# The Mathematics of a Swimsuit

The New Yorker is currently presenting its Swimsuit issue, and one of the more interesting pieces comes from Gregory Buck, a mathematician. In the piece “A Mathematician Goes to the Beach,” Buck considers the mathematics of the swimsuit, breaking out terms such as visual volatility and singularity:

The job of a swimsuit is to uphold decency while you hang out in places where people might, conceivably, swim. We can think of this decency, this modesty, as a load or strain the suit must bear. Different suit designs solve this problem in different ways, though each must take into account the regions which must be covered (RMBCs). There has, it’s well known, been a considerable decline in the percentage of skin area covered by swimsuits over the last hundred years (which has increased visual volatility—dramatic swings to both ends of the attraction/repulsion spectrum). As the suit becomes smaller and smaller, each square inch takes on more and more of the weight of propriety.

The equation here is pretty straightforward. For example, let DL represent the total decency load. DL has been declining with time, but can be considered fixed during any given beach season. Let SA be the surface area of the suit, and SK the surface area of the skin. Then if VV is the visual volatility, we have:

The proper mathematical way to look at this is to say that since, as the suit shrinks, a finite decency mass is concentrated into an ever smaller region, the decency density grows larger and larger—growing toward infinity. This point of infinite density is called a singularity. So we have that each RMBC has an associated singularity. And each beach-goer, on each beach, has an associated decency surface, with some number of singularities. The first thing a mathematician does, when faced with a surface or space with singularities, is, naturally enough, count them. A most unusual aspect of this particular singularity problem is that the count is culturally dependent—in fact there are countries where the sum is less than it is in the United States. I have heard that there are beaches where a bather’s decency surface might have no singularities at all, a prospect I have not the courage to consider.

Hilarious and enlightening.