Headline:Emotion is messy, and I have the figures to prove it.
Date:Friday, January 17, 2020
Posted By:Plaid Hatter Games

I am continuing my thoughts from Color and Emotion, and trying to come up with a mathematically expressible vocabulary for emotion. I need this because my action/reaction system for agents will emit emotions experienced by the parties involved, and those emotions will inform the agents of how to react.

This scheme will build on the Hue/Saturation/Lightness color model. Colors have a hue, their frequency, which is actually an angle on a circle that encompasses the entire rainbow. We will have three primary colors: which correspond to our magic system's three seats of conciousness:

The first matter to consider is the actual color of an emotion. We will assume that the hue of an emotion is the sum of the interference of the seats of consciousness that produce that emotion. Intellectual pursuits are blue in tint. Self-centered acts are reddish. Holistic acts are greenish. Complex interactions can yield non-intuitive colors.

The mental clarity of an emotion will be our saturation field. Pure, coherent thought is 100% saturation. Anger, distraction and panic approach 0% saturation.

Finally there is enlightenment. Enlightenment is thought that transcends the self, and conducted on a higher level than consciousness. We can't see those colors, but we can see the loss of color because all of the parts of the brain are firing off at once.

Next we need to lay down the list of emotions we wish to support. It will probably also help if we consider the normal pattern of intellectual development in humans.

newborn cry neutral discontent other
3-4 months smile laugh joy delight other
7-12 months fear disgust anger sadness other
1-2 years verbal shame embarrassment pride other
3-6 years other

Another factor to consider is Temperament. We also have to consider that Mood and Affect are distinct from Feeling.

Moods are generally positive or negative, and last from several minutes to several weeks. They can vary in intensity from neutral to severe. But, fortunately, they are pretty easy to model. A number. A postive number is a positive mood. A negative number is a negative mood. The bigger the number, the more intense the mood.

Feeling is what the individual is detecting as their own mood. That is pretty much the color scale we are working on.

Affect is what people do in response to a feeling and mood. Affect happens in three dimensions: Valence (positive or negative), Arousal (reaction of sympathetic nervous system), and Motivation (impulse to act). However, simply knowing that doesn't tell me to what extent a particular emotion will invoke Valence, Arousal, and Motivation in a particular individual. Based on my minimal research, individual responses in terms of Valence, Arousal and Motivation to the same stimulis varies by individual, and even with the same individual varies with their mood and the novelty of the input. For our purposes, it Affect will be random or as complex as to be nearly random, albeit with distributions affected by agent personality, mood, and feeling.

The best data on actual feelings that I have are actually from computer animation. Artists regularly use a palette of facial expressions to breathe life into their characters. It gets complicated, but there is good data on how to replicate the appearance of Anger, Contempt/Disgust, Fear, Happiness, Sadness/Agony, Surprise. We even know which emotions can be faked (Happiness and Anger) and which are all but involuntary (Saddness/Agony, Surprise).

Numerically, there was a neat paper in 1979 by James A. Russel , where he sampled what category people placed 28 emotions in categories by Valence and Arousal, and then worked out a way to plot those emotions in a circle. Subsequent Research has shown that repeating the experiment with native speakers of different languages yields different results.

The problem with Circumplex models is that they are really noisy. You get a range of plausible answers from people. But for our purposes that is perfectly ok! I have converted the data from Russel's 1979 paper into a form that's a little easier for me to make a few points. The thing to keep in mind is that categories are placed along a wheel like so:

We start with the survey data. Now, the 1979 paper only interviewed 36 people, so it's a great preliminary set. However I haven't found the underlying data for any of the follow-on papers, so I'm just going to have to live with it. What we see is for each of the 28 emotions, how many of the subjects classified them into each of the 8 categories:

Emotion Pleasure Excitement Arousal Distress Misery Depression Sleepiness Contentment
Happy 21 8 2 5
Delighted 15 16 3 2
Excited 2 29 5
Astonished 17 18 1
Aroused 14 21 1
Tense 8 18 9
Alarmed 6 19 11
Angry 5 21 5 3 2
Afraid 2 11 22 1
Annoyed 1 12 14 4 4 1
Distressed 4 25 5 2
Frustrated 2 5 19 4 6
Miserable 3 23 10
Sad 10 6 19
Gloomy 2 11 22 1
Depressed 4 7 24 1
Bored 3 2 14 17
Droopy 1 1 8 26
Tired 1 1 34
Sleepy 1 32 3
Calm 4 3 29
Relaxed 6 4 26
Satisfied 3 1 32
At Ease 7 3 26
Content 6 1 29
Serene 8 2 26
Glad 20 4 12
Pleased 22 2 2 10

From that data we can use that table to map each emotion into an X and Y component based on the number of times each emotion was placed into each category. With answers in different buckets pulling each emotion in a different direction. Like a game of tug-of-war:

Emotion Valence Arousal Theta Noise

The Theta I generate matches up with the original paper. That is the angle the emotion makes when we sum up all of its Valences and Arousal. But for my game I also want to capture the noisiness of the data. I do that with the following two formulas:

Signal is a measure of the largest number of samples that fell into a bucket. An emotion that everyone agrees on the category approaches 1.0. Noise is a measure of how many degrees (plus or minus) can I randomize the angle and still get plausible answers. Tired has virtually no noise (+/- 3.8 degrees). Annoyed is all over the map (+/- 82.5 degrees).

My noise system doesn't perfectly fit the data. But I'm not going for a perfect fit. I need something simple enough that a computer can do it, and a person watching the computer can do it can believe the computer is having an emotion.

Now... this data is great for gauging people's REACTION to emotion, but I still need a color chart for emotions themselves. I'm also completely missing the Motivation dimension. But... we'll just have to get to that. What I do have now, what I didn't have before, is a list of emotions that I can more or less count on having good data for. Step one would be to try to reconcile those emotions from my marketing and aura work in Color and Emotion.

I will start with Anger, because marketing and auras agree anger and aggression are red. We also know that auras and marketing agree that orange is the color of excitement and energy. So we know what direction to take things. So let's just try the following formula to see of the theta for our Valence/Arousal calculations can be turned into a color using Hue/Saturation/Lightness:

Emotion Theta Hue Saturation Color
Happy 7.8 82.20 41.70  
Delighted 24.9 65.10 44.40  
Excited 48.6 41.40 80.60  
Astonished 69.8 20.20 50.00  
Aroused 73.8 16.20 58.30  
Tense 91.3 358.70 50.00  
Alarmed 96.5 353.50 52.80  
Angry 99.4 350.60 58.30  
Afraid 118.6 331.40 61.10  
Annoyed 128.8 321.20 38.90  
Distressed 184.9 265.10 69.40  
Frustrated 142.4 307.60 52.80  
Miserable 188.7 261.30 63.90  
Sad 193.5 256.50 52.80  
Gloomy 208.4 241.60 61.10  
Depressed 209.6 240.40 66.70  
Bored 240.5 209.50 47.20  
Droopy 256.6 193.40 72.20  
Tired 267.2 182.80 94.40  
Sleepy 271.9 178.10 88.90  
Calm 316.2 133.80 80.60  
Relaxed 317.4 132.60 72.20  
Satisfied 320.2 129.80 88.90  
At Ease 319.9 130.10 72.20  
Content 324.0 126.00 80.60  
Serene 328.6 121.40 72.20  
Glad 349.8 100.20 55.60  
Pleased 353.2 96.80 61.10  

In my search for Motivation data, I uncovered some interesting research on word association. As it turns out, there has been a lot of effort to analyze how people feel about certain words as measured by Valence, Arousal and in this case Dominance (which is as near as makes not difference to the Motivation I'm looking for.) My thought was look up the terms on in this database that I'm hoping to measure Motivation on and use those values. Problem is, apparently there are marked differences between the way males and females rate words.

So... keeping things strictly to emotion, let's evaluate our 28 terms based on the data from the spreadsheet attached to that paper:

Emotion Equivilent Valence all Arousal all Dominance all Theta Hue Color all Color+dom all Valence male Arousal male Dominance male Theta Hue Color male Color+dom male Valence female Arousal female Dominance female Theta Hue Color female Color+dom female
Happy happiness 0.70 0.30 0.41 23.32 66.68     0.60 0.35 0.44 30.26 59.74     0.73 0.27 0.38 19.92 70.08    
Delighted delighted 0.55 0.00 0.24 0.00 90.00     0.47 0.05 0.09 6.12 83.88     0.56 -0.03 0.34 -3.06 93.06    
Excited excitement 0.52 0.24 0.27 24.79 65.21     0.58 0.12 0.20 11.73 78.27     0.48 0.31 0.31 32.80 57.20    
Astonished astonished 0.28 0.15 -0.03 27.21 62.79     0.20 0.28 0.12 54.07 35.93     0.31 0.07 -0.10 13.08 76.92    
Aroused aroused 0.19 0.46 0.12 67.56 22.44     0.33 0.33 0.17 45.00 45.00     0.16 0.51 0.05 72.30 17.70    
Tense tense -0.45 0.06 -0.06 171.91 278.09     -0.56 0.00 -0.03 180.00 270.00     -0.41 0.12 -0.09 163.58 286.42    
Alarmed nervous -0.29 0.10 -0.20 160.50 289.50     -0.32 -0.08 -0.27 -166.64 256.64     -0.28 0.27 -0.16 135.42 314.58    
Angry angry -0.49 0.24 -0.18 154.09 295.91     -0.27 0.14 -0.23 152.24 297.76     -0.54 0.34 -0.13 147.71 302.29    
Afraid afraid -0.55 0.02 -0.46 177.50 272.50     -0.67 -0.05 -0.45 -175.71 265.71     -0.53 0.06 -0.46 173.97 276.03    
Annoyed annoyed -0.44 0.06 -0.18 172.49 277.51     -0.60 0.09 0.00 171.84 278.16     -0.41 0.03 -0.27 175.84 274.16    
Distressed distressed -0.32 0.26 -0.17 141.69 308.31     -0.28 0.31 -0.12 132.48 317.52     -0.38 0.23 -0.22 148.55 301.45    
Frustrated frustrated -0.49 0.08 -0.23 170.73 279.27     -0.40 0.09 -0.25 166.78 283.22     -0.51 0.07 -0.21 171.90 278.10    
Miserable miserable -0.48 0.01 -0.23 178.57 271.43     -0.56 0.13 -0.06 166.54 283.46     -0.45 -0.05 -0.37 -173.72 263.72    
Sad sad -0.58 -0.30 -0.23 -152.49 242.49     -0.60 -0.28 -0.30 -154.83 244.83     -0.58 -0.31 -0.19 -151.40 241.40    
Gloomy gloomy -0.37 -0.34 -0.37 -137.76 227.76     -0.20 -0.22 -0.44 -132.80 222.80     -0.43 -0.48 -0.36 -131.59 221.59    
Depressed depressed -0.55 -0.15 -0.22 -164.64 254.64     -0.53 -0.43 -0.22 -140.87 230.87     -0.56 0.00 -0.23 180.00 270.00    
Bored bored -0.41 -0.27 -0.01 -146.63 236.63     -0.47 -0.34 0.00 -143.72 233.72     -0.36 -0.23 -0.01 -147.43 237.43    
Droopy droopy -0.20 -0.36 -0.12 -118.79 208.79     -0.22 -0.52 -0.10 -113.12 203.12     -0.18 -0.29 -0.12 -122.29 212.29    
Tired tired -0.14 -0.27 0.01 -118.09 208.09     -0.10 -0.37 0.10 -105.05 195.05     -0.16 -0.21 -0.08 -126.44 216.44    
Sleepy sleepy -0.13 -0.39 -0.09 -108.08 198.08     -0.20 -0.20 -0.14 -135.00 225.00     -0.05 -0.50 -0.05 -95.26 185.26    
Calm calm 0.38 -0.67 0.49 -60.42 150.42     0.22 -0.54 0.49 -67.55 157.55     0.50 -0.73 0.49 -55.52 145.52    
Relaxed relaxed 0.45 -0.50 0.42 -48.13 138.13     0.43 -0.50 0.45 -49.44 139.44     0.46 -0.50 0.39 -47.49 137.49    
Satisfied satisfied 0.43 -0.21 0.25 -25.92 115.92     0.47 -0.24 0.26 -27.25 117.25     0.42 -0.19 0.24 -24.36 114.36    
At Ease tranquil 0.42 -0.48 0.19 -48.56 138.56     0.45 -0.45 0.10 -44.75 134.75     0.38 -0.49 0.27 -52.27 142.27    
Content content 0.34 -0.37 0.18 -47.11 137.11     0.44 -0.60 -0.08 -53.75 143.75     0.31 -0.28 0.49 -42.05 132.05    
Serene serene 0.38 -0.07 0.30 -9.85 99.85     0.24 -0.13 0.20 -29.18 119.18     0.43 -0.03 0.38 -4.56 94.56    
Glad glad 0.51 -0.26 0.40 -26.83 116.83     0.53 -0.40 0.35 -36.84 126.84     0.51 -0.19 0.45 -20.18 110.18    
Pleased pleased 0.56 -0.15 0.37 -14.89 104.89     0.51 0.00 0.17 0.00 90.00     0.64 -0.23 0.48 -19.65 109.65    

There was a wee bit of mathematical translation to do. Valence, Arousal, and Dominance were given on a scale of 1 to 9, with 5 being neutral, 1 negative, 9 positive. So I had to their numbers and subtract 5 to get an equivilent to the circumplex model. While raw figures were not provided, they did provide a standard distribution. And from that I could approximate noise for computing saturation.

At first glance, our VAD spectrum of colors has a passing resemblance to our Circumplex colors. But if we look closer:

Emotion Circumplex VA VAD
Happy      
Delighted      
Excited      
Astonished      
Aroused      
Tense      
Alarmed      
Angry      
Afraid      
Annoyed      
Distressed      
Frustrated      
Miserable      
Sad      
Gloomy      
Depressed      
Bored      
Droopy      
Tired      
Sleepy      
Calm      
Relaxed      
Satisfied      
At Ease      
Content      
Serene      
Glad      
Pleased      

Behold. There is no red, anywhere. Anger is purple. But we also have to consider that Circumplex has no dimension of motivation/dominance. And as this is an interference pattern, what if Arousal and Dominance were added together? What if I need to scale arousal? I tried various schemes to calculate theta differently. They didn't work. But they look pretty:

Emotion Circumplex theta Color V/A Theta Color V/D Theta Color V/(A+D)/2 Theta Color V/max(a,d) Theta Color V/5*A Theta Color
Happy 7.8   23.32   30.50   27.02   30.50   65.11  
Delighted 24.9   0.00   24.00   12.55   24.00   0.00  
Excited 48.6   24.79   26.91   25.86   26.91   66.58  
Astonished 69.8   27.21   -5.23   11.93   27.21   68.74  
Aroused 73.8   67.56   31.41   56.59   67.56   85.28  
Tense 91.3   171.91   -172.91   179.49   171.91   144.58  
Alarmed 96.5   160.50   -145.76   -170.73   -145.76   119.45  
Angry 99.4   154.09   -160.18   176.41   154.09   112.38  
Afraid 118.6   177.50   -140.21   -158.47   -140.21   167.69  
Annoyed 128.8   172.49   -157.31   -171.85   -157.31   146.61  
Distressed 184.9   141.69   -152.59   172.27   141.69   104.20  
Frustrated 142.4   170.73   -154.86   -171.30   -154.86   140.77  
Miserable 188.7   178.57   -154.59   -167.32   -154.59   172.87  
Sad 193.5   -152.49   -158.20   -155.28   -152.49   -111.01  
Gloomy 208.4   -137.76   -135.00   -136.35   -135.00   -102.42  
Depressed 209.6   -164.64   -158.23   -161.38   -158.23   -126.05  
Bored 240.5   -146.63   -178.88   -161.27   -146.63   -106.89  
Droopy 256.6   -118.79   -149.89   -129.81   -118.79   -96.27  
Tired 267.2   -118.09   175.17   -138.19   -118.09   -96.09  
Sleepy 271.9   -108.08   -145.49   -118.07   -108.08   -93.74  
Calm 316.2   -60.42   52.24   -13.25   -60.42   -83.52  
Relaxed 317.4   -48.13   42.89   -5.33   -48.13   -79.84  
Satisfied 320.2   -25.92   30.26   2.78   30.26   -67.64  
At Ease 319.9   -48.56   24.01   -18.96   -48.56   -79.99  
Content 324.0   -47.11   28.42   -14.98   -47.11   -79.47  
Serene 328.6   -9.85   38.29   17.11   38.29   -40.97  
Glad 349.8   -26.83   38.11   7.93   38.11   -68.43  
Pleased 353.2   -14.89   33.12   10.94   33.12   -53.06  

Finally I had to go back into the data and examine what is different about our various emotions between how Circumplex computes Valence and Arousal, and how it was Valence, Arousal and Dominance were measured empirically in the later study.

Emotion Valence Arousal Signal Vad Equivilent Valence Arousal Dominance VSD ASD DSD
Happy 0.84 0.11 0.42 happiness 0.87 0.38 0.51
Delighted 0.77 0.36 0.44 delighted 0.69 0.00 0.30
Excited 0.63 0.71 0.81 excitement 0.66 0.30 0.33
Astonished 0.31 0.85 0.50 astonished 0.35 0.18 -0.03
Aroused 0.26 0.88 0.58 aroused 0.24 0.57 0.15
Tense -0.02 0.83 0.50 tense -0.56 0.08 -0.07
Alarmed -0.10 0.86 0.53 nervous -0.36 0.13 -0.25
Angry -0.12 0.74 0.58 angry -0.62 0.30 -0.22
Afraid -0.41 0.76 0.61 afraid -0.69 0.03 -0.57
Annoyed -0.43 0.53 0.39 annoyed -0.55 0.07 -0.23
Distressed -0.87 -0.08 0.69 distressed -0.41 0.32 -0.21
Frustrated -0.56 0.43 0.53 frustrated -0.61 0.10 -0.29
Miserable -0.89 -0.14 0.64 miserable -0.60 0.01 -0.29
Sad -0.74 -0.18 0.53 sad -0.72 -0.38 -0.29
Gloomy -0.78 -0.42 0.61 gloomy -0.46 -0.42 -0.46
Depressed -0.72 -0.41 0.67 depressed -0.68 -0.19 -0.27
Bored -0.39 -0.69 0.47 bored -0.51 -0.34 -0.01
Droopy -0.20 -0.86 0.72 droopy -1.00 -0.45 -0.15
Tired -0.05 -0.96 0.94 tired -0.18 -0.33 0.01
Sleepy 0.03 -0.95 0.89 sleepy -0.16 -0.49 -0.11
Calm 0.68 -0.65 0.81 calm 0.47 -0.83 0.61
Relaxed 0.68 -0.62 0.72 relaxed 0.56 -0.63 0.52
Satisfied 0.73 -0.61 0.89 satisfied 0.54 -0.26 0.31
At Ease 0.71 -0.59 0.72 tranquil 0.53 -0.60 0.24
Content 0.76 -0.55 0.81 content 0.43 -0.46 0.23
Serene 0.77 -0.47 0.72 serene 0.48 -0.08 0.38
Glad 0.87 -0.16 0.56 glad 0.64 -0.32 0.00
Pleased 0.85 -0.10 0.61 pleased 0.71 -0.19 0.46

In short... the data coming in for some key terms is wildly different. On other cases, they are similar. But over breakfast, another thought occurred to me. Perhaps Valence, Arousal, and Dominance are like the Red Green and Blue channels of color? And as it turns out, the math to convert between RGB and HSL is pretty involved.. So first try is to just feed V A D into R G B and see of we magically get something. We can also try mapping VAD as CMY.

# Derived from https://www.rapidtables.com/convert/color/rgb-to-cmyk.html
proc rgb_to_cmyk {red green blue {N 100}} {
  set r [expr {1.0*$red/$N}]
  set g [expr {1.0*$green/$N}]
  set b [expr {1.0*$blue/$N}]
  set K [expr {1-max($r,$g,$b)}]

  set C [expr {(1-$r-$K)/(1.0-$K)}]
  set M [expr {(1-$g-$K)/(1.0-$K)}]
  set Y [expr {(1-$b-$K)/(1.0-$K)}]

  return [list [expr {int($C*$N)}] [expr {int($M*$N)}] [expr {int($Y*$N)}] [expr {int($N*$K)}]]
}
# Derived from https://www.rapidtables.com/convert/color/cmyk-to-rgb.html
proc cmyk_to_rgb {cyan magenta yellow {black 0} {N 100}} {
  set c [expr {1.0*$cyan/$N}]
  set m [expr {1.0*$magenta/$N}]
  set y [expr {1.0*$yellow/$N}]
  set k [expr {1.0*$black/$N}]

  set R [expr {(1-$c)*(1-$k)}]
  set G [expr {(1-$m)*(1-$k)}]
  set B [expr {(1-$y)*(1-$k)}]
  return [list [expr {int($R*$N)}] [expr {int($G*$N)}] [expr {int($B*$N)}]]
}

Of course... we should probably test that CMYK code...

Color Red Green Blue Cyan Magenta Yellow rgb_to_cmyk cmyk_to_rgb
red 100 0 0 0 100 100 0 100 100 0 100 0 0
yellow 100 100 0 0 0 100 0 0 100 0 100 100 0
green 0 100 0 100 0 100 100 0 100 0 0 100 0
cyan 0 100 100 100 0 0 100 0 0 0 0 100 100
blue 0 0 100 100 100 0 100 100 0 0 0 0 100
magenta 100 0 100 0 100 0 0 100 0 0 100 0 100

So let's see our results side-by-side with our circumplex color, the color derived from Valence/Arousal, and the composite where we use Valence/Arousal for hue and dominance for lightness.

Emotion Vad Equivilent Valence Arousal Dominance Circumplex VA (original) VAD (original) VAD -> RGB VDA -> RGB AVD -> RGB ADV -> RGB DVA -> RGB DAV -> RGB VAD -> CMY VDA -> CMY AVD -> CMY ADV -> CMY DVA -> CMY DAV -> CMY
Happy happiness 94.00 72.00 78.00                              
Delighted delighted 86.00 55.00 69.00                              
Excited excitement 84.00 69.00 70.00                              
Astonished astonished 71.00 63.00 54.00                              
Aroused aroused 66.00 81.00 62.00                              
Tense tense 30.00 59.00 52.00                              
Alarmed nervous 39.00 61.00 44.00                              
Angry angry 28.00 68.00 45.00                              
Afraid afraid 25.00 56.00 30.00                              
Annoyed annoyed 31.00 58.00 45.00                              
Distressed distressed 37.00 69.00 46.00                              
Frustrated frustrated 28.00 60.00 42.00                              
Miserable miserable 28.00 56.00 42.00                              
Sad sad 23.00 38.00 42.00                              
Gloomy gloomy 35.00 36.00 35.00                              
Depressed depressed 25.00 47.00 43.00                              
Bored bored 32.00 40.00 55.00                              
Droopy droopy 44.00 35.00 49.00                              
Tired tired 47.00 40.00 56.00                              
Sleepy sleepy 48.00 33.00 50.00                              
Calm calm 76.00 18.00 82.00                              
Relaxed relaxed 80.00 27.00 78.00                              
Satisfied satisfied 79.00 43.00 69.00                              
At Ease tranquil 79.00 28.00 66.00                              
Content content 74.00 35.00 65.00                              
Serene serene 76.00 51.00 72.00                              
Glad glad 83.00 41.00 77.00                              
Pleased pleased 86.00 47.00 76.00                              

Long story short... no. Nothing works. No mapping of one channel to another seems to act as my magical Valence/Arousal/Dominance to color. Ok, well I have at least 7 different mappings, but they don't match up to what the circumplex model produces. And the circumplex model is soooo pretty.

The other thought I had is that, perhaps, dominance is backwards. A more dominance heavy emotion would be darker:

Emotion Vad Equivilent Valence Arousal Dominance Circumplex VA (original) VAD (original) VAD -> RGB VDA -> RGB AVD -> RGB ADV -> RGB DVA -> RGB DAV -> RGB VAD -> CMY VDA -> CMY AVD -> CMY ADV -> CMY DVA -> CMY DAV -> CMY
Happy happiness 94.00 72.00 21.00                              
Delighted delighted 86.00 55.00 30.00                              
Excited excitement 84.00 69.00 29.00                              
Astonished astonished 71.00 63.00 45.00                              
Aroused aroused 66.00 81.00 38.00                              
Tense tense 30.00 59.00 47.00                              
Alarmed nervous 39.00 61.00 55.00                              
Angry angry 28.00 68.00 54.00                              
Afraid afraid 25.00 56.00 69.00                              
Annoyed annoyed 31.00 58.00 54.00                              
Distressed distressed 37.00 69.00 53.00                              
Frustrated frustrated 28.00 60.00 57.00                              
Miserable miserable 28.00 56.00 57.00                              
Sad sad 23.00 38.00 57.00                              
Gloomy gloomy 35.00 36.00 65.00                              
Depressed depressed 25.00 47.00 56.00                              
Bored bored 32.00 40.00 44.00                              
Droopy droopy 44.00 35.00 50.00                              
Tired tired 47.00 40.00 43.00                              
Sleepy sleepy 48.00 33.00 49.00                              
Calm calm 76.00 18.00 17.00                              
Relaxed relaxed 80.00 27.00 21.00                              
Satisfied satisfied 79.00 43.00 30.00                              
At Ease tranquil 79.00 28.00 34.00                              
Content content 74.00 35.00 34.00                              
Serene serene 76.00 51.00 27.00                              
Glad glad 83.00 41.00 22.00                              
Pleased pleased 86.00 47.00 24.00                              

Both efforts are a lot of pretty colors to show that, while my original hue/saturation/lightness model produces different color mappings than the original circumplex model, the "gist" is right. Most happy ideas are in the green and yellow. Intense thoughts are redder. Negative thoughts are purple and blue.

The issue is that I get very different scores for "Anger" from my circumplex data and this follow-on study.

Part of the problem is the methodology used for calculating the Valence Arousal Dominance data. They basically asked a bunch of semi-random residents of the US who happend to be Amazon Mechanical Turk ... subscribers? Whatever one calls people that do menial tasks for a buck or two a pop. What they "felt" about works provided. And also, when surveyed they actually rated from 1 (happy) to 9 (unhappy). The conversion to a 1 (unhappy) to 9 (happy) was done in post processing.

The subjects were also asked about "anger" as a word and concept. Not as a personal experience of the emotion. So, odds are they are going to have different interpretations of words. As you can see, I didn't find every one of the emotions, so I sometimes had to go with a synonym.

The other issue is noise. In my circumplex data, every emotion was filed in at least 3 bins. In the Valence/Arousal/Dominance data people provided different opinions from 1 to 9. Different people provided different answers. And to account for that, the number published was the Mean, the average. Also provided was the standard distribution. Namely the range, plus or minus, where 50% of the responses fell around that mean.

So let us take a look at just the noise from Circumplex and the standard deviation from VAD:

I have to conclude that for aesthetics, the valance/Arousal relationship as a hue works.

Emotion Lemma Circumplex Noise Circumplex Color Valence SD Arousal SD Dominance SD Nominal VAD Color Nominal VAD+ Color Min Valence Min Arousal Min Dominance Min Theta Min Hue HSL (50%L) HSL (min L) HSL (max L) Max Valence Max Arousal Maz Dominance Maz Theta Maz Hue HSL (50%L) HSL (min L) HSL (max L)
Happy happiness 52.5   0.81 2.63 2.16     0.53 -0.23 -0.12 -22.94 112.94       0.86 0.83 0.94 43.91 46.09      
Delighted delighted 50.0   1.05 2.28 2.24     0.34 -0.46 -0.21 -53.45 143.45       0.76 0.46 0.70 31.03 58.97      
Excited excitement 13.1   1.38 2.50 2.28     0.25 -0.26 -0.23 -46.13 136.13       0.80 0.74 0.77 42.85 47.15      
Astonished astonished 33.8   1.47 2.27 2.04     -0.01 -0.31 -0.48 -91.86 181.86       0.58 0.60 0.43 46.07 43.93      
Aroused aroused 28.1   1.85 2.47 2.40     -0.18 -0.03 -0.38 -169.30 259.30       0.56 0.95 0.61 59.59 30.41      
Tense tense 33.8   1.33 2.62 2.42     -0.72 -0.46 -0.58 -147.28 237.28       -0.18 0.59 0.47 107.38 342.62      
Alarmed nervous 31.9   1.79 2.65 2.25     -0.65 -0.43 -0.73 -146.47 236.47       0.07 0.63 0.33 83.68 6.32      
Angry angry 46.9   1.74 2.57 2.49     -0.84 -0.27 -0.69 -161.97 251.97       -0.15 0.75 0.34 100.96 349.04      
Afraid afraid 35.0   1.16 2.57 1.90     -0.78 -0.49 -0.97 -147.93 237.93       -0.32 0.54 0.06 120.59 329.41      
Annoyed annoyed 82.5   1.20 2.53 2.64     -0.68 -0.45 -0.69 -146.62 236.62       -0.20 0.56 0.32 109.53 340.47      
Distressed distressed 27.5   1.99 2.11 2.01     -0.72 -0.17 -0.59 -167.05 257.05       0.07 0.68 0.25 83.77 6.23      
Frustrated frustrated 53.1   1.00 2.29 2.31     -0.69 -0.38 -0.69 -151.28 241.28       -0.29 0.54 0.23 118.33 331.67      
Miserable miserable 24.4   1.90 3.04 2.12     -0.86 -0.60 -0.84 -145.28 235.28       -0.10 0.62 0.38 99.16 350.84      
Sad sad 31.9   0.91 2.21 2.21     -0.76 -0.74 -0.67 -135.68 225.68       -0.40 0.14 0.21 160.62 289.38      
Gloomy gloomy 35.0   1.63 2.12 1.63     -0.70 -0.76 -0.79 -132.48 222.48       -0.04 0.09 0.05 116.57 333.43      
Depressed depressed 30.0   1.48 3.24 2.82     -0.84 -0.80 -0.87 -136.54 226.54       -0.25 0.50 0.43 116.66 333.34      
Bored bored 47.5   1.58 2.54 2.39     -0.73 -0.78 -0.52 -133.02 223.02       -0.09 0.24 0.50 111.55 338.45      
Droopy droopy 25.0   1.84 1.79 1.98     -0.57 -0.72 -0.47 -128.19 218.19       0.17 -0.01 0.24 -2.05 92.05      
Tired tired 3.8   1.35 2.18 2.38     -0.41 -0.70 -0.42 -120.41 210.41       0.13 0.17 0.45 53.02 36.98      
Sleepy sleepy 7.5   1.36 2.51 2.18     -0.40 -0.89 -0.59 -114.11 204.11       0.14 0.11 0.41 37.38 52.62      
Calm calm 13.1   2.00 1.91 2.28     -0.02 -1.05 0.11 -91.20 181.20       0.78 -0.28 0.87 -20.05 110.05      
Relaxed relaxed 18.8   1.92 2.51 2.03     0.07 -1.00 -0.08 -86.24 176.24       0.83 0.00 0.92 0.00 90.00      
Satisfied satisfied 7.5   1.26 2.67 1.88     0.18 -0.74 -0.28 -76.40 166.40       0.68 0.32 0.79 25.35 64.65      
At Ease tranquil 18.8   2.02 2.35 2.51     0.02 -0.95 -0.28 -88.91 178.91       0.83 -0.01 0.66 -0.55 90.55      
Content content 13.1   2.05 2.64 2.57     -0.07 -0.89 -0.34 -94.48 184.48       0.75 0.16 0.71 12.19 77.81      
Serene serene 18.8   1.48 2.72 2.02     0.08 -0.61 -0.24 -82.16 172.16       0.68 0.48 0.84 35.26 54.74      
Glad glad 30.0   1.44 2.57 1.46     0.22 -0.77 -0.11 -73.96 163.96       0.80 0.26 0.91 17.79 72.21      
Pleased pleased 35.0   1.18 3.01 2.57     0.33 -0.75 -0.23 -66.43 156.43       0.80 0.45 0.97 29.47 60.53      

The table above shows what the colors would be at the outer edges of what the data supports. If you were to take the minimum of Valance-standard_devation and the maximum of Valence+standar_deviation, and repeated for Arousal and Dominance. To quote Captain Noah: "I can see a Rainbow."

In essence, that VAD information is so noisy it is essentially useless. The Circumplex data is so pretty, but it lacks Dominance, and is also useless. While it's possible to take a Valance an Arousal and a Dominance and try to map them back to an emotion, it's going to be random what you get back. And likewise, you can take an emotion and the Valance, the Arousal, and the Dominance you get back will likewise be, as near as makes no difference to random.

I'm on my own with developing my emotional system. Which is comforting, but also really, really annoying. I was hoping science had a better answer than ¯\_(ツ)_/¯. But I've encountered paper after paper after paper after (entire careers worth of papers) that either produce pretty (but wrong) pictures, or statistics with noise to signal ratios as opposed to signal to noise.

¯\_(ツ)_/¯ is my spirit animal right now...

I'm going to pour a stiff drink. And I'm going to have to start this process over. Though, to be fair to myself, often times an experiment is mostly about finding what the answer is not.