The following material is copyrighted 2009. All rights reserved.
Lately, I’ve been reading The Motion Paradox by Joseph Mazur. The author starts off with the discoveries of the ancient Greek mathematicians, and how they believed numbers and their manipulation can unlock the secrets of our world, and in many ways those of the human experience. The relationship between music and mathematics is a good example. The ancient Greeks were always interested in form, and what had captured my imagination, while writing Novelsmithing, is how story by its very nature has form. When Mazur started discussing the pentagon as a geometric figure and how, for the Greeks, it had a mystical, perhaps even a divine, significance, it peaked my interest. One particular sentence stopped me cold: “They saw numbers in their plays, built on structured themes of crimes and curses.” (Page 17.) I’m still investigating the ancient references behind this statement, but it set me to thinking about story structure and its possible relationship to the pentagon.
I’ve never been totally satisfied with the storyline diagram on page 24 of Novelsmithing.

The vertical axis does not represent intensity of conflict, which is how some people have interpreted it. I’ve always had difficulty describing what it does represent. Yet, the five points along the diagram, from locking the conflict to resolving it, are specific, important and fit together to form a unity of story. They’ve always appeared to form a closed system, a cycle of sorts, both starting and ending the central conflict. Using the pentagon to represent the plotline seemingly solves all these problems, and all I have to do to create the storyline in this form is to shrink the baseline to the same length as the other sides of the diagram, like so:

I had been drawing a pentagon all along and didn’t realize it.
The pentagon has been around a long time. It was adopted by the ancient Greek society who called themselves “the Pythagoreans” (5th Century BC) as the symbol of their brotherhood. Proclus called the five-pointed star, formed by connecting the points, the “cosmic figure.” (See The Motion Paradox, page 16.) To some, the pentagon represented the five elements: fire, water, air, earth, and the divine. Christians later adopted it as the symbol of Christ’s stigmata. Today many cults have adopted the symbol to various uses. Of course, the most famous example of a pentagon is the US Department of Defense building called “The Pentagon” because of its floor plan. This building and what goes on inside is the essence of story because its mission is the close study, strategic planning, and fighting of war–human conflict at its most extreme.
So the geometrical figure has a history, and it seems to me that the basic structure of storytelling conforms to the pentagon’s shape. In the figure below, I illustrate how the pentagon might represent a novel’s plot structure. Story progression starts somewhere along the baseline and proceeds clockwise around the pentagon.

The setup, prelude to point 1, is along the baseline. The denouement, after Story Milestone 5 (Conflict Resolution), is also along the baseline. These two join and thus complete the pentagon and conclude the story. The pentagon in this form is then the Premise incarnate. The Premise is defined and explained in detail on pages 14-22 of Novelsmithing.
Note that the mid-novel reversal occurs at the point farthest away from the baseline (and conflict resolution), and that first we go away from resolution, and then, at the reversal, we turn toward the baseline (and conflict resolution). What goes up, must come down, so to speak. Thus, we complete the full cycle. The novel is specifically not a circle, because in a circle all points have equal value. With a pentagon, they do not.
Premise is the essence of conflict. How might the pentagon represent the multitude of Premises inherent in all stories? By extending the lines of the pentagon, we create another larger pentagon outside the initial one, and by connecting all the points, a smaller one is created inside. This construction can be continued, leading to an infinite number of both larger and smaller pentagons. This can be construed to represent the many levels of Premise possible in any story: cosmic Premise (good vs evil), initial concept Premise (liberty overcomes bondage), character Premise (Harry Potter overcomes Voldemort), etc.
The following figure is a representation of the pentagon from The Motion Paradox, Figure 2. It also has my chicken scratching to extend the lines outward to create a larger pentagon. Note that I have hashed the baseline and indicated the principal story milestones. (Yes, I know that I started on the side rather than on the bottom. My bad, but I did this during my period of insomnia in the middle of the night.)

A further problem is the titles “Plot Point 1” and “Plot Point 2.” These designations have been around a long time, and in particular used by Syd Field in his classic book Screenplay, as well as a host of others. Even the three-act drama has contributed to the problem. Or maybe it isn’t a problem for them, but for my approach to storytelling, the mid-story reversal is of equal importance, and I consider all five points plot points. To avoid this confusion, I am going to coin the term “story milestones” to designate the five points around the story pentagon. From here on, I will refer to them as SM1, SM2, etc. This change will be reflected in a future revised edition of Novelsmithing.
As a point of curiosity, note that the ever-shrinking pentagons, as they are created inside each other, reverse directions. First, they point up, then down, then up again, etc. Some cults have used the upward pointing pentagon to represent benevolence (good) and the downward pointing pentagon to represent malevolence (evil). This might be construed to indicate the nature of the struggle (conflict) between good and evil. This reversal from one to the other could indicate that the many levels of Premise can have opposite outcomes within a novel. Or perhaps you can think of a more profound interpretation.
Of course, I’ve used the original “flat” diagram for character arc also, and it may well be that a revision of it is also in order. And, the chapter diagram on page 114 could present a particular problem. I’m looking into the matter.
All very interesting stuff.
You might consider contacting me if this new thinking gives you great joy, or possibly a hernia. dshep@novelsmithing.com.
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