beautiful explanations

Leonard Bernstein delivering his Norton Lecture at Harvard University using Beethoven’s Piano Sonata No. 18 in E-flat Major as an example. The lectures are available from your public library in a DVD set called The Unanswered Question: Six Talks at Harvard by Leonard Bernstein.
I pretty much killed myself the night before last, staying up all night to finish The Wind Up Bird Chronicle. I’ll have some thoughts about that book later, but I still need to process it a bit more.
What I’ve been obsessed with at work during my semi-unsanctioned browsing time is the plethora of responses from scientific plenipotentiaries to’s annual question for 2012: What is your favorite deep, beautiful, or elegant explanation? The responses include Eratosthenes’ measurement of the Earth’s circumference, Boscovich’s Explanation Of Atomic Forces, and are uniformly thoughtful and written with insight and passion.
I always find it fascinating to listen to people that have the magic combination of passion, expert knowledge of their field, and the old fashioned gift of gab. Becoming specialized in a field changes the way you look at your field, and the way that you see the world, and that change in perspective can be hard to communicate to other people. That gives it extra power when it does succeed. The responses really deserve to be read together as a piece, but to give you a taste of the flavor of the writing, here’s the punchline to the entry on Eratosthenes:

Eratosthenes brought together apparently unrelated pieces of evidence—the pace of caravans, the Sun shining to the bottom of a well, the length of the shadow of an obelisk—, assumptions—the sphericity of the Earth, its distance from the Sun—, and mathematical tools to measure a circumference that he could only imagine but neither see nor survey. His result is simple and compelling: the way he reached it epitomizes human intelligence at its best.
Was Eratosthenes thinking concretely about the circumference of the earth (in the way he might have been thinking concretely about the distance from the Library to the Palace in Alexandria)? I believe not. He was thinking rather about a challenge posed by the quite different estimates of the circumference of the Earth that had been offered by other scholars at the time. He was thinking about various mathematical principles and tools that could be brought to bear on the issue. He was thinking of the evidential use that could be made of sundry observations and reports. He was aiming at finding a clear and compelling solution, a convincing argument. In other terms, he was thinking about representations—theories, conjectures, reports—, and looking for a novel and insightful way to put them together. In doing so, he was inspired by others, and aiming at others. His intellectual feat only makes sense as a particularly remarkable link in a social-cultural chain of mental and public events. To me, it is a stunning illustration not just of human individual intelligence but also and above all of the powers of socially and culturally extended minds.

The question and answers made me think about the concept of elegance as well. It’s an interesting concept; the dictionary definition refers to concepts that are both aesthetic (graceful, tasteful, dignified, restrained) and more objective (precise, neat). And I can think of few adjectives that so easily describe both people and completely abstract concepts with little deviation in meaning.
I thought I’d share a couple of classical pieces that I think are elegant. Although all of them are among my favorite pieces of music, this is a different list than favorites, or greatest, or most beautiful.

  • J.S. Bach’s Chaconne from the Partita for Violin No. 2. Bach manages to take very limited materials: a descending chord pattern, a single melody instrument made of four strings, and manages to spin it into a 15 minute monster that has managed to stay one of the hardest pieces in the violin repitoire since it was written around 1720.


  • W.A. Mozart’s Jupiter Symphony. Four catchy themes introduced. Then they’re mixed together like fire and gunpowder.
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  • Steve Reich’s Piano Phase. One line of music. Two pianos.
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    3 responses to “beautiful explanations”

    1. Edge is one of my favorite websites. Sadly, this is as elegant as I become. As I go on, my stumbling with words becomes apparent, but I can’t keep from commenting on the deft handling of them by others. Love your blog.

    2. Thanks for the mention. In Richard Armitage news, one of my roomates has been watching North & South, so your world has been encroaching on mine;

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