Sunday, March 13, 2005

Elegance versus ugly theories

I'm intrigued by the concept of elegance as it applies to technology and science, in addition to the arts, and life in general. At least in computer science and computer software, approaches that can be labeled "elegant" are frequently dramatically superior to "ugly" solutions. Not always, but quite frequently. The same appears to be true in science. Truly robust theories seem not only to explain a phenomenon, but to do so in an extremely elegant manner, with a sense of beauty.

So, the question is whether this is all simply an illusion and an example of selective thinking, or is there something going on here.

Simple question: does anyone know of any well-settled and extremely robust theories that are truly "ugly" to contemplate?

I suspect that it's also possible that some theories are still too incomplete to have streamlined themselves to the point of elegance. Theorists keep adding warts to explain away anomalies until they finally get to the point where they "see the light" and can then replace all the warts with an elegant theoretical model.

I have a handout from Sir Roger Penrose's recent talk here at the Boulder Book Store in Boulder, Colorado that has some diagrams from his new book, The Road to Reality : A Complete Guide to the Laws of the Universe. The diagram for a string theory D-brane is truly ugly. Penrose insists that you don't need any higher-order dimensions. In contrast, his diagram of a twistor (two nested toruses) is extremely elegant.

As an aside, here's a link to a conference on "Twistor String Theory", where the goal is to do what string theory is trying to do, but using twistors rather than higher-order dimensions.

And take a look at the PDF for his hand-drawn Twistor Theory lecture notes, which includes a variation of the nested torus diagram from his book.

Just to be clear, I'm not suggesting that appearance of elegance makes a theory or conjecture correct or that ugliness necessarily makes it incorrect, but simply that there does seem to be a somewhat positive correlation between elegance and truth, even if there is no demonstrable causality.

File all of this under the aesthetics category of philosophy.


At 10:06 PM MDT , Anonymous ugliest said...

Hi Base Technology, I recently started a new blog called Ugly Blog so I've been searching around for ugliness related blogs to check out and possibly trade links with. I found this entry (Elegance versus ugly theories) in my search so I thought I'd drop a line to let you know. Anyway nice blog and have a good day!


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