THE TOPOLOGY OF BODIES

By RANDOLPH COHEN

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Professor Cohen Responds to Matthew Wolf's Criticism of His Article, "The Algebra of True Love"

Love Is (Somewhat) Blind

Mr. Wolf begins his response to my article, "The Algebra of True Love," by ridiculing mathematicians for being fat, bald and unpopular. Matt, at least get your stereotypes right! I'm no mathematician, but even I know math guys are supposed to be short, skinny little wimps, not big, fat bald guys. That's the stereotype for computer guys. Or maybe short-order chefs.

Rather than focusing on the algebra of love, Mr. Wolf's only concern seems to be the topology of bodies. In his reply, he describes all potential suitors (and suit-ees) as fat or thin, bald or hairy, old or young, ugly or exquisite. But my article never suggested that physical attractiveness is the primary determinant, or even a major determinant, of the suitability of a marriage prospect.

Granted, few of us are high-minded enough to disregard the physical, but even fewer of us have our minds as deep in the gutter as Mr. Wolf. And part of the appeal of the mathematical solution I proposed to the question of when to choose a mate is that it allows you to use your own standard for deciding when to marry. If you're a totally superficial Maxim guy, then marry the first person you meet after age 25 who is more beautiful than your Best Ex (whom you chose strictly based on looks in the first place). But if you're more interested in some other characteristic -- anything from knowledge of Star Trek (those stereotypes again!) to moral integrity -- then the solution works just as well. Use your own standard, and marry the first person you meet after age 25 who is better, by your own lights, than the best person you met before age 25. It's that simple.

Mr. Wolf, I Assume

In addition to overemphasizing physical beauty, Mr. Wolf's response also gave me a strange sense of déjà vu. Where had I heard these objections raised before? Wait -- it's coming to me -- they were in my original article! "The Algebra of Love" admitted that its assumptions aren't true in all cases -- if they were, we wouldn't need to assume them! Assumptions help us get to general truths even if they aren't strictly true in every case. That's why they're called simplifying assumptions.

I made a number of explicit assumptions: that marriage prospects are offered to you, that they come along steadily (not, as Mr. Wolf points out, with periodic feasts and famines), and that people want to maximize their chance of ending up with that one perfect love (rather than maximizing some kind of expected spouse quality or simply avoiding a worst-case scenario that would inspire the regret that Mr. Wolf emphasizes). Are these assumptions precisely true for everyone? No, but they're approximately true for many people. And taken together, they provide significant insights into the question of when to marry -- insights, interestingly, that many people have already reached on their own, without the math.

That leads me to answer a few related questions I received from readers after the article was posted:

  1. Do you think people should really try to follow the advice your model recommends?
  1. Don't be ridiculous -- for goodness' sake, this isn't The Rules. As I noted above, the model makes many simplifying assumptions that guarantee that it will not strictly apply to any real person. And in the end, I trust people's gut instincts a lot more than a mathematical model when it comes to matters of the heart.

    For example, the model tells you not to marry before age 25, but if your gut is telling you at age 23 that this is THE ONE, your gut is probably right and the model, wrong. Not because the math is wrong (trust me, the math is right), but because one of the assumptions doesn't apply in your case -- most likely the one about you having no information about what kind of marriage opportunities you will have other than past marriage opportunities.

    Similarly, if at age 35 you meet someone you love just a tiny bit less than you loved your Best Ex -- who has long since married and become a conductor on the Trans-Siberian Railroad, and your gut is telling you not to let this one go too, despite that damn model -- then follow your instincts. Most likely (once again), an assumption does not apply to you. In this case, it's probably the assumption that says you only care about getting the absolute perfect person -- and if you don't get that person then you don't give a hoot about who ends up as your spouse. Remember, the model assumes you are a hopeless romantic; practical-minded folks should be wary of its suggestions.

    However, as a rough prescription -- from which people should often diverge -- the model has value. And as a description of how many people behave, I think it's right on the mark. One of the model's interesting features is how much it replicates people's simple instinct about when to marry: older people, with experience, make better marriage choices, but if you wait too long, you risk missing the boat, and missing out on a truly great marriage.

    In the end, the model just says to look around a bit before you leap. This is sensible advice any one of us would give to a kid brother or sister -- math or no math. Think about the people you know, and ask yourself whether it fits their choices. How many of your friends (including you?) gave up somebody pretty great simply because it was too early to commit? How many of them held on tight a few years later as soon as they found someone who could surpass or at least match that early love?

    People like to pretend that logic and love exist in different universes, but that's not how they act. Folks may not fall in love for logical reasons -- let's hope not anyway -- but it seems they're pretty logical about deciding when to ride that love wave all the way to the altar.
  1. What does it take to be a Best Ex? Or an Ex at all?
  1. Well, unless someone pops the question to you, you never know for sure. My view is that for someone to be your Ex, for these purposes, you must believe your relationship with that person could have led to marriage if you'd really wanted it to. That definition leads to interesting results. In some cases, a true friend with a longtime crush on you, but whom you never dated, could count as an Ex. So could an amazing one-night stand where the feelings were so intense that you feel that only your unwillingness to relocate to Oklahoma kept you from eloping. On the other hand, a person with whom you had a seven-year intense relationship, but who left you for someone else, is not an Ex for these purposes. Unless, that is, you think you could have made the relationship permanent had you pursued that goal with a whole heart. In the end, only you can decide who your Exes were, and only you can choose your Best Ex.
  1. What's your model for optimal divorce?
  1. Despite their coldhearted reputation, mathematicians have not attacked this problem with the same eagerness they have applied to marriage. But let's give it a go, working under the assumptions of the Classical Marriage Problem ("CMP") described in my initial article, and also assuming pure selfishness on the part of the individual (thus no concern whatever for the feelings of your beloved spouse), no children involved, no divorce costs, and so on. Under these circumstances, we'd be forced to conclude as follows: if additional time with your spouse, after you marry, convinces you that your spouse is less suitable than your Best Ex, then you should leave your spouse. This is because the CMP is all about finding the very best person -- and once you know your spouse is not that person (how could they be, if your Best Ex is better?) then you have to follow Neil Young and keep on searchin' for that heart of gold. Even if you're gettin' old.

Randolph Cohen, Ph.D., is an Assistant Professor of Finance at Harvard Business School. His e-mail address is rcohen@hbs.edu.

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