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24th of January 2018


Love: A Lab Report -

Love is not simple nor solvable. Nor is it finite, nor perfect, nor finitely generated, nor even countable. What is it, anyway? Matthew Zaremsky does some calculations.



Love. What is it? Let’s analyze this question using mathematical group theory. Love is not simple nor solvable. Nor is it finite, nor perfect, nor finitely generated, nor even countable. So, it could be the general linear group over the complex numbers: uncountable, imperfect, non-solvable, complex, universal, a faithful representation—all these things could describe love. Except love isn’t always smooth and linear; it can’t be reduced and classified so easily as the general linear group.

We need a new hypothesis.

Maybe love is like a free group on uncountably many generators. Every group in existence is the projection of a free group, so might love similarly be the genesis of all other things? Also, free groups expand outward forever, in an infinitude of directions. (Yes, this sounds like a sufficiently romantic simile.) Except in a free group there’s only ever one path from point A to point B, and any attempts at nonconformity ensure you will never reach your goal.

Love isn’t like that at all. People find love in all kinds of unexpected ways.

This hypothesis is faulty too. Hmm.

What then? Is it possible that love cannot be explained by group theory? Maybe we need some cohomological considerations, or differential geometry, or even analytic number theory. Maybe love is a topological space?

My love is like a red, red wedge product of n copies of a topological 1-sphere …


Equipment Needed:

As Huey Lewis once said—and I quote from memory here—”Don’t need money, don’t need fame, don’t need no credit card to ride this train. Just need a Bunsen burner, an Erlenmeyer flask, and 500 mg of sodium benzoate. That’s the power of love!”



I met Sam during our freshman year of college. Her dorm room was two doors down from mine, and we gradually got to know each other through mutual friends. We spent so much time together that when we told our friends we were officially a couple, they thought it was old news. I’m not sure how most married couples first meet, but in our case, and also in my parents’ case 30 years ago, it was like that: we were in the same circle of friends and drifted together.

I made it to the top, where she stood waiting, looking more beautiful than the proof of the Poincaré conjecture.

This, of course, is not how it happens in the movies. People meet in a bar, or while walking their dogs and getting tangled in the leashes, or while trapped on a speeding bus.

In real life I don’t think I’ve ever heard of a couple who met at a bar, but it must happen. Among my circle of friends, looking for love in a bar might not go so well …

Check her out, she’s totally hot.

Eh, she’s like homotopy equivalent to hot.

Naw, dude, she’s at least homeomorphic to hot.

Pfft. Maybe in the discrete topology.

I was lucky. I found Sam without having to write any search algorithms or invoke the axiom of choice—then, certain logicians might doubt her existence—but rather in the good old-fashioned way of being friends first.



The procedure of actually getting married was more difficult than we expected. It turns out the State of Connecticut doesn’t recognize officiants ordained by the Universal Life Church. It also doesn’t definitively state this anywhere online, and to get a real answer we had to call four different government organizations. We discovered this only about a month before the wedding, and had to scramble to find a Justice of the Peace. I’m still a little surprised that Connecticut, of all states, has such a restriction.

After nearly a year of preparation, our wedding was, by all accounts, a success. It was held outside at a farm with chickens and cows milling around; the reception was in a restored historic barn. The weather was crisp, cloudless, and October-y. Before I was allowed to see Sam that morning I had to pass the bridesmaids’ “tests.” This consisted of ascending a staircase blindfolded, one step at a time, after correctly answering questions about my wife-to-be.

I did pretty well (though I had no idea her favorite color was blue; I was stuck on that step for an embarrassingly long time) and made it to the top, where she stood waiting, looking more beautiful than the proof of the Poincaré conjecture.



No one brags to his friends that his daughter is marrying a mathematician.

Studying math isn’t quite as canonical as, say, medicine or finance. When I tell people what I do, they make a face, declare their hatred for high-school math, and change the subject. But Sam’s parents thought it was great that I was a math guy.

My father-in-law, Bob, is a sports guy. I’m not being idiomatic: his job is, literally, to be a sports guy. He’s also a diehard Giants fan who speaks of the “Miracle at New Meadowlands” Eagles upset win as the “Crime of the Century.” Anyone who saw that game can understand how displeased it made Bob, who immediately took to Twitter to express his disappointment.

I actually do like football. I like that scoring is infrequent enough to make it exciting when it happens (unlike basketball) but still frequent enough to keep things interesting (unlike most soccer games). I also, naturally, like all the numbers and statistics involved, and how the first-down system resembles modular arithmetic. The football itself has a pretty cool geometry. I’m sure Bob appreciates all these factors, and could probably think of a few more math-y aspects of football, too.

I’d like to think there is a kinship between us. Sam’s family really has embraced me with open arms. I may not be on track to be a surgeon or a stock trader, but they couldn’t be more pleased that I’m a math guy. And the fact that I’m a math guy who also happens to like Bruce Springsteen is probably what sealed the deal.



Sam and I have been married for three months now. We happily don’t resemble the Lockhorns, or the Honeymooners, or any of those other wacky married couples from pop culture—at least not yet. Well, maybe if The Big Bang Theory featured a married couple …

Not tonight, honey.

But in 247 seconds, it will be 01-22-10 01:22:10! That level of palindromery won’t happen again for 22 months!

… Goodnight.

No, the reality is much more boring. We’ve found that on the surface, being married really isn’t that different from when we were just living together. Yes, we pay less for car insurance, and we’ll soon get to file a joint tax return for the first time—but we still have to explain to people that we have different last names, and I don’t think our cats care one lick that their mommy and daddy are no longer living in sin.

There is something, though. Neither of us can really articulate it, but Sam and I agree that marriage does feel somehow—ineffably, incalculably—different. One of our friends, who has been married for a couple years, put it this way: “It’s pretty much the same, but a little bit better.”

Is this a well-formed conjecture? Are the definitions rigorous? Can we quantify “a little bit better” with a delta-epsilon argument? Not really. But that’s OK. Maybe we should take a hint from Kurt Gödel—any sufficiently complex system cannot be completely understood just with mathematics. And love may not be smooth, simple, linear, solvable, or countable, but it certainly is complex.

And in the end the love you take is canonically isomorphic to the love you make.


More From Our Spe­cial Mar­riage Section:

Even stel­lar rela­tion­ships lose their spark over time; here are the ingre­di­ents of a last­ing, fruit­ful part­ner­ship, and tech­niques for weath­er­ing the the stormy times: What Your Mar­riage Needs to Survive

When Tom For­ris­ter tran­si­tioned from female to male, his same-sex mar­riage became a federally recognized, “tra­di­tional” mar­riage. The one con­stant was the bond he shared with his wife: My Exem­plary, Every­day Marriage

Guys may think leav­ing is the right thing to do for the sake of the fam­ily, but accord­ing to fam­ily lawyer David Pis­arra, there are a few things they should know before—and after—they walk out that door: A Guy’s Divorce Sur­vival Guide

The night­mare of fam­ily court is enough to deter a guy from even think­ing about tying the knot. Marriage: Just Don’t

Encour­ag­ing princess culture—however innocently—contributes to the sex­u­al­iza­tion of girls. Men can be part of the solu­tion to the “princess prob­lem”: Men and the Sex­u­al­iza­tion of Young Girls

If you’re mar­ried and using Inter­net porn reg­u­larly, your sex life—the one with your wife—is prob­a­bly a lot less sat­is­fy­ing than it could be: How Porn Can Ruin Your Sex Life—and Your Marriage

Men are more promis­cu­ous than women, but that doesn’t mean we should buy the cul­tural fal­lacy that men are pro­grammed to cheat; the vast major­ity of men are hap­pily, nat­u­rally monog­a­mous: Are Men Natural-Born Cheaters?

Tom Mat­lack talks to mar­ried men to find out when they knew their wife was “the one”: She’s the One

Monogamy sounds like “monot­ony,” but it doesn’t have to be monot­o­nous. Hugo Schwyzer explores how we can have the security—and the novelty—we desire in our rela­tion­ships: Red-Hot Monogamy

Guys may think leav­ing is the right thing to do for the sake of the fam­ily, but accord­ing to fam­ily lawyer David Pis­arra, there are a few things they should know before—and after—they walk out that door: A Guy’s Divorce Sur­vival Guide


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