EXPERT WITNESS: Allegorical economics--Storytelling with mathematical allegories (part two)


By John F. Sase, Ph.D.
Gerard J. Senick, general editor
Julie Gale Sase, copyeditor

"Wise men talk because they have something to say, fools because they have to say something. Be kind, for everyone you meet is fighting a hard battle."
-Plato, ancient Greek philosopher

Last month, we began to explore Allegorical Economics by delving into the source of all economic understanding-ourselves as human storytellers. Economists and Attorneys tell stories in both the classroom and the courtroom. Attorneys need to condense client backgrounds and their respective cases in order to evoke understanding and empathy from jurors. This month, we address the issue of using numbers in the stories that we tell in the courtroom and the classroom.

Having taught more than 10,000 students of Economics and Business, I (Dr. Sase) have learned to keep math-laden examples as simple as possible without losing the meaning and intent of the underlying economic story. I accomplish this by using "easy" numbers. For example, instead of using a number such as $357.84, I have found that the rounded value of $360 appears more comprehensible for students, especially when the story contains numbers and calculations throughout the tale. I find that limiting the math (whenever appropriate) to elementary addition, subtraction, multiplication, and division tends to provide both understanding and a universal appeal. However, the simplicity in the calculations, as well as the numbers themselves, are not enough. The interrelation of the values provides the necessary ingredient for following the mathematical progression in a story.

Plato understood this concept of simplicity and clarity well. He developed allegories by using the mathematics that his predecessor Pythagoras brought to Greece. As a young man, Pythagoras traveled from his home on the Aegean island of Samos to Giza, Egypt, where he devoted two decades of his life to being an initiate at the Temple School at Giza. Following the Babylonian invasion of Egypt and the burning of the school, Pythagoras, fellow initiates, and teachers were captured and taken to Babylon. During their years of captivity, they assimilated knowledge from Babylonia as well as from more ancient civilizations. Finally, Pythagoras returned home to the Isle of Samos at the age of 56. He devoted the remainder of his life to teaching in the Mediterranean region and to apply his knowledge of mathematics to the fields of Art, Music, and the Sciences. One still can observe the influence of his mathematical methods throughout these fields, where we find a basis in the sums, products, and dividends of the powers of "2" and "3." Before we begin our tutorial example, we will consider the methods of Pythagoras in greater detail.

Within the century after the death of Pythagoras, the mathematical relationships that he introduced found their way into the allegories composed by Plato, especially those concerning the cities of Atlantis, Athens, and Magnesia. These stories continue to resonate with economists, musicians, and others in modern times.

Contrary to popular belief, the elaborate descriptions of the structure of and behavior in Atlantis were created by Plato as an allegorical tale rather than a factual one. He appears to use the Atlantean story in order to present a cosmology based upon the interrelationship of numbers. Plato's other allegories about the ancient Greek cities of Athens and Magnesia support this current view. The real cities of his time bore little resemblance to those in his stories, which use the locales and basic details of these cities as a springboard into mathematically-based morality tales.

Four centuries later, John the Theologian constructed a similar allegory while living on the Aegean Isle of Patmos, which is twenty-one miles from Pythagoras's birthplace of Samos. This writing of John has emerged as the text known throughout Christianity as the Book of Revelations. In his writing that has with colorful apocalyptic images embedded, the text contains many of the same numerical constructs and relationships used by Plato, based upon the work of Pythagoras.

The ancient tools of Pythagoras have been brought forward in western civilization through other writings of the past two millennia. In our following tutorial, we explore the application of these tools to develop a tale about the growth of financial assets through interest rates and inflation rates. Here, Economics interfaces with Law.

Our simple example contains four essential elements: the locations, the players, the storyline, and the number palette. Some aspects of our story come from "old wisdom" that I learned from my grandfather along the shore of Tawas Bay as well as from other interesting childhood experiences. Other aspects emerge from various writers whom I respect and who have influenced me. As we begin our tutorial, let us identify these essentials in further detail.

The Locations

For our tale, we borrow two locations from Zothique, a series of short stories by the American writer Clark Ashton published in Weird Tales magazine in the 1930s. In 1970, Ballantine Books published these stories in a paperback edition edited by Lin Carter. This work collects all sixteen tales of the Zothique cycle as well as a related poem by the author. Smith sets his stories on Zothique, the last continent on Earth, in a far-distant future. His locations include this continent along with the mysterious Isle of Na'at that exists in the sea beyond. These locales provide the necessary basis for the circular-story progression known as "The Hero's Journey." (We discussed this concept, which was made popular by American mythologist Joseph Campbell, in last month's column.) In this month's column, we use Smith's locales to describe a journey that takes a fishing boat and a crew of 24 on a challenging odyssey from the known land of Zothique to the unknown Isle of Na'at and back home again. I have used this article as an homage to Smith to create my tale. Some of the details herein also are taken from my song "Zothique" that I wrote between undergrad and grad school.

The Players

The crew from Zothique is an egalitarian group with subgroups identified by the special tasks that they perform. For example, a traditional fishing boat that can hold a crew of 24 along with their prospective catch may include twelve interchangeable rowers as well as two crewpersons on the steering board at the stern. Also, some of the crew members ply their navigational skills at various moments of the voyage. For example, one guides the boat outward to the best fishing "grounds." Later, the one-at-the-head (the head being the large timber that extends upward at the bow from the stem that rises from the keel) stands and guides the vessel, crew, and catch safely back to shore.

In the land of Zothique, we encounter a group of six wise women who pass along a "special gift" of 360 Magifish to the crew through a chosen steward. These powerful, magical fish appear as the "McGuffin." Film director Alfred Hitchcock used this term to describe something of value that everyone wants to get. The Magifish McGuffin forms the basis for our economic calculations.

On the Isle of Na'at, the crew encounters groups of Na'atians attired in long dark robes. Some of the Na'atians share vast learning and knowledge; however, others have a darker side. They are necromancers who raise the corpses of sailors who have drowned after crashing upon the rocks. Restored to a semi-life, these zombies must do the bidding of the necromancers.

The Storyline

Our economic storyline focuses on the Magifish that propagate at a rate of 7% annually. As these fish age, their value diminishes at a rate of 4% per annum. Our story spans 60 years in this exercise of nominal and real interest rates compounded "simply" each year. When the crew returns home from their odyssey, the steward will divide the cache of Magifish that had been left behind in the care of the aquarist, a professional caretaker of fish. The steward will make this distribution of Magifish through a pre-determined formula.

The Number Palette

The core set of Pythagorean numbers used in many allegories of the past 2,500 years include the values of "2" taken to the zero through the ninth power and "3" taken to the zero through sixth powers. The ratios of the powers of "2" to the power of "3," along with their sums, differences, and products, form the basic building blocks for these economic stories. With a heightened intuition, the resulting values allow the audience to follow the progression of simple interrelated numbers.

In the following example, we use these values:

"4" ("2" squared);

"6" ("2" times "3");

"7" ("2" squared plus "3");

"12" ("2" squared times "3");

"15 (the sum of "2" plus "3," times "3");

"24" ("2" cubed times "3");

"25" (the sum of "2" plus "3" times itself);

"36" ("2" squared times "3" squared);

"45" (the sum of "2" plus "3," times "3" squared);

"60" ("2" times "3" times "2" times the sum of

"2" and "3");

"108" ("3" times "36");

"72" ("2" cubed times "3" squared);

and "144" ("24" times "2" squared).

Also, "10" ("2 times the sum of "2" and "3") to the first, second, and third powers are used as multipliers to take values to the hundreds and thousands.

A Fisher's Tale: Similarities to Any Fish, Living or Dead, Is Purely Coincidental

In this section, let us use the six wise women from Zothique as examples. These women own a 25% interest in a fishing boat, secured by 360 Magifish. Before leaving for an unknown place, these wise women transfer their school of Magifish to the crew of the boat with explicit instructions on how to care for them. The wise women place these valued fish in the care of the one-at-the-head, whom they have chosen to serve as the steward.

Magifish breed once per annum. However, most of these fish live longer than a human lifetime. On average, the fish propagate at a rate of 7% per year. The one-at-the-head contemplates the task at hand and asks, "If I spend my day babysitting a school of Magifish, what does that make me at the end of the day?" In response to this concern, the wise women find an aquarist and entrust the feeding and breeding of the fish to him or her. This decision frees the one-at-the-head and the rest of the crew to set out on their long odyssey.

The crew sets the sails of its crimson craft in order to brave the dark waters that surround the mystical Isle of Na'at. The crewpersons feel the necessity to embark on this mission covertly and quickly because many in the land of Zothique misunderstood the crew due to their involvement in the matter of the Magifish. Some members of the crew were berated and even beaten for their thoughts about the matter, which they held as good. As the crew heads outward to sea, they find themselves engulfed by an inexplicable storm, which is swirling with weird energy and strange lights. The terror of this storm puts them at risk of running aground on what they believe is the mythical Na'at, a belief that comes from their spotting of the legendary natives dressed in long dark robes. The navigators of the fishing boat manage to bring the crew to safety on shore. However, other vessels have smashed upon the rocks. The dead bodies of their crews have washed ashore, and the necromancers turned into zombies.

Upon the Isle, our crewpersons remain alive outside of the bounds of space and time through the darkness of the long night. Upon this island retreat, they "inherit" good powers from the dawn of life through the source of all creation. The crewpersons develop higher levels of awareness and wisdom than they could have achieved in Zothique through delving further into the caverns of their subconscious. The crew proceeds to gather the intellectual and emotional means that will allow them to avoid the confusion that they expect to find among the various collective schemes in Zothique when, or if, they return home.

Space and time re-emerge as the morning breaks. The Na'atians signal the crew that the hour has come for them to return to the land of Zothique, laden with the knowledge that they begot on their journey outside of time and space. The power that envelops them speaks softly as their new life-purpose resounds within. As boat and crew return from Na'at, the navigators bring the vessel past the shoals and rocky cliffs that separate the sea from the earth along the sky/sea/earth horizon. The one-at-the-head focuses on the sky/earth horizon along the shore to guide the boat to solid ground. The crew members reenter Zothique but hear not a sound. Some people of Zothique gathered on shore gaze at the crewpersons in silence. Though the members of the crew feel the same as they did when they departed the day before, they soon discover that sixty years of "real" time have passed in their homeland.

This long passage of time and the knowledge that the Magifish breed once per year throughout their long life-expectancy suggests to the crew that a significant increase in the population of the Magifish could have occurred. The navigator serving as the steward of the Magifish recounts an earlier discussion about setting aside a portion of the expected gain in order to maintain the 25% share of the boat, both in the present and in the future. Their distribution plan requires the setting aside of shares from the total gain in order to ensure the replacement of the boat if necessary. The steward reminds the crew that the Magifish are known to propagate at an average rate of 7% per annum. This behavior suggests that, over the sixty years elapsed since the transfer of stewardship from the six wise women, the 360 Magifish will have increased to a total of 21,600 (360 times 60).

The six wise women transferred the fish with the goals of preserving the 25% ownership of the fishing boat and providing for significant repair of the boat if the hull was to rupture from striking the rocks, as it had done once before. The traditional method for handling such occurrences had been through self-funding with accumulated gains. Simple economic math will help us to determine the number of Magifish needed to maintain the original investment and to make at least one major repair.

As the Magifish age, their value diminishes. As a result of the devaluation, significantly more Magifish will be needed now to replace the 25% holding and to ensure against another cataclysmic event. This matter of depreciation reflects the economic principle of inflation, which averages about 4% per annum in Zothique (a factor of 10 for 60 years when compounded once per year). After 60 years, the number of Magifish needed will have increased from 360 to 7,200 (360 times 2 times 10, for which 2 represents the replacement of the 25% as well as for catastrophe insurance). This change means that the real gain is only 14,400 (21,600 minus 7,200).

Therefore, we have 14,400 Magifish left to divide among the 24 members of the crew. Given the original 360, the share per crew member would have been 15 at the time of their departure to Na'at. However, the individual shares of the crew have increased to 600 (14,400 divided by 24) over a period of sixty years. The adjustment for inflation leaves a real gain of 450 (600 less 15 times 10) per crew member. (Please do not confuse this with the procedure of year-by-year discounting to present value. This exercise is a comparison of end values for which the annual gain gets rolled into the principle in each of the 60 years. One may think of the example of the price of a candy bar that increases ten-fold while the cash in one's wallet increases by sixty-fold.) From this point of distribution, the 24 fishers will handle the tithing, taxes, and any further distribution on an individual basis. For the present time, the one-at-the-head continues to act in the capacity as the steward of the Magifish. This steward explains to the other 23 crew members that they are free to leave and to take their shares with then if they so desire. Alternately, they are invited to sign on for a subsequent adventure similar to the first. The steward concludes by saying, "What we need to do next is to retrieve the original signed documents from sixty years ago and retain some appropriate attorneys to assist us."

No Fish Were Harmed in the Writing of This Story

I have used my background and knowledge to create a tutorial allegory that explains how to incorporate mathematical figures and functions in an accessible manner. Attorneys also can use this format to address the mathematics in their respective areas of expertise. We hope that the math progression in our example has had sufficient simplicity and clarity for our audience to follow. The plot and scenery constitute the elements that one may interchange as appropriate for a specific case or lecture presentation. If you want to learn more about the Pythagorean math that we have used, let us refer you to a playlist that I (Dr. Sase) have put together on my YouTube workshop channel supported by my practice of Forensic Economics. Go to and enter the following search term: Pythagoras Math Music and Light (432 v 440 Hz).

We wish all of our reading audience a healthy and happy holiday season and a successful and profitable New Year.


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 (

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 (

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 copyedits (

Published: Wed, Dec 20, 2017


  1. No comments
Sign in to post a comment »