Economics for everyone (episode sixteen)—Lessons from a more distant past, part one
By John F. Sase, Ph.D.
Gerard J. Senick, senior editor
Julie G. Sase, copyeditor
William A. Gross, researcher
“This City is what it is because our citizens are what they are.”
—Plato, 5th Century BCE Athenian-Greek polymath and author
“The Prefect telegraphed: Proclaim a state of plague / stop / close the town.”
—Albert Camus, 20th Century Algerian-French Philosopher, Author, and Journalist in his book “The Plague” (Fr. La Peste, Paris: Gallimard, 1947)
Over the past year or so, we plunged into the polymathic whirlpool of ideas and reflections that link together in this series, which now includes sixteen episodes. Our pursuit reflects the goal of developing a human world of sufficient affluence for all within a sustainable economy. Radiating ideas within a circle of thought unite as a whole to reflect this goal. Along our journey, we find ourselves in a spot at which we need to define the central whorl (a convex hull) of what we can call our Imagineering Project of Social Development, that is, the concept of the Monocentric City, which has a central seat of government surrounded by expanding residential and commercial subcenters. If we ignore national boundaries for a moment, Detroit-Windsor provides us with an excellent example of the circular, monocentric urban area that has expanded outward radially from the strait (i.e. Detroit River) where the urban center of government and the financial centers are located. Along the radial paths, we find business and retail subcenter locations that have survived within city borders and newer subcenters that continue to develop beyond the city limits.
Through these next two episodes, we will explore the roots of this process by unveiling a central thematic element that forms the Spindle of Necessity at the center of the city as a microcosm of the universe (thank you, Plato) around which our developing whorl of ideas rotates. In order to present this concept, let us return to some research that I (Dr. Sase) began 33 years ago while sitting on the basement floor of the Purdy Graduate Library at Wayne State University. As I sat, I consumed the thoughts of ancient polymaths such as Plato, Pythagoras, and other luminaries who faced the same problems of human survival that we are experiencing today.
The modern practices of Law and Economics create and depend on civil societies. The success of these professions depends upon a stable but flexible established sense of human living space. Some of us were fortunate enough to experience the classic languages of Latin and Greek in secondary school. Following this thought, it behooves Attorneys and Economists to know about the historical and cultural significance of the Platonic concepts of cities, law, and government in dealing with concerns and cases that include urban planning and zoning, real estate law, racial/ethnic redlining, political gerrymandering, and other challenges.
The culmination of monocentricity in early Greek thought
Let us travel back in time. It appears that early Greek cosmologies inspired the monocentric urban allegories of Plato. In his book “The Greek Cosmologists” (Cambridge: Cambridge University Press, 1987), English philosopher David J. Furley presents the Greek cosmologies of Anaximander and Parmenides that provide us with intellectual models for understanding the social and economic relations of ancient Greek culture. With the mathematics communicated by Pythagoras through the ancient Pythagorean Society, Plato applies these models conjunctively to create mathematical alle-gories of perfect and less-perfect city-states. As suggested previously, it appears that Pythagoras introduced the analytical tools used by Plato in ancient Greece because these models form the pertinent aspects of Pythagorean teachings.
Essentially, Plato models his principles into mathematical allegories. In his book “Plato’s Mathematical Imagination” (New York: American Book Stratford Press, Inc., 1954), American philosopher Robert S. Brumbaugh discusses that much of the work that the early Greek philosophers and scientists thought of as mathematics is not “mathematics” in our current way of thinking. However, their fundamental concepts of algebra, proportions, and geometry form the basis of contemporary mathematics. For example, English historian of Greek mathematics D. H. Fowler explains that the ratio theories of the Academy of Plato translate into modern exponential functions and often represent special cases of general formulae (The Mathematics of Plato’s Academy, Oxford: Clarendon Press, 1987). This body of ancient mathematics suffices for the construction of the allegorical city-states of Plato.
Plato constructs four allegorical city-states: ancient Athens, an ideal one; modern Athens (Calliopolis), also perfect but only inhabited by an essential population; Atlantis, a luxurious city-state of destructive excesses; and Magnesia, the practicable city-state.
In his book “The Pythagorean Plato” (York Beach: Nicolas Hays, 1984), American musician/mathematician Ernest G. McClain suggests that Plato constructs his allegorical city-states from abstract material developed in his earlier mathematical allegories. “The Myth of Er,” a parable, contains his cosmological model embodied in the Spindle of Necessity, a parable that ex-pounds on the mathematical concepts essential for understanding the four city state models of Plato. In “The Republic” (translated by F.M. Cornford, New York: Oxford University Press, 1957), Plato describes the Spindle of Necessity as having a center column that appears as a straight shaft of light that stretches from above and that shines throughout Heaven and Earth. The Spindle of Necessity represents the dynamics of the universe. Furthermore, Plato describes a set of eight bowl shaped whorls (convex hulls). These whorls spin about the vertical shaft of light that extends infinitely upward and downward through the bottom center of all the bowls. The mathematical allegory of the Spindle of Necessity resembles the cosmological image that Mircea Eliade associ-ates with village-construction rituals of primitive and traditional societies.
The Spindle of Necessity embodies a curvilinear mathematical function, fundamental to city-state allegories of Plato, which approximates the negative-exponential function (a line that extends downward but never reaches the horizontal axis) used by American Economist Edwin Mills and other modern-age thinkers. The bridge between the Spindle and the negative exponential functions forms the diatonic musical scale, such that musical pitches, expressed as cycles per second, graph as a convex curvilinear function. McClain further details the correlations between the musical scale and the nested whorls in the Spindle of Necessity that determine the shape of the coils, the width of the rims, the patterns of the colors, the speeds, and other relevant aspects. This body of harmonic mathematics forms the essential tools that Plato uses to construct his allegories.
The Monocentric concept is essential to the urban allegories of Plato. He establishes the Monocentric concept in other allegories through the ideas of circularity and axis. 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 (“Timaeus and Critias,” translated by H.D.P. Lee., Baltimore: Penguin Books, 1971). Through the voice of Timaeus, Plato identifies the circularity and axes of his allegorical 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 classics scholar James Adam interprets these passages as the “State,” growing like a circle drawn with a compass. As a result, this circular State forms the basic ground-plan for all of the city-state models created by Plato. As a circle drawn with a compass and pivoting at the center, all of these models are monocentric.
In effect, Plato creates four variations of a monocentric city-state. Each has a seat of power at its center: ancient and new Athens have a temple of Zeus; Atlantis has the palace of Poseidon; and Magnesia has its capital city, the seat of its government.
(Continued) ....
