Here’s another clue for you all….
Though it wasn’t discovered through mathematics, Dramatica’s model of story psychology can, in fact, be described by mathematics – at least to an extent.
Here’s the clue – In the Dramatica quad, there are found kinds of pair relationships among any two items: Dynamic (diagonal), Companion (horizontal), and Dependent (vertical). There are two of each in every quad and one will possess a positive charge and the other a negative charge.
Dynamic relationships (diagonal) are about direct conflict. A negative Dynamic relationship is where both parties beat each other into the ground until nothing is left and all potential is lost. Kinda like the two parties in congress. A positive Dynamic relationship is where both parties conflict, but as a result a new idea is sparked – synthesis – in which a solution or improvement is created that could not have occurred by the actions of either party separately – only through direct conflict.
Dynamic relationships, positive and negative, can be described by Sine and Cosine.
Companion relationships (horizontal) are about indirect impact of one party on the other. In other words, without directly conflicting, the normal actions of one party can have a beneficial (positive) fallout on the other party or a negative one. In a sense, it is like one party unintentionally bumping into the other party just as a result of doing what it does naturally. And that bump sends the other party either into a better or worse trajectory.
Companion relationships, positive and negative, can be described by Tangent and Cotangent.
Dependent relationships (vertical) are about dependencies. You can see this in human behavior with a positive dependency being “I’m okay, you’re okay, together we’re terrific!” – better than the sum of their parts in which each acts as a catalyst to the other. A negative dependency is “I’m nothing without my other half” in which neither party can function at all without the other.
Dependent relationships, positive and negative, can be described by Secant and Cosecant.
But now we come to the interesting part. There is a fourth kind of relationship among items in a quad – whether all four items will be evaluated or seen as being independent components or as a collective family, tribe, or classification. For example, which is correct – “This IS the United States” or “These ARE the United States”?
In the first case, we see a single county (family) which can be sub-divided into smaller units called states. In the second case we see a confederation of independent sovereign states (“state” originally meant sovereign, after all). When the country was formed, it was seen more as a confederation. This sentiment was carried on into the Civil War when the south became the Confederate States of America, siding on the philosophy that power derived from the individual sovereign states, bound by mutual agreement into a confederacy. But the north maintained that is was “one nation” as in the pledge of allegiance, and states were more like national counties.
Back to math, specifically trig – what function represents that? Well, I’m not much of a mathematician, but twenty years ago when we first considered the relationship of trig to the pair relationships by function, it occurred to us that we needed an additional dimension of function to describe that relationship. We jokingly said that somebody someday was going to have to come up with “quadronometry” as an expansion to trig.
But now I’m not so sure that is far off the mark. After all, the quad includes all four dimensions – Mass, Energy, Space and Time. And if we look at it in terms of psychology (the Story Mind) we see the internal equivalents of these – Knowledge, Thought, Ability and Desire. I’ve written elsewhere about the correlations between the external and internal dimensions, so I won’t belabor it here. Point is – trig provides three dimensions and Dramatica’s functions require four.
Here’s an example…
If you plot a sine wave function on the xy coordinate plane it describes a circle as it passes through 90 degrees, 180, 270 and finally 360. That comprises one complete cycle of a sine wave. But, as the function continues to operate (as the sine wave progresses through more cycles) you go past 360 another 90 degrees to 450, then 540, then 630, the 920 and on and on, circumscribing the same circle on the plane over and over again.
In Dramatica, we describe our functions somewhat differently, thus:
Think of a slinky toy – that coiled ribbon of metal that “walks” down stairs. From the end, it looks like a circle, stretched out from the side it looks like a sine wave, but seen from a 3/4 angle you can see its true nature as a helix. In fact, Dramatica is a quad-helix, unlike the double-helix of DNA. It includes a helical description not only of the arrangement of story elements and dynamics in a double-helix, but also a second double-helix that describes how these things will unfold over time. As a side note, we have often wondered that while the double-helix of DNA describes what genes are present and how they are arranged, might there not also be a second conceptual double-helix describing how they will be brought into play in the actual construction of an organism – the physical double-helix providing the blueprint and the conceptual double-helix providing the sequence of construction? But, that’s another story.
For now, consider what adding a fourth dimension to trig would do. For one thing, you’d need to plot a sine wave not just on the xy plane but to include the z axis as well to plot its vertical progression. Further, because one dimension is being added, it would push everything down a rung. For example, it is my belief that in such a mathematical system imaginary numbers such as the square root of -1 would become incorporated in the real number plane, enabling the solving of equations that are not currently supported. And philosophically, from a math perspective, it would tie in nicely therefore as a tool for everything from quantum theory to chaos theory.
But, again, I’m not much of a mathematician – I’m just a poor country theorist with some odd ball ideas and a patented story engine that has been accurately predicting story structure and human behavior for twenty years.
Besides, I’m getting too old to want to do all the work necessary to carry things like this any farther. So, I leave it to the next generation, or at least those better at math than I, to take a crack at this – either to build it or refute it. Don’t matter to me which. I’m satisfied just having the chance to say my piece.