The mental spatial models are mental representations that preserve information about objects and the spatial relations among them and are updated as new information comes in (p 6). Through our bodies, we perceive and act on the world around us and learn about the consequences of our actions. One way that we view and think about bodies is as objects. Common objects can be referred to at several levels of abstraction (p 5). Bodies are a privileged object for humans. Unlike other objects, they are experienced from inside as well as outside (p 4).

[OED]: 17. a. Physics. The area or space under the influence of, or within the range of, some agent; a state or situation in which a force is exerted on any objects of a particular kind (e.g. electric charges) that are present; the action of such a force; the value (or direction) at any point of the force on an object defined as having unit magnitude, or the set of the vectors that represent this force at each point in a region.

...the study of rotation and the development of surfaces throws considerable light on the development of geometrical ideas (p 273). ...can [children] rotate the sides of a solid onto the frontal plane, and unfold, or 'develop' the regular curved surfaces, such as the cylinder or the cone (p 273).

Alternatively, a pattern can be seen as a network, which itself can have a form, a degree of connectedness, a scale, or a degree of specialization. Many of these characteristics can be precisely described in mathematical language of graph theory. A network description is clearly appropriate when describing flows and flow facilities, but it can also apply to other kinds of linkages: social, economic, or even visual ones (p 357).

People form long-term representations of areas, but long-term knowledge of specific spaces may vary considerably in completeness (p 14). People...code location in terms of distance and direction information within a region, taking its shape and edges as a frame of reference (p 17).

[OED]: 3. The amount of surface contained within given limits; superficial extent; 4. a. A particular extent of surface, esp. of the earth's surface; a space, region, tract.

Constituents of the space of navigation include places, which may be buildings or parks or piazzas or rivers or mountains, as well as countries, planets or stars, on yet larger scales. Places are interrelated in terms of paths or directions in a reference frame (p 9). Places [are] configurations of objects such as walls and furniture, buildings, streets and trees...(p 10). The brain has areas selectively sensitive to only a small number of kinds of things, places, faces, objects, and bodies, suggesting both that these entities have special significance to human existence and that they are at least somewhat computationally distinct (p 10).

‘The terms “neighborhood” and “community” are often used interchangeably. … But neighborhoods have to do with natural topographic boundaries and even transportation lines. Community refers to the delicate lattice of human networks and social institutions. Community also represents the shared meaning of residents, a moral order and ideals, memory and expectations; … needs that are upheld, if only in the breach, in streets and homes, businesses and public institutions.’

[OED]: 2 b. A tract of land with its distinguishing characteristics and features, esp. considered as a product of modifying or shaping processes and agents (usually natural).

[OED]: 2 b. A definite region or area of the earth, or of any place or space, distinguished from adjacent regions by some special quality or condition (indicated by a defining word or phrase),.

4a. Something that encircles like a girdle; a circumscribing or enclosing line, band, or ring.

Landmarks are frequently perceptually salient, familiar and/or functionally important entities...the only functionally vital attribute for a landmark is that it should be unlikely to move (p 14). Two types of landmarks can be distinguished: landmarks that are treated as points (e.g. an elm tree in left field) and landmarks seen as constituting a region (e.g. left field itself) (p 15).

[OED]: II. In extended use. A compartment; an enclosed space, cavity, or sac. 7b. gen. Any one of a number of small compartments or niches into which a larger structure is divided, as a compartment of a dovecote, a section of a drawer or cabinet, a pigeonhole, etc.;
14. Any one of a number of spaces into which a surface is divided by linear partitions: spec.; e.g. a. Archit. Any one of the spaces between the ribs of a vaulted roof.; b. Entomol. Any of the spaces between the nerves of the wings of insects.; 15. Biol. a. The fundamental, usually microscopic, structural and functional unit of all living organisms

[OED]: 2a. gen. A very small particle.

2b. fig. and in extended use. The smallest unit of something; an individual person, esp. regarded as the smallest unit of a community.

[OED]: 3a. The centre or core of a material object; esp. a central part or thing around which other parts or things are grouped or collected; the centre or kernel of an aggregate or concretion.

[OED]: 4. fig. The channel or medium by which anything (e.g. knowledge, influence, wealth, etc.) is conveyed

[OED]: 2. a. A series of concentric circles or rings in which a pliant body has been disposed; hence, such a disposition or form in a body which is rigid.

[OED]: 2. The forming (of anything) by combination of various elements, parts, or ingredients; formation, constitution, construction, making up.

The arrangement of interconnecting parts or components of objects, structures, organisms, and (by analogy) systems, processes, organizations, and information (e.g., languages). Construction is the process of forming a structure. The characteristics of structures include (physically or figuratively) foundations, framework, loads, plans, size, stability, supports, symmetry, etc. Representationsof structures include compartments, cutaways, diagrams, plans, sections, etc.

Size constancy...is linked with the coordination of perceptually controlled movements...(p 11) it is in terms of...grouping of movements, and the permanence attributed to the object, that the latter acquires fixed dimensions and its size is estimated more or less correctly, regardless of whether it is near or distant (p 11).

Individuals form scan paths that enable them to recognize similar perceptual objects (e.g. triangles that look approximately the same). When several different types of triangular perceptual objects are abstracted and associated with the word triangle, an early conceptualization of triangle is created. However, at this early stage of recognition, an individual's ""conceptualization"" of triangle is usually limited to a small set of prototypes and is holistic in nature (p 856-7).

[OED]: 4. In extended use: The constitution, structure, or substance of anything with regard to its constituents or formative elements.

[OED]: 1a. A dense aggregation of objects having the appearance of a single, continuous body

5b. Physics. The quantity of matter which a body contains, as measured by its acceleration under a given force or by the force exerted on it by a gravitational field; an entity possessing mass.

[OED]: 1. a. That which serves to indicate the bounds or limits of anything whether material or immaterial; also the limit itself.

Although objects have many features, parts constitute the features most diagnostic of the basic level of categorization (p 3). Parts may be critical to the basic level because they form a link from perception or appearance of an object to its function (p 4). Mental representations of the space of the body reflect the functions of the body parts (p 6).

[OED]: 4. transf. A distinctive or characteristic part of a thing; some part which arrests the attention by its conspicuousness or prominence.

...a distribution may also be abstracted as a series of focal points of special intensity or character. So a city can be single-, or many-centered; its foci may be multi-purpose or very specialized; its information flows may peak at certain points, or be broadly dispersed; and so on (p 357).

[OED]: 2a. A thickness of matter spread over a surface; esp. one of a series of such thicknesses; a stratum, course, or bed.

A bed, coating, layer, sheet, or zone (horizontally extended) with distinct boundaries (q.v.) and more or less uniform properties. The stratosphere is the outer layer of the atmosphere. Stratigraphy is the study of the sequence of accumulated rock types (and ages). Flow that follows flat trajectories is laminar. The skin is made up of distinct layers of cells. By analogy, the organization of information, or of human endeavors, may be 'layered'.

For human cognition, the void of space is treated as background, and the things in space as foreground. They are located in space with respect to a reference frame or reference objects that vary with the role of the space in thought or behavior. Which things, which references, which perspective depend on the function of those entities in context, on the task at hand. In human cognition, the spatial relations are typically qualitative, approximate, categorical, or topological, rather than metric or analog (p 1-2).

Recognize temporal diffusion over space and time (p. 698)

...to understand human cognitive functioning, we must understand how people code the locations of things and navigate around the world, and how they represent and mentally manipulate spatial information (p 2). A fundamental distinction is that the location of objects can be coded in two basically different but coordinated ways: with respect to external landmarks, or with respect to the self (p 14). A core idea in developing competence...is understanding how to meaningfully enumerate rectangular 3D arrays of squares and cubes, respectively (p 897).

[OED]: 2b. The physical surroundings or conditions in which a person or other organism lives, develops, etc., or in which a thing exists; the external conditions in general affecting the life, existence, or properties of an organism or object.

c. With modifying word: a particular set of surroundings or conditions which something or someone exists in or interacts with.

The background, context, environment, layout, scene, situation, surroundings etc. of a perceived event, object, or representation. The setting influences the perception of depth, location, motion, size, and surface detail, and also figure/ground discrimination. In other words perception is 'contextual' or 'situated'. Camouflage and animal markings are examples of the difficulty of discerning an embedded figure against a background. Other perceptual modes (sound, smell, taste, touch, and other somatic receptors) will generally influence vision as a distraction, attention attractor, or identification aid. Some visual illusions depend on surroundings such as the appearance of the moon as larger when it is close to the horizon.

[OED]: 2 b. In scientific use, a position or location in or on something, esp. one where some activity happens or is done.

3a. The ground or area upon which a building, town, etc., has been built, or which is set apart for some purpose.

[OED]: 1 a. The place, position, or location of a city, country, etc., in relation to its surroundings.

a. Place or position of things in relation to surroundings or to each other.

[OED]: 2. (a) Relating to or encompassing the whole of anything or any group of things, categories, etc.; comprehensive, universal, total, overall. (b) Of, relating to, or involving the whole world, worldwide; (also in later use) of or relating to the world considered in a planetary context

[OED]: 1a. Relating to or concerned with

In fine, it is apparent how simply and rapidly simple projective relations develop from topological relations as soon as they are organized according to coordinate points of view...Once the three topological dimensions arising from the relationships of order ('between') and enclosure are connected with a specific viewpoint they acquire a new significance (p 192).

To speak of 'coding distance' does not imply use of a formal system of measurement (however) mental measurement 'by eye' can sometimes be quite exact (p 18)....coding distance with respect to distal external referrents is a very flexible and powerful system, one that is the final arbiter of location for mature organisms in cases where coding systems conflict (p 74). Place learning involves specifying the distance and/or direction of a to-be-located object with respect to landmarks (p 17).

...most spatial coding situations require the use of two dimensions, rather than just one...adults remember both the distance of a point from the center of a circle (radial location) and the angular relation of the point to the radii of the circle (p 96). Distance and direction information with respect to either the self or to external landmarks, can be encoded at different levels of resolution and is known with varying degrees of certainty (p 27).

Accessibility of directions depends on asymmetries of the body and asymmetries of the world (p 7). Along the [front/back] axis, front has a special status, as it is the direction of orientation, of perception, and of potential movement (p 7).

Movement, flow (q.v.), shift, transport of objects relative to the surroundings, internal motion, rotations; motions of objects such as rotation of the Earth; pitch, roll and yaw of aircraft and vessels; growth of organisms. Heat is the internal motion of atoms and molecules (translation, rotation and vibration). See Path.

[OED]: 1. A change of physical location. a. The action or process of moving; change of position or posture; passage from place to place, or from one situation to another.

[OED]: 1. The action of dispersing or scattering abroad; the condition or state of being dispersed; scattering, distribution, circulation; 2. The action of diffusing or spreading; diffusion.

[OED]: 2. a. The action of spreading abroad; the condition of being widely spread; dispersion through a space or over a surface; wide and general distribution.

[OED]: 1a. trans. To convey or take from one place, person, etc. to another; to transmit, transport; to give or hand over from one to another.

[OED]: 1 a. trans. To carry, convey, or remove from one place or person to another; to convey across.

[OED]: 1a. The movement of a person or people from one country, locality, place of residence, etc., to settle in another; an instance of this.

2. Chiefly with reference to material or immaterial objects, ideas, etc.: the action of passing (or occas. being passed) from one place to another; an instance of this. Also (occas.): the means by which such movement is effected.

[OED]: 3a. esp. To search into or examine (a country, a place, etc.) by going through it; to go into or range over for the purpose of discovery

[OED]: (form, v.) 1a. trans. To give form or shape to; to put into or reduce to shape; to fashion, mould.

(form, n.) I. Shape, arrangement of parts.

[OED]: (destroy) 3a. To undo, break into useless pieces, or reduce into a useless form, consume, or dissolve (any material structure or object).

[OED]: 7 a. Of things material or immaterial: To increase gradually in magnitude, quantity, or degree.

[OED]: 1 a. trans. To spread out; to spread out flat or smooth; to open out, unfold

[OED]: 1a. To make (or cause to appear) less or smaller; to lessen; to reduce in magnitude or degree.

6. Archit. To make (a thing) such that its successive parts in any direction are continuously less and less; to cause to taper or progressively decrease in size, as a tapering column

[OED]: 3a. trans. To cause (separate components, esp. commercial organizations) to combine to form a single entity

[OED]: 4b. To divide or break up into separate parts or portions.

[OED]: 1. Physics. Of or pertaining to that which is thrown or hurled through the air or space.

B.n. 1 a. Physics. The path of any body moving under the action of given forces

2. Geom. A curve or surface passing through a given set of points, or intersecting each of a given series of curves or surfaces according to a given law, e.g. at a constant angle.

Waves are regular oscillations in space (or a medium in space) that are generated by an oscillator. Waves are characterized by the interrelated variables of frequency (or wavelength), period, and velocity, and have amplitudes (heights) and energies. Common forms of waves are electromagnetic radiation (light, Xrays, infrared energy, etc.), sound and water waves, and earthquake waves (primary or compressional, and secondary or shear waves). Waves can combine to form abrupt singularities called solitons such as shock waves or huge pyramidal waves at sea. Standing waves are oscillations in place resulting from reflectionsand interference. Tsunamis (Japanese for 'harbor wave') are high velocity, low amplitude ocean waves produced by submarine earthquakes. When tsunamis reach shores, they slow and increase amplitude, reaching destructive energies close to the generation point.

From the point of view of biological adaption, a central purpose of representing the environment is to allow for the planning of routes to get to desired objectives (p 140). A variety of means can be used to code location and hence to plan routes. Movement can be planned and monitored either with reference to landmarks as continuously available ""beacons"" or by using landmarks on a more periodic basis to assess and correct a route encoded from kinaesthetic and proprioceptive feedback about length and direction of movement (p 133)....being able to perform a spatial planning task requires...the mental construction and comparison of alternative possible routes (p 140).

[OED]: 3. a. A recurrent round or course (of successive events, phenomena, etc.); a regular order or succession in which things recur; a round or series which returns upon itself.

A general gestalt structure for force: First, force is always experienced through interaction...Second, our experience of force usually involves the movement of some object (mass) through space in some direction. In other words, force has a vector quality, a directionality...Third, there is typically a single path of motion...Fourth, forces have origins or sources, and because they are directional, agents can direct them to targets...Fifth, forces have degrees of power or intensity. Where there is power there exists the possibility of measuring the force it generates...Sixth, because we experience force via interaction, there is always a structure or sequence of causality involved (p 43-44)

[OED]: 6b. To drive or force back (something moving or advancing), esp. by physical resistance. Also in figurative contexts.

[OED]: 5. The attractive force by which all bodies tend to move towards the centre of the earth; the degree of intensity with which a body in any given position is affected by this force, measured by the amount of acceleration produced. Also often in wider sense, the degree of intensity with which one body is affected by the attraction of gravitation exercised by another body.

[OED]: 1c. The emission of energy of any kind in the form of rays or waves (esp. electromagnetic waves), or subatomic particles.

5a. Divergence from a central point; radial dispersion, arrangement, or structure; an instance of this.

[OED]: a. The action of carrying; conveyance; spec. the transportation of heat or electricity by the movement of a heated or electrified substance, as in the ascension of heated air or water.

[OED]: 2. [...] To swallow up, to include or take a thing in to the loss of its separate existence; to incorporate. to be absorbed , to be swallowed up, or comprised in, so as no longer to exist apart.

[OED]: 7a. trans. To remove or loosen (a physical restraint) so as to allow something to move, act, or flow freely.

[OED]: (erode) 2. Geol. Of the action of currents, glaciers, etc.: a. To wear away; to eat out.

[OED]: 1 (a) The bursting forth (of water, fire, air, etc.) from natural or artificial limits.

3. Of persons: The action of breaking forth, of issuing suddenly and violently from within boundaries;

Flows are the bulk transport of matter in deformable (low viscosity) media (i.e. fluids). Flow also describes the time rate of change of a local variable such as temperature. Natural flows include streams, tides, ocean currents, wind, and advection and convection in the ocean and atmosphere. Internal and external flows of air and fluids are maintained by organisms. Magma flows occur in volcanic eruptions. Flow concepts can apply by analogy to population migrations and human activities such as transportation.

Coding distances and directions of movement, using information from vestibular, kinaesthetic, and visual sources, is a powerful system of viewer-centered spatial coding, often called dead reckoning or inertial navigation (p 19). Human updating of spatial coding on the basis of movement appears to take place in a relatively automatic and effortless way (p 20)....people use maps to plan routes and to find their way...[several researchers] have found that children as young as 4 years benefit from maps and can use them to guide navigation in a simple situation (p 167).

[OED]: 3. a. Alteration of form or shape; relative displacement of the parts of a body or surface without breach of continuity; an altered form of.

[OED]: 1. The quality or state of being adjacent, or of lying near; contiguity.

The most elementary spatial relationship which can be grasped by perception...corresponding to the simplest type of perceptual structurization, namely the 'nearby-ness' of elements belonging to the same perceptual field (p 6)

[OED]: (central) 1a. Of or pertaining to the centre or middle; situated in, proceeding from, containing or constituting the centre.

Center: 1a. The point round which a circle is described; the middle point of a circle or sphere, equally distant from all points on the circumference.

4. The point, pivot, axis, or line round which a body turns or revolves; the fixed or unmoving centre of rotation or revolution.

6a. The point round which things group themselves or revolve, or that forms a nucleus or point of concentration for its surroundings. spec. (orig. U.S.) a place or a collection of buildings forming a central point in a town, district, etc., or the main area for a particular activity, interest, or the like

[OED]: 3. a. The orderly dividing of a mass or collective body into parts with distinctive characters or functions; the orderly arrangement of the parts into which any whole is divided; division and arrangement; classification.; 3. c. Statistics. The way in which a particular measurement or characteristic is spread over the members of a class.

[OED]: 2. a. Physics. The degree of consistence of a body or substance, measured by the ratio of the mass to the volume, or by the quantity of matter in a unit of bulk.

[OED]: He who or that which contains, esp. a receptacle designed to contain or store certain articles;

[OED]: 1 a. Situated or lying outside; pertaining to, or connected with, the outside or outer portion of anything. external angle: one made by producing outwardly a side of a figure

[OED]: 1a. Situated or existing within or in the interior of something; of or pertaining to the inside (e.g. of the body); inward.

[OED]: 3a. Position as marked by a horizontal line; an imaginary line or plane perpendicular to the plumb-line, considered as determining the position of one or more points or surfaces.

(or spatial succession). an essential relationship...established when two neighboring though separate elements are ranged one before the other (p 7). In the perceptual realm there is one relation in particular, of which order contitutes a fundamental part. This is the relation of symmetry, represented in the simplest case by the double order -- CBA/ABC -- whose role is well known in the construction of 'good configurations'...such as a face (p 7-8).

...arrangements of (objects) might also create observable patterns. Patterns ordered or sequenced by size can create a hierarchy, or, if the objects exist within certain distances, different clusters and densities may arise. Although pattern is an example of a composite construct - dependent in various degrees on place, size, and distance - it is included as a primitive within this framework because it is observable and measurable, and forms the basis for other observable spatial properties. (p 174)

[OED]: 2a. The relation existing between one thing and another in terms of size, quantity, number, or the like; comparative relation, ratio.

a. Size, extent, magnitude, scale, esp. in relation to some standard; relative or comparative size.

[OED]: 2a. Not crooked; free from curvature, bending, or angularity.

[See also chirality.] The regular proportions in symmetrical objects or patterns are defined by 'symmetry operations' - (1) A physical or mental lateral shift (translation); (2) A reflection in a virtual mirror (or point) cutting through the object; or (3) A rotation of the object by some fraction of 360 degrees about an axis. At the completion of the operation the object looks identical with the starting configuration. Translational symmetry creates tiling patterns or tessellations. Frequently the only symmetry the novice recognizes is two-fold reflective (bilateral) symmetry. Rotational (or radial) symmetry occurs in such everyday objects as a double-ended threaded bolt, the recycling symbol, and a pinwheel. Terms that can be used with children for the operations are 'slide', 'twist'. And 'flip'.

[OED]: Of a crystal or three-dimensional form: not superposable on its mirror image.

...competent map use includes an understanding of alignment, that is, knowledge of the relation of the self both to the physical world and to the represented world (p 151)....viewers must ensure that their representations of the map and the world are in alignment in the plane, either by physically turning the map or by mentally rotating one or the other representation (p 151).

Change in the value of a variable in spatial coordinates. A field is the rate of change of a variable with distance from a reference point or surface. The rate (slope) may be more or less 'steep' by analogy with topography. The oceanic 'thermocline' is the rapid fall off in temperature with depth below the uniformly mixed layer at the surface. Physiological processes often depend on the maintenance of ionic gradients, e.g. in nerve tissue, the kidneys, the mitochondrial membrane, chloroplasts, etc.

[OED]: 1. a. The action of connecting or joining together; the condition of being connected (conjoined, fastened or linked) or joined together; 3. The condition of being related to something else by a bond of interdependence, causality, logical sequence, coherence, or the like; relation between things one of which is bound up with, or involved in, another.

Without links we could neither be nor be human. We come into the world tethered to our biological mothers... (p 117). In...simple physical cases there is a spatial contiguity and closeness of the linked objects, and the connected objects are related via the link. Linkages are not only physical and spatial. (We) experience temporal connections. Event A is linked to event B by a series of temporally interceding events...linked because we experience them as...somehow being part of the same temporal sequence (p 118). (An) instance of causal relatedness is the functional linking of parts or entities...linking is a fundamental way of forming unities, of which functional assemblies are a prominent type (p118).

[OED]: 2a. That with which a thing is bound or tied down, or together, so as to keep it in its position or collective form:

Interaction may be considered as a combination of distance and adjacency and rests on the intuitively obvious idea that nearer things are ""more related"" than distant things, a notion often referred to as the first law of geography (Tobler, 1970) (p. 36/see source for more).

[OED]: I. An organized or connected group of objects.

1a. A set or assemblage of things connected, associated, or interdependent, so as to form a complex unity; a whole composed of parts in orderly arrangement according to some scheme or plan; rarely applied to a simple or small assemblage of things

[OED]: 3. The action of arranging, or condition of being arranged or combined, in due order or proper relation.

[OED]: Biol. A biological system composed of all the organisms found in a particular physical environment, interacting with it and with each other. Also in extended use: a complex system resembling this.

...in order to use a map to learn about distances, viewers must appereciate the notion of scale. That is, they must understand that most maps evenly transform real-world distances into smaller ones and that this transformation rule can be used to judge real-world distance (p 151).

[OED]: (rotate) 1a. intr. To turn about a centre or axis, usually a centre or axis inside the thing that is turning; b. trans. To cause (a thing) to rotate.

[OED]: 2a. The drawing, esp. on mathematical principles, of a map or plan of a surface, or of a two-dimensional diagram of a three-dimensional object; esp. (more fully map projection) the representation on a plane surface of (part of) a spherical surface, esp. that of the earth or the celestial sphere; any of the geometrical or cartographic methods by which this may be done. Also: a drawing, plan, or map so made.

2b. Geom. The drawing of straight lines or rays (esp. from a fixed point) through every point of a given figure, usually so as to intersect a surface and describe on it a new figure each point of which corresponds to a point of the original. Also: the resulting figure. Hence more generally: a representation of a figure on a surface according to a particular system of correspondence between its points and the points of the surface; an analogous operation performed in a space of different dimension. Also fig.

Topic CF5-8. Describe the ways in which a spatial perspective enables the synthesis of different subjects (e.g., climate and economy); Describe the common constraints on spatial integration; Use established analysis methods that are based on the concept of spatial integration (e.g., overlay).

Estimating the value of a field at places where it has not been measured, using, e.g., contour interpolation, inverse distance weighting, natural neighbor, radial basis functions, linear and non-linear triangulation, and geostatistics. ""If spatial sampling is an efficient way of capturing knowledge of spatial variation, then there must be reliable ways of filling in the unknown variation between sample points. Spatial interpolation attempts to do this, by providing a method of estimating the value of a field anywhere from a limited number of sample points. Spatial interpolation is no more and no less than intelligent guesswork, supported by Tobler's First Law. Many methods of spatial interpolation exist, all of them based to some extent on the principle that conditions vary smoothly over the Earth's surface. Methods have even been devised to cope with exceptions to Tobler's First Law, by recognising the discontinuities that exist in some geographic phenomena, such as faults in geologic structures, or the barriers to human interaction created by international boundaries.""

Planimetrically correct representations of the spatial distribution of phenomena; maps (whether topographic or thematic), simplify and scale the world. ""Historically, maps have been the primary means to store and communicate spatial data. Objects and their attributes can be readily depicted, and the human eye can quickly discern patterns and anomalies in a well-designed map. Points can be shown as symbols of various kinds, depicting anything from a windmill to a church; lines can be symbolised to distinguish between major roads, minor roads, and rivers; and areas can be symbolised with colour, shading, or annotation. Maps have traditionally existed on paper, as individual sheets or bound into atlases (p. term that originated with Mercator, who produced one of the first atlases in the late 16th century). The advent of digital computers has broadened the concept of a map substantially, however. Maps can now take the form of images displayed on the screens of computers or even mobile phones. They can be dynamic, showing the Earth spinning on its axis or tracking the movement of migrating birds. Their designs can now go far beyond what was traditionally possible when maps had to be drawn by hand, incorporating a far greater range of colour and texture, and even integrating sound.""

[OED]: 2. An illustrative figure which, without representing the exact appearance of an object, gives an outline or general scheme of it, so as to exhibit the shape and relations of its various parts.

[OED]: 1. A kind of symbolic diagram (used in Chem., Mathematics, etc.) in which a system of connections is expressed by spots or circles, some pairs of which are colligated by one or more lines.

2. Algebra. A graphical representation of the locus of a function; the traced curve of an equation. In wider use: A line or curve representing the variation of one quantity with another, each quantity being measured along one of a pair of axes at right angles.

[Cognitive maps are] the mental representations that we draw on to answer questions about directions and distances, to tell someone how to get from A to B, to make educated guesses about weather patterns, population migrations, and political spheres of influence, and to find our ways in the world (p 12). [They] appear to be fragmented, schematized, inconsistent, incomplete, and multimodal. This is an inevitable consequence of spatial knowledge acquired from different modalities, perspectives, and scales (p 12).

Create a spatialized way to present data or information (p. 92)

Inferring spatial associations by comparing mapped variables by locations. Superimposing maps to describe and analyze relationships between different features of the same location or geographic space. Intersections and unions of areas, lines, and points to identify patterns and relationships; mashups of different data registered to the same locations or areal units; merging, aggregating, and disaggregating areas based on joining areal units.

Places are interrelated in terms of paths or directions in a reference frame (p 9). In...diagrams, notably maps and graphs, lines are one-dimensional paths that connect other entities, suggesting that they are related (p 17).

Identifying arrangement of a distribution (p. 92)

[OED]: 2. Math. a. Each of a system of two or more magnitudes used to define the position of a point, line, or plane, by reference to a fixed system of lines, points, etc. (Usually in pl.)

A singular location, locus or position; e.g. an exact time on a timeline. A mathematical point has no extension. An isolated electron approaches being a 'point charge'. Positions in geometric arrangements (e.g. a crystal lattice) are points. The intersection of an artificial horizon or computed boundary and a trajectory may be a 'point of no return', or a decision point in a search pattern. An abrupt transition is a point, e.g. a boiling point. Some structures are 'pointed', e.g. a thorn. [There are cognitive analogues to the points made here commencing with the use of the index finger by infants.]

The concept of the straight line results from the child's first attempts to relate objects spatially in a system of projective viewpoints or coordinates...Drawing or imagining a straight line...presupposes a projective or euclidean space... (p 155). The construction of a straight line may be defined as the linking of distant points by the interpolation of a series of points along a direct path...(p 155).

Determining areas with irregular edges (p. 92)

[OED]: 1. A solid figure or body having many (usually more than six) plane faces.

In a route perspective, a narrative takes a changing point of view within an environment, addressing the reader or listener as you, describing you navigating through an environment, locating landmarks relative to your changing position in terms of your left, right, front, and back (p 10).

In a survey perspective, the narrative takes a stationary viewpoint above the environment, locating landmarks relative to each other in terms of an extrinsic frame of reference, typically, north-south-east-west (p 10).

disciplinary perspectives on "spatial autocorrelation"

Learning Objectives

• Why are spatial data fundamentally heterogeneous?
• What relation does spatial heterogeneity have with scale of analysis?
• How is spatial heterogeneity measured?
• How does spatial heterogeneity influence sampling and interpolation?

disciplinary perspectives on "spatial association"

A complex concept that combines numeracy, distance, ratio, and gradient (p. 95)

Activities are assumed to locate according the (the) relative cost(s). Measurements of access (to open space, to services, to jobs, to markets, etc.) appear frequently in reports. An entire branch of engineering is concerned with the analysis and manipulation of access...(p 187) Access may be classified according to the features to which access is given and to whom it is afforded (p 188). There are numerous ways of measuring the components of access (p 200)

[OED]: (available); 3. Capable of being employed with advantage or turned to account; hence, capable of being made use of, at one's disposal, within one's reach.

[OED]: Physics. Exhibiting equal physical properties or actions (e.g. refraction of light, elasticity, conduction of heat or electricity) in all directions: opp. to

...the purely formal match of environmental structure to nonspatial structure. Are big places associated with big groups and main channels with main flows? (p 138)