The Millennium Problems

On a recent visit to the library, Lissa picked up The Millennium Problems, by Keith Devlin, thinking I might find it amusing. I do. It is the story of a set of seven mathematical problems for which the Clay Foundation has offered million dollar prizes.

Devlin offers up for himself what he acknowledges at the outset is an impossible task – to explain to us, dear readers, that which is not reasonbly explainable:

For the most part, I do not aim at a detailed description of the problems. It is just not possible to describe most of them accurately in lay terms – or even in terms familiar to someone with a university degree in mathematics.

This does not make the book, at least so far, any less enjoyable for the knowledge that when I’m done I won’t understand the problems. I’ve become comfortable with black boxes, with knowing that there are thinks I won’t understand, and don’t need to. As long as one carefully circumscribes the box and understand its place in the system, one can get by quite nicely as long as one can place trust in the box builder. A lot of my science writing falls into this realm. In some cases I understand the box’s inner workings, but leave it as a box for readers. In some cases it’s a box in my own mind.

Think of the boxes as functions, a concept I take for granted in writing computer code but that was a thoughtful innovation a century-and-a-half ago. Quoting Devlin here, if I may be tricky and self-referential:

A function can be any rule that takes objects of one kind and produces new objects from them. According to this new conception, the rule that associates with each country in the world its capital city is a bona fide function (albeit a non-mathematical one.)

Mathematicians began to study the properties of abstract functions, specified not by some formula by their behavior.

So my black boxes are functions:

capital = f(country);

If I want, I can look at the way the author of my library (I slip into softwarespeak here) has written the function to return national capitals. Or I can trust the library, and treat it as a black box, thinking instead about the context rather than the ugly details.

Years ago, I was visiting my friend John in Olympia, Wash., and he took me for a late-night hike down through the woods to the water’s edge. It was pitch black, and for the first mile or so I was incredibly frustrated and on edge as I tried to peer down through the blackness to see my footfalls. After a while, though, I realized I could just unfocus my eyes and fix my gaze on John’s white T-shirt ahead of me and just follow it. And then I was fine.

Sometimes you have to just let go of the details.