November 28, 2018

"Despite the apparent ease with which sheets of paper are crumpled and tossed away, crumpling dynamics are often considered a paradigm of complexity..."

"One of the key assumptions physicists make is that there are some universal properties that are shared between many disordered complicated systems... Studying one complicated system could teach us a lot about other systems as well."

Said Omer Gottesman, a physicist, quoted in "This Is the Way the Paper Crumples/In a ball of paper, scientists discover a landscape of surprising mathematical order" (NYT).

Also quoted, Martin Creed, a conceptual artist, about his "Work No. 88" (one crumpled up sheet of paper): "I feel like you can have a microcosm of the world in a work."

35 comments:

rhhardin said...

I've been hyping crumpled paper as an unsolved physics problem for a couple of decades.

The other one is what governs the speed of an hourglass.

Wilbur said...

How does a "conceptual artist" make a living? Wealthy patrons? Government grant?

Because Wilbur needs one of those gigs.

Narayanan Subramanian said...

Isn't origami art of crumpling?

tim in vermont said...

Boy, that was a lot of fluff to try to try to get us excited about a pretty straightforward finding. “If you sum the length of the creases after each crumple, it grows logarithmically." I guess you could say that this guy is like Kepler describing the paths of the planets, and the next thing that happened then was that Newton came along and worked it all out! So wake me up when Sir Isaac Newton shows up.

There is always a belief that some simple solution underlies baffling phenomena, but this is just an article of faith, based on the self interested fact that if it’s not true, scientists are unlikely to make much progress. Obviously the Earth, the Moon, and the Sun, for example, have solved the three body problem, we haven’t.

tim in vermont said...

How does a "conceptual artist" make a living?

Brass balls.

AllenS said...

If you're going to burn your paper, like I do, it has to be crumpled. Flat paper on top of each other will not burn except for the top one or two papers and on the edges. Lack of oxygen is why a folded newspaper will never fully burn. Same thing about trying to burn bailing twine. You can start a large pile of twine on fire, but you have to keep tossing it with your pitchfork to get the lower pieces to burn. Everyone has a pitchfork right?

Guildofcannonballs said...

Design of the hourglass (shape/size of the hole* for example) and material inside.

Are two cups of sand identical?

Generally sure, but microscopically of course not.

I am on the cusp of knowing/not knowing a tiny bit of what I for sure don't know I don't know.

*assuming one.

James Smith said...

Does anti-matter fall up? Inquiring minds want to know

Darrell said...

Everyone has a pitchfork right?

Damn straight!

William said...

That's the way the cookie crumbles.

tcrosse said...

This is the maiden all forlorn, That milk'd the cow with the crumpled horn....

dustbunny said...

Creed’s works aren’t totally conceptual, he makes objects that can be and are sold for lots of money. They can also be quite engaging.

Leslie Graves said...

I had an (elementary? junior high?) teacher who would become incensed by our sentences if they contained "I feel like" followed by a thought.

Owen said...

Is the paper crumpling an example of how force (along one dimension) is translated into a 2-dimensional frame (the paper) which is then translated into 3 dimensions? The energy is conveyed into (stored in?) the collapsed volume. Which has much more complexity. Is the complexity analogous to the dissipation of heat, an increase in randomness, entropy?

Fascinating.

Henry said...


Blogger tim in vermont said...
How does a "conceptual artist" make a living?

Brass balls.


Perfect answer.

Even a painting has to be ballsy

rhhardin said...

On a surface there are two radiuses of curvature. For paper, one of them must be infinite - you can bend it only in one direction at once. If you try to violate that, there's a crease produced so that the rest of the paper can keep an infinite radius in one direction. Creases begin and end at other creases. The problem of figuring out the statistics of the crease pattern is one whose analysis is not clear.

wildswan said...

The long straight lines, equidistant and parallel to the long axis at the center, get shorter. They come to have on them areas of lines bending in and out and so more and less than equidistant and at angles to the long axis at the center. The lengths involved in bending in and out get longer. Surface area lines become volume lines?

wildswan said...

The long straight lines, equidistant and parallel to the long axis at the center, get shorter. They come to have on them areas of lines bending in and out and so more and less than equidistant and at angles to the long axis at the center. The lengths involved in bending in and out get longer. Surface area lines become volume lines? Flower form has this problem.

mockturtle said...
This comment has been removed by the author.
Owen said...

rhhardin and wildswan: thanks. I am obviously no math geek and have only a simpleton’s appreciation for topology and geometry. But I think the energy absorption/storage aspect is interesting and may be fertile. The paper sheet stores less energy —or represents less work—than the crumpled sheet. I am stuck back there thinking of crash testing and how sheet metal is sacrificed to spare the occupants a fatal acceleration.

Some tiny bias will propagate the crease, no? Like a crack in a stressed wing spar?

Fascinating.

wildswan said...

A dandelion forms inside a cylindrical bud, unfolds flat, refolds into a similar cylindrical "bud" and unfolds into a ball. In other words it has the same "creases" twice. Our friend, Nature, knows many secrets.

Leland said...

Hmm, physicist writing that crushing a single paper of set dimension using 5 digits results in something that appears to be chaos actually having some order. It is like a pre-school primer of material science, which is probably the perfect level for NYT readers.

EDH said...

I tear my paper in half before crumpling. Just in case some prying eyes might want to read what was written on it.

Owen said...

EDH: I fold my paper on itself and then flush.

Owen said...

wildswan: love the dandelion example. Yes, Nature has "solved" this. Similarly the celestial bodies "solve" the 3-body (and 4-body? And N-body?) problem. Which is perhaps only a problem because our monkey brains can't see farther than they do. We play on the surface of things or, like Newton, collect pretty pebbles on the shore.

I still think the conservation of energy is a big player here. The dandelion takes its form based on a least-effort trajectory, no?

Rick Turley said...

At least Richard Feynman can explain to us why a rubber band heats up and cools down when it is stretched and relaxed:

https://www.youtube.com/watch?v=baXv_5z7HVY

n.n said...

We can estimate each succeeding vertex with a 50% probability. The problem of prediction is due to incomplete or insufficient characterization, and unwieldy calculations, down to the known subatomic level and beyond.

gilbar said...

James Smith said... Does anti-matter fall up? Inquiring minds want to know

positrons have the same mass as electrons; so the answer to your question is NO

Owen said...

n.n.: what you said, about incomplete characterization. Any initial imprecision will, upon replication, tend to enlarge. Unless we have some restoring function, some way to match (and return) the current instance to the reference set, we drift away.

Not sure what the rate of departure is, but I'm guessing, exponential.

Owen said...

What others have said, but I am quite obsessed here. With the idea that whatever shape the crumpled paper takes, it's the "least energy" form. As all things in the world try, over time, to achieve. Laziness: it's the explanation.

n.n said...

Owen:

We have a good idea of the forces at the macro level (i.e. characterization), and repeatable observations that justify estimation to a certain extent, but our models lose accuracy at lower levels, with quantity, and evolution (i.e. chaos). What would it require to forecast a non-linear process with indefinite influences? There are, of course, boundary conditions, that simplify, and understate, the problem. A human life is the prototypical example.

PB said...

I don't crumple. It's a waste of the energy and space.

Robt C said...

@Lesley Graves --
When I taught history at a four-year college here in Central Texas, I had to tell my students to not put "I think" or "I feel" in front of their declarations. I told them the assumption was that they wrote the paper, so it must be their thoughts or feelings. (And it that wasn't the case, come see me because you must be a plagiarist.)

Kirk Parker said...

AllenS,

"A" pitchfork? Well, ok, maybe the really really poor among us only have a single pitchfork...

Bruce Hayden said...

"The long straight lines, equidistant and parallel to the long axis at the center, get shorter. They come to have on them areas of lines bending in and out and so more and less than equidistant and at angles to the long axis at the center. The lengths involved in bending in and out get longer. Surface area lines become volume lines?"

Just reminds me of one of my favorite classes as an undergraduate: Non-Euclidian Geometries. Where parallel lines can meet, and the sum of the angles of triangles need not be 180 degrees. Easiest example maybe is the surface of a sphere, which is why, BTW, Colorado and Wyoming aren't quite rectangles, with their northern borders being slightly shorter than their southern borders, despite their eastern and western borders being "parallel" (but meeting at both poles). An hour or two every day of "let's pretend".