Geometry as Language of Authority
There is an anecdotal story about the philosopher Aristippus, which has come down to us through the Roman architect Vitruvius. The philosopher was once stranded on an unknown island after a shipwreck. One day, after seeing a few geometric figures drawn in the sand, he announced to his fellow castaways, “Let’s be of good cheer, for I see traces of human beings.” Geometric shapes like rectangles, cubes, or straight lines are rare in nature. The circle and the sphere are the only geometric shapes one encounters outside human societies. The full moon approximates a circle, and so does the horizon if one stands in the middle of a desert. Spheres are more common, seen in the shapes of many fruits.
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The circular shape has been elevated to sacred status in many traditional cultures. The anthropologist Clifford Geertz informs us that for the Oglala (a branch of the Sioux Native Americans), the circle is sacred because the Great Spirit caused most things in nature to be round. Stones, not being round, were seen as implements of destruction. The sun, sky, Earth, and moon are round like a shield that protects. Everything that breathes, such as the stem of a plant, is round. For this reason, the Oglala made their tepees circular and their camp a circle.[i] Despite such beliefs, the widespread use of the circular shape in traditional societies suggests practical reasons behind it.
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Houses found at the sites of the earliest Neolithic sites were circular. Such houses are still found in many parts of Africa. In the early Neolithic period, even the villages had a circular plan. Families lived in houses built around a central compound where cooking and processing of crops were done. A 19th-century engraving of a Zulu village known as Khoikhoi shows houses arranged in a row around a large central compound. Some remote societies have retained that layout. The Yanomamo horticulturists of Amazonia live in a unique type of circular village. They do not build separate family huts; the entire community lives under a single roof, resembling a covered stadium with an open central compound. A settlement once inhabited by the Monongahela, a native North American community, has been discovered by archaeologists at Fort Hill, Pennsylvania. The relics show that the village initially had one circular row of houses. When the population increased, it added a second circular row of houses.[ii]
According to Kent Flannery, the circular shape was the manifestation of egalitarianism.[iii] His opinion is echoed in a posting by the department of tourism of New Caledonia in the South Pacific. The posting explains that circular space is conducive to discussions and exchanging ideas, thus, suitable for maintaining community spirit. They may have a point. A circle does not have any unique or salient point, which gives all points on the circle the same significance. People in traditional societies sit in a circle to meet and discuss their problems. At the United Nations Security Council, members sit around a round table. By contrast, seats at a corporate board meeting are arranged around a rectangular table, with the chairperson sitting at one end. The arrangement clearly identifies the boss. A village with houses around a central compound is like a round table meeting where every family feels equal.
Non-circular geometric shapes are inventions of sedentary societies. Farming was initially a collective enterprise; the community owned the land, and families shared the harvest. But as agriculture became more labor-intensive and productive, communal cultivation gave way to family-based farms. Ancient people must have discovered that the best way to divide communal land was to create rectangular plots. That may be how the rectangular shape was first recognized.
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The circular ground plan was abandoned when communal living gave way to nuclear families. Rectangular architecture replaced round houses. Kent Flannery suggests that a rectangular floorplan became the choice for nuclear families because adding new rooms for children and other purposes was easy.[iv] The rectangular shape offers the best “packing performance,” architect Phillip Steadman observes.[v] Anyone who regularly stores food in a freezer knows that rectangular boxes use the freezer space more efficiently than round boxes. Even in an open space, a rectangular shape offers some advantages over a circular shape. As Steadman explains, “It is always possible to divide any rectangle into two or more rectangles, and to divide each of these into two further rectangles, and so on.” With a rectangular floor plan, a builder can divide a house into multiple rooms or, when necessary, can add a new room to an existing home. That is not possible with a roundhouse.
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A house built on a rectangular floorplan has the shape of a cuboid or a box, the most common three-dimensional shape encountered daily—in books and buses to houses and coffins. We are so familiar with this shape that we conceptualize the external world and even abstract ideas through the box metaphor. Thus, we speak of four (not three or eight) cardinal directions, think of going to all four corners of the world, examine an issue from all angles, and consider life’s problems from all sides.
The rise of nuclear families marked the transition to a higher stage of agriculture. Productivity increased, and some families began accumulating wealth. Economic progress, however, ended the old societal order, characterized by collective decision-making and egalitarianism. The ground plans of the Neolithic villages of this period changed too. Nuclear family houses began to be raised on rectangular foundations and were no longer built around a central compound. The haphazard layouts of Tsimane villages show how a farming society without any form of social leadership may still live as a community. But unlike in the Amazonia, many Neolithic villages were swelled by the arrival of migrants, forcing new forms of organizing societies. Population growth and economic diversification called for political leadership. Prehistoric Beidha is an early example of such a village, and its central public space represented the presence of political leadership. A central space and a network of streets emerged as two important elements of a town’s geometry.
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As the political leadership strengthened, the central space attained more prominence. In chiefdom societies, this space was reserved for the rulers. In pre-Colombian Taino chiefdoms of Haiti, the chief’s house was at the center, with commoner residences built around it. In Alto Magdalena, Colombia, the burial ground for rulers was located at the center. In places where the political leadership took a collective form, town planning followed the Beidha model, with public facilities, such as markets, temples, and offices for municipal services located at the central plaza. In some sense, the town plaza represented the reincarnation of the central compound of prehistoric circular villages. Apart from the center, the rest of the town remained haphazardly built. The narrow and winding streets in residential areas were apparently an afterthought, built on the land donated by neighbors to give access to those surrounded by others.
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Most cities continued to grow in this manner for thousands of years. The medieval cities of Europe, such as Sienna and Bruges, are the finest living examples of that age. They are major tourist attractions today. Their large and impressive town squares are lined with important buildings like churches, merchant guilds, city halls, and rulers’ palaces. The colonial expansion and international trade, beginning in the fifteenth century, brought prosperity to the continent but also brought new problems. Cities were ill-prepared to cope with population growth and its social and political consequences. At the dawn of the modern era, those cities were not as clean as they are today. The philosopher-mathematician Rene Descartes wrote in disgust, “These ancient cities that were once mere straggling villages and have become in the course of time great cities are commonly quite poorly laid out compared to those well-ordered towns that an engineer lays out on a vacant plane.” He continued, “Upon seeing how the buildings are arranged—here a large one, there a small one—and how they make the streets crooked and uneven, one will say that it is chance more than the will of some men using their reason that has arranged them thus.”[vi]
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James Scott likened a city’s plan to a language. Bruges’ street plan is like a dialect that only locals understand. Tenochtitlan’s town plan was, by contrast, like a formal language everyone understood. Orthogonality was an important element of their common vocabulary. That vocabulary was known to many civilizations. From Aristotle, we learn about the ancient Greek polymath Hippodamus of Miletus, who lived in the 5th century BCE and was involved in planning two port cities, Piraeus and Miletus. These were small democratic societies that were not facing any enemies or trying to show off power. Yet, Hippodamus planned streets like a rectangular grid. He aimed to create cities that were “democratic, dignified, and graceful”.
Cities in the modern world follow the orthogonal planning approach for different reasons. Elton McGoun of Bucknell University explains that an orthogonal ground plan makes financial and administrative sense.[ix] Planning and building a new city becomes more straightforward when the layout is based on linear geometry. Setting prices is easier for property developers when houses are mass-produced on selfsame streets. And buyers feel more confident when they can find the going rates by checking the price of the last home sold. For governments, the valuation of urban property and setting tax is easiest when each property in a neighborhood has the same details as the rest. Uniformity allows developers to build at a lower cost. The influential urban geographer Lewis Mumford lamented that “with a T-square and a triangle, finally the municipal engineer could, without the slightest training either as an architect or a sociologist, ‘plan’ a metropolis, with its standard lots, its standard blocks, and its standard streets.” [x]
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The orthogonal plan has another advantage. As James Scott observed, such a plan is the simplest way to codify locational information. The Roman army knew this two thousand years ago. The Romans built their garrison towns according to the same blueprint based on an orthogonal ground plan. Every building had a predetermined position. Even in the middle of the night, a messenger from Rome would know where to find the commanding officer’s residence in the town. The human brain operates on the principle of cognitive least effort, which is why a subway map is a linearized version of the geographical map. It is easier for riders to understand and remember. An orthogonal street plan, likewise, is convenient not only for the military and tax collectors but also for firefighters, mail carriers, and utility operators. When an institution of authority envisages an urban development project, orthogonality is the default choice.
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End Notes:
[i] Clifford Geertz; The Interpretation of Cultures; Basic Books, New York, 1973
[ii] John L. Creese, “Village Layout and Social Experience: A Comparative Study from the Northeast Woodlands”; Midcontinental Journal of Archaeology, Vol. 39 No. 1, Winter, 2014, 1–29
[iii] K. V. Flannery; “The Origins of the Village as a Settlement Type in Mesoamerica and the Near East: A Comparative Study”; In Man, Settlement and Urbanism, edited by P.J. Ucko, R Tringham and G.w. Dimbleby; Duckworth, London; 1972
[iv] K. V. Flannery; “The Origins of the Village as a Settlement Type in Mesoamerica and the Near East: A Comparative Study”; Man, Settlement and Urbanism, edited by P.J. Ucko, R Tringham and G.w. Dimbleby; Duckworth, London; 1972
[v] Phillip Steadman, “Why are most Buildings Rectangular?”, Architectural Research Quarterly, Vol. 10, pp. 119-130; 2006
[vi] James Scott; Seeing Like a State, Yale University Press, 1998
[vii] Kurl W. Butzer; “Other Perspectives on Urbanism – Beyond the Disciplinary Boundaries”; in The Ancient City – edited by Joyce Marcus and Jeremy Sabloff; School for Advanced Research, Santa Fe; 2008
[viii] Ibid.
[ix] Elton G. McGoun; Accounting on the Landscape;
[x] Lewis Mumford; The City in History; quoted in James Scott, Seeing Like a State, Yale University Press, 1998