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Under the Hood: How the Extended Zodiac Quiz Determines Aspect

Summary:

As far as I can tell, this has been an untapped avenue of analysis. Until now.

Alternate title: Making Sense of the Aspect Wheel.

Notes:

Here's a link to the quiz if you want to take it before reading this, and/or if you want a reference to see what I'm talking about.

This is mostly intended just to put the information out there and give people more data for aspect theory. I may expand upon my personal interpretations in a future work.

(As a disclaimer, I don't have official confirmation of this analysis, nor am I aware of any way to access the code directly. However, I've tested this on over ten thousand random inputs to the quiz, and it has never failed to predict the correct output. I'm quite confident, therefore, that I'm correct.)

 

Edit 2024-07-06: It seems I'm not actually the first person to figure this out. This tumblr post (archive link) was made by Katanahime in late 2017, shortly after the quiz was first released, and they arrived at the same set of numbers I did. Props to you, Katanahime, and I think it speaks to the accuracy of these findings that at least two different people, working independently and using different methodologies, reached the same conclusions. (Moreover, their post suggests that yet another person, also independently, came to a more complicated but mathematically equivalent set of numbers, but I haven't found that analysis which can be found here; archive link here. I haven't done the math to verify that this is equivalent, but both they and Katanahime claim that it is.)

Work Text:

The Extended Zodiac quiz's 12-question section on Aspects has long seemed to me like a potential goldmine of information, if only we knew how it were scored. Eventually, I decided to take it upon myself to crack the code. Here's what I found.

First of all, you may have already guessed this, but the quiz works by assigning a score to each of your answers for each of the aspects it might indicate, and then assigning you the aspect with the highest total score. For instance, Question 5 asks:

If you could choose one ability, which would it be? The ability to travel to any period in history on Earth at will, past or future? Or the ability to safely travel (such as, on a nice ship) anywhere in the universe at will, instantly?

If you choose option A ("Definitely time travel. No question."), the quiz will give you 6 points towards the Time aspect.

The assignment of these scores in general is symmetrical and based on the Aspect Wheel, which looks like this:

A wheel of twelve symbols each representing one of the twelve Homestuck aspects. Clockwise from top, they are Breath, Life, Light, Time, Heart, Rage, Blood, Doom, Void, Space, Mind, and Hope.

Each question is associated with a particular axis, connecting two Aspects on opposite sides of the wheel. The most obvious, in my opinion, is question 5, which is connected with the Time-Space axis. I mentioned that choosing option A gives you six points towards the Time aspect. In general, choosing option A gives you the most possible points towards the Aspect at one end of the axis, and choosing option E gives you the most possible points towards the Aspect at the other end. So if option A gives you 6 points for Time, then option E will give you 6 points for Space.

Depending on which Aspect you're focusing on, the full scoring for a given question along its associated axis will look either like this:

A: 6 points
B: 4 points
C: 0 points
D: 2 points
E: 2 points

Or like this:

A: 2 points
B: 2 points
C: 0 points
D: 4 points
E: 6 points

This means that a pair of opposite Aspects are not diametrically opposed — choosing "Definitely time travel. No question." will give you more points for Space than saying "Too hard to choose." Just having an opinion on the matter gives you points!

You may be wondering why I chose to represent the scoring as 2, 4, and 6 instead of 1, 2, and 3, which would be equivalent. You may also be wondering how the wheel comes into play, beyond just providing pairs of associated Aspects. You may begin to suspect that these things are related. And you would be right.

In addition to the primary axis associated with a question, points are also assigned based on the two adjacent axes as depicted on the wheel. For the Time-Space axis, for instance, these would be the Heart-Mind and Light-Void axes. Aspects on adjacent axes are given half as many points as their neighbors on the primary axis. So an answer that gives 6 points for Time will not only give 2 additional points for Space; it will also give 3 points each for Heart and Light, and 1 point each for Mind and Void. Likewise, an answer giving 4 points for Time will give 2 points each for Heart and Light (its adjacent Aspects), 2 points for Space (its opposite Aspect), and 1 point each for Mind and Void (those adjacent to Space). Therefore any answer to the quiz will assign at least one point to each of six Aspects — unless you answer C, in which case the quiz doesn't give any points for any Aspect.

There are twelve questions on the quiz, two for each axis. The questions are paired up, so that the first two questions are Breath-Blood, the next two are Light-Void, and so on. In addition, the order is the same for both questions in each pair — answer A will represent the same Aspect for both.

The only other issue is dealing with ties. If two or more Aspects are tied for the most points, the tie is broken by choosing the highest-ranking Aspect according to the following order:

  1. Time
  2. Space
  3. Heart
  4. Mind
  5. Hope
  6. Rage
  7. Light
  8. Void
  9. Breath
  10. Blood
  11. Life
  12. Doom

This means, for instance, that Time will win any tie, while Doom will never win a tie. I'm not sure what the significance of this ordering is, if any. It does seem to be the order in which the Aspects are consistently indexed on the site (including in filenames and such — e.g., the image for the Hope symbol is called "aspect_5.png").


Now that we have all the relevant information, let's look at the questions.

The first two are associated with the Breath-Blood axis.

1. Think about your life as if it's a story, and you're the main protagonist. Do you tend to view yourself as lone hero, who along the way meets other supporting characters, who only have a tangential relation to your personal journey? Or do you view yourself as just one hero in an ever-shifting ensemble of important protagonists?

A: Loner hero, all the way. (6 Breath, 3 Hope, 3 Life, 2 Blood, 1 Rage, 1 Doom)

B: Often lone hero. Not always. (4 Breath, 2 Hope, 2 Life, 2 Blood, 1 Rage, 1 Doom)

C: Either one. Can't say for sure.

D: Often part of an ensemble. Not always. (4 Blood, 2 Rage, 2 Doom, 2 Breath, 1 Hope, 1 Life)

E: Part of an ensemble, all the way. (6 Blood, 3 Rage, 3 Doom, 2 Breath, 1 Hope, 1 Life)

2. When you want to help people accomplish something, and they don't know what they're doing, are you inclined to show them how to do it? Or are you inclined to make them feel motivated or inspired to do it?

A: Definitely show them. (6 Breath, 3 Hope, 3 Life, 2 Blood, 1 Rage, 1 Doom)

B: Lean toward showing them. (4 Breath, 2 Hope, 2 Life, 2 Blood, 1 Rage, 1 Doom)

C: I'll go either way.

D: Lean toward motivating them. (4 Blood, 2 Rage, 2 Doom, 2 Breath, 1 Hope, 1 Life)

E: Definitely motivate them. (6 Blood, 3 Rage, 3 Doom, 2 Breath, 1 Hope, 1 Life)

The next two are Light-Void.

3. When you are learning about a new subject, or reading a fascinating story, do you feel a strong desire to know everything about it, and have all your questions answered? Or are you more compelled or inspired by the feelings of mystery surrounding not knowing everything?

A: I absolutely need to know everything. I'm obsessive about it. (6 Light, 3 Time, 3 Life, 2 Void, 1 Space, 1 Doom)

B: I'm very curious, drawn toward knowing. (4 Light, 2 Time, 2 Life, 2 Void, 1 Space, 1 Doom)

C: Can't decide.

D: I'm ok not having all answers. Sense of mystery is fun. (4 Void, 2 Space, 2 Doom, 2 Light, 1 Time, 1 Life)

E: Totally fine not knowing everything. I'd rather relax. (6 Void, 3 Space, 3 Doom, 2 Light, 1 Time, 1 Life)

4. When you hear someone explaining something to someone else, in a way that is questionable, or in a way that makes you suspect they don't fully understand the subject they are explaining, are you more inclined to: teach them everything you know about the subject, to set the record straight? Or just cast doubt on the misinformation, without offering much in the way of correction?

A: I'll jump right in, set the record straight on everything. (6 Light, 3 Time, 3 Life, 2 Void, 1 Space, 1 Doom)

B: I'll provide a correction or two, but won't get carried away. (4 Light, 2 Time, 2 Life, 2 Void, 1 Space, 1 Doom)

C: I'd probably stay out of it.

D: I wouldn't be too specific, but I'd let people know it sounds fishy. (4 Void, 2 Space, 2 Doom, 2 Light, 1 Time, 1 Life)

E: I wouldn't bother reeducating people, but I'd absolutely punch as many holes in their story as I could. (6 Void, 3 Space, 3 Doom, 2 Light, 1 Time, 1 Life)

Then we have Time-Space, including Question 5 as seen earlier.

5. If you could choose one ability, which would it be? The ability to travel to any period in history on Earth at will, past or future? Or the ability to safely travel (such as, on a nice ship) anywhere in the universe at will, instantly?

A: Definitely time travel. No question. (6 Time, 3 Heart, 3 Light, 2 Space, 1 Mind, 1 Void)

B: Leaning toward time travel, but the other sounds pretty cool. (4 Time, 2 Heart, 2 Light, 2 Space, 1 Mind, 1 Void)

C: Too hard to choose.

D: Leaning toward space travel, but the other sounds pretty cool. (4 Space, 2 Mind, 2 Void, 2 Time, 1 Heart, 1 Light)

E: Definitely space travel. No question. (6 Space, 3 Mind, 3 Void, 2 Time, 1 Heart, 1 Light)

6. If you are working on a project (something you're doing for yourself, not for anyone else), are you obsessively focused on the end result of the project? Or are you enjoying the process, regardless of how it turns out?

A: End result is easily the most important thing. (6 Time, 3 Heart, 3 Light, 2 Space, 1 Mind, 1 Void)

B: Result is very important, but would like to enjoy it along the way too. (4 Time, 2 Heart, 2 Light, 2 Space, 1 Mind, 1 Void)

C: Result and process about equally important.

D: Enjoying the process is very important, but would like it to feel worthwhile at end too. (4 Space, 2 Mind, 2 Void, 2 Time, 1 Heart, 1 Light)

E: Enjoying the process is easily the most important thing. (6 Space, 3 Mind, 3 Void, 2 Time, 1 Heart, 1 Light)

Next is Heart-Mind.

7. Which option best describes what's more important to you? Understanding yourself, and fully knowing who you are? Or thinking rationally, and making strong decisions?

A: Definitely understanding myself. If I had to pick one over the other, that would be my clear priority. (6 Heart, 3 Time, 3 Rage, 2 Mind, 1 Space, 1 Hope)

B: Leaning toward understanding myself. (4 Heart, 2 Time, 2 Rage, 2 Mind, 1 Space, 1 Hope)

C: Can't really decide.

D: Leaning toward thinking rationally. (4 Mind, 2 Space, 2 Hope, 2 Heart, 1 Time, 1 Rage)

E: Definitely thinking rationally. If I had to pick one over the other, that would be my priority. (6 Mind, 3 Space, 3 Hope, 2 Heart, 1 Time, 1 Rage)

8. What idea is more interesting to you? The ability to fully understand your potential as a person? Or the ability to fully understand all potential consequences of your actions before taking them?

A: Want to understand my personal potential, no question. (6 Heart, 3 Time, 3 Rage, 2 Mind, 1 Space, 1 Hope)

B: Somewhat more interested in understanding my personal potential. (4 Heart, 2 Time, 2 Rage, 2 Mind, 1 Space, 1 Hope)

C: Both equally desirable.

D: Somewhat more interested in understanding all consequences of my actions. (4 Mind, 2 Space, 2 Hope, 2 Heart, 1 Time, 1 Rage)

E: Want to understand all consequences of my actions, no question. (6 Mind, 3 Space, 3 Hope, 2 Heart, 1 Time, 1 Rage)

The penultimate pair deals with Hope-Rage.

9. Which better describes your attitude? Having great conviction in certain beliefs or ideas you're attracted to? Or casting strong doubt on beliefs or ideas you dislike?

A: Definitely having conviction in beliefs I like. (6 Hope, 3 Mind, 3 Breath, 2 Rage, 1 Heart, 1 Blood)

B: A little more attracted to having conviction in beliefs I like. (4 Hope, 2 Mind, 2 Breath, 2 Rage, 1 Heart, 1 Blood)

C: Can't decide.

D: A little more attracted to casting doubt on beliefs I dislike. (4 Rage, 2 Heart, 2 Blood, 2 Hope, 1 Mind, 1 Breath)

E: Definitely casting doubt on beliefs I dislike. (6 Rage, 3 Heart, 3 Blood, 2 Hope, 1 Mind, 1 Breath)

10. When circumstances are intolerably bad, which are you more inclined to do? Come up with the best alternatives or solutions, and work as hard as you can to make those happen instead? Or don't worry about a better alternative, burn it all down, and whatever follows, you'll just deal with it as it comes?

A: I'm not doing a thing until I have a better solution in place first. (6 Hope, 3 Mind, 3 Breath, 2 Rage, 1 Heart, 1 Blood)

B: Inclined to have a solution first, but not absolutely. (4 Hope, 2 Mind, 2 Breath, 2 Rage, 1 Heart, 1 Blood)

C: I don't have an opinion on this.

D: Inclined to get out the bad situation as soon as possible, but not averse to considering alternatives. (4 Rage, 2 Heart, 2 Blood, 2 Hope, 1 Mind, 1 Breath)

E: Burn it down. I'm absolutely getting out of the bad situation asap, will deal with the consequences later. (6 Rage, 3 Heart, 3 Blood, 2 Hope, 1 Mind, 1 Breath)

Finally, we have Life-Doom.

11. If you see someone suffering, are you most inclined to do whatever you can to help them get better? Or is your instinct to relate to their suffering, to empathize, without necessarily considering how you can help?

A: I'll do whatever's in my power to help them. That's all I'm thinking about. (6 Life, 3 Light, 3 Breath, 2 Doom, 1 Void, 1 Blood)

B: I'll focus mostly on helping, but won't be able to stop myself from relating to the problem somewhat. (4 Life, 2 Light, 2 Breath, 2 Doom, 1 Void, 1 Blood)

C: Not sure how I'd react.

D: My first impulse would be to empathize with their suffering, but after that I'd probably figure out what I could do to help. (4 Doom, 2 Void, 2 Blood, 2 Life, 1 Light, 1 Breath)

E: I'm really not great at helping. I'm generally overcome with other feelings relating to their suffering, which makes me not that useful. (6 Doom, 3 Void, 3 Blood, 2 Life, 1 Light, 1 Breath)

12. When someone suffers misfortune so terrible that you know there is nothing anyone can do for them, are you most inclined to: feel horrible that nothing can be done? Or feel resigned to the sense that this is the way of the world, and some things just can't be helped?

A: Feel absolutely horrible that there's no way to help this person. Would probably end up trying to think of ways to help regardless. (6 Life, 3 Light, 3 Breath, 2 Doom, 1 Void, 1 Blood)

B: Would feel bad there's nothing that can be done. Would probably accept there's no way to help though. (4 Life, 2 Light, 2 Breath, 2 Doom, 1 Void, 1 Blood)

C: Hard to say.

D: Likely would feel somewhat resigned right away. Might briefly consider how to help, but... no. It's not realistic. (4 Doom, 2 Void, 2 Blood, 2 Life, 1 Light, 1 Breath)

E: Feel absolutely resigned to their terrible situation, because that's just the way things so often are. (6 Doom, 3 Void, 3 Blood, 2 Life, 1 Light, 1 Breath)

Using these point values, the quiz will determine which Aspect has the highest score for a given set of answers, and thus determine which result to give (breaking ties as above).


Whew, that's a lot of information at once. Let's try presenting it in a way that's a bit more digestible, a bit more conducive to actual analysis. I'll go around the wheel, and for each Aspect, I'll list:

  1. The players who have that Aspect in canon.
  2. The two six-point answers for that Aspect.

Keep in mind that each Aspect's six-point answers are also three-point answers for each of the adjacent Aspects. The first Aspect on this list (Life) is adjacent to the last (Breath).

Life (Jane, Feferi, Meenah)
11 A: I'll do whatever's in my power to help them. That's all I'm thinking about.
12 A: Feel absolutely horrible that there's no way to help this person. Would probably end up trying to think of ways to help regardless.

Light (Rose, Vriska, Aranea)
3 A: I absolutely need to know everything. I'm obsessive about it.
4 A: I'll jump right in, set the record straight on everything.

Time (Dave, Aradia, Damara, Caliborn)
5 A: Definitely time travel. No question.
6 A: End result is easily the most important thing.

Heart (Dirk, Nepeta, Meulin)
7 A: Definitely understanding myself. If I had to pick one over the other, that would be my clear priority.
8 A: Want to understand my personal potential, no question.

Rage (Gamzee, Kurloz)
9 E: Definitely casting doubt on beliefs I dislike.
10 E: Burn it down. I'm absolutely getting out of the bad situation asap, will deal with the consequences later.

Blood (Karkat, Kankri)
1 E: Part of an ensemble, all the way.
2 E: Definitely motivate them.

Doom (Sollux, Mituna)
11 E: I'm really not great at helping. I'm generally overcome with other feelings relating to their suffering, which makes me not that useful.
12 E: Feel absolutely resigned to their terrible situation, because that's just the way things so often are.

Void (Roxy, Equius, Horuss)
3 E: Totally fine not knowing everything. I'd rather relax.
4 E: I wouldn't bother reeducating people, but I'd absolutely punch as many holes in their story as I could.

Space (Jade, Kanaya, Porrim, Calliope)
5 E: Definitely space travel. No question.
6 E: Enjoying the process is easily the most important thing.

Mind (Terezi, Latula)
7 E: Definitely thinking rationally. If I had to pick one over the other, that would be my priority.
8 E: Want to understand all consequences of my actions, no question.

Hope (Jake, Eridan, Cronus)
9 A: Definitely having conviction in beliefs I like.
10 A: I'm not doing a thing until I have a better solution in place first.

Breath (John, Tavros, Rufioh)
1 A: Loner hero, all the way.
2 A: Definitely show them.

And then we come full circle back to Life.


You may want to know how I figured this out. I'll spare the gory methodological details unless people really want them, but here is a rough overview of my process.

  1. I wrote a program that generated 10,000 random sets of inputs to the quiz and tested each of them on the site, thus compiling a database of 10,000 canonical input/output data points.
  2. I wrote another program that generated possible sets of weights that could explain this data, and gave me the average of many possible sets it found. I figured this would be likelier to produce the "true" weights than just one possible set of weights.
  3. I looked at the numbers generated and began to notice patterns, such as that each Aspect was associated most strongly with its corresponding pair of questions. I eventually had the idea that weights might be related to the distance along the wheel, and took further averages based on that idea.
  4. I fiddled with the numbers until a very neat weighting scheme popped out and caught my attention.
  5. I tested this scheme on the original 10,000 sets of inputs, as well as on 1,000 more random sets of inputs that hadn't been used to generate the weights in the first place, plus several sets of inputs I personally constructed to stress-test this scheme. I did not find any sets of inputs where the site's official output contradicted the weighting scheme I'd discovered.

Given both the robustness of my findings and the sense it seems to make in light of the Aspect wheel (edit 2024-07-06: as well as the fact that someone else already came up with these same numbers using a different method), I'm pretty dang sure I've found the correct solution — sure enough, in fact, that I'm willing to present it here as the truth. Nevertheless, if you identify any flaws or areas for improvement, please let me know!