Mathematical beauty in science (NYTimes)
March 26, 2002 8:13 AM   Subscribe

Mathematical beauty in science (NYTimes) Though I can't say I've seen a moment of God's glory in finding a balanced checkbook (on the first go), I have been in academia in physics and math enough to know the almost mystical pleasure its practitioners get from the "unreasonable effectiveness of mathematics", and the simplicity and elegance of the equations at its core. I was wondering -- are there other fields where this occurs, where people get the feeling they've tapped into some bare beauty of nature? Philosophy? Art? Architecture?
posted by meep (24 comments total)
I believe it can happen in any field. I've seen it happen to my father in law when he builds a nice piece of furniture, and all the pieces fit, and everything is "just so." Doctors get it when they make some crucial decision that saves a life. I get it when I read Nabokov, hear certain Beethoven string quartets, or listen to the opening measures of the Flamin' Groovies' "Shake Some Action."
posted by Faze at 8:18 AM on March 26, 2002

You know, I am a fairly traditional visual artist, with a lot of the scatterbrained stereotypes that come with it - I often live too much with the pretty pictures in my own head.

But. Some of the most beautiful, mystical art I create is when I do database work in programming for websites. I. Love. Databases. I get the same feeling working with a database as I do when creating visual art - a sort of peaceful sense of balance and rhythm. I love manipulating data, working out the relationships between sets of data, finding ways of making data retrieval more efficient. I noticed this very early in my computer experience, when I was first taught about databases in high school.

I am not a math-oriented person, though I'm good with basic numbers. I feel aversely toward higher math - I usually don't want to put out the effort to work through a math problem, because I'm never confident of the result and therefore don't get the "reward" of a problem solved when it's all said and done. Yet, somehow I ended up being a programmer, and liking it, and working with databases, and loving it. Databases show me the interconnectedness of things - I can make beautiful things happen with information.

It's a neat feeling.
posted by annathea at 8:22 AM on March 26, 2002

How about building a valid XHTML CSS-P webpage that works in IE, Netscape and Opera on multiple platforms and degrades acceptably in Netscape 4? It's like knitting your own tesseract.
posted by rory at 8:33 AM on March 26, 2002

That's fabulous. I've got to say that alot of mathematicians feel sad that other people can't see the beauty that they can see (I've definitely felt that way about probability), and we do feel that it should be accessible to anybody. We also have a bad habit of turning everything into math, which is unsurprising because, at its heart, math is only about patterns - not numbers, not shapes, not even logic - but looking at jumbles of things and trying to see how it can be organized to create even more things.

But this is a matter of chauvinism, as has been noted -- we could call this whole thing "Art", that of seeing patterns and creating new ones -- and people have their preferences for their creative impulse: databases, math theorems, or even crocheting.

Speaking of knitting tesseracts, how about crocheting hyperbolic planes?
posted by meep at 8:40 AM on March 26, 2002

There's nothing like writing a thousand lines of code (and not testing little chunks on the way), compiling it, getting an error because you forgot a semicolon, recompiling it, running it, and having it just work on the first go. That's when I touch God. (No, not that way! We're just friends!)
posted by kfury at 8:59 AM on March 26, 2002

I am a theatre director, and the way i make my work is often through a deliberate reversal of process, which i have come to think of as 'cultivating serendipity'.

The way it works is basically that we create external aspects of the performance's score before we really know how it is going to fit into the logic of the narrative. For instance, my collaborators and i will create elaborate physical scores (choreography) based on assignments that are only thematically or abstractly related to the material of the project. Then it is my job as the director to figure out how to make this choreography serve as the skeleton for a scene which cogently tells a story.

The idea behind it is to subvert the cliches that immediately would come to mind if i set out to 'block' the action in a way that makes sense, and search instead for a kind of physical/visual vocabulary that interacts with the text or the context in a way that is multi-layered and abstract ('poetic'?) yet meaningful.

Sometimes making this work is very hard. Usually, however, transforming this material into something which makes sense is totally intuitive and works beautifully. What makes it transcendent when it works is that it is a collaborative effort, and i make it a point not to explain the transformation to the actors, working instead through a series of small adjustments and changes of context.

When the group, collectively, begins to understand the potential meaning of one group of signs, which they have codified in a certain context, as it is brought into another, it is a magical moment and the universe seems to be full of order just waiting to be realized and reified.
posted by milkman at 8:59 AM on March 26, 2002

O logarithm,
for you i sigh struck with love.
your hair twirls braided twixt a center line,
and you speak of equality and of two sides
that by your grace are as one.
To Warshall give you your salute,
Djikstra and Turing noble too;
O logarithm,
for you i sigh struck with love.
posted by moz at 9:47 AM on March 26, 2002

I've been messing around with magic squares lately and have worked out a couple of formulas to figure out what each row and column should add up to, that sort of thing. I find that I get so engrossed in the patterns and numbers that I tune out all else, including people calling my name.

The only other activities that consume me like that are writing poetry and web design. I see all three (math, poetry, design) as being relational—what happens if I put this next to that? It's about creating order. With math, that order is already prescribed, but in poetry and design I make my own order. It's very satisfying, as if I've reclaimed a small corner of the world from chaos.
posted by gutenberg at 9:58 AM on March 26, 2002

you can make your own order in math. describe your own notation, invent new operators; don't feel locked into the rules set down ages past.
posted by moz at 10:02 AM on March 26, 2002

...don't feel locked into the rules set down ages past.
Unless you actually want to be of some use to the world. Otherwise, feel free. Play with your toes.
posted by Faze at 10:25 AM on March 26, 2002


you should be glad that some people describe their own mathematical notations. the software on your computer was no doubt developed in such a made-up notation.
posted by moz at 10:35 AM on March 26, 2002


"It's miraculous, fantastic, everyone knows what to do, no cares, it's perfect"
--Dr. Blinkova UT-Austin

that was one of my professors that just said that in class, i had to write it down. molecular biology and genetics is so fantastically complex and interconnected... and knowing how selection has created such systems is beautiful. looking at a tree and realizing how it works, and how complex it really is, and then linking that with ecology and how the tree is only a small part of the planet-system of which we're also just as much a part, yea that's god.

mefi is being very philosophical today
posted by rhyax at 10:46 AM on March 26, 2002

for me, lately, the sweet spot of the beauty & order thing is in tessellations and tiling patterns and so on.
posted by beth at 10:55 AM on March 26, 2002

Old style, contrapuntal music, starting in the Renaissance an sort of cultivating with Bach has a similar sort of inner beauty, both in the mathmatical relationships between the notes, and in the sound of the music. Bach's Goldberg Variations is sort of an extreme example here. It is a threme, with 30 variations, but the variations are based on Harmonic structure (ie: the chord changes) as opposed to the melody (as they are in standard theme-and-variation type works). The variations are in groups of three, with the third in each set being a cannon (like a round, where a melody starts, then starts again in a new voice, with both moving along offset by 2 or 4 beats, but exactly the same. But here, the second voice is in consecutively larger intervals from the original melody. The first is a second away, the second is a thrid away, and so on all the way up to a ninth. There are some more hidden structures that I can't remember. Basically what I am saying here is that this beautiful sounding piece has layer upon layer of mathmatical relationships.
posted by bob bisquick at 11:05 AM on March 26, 2002

In writing dramatic fiction, my main goal is to tap into some sort of structure of tension and rhythm that is already built into the fabric of things, that the reader of the audience can recognize intuitively because it was already there, hanging invisibly in the air, and I've merely painted it to give it shape. I'm always baffled by people who write fiction but don't believe in such an invisible fabric; the degree and method of reference to it is, I believe, the only standard by which the quality of art can be measured.

The most transcendant moments as a viewer of movies or reader of novels come when I'm on the receiving end of an aesthetically flawless technique that I've never even thought about before. In such cases, there is no need for elaborate critical papers or analysis; the proof is in the pudding; the technique works, you feel it work, the author knew that you were going to feel it work. It is not a coincidence; it is an extra-linguistic communication that requires, and asks for, zero justification. This is why, I believe, many of the greatest artists are reticent to discuss their technique in detail. Once the actual work is done, the artist has fulfilled her goal of communicating with the audience on aesthetic terms. To say any more seems childish.

A great example of this can be found in a fragment of the altogether great History of American Film documentary by Martin Scorcese. There's a clip of John Ford, who did so much for laying the foundation of how movies work that it hardly seems fair to just call him a director. Ford sits silently as an eager film student attempts to interview him from off-camera. The student asks some fairly insightful and relevant questions, and he does so respectfully and clearly. Ford's answers are all on his silent face: he is annoyed by the implication that his ability (or willingness) to answer these questions makes any difference; he's annoyed that the interviewer believes it's possible to really appreciate his films, and to still actually believe he has the right to ask for insight into the process that is not nearly as important as the product. After a while, Ford simply shifts his eyes a tiny but clearly discernible degree, shifting his focus from the interviewer to the technician actually making the equipment work, and says, with zero irony or humor, "Cut." As a film student watching it, I was disappointed; as a writer I was overwhelmed with respect.

And then there are pseudo-academics like myself, who consider themselves artists but have been trained mostly in criticism and analysis, and/or have been through a formal education on such an ambitious subject as "how to create art that works" or some variation of such...I think that those of us who really care about the emotional and intuitive quality of art are constantly caught between analyzing our own work too much, and shunning everything we've learned in order to get back to the subconscious aesthetic flow that all the art-based academia is just swirling eddies around.
posted by bingo at 11:32 AM on March 26, 2002

Here're a bunch of quotations from mathematicians and others about beauty and truth in mathematics. My personal favorites:

"The world of ideas which it [mathematics] discloses or illuminates, the contemplation of divine beauty and order which it induces, the harmonious connexion of its parts, the infinite hierarchy and absolute evidence of the truths with which it is concerned, these, and such like, are the surest grounds of the title of mathematics to human regard, and would remain unimpeached and unimpaired were the plan of the universe unrolled like a map at our feet, and the mind of man qualified to take in the whole scheme of creation at a glance. " -- J.J. Sylvester

"When I'm working on a problem, I never think about beauty. I think only how to solve the problem. But when I have finished, if the solution is not beautiful, I know it is wrong." -- R. Buckminster Fuller

And of course, there's Edna St. Vincent Millay.
posted by gleuschk at 11:38 AM on March 26, 2002

(for those whose work filters won't let them follow the above link)

Euclid alone has looked on Beauty bare.
Let all who prate of Beauty hold their peace,
And lay them prone upon the earth and cease
To ponder on themselves, the while they stare
At nothing, intricately drawn nowhere
In shapes of shifting lineage; let geese
Gabble and hiss, but heroes seek release
From dusty bondage into luminous air.
O blinding hour, O holy, terrible day,
When first the shaft into his vision shone
Of light anatomized! Euclid alone
Has looked on Beauty bare. Fortunate they
Who, though once only and then but far away,
Have heard her massive sandal set on stone.

Edna St.Vincent Millay
posted by annathea at 12:02 PM on March 26, 2002

Wow - never occurred to me. Is it the "bondage" bit?
posted by gleuschk at 1:46 PM on March 26, 2002

No, my job just has silly filters. For example - I can't visit MeTa, because the filter thinks it's a gaming site. And I can't visit Webmonkey, for the same reason. I knew what poem it was though, from your very handy title- so I grabbed it and posted it. :)
posted by annathea at 2:11 PM on March 26, 2002

symbolic logic
posted by sadie01221975 at 2:32 PM on March 26, 2002

When I find a more elegant algorithm I tell my girlfriend about it.
posted by holloway at 3:19 PM on March 26, 2002

i kind of got that feeling reading this newscientist article about proving the riemann hypothesis :)
For decades, this idea was only wishful thinking. Then in 1972 came a hint that it could work. Hugh Montgomery, at the University of Michigan, had found a formula for the spacings between Riemann zeros. Visiting the Institute for Advanced Study at Princeton, he ran into physicist Freeman Dyson at afternoon tea, and mentioned his formula. Dyson recognised it immediately. It was identical to a formula that gives the spacings between energy levels in a category of quantum systems--quantum chaotic systems, to be precise.
i know i can't properly appreciate it all cuz i suck pretty hard at math, but it's really cool reading about it! math is weird.

btw, anonymizit is a good way to get around work filters :) "Explore the web without limits. Let your mind, and browser, wander where it might never've, or could never have gone. Learn from your experience!"
posted by kliuless at 4:11 PM on March 26, 2002

annathea: same here. I'm not a math-oriented person and I tend to be more visual-oriented, therefore my database skills relly heavilly on my hability to 'draw' the relations between datasets.

I've managed to get over with 'higher math' in college (calculus - integral, diferential, numeric, computational - linear algebra, analytic geometry, probability, statistics and ,my personal kharma, diferential equations (it took me quite a while to succeed on DE, but when I did it, I did it with honors), although I'm a bit lazy about it.

Nevertheless, I can totally understand the pattern repetition scheme of it. And it makes me a hell of a code debugger. This is when I most easily achieve the 'mystical pleasure' status: when I debug code and manage to find the issues.
posted by rexgregbr at 4:18 PM on March 26, 2002

Mathematics is everywhere. My favorites for the peak experience come in music and chess.
posted by onegoodmove at 1:39 PM on March 27, 2002

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