On Dichotomania

by MaryLena Bleile

The main axiom by which I live my life is as follows: Beauty is the dominant Eigenvalue and is the final end that I live for. Further, Beauty is achieved through balance. Why I believe these is kind of outside the scope of what I want to write about today, so I’ll just leave it at that. Rather, what I want to discuss is one of the obstacles to balance, which has far-reaching effects and which I think may be at the root of a lot of homophobic viewpoints.

This major challenge to achieving balance is the plethora of false dichotomies that are commonly accepted as truth. Logic and emotions, as previously mentioned, is one of them – as is the one that we try to impose, between mathematics and art. Mathematics is really just a formalized version of philosophy; a method of communicating ideas about the underlying phenomenon of the universe, of Existence, the essence of which is again, Beauty. So, too, is music a language; and using that language, art conveys profound truths about the world. Thus, art and math share the same common goal – and I would even go so far as to say they complement each other; all languages are inherently flawed, but when mathematics breaks down, we can turn to art for the answers and vice versa, like a way of piecing together the profile of beauty, like a Principal Components Analysis – and Beauty is best understood when one has a solid understanding of both.

Statistician Stephen Senn coined a term for the process of falsely dichotomizing continuous variables: Dichotomania. In his 2017 paper Statistical Errors in the Medical Literature, statistician David Harrell voices his affirmation for the existence of this phenomenon, and outlines several prominent examples where chopping up dichotomous variables like this in an effort to “simplify” them, has led to disastrous effects on statistical analyses in various papers – and not just any papers; articles where lives are potentially contingent on the results. Similarly, one of the major problems with modern statistics can be reduced to an example of dichotomania. A plethora of scientific papers are based on the blind acceptance or rejection of a hypothesis, purely based on whether this one continuous statistic, p, is greater or less than a particular value: a false dichotomy completely unfounded and arbitrary, with zero theoretical justification for the cutoff point, and often without a solid understanding of what the p-value actually represents.

Grant Sanderson, in his TedX talk on what compels people to engage with mathematics, calls out another false dichotomy: theory vs. application, or equivalently “wonder” vs “relevance.” I remember the moment I decided that I had to pursue mathematics; it was a pure “wonder” moment. Essentially, this happened when I saw a graphic that illustrated how we find the roots of x2 + 1 by introducing a new dimension of numbers; the complex plane.

And it blew my mind, like. whaaaaat there’s a whole other WORLD of new NUMBERS I just diDn’T knOW ABOUT???!??

And so it was.

It is interesting to note, however, that this beautiful subsection of mathematics dealing with imaginary numbers, is extremely useful for many applications; wonder and relevance are innately intertwined in math.

Of course the mathematics elitists would be very quick to jump on the fact that I am a statistician, and “Statistics isn’t math”. But honestly, I think that that is actually another great illustration of the malevolent phenomenon I’m trying to illustrate: the whole “is statistics math” question is irrelevant, since the field of mathematics does not have well-defined boundaries; the scale of math to science to engineering is continuous, and trying to forcibly impose a boundary like that, is an example of dichotomania. Statistics is in the ambiguous grey overlap area between math and science, and no amount of statistical apologetics nor mathematics gatekeeping will force it exclusively into one section or the other. It lives happily in the ambiguity, in harmony with measure-theoretic probability (the corresponding branch of pure mathematics on which statistics rests): measure theory is what infuses statistics with mesmerizing wonder, while statistics breathes a refreshing air of relevance and applicability to measure and probability theory and the way they intimately interlace is a profound expression of Beauty.

But of course, we hate that. Humans – particularly humans who work in STEM fields – can’t stand ambiguity, especially when we expect something to fit distinctly into one of two exclusive sets. This is clearly seen when one considers how often androgynous-presenting people get rude inquiries about what genitals they have. I believe dichotomania is also one of the reasons why there is such major resistance to the idea of sexuality and gender as a spectrum; we hate the ambiguity, and prefer when things fit into nice little boxes with labels.

I think this drives a good part of biphobia as well: the false dichotomy between attraction to men and attraction to women. I don’t even prefer to describe myself on the typical zero to 100 scale between “gay” and “straight”, because I don’t accept the idea that having a greater attraction to women implies having a lesser attraction to men; the two “opposing ends” of the scale aren’t opposites.

Humans like compartmentalizing things. We like chopping things up into neat little independent packages and trying to make the contents of each stay in their own lane. Things are neater, simpler, and less messy when they can be discretized – but life isn’t neat, or simple. It’s messy, confusing, and ambiguous… and beautiful that way.

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