On Orthogonality

An orthogonal set is a minimalistic set of attributes which can be combined (at different values) to create any object in a category of objects defined by said attributes.

Ok, I just kinda vomited that up. Lemme see if I can write that in a way that I'll be able to understand it next month when I read my own blog. I know, I'll give a couple examples.

There exists a category (called two-dimensional space) of objects (called "points") that are fully defined by two attributes ("x-coordinate" and "y-coordinate"). Substituting these specific words into my definition above, we find that the x-coordinate and the y-coordinate make up an orthogonal set. Don't believe me? Watch:

The x- and y-coordinates are a minimalistic set of attributes which can be combined (at different values) to create any point in two-dimensional space.

So, if some attributes make up an orthogonal set, then each such attribute is said to be orthogonal to each other such attribute. Hence, the x-coordinate is orthogonal to the y-coordinate.

This isn't the whole story on orthogonality ... I'm still digesting the notion. But this gets me far enough to talk about orthogonality in programming languages.

Orthogonal languages try to implement a minimalistic set of features which can be combined to create any semantic in the range of the language.

Now Larry and Matz (of Perl and Ruby, respectively) have both (at different times) expressed a dislike for languages that try to be very orthogonal (like Java, C, etc). Orthogonal languages are small (in features) and often easy to learn completely. But they also often yield very verbose code, that people of the non-orthogonal persuasion would call unreadable.

Non-orthogonal languages like Perl and Ruby are large (especially Perl). They give you thirty ways to do the same thing. The idea is that the best way to do X in one place is not necessarily the best way to do it in another place. As a result, you can write very terse code. A person who knows a lot of the language finds this terse code super-readable.

The drawback to non-orthogonality is barrier to entry. Perl, for instance, can take a long time to learn. On the flip side, you can begin to be productive with Perl even if you only understand a very small subset of the language. Larry likes to use this fact in a comparison to natural languages. If all you know of Spanish is "te quiero", you already know enough to get a date, even though there is much more of the language to learn. (That is my example, not Larry's.)