Linear Algebra meets INTJ

My friend Brooke posted a link to this personality test on her blog. Kelly took the test and liked it, so she got me to take the test and I liked it too. I’m an INTJ and Kelly’s an INFJ. That’s jut a preface for the nerdy things I decided to do next.

So Brooke posted an image of a grid with all of the personality types in it. I noticed that each of the personality types has these little doors to some of the other types (but not all of them). I didn’t figure out what the little doors meant, but it made me imagine a four-dimensional cube with all of the different personality types in it, a dimension for each of the letters you get in the test results. I thought it would be fun to draw the cube (and probably more fun to look at for anyone that reads this), but I don’t know how to draw in 4-D. I know how to do math in 4-D, so that’s what I did instead.

So, the basic idea is that if I have two scores (presumably from two different people), and I consider them as points in four-dimensional space, then I can calculate the difference between the points and that will tell me how similar two personalities are. (Note that I don’t actually think this has any bearing on compatibility. That’s probably very different and more complex than similarity, which is what I’m going for.)

At first I just assigned each letter option a one or a zero, but it turns out that finding distance that way is the same as just counting how many letters are different between two people’s results. It wasn’t very interesting (and it wasn’t very fun for me because counting doesn’t require much math). So next I thought I could use the “strength of the preferences” to get a better distance. So I consider each letter to be either positive or negative, and the strength to be the value, and then calculate distance. The distance would actually be the the dissimilarity between two personalities, but since the strengths are given as a percentage I know there’s a maximum dissimilarity so I can turn that into similarity by inverting it.

I know you probably didn’t care about any of that, but here’s my little calculator to tell you how similar two personality scores are to each other. I hope it’s as fun to play with as it was to make!

Person 1
Person 2



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14 Responses to Linear Algebra meets INTJ

  1. xarissa says:

    How funny, I’m an INFJ as well! I have my own percentages, but I need someone else’s as well to plug in. You and Kelly want to volunteer yours? Or shall I just bludgeon some other friends into giving up their numbers?

  2. bryant says:

    I found this page where someone has figured out the personality types of all of the Harry Potter characters, so now you can see which character you’re most like. (I’m most like Malfoy. I don’t know if I should be disturbed by that.)

  3. Kathy Anderson says:

    E-1%, S-12%, F-38%, J-56%

  4. kelly says:

    Interesting how we change. In 2008, I was INFJ (11, 62, 75, 56). Today I still got INFJ, with numbers (33, 38, 50, 56). That means I’m 89.7% similar to the person I was in 2008. And Me Today is 75.8% similar to Bryant in 2008.

    • bryant says:

      Aight, I took it again too. I’m still INTJ, this time (67, 75, 12, 11).

      So that makes me 87.6% similar to my old self, 71.6% similar to the old Kelly, and 77.1% similar to the new Kelly. (And for context the old Kelly was 71.3% similar to the old Bryant.)

      I guess I’m not surprised for us to become more similar over time, but I don’t think I would have guessed these numbers. If I look at the actual scores then the only things we’ve become more similar on are that we’ve both gotten more introverted, and we’ve come slightly closer to middle on the feeling/thinking axis.

      (I thought I’d become a little bit more of a people-person since last time, so I was a little bit surprised that I’ve become more introverted and not less. I guess the only change is the increase in “feeling”. Maybe that just makes me less of a jerk. Imagine how I used to be!)

  5. kelly says:

    Also, I just looked at that Harry Potter website you posted, Bryant, and it’s funny to read the descriptions that match Mom, Dad, you, and me. They seem to fit pretty well.

    Dad–ISTJ: Defined by their honor and duty. Take any task seriously and give it more than their best. Somewhat reserved and prefer to work alone, but can make great team members if the need arises. Deeply value traditions and loyalty and often put duty before pleasure.

    Mom–ESFJ: Warmhearted, conscientious, and cooperative, want harmony in their world and work with determination to establish it. Like to work with others to complete tasks accurately and on time. Notice what others need in their day-to-day lives and try to provide it.

    You–INTJ: Natural leaders that strive for perfection. Objective, independent, conceptual, and adaptable. Quickly see patterns in external events and develop long-range explanatory perspectives. Skeptical and independent, tend to have an aura of definite self-confidence.

    Me–INFJ: Seek meaning and connection in ideas, relationships, and the natural world. Want to understand what motivates people and are insightful about others, organized and decisive about implementing their ideas [decisive is not an adjective I'd use for myself though]. Private, intuitive, and complex by nature.

    Bryant, you should have Sam take the test and see if he’s an ENFJ: Warm, empathetic, responsible. Highly attuned to the emotions, needs, and motivations of others. Find potential in others, want to help them fulfill it. May act as a catalyst for individual and group growth. Provide inspiring leadership.

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