What is orthogonality?

[rm]

Bill Baxter wrote:
> The world orthogonality has been thrown around a bit here, me included.
> I just read this interesting interview with Matz, Ruby's creator where
> he says he doesn't like orthogonality and gives an example of why it's bad:
> 
>  "An example of orthogonality is allowing any combination of small
>  features or syntax. For example, C++ supports both default parameter
>  values for functions and overloading of function names based on
>  parameters. Both are good features to have in a language, but because
>  they are orthogonal, you can apply both at the same time. The compiler
>  knows how to apply both at the same time. If it's ambiguous, the
>  compiler will flag an error. But if I look at the code, I need to apply
>  the rule with my brain too. I need to guess how the compiler works. If
>  I'm right, and I'm smart enough, it's no problem. But if I'm not smart
>  enough, and I'm really not, it causes confusion. The result will be
>  unexpected for an ordinary person. This is an example of how
>  orthogonality is bad."  -- Matz
> 
> First a definition. My concept of orthogonal comes mostly from linear
> algebra.  If you have two vectors that are orthogonal there is no
> component of one that can be represented using the other.  I.e. the
> projection of one onto the other is zero.  They have zero overlap.
> 
> What Matz is talking about is more like "syntactic orthogonality".  The
> syntax of those two features is orthogonal so they can coexist without
> issues.  The syntax subspaces they cover have zero overlap.
> 
> That's important, but I think a low-level kind of orthogonality.  What
> I'm talking about is more of a "semantic orthogonality".  What does the
> feature let you express?  In the semantic sense his example of
> overloading functions by number of paramters versus using default
> parameters is exactly 100% UN-orthogonal.  They both achieve exactly the
> same behavior.  They overlap 100% in terms of what you can express.
> 
> In the end he says he wants things to be "harmonious", which I think is
> more or less equivalent to "semantically orthogonal".  Harmonious in the
> sense that I do my job and you do yours, and we don't step on each
> other's toes.  But that's precisely what orthogonality is -- not
> overlapping.
> 
> The full interview is here:
> http://www.artima.com/intv/ruby.html
> 
> --bb

IMHO - in the C++ world - STL is a much better example of orthogonality.
e.g. the algorithms and containers are type independent.
So a sort algorithm for a vector containing ints can be the same as for
a vector containing chars.

roel