Geography

Geography is the study of the physical and geopolitical aspects of the surface of Earth. Physical geography describes the different surface and climatic conditions around the world. Political geography is concerned with the division of the world into various levels of government, human activity, and production. Geography is not confined to merely describing Earth as it is now, but also understanding how it has evolved and how it may change in the future.

The problems that faced humankind at the dawn of history stimulated both geography and mathematics. In fact, much of early mathematics was concerned with making measurements of the land; so much so that a whole branch of mathematics became known as Earth-measurement, which in Greek is geometry. Geometry as a mathematical study is less concerned with its practical roots, but for geographers, geometry and trigonometry are invaluable tools.

Outside of the activities associated with mapmaking, geography was for many years mainly descriptive. The information collected about the physical and social characteristics of the world was reported in a narrative form with little attempt to analyze the data that had been collected. In the late 1940s and early 1950s, a revolution took place in geography when the acceptance of any theory within the science became subject to mathematical analysis. As with other sciences, geography began to use mathematics as the language to describe relationships in the discipline.

The Geographic Matrix

An observation made by a geographer has two main attributes—a location and a physical attribute associated with that location. Each place may have more than one characteristic and each characteristic may be found at more than one location. These data can be recorded in a matrix with rows representing characteristics and columns the places where the

observations have been taken. The organization of data into a matrix greatly aids geographers with the mathematical analysis of the information they gather.

Before geographers collect data, they must select the locations within the region where they will measure the characteristics of interest. This requires an understanding of the sampling techniques found in mathematical statistics. From statistical sampling theories the geographer calculates how many locations will be required, which will consequently reveal the number of columns in the matrix. In establishing the appropriate number of locations, it is necessary to ensure that there is sufficient data so that the samples are representative of the whole region.

Three main types of sampling systems are used in selecting locations. The first type is a totally random sample, in which each location in the study is selected at random from all possible points in the region. The second type of sample is a systematic sample, in which an initial point is chosen at random and all other points are determined by fixed intervals from the randomly chosen point. The third type of sample is a stratified sample, in which the region is subdivided into subregions. Within the subregions, points are chosen by either using a totally random sample, or a stratified sample, or by dividing into further subdivisions. This process can continue until the degree of accuracy required matches the number of sampling points. For example, in studying a country, a geographer may first break the country into regions. Then the regions may subdivide by using political divisions such as a state, and this may go further by using counties, and at this level there may be a random selection of sampling points.

Ultimately, the selection of sampling locations should permit a rapid, accurate, and economical amount of calculation in order to analyze the data. The selection process should also be such that final analysis is comparable to data collected in other regions so that regional comparisons may be made. In addition, consideration needs to be given to national and international standards, and to enabling comparisons with data collected over time.

Analysis of the Geographical Matrix

When the collected data have been placed in a geographic matrix, an analysis of a region can proceed in many ways. One common method of analysis is an examination of how a characteristic is distributed over a region by examining the row of the matrix for that characteristic. For example, attention may be focused on the way in which the rural population is distributed over an area such as the Great Plains of the United States.

Secondly, a geographer may try to get an understanding of the complexity of a location by identifying its characteristics. In other words, the column for that location may be analyzed. For instance, interest may be in the rainfall, soil type, or most successful crop production at a location in order to make recommendations for other places with similar characteristics. If the location is an urban area, a geographer might try to connect transportation access data, raw material availability, and expert labor supply, in order to explain why a particular industry is successful at that location.

A third way to make comparisons is between rows. This enables an understanding of which characteristics are found together or separately, or to what degree they might mix. For example, looking at common characteristics for two economically successful locations can show why they contribute to the locations' success.

A fourth option for a method of analysis is to make a comparison of columns. This allows the geographer to describe which locations are similar and which are very different. For instance, by analyzing locations where the weather data are the same, a geographer can classify climates that are similar. All of these analyses require the statistical techniques of correlation and regression (defining and characterizing relationships among data).

Optimization Problems Solved by Geographers

Although mathematics has become an essential tool of modern geography, it was also present in the geography of the nineteenth century. In 1826, Von Thünen collected data on land values in agricultural communities; he also collected data on how farmers used land. His data were centered on a town that was the main market for a region.

Von Thünen found that for each particular type of crop the costs of getting the produce to market was a product of the distance from town, r, the volume of the crop produced in a unit area of land, v, and the cost of transportation per unit of distance, c. If the crop sells at a price of p and the fixed costs of producing the crop are a, then the net profit is expressed as R = (p − a )v − rcv.

Von Thünen constructed graphs of profit R plotted against the distance from town, r for various crops. The figure above shows the graphs for three crops. Crop 1 produces the highest profit as long as it is inside a distance of r ₁ of the market. Between a distance of r ₁ and r ₂ crop 2 is the most profitable, and between r ₂ and r ₃ crop 3 is the most profitable. At r ₃ all three crops become unprofitable. Von Thünen suggested that the land around a market be used to reflect these rings, and that there should be no cultivation of these crops beyond r ₃ at all, as there was no profit in farming at this distance (see below).

The modern equivalent of this geographical distribution model is the understanding of why the location of a shopping center or a factory affects each one's success or failure. From the geographical matrix the locations of various resources that are required by a manufacturing plant can be established. Given the locations of different raw materials, labor resources, and transportation of raw materials to the factory, the location for the optimum manufacturing plant can be calculated and compared to an existing plant.

A geographer's data can also be used to support or refute the location of a manufacturing plant at a particular location. However, this is only part of the solution, for once the goods have been manufactured they have to be distributed to market centers, and this has an associated cost that can affect the decision concerning a manufacturing plant's location. By weighting distances with regard to cost, an optimum location can be found by finding the equivalent of the center of gravity of the system.

In the location of a factory, one of the problems that has to be tackled is the distribution of the product to market. Here another branch of mathematics aids the analysis. Graphs and trees deal with the analysis of networks, and can be employed in finding solutions to this part of the problem. One of the classic problems of networks, the travelling salesman problem, is concerned with the most efficient route for a travelling salesman to take in order to cover all the customers. This is also the route that the supply trucks will be interested in following. The full understanding of this problem is still the object of mathematical research.

Calculus in Geography

A major problem of geography is the modeling of population change. Change in populations implies that geographers are interested in data that are time dependent. Therefore any data collection has to be repeated at various intervals, the most familiar way being the United States census that is required every 10 years by law.

The census gives data over long periods of time, but annual sampling is necessary in order to monitor more detailed changes. The data can then be matched to a mathematical model. The most common model for population growth results in the construction of a differential equation in which the change in population, with respect to time, varies directly with time and can be solved through calculus.

Calculus also helps model the way in which the profile of a hill develops. Another application of calculus gives a mathematical model of the freezing of water in a lake. If air above a lake maintains temperatures below the freezing point of water for a prolonged period of time, the thickness of the ice will continue to increase. The rate of advance of the ice depends on the rate at which heat can be carried away from the surface by convection currents in the water below the ice surface. The model leads to a differential equation .

Fractals and River Watersheds

The way in which rivers begin their life as a collection of small springs or gullies that collect rain and spill into brooks or streams has been better understood in recent times by the analysis offered by mathematics through fractals . In river systems, fractal scaling can be seen in the organization of the river network at various levels of observation; that is, they conform to the fractals first described by Benoit B. Mandelbrot. Research around 1990 described the scaling properties of the geometry of several river systems and a calculation was made of their fractal dimension.

Probability and the Layout of Villages

Probability leads to an understanding of the way villages develop over a long period of time, given that there has been no deliberate planning. The model requires the description of two objects, a closed cell with an entrance, and an open cell (see figure below).

These cells are joined together to form a doublet so that the entrance always faces onto an open cell—corresponding to a house opening out onto the public space. In the modeling process, the doublets are allowed to accumulate with the condition that each new doublet that joins the village does so with its open cell having at least one edge common with another open cell. Which open cell a new doublet joins is chosen at random. This modeling process has been successful in describing a number of old villages in which town planning did not influence the layout.

see also Cartographer; Fractals; Global Positioning System; Mandelbrot, Benoit B.; Maps and Mapmaking; Probability, Theoretical.

Phillip Nissen

Bibliography

Haining, Robert. Spatial Data Analysis in the Social and Environmental Sciences. Cambridge, U.K.: Cambridge University Press, 1993.

Hillier, B., and J. Hanson. The Social Logic of Space. Cambridge, U.K.: Cambridge University Press, 1984

Rodriguez-Iturbe, Ignacio, and Andrea Rinaldo. Fractal River Basins: Chance and Self-Organization. Cambridge, U.K.: Cambridge University Press, 1997.

Wilson, A.G., and M. J. Kirby. Mathematics for Geographers and Planners. Oxford, U.K.: Clarendon Press, 1975.

geography the science of place, i.e., the study of the surface of the earth, the location and distribution of its physical and cultural features, the areal patterns or places that they form, and the interrelation of these features as they affect humans.

Methods and Branches

Geography is a synoptic science that uses the same elements as the other sciences but in a different context. It integrates data spatially, making elaborate use of maps as its special tool. Geography may be studied by way of several interrelated approaches, i.e., systematically, regionally, descriptively, and analytically. The systematic approach organizes geographical knowledge into individual categories that are studied on a worldwide basis; the regional approach integrates the results of the systematic method and studies the interrelationships of the different categories while focusing on a particular area of the earth; the descriptive approach depicts where geographical features and populations are located; the analytical approach seeks to find out why those features are located where they are.

In the study of geography two main branches may be distinguished, physical geography and human (or cultural) geography, originally anthropogeography. The first, based on the physical sciences, studies the world's surface, the distribution, delineation, and nature of its land and water areas. Climate , landforms (see geomorphology ), and soil are examined as to origin and are classified as to distribution. Drawing on the biological sciences, fauna and flora (biogeography) are brought into an areal pattern. Through the mathematical sciences the motion of the earth and its relationship to the sun (seasons), the moon (tides), and the planets are studied, as well as mapmaking and navigation.

Human geography places humans in their physical setting; it studies their relationship with that environment as well as their conscious activities and continuous progress in adapting themselves to it (and to other humans) and in transforming their environment to their needs. Human geography may in turn be subdivided into a number of fields, such as economic geography, political geography (with its 20th-century offshoot, geopolitics ), social geography (including urban geography, another 20th-century ramification), environmental perception and management, geographical cartography, geographic information systems, and military geography. Historical geography (which reconstructs geographies of the past and attempts to trace the evolution of physical and cultural features) and urban and regional planning are sometimes considered branches of geography.

History of Geographic Study

Evolution

Geography was first systematically studied by the ancient Greeks, who also developed a philosophy of geography; Thales of Miletus, Herodotus , Eratosthenes , Aristotle , Strabo , and Ptolemy made major contributions to geography. The Roman contribution to geography was in the exploration and mapping of previously unknown lands. Greek geographic learning was maintained and enhanced by the Arabs during the Middle Ages. Arab geographers, among whom Idrisi , Ibn Battutah, and Ibn Khaldun are prominent, traveled extensively for the purpose of increasing their knowledge of the world. The journeys of Marco Polo in the latter part of the Middle Ages began the revival of geographic interest outside the Muslim world.

With the Renaissance in Europe came the desire to explore unknown parts of the world that led to the voyages of exploration and to the great discoveries. However, it was mercantile interest rather than a genuine search for knowledge that spurred these endeavors. The 16th and 17th cent. reintroduced sound theoretical geography in the form of textbooks (the Geographia generalis of Bernhardus Varenius ) and maps (Gerardus Mercator 's world map). In the 18th cent. geography began to achieve recognition as a discipline and was taught for the first time at the university level.

Modern Geography

The modern period of geography began toward the end of the 18th cent. with the works of Alexander von Humboldt and Karl Ritter . Thenceforth two principal methods of approach to geography can be distinguished: the systematic, following Humboldt, and the regional, following Ritter. Of the national schools of geography that developed, the German and the French schools were the most influential. The German school, which dealt mainly with physical geography, developed a scientific and analytical style of writing. The French school became known for its descriptive regional monographs presented in a lucid and flowing manner; human and historical geography were its forte. Although emphasis has shifted several times between the approaches and viewpoints, their interdependence is recognized by all geographers.

Since the end of World War II, geography, like other disciplines, has experienced the explosion of knowledge brought on by the new tools of modern technology for the acquisition and manipulation of data; these include aerial photography, remote sensors (including infrared and satellite photography), and the computer (for quantitative analysis and mapping). The quantitative method of geographical research has gained much ground since the 1950s, Edward Ullman and William Garrison of the United States and Peter Haggett of Great Britain being leading exponents.

Important contributions to the advancement of geography and to the development of geographic concepts have been made by Ferdinand von Richthofen , Albrecht Penck , Friedrich Ratzel , Alfred Hettner , Karl Haushofer , and Walter Christaller in Germany; Paul Vidal de la Blache , Jean Brunhes, Conrad Malte-Brun , Elisée Reclus , and Emmanuel de Martonne in France; and William Morris Davis , Isaiah Bowman , Ellen Churchill Semple , Carl O. Sauer , Albert Brigham , and Richard Hartshorne in the United States. Today geography is studied by governmental agencies and in many of the world's universities. Research is stimulated by such noted geographic institutions as the Royal Geographical Society (1830, Great Britain), the American Geographical Society (1852, United States), and the Société de Geographie (1821, France).

Bibliography

See N. Ahmad, Muslim Contribution to Geography (rev. and enl. ed. 1965); J. O. Thomson, History of Ancient Geography (1965); J. O. Broeck, Compass of Geography (1966); G. H. Kimble, Geography in the Middle Ages (1938, repr. 1968); E. Fischer et al., A Question of Place (2d ed. 1969); R. Murphy, The Scope of Geography (1969); R. Hartshorne, Perspectives on the Nature of Geography (1987); J. H. Bird, The Changing Worlds of Geography (1989).

geography Science studying the physical nature of the Earth and people's relationship to it. It includes land masses and features, seas, resources, climate and population.