Engineers and scientists like to know how things work. They seem to be born with an inner drive to understand the fundamental nature of things. So, naturally, they may have some reservations about using an algorithm if the way it functions is not clear.

When we can’t see the details about how something works, we often refer to it as a *black box*. Input goes in and output comes out, without any knowledge of its internal workings.

*Black box* sometimes has a negative connotation, because knowing how something works is usually a good thing. But if we evaluate the idea of a black box, we find that many common processes and tools – including the human brain – actually fall into this category.

For example, most users of the finite element method have some basic knowledge of its underlying mathematical theory. But many of the element types available in commercial software packages are based on advanced formulations that few users completely understand. These advanced formulations are necessary to overcome deficiencies in the element behavior, and users can apply them accurately without knowing all the mathematical formalities. There are many similar examples in computational mechanics. Continue reading