Oh, they were looking for their Missing Piece

There are a few biological arguments for why you’d expect people to have somewhat idiosyncratic preferences in their ideal mate. An evolutionarily stable behavioral equilibrium might be more likely to be a mixed strategy rather than a pure strategy, involving “different strokes for different folks” coexisting in some stable ratio. A social or ecological environment might have multiple niches that different behaviors, personality types, or physical forms might fill better or worse.

A third argument is analogous to the idea that people might prefer individuals with more dissimilar immune systems, but is a bit more general and depends on slightly different reasoning, so I thought I’d write it down. The idea is that, under conditions of stabilizing selection, a single value for certain traits is preferred, and importantly , this value is not at the extreme of the distribution of traits. (In the words of one influential paper, “Attractive Faces are Only Average;averaging thousands of people’s faces tends to make more attractive composites– the same thing applies to traits other than facial characteristics.)


So, let’s imagine a population of individuals who have a distribution of two traits, x and y, around some ideal value for each- everybody has some error, and nobody’s perfect (each blue dot represents a given person’s trait values) :


Assuming that the value of an offspring’s trait are determined by averaging the value of both parents and then adding some random error due to mutation or developmental noise, the ideal mate for each individual in the population isn’t the one that is closest to the ideal value, but one that is “complementary”- ie, equally distant from the ideal value, but from the opposite side (blue dots represent individuals’ traits, red dots represent their ‘ideal complement’):


If everyone could find their ideal complement, their offspring (green dots below) would be significantly closer to the ideal value than the two parents are:


The interesting thing about this argument is that it only applies in situations of stabilizing selection. In situations of directional selection, in which trait values at the extreme of the distribution are favored, suddenly everybody’s “ideal mate” can be the same person.You can still imagine various kinds of algorithms that allow people to pair off successfully; I think OKCupid and other dating sites actually use some of these algorithms explicitly. But the pairings are intrinsically  less stable in a directional selection model, since individuals are incentivized to defect to find a “higher-value” mate rather than stick with their individual complement.


Human societies have obviously always been a long way from ideally monogamous, but it remains interesting that we are so much more monogamous than most other mammals, let alone our closest relatives the chimpanzees, who are almost entirely promiscuous. Human dads may not often live up to the high standards of say, penguins or other pair-bonded birds, but we’re a helluva lot better than pretty much any other primate.  In the Symbolic Species, Terrence Deacon hypothesizes that conceptualizing and keeping track of pair bonds in hominid communities may have been an inducement to the development of complex symbolic thinking and language; it’s not entirely convincing, though to me it’s more convincing than Geoffrey Miller’s argument that there was direct selection for intelligence as a kind of “Peacock’s Tail.” There’s obviously been some evolution for greater monogamy (we have lower sperm and white blood cell counts than truly promiscuous species, for instance), even as genetic evidence suggests a great degree of historical volatility in male survival and reproductive success. Could there be some historical switches between unstable equilibria of directional selection, which disfavors monogamy, and then back to stabilizing selection which favors it?

There are of course lots of literary versions of the idea of love and pair-bonding as a matter of complementary characteristics.  Shel Silverstein more-or-less rejects the idea of love as completion in his downbeat 70s children’s book The Missing Piecewhile the character of the playwright Aristophanes tells a sunnier version of it in Plato’s Symposium:

Aristophanes professed to open another vein of discourse; he had a mind to praise Love in another way, unlike that of either Pausanias or Eryximachus. Mankind, he said, judging by their neglect of him, have never, as I think, at all understood the power of Love. For if they had understood him they would surely have built noble temples and altars, and offered solemn sacrifices in his honour; but this is not done, and most certainly ought to be done: since of all the gods he is the best friend of men, the helper and the healer of the ills which are the great impediment to the happiness of the race. I will try to describe his power to you, and you shall teach the rest of the world what I am teaching you.

In the first place, let me treat of the nature of man and what has happened to it. The original human nature was not like the present, but different. The sexes were not two as they are now, but originally three in number; there was man, woman, and the union of the two, of which the name survives but nothing else. Once it was a distinct kind, with a bodily shape and a name of its own, constituted by the union of the male and the female: but now only the word ‘androgynous’ is preserved, and that as a term of reproach.

In the second place, the primeval man was round, his back and sides forming a circle; and he had four hands and the same number of feet, one head with two faces, looking opposite ways, set on a round neck and precisely alike; also four ears, two privy members, and the remainder to correspond. He could walk upright as men now do, backwards or forwards as he pleased, and he could also roll over and over at a great pace, turning on his four hands and four feet, eight in all, like tumblers going over and over with their legs in the air; this was when he wanted to run fast.

Now the sexes were three, and such as I have described them; because the sun, moon, and earth are three; and the man was originally the child of the sun, the woman of the earth, and the man-woman of the moon, which is made up of sun and earth, and they were all round and moved round and round because they resembled their parents. Terrible was their might and strength, and the thoughts of their hearts were great, and they made an attack upon the gods; of them is told the tale of Otys and Ephialtes who, as Homer says, attempted to scale heaven, and would have laid hands upon the gods.

Doubt reigned in the celestial councils. Should they kill them and annihilate the race with thunderbolts, as they had done the giants, then there would be an end of the sacrifices and worship which men offered to them; but, on the other hand, the gods could not suffer their insolence to be unrestrained. At last, after a good deal of reflection, Zeus discovered a way.

He said: ‘Methinks I have a plan which will enfeeble their strength and so extinguish their turbulence; men shall continue to exist, but I will cut them in two and then they will be diminished in strength and increased in numbers; this will have the advantage of making them more profitable to us. They shall walk upright on two legs, and if they continue insolent and will not be quiet, I will split them again and they shall hop about on a single leg.’

He spoke and cut men in two, like a sorb-apple which is halved for pickling, or as you might divide an egg with a hair; and as he cut them one after another, he bade Apollo give the face and the half of the neck a turn in order that man might contemplate the section of himself: he would thus learn a lesson of humility. Apollo was also bidden to heal their wounds and compose their forms. So he gave a turn to the face and pulled the skin from the sides all over that which in our language is called the belly, like the purses which draw tight, and he made one mouth at the centre, which he fastened in a knot (the same which is called the navel); he also moulded the breast and took out most of the wrinkles, much as a shoemaker might smooth leather upon a last; he left a few, however, in the region of the belly and navel, as a memorial of the primeval state.

After the division the two parts of man, each desiring his other half, came together, and throwing their arms about one another, entwined in mutual embraces, longing to grow into one, they began to die from hunger and self-neglect, because they did not like to do anything apart; and when one of the halves died and the other survived, the survivor sought another mate, man or woman as we call them,–being the sections of entire men or women,–and clung to that.

Thus they were being destroyed, when Zeus in pity invented a new plan: he turned the parts of generation round to the front, for this had not been always their position, and they sowed the seed no longer as hitherto like grasshoppers in the ground, but in one another; and after the transposition the male generated in the female in order that by the mutual embraces of man and woman they might breed, and the race might continue; or if man came to man they might be satisfied, and rest, and go their ways to the business of life. So ancient is the desire of one another which is implanted in us, reuniting our original nature, seeking to make one of two, and to heal the state of man.

Each of us when separated, having one side only, like a flat fish, is but the tally-half of a man, and he is always looking for his other half. Men who are a section of that double nature which was once called androgynous are lovers of women; adulterers are generally of this breed, and also adulterous women who lust after men. The women who are a section of the woman do not care for men, but have female attachments; the female companions are of this sort. But they who are a section of the male follow the male, and while they are young, being slices of the original man, they have affection for men and embrace them, and these are the best of boys and youths, because they have the most manly nature.

Some indeed assert that they are shameless, but this is not true; for they do not act thus from any want of shame, but because they are valiant and manly, and have a manly countenance, and they embrace that which is like them. And these when they grow up become our statesmen, and these only, which is a great proof of the truth of what I am saying. When they reach manhood they are lovers of youth, and are not naturally inclined to marry or beget children,–if at all, they do so only in obedience to custom; but they are satisfied if they may be allowed to live with one another unwedded;

And such a nature is prone to love and ready to return love, always embracing that which is akin to him. And when one of them meets with his other half, the actual half of himself, whether he be a lover of youth or a lover of another sort, the pair are lost in an amazement of love and friendship and intimacy, and one will not be out of the other’s sight, as I may say, even for a moment: these are the people who pass their whole lives together, and yet they could not explain what they desire of one another. For the intense yearning which each of them has towards the other does not appear to be the desire of lover’s intercourse, but of something else which the soul of either evidently desires and cannot tell, and of which she has only a dark and doubtful presentiment.

Suppose Hephaestus, with his instruments, to come to the pair who are lying side by side and to say to them, ‘What do you mortals want of one another?’

They would be unable to explain. And suppose further, that when he saw their perplexity he said: ‘Do you desire to be wholly one; always day and night in one another’s company? for if this is what you desire, I am ready to melt and fuse you together, so that being two you shall become one, and while you live live a common life as if you were a single man, and after your death in the world below still be one departed soul, instead of two–I ask whether this is what you lovingly desire and whether you are satisfied to attain this?’–

There is not a man of them who when he heard the proposal would deny or would not acknowledge that this meeting and melting into one another, this becoming one instead of two, was the very expression of his ancient need.

And the reason is that human nature was originally one and we were a whole, and the desire and pursuit of the whole is called love. There was a time, I say, when we were one, but now because of the wickedness of mankind God has dispersed us, as the Arcadians were dispersed into villages by the Lacedaemonians. And if we are not obedient to the gods, there is a danger that we shall be split up again and go about in basso-relievo, like the profile figures showing only one half the nose which are sculptured on monuments, and that we shall be like tallies. Wherefore let us exhort all men to piety in all things, that we may avoid evil and obtain the good, taking Love for our leader and commander.

Let no one oppose him–he is the enemy of the gods who opposes him. For if we are friends of God and at peace with him we shall find our own true loves, which rarely happens in this world at present. I am serious, and therefore I must beg Eryximachus not to make fun or to find any allusion in what I am saying to Pausanias and Agathon, who, as I suspect, are both of the manly nature, and belong to the class which I have been describing. But my words have a wider application–they include men and women everywhere; and I believe that if our loves were perfectly accomplished, and each one returning to his primeval nature had his original true love, then our race would be happy. And if this would be best of all, the best in the next degree must in present circumstances be the nearest approach to such a union; and that will be the attainment of a congenial love.

Wherefore, if we would praise him who has given to us the benefit, we must praise the god Love, who is our greatest benefactor, both leading us in this life back to our own nature, and giving us high hopes for the future, for he promises that if we are pious, he will restore us to our original state, and heal us and make us happy and blessed.

This, Eryximachus, is my discourse of love, which, although different to yours, I must beg you to leave unassailed by the shafts of your ridicule, in order that each may have his turn; each, or rather either, for Agathon and Socrates are the only ones left.

2 thoughts on “Oh, they were looking for their Missing Piece

  1. The whole thing reads as an apologia for gay men at this juncture (having the most manly nature and so on)–think maybe Plato was getting heat for being gay and made up this story?


    1. If by whole thing you mean the whole Symposium, I think I agree, and that struck me when I first read it- that Aristophanes’s speech naturalized heterosexual love in a way that is at odds with the rest of the dialogue. It’s also interesting that Aristophanes appears elsewhere (e.g., in the Apologia) as an antagonist of Socrates and here is an amicable friend.


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