Love Is Not a Metric Space

Here's the promise, stated as fairly as I can, because the talk depends on taking it seriously. Describe yourself in enough detail. Get enough other people to do the same. Build a good enough matching function. Then the right person for you is a query away.

That's not a stupid idea. It's a very good idea, built by very good engineers, and for a lot of problems it works. It finds you a song, a restaurant, a used car. So I'm going to grant them everything: the data, the scale, the algorithms, the good intentions. And then we're going to watch the idea fail anyway, on its own terms, on one person.

This is Sam. Thirty-four. Climbs, reads, gets up early. Interested in men and women. One line on the card, written at eleven at night, about wanting someone who laughs at the wrong moment. Sam filled out the long questionnaire honestly, which is more than most people manage.

On the left is Sam the way you'd see them in the app. On the right is Sam the way the app sees them: the same person as a column of numbers, one per attribute. That column is called a feature vector, and what that means is worth a beat, because the whole talk lives in the next two pictures.

Take two of Sam's numbers: age, and the score the app gave them for dark humour. Age along the bottom, humour up the side, and Sam becomes a point. Every other profile becomes a point too. And the moment they're points, you can measure between them. That dashed line is a ruler on the plane, from Sam to the nearest other profile. "Who is most like Sam" has just become "which point is closest," and closeness is a number. That's the entire trick.

Add a third number, how far they live from family, and the plane becomes a space. Same people, same Sam, and the ruler still works. Now add a fourth axis. You can't draw it, and neither can I, but the arithmetic doesn't care. Add the other few hundred questions, one axis each. That's a feature space: one axis per attribute, one point per person, and a ruler that works in any number of dimensions. Matching is geometry. Find the points nearest Sam's and show them to Sam in order.

So there are two ways to meet someone, and you'll see both tonight. One is the query: describe yourself, describe what you want, let the system find the nearest point. The other is a room. A climbing gym at six in the morning. A reading group for a book nobody's heard of. A weird party. A room full of people who came for the same strange reason, where nobody has been ranked. Keep the weird party in your pocket. Sam spent a year on the query first.

Here's the claim, and what it isn't comes first. It isn't that compatibility can't be measured. Recommender systems measure the fit between two things every day, and you have a playlist that proves it. The claim is narrower. Compatibility isn't a distance. A distance weighs every feature the same way for everyone. Compatibility doesn't: the weight on every feature changes with who's at the other end. And a quantity that changes its weights with the pair doesn't add up across people. You can't get from "Sam fits B" and "B is like C" to "Sam fits C." Compatibility doesn't triangulate. That's the talk.

Sam's first match came with a number next to it. Ninety-seven percent. A woman, a few years younger, who had also filled the whole thing out honestly. They met for a drink. She was pleasant. Sam was pleasant. They agreed about everything the questionnaire had said they'd agree about, and by the second drink they had run out of it. She was a stranger at the table, and she stayed one.

What was the ninety-seven? One ruler, for everyone. The app had weighted the questions once, the same way for every pair in the city, and the weights that dominated were the big numbers: miles from Sam's apartment, a politics question with a wide scale. Those were never Sam's weights with her. They were nobody's weights with anybody. They were the questionnaire's.

And you've felt this, if you've used one of these. The top match who turns out to be, as far as you can tell, a random person. That isn't a bug you happened to hit. That's one ruler for everyone, doing exactly what it was built to do, on a question it was never built for.

Some of you have been waiting to say something, so I'll say it for you. Fine. Nobody serious uses a ruler off the shelf. You learn the metric. Take every pair that matched and every pair that didn't, and train a model to weight the questions so the ones that mattered count. That's what recommenders do, and every graduate student learns it in the first year.

And you're right, and it deserves granting properly, because it's the strongest thing on the other side. Recommenders find compatibility every day: not a property of you, a fit between you and a thing. They do it with one move. If you liked B, and B resembles C, you'll probably like C. That step is the whole engine, and it works because taste transfers. Your taste in films is roughly one thing, carried from film to film. Granted, completely, for films.

The question is whether the step transfers to people. Which brings us to Sam's second date.

The app ranked him low. He'd answered three heavily weighted questions the wrong way: he doesn't get up early, he doesn't climb, and he wants to live near his family. Sam went because the restaurant was near the gym.

He was four minutes late and said so without apologizing twice. He noticed the waiter was having a bad night and made it easier. There was a silence, a minute in, that should have been awkward and wasn't. And he laughed at the wrong moment, which is the one thing Sam had actually asked for, and the questionnaire had no way to ask about.

Here's the part that matters for the engineers. Wanting to live near your family had been, for Sam, a dealbreaker with someone else. With him it was the point. The same answer, the opposite weight. The weight didn't belong to Sam and it didn't belong to him. It belonged to the pair.

That's the turn. Learning the metric means learning one set of weights: which questions matter, for everyone, once. Maybe one set per person, if you're careful. But the second date says the weight on "lives near family" wasn't Sam's and wasn't his. There's no single metric to learn, because there's no single ruler. The ruler is different on every line between two people.

This is the picture the whole argument rests on. Three people: Sam, B, and C. On the left, one ruler for everyone. Sam is two from B, B is two from C, so Sam can't be more than four from C, and here they're three. The sides add up. That's what a distance is: a near neighbor of a near neighbor is near. That's the recommender's step, and on the left it's legal.

On the right, the same three people, but each pair measured with its own weights, because that's what the second date showed. Sam to B, two. B to C, two. Sam to C, under that pair's weights, nine. The sides don't add up. No triangle closes. "Sam fits B and B is like C" tells you nothing about Sam and C, because the ruler that measured Sam and C isn't the ruler that measured the other two sides. Compatibility doesn't triangulate. This is the picture of it.

The engineers are already thinking: fine, learn a weight per pair. Two things stop you. The pair space is n squared: a city's worth of people is a city's worth of people squared in pairs, and the data on each pair is at most one date, usually none. You can learn one ruler from a million matches. You can't learn a million rulers from one date each.

And the data you do have is the wrong data. The model trains on what people tapped, a two-second decision with a thumb. Sam's second date never got logged; the app has no field for "the silence was fine." A match that works, two people who meet and delete the app, is a lost user. Twice.

Compatibility doesn't triangulate, and no amount of data makes it. That's why the rebuttal, which is right about everything it says, is aimed at the wrong problem.

This next frame isn't mine. Iain McGilchrist, a psychiatrist and philosopher, published The Master and His Emissary in 2009 with Yale University Press. The book is about a good deal more than dating apps. I'm borrowing one frame and nothing more, and I'm not making claims about your brain.

The frame: two modes of attention, and we need both. One isolates a thing, takes it apart, and re-presents it as a model. The other attends to the whole, to what's between people. The first is the emissary: powerful, useful, meant to serve. The second is the master. The trouble starts when the emissary decides it's in charge.

A profile is a re-presentation. Turning Sam into that column is the emissary's move, and it's a good move; it built medicine and bridges. The usurpation isn't that we abstract. It's that we mistake the map for the territory and optimize against the map. We ask the column what only the table could tell us, and when the column answers, because a model always answers, we believe it, because it came with a number. Ninety-seven.

Go back to the second date and try to put it on the form. Timing. How he treated the waiter. Whether the silence was fine. The laugh at the wrong moment. Now write the questions. "Treats waiters well: yes." "Silence: comfortable." You can hear that it's absurd. These aren't missing features waiting for a better questionnaire. They're properties of the whole encounter. They exist at the level of two people at a table, and nowhere else. He doesn't have "good timing" in a drawer at home. It happened, in front of Sam, or it didn't.

That's where the weights come from. The weight on "lives near family" was set by things that were never in the schema, and some of them didn't exist before the two of them sat down. Sam said the honest answer to about a third of the questionnaire was "it depends on who's asking," and there was no box for that. "It depends on who's asking" is a weight that changes with the pair. That answer is the whole talk.

The weights were never in the column, so Sam was never in the column. That's not a complaint about the column. It's just where Sam wasn't.

One more thing before the party, and it isn't a prediction; you watched it happen. The apps mostly abandoned the questionnaire. What replaced it was the swipe: a photo, a name, an age, and one decision, yes or no, in about a second, by a thumb, on a couch. Whatever that measures, it's one number about one person. Desirability. Everything Sam wrote at eleven at night is a tap away that nobody taps, because the photo has already answered the only question the interface is asking.

Here's what that looks like. One dimension. Every person is a dot, the line is desirability, and Sam is one of the dots. Notice what's gone: there are no pairs. Desirability ranks individuals; compatibility relates two; and a line has room for a rank and nothing else. The triangle problem is solved, because there's no triangle. The math got easy by removing the thing being measured. That's the substitution, and it's addictive enough that nobody minded.

So here's something to do, because you came out tonight and a critique gives you nothing for Saturday. If compatibility exists only in the encounter, the only instrument that detects it is the encounter. There's no shortcut through the database, because the thing isn't in the database. The question is how to get into good encounters.

Take the weird party out of your pocket. Go where the filtering happens on what people do, not on what they say about themselves. A room full of people who came for the same strange reason is a better-conditioned sample than anything a query returns, and it filters on the one thing no profile captures: what someone does with their time. You don't have to describe yourself as the kind of person who'd be there. You're there.

Sam went to one, a friend of a friend's, too many people in an apartment, thrown for a reason I've promised not to explain. Sam almost didn't go, which is how these things always start. I won't tell you who Sam met, because the talk doesn't know them yet, and that's the point: neither did any database. Nothing about that person was in a column anywhere, ranked next to Sam. They were in the room for the same strange reason, and the rest happened on the line between them, the way it always does.

This is the part that costs something, and I won't pretend otherwise. The query is easy; you do it on the couch. The room asks you to go somewhere, at six in the morning or on a Tuesday night, and be a stranger for a while. Sam did a year of the easy thing and one evening of the hard thing, and you know which one worked, because it's the same for everyone in this room, which is why you're in a room.

Some of you met your partner on an app, and you're wondering whether I've called your marriage a rounding error. I haven't. The app put two people in a room. Then the room did the work, the timing and the waiter and the silence, and it would have done the same work at a bus stop. The app was the bus stop. That's a fine thing to be, and it's what the swipe is honestly good at. What it can't do is the part you remember.

The apps set out to solve search, and I'll give them this, because I said I'd grant them everything: they solved it. Sam can find more people faster than anyone in history. The search was never the hard part. Love was never a search problem.

Go to the weird party.