Warning: This blog post is describing an idea that lead to a logical dead end. I'm including it because creativity is as much about trying and failing as trying and succeeding. If you just want to cut to the insight, the failure if this idea inspired a more fruitful idea: Network Model of Personality

I am working on building a mathematical (or at the very least, software implementable) model based on my post, Mapping Attributes to NPC Personalities. And as I go I'm not terribly happy with the way I sort out Introvert and Extrovert. That model also seems to make a mess out of the boundary between self and society. So I am tempted to add a fourth attribute that abstracts out the confused elements out of the other three. Instead of Mind/Soul/Will the system would be Chaos, Order, Mystery, and Self. Whereas before we were looking at the intersection of three circles on a plane, now we have the intersection of 4 spheres:

Of course, what I always fail to take into consideration is that adding another dimension doesn't make things slightly more complicated. Or proportionally more complicated. Or even exponentially more complicated. I now have a giant ball of mess. Now instead of one nice diagram like:

I now have 4 separate diagrams! Each face on the pyramid is the interaction between three of the spheres. At no time can I represent the interaction of all of the spheres in two dimensions.

I'm going to put my mathematician hat on for a moment, and take a shot at trying to represent the problem in three dimensions. But I promise there will be lots of pretty pictures to follow along with.

Let us accept as a givent that there are possibilities that I can outright throw away. Instead of just accepting any old random number for each attribute, we are now modeling a shape. Our factors are now how strong a force is pulling each corner of the shape toward one of the spheres. If they are all pulling with the same force, or no force at all, we end up with a tetrahedron that is a unit length on each side.

When one or more forces dominate over the other forces, it distorts the perfect shape. Let us say we have an individual inclined to chaos at the expense of all else:

Three of the sides (Chaos/Mystery/Order, Chaos/Mystery/Self, Chaos/Order/Self) increase in area, and one of the sides (Mystery/Order/Self) decreases in area.

If two sphere dominate, say Order and Self:

Two sides get longer, and two sides get shorter. Mystery/Order/Self and Chaos/Order/Self get larger. Chaos/Order/Mystery and Chaos/Mystery/Self get smaller.

What if three Spheres dominate over the remaining sphere?

One side gets bigger, and the other three get smaller.

We could build a system with metric tied to the area of each face, and ascribe an attribute for if that face area is abnormally large or abnormally small. We can also tie a metric to the length of each of the edges of our tetrahedron. That gives us 4 areas and 6 edge lengths, for a total of 10 attributes.

But before I get to that, why do I need the extra dimension? Or maybe a better starting point would be, what do the new dimensions mean?

Chaos The need to change. To alter the world. Energy.
Order The need to create. To maintain structure. Matter.
Self The realization of individuality.
Mystery The connection to the all things.

The reason I had to break things up was that Will was doing too many things. It represented both selfish ego AND sociability. Mind was also a bit of a mess. Was it describing concrete analytical thoughts? Imagination? Both? Spirit was ending up as the dumping ground for what I couldn't fit somewhere else. Yes, I could map personalities from the MTBI into the new system, but when I sat down and tried to describe to the computer what was going on, I was running across too many ambiguities.

One thing to consider is that many of the properties on the MWS scale were actually combinations of other ideas. It's like trying to discuss chemistry without an understanding of the elements. You think you have a system, then boom one chemical reaction completely messes with every theory you've ever made.

I still view D&D as the gold standard for RPG attribute systems. I'm also fond of the SPECIAL system from Fallout. So where possible, lets make these metrics connect up to concepts from those systems. I also want a few things to naturally pop out of the system:

I spent a good deal of time on this idea, and I thought it had promise, but after days of toil, struggle, and banging my head on the keyboard, I can't say it's doing anything useful, let alone making an improvement over Mapping Attributes to NPC Personalities.

Not all is lost though. The realization that there is a "volume" and an "edge" brought me to thinking about the problem in terms of a network diagram. And that concept I will speak about in depth in a follup post: Network Model of Personality