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!