# Sexuality explained through mathematics — a non-biased language approach

joão pestana

So you think you've got sexuality pretty much figured out, right? If you're born a male, you're attracted to women and the other way around. If you've ever had sex, it's not a big mystery and the mechanics are quite simple. Right? Think again. Biologists and psychologist are still working their way into figuring out how it all works out. What do I think I do better? Nothing at all, to be honest. I'll just try and use the language of mathematics not to explain how and why things are the way they are, but rather to give you a glimpse of how complex the whole subject is.

Maybe, just maybe, you're a somewhat open-minded person and you allow yourself to accept the concept of homosexuality. Great! Does it help? Well... Yes and no. It complicates things on my end, but it does take you a step closer to a fantastic member of modern society. But now that we can work with both heterosexual and homosexual men and women, we have much more ways we can arrange people. Both men and women can either be attracted to their own gender or the opposite one. This give us 4 different sets in which we can arrange people into (table 1).

 Man Woman Man Homosexual Heterosexual Woman Heterosexual Homosexual
Table 1 — Assigning men and women to each other in couples and grouping them into two different sets.

Now for the fun part — the mathematics, of course! Let m_i in M be some random male-born person and w_i in W be some random female-born person each belonging to the set of all Men and Women, respectively. We can thus arrange each m_i and w_i into couples (a tuple of length 2) such as (x_i,x_j) where x can either be m or w. We can define as homosexual any couple that is fully contained within just one of the larger sets M or W, that is (x_i,x_j) in W or M. An heterosexual couple can then be defined as any couple that is not fully contained within just one of the larger sets, but can only be contained by the union of both, that is (x_i,x_j) in M uu W.

What if some person is attracted to both genders? Should we allow for bisexuality? Of course, definitely! Let's do it. Let's fix the first member of the couple and keep the second one as undefined. Assuming that the order of the pair does not matter, we can define a bisexual man or woman as the first member of either (m_i,x_j) or (w_i,x_j) in M uu W. But isn't the constrain to a tuple of length 2 too strong? I guess we are mostly a monogamous species, but nonetheless, some people do find themselves as an element of a tuple with length larger than 2. Under such conditions, it is certain that whenever n > 2 two or more elements of the n-tuple has to be bisexual.

Let Q = (x_1,x_2,x_3,...,x_(n-1),x_n) be some n-tuple where n people are in a mutually consensual polygamous relationship such that x_i in M uu W. It should be obvious that at least two of the elements of the tuple must be bisexual. For example, we can have arrangements of 3 people in 2 different ways: (m,m,w) or (m,w,w), because the order doesn't matter and we have only two different possible elements to fill three positions. In the first situation, the men must be bisexual and in the second situation, the women must be bisexual. I'm excluding the all men and all women tuples deliberately, because they add no complexity to the analysis.

Of course, the subject of bisexuality is more complex then either homosexuality or heterosexuality. While some really have no preference over gender, there are some who do have a stronger inclination towards on. While sexual arousal is mostly set specific in men, with both heterosexual and homosexual men responding mainly to respectively female and male stimuli; women show no such preference which suggests a natural bisexual tendency as described by Chivers ML, Rieger G, Latty E, Bailey JM. A sex difference in the specificity of sexual arousal. Psychol Sci. 2004 Nov;15(11):736-44.

Maybe we can define a coefficient of bisexuality, say beta, and allow it to run all the way from 0 to 1, where 0 indicates heterosexuality, 0.5 perfect bisexuality and 1 homosexuality. The range where beta in (0,0.5) shall be called imperfect bisexuality with heterosexual inclination and the range beta in (0.5,1) shall be the imperfect bisexuality with homosexuality inclination. But how to calculate? Well... I don't believe it to be something that is easily measurable, so we must use some proxy. What about the relationship history of an individual? It might just work! Let's define the homosexuality counting function as:

pi_(x_i) (x_j) = {(1,if (x_i,x_j) in X),(0,text{otherwise}):}

Where pi_(x_i) counts in respect to person x_i and is 1 whenever x_i is paired with a x_j from the same larger set X which can either be M or W and 0 otherwise. Let's say we have H={x_1,x_2,x_3,...,x_(t-1),x_t} the ordered set of all people x_i has been in a relationship with (even if it was a one-time event) at time t and it can have any length N >= 0. Then, x_i's bisexuality coefficient is simply:

beta (x_i) = 1/N sum_(t=1)^N pi_(x_i) (x_t) and x_t in H

Or equivalently, it's simply the average of all x_t in X such that x_i in X. That is:

beta = text{all people of the same gender within the history} / text{all people within the history}

So what does all of this tell us? Absolutely nothing. Should we categorize people into distinct groups? Of course not! I just showed to you that bisexuality is a continuous function from 0 to 1 and thus cannot be split into finite groups unequivocally. Where along the line should you define the limits of each category? Why 0.32 and not 0.315?

Think we've got it all pretty much covered up? No. That's just half of it! What if you're a woman who is attracted to men? Are you heterosexual? Yes, you are. By our previously stated definition. But what if you were born with a male body? Does that make you homosexual? No, that's preposterous! In the same way that you as a person suffer zero change when you move from the inside of a Mercedes-Benz to a Tesla Motors vehicle, you suffer the same amount of change when you move from a male body into a female body and vice-versa: zero.

The body in which you are born, your sexual identity and your sexual orientation are completely different and independent things that have absolutely no influence over each other. Your body does not determine your sexual identity and even less influences your sexual preference. Your body is merely the vehicle that was assigned to you by default and sometimes mistakes do happen. Finally, I'd like to roughly quote John Oliver on this — "sexual identity is who you are, sexual orientation is whom you love."

Let's do some more mathematics! If we define theta = {XX,XY} as the property of your body, then it can assume only one of two values — even if you decide it should change at some point — XX for female and XY for male. Your sexual orientation can be determined by the bisexual coefficient beta. What about your sexual identity? Should we fall victims of Occam's Razor and define it can also — like your body — assume only one of two possible values? I'll do that only for mathematical simplicity, but explicitly state that it is seldom as simple as that. Let's just say that your sexual identity is omega={m,w}.

Using our previously defined variables, we are now ready to poorly classify a person using a 3-dimensional function P( theta , omega , beta ). This is a very strange and curious function, because two variables are discrete and one is continuous within the range from 0 to 1. Again, and only for the sake of the argument, let's say beta can be mapped into a discrete function in such a way that the limits 0 and 1 correspond to heterosexual preference and homosexual preference, respectively, leaving every other possible value to assume the value of no preference. Now, our P function can assume any of only 12 possible values. Because I believe a graph would be too confusing, I'll display these in table 2.

 Body (theta) Identity (omega) Preference (beta) P( theta , omega , beta ) XX w het heterosexual woman XX w hom homosexual woman XX w no bisexual woman XX m het heterosexual man XX m hom homosexual man XX m no bisexual man XY w het heterosexual woman XY w hom homosexual woman XY w no bisexual woman XY m het heterosexual man XY m hom homosexual man XY m no bisexual man
Table 2 — The possible values for P when mapped into a discrete domain.

The sole purpose of table 2 is to illustrate that no matter how you want to categorize people, in the end, the difference is negligible. I hope you are now capable of understand, by how ridiculous this article is, that you are only definable by your own identity and preferences. Your body has no influence whatsoever in the person that you are and is nothing but a mere shell for others to see and even that can now be changed. Sexuality is a complex issue and cannot and must not be expressed in a finite number of sets — that is, people are not categorizable. Every single person is unique and ever as interesting as the next one.

As a final note, for those of a more curious mind, you can search for terms like pansexuality, androphilia, gynephilia, ambiphilia and polysexuality. The way I see it is this: we'll create so many categories for people that, in the end, there is a category for every single one of us and then we abandon all categories, because we are already identifiable by other things — like our own name — that are singletons as well.