Not exactly a quote – I don’t have the exact wording and I am not certain who said it (I am separated from the original by at least two degrees) – but it makes an important enough point that I think it’s worth writing about.

A well designed linear algebra library should teach the underlying mathematics of linear algebra.

Attributed to Jim Blinn

Jim Blinn is a big name in the computer graphics world. I heard this quote in the context of computer graphics (which uses a lot of linear algebra) but you can substitute anything you’d write a library for e.g. statistics, databases, containers, date and time calculations. I don’t know exactly what features of a library Jim Blinn had in mind, but that isn’t going to stop me speculating.

Why might it be important to follow the advice in the quote?

• If you already know about the subject it will be easier to start using the library.
• If you don’t know about the subject (but have to use the library) you’ll learn about the subject, and can also supplement that learning with other teaching material.
• If you are writing a library, this advice gives you an additional design tool.

Moving on, what features of a library help teach the underlying theory? I can think of a few, I am sure there are many more – please add to this list in the comments.

• Nomenclature. Naming comes up over and over again as an important topic. If there are already standard names for things, use them in your library.
• Clarity of data. Is it obvious what data is required for a given function (or class or module) to do it’s job? I often find that there’s more data available than is required, and as a newcomer digging through the library it can take me some time to work out what is really needed. Simple functions that take exactly the data they require and return exactly the thing to be calculated are great. The STL algorithms do this – they only take the values that are necessary for them to do their job, and they are very specific about the types of iterators required.
• No short cuts. In a 3D graphics library it is very tempting to make points and vectors the same thing. They both have x, y, z values, they have a fair number of operations in common and the ones that aren’t strictly in common usually have an obvious and reasonable meaning for them both. However, points and vectors are not the same thing. This is an example where using the type system helps.