11 NA 2 2 -1 25 22 12 35 -5 8 -30 -6 -4 -18 -13 -5 -25 -17

11 Anders 7 -5 3 -2 -7 -31 7 6 3 -7 NA -26 12 -38 16 -36 3 -36 -14 -35 -18 -28 -3 -25 8 -18 -12 -11

12 Nate 9 -27 -23 -53 -16 -48 0 -3 -3 -37 NA -47 3 -17 14 -19 -1 -25 5 -36 4 -28 -3 -49 9 -18 -6 -33

13 Caitlyn 5 -15 9 -19 -9 -31 -5 19 -2 23 NA 11 5 23 21 60 19 84 -14 39 -16 31 -7 35 3 45 -9 12

14 Peter -6 1 -16 -5 -8 -29 6 61 -2 12 NA 33 -1 4 -5 22 21 91 3 70 -39 -9 -7 11 -21 24 -42 14

15 Toral -25 -15 -32 -35 0 -3 -3 55 -5 -7 NA 18 29 3 24 25 19 54 -29 -18 -40 -29 4 13 -27 4 -11 -13

16 Natty 16 11 3 3 -11 -31 3 23 0 8 NA 4 -4 9 8 22 9 19 1 0 6 9 -8 5 -11 9 2 4

17 Abel 22 5 0 -3 -7 -7 19 33 1 18 NA 19 1 30 18 24 10 21 -24 0 -22 13 0 23 5 41 5 28

18 Christine -12 -14 -10 7 -7 -6 -10 45 -11 37 NA 11 -2 2 23 1 9 -5 4 -1 19 21 -8 13 -9 47 -12 21

19 Nicole 4 8 -12 -25 -11 -31 6 18 -2 12 NA 29 -13 9 3 24 15 53 -7 22 -20 46 -8 33 -5 39 0 15

20 Philip -5 5 0 -3 -8 -9 -11 41 3 29 NA 38 1 4 14 28 19 25 -12 -16 -21 -5 -5 33 -5 31 1 7

21 Hannah -20 -12 -24 -3 -28 -13 -16 80 4 53 NA 73 4 31 29 47 15 17 -7 18 -13 17 -8 35 -23 30 -8 11

22 Nick 16 15 -6 3 -5 -30 -9 3 3 -12 NA 0 -1 17 20 40 9 53 -9 3 -39 21 -6 25 3 38 4 20

23 Chris -4 6 2 -3 -12 -12 -7 1 6 7 NA 42 -8 10 2 21 4 3 -2 -5 -3 -1 -9 22 -1 33 -1 23

-2 2 -9 -6 -10 -12 3 31 1 15 NA 16 3 6 13 21 13 25 -11 6 -17 5 -4 10 -4 20 -7 7


1/30/2009

Car

Average

Car

Car

1/15/2009

1/14/2009

1/16/2009

1/23/2009

1/23/2009

Car

Car

Car

1/25/2009

Cross St & Route 7

Site 6




Site 4

Washington St & High St

Elm St & Seymour St

Site 10


Site 11


Site 14

Shannon St

Site 12 Site 13


Car

Subject

Site 9Site 7


South St & Main St

Site 8Site 5

1/8/2009

Site 2 Site 3

Old Chapel Rd

Site 1

Adirondack Circle

Walk




(fold out)

131

Figure 5 Judgement H

istograms

Figure 5 Judgment Histograms

Site 4

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =-3.26Std. Dev. = 13.545

N =23

Site 2

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =9.39Std. Dev. = 14.282

N =23

Site 3

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =9.57Std. Dev. = 9.144

N =23

Site 5

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =-0.52Std. Dev. = 5.559

N =23

Site 1

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =1.57Std. Dev. = 18.108

N =23

Site 7

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =-2.61Std. Dev. = 9.442

N =23

Site 3

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =11.83Std. Dev. = 21.737

N =23

Site 4

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =-31.13Std. Dev. = 26.265

N =23

Site 1

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =-2.13Std. Dev. = 17.713

N =23

Site 2

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =5.83Std. Dev. = 19.194

N =23

Site 5

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =-14.65Std. Dev. = 22.376

N =23

Site 6

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =-16.3Std. Dev. = 29.496

N =23

Site 7

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =-5.52Std. Dev. = 22.691

N =23

Site 8

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =-13.43Std. Dev. = 12.838

N =23

Site 9

9060300-30-60-90

Freq

uenc

y12

10

8

6

4

2

0

Mean =-13.17Std. Dev. = 8.004

N =23

Site 10

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =11.22Std. Dev. = 12.165

N =23

Site 11

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =17.04Std. Dev. = 19.305

N =23

Site 12

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =4.09Std. Dev. = 3.813

N =23

Site 13

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =4.17Std. Dev. = 13.276

N =23

Site 14

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =7.17Std. Dev. = 14.711

N =23

Site 8

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =-21Std. Dev. = 21.288

N =23

Site 9

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =-24.91Std. Dev. = 30.476

N =23

Site 10

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =-5.65Std. Dev. = 29.365

N =23

Site 11

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =-5.43Std. Dev. = 22.209

N =23

Site 12

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =-9.57Std. Dev. = 23.063

N =23

Site 13

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =-20.13Std. Dev. = 23.932

N =23

Site 14

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =-6.91Std. Dev. = 16.465

N =23

Carol’s Judgement Histograms

North Judgement Histograms

All histograms are constructed from judgment errors (Appendix 2, Figure 4). No error from actual bearing is 0°, but 0 error judgments were placed in 0-5° bins.





(fold out)

131

Figure 5 Judgement H

istograms

Figure 5 Judgment Histograms

Site 4

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =-3.26Std. Dev. = 13.545

N =23

Site 2

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =9.39Std. Dev. = 14.282

N =23

Site 3

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =9.57Std. Dev. = 9.144

N =23

Site 5

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =-0.52Std. Dev. = 5.559

N =23

Site 1

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =1.57Std. Dev. = 18.108

N =23

Site 7

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =-2.61Std. Dev. = 9.442

N =23

Site 3

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =11.83Std. Dev. = 21.737

N =23

Site 4

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =-31.13Std. Dev. = 26.265

N =23

Site 1

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =-2.13Std. Dev. = 17.713

N =23

Site 2

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =5.83Std. Dev. = 19.194

N =23

Site 5

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =-14.65Std. Dev. = 22.376

N =23

Site 6

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =-16.3Std. Dev. = 29.496

N =23

Site 7

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =-5.52Std. Dev. = 22.691

N =23

Site 8

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =-13.43Std. Dev. = 12.838

N =23

Site 9

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =-13.17Std. Dev. = 8.004

N =23

Site 10

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =11.22Std. Dev. = 12.165

N =23

Site 11

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =17.04Std. Dev. = 19.305

N =23

Site 12

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =4.09Std. Dev. = 3.813

N =23

Site 13

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =4.17Std. Dev. = 13.276

N =23

Site 14

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =7.17Std. Dev. = 14.711

N =23

Site 8

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =-21Std. Dev. = 21.288

N =23

Site 9

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =-24.91Std. Dev. = 30.476

N =23

Site 10

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =-5.65Std. Dev. = 29.365

N =23

Site 11

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =-5.43Std. Dev. = 22.209

N =23

Site 12

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =-9.57Std. Dev. = 23.063

N =23

Site 13

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =-20.13Std. Dev. = 23.932

N =23

Site 14

9060300-30-60-90

Freq

uenc

y

12

10

8

6

4

2

0

Mean =-6.91Std. Dev. = 16.465

N =23

Carol’s Judgement Histograms

North Judgement Histograms




133Bibliography

Bibliography

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which way? perceptual surveying as a tool for schematic map making

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