(Continued) ....
Economics for everyone (episode seventeen)
Brain calisthenics from the distant past
The approach of using a 360-degree circle presented limitations, since many of the microtones fell in between degrees. Historical records suggest that Plato obtained his advanced education at Alexandria, Egypt, which remained a hub for scholars throughout the Mediterranean area, the Near East, and the Far East. Having an acquaintance with scale systems of 17, 22, 24, and 72 intervals, I consider the probability that Plato and Pythagoras may have developed a knowledge of sound that extended beyond the Grecian world. In addition to these theories, a matter of convenience suggests doubling the number of intervals to 720 to gain a more satisfactory degree of accuracy for the mathematics needed.
Following a lengthy cursory review of the 121 notes/frequencies/vibrations in the Atlantis allegory, I found that the middlemost seventh (VII) level is unique and very symmetrical.
However, in exploring the other twelve levels, I encountered several anomalies. Expanding my inquiry above and below the seventh level, I discovered a wide variation in the number of points that Plato placed on each of the other levels. I found that a definite symmetry appears between pairs of the remaining twelve levels. For example, level XIII at the top matches level I at the bottom. This pattern remains consistent through classes VIII and VI that exist immediately above and below level seven (VII).
As Above, So Below
This phase of analysis provides a great mental exercise in and of itself. For those looking for more fun, connecting the dots reveals even more "secrets" that Plato produced.
The patterns on his Atlantian levels form six pairs of mirror images. Inversely flipping levels VIII through XIII to the left creates patterns that mirror those on levels I through VI. The designs that the math of Plato produce on levels above the unique seventh level reflect in the corresponding levels below. As above, so below. At this point, I began to wonder whether Plato intended to produce a "simple" allegory about a city of excess or modeled something entirely different and more esoteric.
Exercise Five-The 500 Pound Bench Press
Given the details outlined above by Plato, we move to a three-dimensional interpretation of the Platonic model. As rendered by Ernest McClain, the primary platform includes three concentric circles of land with water in between, a navigable channel that cuts through these three rings, and a central island on which Plato locates a temple. In this depiction of Atlantis, I replaced microtonal musical pitches rendered by McClain with an exacting pattern based on 720 radii (doubling 360 degrees on a compass). As mentioned earlier, 121 position points conform to the description by Plato.
On this sketch (for which you may download a higher-resolution version in color), each of the four landmasses contains a different number of points clustered in groups on the left-hand side. They form near-mirror images of the patterns on the right. The middle island holds 11, while the smallest ring contains 24, the middle ring 36, and the outer ring 50. However, Plato broke and distributed these point-groups across the 13 levels. The most significant number of points (15) appears on the third level from the bottom and the third one from the top.
This simplified view of the thirteen levels of Atlantis reminds me less of a city and more of a fantastic direct-energy technology created by Nikola Tesla.
Some Afterthoughts
The preceding model of thirteen flat tiers allows us to create 3-D practical models using old CDs, DVDs, or plastic storage-container lids. However, if we follow the progression developed by McClain using a continuous progression of sound (music) frequencies, we might consider modeling Atlantis as an elongated spiral. For purely mathematical work, this approach allows us to explore the sound and light ranges of frequencies with greater precision using Hertz and Terahertz that are separated by a range of forty doublings (octaves).
Nevertheless, we can choose to use a log-linear transformation of the elongated spiral. This transformation allows us to simplify our mathematical calculations in a spreadsheet and on a 3-D graph. We can perform various calculations and do other activities, such as studying the 7,200 intervals that exist between the values of 1 and 2 across the thirteen levels of the Allegorical City of Atlantis developed by Plato. Also, this shape resembling the Archimedes Screw facilitates calculations by using a profile that closely parallels the stack of thirteen plains with which we began our discussion.
Takeaway
We hope that our readers who quarantine, cocoon, or work from home as we survive the Pandemic of 2020 remember not to watch too much cable news or binge on reruns of Friends, The Sopranos, Game of Thrones (or whatever else floats your boat). As the New Normal becomes Normal, we hope that all of us remember to keep our minds and well as our bodies in shape through activities that also feed our souls. To that end, we hope that the brain calisthenics of Pythagoras and Plato described above will help our readers to do just that. As a soundtrack to the exercises, we suggest such songs as “Those Were the Days” by Cream (Wheels of Fire, Atlantic, 1968) and Atlantis by Donovan (Barabajagal, Epic, 1969). Enjoy!
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Dr. John F. Sase teaches Economics at Wayne State University and has practiced Forensic and Investigative Economics for twenty years. He earned a combined M.A. in Economics and an MBA at the University of Detroit, followed by a Ph.D. in Economics from Wayne State University. He is a graduate of the University of Detroit Jesuit High School (www.saseassociates.com).
Gerard J. Senick is a freelance writer, editor, and musician. He earned his degree in English at the University of Detroit and was a supervisory editor at Gale Research Company (now Cengage) for over twenty years. Currently, he edits books for publication (www.senick-editing.com).
Julie G. Sase is a copyeditor, parent coach, and empath. She earned her degree in English at Marygrove College and her graduate certificate in Parent Coaching from Seattle Pacific University. Ms. Sase coaches clients, writes articles, and edits copy (royaloakparentcoaching.com).
