Reality lurking inside spaces

koi leaping

A friend and I had a disagreement about what art is.  She said, “Art is not always about painting a pretty picture or giving people a pleasant tune. Art must be free to convey the gamut of emotions, including the ones that make us uncomfortable.”  We weren’t really disagreeing about art, it was something else.  But I was struck by this claim which one hears everywhere.

There is nothing controversial about what she said, so far as it goes.  I think of Rembrandt’s Blinding of Samson.  (Ouch.  That’s gotta hurt.)  But this oft repeated formula has morphed into something about which we should be very suspicious.  That art is sometimes about “uncomfortable things” has developed an equals sign.   It’s become serious art = edgy/shocking/uncomfortable/indecent/violent/fill in negative value here.

Umm, I just don’t think so.  True, nature is sometimes tooth and claw, but it’s also fields of daisies and sometimes it’s hamsters.  As I wrote in the previous post, mathematicians find that nature leans toward the aesthetic.  When it became fashionable to question whether beauty was necessary, somebody forgot to do the math — which is to say, no one said, “hold on there, not so fast, since when is creating beauty easy?  Indeed, are we sure we even know what beauty IS?”

I find that painting a pretty picture is so darned difficult — I want to ask what sort of thing beauty is — how does one recognize it?  You can respond to beauty in things and have beauty resist you to the nth degree when once you attempt to catch its likeness.  Beauty is still a high calling.  It’s still a hard gig to get.  Many try, few succeed.  It’s Everest.  It’s a mirage.  It’s a dream that fades upon waking.

Sometimes a thousand twangling instruments
Will hum about mine ears; and sometime voices,
That, if I then had wak’d after long sleep,
Will make me sleep again; and then, in dreaming,
The clouds methought would open, and show riches
Ready to drop upon me; that, when I wak’d,
I cried to dream again–

Caliban does himself fit perfectly into the art=ugliness formula but his cry, his dream, that’s all gauzy beauty-and-splendor floating in one’s gaze.  When I look at my koi, I am stalking beauty.  I know it’s out there in the world somewhere.  I intend to persist.  I will relentlessly search.  The fishes have hid it around the edges of their shapes and inside the spaces that separate them from each other.  Sometimes it peeks out from the corner where one shape intrudes upon another.  Sometimes it catches you between layers of paint, between this-that-was-a-mistake and this-that-I-painted-above.  In the lines, in the color patches, in the differences between big and little, in the topography of ideas and forms, beauty lives.

Like a hamster hidden inside a pile of wood shavings, like the most commonplace flower, like the plain daylight streaming, like the gnats hanging in the air, like so many other quite ordinary and decent and indifferent experiences, beauty lifts its head and gazes out into one’s face.  I’m still going out on a limb, and I’ll define “art” as the electric and ephemeral contact with reality that happens by chance and by desire.  Before I lumber off in search of edginess, I will stake my claim on ordinariness.

It’s hard to accept that somehow we trump reality.

Learning Beauty

alice at the easel

My kid had math homework this weekend that she didn’t know how to do, and since she hadn’t brought her textbook home, she lacked instructions and definitions to help guide her back toward the path.  Unfortunately, while being a rational enough gal, I have no talent for numbers or numerical relationships.  Dad is good at math, but he happened not to be available at the height of the crisis.  The homework consisted of adding, subtracting, multiplying and dividing positive and negative numbers.  I vaguely recalled that rules exist, but couldn’t remember what they are.  So I suggested to my daughter that she experiment — perform some different approaches and see what results she got, and from those results have a guess at which rule is “it.”

She wouldn’t.  And so I pulled Music of the Primes off the shelf and started reading.  Music of the Primes is Math, the Movie — or an elegant, suspense-filled heart-tugging page turner of a math adventure book.  Yes, I know that’s hard to believe but tis true.  Math made thrilling for folks like me and thee.  Math the dream.  Math the you-should-have-been-there experience.

Unfortunately, Music of the Primes wasn’t working for her.  Too grown-uppy.  And by sixth grade a certain sense of, shall I call it, false reality sets in and a child gets mislead into supposing that “the answers” are out there sitting on a drab shelf ready to be innocently “learned” at the public school house.  I cannot blame my kid for having internalized this sensibility; it’s been drummed into her for years now.

Given the data available at the start of the nineteenth century, Legendre’s function was much better than Gauss’s formula as an approximation to the number of primes up to some number N, but the appearance of the rather ugly correction term 1.08366 made mathematicians believe that something better and more natural must exist to capture the behaviour of the prime numbers.

Such ugly numbers may be commonplace in other sciences, but it is remarkable how often the mathematical world favours the most aesthetic possible construction.  As we shall see, Riemann’s Hypothesis can be interpreted as an example of a general philosophy among mathematicians that, given a choice between an ugly world and an aesthetic one, Nature always chooses the latter.  [my emphasis] It is a constrant source of amazement for most mathematicians that mathematics should be like this, and explains why they so often get wound up about the beauty of their subject.

Imagine that: choosing a mathematical order — a beautiful one over the ugly alternatives — that in math one can sketch out ideas and test them, and even choose among them using an intuition that surprisingly sometimes matches the visible natural order.  In so many spheres of life we are offered chances to choose, to act, to inquire boldly, to investigate, to discover.  Oh would that we could instill even a nano-quantity of that free-spiritedness into the school house!

Above, Alice has boldy chosen to paint a dog leaping.  She has no qualms at all about portraying her Public Enemy Number One.  And she even makes him beautiful.