Thinking like a Mathematician
Warning! Math-related post! Don’t let that scare you off! Math can actually be fun, and will help your reasoning abilities.
As I was wandering around the blogosphere, I stumbled upon an interesting article over at Michellalianna that has nothing to do with what I am going to write about. Well, nothing but the image that was used for the post. The image is in fact the featured image for this post. This picture bothers me. Not as an androsexual transwoman, but instead as a mathematician—in training. As a math-loving person, the notation bothers me. I think that the usage of the equals sign doesn’t make sense. So, I am going to argue that the proper subset notation should be used.
Some preliminary stuff first: I don’t disagree with the message of the picture; I simply think the notation is off. Clearly this post will have some math in it, but I will do my best to keep it simple, easy to understand, and informal.
Before I dive into why I think the proper subset notation should be used, let me give you some mathematical details on the two symbols. I am thinking in terms of set theory. A set is simply a collection of elements—like an array in programming or simply an unordered list. Now, a set A is a subset of the set B if and only if every element in A is an element of B, i.e. A is contained in B. In set theory we would denote this by , and read it as A is a subset of B. It’s important to note here that every set is subset of itself because every set contains itself. Now, two sets are equal if and only if , i.e. they both contain each other thus A=B. Lastly, A is a proper subset of B if and only if A is contained in B, but A != B. This is denoted in set theory as , and read as A is a proper subset of B. Easy enough, right?
Well, I am going to state my case mathematically, then I will use words to describe what I am talking about. Let P be the set of all human beings. Let G be the set of all sets of people that share a common trait, and let GP be in G and be equal to P. Let Ra denote a unary relation that produces the set of all civil rights related specifically to that set—how this looks, I have no idea.
Now, lets —this constrains X to only being groups in G—then . We want X to be equal to GP because then RX would contain everyone’s civil rights. In the case of the picture, X is the set of all trans people—as broadly speaking as possible—so, —while X is in G, it is not equal to GP which implies that RX isn’t equal to RGP. So, in order for the equals sign to make sense, the set on the left must be the human species, i.e. . Now, RGP contains everyone’s civil rights, thus —for every group g in G that is not equal to GP, g is a proper subset of GP which implies that Rg is a proper subset of RGP.
Did you skip that? It might make more sense after I give some explanation. In order for X rights—the rights of the set we are talking about—to be equal to civil rights, it needs to contain everyone. In the picture, X doesn’t contain everyone; it only contains trans people. Thus the equals sign should be a proper subset sign.
Realistically speaking, this isn’t important at all. The message of the picture is clear. It’s really about the perspective you are using. If you look at the image mathematically, then it’s invalid. If you instead look at it sociopolitically, then everything is in order. The math perspective is useful for skeptics because math improves one’s reasoning abilities. Skepticism and Math both require attention to detail, and biasless—okay, minimized bias—approaches to finding the truth.
P.S. While wordpress is supposed to support LaTeX out of the box, it’s not parsing it. If you would like a copy of the article, email me.