The scale of a map is the ratio of a distance on the map to the corresponding distance on the ground. This simple concept is complicated by the curvature of the Earth 's surface, which forces scale to vary across a map. Because of this variation, the concept of scale becomes meaningful in two distinct ways.
132-635: A map is a symbolic depiction of interrelationships, commonly spatial, between things within a space . A map may be annotated with text and graphics. Like any graphic, a map may be fixed to paper or other durable media, or may be displayed on a transitory medium such as a computer screen. Some maps change interactively. Although maps are commonly used to depict geographic elements , they may represent any space, real or fictional. The subject being mapped may be two-dimensional such as Earth's surface, three-dimensional such as Earth's interior, or from an abstract space of any dimension. Maps of geographic territory have
264-615: A {\displaystyle a} is the radius of the sphere, λ {\displaystyle \lambda } is the longitude from the central meridian of the projection (here taken as the Greenwich meridian at λ = 0 {\displaystyle \lambda =0} ) and φ {\displaystyle \varphi } is the latitude. Note that λ {\displaystyle \lambda } and φ {\displaystyle \varphi } are in radians (obtained by multiplying
396-546: A δ φ {\displaystyle a\,\delta \varphi } where a {\displaystyle a} is the radius of the sphere and φ {\displaystyle \varphi } is in radian measure. The lines PM and KQ are arcs of parallel circles of length ( a cos φ ) δ λ {\displaystyle (a\cos \varphi )\delta \lambda } with λ {\displaystyle \lambda } in radian measure. In deriving
528-506: A conceptual framework . In the 19th and 20th centuries mathematicians began to examine geometries that are non-Euclidean , in which space is conceived as curved , rather than flat , as in the Euclidean space . According to Albert Einstein 's theory of general relativity , space around gravitational fields deviates from Euclidean space. Experimental tests of general relativity have confirmed that non-Euclidean geometries provide
660-690: A geocentric cosmos. He backed the Copernican theory that the universe was heliocentric , with a stationary Sun at the center and the planets—including the Earth—revolving around the Sun. If the Earth moved, the Aristotelian belief that its natural tendency was to remain at rest was in question. Galileo wanted to prove instead that the Sun moved around its axis, that motion was as natural to an object as
792-515: A map legend on the margin of the map, or on a separately published characteristic sheet. Some cartographers prefer to make the map cover practically the entire screen or sheet of paper, leaving no room "outside" the map for information about the map as a whole. These cartographers typically place such information in an otherwise "blank" region "inside" the map— cartouche , map legend, title, compass rose , bar scale , etc. In particular, some maps contain smaller maps inset into otherwise blank areas of
924-419: A meridian distance of about 10 km and over an east-west line of about 8 km. Thus a plan of New York City accurate to one metre or a building site plan accurate to one millimetre would both satisfy the above conditions for the neglect of curvature. They can be treated by plane surveying and mapped by scale drawings in which any two points at the same distance on the drawing are at the same distance on
1056-400: A metaphysical foundation or a mechanical explanation for his theories about matter and motion. Cartesian space was Euclidean in structure—infinite, uniform and flat. It was defined as that which contained matter; conversely, matter by definition had a spatial extension so that there was no such thing as empty space. The Cartesian notion of space is closely linked to his theories about
1188-400: A point property of the projection at P it suffices to take an infinitesimal element PMQK of the surface: in the limit of Q approaching P such an element tends to an infinitesimally small planar rectangle. Normal cylindrical projections of the sphere have x = a λ {\displaystyle x=a\lambda } and y {\displaystyle y} equal to
1320-402: A ratio , such as 1:10,000, which means that 1 unit of measurement on the map corresponds to 10,000 of that same unit on the ground. The scale statement can be accurate when the region mapped is small enough for the curvature of the Earth to be neglected, such as a city map . Mapping larger regions, where the curvature cannot be ignored, requires projections to map from the curved surface of
1452-613: A better model for the shape of space. Debates concerning the nature, essence and the mode of existence of space date back to antiquity; namely, to treatises like the Timaeus of Plato , or Socrates in his reflections on what the Greeks called khôra (i.e. "space"), or in the Physics of Aristotle (Book IV, Delta) in the definition of topos (i.e. place), or in the later "geometrical conception of place" as "space qua extension" in
SECTION 10
#17327649147171584-470: A broad understanding of the location and features of an area. The reader may gain an understanding of the type of landscape, the location of urban places, and the location of major transportation routes all at once. Polish general Stanisław Maczek had once been shown an impressive outdoor map of land and water in the Netherlands demonstrating the working of the waterways (which had been an obstacle to
1716-517: A clear distinction between the body and mind, which is referred to as the Cartesian dualism . Following Galileo and Descartes, during the seventeenth century the philosophy of space and time revolved around the ideas of Gottfried Leibniz , a German philosopher–mathematician, and Isaac Newton , who set out two opposing theories of what space is. Rather than being an entity that independently exists over and above other matter, Leibniz held that space
1848-480: A clear distinction of the intrinsic projection scaling and the reduction scaling. From this point we ignore the RF and work with the projection map. Consider a small circle on the surface of the Earth centred at a point P at latitude φ {\displaystyle \varphi } and longitude λ {\displaystyle \lambda } . Since the point scale varies with position and direction
1980-402: A concept of neighbourhood is defined, frequently by means of a distance ( metric spaces ). The elements of a space are often called points , but they can have other names such as vectors in vector spaces and functions in function spaces . Space is one of the few fundamental quantities in physics , meaning that it cannot be defined via other quantities because nothing more fundamental
2112-428: A constant separation on the ground. While a map may display a graphical bar scale, the scale must be used with the understanding that it will be accurate on only some lines of the map. (This is discussed further in the examples in the following sections.) Let P be a point at latitude φ {\displaystyle \varphi } and longitude λ {\displaystyle \lambda } on
2244-440: A flat surface. After a while, as the bucket continues to spin, the surface of the water becomes concave. If the bucket's spinning is stopped then the surface of the water remains concave as it continues to spin. The concave surface is therefore apparently not the result of relative motion between the bucket and the water. Instead, Newton argued, it must be a result of non-inertial motion relative to space itself. For several centuries
2376-471: A function of latitude only. Therefore, the infinitesimal element PMQK on the sphere projects to an infinitesimal element P'M'Q'K' which is an exact rectangle with a base δ x = a δ λ {\displaystyle \delta x=a\,\delta \lambda } and height δ y {\displaystyle \delta y} . By comparing the elements on sphere and projection we can immediately deduce expressions for
2508-510: A nascent coordinate system for identifying locations were hinted by ancient Chinese astronomers that divided the sky into various sectors or lunar lodges. The Chinese cartographer and geographer Pei Xiu of the Three Kingdoms period created a set of large-area maps that were drawn to scale. He produced a set of principles that stressed the importance of consistent scaling, directional measurements, and adjustments in land measurements in
2640-399: A particular purpose for an intended audience. Designing a map involves bringing together a number of elements and making a large number of decisions. The elements of design fall into several broad topics, each of which has its own theory, its own research agenda, and its own best practices. That said, there are synergistic effects between these elements, meaning that the overall design process
2772-443: A plane or sphere and, Poincaré argued, the same is true for the debate over whether real space is Euclidean or not. For him, which geometry was used to describe space was a matter of convention . Since Euclidean geometry is simpler than non-Euclidean geometry, he assumed the former would always be used to describe the 'true' geometry of the world. In 1905, Albert Einstein published his special theory of relativity , which led to
SECTION 20
#17327649147172904-498: A point P not on L 1 , there is exactly one straight line L 2 on the plane that passes through the point P and is parallel to the straight line L 1 . Until the 19th century, few doubted the truth of the postulate; instead debate centered over whether it was necessary as an axiom, or whether it was a theory that could be derived from the other axioms. Around 1830 though, the Hungarian János Bolyai and
3036-527: A ratio: if the scale is an inch to two miles and the map user can see two villages that are about two inches apart on the map, then it is easy to work out that the villages are about four miles apart on the ground. A lexical scale may cause problems if it expressed in a language that the user does not understand or in obsolete or ill-defined units. For example, a scale of one inch to a furlong (1:7920) will be understood by many older people in countries where Imperial units used to be taught in schools. But
3168-418: A scale of one pouce to one league may be about 1:144,000, depending on the cartographer 's choice of the many possible definitions for a league, and only a minority of modern users will be familiar with the units used. A small-scale map cover large regions, such as world maps , continents or large nations. In other words, they show large areas of land on a small space. They are called small scale because
3300-453: A separation along the line to the bar scale does not give a distance related to the true distance in any simple way. (But see addendum ). Even if a distance along this line of constant planar angle could be worked out, its relevance is questionable since such a line on the projection corresponds to a complicated curve on the sphere. For these reasons bar scales on small-scale maps must be used with extreme caution. The Mercator projection maps
3432-441: A separation from a parallel to the bar scale we must divide the bar scale distance by this factor to obtain the distance between the points when measured along the parallel (which is not the true distance along a great circle ). On a line at a bearing of say 45 degrees ( β = 45 ∘ {\displaystyle \beta =45^{\circ }} ) the scale is continuously varying with latitude and transferring
3564-481: A similar way to the relations between family members. Although people in the family are related to one another, the relations do not exist independently of the people. Leibniz argued that space could not exist independently of objects in the world because that implies a difference between two universes exactly alike except for the location of the material world in each universe. But since there would be no observational way of telling these universes apart then, according to
3696-431: A smaller area. Maps that show an extensive area are "small scale" maps. This can be a cause of confusion. Mapping large areas causes noticeable distortions because it significantly flattens the curved surface of the earth. How distortion gets distributed depends on the map projection . Scale varies across the map , and the stated map scale is only an approximation. This is discussed in detail below. The region over which
3828-544: A standard meter or simply meter, is defined as the distance traveled by light in vacuum during a time interval of exactly 1/299,792,458 of a second. This definition coupled with present definition of the second is based on the special theory of relativity in which the speed of light plays the role of a fundamental constant of nature. Geography is the branch of science concerned with identifying and describing places on Earth , utilizing spatial awareness to try to understand why things exist in specific locations. Cartography
3960-417: A very long tradition and have existed from ancient times. The word "map" comes from the medieval Latin : Mappa mundi , wherein mappa meant 'napkin' or 'cloth' and mundi 'of the world'. Thus, "map" became a shortened term referring to a flat representation of Earth's surface. Maps have been one of the most important human inventions for millennia, allowing humans to explain and navigate their way through
4092-405: A way that all objects expand and contract in similar proportions in different places on the sphere. With a suitable falloff in temperature, if the scientists try to use measuring rods to determine the sum of the angles in a triangle, they can be deceived into thinking that they inhabit a plane, rather than a spherical surface. In fact, the scientists cannot in principle determine whether they inhabit
Map - Misplaced Pages Continue
4224-416: Is a priori because it belongs to the subjective constitution of our mind as the form or manner of our intuition of external objects. Euclid's Elements contained five postulates that form the basis for Euclidean geometry. One of these, the parallel postulate , has been the subject of debate among mathematicians for many centuries. It states that on any plane on which there is a straight line L 1 and
4356-593: Is hyperbolic-orthogonal to each of the three spatial dimensions. Before Albert Einstein 's work on relativistic physics, time and space were viewed as independent dimensions. Einstein's discoveries showed that due to relativity of motion our space and time can be mathematically combined into one object– spacetime . It turns out that distances in space or in time separately are not invariant with respect to Lorentz coordinate transformations, but distances in Minkowski space along spacetime intervals are—which justifies
4488-510: Is called a cartographer . Road maps are perhaps the most widely used maps today. They are a subset of navigational maps, which also include aeronautical and nautical charts , railroad network maps, and hiking and bicycling maps. In terms of quantity, the largest number of drawn map sheets is probably made up by local surveys, carried out by municipalities , utilities, tax assessors, emergency services providers, and other local agencies. Many national surveying projects have been carried out by
4620-468: Is called the nominal scale (also called principal scale or representative fraction ). Many maps state the nominal scale and may even display a bar scale (sometimes merely called a "scale") to represent it. The second distinct concept of scale applies to the variation in scale across a map. It is the ratio of the mapped point's scale to the nominal scale. In this case 'scale' means the scale factor (also called point scale or particular scale ). If
4752-422: Is commonly illustrated by the impossibility of smoothing an orange peel onto a flat surface without tearing and deforming it. The only true representation of a sphere at constant scale is another sphere such as a globe . Given the limited practical size of globes, we must use maps for detailed mapping. Maps require projections. A projection implies distortion: A constant separation on the map does not correspond to
4884-488: Is conformal since it is constructed to preserve angles and its scale factor is isotropic, a function of latitude only: Mercator does preserve shape in small regions. Definition: on a conformal projection with an isotropic scale, points which have the same scale value may be joined to form the isoscale lines . These are not plotted on maps for end users but they feature in many of the standard texts. (See Snyder pages 203—206.) There are two conventions used in setting down
5016-474: Is curved. Carl Friedrich Gauss , a German mathematician, was the first to consider an empirical investigation of the geometrical structure of space. He thought of making a test of the sum of the angles of an enormous stellar triangle, and there are reports that he actually carried out a test, on a small scale, by triangulating mountain tops in Germany. Henri Poincaré , a French mathematician and physicist of
5148-462: Is derived from Latin oriens , meaning east. In the Middle Ages many maps, including the T and O maps , were drawn with east at the top (meaning that the direction "up" on the map corresponds to East on the compass). The most common cartographic convention nowadays is that north is at the top of a map. Maps not oriented with north at the top: Many maps are drawn to a scale expressed as
5280-427: Is important due to its necessary relevance to survival, especially with regards to hunting and self preservation as well as simply one's idea of personal space . Several space-related phobias have been identified, including agoraphobia (the fear of open spaces), astrophobia (the fear of celestial space) and claustrophobia (the fear of enclosed spaces). The understanding of three-dimensional space in humans
5412-408: Is known at the present. On the other hand, it can be related to other fundamental quantities. Thus, similar to other fundamental quantities (like time and mass ), space can be explored via measurement and experiment. Today, our three-dimensional space is viewed as embedded in a four-dimensional spacetime , called Minkowski space (see special relativity ). The idea behind spacetime is that time
Map - Misplaced Pages Continue
5544-475: Is no more than the collection of spatial relations between objects in the world: "space is that which results from places taken together". Unoccupied regions are those that could have objects in them, and thus spatial relations with other places. For Leibniz, then, space was an idealised abstraction from the relations between individual entities or their possible locations and therefore could not be continuous but must be discrete . Space could be thought of in
5676-523: Is no standard: The terms are sometimes used in the absolute sense of the table, but other times in a relative sense. For example, a map reader whose work refers solely to large-scale maps (as tabulated above) might refer to a map at 1:500,000 as small-scale. In the English language, the word large-scale is often used to mean "extensive". However, as explained above, cartographers use the term "large scale" to refer to less extensive maps – those that show
5808-588: Is not just working on each element one at a time, but an iterative feedback process of adjusting each to achieve the desired gestalt . Maps of the world or large areas are often either 'political' or 'physical'. The most important purpose of the political map is to show territorial borders ; the purpose of the physical map is to show features of geography such as mountains, soil type, or land use including infrastructures such as roads, railroads, and buildings. Topographic maps show elevations and relief with contour lines or shading. Geological maps show not only
5940-481: Is not known, but space is known to be expanding very rapidly due to the cosmic inflation . The measurement of physical space has long been important. Although earlier societies had developed measuring systems, the International System of Units , (SI), is now the most common system of units used in the measuring of space, and is almost universally used. Currently, the standard space interval, called
6072-437: Is often conceived in three linear dimensions . Modern physicists usually consider it, with time , to be part of a boundless four-dimensional continuum known as spacetime . The concept of space is considered to be of fundamental importance to an understanding of the physical universe . However, disagreement continues between philosophers over whether it is itself an entity, a relationship between entities, or part of
6204-767: Is on the multiple and overlapping social processes that produce space. In his book The Condition of Postmodernity, David Harvey describes what he terms the " time-space compression ." This is the effect of technological advances and capitalism on our perception of time, space and distance. Changes in the modes of production and consumption of capital affect and are affected by developments in transportation and technology. These advances create relationships across time and space, new markets and groups of wealthy elites in urban centers, all of which annihilate distances and affect our perception of linearity and distance. In his book Thirdspace, Edward Soja describes space and spatiality as an integral and neglected aspect of what he calls
6336-531: Is postulated that spacetime is geometrically distorted – curved – near to gravitationally significant masses. One consequence of this postulate, which follows from the equations of general relativity, is the prediction of moving ripples of spacetime, called gravitational waves . While indirect evidence for these waves has been found (in the motions of the Hulse–Taylor binary system, for example) experiments attempting to directly measure these waves are ongoing at
6468-439: Is said to be conformal if the angle between a pair of lines intersecting at a point P is the same as the angle between the projected lines at the projected point P', for all pairs of lines intersecting at point P. A conformal map has an isotropic scale factor. Conversely isotropic scale factors across the map imply a conformal projection. Isotropy of scale implies that small elements are stretched equally in all directions, that
6600-438: Is stationary with respect to them; and objects are measured to be shortened in the direction that they are moving with respect to the observer. Subsequently, Einstein worked on a general theory of relativity , which is a theory of how gravity interacts with spacetime. Instead of viewing gravity as a force field acting in spacetime, Einstein suggested that it modifies the geometric structure of spacetime itself. According to
6732-415: Is the mapping of spaces to allow better navigation, for visualization purposes and to act as a locational device. Geostatistics apply statistical concepts to collected spatial data of Earth to create an estimate for unobserved phenomena. Geographical space is often considered as land, and can have a relation to ownership usage (in which space is seen as property or territory). While some cultures assert
SECTION 50
#17327649147176864-459: Is the shape of a small element is preserved. This is the property of orthomorphism (from Greek 'right shape'). The qualification 'small' means that at some given accuracy of measurement no change can be detected in the scale factor over the element. Since conformal projections have an isotropic scale factor they have also been called orthomorphic projections . For example, the Mercator projection
6996-412: Is thought to be learned during infancy using unconscious inference , and is closely related to hand-eye coordination . The visual ability to perceive the world in three dimensions is called depth perception . Space has been studied in the social sciences from the perspectives of Marxism , feminism , postmodernism , postcolonialism , urban theory and critical geography . These theories account for
7128-437: Is understood to have culminated with the publication of Newton 's Principia Mathematica in 1687. Newton's theories about space and time helped him explain the movement of objects. While his theory of space is considered the most influential in physics, it emerged from his predecessors' ideas about the same. As one of the pioneers of modern science , Galileo revised the established Aristotelian and Ptolemaic ideas about
7260-467: Is used by agencies around the world, as diverse as wildlife conservationists and militaries. Even when GIS is not involved, most cartographers now use a variety of computer graphics programs to generate new maps. Interactive, computerized maps are commercially available, allowing users to zoom in or zoom out (respectively meaning to increase or decrease the scale), sometimes by replacing one map with another of different scale, centered where possible on
7392-452: Is useful to note that The following examples illustrate three normal cylindrical projections and in each case the variation of scale with position and direction is illustrated by the use of Tissot's indicatrix . The equirectangular projection , also known as the Plate Carrée (French for "flat square") or (somewhat misleadingly) the equidistant projection, is defined by where
7524-617: The Discourse on Place ( Qawl fi al-Makan ) of the 11th-century Arab polymath Alhazen . Many of these classical philosophical questions were discussed in the Renaissance and then reformulated in the 17th century, particularly during the early development of classical mechanics . Isaac Newton viewed space as absolute, existing permanently and independently of whether there was any matter in the. In contrast, other natural philosophers , notably Gottfried Leibniz , thought that space
7656-510: The LIGO and Virgo collaborations. LIGO scientists reported the first such direct observation of gravitational waves on 14 September 2015. Relativity theory leads to the cosmological question of what shape the universe is, and where space came from. It appears that space was created in the Big Bang , 13.8 billion years ago and has been expanding ever since. The overall shape of space
7788-424: The geoid to a two-dimensional picture. Projection always distorts the surface. There are many ways to apportion the distortion, and so there are many map projections. Which projection to use depends on the purpose of the map. The various features shown on a map are represented by conventional signs or symbols. For example, colors can be used to indicate a classification of roads. Those signs are usually explained in
7920-460: The identity of indiscernibles , there would be no real difference between them. According to the principle of sufficient reason , any theory of space that implied that there could be these two possible universes must therefore be wrong. Newton took space to be more than relations between material objects and based his position on observation and experimentation. For a relationist there can be no real difference between inertial motion , in which
8052-476: The parallel scale is denoted by k ( λ , φ ) {\displaystyle k(\lambda ,\,\varphi )} . Definition: if the point scale depends only on position, not on direction, we say that it is isotropic and conventionally denote its value in any direction by the parallel scale factor k ( λ , φ ) {\displaystyle k(\lambda ,\varphi )} . Definition: A map projection
SECTION 60
#17327649147178184-534: The representative fraction is relatively small. Large-scale maps show smaller areas in more detail, such as county maps or town plans might. Such maps are called large scale because the representative fraction is relatively large. For instance a town plan, which is a large-scale map, might be on a scale of 1:10,000, whereas the world map, which is a small scale map, might be on a scale of 1:100,000,000. The following table describes typical ranges for these scales but should not be considered authoritative because there
8316-576: The " trialectics of being ," the three modes that determine how we inhabit, experience and understand the world. He argues that critical theories in the Humanities and Social Sciences study the historical and social dimensions of our lived experience, neglecting the spatial dimension. He builds on Henri Lefebvre's work to address the dualistic way in which humans understand space—as either material/physical or as represented/imagined. Lefebvre's "lived space" and Soja's "thirdspace" are terms that account for
8448-424: The 1850s, Bernhard Riemann developed an equivalent theory of elliptical geometry , in which no parallel lines pass through P . In this geometry, triangles have more than 180° and circles have a ratio of circumference-to-diameter that is less than pi . Although there was a prevailing Kantian consensus at the time, once non-Euclidean geometries had been formalised, some began to wonder whether or not physical space
8580-714: The British Columbia Pavilion at the Pacific National Exhibition (PNE) in Vancouver from 1954 to 1997 it was viewed by millions of visitors. The Guinness Book of Records cites the Challenger Map as the largest of its kind in the world. The map in its entirety occupies 6,080 square feet (1,850 square metres) of space. It was disassembled in 1997; there is a project to restore it in a new location. The Relief map of Guatemala
8712-453: The Earth to the plane. The impossibility of flattening the sphere to the plane without distortion means that the map cannot have a constant scale. Rather, on most projections, the best that can be attained is an accurate scale along one or two paths on the projection. Because scale differs everywhere, it can only be measured meaningfully as point scale per location. Most maps strive to keep point scale variation within narrow bounds. Although
8844-428: The Earth's surface) and bearing (on the map) is not universally observed, many writers using the terms almost interchangeably. Definition: the point scale at P is the ratio of the two distances P'Q' and PQ in the limit that Q approaches P. We write this as where the notation indicates that the point scale is a function of the position of P and also the direction of the element PQ. Definition: if P and Q lie on
8976-466: The Polish forces progress in 1944). This had inspired Maczek and his companions to create Great Polish Map of Scotland as a 70-ton permanent three-dimensional reminder of Scotland's hospitality to his compatriots. In 1974, the coastline and relief of Scotland were laid out by Kazimierz Trafas, a Polish student geographer-planner, based on existing Bartholomew Half-Inch map sheets. Engineering infrastructure
9108-458: The RF (or principal scale) gives the actual circumference of the Earth. The bar scale on the map is also drawn at the true scale so that transferring a separation between two points on the equator to the bar scale will give the correct distance between those points. The same is true on the meridians. On a parallel other than the equator the scale is sec φ {\displaystyle \sec \varphi } so when we transfer
9240-505: The Russian Nikolai Ivanovich Lobachevsky separately published treatises on a type of geometry that does not include the parallel postulate, called hyperbolic geometry . In this geometry, an infinite number of parallel lines pass through the point P . Consequently, the sum of angles in a triangle is less than 180° and the ratio of a circle 's circumference to its diameter is greater than pi . In
9372-595: The Tissot diagram each infinitesimal circular element preserves its shape but is enlarged more and more as the latitude increases. Lambert's equal area projection maps the sphere to a finite rectangle by the equations where a, λ {\displaystyle \lambda } and φ {\displaystyle \varphi } are as in the previous example. Since y ′ ( φ ) = cos φ {\displaystyle y'(\varphi )=\cos \varphi }
9504-483: The actual printed (or viewed) maps. If the definition of point scale in the previous section is in terms of the projection map then we can expect the scale factors to be close to unity. For normal tangent cylindrical projections the scale along the equator is k=1 and in general the scale changes as we move off the equator. Analysis of scale on the projection map is an investigation of the change of k away from its true value of unity. Actual printed maps are produced from
9636-528: The bucket argument was considered decisive in showing that space must exist independently of matter. In the eighteenth century the German philosopher Immanuel Kant published his theory of space as "a property of our mind" by which "we represent to ourselves objects as outside us, and all as in space" in the Critique of Pure Reason On his view the nature of spatial predicates are "relations that only attach to
9768-477: The community, and managed in their name by delegated bodies; such spaces are open to all, while private property is the land culturally owned by an individual or company, for their own use and pleasure. Abstract space is a term used in geography to refer to a hypothetical space characterized by complete homogeneity. When modeling activity or behavior, it is a conceptual tool used to limit extraneous variables such as terrain. Psychologists first began to study
9900-476: The complex ways in which humans understand and navigate place, which "firstspace" and "Secondspace" (Soja's terms for material and imagined spaces respectively) do not fully encompass. Postcolonial theorist Homi Bhabha 's concept of Third Space is different from Soja's Thirdspace, even though both terms offer a way to think outside the terms of a binary logic. Bhabha's Third Space is the space in which hybrid cultural forms and identities exist. In his theories,
10032-449: The concept that space and time can be viewed as a single construct known as spacetime . In this theory, the speed of light in vacuum is the same for all observers—which has the result that two events that appear simultaneous to one particular observer will not be simultaneous to another observer if the observers are moving with respect to one another. Moreover, an observer will measure a moving clock to tick more slowly than one that
10164-520: The connectivity is significant. The London Underground map and similar subway maps around the world are a common example of these maps. General-purpose maps provide many types of information on one map. Most atlas maps, wall maps, and road maps fall into this category. The following are some features that might be shown on general-purpose maps: bodies of water, roads, railway lines, parks, elevations, towns and cities, political boundaries, latitude and longitude, national and provincial parks. These maps give
10296-549: The dates of onset of a given phenomenon (for example, the first frost and appearance or disappearance of the snow cover) or the date of a particular value of a meteorological element in the course of a year (for example, passing of the mean daily air temperature through zero). Isolines of the mean numerical value of wind velocity or isotachs are drawn on wind maps (charts); the wind resultants and directions of prevailing winds are indicated by arrows of different lengths or arrows with different plumes; lines of flow are often drawn. Maps of
10428-634: The degree measure by a factor of π {\displaystyle \pi } /180). The longitude λ {\displaystyle \lambda } is in the range [ − π , π ] {\displaystyle [-\pi ,\pi ]} and the latitude φ {\displaystyle \varphi } is in the range [ − π / 2 , π / 2 ] {\displaystyle [-\pi /2,\pi /2]} . Since y ′ ( φ ) = 1 {\displaystyle y'(\varphi )=1}
10560-406: The design of buildings and structures, and on farming. Ownership of space is not restricted to land. Ownership of airspace and of waters is decided internationally. Other forms of ownership have been recently asserted to other spaces—for example to the radio bands of the electromagnetic spectrum or to cyberspace . Public space is a term used to define areas of land as collectively owned by
10692-445: The differences between the mean temperatures of the warmest and coldest month). Isanomals are drawn on maps of anomalies (for example, deviations of the mean temperature of each place from the mean temperature of the entire latitudinal zone). Isolines of frequency are drawn on maps showing the frequency of a particular phenomenon (for example, the annual number of days with a thunderstorm or snow cover). Isochrones are drawn on maps showing
10824-405: The distribution of pressure at different standard altitudes—for example, at every kilometer above sea level—or by maps of baric topography on which altitudes (more precisely geopotentials) of the main isobaric surfaces (for example, 900, 800, and 700 millibars) counted off from sea level are plotted. The temperature, humidity, and wind on aero climatic maps may apply either to standard altitudes or to
10956-407: The earth can be regarded as flat depends on the accuracy of the survey measurements. If measured only to the nearest metre, then curvature of the earth is undetectable over a meridian distance of about 100 kilometres (62 mi) and over an east-west line of about 80 km (at a latitude of 45 degrees). If surveyed to the nearest 1 millimetre (0.039 in), then curvature is undetectable over
11088-435: The earth's surface and in the upper layers of the atmosphere. Climatic maps show climatic features across a large region and permit values of climatic features to be compared in different parts of the region. When generating the map, spatial interpolation can be used to synthesize values where there are no measurements, under the assumption that conditions change smoothly. Climatic maps generally apply to individual months and
11220-476: The earth's surface into climatic zones and regions according to some classification of climates, are a special kind of climatic map. Climatic maps are often incorporated into climatic atlases of varying geographic ranges (globe, hemispheres, continents, countries, oceans) or included in comprehensive atlases. Besides general climatic maps, applied climatic maps and atlases have great practical value. Aero climatic maps, aero climatic atlases, and agro climatic maps are
11352-428: The edges of the map. Further inaccuracies may be deliberate. For example, cartographers may simply omit military installations or remove features solely to enhance the clarity of the map. For example, a road map may not show railroads, smaller waterways, or other prominent non-road objects, and even if it does, it may show them less clearly (e.g. dashed or dotted lines/outlines) than the main roads. Known as decluttering,
11484-416: The effect of the history of colonialism, transatlantic slavery and globalization on our understanding and experience of space and place. The topic has garnered attention since the 1980s, after the publication of Henri Lefebvre 's The Production of Space . In this book, Lefebvre applies Marxist ideas about the production of commodities and accumulation of capital to discuss space as a social product. His focus
11616-433: The equations of any given projection. For example, the equirectangular cylindrical projection may be written as Here we shall adopt the first of these conventions (following the usage in the surveys by Snyder). Clearly the above projection equations define positions on a huge cylinder wrapped around the Earth and then unrolled. We say that these coordinates define the projection map which must be distinguished logically from
11748-406: The form of intuition alone, and thus to the subjective constitution of our mind, without which these predicates could not be attached to anything at all." This develops his theory of knowledge in which knowledge about space itself can be both a priori and synthetic . According to Kant, knowledge about space is synthetic because any proposition about space cannot be true merely in virtue of
11880-462: The general theory, time goes more slowly at places with lower gravitational potentials and rays of light bend in the presence of a gravitational field. Scientists have studied the behaviour of binary pulsars , confirming the predictions of Einstein's theories, and non-Euclidean geometry is usually used to describe spacetime. In modern mathematics spaces are defined as sets with some added structure. They are typically topological spaces , in which
12012-403: The ground. True ground distances are calculated by measuring the distance on the map and then multiplying by the inverse of the scale fraction or, equivalently, simply using dividers to transfer the separation between the points on the map to a bar scale on the map. As proved by Gauss ’s Theorema Egregium , a sphere (or ellipsoid) cannot be projected onto a plane without distortion. This
12144-413: The late 19th century, introduced an important insight in which he attempted to demonstrate the futility of any attempt to discover which geometry applies to space by experiment. He considered the predicament that would face scientists if they were confined to the surface of an imaginary large sphere with particular properties, known as a sphere-world . In this world, the temperature is taken to vary in such
12276-480: The left) of Europe has been distorted to show population distribution, while the rough shape of the continent is still discernible. Another example of distorted scale is the famous London Underground map . The geographic structure is respected but the tube lines (and the River Thames ) are smoothed to clarify the relationships between stations. Near the center of the map, stations are spaced out more than near
12408-458: The main isobaric surfaces. Isolines are drawn on maps of such climatic features as the long-term mean values (of atmospheric pressure, temperature, humidity, total precipitation, and so forth) to connect points with equal values of the feature in question—for example, isobars for pressure, isotherms for temperature, and isohyets for precipitation. Isoamplitudes are drawn on maps of amplitudes (for example, annual amplitudes of air temperature—that is,
12540-402: The major axis to the minor axis is sec φ {\displaystyle \sec \varphi } . Clearly the area of the ellipse increases by the same factor. It is instructive to consider the use of bar scales that might appear on a printed version of this projection. The scale is true (k=1) on the equator so that multiplying its length on a printed map by the inverse of
12672-550: The map. The distortion ellipse is known as Tissot's indicatrix . The example shown here is the Winkel tripel projection , the standard projection for world maps made by the National Geographic Society . The minimum distortion is on the central meridian at latitudes of 30 degrees (North and South). (Other examples ). The key to a quantitative understanding of scale is to consider an infinitesimal element on
12804-462: The map: for example: The design and production of maps is a craft that has developed over thousands of years, from clay tablets to Geographic information systems . As a form of Design , particularly closely related to Graphic design , map making incorporates scientific knowledge about how maps are used, integrated with principles of artistic expression, to create an aesthetically attractive product, carries an aura of authority, and functionally serves
12936-430: The meaning of the terms contained in the proposition. In the counter-example, the proposition "all unmarried men are bachelors" is true by virtue of each term's meaning. Further, space is a priori because it is the form of our receptive abilities to receive information about the external world. For example, someone without sight can still perceive spatial attributes via touch, hearing, and smell. Knowledge of space itself
13068-521: The military, such as the British Ordnance Survey : a civilian government agency, internationally renowned for its comprehensively detailed work. The location information showed by maps may include contour lines , indicating constant values of elevation , temperature, rainfall, etc. The orientation of a map is the relationship between the directions on the map and the corresponding compass directions in reality. The word " orient "
13200-579: The most numerous. Maps exist of the Solar System , and other cosmological features such as star maps . In addition maps of other bodies such as the Moon and other planets are technically not geo graphical maps. Floor maps are also spatial but not necessarily geospatial. Diagrams such as schematic diagrams and Gantt charts and tree maps display logical relationships between items, rather than geographic relationships. Topological in nature, only
13332-546: The name. In addition, time and space dimensions should not be viewed as exactly equivalent in Minkowski space. One can freely move in space but not in time. Thus, time and space coordinates are treated differently both in special relativity (where time is sometimes considered an imaginary coordinate) and in general relativity (where different signs are assigned to time and space components of spacetime metric ). Furthermore, in Einstein's general theory of relativity , it
13464-418: The nature of the body, mind and matter. He is famously known for his "cogito ergo sum" (I think therefore I am), or the idea that we can only be certain of the fact that we can doubt, and therefore think and therefore exist. His theories belong to the rationalist tradition, which attributes knowledge about the world to our ability to think rather than to our experiences, as the empiricists believe. He posited
13596-433: The object travels with constant velocity , and non-inertial motion , in which the velocity changes with time, since all spatial measurements are relative to other objects and their motions. But Newton argued that since non-inertial motion generates forces , it must be absolute. He used the example of water in a spinning bucket to demonstrate his argument. Water in a bucket is hung from a rope and set to spin, starts with
13728-475: The outside world—they are elements of an already given systematic framework that humans possess and use to structure all experiences. Kant referred to the experience of "space" in his Critique of Pure Reason as being a subjective "pure a priori form of intuition". Galilean and Cartesian theories about space, matter, and motion are at the foundation of the Scientific Revolution , which
13860-429: The physical surface, but characteristics of the underlying rock, fault lines, and subsurface structures. From the last quarter of the 20th century, the indispensable tool of the cartographer has been the computer. Much of cartography, especially at the data-gathering survey level, has been subsumed by geographic information systems (GIS). The functionality of maps has been greatly advanced by technology simplifying
13992-413: The practice makes the subject matter that the user is interested in easier to read, usually without sacrificing overall accuracy. Software-based maps often allow the user to toggle decluttering between ON, OFF, and AUTO as needed. In AUTO the degree of decluttering is adjusted as the user changes the scale being displayed. Geographic maps use a projection to translate the three-dimensional real surface of
14124-486: The previous section gives For the calculation of the point scale in an arbitrary direction see addendum . The figure illustrates the Tissot indicatrix for this projection. On the equator h=k=1 and the circular elements are undistorted on projection. At higher latitudes the circles are distorted into an ellipse given by stretching in the parallel direction only: there is no distortion in the meridian direction. The ratio of
14256-452: The projection map by a constant scaling denoted by a ratio such as 1:100M (for whole world maps) or 1:10000 (for such as town plans). To avoid confusion in the use of the word 'scale' this constant scale fraction is called the representative fraction (RF) of the printed map and it is to be identified with the ratio printed on the map. The actual printed map coordinates for the equirectangular cylindrical projection are This convention allows
14388-400: The projection of the circle on the projection will be distorted. Tissot proved that, as long as the distortion is not too great, the circle will become an ellipse on the projection. In general the dimension, shape and orientation of the ellipse will change over the projection. Superimposing these distortion ellipses on the map projection conveys the way in which the point scale is changing over
14520-446: The region of the map is small enough to ignore Earth's curvature, such as in a town plan, then a single value can be used as the scale without causing measurement errors. In maps covering larger areas, or the whole Earth, the map's scale may be less useful or even useless in measuring distances. The map projection becomes critical in understanding how scale varies throughout the map. When scale varies noticeably, it can be accounted for as
14652-577: The rights of the individual in terms of ownership, other cultures will identify with a communal approach to land ownership, while still other cultures such as Australian Aboriginals , rather than asserting ownership rights to land, invert the relationship and consider that they are in fact owned by the land. Spatial planning is a method of regulating the use of space at land-level, with decisions made at regional, national and international levels. Space can also impact on human and cultural behavior, being an important factor in architecture, where it will impact on
14784-413: The same meridian ( α = 0 ) {\displaystyle (\alpha =0)} , the meridian scale is denoted by h ( λ , φ ) {\displaystyle h(\lambda ,\,\varphi )} . Definition: if P and Q lie on the same parallel ( α = π / 2 ) {\displaystyle (\alpha =\pi /2)} ,
14916-570: The same point. In-car global navigation satellite systems are computerized maps with route planning and advice facilities that monitor the user's position with the help of satellites. From the computer scientist's point of view, zooming in entails one or more of: For example: The maps that reflect the territorial distribution of climatic conditions based on the results of long-term observations are called climatic maps . These maps can be compiled both for individual climatic features (temperature, precipitation, humidity) and for combinations of them at
15048-545: The scale factor. Tissot's indicatrix is often used to illustrate the variation of point scale across a map. The foundations for quantitative map scaling goes back to ancient China with textual evidence that the idea of map scaling was understood by the second century BC. Ancient Chinese surveyors and cartographers had ample technical resources used to produce maps such as counting rods , carpenter's square 's, plumb lines , compasses for drawing circles, and sighting tubes for measuring inclination. Reference frames postulating
15180-401: The scale factors are: In the mathematical addendum it is shown that the point scale in an arbitrary direction is also equal to sec φ {\displaystyle \sec \varphi } so the scale is isotropic (same in all directions), its magnitude increasing with latitude as sec φ {\displaystyle \sec \varphi } . In
15312-428: The scale factors on parallels and meridians. (The treatment of scale in a general direction may be found below .) Note that the parallel scale factor k = sec φ {\displaystyle k=\sec \varphi } is independent of the definition of y ( φ ) {\displaystyle y(\varphi )} so it is the same for all normal cylindrical projections. It
15444-454: The scale statement is nominal it is usually accurate enough for most purposes unless the map covers a large fraction of the Earth. At the scope of a world map, scale as a single number is practically meaningless throughout most of the map. Instead, it usually refers to the scale along the equator. Some maps, called cartograms , have the scale deliberately distorted to reflect information other than land area or distance. For example, this map (at
15576-607: The sphere (or ellipsoid ). Let Q be a neighbouring point and let α {\displaystyle \alpha } be the angle between the element PQ and the meridian at P: this angle is the azimuth angle of the element PQ. Let P' and Q' be corresponding points on the projection. The angle between the direction P'Q' and the projection of the meridian is the bearing β {\displaystyle \beta } . In general α ≠ β {\displaystyle \alpha \neq \beta } . Comment: this precise distinction between azimuth (on
15708-461: The sphere to a rectangle (of infinite extent in the y {\displaystyle y} -direction) by the equations where a, λ {\displaystyle \lambda \,} and φ {\displaystyle \varphi \,} are as in the previous example. Since y ′ ( φ ) = a sec φ {\displaystyle y'(\varphi )=a\sec \varphi }
15840-513: The sphere. The figure shows a point P at latitude φ {\displaystyle \varphi } and longitude λ {\displaystyle \lambda } on the sphere. The point Q is at latitude φ + δ φ {\displaystyle \varphi +\delta \varphi } and longitude λ + δ λ {\displaystyle \lambda +\delta \lambda } . The lines PK and MQ are arcs of meridians of length
15972-414: The state of rest. In other words, for Galileo, celestial bodies, including the Earth, were naturally inclined to move in circles. This view displaced another Aristotelian idea—that all objects gravitated towards their designated natural place-of-belonging. Descartes set out to replace the Aristotelian worldview with a theory about space and motion as determined by natural laws . In other words, he sought
16104-402: The superimposition of spatially located variables onto existing geographic maps. Having local information such as rainfall level, distribution of wildlife, or demographic data integrated within the map allows more efficient analysis and better decision making. In the pre-electronic age such superimposition of data led Dr. John Snow to identify the location of an outbreak of cholera . Today, it
16236-404: The term hybrid describes new cultural forms that emerge through the interaction between colonizer and colonized. Scale (map) The first way is the ratio of the size of the generating globe to the size of the Earth. The generating globe is a conceptual model to which the Earth is shrunk and from which the map is projected . The ratio of the Earth's size to the generating globe's size
16368-416: The terrain that was being mapped. Map scales may be expressed in words (a lexical scale), as a ratio, or as a fraction. Examples are: In addition to the above many maps carry one or more (graphical) bar scales . For example, some modern British maps have three bar scales, one each for kilometres, miles and nautical miles. A lexical scale in a language known to the user may be easier to visualise than
16500-461: The way space is perceived in the middle of the 19th century. Those now concerned with such studies regard it as a distinct branch of psychology . Psychologists analyzing the perception of space are concerned with how recognition of an object's physical appearance or its interactions are perceived, see, for example, visual space . Other, more specialized topics studied include amodal perception and object permanence . The perception of surroundings
16632-491: The world. The earliest surviving maps include cave paintings and etchings on tusk and stone. Later came extensive maps produced in ancient Babylon , Greece and Rome , China , and India . In their simplest forms, maps are two-dimensional constructs. Since the Classical Greek period , however, maps also have been projected onto globes . The Mercator Projection , developed by Flemish geographer Gerardus Mercator ,
16764-424: The year as a whole, sometimes to the four seasons, to the growing period, and so forth. On maps compiled from the observations of ground meteorological stations, atmospheric pressure is converted to sea level. Air temperature maps are compiled both from the actual values observed on the surface of the Earth and from values converted to sea level. The pressure field in the free atmosphere is represented either by maps of
16896-410: The zonal and meridional components of wind are frequently compiled for the free atmosphere. Atmospheric pressure and wind are usually combined on climatic maps. Wind roses, curves showing the distribution of other meteorological elements, diagrams of the annual course of elements at individual stations, and the like are also plotted on climatic maps. Maps of climatic regionalization, that is, division of
17028-420: Was in fact a collection of relations between objects, given by their distance and direction from one another. In the 18th century, the philosopher and theologian George Berkeley attempted to refute the "visibility of spatial depth" in his Essay Towards a New Theory of Vision . Later, the metaphysician Immanuel Kant said that the concepts of space and time are not empirical ones derived from experiences of
17160-464: Was made by Francisco Vela in 1905 and still exists. This map (horizontal scale 1:10,000; vertical scale 1:2,000) measures 1,800 m, and was created to educate children in the scape of their country. Some countries required that all published maps represent their national claims regarding border disputes . For example: Space Space is a three-dimensional continuum containing positions and directions . In classical physics , physical space
17292-598: Was put in place to surround it with a sea of water and at the General's request some of the main rivers were even arranged to flow from headwaters pumped into the mountains. The map was finished in 1979, but had to be restored between 2013 and 2017. The Challenger Relief Map of British Columbia is a hand-built topographic map of the province, 80 feet by 76 feet. Built by George Challenger and his family from 1947 to 1954, it features all of B.C.'s mountains, lakes, rivers and valleys in exact-scaled topographical detail. Residing in
17424-419: Was widely used as the standard for two-dimensional world maps until the late 20th century, when more accurate projections were more widely used. Mercator also was the first to use and popularize the concept of the atlas : a collection of maps. Cartography or map-making is the study and practice of crafting representations of the Earth upon a flat surface (see History of cartography ), and one who makes maps
#716283