Economics for everyone (episode seventeen)
Lessons from the more distant past, part two
By John F. Sase, Ph.D.
Gerard J. Senick, senior editor
Julie G. Sase, copyeditor
William A. Gross, researcher
"Divide and rule."
-Niccolò di Bernardo de Machiavelli, Italian Diplomat, Philosopher and Writer, in "The Art of War-Book VI, 1521" (trans. Peter Whitehorne, 1560; London: David Nutt, 1905)
"A house divided against itself cannot stand. I believe this government cannot endure permanently half slave and half free. I do not expect the Union to be dissolved - I do not expect the house to fall - but I do expect it will cease to be divided. It will become all one thing or all the other. Either the opponents of slavery will arrest the further spread of it and place it where the public mind shall rest in the belief that it is in the course of ultimate extinction or its advocates will push it forward till it shall become lawful in all the States, old as well as new - North as well as South."
-Abraham Lincoln, Illinois Republican Party Senatorial Nomination, 1858
A house, a village, a city-state, or a larger unit cannot survive if divided. Many Republicans embraced this belief at the time of Lincoln's address quoted above and threw their support behind him. Though he lost the Senatorial race to Stephen A. Douglas, Lincoln did become President of the United States in 1860, two years after his speech.
During that era and beyond, an education in the works of Aristotle, Socrates, Plato, and other luminaries of 2,500 years ago stood as the norm of higher education. This fount of knowledge guided America in the development of our government institutions, our laws, and the growth of cities of all sizes.
A question for our readers: Do students who hope to become successful attorneys continue to ponder the classics of Ancient Greece and Rome or has this pursuit fallen by the wayside? When many of us were in our college-prep phase, the practice studying the classics constituted a norm. Some of us continue to find value in this course of study.
In this episode, we explore a comprehensive sketch of urban design and how cities may function, from ancient times through the modern era by concentrating on Monocentric Urban Models. Nations, states, and metropolitan areas have moved to embrace divisiveness, a fact exacerbated especially by recent events. Therefore, we hope that the following episode will serve as a reminder of what a unified city-state can be.
Over the past year, we have swum the polymath whirlpool of ideas that converge in the world of sufficient affluence within a sustainable economy. Radial ideas within a circle of many views come together to form a unified whole that reflects this goal. Along our journey, we find ourselves in a spot at which need to define the central whorl (a convex hull) of our Imagineering Project of social development.
In this second episode, we explore the roots of this process as we unveil a central thematic element that forms the universal Spindle of Necessity around which our ideas rotate. In presenting this topic, we return to research that I (Dr. Sase) undertook 33 years ago. While sitting on the basement floor of the Purdy Graduate Library at Wayne State University, I consumed the thoughts of ancient polymaths such as Plato and Pythagoras as well as other luminaries who encountered the same challenges to human survival that we experience today. In the current episode of our series, we hope to enlighten our readers by providing some of the insights of these ancient sages, insights that are still relevant and that may provide a framework for our current experience.
The Emergence of Early Western Thought
Let us travel back to the earlier Greek cosmologies of Anaximander, Parmenides, and others that inspired the Monocentric-Urban Allegories of Plato. In his book "The Greek Cosmologists, Volume I" (Cambridge: Cambridge University Press, 1987), the English scholar David Furley presents the cosmologies of Anaximander and Parmenides that provide us with intellectual models for understanding the social and economic relations of ancient Greek culture. Applying the mathematics communicated by Pythagoras through the ancient Pythagorean Society, Plato uses the Pythagorean models conjunctively to create mathematical allegories of perfect and less-perfect city-states. Pythagoras introduced many analytical tools that form pertinent aspects of the teachings used by Plato in ancient Greece. In his book "The Exact Sciences in Antiquity" (Princeton: Princeton University Press, 1952), Austrian Mathematician and Astronomer Otto Neugebauer explains that we can trace these mathematical tools back to the Sumer and Babylonian Empires.
In essence, Plato models earlier principles into his mathematical allegories. In his book "Plato's Mathematical Imagination" (New York: American-Book Stratford Press, Inc., 1954), American philosopher and educator Robert S. Brumbaugh states that much of the work that the early Greek philosophers and scientists thought of as mathematics is not the mathematics prevalent in our modern thinking. Instead, mathematics for the ancient Greeks was derived from influences such as spirituality, philosophy, and applied architecture. However, their fundamental concepts of algebra, proportions, and geometry do form the basis of contemporary mathematics. For example, D. H. Fowler, the English historian of Greek mathematics, explains that the ratio theories of the Academy of Plato translate to modern exponential functions and often represent special cases of general formulae ("The Mathematics of Plato's Academy," Oxford: Clarendon Press, 1987).
Furthermore, this body of ancient mathematics suffices for the construction of the city-state allegories of Plato. In his tales, he describes four city-states: Ancient Athens, an ideal city-state; a modern Athens of his own time known as Calliopolis-a perfect city inhabited only by an essential population; Atlantis, a luxurious one fomenting with destructive excesses; and Magnesia, the practicable one (which appears as a basis of contemporary Urban Economics).
In his book "The Pythagorean Plato: Prelude to the Song Itself" (York Beach: Nicolas Hays, 1984), Ernest G. McClain, professor of the ancient mathematical foundation of music, suggests that Plato constructs his allegorical city-states from abstract material that he developed in his earlier mathematical allegories. In "The Republic" (translated by F.M. Cornford, New York: Oxford University Press, 1957), Plato includes his parable "The Myth of Er," which includes his basic cosmological model, embodied as the Spindle of Necessity. Plato describes the Spindle of Necessity as having a central column that appears as a straight shaft of light that stretches from above through Heaven and Earth. The Spindle represents the dynamics of the universe. Also, Plato describes a set of eight bowl shaped whorls (convex hulls). These whorls spin around a vertical light-shaft that extends to infinity, both upward and downward through the bottom center of all the bowls. Through his symbolic Spindle, Plato expounds on the essential mathematical concepts needed for understanding the four city state models presented in his later writings.
The Spindle of Necessity embodies a curvilinear mathematical function in the city-states of Plato. It also approximates the standard Negative-Exponential function pioneered by American Economists Edwin Mills, William Alonso, and Richard Muth in the 1960s. The bridge between the Spindle and the Negative Exponential functions reflects the diatonic musical scale in which musical pitches, expressed as cycles per second (Hertz), graph as a convex curvilinear function. Meanwhile, McClain, who we mentioned above, details the correlation between musical scales and the nested whorls in the Spindle of Necessity.
The mathematics of harmonics comprises the essential tools with which Plato constructs his urban concept of Monocentricity He further establishes this concept in other allegories through the ideas of circularity and axis. In "Timaeus and Critia," (translated by H.D.P. Lee., Baltimore: Penguin Books, 1971), Plato reveals that the circle constitutes his own primary image, that of the fictional character of Timaeus of Locri, who stars in one of the dialogues by Plato. Timaeus speaks about the nature of the physical world and humanity. Plato reveals that the circle constitutes his primary image in Timaeus and Critias. This revelation follows the concentric circularity of Platonic cities.
In "The Republic," Plato commences his development of an ideal state with a one-dimensional line that evolves into a two-dimensional circle. In his book "The Republic of Plato" (Cambridge: University Press, 1902 and 1969), Scottish scholar James Adam interprets these passages as the city-state growing as a circle drawn with a compass. As a result, a place defined as a circle forms the basic ground-plan for all of the city-state models created by Plato. With the State pivoting at the center of the ring, all of his models are monocentric.
In effect, Plato creates four variations of a monocentric city-state. Each has a seat of power at its center: both old and new Athens contains a temple of Zeus, Atlantis has the palace of Poseidon, and Magnesia has the administrative seat of its government.
Throughout ancient times, land travel remained limited to foot and horse. As a result of transportation modes that are expensive in both material costs and time costs, the preference for residence and occupation tended to be close to the city center in earlier times. We can project that the transition from horse and wagon to motor-truck transport produces the result that the relative costs of hauling goods exceed the costs of moving people within cities. Due to these costs, employment and housing sectors integrate such that citizens live where they work. We can find many older and newer examples of this agglomeration in Metropolitan Detroit and other cities.
Plato describes how the social hierarchy of the city states translates into declining wage- and rent-gradients. In Timaeus and Critias, he offers an example in the allegory of Athens. Plato states that Hephaestos and Athene (the children of Zeus) produced a native race of good men and gave them suitable political arrangements. The craftsmen and the agricultural workers who labored on the neighboring land lived on the immediate slopes of Athens. Further up, the military class lived by itself around the temple of Athena and Hephaestos.
In Athens, Plato sets his society into three class levels. The wealthy ruling class sits literally and figuratively at the top center. Halfway down the mountain, the military holds a mid-ring position. At the base, the agricultural and industrial classes form the outermost circle. These segments of Plato's allegories precurse contemporary studies, which examine the degree of suburbanization of various employment sectors.
Until recent times, the physical gradient of socio-economic classes appears typical for most urban societies. One common reason remains in that well water tends to carry more significant contamination in low lying areas. As a result, the upper classes traditionally have built their housing on high. It is only with the improved pure-water supply and the sewage-disposal technologies of the past century that the enormous health problems that resulted from the increased density of population in cities have been solved. Therefore, higher-income groups have changed their location preferences in part due to improved public health.
Land use in the four city-states of Plato takes two different forms. Athens divides into two semi-circles as a mountain split into residential and occupational faces. In contrast, Plato describes Atlantis having six alternating concentric rings of water and land that surround a central island.
The City of Magnesia brings together both elements. This practicable state consists of two concentric rings around the central city. Beyond this central city, Plato divides the surrounding agricultural land into twelve quasi equal radial segments. In his allegory of Magnesia, Plato constructs a practicable city-state. In his book "Plato's Mathematical Imagination" (noted above), Robert S. Brumbaugh writes that Plato locates his central city in the most efficient way in respect to its territory, for purposes of administration, defense, and trade. This radial plan proves the best for long haul transportation from the perimeter of Magnesia to the central city, planned as the center of symmetry.
In his work "The Laws" (trans. A.E. Taylor, E.P. Dutton, 1960), Plato states that the legislator first must locate the city as precisely as possible in the center of the country. In terms of public choice, citizens will remain economically indifferent to a location around the circular state. Secondly, the legislator must divide the circular country into twelve sections. This symmetry provides for public-choice equilibrium among all segments. Plato continues to describe the physical layout of Magnesia that Brumbaugh presents in his "Map of Magnesia." Twelve highways run to the urban boundary, extending radially from the seat of government services in the central capital city. Protected by border garrisons, this boundary contains secondary employment subcenters, with businesses and services such as taverns to benefit the soldiers. As with military bases throughout history, businesses providing goods and services of many kinds would experience agglomeration economies by locating near the garrisons.
However, the primary employment subcenters exist further inland. In his book "The Pythagorean Plato," Ernest G. McClain describes Magnesia as a double ring. Twelve temple and market districts exist halfway along the radial roads at the bound of the inner circle. These temple/market areas emerged as employment subcenters in the land of Magnesia. In modern times, these kinds of market areas take the form of retail centers. The contemporary expression of the ancient Greek form appears as small towns situated in agricultural regions. In contemporary market towns, society divides the function of the temple between churches and district schools. The market area may appear as a general store; as a livery or gas station; and perhaps as a tavern, a movie house, or a bowling alley. Virtually, this subcenter may provide all of the nonagricultural private-sector employment in the region.
In this century, most of us reside, practice our professions, and do our business in urban areas. A United Nations study conducted in 2018 states that 55% of the world population currently lives in urban areas and expects that proportion to increase to 68% by 2050 (The 2018 Revision of the World Urbanization Prospects, the Population Division of the United Nations Department of Economic and Social Affairs). In order to attain an income level of sufficient affluence in a sustainable economy, we must focus more significant amounts of our attention on understanding the dynamics of cities.
In analyzing the models presented above, it seems that the city-states created by Plato in his allegories provide the most sophisticated and detailed models found in ancient thought. Though Plato did not have the power of modern mathematics at his disposal, he did give us thorough verbal descriptions of the various human relationships in an ideal society. Using the system of harmonic mathematics known to many ancient intellects, Plato produced a series of monocentric urban models that contain both implied and actual rent-gradients. These models embody standard features such as division by concentric rings, division by diagonals, and agglomerative subcenters beyond the urban center. Formations with multiple concentric circles appear in numerous models from the earliest to the most modern. Division of space into numerous radial segments (primarily six and twelve) appears in many models before and after Plato. However, we have seen a lesser use of this modeling technique in recent centuries.
Continued ....
