In Integrating the Enneagram into Mind/Will/Soul I realized that many of the systems that try to break a continuum up into discrete samples may be trying a little too hard. And I pointed out a shape in nature that allows for balanced growth across an infinite number of points, based on the Golden Angle:

When building an ensemble of characters, I have noticed that other writers and audiences expect a spread of personalities. And we recognize these archetypes from our real life. A partnership of two people is generally a pair of opposites. When they add a third, the find (somehow) yet another opposite. But as we add characters to the trio, characters seem to form shifting camps of temperament. The contrasts are sometimes fuzzy, fickle, and subject to be obliterated by current events, experience of the character, etc.

I had a vision as I was writing Integrating the Enneagram into Mind/Will/Soul that populating a cast of characters in an ensemble is exactly like Distributing space stations around a planet. Or a plant wanting to grow leaves around a stem in a pattern that minimizes overlap.

Ancient scholars and modern scholar seem to agree about a basic palette of temperaments. It is in trying to organize them that we run into trouble. I recognized in my blog on the color of emotion that feelings are more of a continuum than a pure list of discrete points. If temperament is based on a core emotion, it too would be pretty messy.

I am reminded of my days of playing tuba. Brass instruments work by resonating a fundamental frequency produced by the lips of the player. When learning to play a brass instrument you just kind of learn that you wiggle your lips in just the right way to make any kind of sound at all. The Tuba will only really resonate when you produce the right frequency. What the valves do is shorten or lengthen the resonating tube. And for each of those different lengths, you learn a slightly different lip pattern.

The takeaway is that our brain may be like a musical instrument. When it's producing a muddled tone, it's hard to hear against the noise of life. But when something resonates with you, you can't mistake it. Each of the temperaments are like an instrument tuned to a different range of sound.

In this blog, we are going to use the Golden Angle to build a cast of characters. And for every character we are going to tag the Hue of their personality.

We can use the Circumplex Model of Emotion to approximate color with emotion.

I am going to be trying to match up the distributions of personality between the Enneagram 9 archetype system, the Myers-Brigs 16 point system, as well as Red Oni/Blue Oni, the Power Trio, the Four Temperament Ensemble, the Five Man Band, and the Magnificent Seven Samurai from TvTropes.

My methodology will be to break the continuum of emotion into 3, then 5, then 9, and finally 16 chunks, using the Golden Angle. So what I will do is first allocate the slots, and then we'll slot each archetype into one of those slots. To Generate Red/Blue for our first core characters we are going to start with Red (0/360) and move counter-clockwise. We'll also include X and Y coordinates to place each slot on a wheel that is 500 units in radius.

The math looks like this:

set GA 2.39996322972865332
set PI [expr {4*atan(1.0)}]
set OFFSET 0
set SLOTLIGHT {}
for {set x 0} {$x < 16} {incr x} {
  set SLOT [expr {$x + 1}]
  set huerad [expr {fmod($offset -$x * $GA,2*$PI)}]
  set theta [expr {int(round($huerad*180.0/$PI)) % 360}]

  dict set SLOTLIGHT $SLOT slot $SLOT
  dict set SLOTLIGHT $SLOT theta $theta
  dict set SLOTLIGHT $SLOT huerad $huerad
}

2 Slots

Slot	Theta	Color	X	Y
1	0		500.0	0.0
2	222		-368.6	-337.7

3 Slots

Slot	Theta	Color	X	Y
1	0		500.0	0.0
2	222		-368.6	-337.7
3	85		43.712	498.08

4 Slots

Slot	Theta	Color	X	Y
1	0		500.0	0.0
2	222		-368.6	-337.7
3	85		43.712	498.08
4	307		304.21	-396.8

5 Slots

Slot	Theta	Color	X	Y
1	0		500.0	0.0
2	222		-368.6	-337.7
3	85		43.712	498.08
4	307		304.21	-396.8
5	170		-492.3	87.090

7 Slots

Slot	Theta	Color	X	Y
1	0		500.0	0.0
2	222		-368.6	-337.7
3	85		43.712	498.08
4	307		304.21	-396.8
5	170		-492.3	87.090
6	32		421.87	268.36
7	255		-129.8	-482.8

9 Slots

Slot	Theta	Color	X	Y
1	0		500.0	0.0
2	222		-368.6	-337.7
3	85		43.712	498.08
4	307		304.21	-396.8
5	170		-492.3	87.090
6	32		421.87	268.36
7	255		-129.8	-482.8
8	117		-230.4	443.72
9	340		469.66	-171.5

12 Slots

Slot	Theta	Color	X	Y
1	0		500.0	0.0
2	222		-368.6	-337.7
3	85		43.712	498.08
4	307		304.21	-396.8
5	170		-492.3	87.090
6	32		421.87	268.36
7	255		-129.8	-482.8
8	117		-230.4	443.72
9	340		469.66	-171.5
10	202		-462.1	-190.7
11	65		211.92	452.86
12	287		149.64	-477.0

16 Slots

Slot	Theta	Color	X	Y
1	0		500.0	0.0
2	222		-368.6	-337.7
3	85		43.712	498.08
4	307		304.21	-396.8
5	170		-492.3	87.090
6	32		421.87	268.36
7	255		-129.8	-482.8
8	117		-230.4	443.72
9	340		469.66	-171.5
10	202		-462.1	-190.7
11	65		211.92	452.86
12	287		149.64	-477.0
13	150		-432.6	250.70
14	12		488.33	107.35
15	235		-287.5	-409.0
16	97		-64.25	495.85

As you can see, our pattern is endless. We can populate all of the information about a slot, because unlike with a polygon or star generated by N points, our points will not change. A 5 person ensemble can have the same core three characters as a power trio, which could start with a Red Oni/Blue Oni pair. We also do not have to limit ourselves to a central character of hue 0 (red). Let's build an ensemble around the primary colors of a mirror universe, where we start at 180:

set GA 2.39996322972865332
set PI [expr {4*atan(1.0)}]
set OFFSET $PI]
set SLOTDARK {}
for {set x 0} {$x < 16} {incr x} {
  set SLOT [expr {$x + 1}]
  set huerad [expr {fmod($offset -$x * $GA,2*$PI)}]
  set theta [expr {int(round($huerad*180.0/$PI)) % 360}]

  dict set SLOTDARK $SLOT slot $SLOT
  dict set SLOTDARK $SLOT theta $theta
  dict set SLOTDARK $SLOT huerad $huerad
}

2 Slots

Slot	Theta	Color	X	Y
1	180		-500.0	6.1232
2	42		368.68	337.74

3 Slots

Slot	Theta	Color	X	Y
1	180		-500.0	6.1232
2	42		368.68	337.74
3	265		-43.71	-498.0

4 Slots

Slot	Theta	Color	X	Y
1	180		-500.0	6.1232
2	42		368.68	337.74
3	265		-43.71	-498.0
4	127		-304.2	396.80

5 Slots

Slot	Theta	Color	X	Y
1	180		-500.0	6.1232
2	42		368.68	337.74
3	265		-43.71	-498.0
4	127		-304.2	396.80
5	350		492.35	-87.09

7 Slots

Slot	Theta	Color	X	Y
1	180		-500.0	6.1232
2	42		368.68	337.74
3	265		-43.71	-498.0
4	127		-304.2	396.80
5	350		492.35	-87.09
6	212		-421.8	-268.3
7	75		129.80	482.85

9 Slots

Slot	Theta	Color	X	Y
1	180		-500.0	6.1232
2	42		368.68	337.74
3	265		-43.71	-498.0
4	127		-304.2	396.80
5	350		492.35	-87.09
6	212		-421.8	-268.3
7	75		129.80	482.85
8	297		230.45	-443.7
9	160		-469.6	171.51

12 Slots

Slot	Theta	Color	X	Y
1	180		-500.0	6.1232
2	42		368.68	337.74
3	265		-43.71	-498.0
4	127		-304.2	396.80
5	350		492.35	-87.09
6	212		-421.8	-268.3
7	75		129.80	482.85
8	297		230.45	-443.7
9	160		-469.6	171.51
10	22		462.17	190.77
11	245		-211.9	-452.8
12	107		-149.6	477.08

16 Slots

Slot	Theta	Color	X	Y
1	180		-500.0	6.1232
2	42		368.68	337.74
3	265		-43.71	-498.0
4	127		-304.2	396.80
5	350		492.35	-87.09
6	212		-421.8	-268.3
7	75		129.80	482.85
8	297		230.45	-443.7
9	160		-469.6	171.51
10	22		462.17	190.77
11	245		-211.9	-452.8
12	107		-149.6	477.08
13	330		432.60	-250.7
14	192		-488.3	-107.3
15	55		287.56	409.03
16	277		64.255	-495.8

Role vs. Temperament

One problem that I didn't think of when I started this exercise was that I was mixing up temperaments with roles in the story. The algorithm I developed is fantastic (in my humble opinion) for figuring out the balance of temperaments for an Ensemble. But as we can see, the algorithm can't tell you what those temperaments are. Red Oni/Blue Oni simply says that the two main character need some contrast. The Five Man band formula doesn't tell you if the Leader is an ENTJ or an IF

As we can see from our distributions of light and dark, we have a few characters that are nearby in hue to characters in their own distribution. We also have characters who are nearby in hue to characters in the OTHER distribution:

While it is true that every personality is unique like a snowflake, we really aren't trying to create a giant tangle of metrics. What we need are Little boxes. Perhaps made of ticky tacky. Humans have limited attention span. 9 doesn't seem to be enough. 16 would seem to be enough, but there is a problem.

A 9 wheel color wheel gives us the primary colors of light, but the primary colors of dark are muddled together. A 16 color color wheel doesn't deliver either all of the primary colors of light, nor the primary colors of dark. We get blue and cyan, everything else is an impure color.

However, a color wheel divisible by 12 gives us all of the primary colors of light, all of the primary colors of dark, and a "cusp" shade in between of each:

A lot of personality systems get wrapped up around whether a mind is inwardly motivated or outwardly motivated, and by what. So for argument's sake, let is say the inward motivation follows the triad described by Carl Jung, of the The Ego, the Personal Unconscious, and the Collective Unconscious. Outwardly motivated personalities conform to the Guna? as described in the Bhagavad Gita: Sattva, Rajas, and Tamas.

Each of these extremes will be placed around the color wheel. And, oddly enough, the placement of the various personalities has an uncanny resemblance to the Circumplex Model of Affect:

I also realized that based on Jung's work, a lot of pop Psychologists use 12 archetypes for personality. On a whim, I decided to just steal those. The nice thing is the descriptions are just concrete enough to present and argument, but just vague enough to sidestep the awkward questions.

Instead of the Myers' Briggs idea of orthogonal dichotomies, my system uses the idea of a continuum that when sampled in 12 chunks seems to produce a pleasing pattern. Like crayons in a box. And like crayons in the box, people have 1000 different names for a particular hue. But if you just show it to them, they'll recognize it.

Because, as an author and occasional dungeon master, I'm not trying to recreate the actual human mind. I'm trying to recreate how actual human minds try to fool other actual human minds into thinking they are normal.

Now I will posit that everyone can be any one of the personality types. It's just that as people form habits, they gravitate to one or more depending on the mood they are in. Infants are ambidextrous because they don't do things with their hands. Grown ups usually have not only a dominant hand, they have a "good" knee and a "Bad" back. We tend to favor what we are good at, and what we are good at is what we generally have experience in. And sometimes, when we over-use what we are good at, we have to develop another skill to replace what was destroyed by repetitive use.

Like with Enneagrams, a person with a dominant personality in on "archetype" can switch to another to fit the situation, in response to trauma, or after a few pints at the bar. It's only people that have become old and inflexible that are stuck in one personality, even if that personality isn't appropriate for the situation they are in.

Unlike Enneagrams, or the MBTI, or horoscopes, there are no solid walls between the bins. The archetype is just the most exaggerated color in the range, to make it easier to recognize and discuss.

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