# Weirdness.

In general, is being “strange” a good thing or a bad thing?

Math is going to have a hard time answering this because those terms are hard to quantify, but we can avoid the problem by making loads of unwarranted assumptions.

Start by assuming that all characteristics can be ranked. You don’t have to actually describe a scale from one to ten or anything, just as long as it’s possible to say that one person is more [adjective] than another. You’d end up with one line like that for every characteristic, and a finite (but, if you want to describe everyone perfectly, very large) number of lines.

This assumption is pretty plausible. And people do it in the real world, too. The Myers-Briggs test is one example: They pick four lines (Introvert-Extrovert, iNtuitive-Sensing, Thinking-Feeling, Judging-Perceiving) and assign everyone a number on each one. So they could describe your personality in four numbers. Of course, if they wanted to be more precise they’d have to use more. eHarmony uses twenty-nine core traits, which is mathematically interesting if you like being a point in 29-dimensional personspace.

Also assume that where everyone falls on those axes is a normal distribution. (That was the plural of axis. The other interpretation of the sentence would be rather more painful.) There’s really no reason to assume that each individual’s numbers follow any particular distribution, but thanks to the central limit theorem we get to pretend the distributions for humanity in general are normal and there are enough people that we’ll be really close to right. Can I just get three cheers for math? No? OK then.

Now, strange just means far enough from average. (Someone needs to update Google’s dictionary. I asked it to “define: weird” and…well, it hasn’t had anything to do with fate for at least a couple hundred years, has it?) I’m going to arbitrarily say that “far enough” means “one standard deviation,” just because I have to pick a number. If that’s a good number, then for any given characteristic X, about 16% (15.865, if you insist) of everyone would be unusually X and 16% would be unusually not-X.

Using the Myers-Briggs example,¹ 16% of people would be unusually introverted, another 16% would be unusually extroverted, and so on. Most people would be “weird” in at least one way, which fits real life pretty well.

If you assume that the characteristics are independent (they’re not) then 78% of the population could correctly be called strange in one way or another. (Actually less, because they’re not independent so anyone who is unusually Introverted is probably also unusually Thinking, and stuff like that leads to double-counting.)

Calculating the total amount of strangeness could be done² and then you get to determine whether someone is strange enough that that is itself strange, or even normal enough that it’s weird. And that would be fun.

So the question is whether being weird is usually a good thing or a bad thing. Math can’t answer that one directly, not unless you already know the best possible values of each character trait. (Legend tells of one man who did. After learning calculus from Aristotle, he interviewed the entire population of Earth, described everybody in terms of a bunch of scales from one to ten, and ranked everybody from best to worst. Then he spent the rest of his life trying to be exactly as adjective as the World’s Best Person for every possible adjective, and he was naturally completely miserable.)

Instead of ending up like that guy, I’m just going to assume that there is some optimal point and not worry about where it is. This probably isn’t true,³ but if it’s not then my usual approach becomes useless. Anyway, whoever that fictional philosopher would have ranked as the World’s Best Person* is probably going to be strange. Just in terms of the probabilities, he has almost a 78% chance of being unusual on at least one of the MBTI four dimensions, and if you use 29 then that number jumps to 99.998%. To actually describe a personality completely, you’re probably going to need a lot more than 29. Most people are going to be pretty far from wherever he is in 29-dimensional personspace (I really like that phrase) and if you want to be as awesome as he is, you’re going to have to be weird.

But even if weirdness is a prerequisite for being the World’s Best Person, that doesn’t mean it’s good in general. If someone is completely average in every way, you know they can function perfectly in society and stuff, and they are more or less the definition of adequate. They’ll be fine. If you have no information about someone other than the fact that they’re strange, you probably don’t think, “He’s probably the World’s Best Person!” There are a lot more ways to go wrong than right. (When Aristotle said this he was talking about 1870s Russian families, but it generalizes pretty well.)

This is why I can’t automatically take being called weird as a compliment: it is probably a bad thing. If it’s followed up with “weird, in a good way” then it actually is a compliment. (This separates it from most generally bad things you can say about someone. “An axe murderer…in a good way” just doesn’t work.)

So in conclusion, weirdness is not usually a positive trait. It can be (if you think the majority is just wrong, then you definitely don’t want to be normal), but those are exceptions. But don’t let that stop you.

¹The problem with this example is, surprisingly, not the fact that half the numbers are arbitrary. Well, not the main problem. The main problem is that the MBTI doesn’t collect enough of the information you’d need to declare someone to be strange. Maybe the eHarmony descriptors do, but I don’t actually know what their Core TraitsTM are.

²[√(Σ(Cii)]. I kind of cheated by defining “strange” as “strange along any of n dimensions.” The better number would be to look at the distance in n-dimensional personspace (Yay!) and see if that’s within one standard deviation for the population, since that doesn’t depend so much on how many characteristics you measure. That’s where this comes in.

³I’m definitely not saying this is true globally, but it could plausibly be true locally. Like, if you’re already extremely I, N, and J, and evenly split between T and F, then it’s probably better* to be more T.

*References to ranking people from best to worst are not meant to be taken seriously. Egalitarians, please don’t eat me.

## 4 thoughts on “Weirdness.”

1. Montague

I’m pretty sure personality tests assume egality is idiocy, if egality means treating everyone as if they were the same, or that all people can do all things alike. On that note of “best person” do you have any thoughts, as a Mathematician, on the Medieval idea of the hierarchy of being and the “golden chain” (okay, so that’s renaissance as well). Or rather, your thoughts on Christian/Platonic idealism as it relates to Mathematics?

1. comparativelysuperlative Post author

If you mean the belief that math is abstract and doesn’t do anything causally, then I’d agree. Math is a bunch of a priori statements that A follows from B that are true no matter what. The universe also runs on math, which is really cool, but that’s a property of the universe not the math.

I’ve never been a fan of the great chain of being, just because for the chain metaphor to make sense there has to be a finite distance between any two points. And I don’t think that’s right. It makes sense for reductionists, of the “given enough time, hydrogen will start to wonder where it came from” variety, (of course, then they have to define “superior” and that has separate issues) but I have no problem saying that I am qualitatively different from an amoeba, just like I have no problem saying that an infinite being is qualitatively different from a human. It’s less like far apart on one hierarchy and more like being on completely different planes. No matter how far you increase along a bounded sequence (and humans are still bounded, unfortunately), you’ll never get to be God. And the World’s Best Amoeba is still an amoeba.

If you look at the tiny sliver of the great chain of being involving humans, then you can have an optimum point for best human and it’s a nice monotonic function of rank. The king at the top, then the nobles below him, and so on. Mathematically it’s unlikely that it’s a single-variable function, but I’m less concerned with that than with the political and philosophical problems. Seriously, rank? At least it’s relatively simple to optimize. If you leave out the original formulation of who gets to be on top, then it’s just saying that there exists some ordering of all people from best to worst. At least then we get to do math.

As for equality, it doesn’t require that everyone’s the same. We do have four axes to measure them on, after all (or 29, or whatever other number). The strongest egalitarian claim would be that the function of how valuable a person is is constant with respect to their position on those other axes. Exactly what definition of valuable is being used is up for debate. Claiming that they’re all at identical points on those axes would just be empirically wrong.

2. 27cha

Perhaps all the people who are weird in extremely horrible ways are already dead.

Also, perhaps weirdness in a population is not distributed randomly between all a person’s traits. It might cluster in various ways – everyone is essentially average in areas X, Y, Z, while in areas A, B, C there are a few people who stand very far away from the norm.

I think your analysis holds up overall, just adding some extra complications.

3. Isaac

It’s worth noting that the MBTI scores for each type measure the clarity of that type; not the strength of that type. Someone who scores highly as an Extravert (which is the correct spelling when talking about the MBTI) is not necessarily extremely extraverted, they are very clearly and extravert.

They may be 1.087975% more extraverted than introverted, and have a higher score than someone, who at any given time, is between -12% and 357% more extraverted than introverted.