“There are many theories about prostitution. The theory devised by Marina Della Giusta, Maria Laura Di Tommaso and Steinar Strom is one of the few that involves partial differential equations… U is your satisfaction. It’s what you, as a prostitute, care about — the satisfaction you gain from selling your services. Economists like to call it ‘utility’, which is why they like to use the letter ‘U’. L is the amount of leisure you have. C is the amount of goods and services you, as a consumer, consume. S is the amount of prostitution you, as a prostitute, sell to your customers. W is the going price for prostitutes. R is a measure of your reputation. The whole situation, seemingly so complicated, boils down to a nice partial differential equation… You, a prostitute, find it worthwhile to sell your services when: [(U/L) / (U/C) | Sp=0] ≤ w – [(U/r) / (U/C) | S = 0] That’s the poetic, simple way of putting it. But prostitution is by tradition considered vulgar, so the team also gives a vulgar, all-words description: ‘An individual will start to sell prostitution if the price for selling the first amount of prostitution, minus the costs of a worsened reputation for doing so, exceeds the shadow price of leisure evaluated at zero prostitution sold.’” — Guardian (UK)

You don’t have to understand differential calculus to marvel at the fact that such a seemingly complex human interaction can be reduced to a formula. People tend to object to being “treated as a number,” and yet this formula suggests that everyone involved in prostitution more or less obeys a numerical law, an algorithm balancing shame, desire, and pleasure. One of the authors’ papers on the topic goes even further, noting that “in our model everybody can be either prostitute or client, depending on his or her economic circumstances and available alternatives.” In other words, if you look down on prostitution, it’s simply because you’re lucky enough to maintain an economic status that puts you on the plus side of the equation. A lot of people — especially from economically turbulent countries — aren’t so lucky. That’s a self-evident conclusion from a mathematical abstrusity.

The authors’ papers on prostitution abound in insights like this. This one discusses the theory that the service offered by prostitutes is not sex but “control of sex,” with the ironic “subversion” being that “both prostitutes and clients tend to describe themselves as in control of the relationship.” They talk about the inverse relationship between prostitution and marriage, in which the high fees of prostitution are explained “in terms of a loss of position in the marriage market.” Another paper asserts that “lack of mobility between the two markets — married women are discouraged from entering prostitution and prostitutes are not acceptable marriage candidates — increases fees for sexual services to the point that lifetime ‘gains’ from prostitution become equivalent to the lifetime gains from marriage.” If that really means what it looks like it means, i.e. that a hooker earns in her lifetime what a spouse earns from being married, it’s an astonishing conclusion. Of course, the cynical might also say that this would make some men hesitate to get married. If it costs as much to have a wife, wouldn’t many men prefer the variety of prostitution?

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