While the design process is a learning process, an elegant design can be considered a teaching tool. In order to justify this argument, I'll have to explain what I mean by elegance.

I use an operational definition of solution elegance. Recalling Fred Brooks, solution complexity can be broken down into two components:

- There is the essential complexity, which is complexity inherent in the solution you are trying to provide,
- And there is the accidental complexity, which is not.

In my opinion, a solution can be called elegant when it has a high essential-complexity to total-complexity ratio. As an equation, I'd say:

TotalComplexity = EssentialComplexity + AccidentalComplexity Elegance = EssentialComplexity / TotalComplexity

With an "Elegance" value of 1 representing a perfectly elegant solution (i.e., a solution in which *all* the solution complexity is essential, and none is accidental), and a value close to 0 representing a big
ball of mud. (A value of 0 is considered impossible, as any solution must have *some* essential complexity.) This is an equation, but because this is an equation describing a subjective phenomenon
(the perception of elegance), it's built with subjective terms (essence, accident, complexity). Still, we're all humans, we're all more similar than we are different, it's likely that we'll share the
same basis for deciding what is complex, what is essential, and what is not.

This is my basis: perceived complexity is proportional to the amount of effort one must spend in developing understanding of the system under study. (I won't go further into it here, but note that the word "perceived" is used to point out that the experience of complexity will vary with the observer.) Essential complexity is recognizable as that part
of the implementation that teaches you something about *all* possible solutions, while accidental complexity is what's left.

In other words, a design (including implementation code) is recognizable as elegant when it teaches you about the domain. An elegant design can be used as a teaching tool.