Jeff writes:

My little finger keeps telling me that sine, cosine, tangent, and cotangent has something to do with the conceptualization of the story mind at some level—possibly explaining the crossovers between Spacial and Temporal, or quad relationships.

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Jeff, here’s a clue:

You’ll see those functions showing up throughout the structure. But you forgot Secant and Cosecant.

So, you’ve got Sine and Cosine, Tangent and Co-tangent, and Secant and Co-secant.

Now, look to the three kinds of pairs, Dynamic, Companion, and Dependent. Note that each has a positive and negative aspect. You’ll find a direct correlation.

Also note that there is the fourth kind of relationship in each quad – the “Associative” in which all four items are either seen as individual Components or as a single Collective.

This last relationship is a bit different than the other three insofar as it deals with all four items at once, rather than two. It also differs in that it is NOT necessary that one be positive and the other negative. Both could be positive or both could be negative or you could have one of each (creating a quad of “charge” options).

This last relationship is what happens if you plot a function in Trig along the Y axis instead of the X axis. In that case, you violate the definition of a function, so it is not allowed in Trig. Some of the results can create imaginary numbers.

In Dramatica, because Time must be seen as a component rather than a line against which to plot a sine or cosine, we needed to allow functions to move into one more dimension. This wasn’t because of our concept, but because that fourth dimension, the Associative relationship actually exists in the real world and REQUIRED that dimension to explain it.

Unfortunately, since Trig couldn’t allow it, we needed to define a fourth set of functions. They really should be called the Independent and Co-dependent (to match the semantic naming pattern of Sine and Co-Sine) but since we already use the word Dependent in Dependent pairs – where it is more descriptive – we ended up calling the functions Component and Collective.

One last clue – note that the quad looks not unlike the quadrants in trig. In fact, you’ll find that the Dramatica quads correspond to them as a framework, but move counter-clockwise instead of clockwise.

So, on the one hand, each quad handles the four items in three dimensions (as does Trig) cycling through them over time to create the standard functions. In three dimensions this creates a circle (plotted on the quad) or the plot of the standard functions (such as sine and cosine) as the story unfolds over time, linearly. But, if you move onto the RELATIONSHIPS of the items in each quad, it adds that extra dimension and that extra function.

In other words, the quad and the relationships allow both a three dimensional and four dimensional projecting of reality to exist in the same time/space.

You can get a feel for this by looking at how Trig plot out a sine wave. In a quadrant, it seems to run around the quadrants creating a circle. But, plotted over time along an access, you get the never-ending sine wave.

But, if you add the extra dimension, you see a helix, like a Slinky toy, which from the end looks like a circle but when stretched out and seen from the side looks like a sine wave.

The circle is the particle, the side view is the wave. Dramatica adds one more dimension to see the helix so that it can describe the relationship between the particle of story and the wave of story – the meaning of the story as it relates to the order in which the elements are explored- what the story is about as it relates to how the story unfolds.

Well, that’s enough of a clue. Now, an “assignment” for all your math junkies:

Of Sine, Tangent, and Secant, which function is associated with which relationship – Dynamic, Companion, and Dependent?