Wednesday, November 28, 2012

The mathematics of desire

(Originally posted by Pat on 6/22/10)

Or, using cognitive and social psychology to find a happy medium between fantasy romance and evolutionary reductionism
I've noticed that atheists and religious people have very different ideas about sex and romance. For the most part, I think atheist ideas are better. We aren't nearly as guilt-ridden about everything remotely sexual; we don't obsess as much over displays of body parts; we have more egalitarian attitudes toward women and LGBT people. Atheists are much more likely to admit that sex is good, it's part of who we are and what we do.
Yet there is a facet of atheist views on sex that I find troubling. This is the general tendency among atheists to either 1) treat sex as casual and meaningless or 2) reduce it to callous Darwinian calculations. The two often go together as well; if sex is just “mingling genes”, then what's the big deal? (I wasn't able to find any examples of this among prominent atheist bloggers, which is good to see; but I encounter it a lot in private interactions, and it's part of the sentiment of this Onion article—the Onion editors are clearly atheists, as you can see from any of their religion and science articles.)
I think this kind of thinking comes from an eagerness to reject everything of religious culture; in particular we want to reject religious norms of marriage and the pseudo-religious idea of a “soul mate” for each person. This is a healthy impulse—we should challenge religious norms and superstitious ideas wherever we find them—but we must also be careful not to let our proverbial infants be lost in their proverbial drainwater.
(NSFW warning: Mild. It's about sex, but not very explicit.)

What I really think most atheist discourse is missing is an understanding and acceptance of relationships, of the cognitive and social psychology of romantic experience. There is not enough consideration of what it means for two (or more) people to engage in an intimate relationship, and why that might in fact be desirable even if we were asexual organisms.
Of course humans are evolved animals, and so our sexuality must be such as natural selection has made it; but we must not presume, like most popular evolutionary psychology is wont to presume, that this means that heterosexual mate competition is the only experience of that sexuality.
For sex isn't just about mixing genes. It is about that, but it isn't just about that. Because we Homo sapiens are an intelligent, social species, a substantial proportion of our sexual activity has nothing to do with reproduction—and despite what religious people may think, this has always been true, long before “free love” or contraception. Fellatio was not invented in the 1970s; indeed, it its practiced by a number of different primates, and recently it was found in bats. Ethological accounts of why animals practice fellatio always say something about “couplings including fellatio lasted longer and were more likely to conceive offspring”; but why is that true?
I contend that it is because:
  1. Fellatio feels good, especially for the recipient.
  2. Males who receive fellatio in the course of mating enjoy the mating more and are more committed to the pairing, so they invest more in pleasing their partners in turn.
  3. Females realize this, and offer fellatio to secure their bonds with males.
Mutatis mutandis for other forms of non-reproductive sex, like cunnilingus and mutual masturbation. Hence, the essential force here is reciprocity, an inextricably social relation; hence, it's not surprising to me that the species with the most oral sex are also the species with the most reciprocal altruism. (We are by far on top in both categories, though in oral sex bonobos do offer some competition.)
Well, reciprocity is not dependent upon sexual anatomy. I can engage in reciprocal altruism with people of any anatomical configuration (though what kind of reciprocity I could engage in might be anatomy-dependent). Reciprocity is intrinsically bisexual—which is why bonobos are innately bisexual and I think humans are as well.
Why, then, don't friends exchange sexual favors? Well, sometimes they do. But typically they do not, and this too requires explanation. If sex is a primarily social act, why then are our social lives so much richer than our sex lives?
It could be that oppressive religious norms have made their mark upon our minds and society, and in a more liberated world we would be more sexual with our friends and acquaintances. No doubt this is to some extent true. As much as I'd like to think so, I haven't completely eradicated the stench of Catholicism from the far corners of my psyche.
But I think there is something more as well. Sex represents an extreme form of intimacy; in sex we make ourselves physically and emotionally vulnerable to an extent unmatched by really any other activity. As much as we might try to pretend that sex is just some casual activity that people occasionally do, it isn't—sex involves intense hormones, strong emotions, the exposure of our most vulnerable body parts, risks of injury and infection, and the revelation of our deepest, most private thoughts and desires. Sexual intercourse is the closest two bodies can possibly be to one another, and I would contend that is often the closest two minds can be as well.
Moreover, this is why I like sex—and I don't think I'm alone in that. I've had sex that wasn't intimate in this way, because we explicitly planned it out so that it would not be. We carefully closed as many channels of intimacy as possible—we don't get to know each other, we don't have much in common, we don't spend time together, we barely even talk. He shows up, we strip, I suck him, he sucks me, he leaves; I never see him again. That kind of sex approaches genuine casualness; but it's also incredibly unsatisfying. It's the kind of sex that leaves me thinking, “Why didn't I just masturbate? It would have been just as good and a lot easier.”
Yet the few times—all too few—I've had sex where I really felt an emotional connection, really felt intimate on a number of different levels, were the most wonderful experiences in my life. There were only three people with which I've had such experiences, and then only on a handful of occasions; but there was something beautiful about each occasion, and I expect to remember all three of these people for the rest of my life.
So why don't friends have sex? Because friendship is not quite the same level of intimacy that really makes for satisfying sex. It is comparable, which is why friends do sometimes become sexually involved; but it is not the same, which is why most don't and those who do find that it changes their relationship dramatically.
What of the idealistic romantic concept of “soul mates”? Isn't it silly to think that there is one person out there, the perfect one for you?
In so many words, yes. But in fact there are good reasons to think that something like that really does exist, at least for most people in most circumstances.
The universe is not run by a central planning agency; no unified authority regulates your chromosomes at birth to ensure that you have a perfect match somewhere. You have some degree of compatibility and incompatibility to everyone else in the world, and the challenge of dating lies in finding the most compatible person you can. You desire certain people, certain people desire you; the trick is making the two line up.
Indeed, this desirability is multidimensional—what you need in a friend is not necessarily what you need in a lover, which is not necessarily what you need in a lifelong partner, and each these in turn may be time-dependent or circumstance-dependent. But I do think there is a strong correlation (I'm certainly more likely to be attracted to someone I actually like as a person), and not too much change over time or circumstances, so for now let's presume that we can express romantic compatibility in a single constant value. WOLOGIMBAT this number ranges from 0 (completely incompatible) to 1 (completely compatible).
Now, it should be apparent that different people have different desirability metrics, and furthermore that these metrics are not symmetric. Someone could be the very apotheosis of my desire and nonetheless have no interest in me at all; or conversely someone could be very strongly attracted to me while I am only interested in them on a platonic level.
Presume that the human population is finite (so far, so good). Presume that for any given person, everyone else in the world has a well-defined desirability value (seems plausible, if accept that we don't actually know these values a priori). Then, it follows from the well-ordering of the real numbers that:
  1. There is a person who is most desirable to you
  2. There is a person for whom you are most desirable
  3. There is a person for whom the product of your mutual desirability is maximal
So, is there a soul mate after all? No... because, unfortunately, there is no reason to think that these three properties describe the same person. Indeed, in the general case they are most likely to be completely different people.
For instance, consider this simple population of 4 individuals, A, B, C, and D, and their respective desirability matrix (the diagonal is 0 because masturbation isn't as fun as sex):
Consider the situation for A:
The most desirable mate for A is D—f(A,D) = 1.
The mate who most desires A is C—f(C,A) = 1.
The mate with the highest product of mutual desirability for A is B—f(A,B)*f(B,A) = 0.25.
So, what should A do? It's hard to say. Maybe it depends whether A most values being with a desirable mate (choose D), being desired (choose C), or having equal mutual compatibility (choose B).
It gets worse. It is possible for the preferences in the system to be intransitive, resulting in what are essentially voter paradoxes. Suppose there are only three people, and their compatibility matrix looks like this:
There are three possible arrangements, presuming monogamy:
A and B can pair, leaving C alone; call this AB,C.
B and C can pair, leaving A alone; call this A,BC.
Finally, A and C can pair, leaving B alone; call this AC,B.
The preferences look like this:
A: AB,C > AC,B > A,BC
B: A,BC > AB,C > AC,B
C: AC,B > A,BC > AB,C
This is isomorphic to Condorcet's paradox, which is easier to see if we write it this way:
AB,C = X
AC,B = Y
A,BC = Z
A: X > Y > Z
B: Z > X > Y
C: Y > Z > X
Suppose we choose X. Then it seems we should have chosen Z, because 2/3 of people prefer Z > X.
So now, we choose Z. Then we should have chosen Y, because 2/3 of people prefer Y > Z.
What if we instead choose Y? We should have chosen X, because 2/3 of people prefer X > Y!
Now, what if we allow polyamory? Doesn't that solve the problem? Not really.
If it were really possible to love n people as much as you love 1 person, for all n (or at least for relatively large n), then polyamory would solve the problem—the optimal result comes when everyone just sleeps with everyone in a mass kibbutz-orgy. (Or if sex with some people is so bad it's worse than no sex at all, then you just don't have sex with those people and have sex with everyone else.)
But because in real life adding another partner forces you to divert time and energy away from other partners, polyamory doesn't resolve the paradox—it only compounds it. Sometimes it might produce the best outcome, depending on the specifics of the cost-benefit function for each partner, but often it won't. Each of the partners you already have would prefer you not add any more, but each of the people who isn't your partner wants you to add them. Sometimes adding another partner will make you yourself happier, but not always. The conflict between these interests is inevitable, and at some point you'll have to decide how to weigh them against each other.
It turns out dating is as complicated as we always feared!
There is good news, however. We don't live in the general case. The specific features of our real situation actually give us reason to hope.
In real life, there are two primary components to desirability, objective value and compatibility.
Objective value is basically evolutionary value; it includes the things that pretty much everyone wants, like good health, a sexy body, well-endowed sex characteristics, intelligence, wealth, status. Brad Pitt and Angelina Jolie have very high objective value.
Compatibility, on the other hand, is based on how similar someone is to you, what you have in common, how your tastes and personality traits mesh with theirs. It's not quite the same as similarity, since for instance a straight man wants a straight woman, a top wants a bottom; but in general it is a symmetric relation—if I am compatible with you, you are compatible with me.
Desirability can be taken as a sum of these two:
D = O + C
The desirability matrix, then, is the sum of an objective component and a symmetric component.
The objective component would look like this:
A and B have high objective value, so they get 0.5 across the board.
C and D have low objective value, so they get 0.2 across the board.
The symmetric component would look quite different however:
A is much like B and C is much like D, so the compatibility scores reflect this. (C is much like C, etc., but like I said, sex is more fun than masturbation.)
Summing these two gives the following desirability matrix:
A0.5+0.0 = 0.50.5+0.5 = 1.00.2+0.1 = 0.30.2+0.1=0.3
B0.5+0.5 = 1.00.5+0.0 = 0.50.2+0.1 = 0.30.2+0.1=0.3
C0.5+0.1 = 0.60.5+0.1 = 0.60.2+0.0 = 0.20.2+0.5=0.7
D0.5+0.1 = 0.60.5+0.1 = 0.60.2+0.5 = 0.70.2+0 = 0.3
To clean that up in case it's not obvious:
Now the answer is obvious:
A's best choice is B, and B's best choice is A, so A and B should be together.
C's best choice is D, and D's best choice is C, so C and D should be together.
In evolution this is called positive assortment; like mates with like.
But more importantly, everyone wins! Perhaps there are soul mates after all!
Of course, reality is much more complicated than this simple example. So, as I started by saying, the answer is somewhere in between.
There are additional considerations besides objective value and compatibility, though those are the two primary factors. Even with just these two components it can happen that (say) D is so objectively undesirable, that C would still be better off with A, even though A and C aren't very compatible. Given the vicissitudes of attractionality, it could turn out that C wants D but D doesn't want C. And even when two people are compatible, other factors can prevent a relationship from working out.
Moreover, if you allow polyamory, there is a cost-benefit analysis to be done in each case for each person—essentially, is this new person so desirable and compatible that it is worth adding them to the mix even though it takes time away from my other partners?—and this is a relation that can be expected to typically assort positively as well. But it won't always, and again we need conflict resolution.
Yeah, it's complicated. Often, it doesn't work out. But I have gone through all of these mathematical machinations to make the following central point: It's not unreasonable to think that there is a best person for you.
It would be unreasonable to think that there is a perfect person for you—no one is perfect. It would be unreasonable to think that you will be able to accurately gauge your compatibility with a single glance—there is so much you need to know, it will take months if not years of a relationship to discern your real compatibility. It would be unreasonable to think that you will automatically meet your soul mate and never have to work at building or maintaining a relationship—there is no central planning of the universe to allow such things.
Yet it is not unreasonable to think that there is in fact someone, somewhere in the world, who is the best choice for you—and furthermore, it is not unreasonable to think that you will be the best choice for them as well. With high probability, we can predict that your match is out there somewhere. Moreover, you needn't search the whole world, because compatibility is in large part made of similarity, and the kind of people you spend a lot of time with, your friends, colleagues, co-workers, acquaintances, are likely to be quite similar to you.

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