Found Functions

February 8, 2010 3:49 PM

Found Functions. An elegant demonstration of beauty in mathematics (and landscape). Nikki Graziano is a math and photography student at Rochester Institute of Technology; some of her photographs were recently featured in Wired. Graziano "overlays graphs and their corresponding equations onto her carefully composed photos. ... Graziano doesn’t go out looking for a specific function but lets one find her instead. Once she’s got an image she likes, Graziano whips up the numbers and tweaks the function until the graph it describes aligns perfectly with the photograph."
posted by jokeefe (32 comments total)

photos nice, graphs stupid... shes doing herself a disservice by superimposing them on her nice images.
posted by nathancaswell at 3:58 PM on February 8, 2010

I think they're great. But then I think grid-lines are gorgeous.
posted by vacapinta at 4:01 PM on February 8, 2010

I think grid lines can be used effectively (though they're going to be extremely played out in graphic design about six months from now... trust me) but not like this.
posted by nathancaswell at 4:06 PM on February 8, 2010

Kudzu knows more about analysis than you could possibly imagine.

-*-

More seriously, as an art school dropout cum math graduate student, I can appreciate the search for mathematical beauty in the everyday world. I've become a bit more cynical about said search as I've learned more, though: We invent mathematics and then find ways to superimpose it on the world, just as these photographs do. Some of us remember this, and keep in mind the deviations from our prior findings, and others eventually come to forget the photograph entirely, focused entirely on the graphs scrawled shoddily over it. In fact, I think this forgetfulness of the world informing the mathematics explains the last hundred years of economic theory...
posted by kaibutsu at 4:08 PM on February 8, 2010 [3 favorites]

photos nice, graphs stupid... shes doing herself a disservice by superimposing them on her nice images.

I think the photos would be incredibly dull without the superimposition.
posted by delmoi at 4:10 PM on February 8, 2010

Neat!
posted by brundlefly at 4:14 PM on February 8, 2010

I think the photos would be incredibly dull without the superimposition.
posted by delmoi at 7:10 PM on February 8 [+] [!]

I concur.
posted by The Esteemed Doctor Bunsen Honeydew at 4:14 PM on February 8, 2010

To each their own... I think a lot of her photos that don't have the superimposition show a pretty good eye for composition and light.

Regarding the grids, all I'm saying is I know a bunch of designers who are always right in the here and now of design (to a fault) and they've been all about grids for about 8 months now. Which means, like band names that include "Wolf", the jig is up.
posted by nathancaswell at 4:14 PM on February 8, 2010

nathancaswell: "Which means, like band names that include "Wolf", the jig is up."

This is a thing?
posted by brundlefly at 4:18 PM on February 8, 2010 [1 favorite]

Wolf Mother
Wolf Parade
Sea Wolf (album title: You're a Wolf)
Wolf Eyes
We Are Wolves
AIDS Wolf

I can go on and on.
posted by nathancaswell at 4:20 PM on February 8, 2010

Sorry, Sea Wolf's single was "You're a Wolf", not the album.
posted by nathancaswell at 4:21 PM on February 8, 2010

And it's not just me that noticed:

http://articles.sfgate.com/2006-01-01/entertainment/17276867_1_band-names-new-wolves-fiery-furnaces
posted by nathancaswell at 4:24 PM on February 8, 2010

The calculus is the story this world first told itself as it became the modern world.

-David Berlinski

posted by logicpunk at 4:29 PM on February 8, 2010 [2 favorites]

Huh. I had no idea.
posted by brundlefly at 4:29 PM on February 8, 2010 [1 favorite]

We invent mathematics and then find ways to superimpose it on the world

That is true to more or lesser extents, though. And in this, does anybody think that kudzu grew that way governed by that particular mathematical formula? There's plenty of math in nature -- that is, evolution guided by underlying mathematical phenomenoa -- but these photographs don't demonstrate that. There's no inherent meaning between the image and the function. She's identified coincidences.

Now this. This is an elegant demonstration of beauty in mathematics.
posted by one_bean at 4:30 PM on February 8, 2010

To each their own... I think a lot of her photos that don't have the superimposition show a pretty good eye for composition and light.

The composition is OK but mostly the colors are pretty common place. You can find tons of pictures that good on flickr at any given moment.
posted by delmoi at 4:35 PM on February 8, 2010

Now this. This is an elegant demonstration of beauty in mathematics.

It's also a self portrait, apparently.
posted by clarknova at 4:44 PM on February 8, 2010

I concur

I concur with your concurrance. I found the original images to be in the realm of decent stock photos. What I really liked was that she knows her math - it's not make-believe equations to exactly mimic the shapes in the photos.

It made me think of a line from A Beatuiful Mind - "There has to be a mathematical explanation for how bad that tie is." Math can make otherwise dull items interesting.
posted by filthy light thief at 5:04 PM on February 8, 2010

You forgot Guitar Wolf.
posted by Joakim Ziegler at 5:11 PM on February 8, 2010

These are delightful. Thanks for sharing them.
posted by Alt F4 at 5:28 PM on February 8, 2010

And you don't want to forget about Guitar Wolf. They'll destroy you with their guitar/samurai sword.
posted by brundlefly at 5:57 PM on February 8, 2010

From the Wired article: “I wanted to create something that could communicate how awesome math is, to everyone,” she says.

But these, in my mind, are just pretty pictures. The beauty in mathematics comes from the underlying patterns and structure of the objects involved, which frequently has nothing to do with the way we commonly write them on paper. Consider Penrose tilings, for instance. They may be pretty to look at -- hell, with a nice coloring they're downright gorgeous -- but that's not what's exciting about them. The aesthetic beauty absolutely pales in comparison to their structure: a Penrose tiling is aperiodic, and yet you can fill the plane with it. What's more, if you select any finite section of it, you can make that section reappear as many times as you want -- a thousand, a million, 2^256 times -- as long as you keep laying down tiles. To all hell with colors, that melts my goddamn mind.

This is not to say that I don't think Graziano's work has merit, but it does nothing to communicate the really beautiful things about math. The functions are ultimately arbitrary and give the illusion of a deep relationship between the images where there isn't one. Mathematics, on the other hand, is all about finding non-obvious patterns, especially those which run contrary to superficial impressions.

Angry side note:

When graphed, this trigonometry function produces an ever-repeating wave of peaks and valleys that mirror the natural curves Graziano sees in plants.

This kind of sloppy writing is exactly why I don't read Wired. Whoever allowed that sentence to be published should be banished to editorial hell.
posted by Commander Rachek at 6:01 PM on February 8, 2010 [2 favorites]

I like these pretty pictures. They are pleasing to my eyeballs. Everyone that doesn't like them should chilllllllll out.

Thanks for posting!
posted by beepbeepboopboop at 6:11 PM on February 8, 2010

Someone needs to work on their curve-fitting! Those R-squared values are horrendous.
posted by rubah at 6:54 PM on February 8, 2010 [2 favorites]

The functions are ultimately arbitrary and give the illusion of a deep relationship between the images where there isn't one.

This is what makes them interesting as artworks, rather than works of mathematics.
posted by stammer at 9:46 PM on February 8, 2010 [1 favorite]

I think she needs to learn about some more functions.
posted by scose at 12:37 AM on February 9, 2010

So were the arbitrary constants a stylistic choice or something? They're just sort of there for no apparent reason. You look at them askance, half saying--hey, you, over there. Shouldn't you be with your buddies in the applied parts of the world, or the grade school textbooks. As in, not over here in math territory--but they just sit there and ignore you.

Because they just feel so artificial to me. Sort of like the comparisons between the natural images and the mathematical functions. Oh, hey, I get it.
posted by Bobicus at 1:25 AM on February 9, 2010

f(x)=1/3*(x^3+y^3)=6xy

That's no function.

Still, this is cool. Thanks!
posted by albrecht at 7:45 AM on February 9, 2010

I think the interesting thing about these pictures is they demonstrate the *beginning* of a mathematical thought process:

"Hey, look at that, there seems to be a pattern there, I wonder what it might be?"

and then trying to come up with a pattern that fits it. From there you might ask if this pattern is part of some larger, deeper truth, or is just a (possibly forced) coincidence, as many people here have groused that these pictures are.

Nevertheless, I like her illustration that you can look at the particular, complicated objects in our world, simplify them, and then make a mathematical model of that simplification that you can then go ahead and contemplate, and maybe try to find some deeper truth in the simpler form.
posted by Reverend John at 9:34 AM on February 9, 2010

So that's where I left my fishing net!
posted by Faint of Butt at 1:13 PM on February 9, 2010

ffffound functions
posted by quoquo at 2:39 PM on February 9, 2010

f(x)=1/3*(x^3+y^3)=6xy

That's no function.

Still, this is cool. Thanks!

Could be a height map function of z?
posted by rubah at 4:40 PM on February 10, 2010