Elegance, a quest.

Have you ever noticed your math teacher exclaim about how elegant a solution was? Have you ever exclaimed in joy when you managed to cut through the sordid, confusing muck in a problem and found a solution that was simply brilliant!

If you’re an Engineer, or want to be one you know what I mean.

But what’s the big deal? Why is elegance so important? Perhaps we need to see what its really about:

Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry – Bertrand Russell

OR perhaps this rather vague one by the late great Paul Erdős -

 "Why are numbers beautiful? It's like asking why is Beethoven's Ninth Symphony beautiful. If you don't see why, someone can't tell you. I know numbers are beautiful. If they aren't beautiful, nothing is."

I don’t know about you. But to me they don’t really seem to know what they’re talking about do they? There, done, now bear with me for a moment, before you condemn me to the pits for such sacrilege.

Look at those two statements, look at the words they use and the feeling they seek to evoke. Its ill defined and nebulous at best. And that, I feel is because they’re tapping into one of those poles that define human thought. They aren’t able to explain what it is that they’re talking about because it isn’t possible to do so. Other things are defined in relation to our need for elegance. It, itself is a part of out minds as much as ‘wonder’ is.

We seek elegance in all things. And unlike so many of the other things that define what it is to be human, its a very concrete thing. Elegance can be seen and felt. It can be crafted and imagined and built. Of course, I refer to the elegance of simplicity. The elegance in which the form that is defined by function is in itself a beautiful thing. The faux notion of elegance – the one so often applied to fashion doesn’t appeal to me. It might to you, but to me it doesn’t carry anything like the primal weight that accompanies the elegance sought after by the sciences.

Elegance is simplicity. Elegance is where everything falls into perfect place with the least effort. Elegance is economy without any loss of efficacy. Elegance.

So much of mathematics is driven by our primal desire to seek elegance. So much of physics is driven by our desire (unfounded though, it may be) to define the universe in elegant terms. Indeed, the LHC was built, in a large part to satisfy our hunger for elegance – our current understanding of the universe (the standard model) is about as far from elegant as physicists could stand to be.

And it has an obvious origin. Elegance, as I said, is economy. And when economy and efficiency is the difference between being a meal and catching one – as it surely would have been to our ancestors hunting the Pleistocene savannah, it pays.

The quest for elegance among engineers is probably closer to that primeval need than the desire that drives mathematicians and physicists. In engineering, an elegant solution is often intuitive. And and intuitive solution is easy to verify. It matters in a physical sense too – a simple solution is often much cheaper than a complex one (but don’t let your intuition fool you – this is not often the case) and it is usually much easier to debug.

But its mostly some combination of economy of effort (read: laze) and economy of expense that drives us engineers towards elegance.

So where is this heading? Nowhere for now. I just wanted to set the stage for an argument I intend to post here soon (or at least as soon as is feasible).